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THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

PRESENTED  BY 

PROF.  CHARLES  A.  KOFOID  AND 
MRS.  PRUDENCE  W.  KOFOID 


u> 


A 

COURSE   OF  LECTURES 


ON 


NATURAL    PHILOSOPHY, 

&c. 


VOLUME  I TEXT. 


COURSE  OF  LECTURES 

ON 

NATURAL    PHILOSOPHY 

AND    THE 

MECHANICAL  ARTS. 

BY   THOMAS    YOUNG,    M.D. 


A    NEW     EDITION,     WITH     REFERENCES    AND     NOTES, 

BY   THE 

REV.  P.  KELLAND,  M.A.,  F.R.S.,  LOND.  &  EDINB., 


J,    ETC.   IN   THI 


fcp  ftumerous  (Engrabings  on 


IN  TWO  VOLUMES. 
VOLUME    I.  -  TEXT. 

.  4!  >.        ' 

r 

LONDON: 
PRINTED   FOR   TAYLOR   AND    WALTON, 

UPPER   GOWER   STREET. 
1845. 


Printed  by  J.  &  H.  COX,  BROTHERS  (LATE  COX  &  SONS), 
74  &  75,  Great  Queen  Street,  Lincoln's-Inn  Fields. 


PREFACE  BY  THE  EDITOR. 


THE  Lectures  which  are  now  a  second  time  presented  to  the  public, 
are  so  well  known,  and  so  justly  celebrated,  amongst  those  who  are 
most  capable  of  judging  of  their  merits,  that  very  little  need  be  offered 
by  way  of  preface  to  this  volume.  Whether  we  regard  the  depth  of 
Dr.  Young's  learning,  the  extent  of  his  research,  the  accuracy  of  his 
statements,  or  the  beauty  and  originality  of  his  theoretical  views,  in 
whatever  way  we  contemplate  these  Lectures,  our  admiration  is  equally 
excited.  They  embody  a  complete  system  of  Mechanical  Philosophy, 
drawn  from  original  sources,  and  illustrated  by  a  hand  capable  of 
reducing  them  to  the  most  perfect  subjection.  Unlike  other  popular 
writers,  who,  for  the  most  part,  either  take  the  sciences  at  second 
hand,  or  content  themselves  simply  with  extracting  the  discoveries 
and  adopting  the  hypotheses  of  more  distinguished  philosophers,  Dr. 
Young  travelled  over  the  whole  literature  of  science,  and  whilst  we 
are  astonished  at  the  rich  store  of  materials  which  he  has  collected,  we 
find  nothing  more  prominent  than  the  impress  of  his  own  acute  and 
powerful  mind.  It  is  particularly  conspicuous  in  his  treatise  on 
motion  and  force,  which,  with  their  applications  to  the  useful  arts, 
forms  the  first  part  of  these  Lectures.  In  comparing  this  treatise 
with  others  of  similar  pretension,  we  are  forcibly  impressed  with  the 
fact,  that  whilst  their  authors  have  been  driven  to  popularize  from  in- 
ability to  grapple  with  mathematical  researches,  Dr.  Young  has  been 
enabled  to  do  so  from  his  thorough  mastery  of  those  researches.  It 
combines  correctness  with  simplicity.  The  popular  reader  may  trust 
to  it  as  always  based  on  right  principles,  and  calculated  to  pave  his 
way  to  a  more  extensive  and  intimate  research ;  the  mathematical 
reader  will  find  in  it  the  clearest  statement  of  arguments  which 
have  already  been  presented  to  him  in  another  form.  The  remaining 
parts  of  these  Lectures  are  equally  valuable  on  account  of  the  origi- 
nality of  the  views  which  they  unfold,  and  of  the  unity  and  simplicity 

a  2 

M363122 


iv  PREFACE  BY  THE  EDITOR. 

which  they  give  to  physical  science.  Here  will  be  found,  for  the  first 
time,  correct  notions  on  capillary  action.  Here  Dr.  Young  developed 
the  beautiful  principle  of  interference,  "  that  fine  discovery,"  to  use  the 
words  of  M.  Arago,  "  which  will  render  his  name  imperishable." 

What  Dr.  Young  has  done  cannot,  however,  be  better  explained 
than  in  'his  own  Preface,  of  which  it  is  sufficient  to  remark,  that  the 
Author  has  in  no  instance  over-estimated  the  importance  of  his  labours. 

It  only  remains  to  add  a  few  words  relative  to  the  present  edition. 
In  some  of  the  subjects  treated  of,  considerable  advances  have  been 
made  since  the  Lectures  were  first  published.  To  render  the  work  as 
complete  as  possible,  the  Editor  has  supplied  brief  expositions  of  what- 
ever additional  discoveries  have  been  made,  which  are  printed  along 
with  the  Lecture  on  that  branch  to  which  they  belong,  and  distin- 
guished by  being  inclosed  within  brackets.  They  serve,  for  the  most 
part,  to  complete  the  subject  according  to  the  plan  of  the  Author.  In 
the  case  of  Electricity,  and  its  kindred  branches,  so  much  addition 
has  been  made  within  the  last  half-century,  that  it  would  greatly 
exceed  the  necessary  limits  to  treat  of  those  sciences  satisfactorily. 
All  that  has  been  attempted  is  to  offer  a  very  brief  sketch  of  the 
nature  of  the  extension  of  those  sciences,  without  entering  at  all  into 
details. 

The  authors  to  whom  Dr.  Young  directly  refers  in  the  Lectures  are 
given  at  the  foot  of  the  page,  the  name  and  date  of  the  work  being 
added,  and  in  many  cases  the  page  which  is  referred  to.  Accompany- 
ing these  references  will  be  found  others  to  authors  who  have  treated 
on  the  same  subject.  At  the  end  of  each  Lecture  is  given  a  table  of 
additional  authorities,  a  portion  of  which  have  been  extracted  from  Dr. 
Young's  own  catalogue.  Indeed  these  tables  embrace  every  important 
work  which  the  catalogue  contains,  and,  except  in  Meteorology  and 
Astronomy,  reference  to  all  the  most  valuable  memoirs  found  in  the 
different  scientific  transactions.  In  the  excepted  cases,  the  lists  were 
too  extensive,  and  too  little  suited  to  the  character  of  this  work  to  be 
given  entire,  whilst  abridgement  would  have  answered  no  useful  purpose. 
With  respect  to  the  additions  which  the  Editor  has  made  to  this  branch, 
they  will  be  found  to  be  very  extensive ;  and  it  is  believed  the  whole 
forms  a  tolerably  complete  body  of  scientific  literature.  There  must 
necessarily  be  expected  some  important  omissions,  but  it  is  hoped  they 
are  not  numerous.  For  the  guidance  of  those  who  shall  consult  these 
catalogues,  it  is  necessary  to  point  out  the  fact,  that  condensation  has 


PREFACE  BY  THE  EDITOR.  v 

been  an  object,  so  that  a  repetition  of  reference  to  the  same  work  has 
been,  as  much  as  possible,  avoided.  Thus  most  of  the  works  which  are 
mentioned  under  one  branch  of  the  mechanical  sciences,  embrace  many 
others  under  which  they  are  not  quoted.  For  example,  the  autho- 
rities on  central  forces  (Lect.  IV.)  do  not  include  Laplace,  Lagrange, 
and  others,  because  these  authors  have  been  already  given  in  Lect.  II., 
as  treating  on  a  branch  of  the  same  subject.  This  want  of  repetition 
may  be  considered  a  defect,  but  it  must  be  remembered,  that  the  cata- 
logue has  already  extended  to  several  thousand  articles.  On  the 
whole,  it  is  expected  that  this  edition  will  supply  a  work  greatly 
needed,  in  which  correct  exposition  is  combined  with  extensive 
research. 

Great  pains  have  been  taken  to  render  the  Table  of  Contents  and 
Index  as  complete  and  accurate  as  possible.  In  framing  these,  the 
Editor  has  received  the  valuable  assistance  of  Mr.  Stewart,  which  he 
begs  thankfully  to  acknowledge. 


AUTHOR'S  PREFACE. 


HAVING  undertaken  to  prepare  a  course  of  Lectures  on  natural  philo- 
sophy, to  be  delivered  in  the  theatre  of  the  Royal  Institution,  I  thought 
that  the  plan  of  the  institution  required  something  more  than  a  mere  com- 
pilation from  the  elementary  works  at  present  existing  ;  and  that  it  was 
my  duty  to  collect  from  original  authors,  to  examine  with  attention,  and 
to  digest  into  one  system,  every  thing  relating  to  the  principles  of  the  me- 
chanical sciences,  that  could  tend  to  the  improvement  of  the  arts  subser- 
vient to  the  conveniences  of  life.  I  found  also,  in  delivering  the  lectures, 
that  it  was  most  eligible  to  commit  to  writing,  as  nearly  as  possible,  the 
whole  that  was  required  to  be  said  on  each  subject ;  and  that,  even  when 
;an  experiment  was  to  be  performed,  it  was  best  to  describe  that  experiment.! 
1  uninterruptedly,  and  to  repeat  the  explanation  during  its  exhibition.' 
Hence  it  became  necessary  that  the  written  lectures  should  be  as  clearly 
and  copiously  expressed,  and  in  a  language  as  much  adapted  to  the  com- 
prehension of  a  mixed  audience,  as  the  nature  of  the  investigations  would 
allow ;  and  that  each  experiment,  which  was  to  be  performed,  should  also 
be  minutely  described  in  them.  If,  therefore,  there  was  any  novelty  either 
in  the  matter  or  the  arrangement  of  the  lectures,  as  they  were  delivered 
for  two  successive  years,  it  is  obvious  that  they  must  have  possessed  an 
equal  claim  to  the  attention  of  a  reader,  had  they  been  published  as  a 
book  ;  and  upon  resigning  the  situation  of  Professor  of  Natural  Philosophy, 
I  immediately  began  to  prepare  them  for  publication. 

I  had  in  some  measure  pledged  myself^  in  the  printed  syllabus  of  the 
lectures,  to  make  a  catalogue  of  the  best  works  already  published  on  the 
several  subjects  ;  with  references  to  such  passages  as  appeared  to  be  most 
important :  it  was  therefore  necessary  >  as  well  for  this  purpose,  as  in  order 
to  procure  all  possible  information  that  could  tend  to  the  improvement 
of  the  work,  to  look  over  a  select  library  of  books  entirely  with  this 
view,  making  notes  of  the  principal  subjects  discussed  in  them,  and  exa- 
mining carefully  such  parts  as  appeared  to  deserve  more  than  ordinary 
attention.  Hence  arose  a  catalogue  of  references  ;  respecting  which  it  is 
sufficient  to  say,  that  the  labour  of  arranging  about  twenty  thousand, 
articles  in  a  systematic  form,  was  by  no  means  less  considerable  than  that 
of  collecting  them.  The  transactions  of  scientific  societies,  and  the  best 
and  latest  periodical  publications,  which  have  so  much  multiplied  the 
number  of  the  sources  of  information,  constituted  no  small  part  W  the 
collection,  which  was  thus  to  be  reduced  into  one  body  of  science. 


viii  AUTHOR'S  PREFACE. 

With  the  addition  of  the  materials  acquired  in  making  this  com- 
pilation, and  of  the  results  of  many  original  investigations,  to  which 
they  had  given  rise,  it  hecame  almost  indispensable  to  copy  the  whole  of 
the  lectures  once  more,  and  to  exchange  some  of  them  for  others,  which 
were  wholly  new ;  at  the  same  time  all  possible  pains  were  taken  to  dis- 
cover and  to  correct  every  obscurity  of  expression  or  of  argument. 

Drawings  were  also  to  be  made,  for  representing  to  the  reader  the  appa- 
ratus and  experiments  exhibited  at  the  time  of  delivering  the  lectures,  for 
showing  the  construction  of  a  variety  of  machines  and  instruments  con- 
nected with  the  different  subjects  to  be  explained,  and  for  illustrating  them 
in  many  other  ways.  These  figures  have  been  extended  to  more  than 
forty  plates,  very  closely  engraved,  and  the  execution  of  the  engravings  has 
been  minutely  superintended.  But  the  text  of  the  lectures  has  been  made 
so  independent  of  the  figures,  that  the  reader  is  never  interrupted  in  the 
middle  of  a  chain  of  reasoning,  but  is  referred,  at  the  end  of  a  paragraph, 
to  a  plate,  which  has  always  a  sufficient  explanation  on  the  opposite  page. 

The  bulk  of  this  work  is  not  so  great  as  to  require,  for  its  entire  perusal, 
any  unreasonable  portion  of  time  or  of  labour.  There  may,  however,  be 
some  persons  who  would  be  satisfied  with  attending  to  those  parts  in  which 
it  differs  most  from  former  publications,  without  having  leisure  or  inclina- 
tion to  study  the  whole.  To  such  it  may  be  desirable  to  have  those  sub- 
jects pointed  out  which  appear  to  the  author  to  be  the  most  deserving  of 
their  notice. 

I  The  fundamental  doctrines  of  motion  have,  in  the  first  place,  been  more 

II  immediately  referred  to  axioms  simply  mathematical  than  has  hitherto  been 
1  usual ;  and  the  application  of  these  doctrines  to  practical  purposes  has 

perhaps  in  some  instances  been  facilitated.  The  passive  strength  of 
materials  of  all  kinds  has  been  very  fully  investigated,  and  many  new 
conclusions  have  been  formed  respecting  it,  which  are  of  immediate 
'  importance  to  the  architect  and  to  the  engineer,  and  which  appear  to  con- 
tradict the  results  of  some  very  elaborate  calculations. 

The  theory  of  waves  has  been  much  simplified,  and  somewhat  extended, 
and  their  motions  have  been  illustrated  by  experiments  of  a  peculiar  nature. 
A  similar  method  of  reasoning  has  been  applied  to  the  circulation  of  the 
blood,  to  the  propagation  of  sound,  either  in  fluids  or  in  solids,  and  to  the 
vibrations  of  musical  chords ;  the  general  principle  of  a  velocity  corre- 
sponding to  half  the  height  of  a  certain  modulus  being  shown  to  be  appli- 
cable to  all  these  cases,  and  a  connexion  has  been  established  between  the 
sound  to  be  obtained  from  a  given  solid,  and  its  strength  in  resisting  a 
flexure  of  any  kind  ;  or,  in  the  case  of  ice  and  water,  between  the  sound 
in  a  solid  and  the  compressibility  in  a  fluid  state. 

The  doctrine  of  sound,  and  of  sounding  bodies  in  general,  has  also 
received  some  new  illustrations,  and  the  theory  of  music  and  of  musical 
intervals  has  been  particularly  discussed. 

With  respect  to  the  mathematical  part  of  optics,  the  curvature  of  the 
images  formed  by  lenses  and  mirrors,  has  been  correctly  investigated,  and 
the  inaccuracy  of  some  former  estimations  has  been  demonstrated.  . 

In  the   department  of  physical  optics,  the  phenomena  of   halos  and 


AUTHOR'S  PREFACE.  ix 

parhelia  have  been  explained  upon  principles  not  entirely  new,  but  long 
forgotten  ;  the  functions  of  the  eye  have  been  minutely  examined,  and  the  | 
mode  of  its  accommodation  to  the  perception  of  objects  at  different  dis-  \ 
tances  ascertained ;  the  various  phenomena  of  coloured  light  have  been 
copiously  described,  and  accurately  represented  by  coloured  plates ;  and 
some  new  cases  of  the  production  of  colours  have  been  pointed  out,  and 
have  been  referred  to  the  general  law  of  double  lights,  by  which  a  great 
variety  of  the  experiments  of  former  opticians  have  also  been  explained  ; 
and  this  law  has  been  applied  to  the  establishment  of  a  theory  of  the  nature 
of  light  which  satisfactorily  removes  almost  every  difficulty  that  has 
hitherto  attended  the  subject. 

The  theory  of  the  tides  has  been  reduced  into  an  extremely  simple 
form,  which  appears  to  agree  better  with  all  the  phenomena  than  the  more 
intricate  calculations  which  they  have  commonly  been  supposed  to  require. 
With  respect  to  the  cohesion  and  capillary  action  of  liquids,  I  have  had 
the  good  fortune  to  anticipate  Mr.  Laplace  in  his  late  researches,  and  I 
have  endeavoured  to  show  that  my  assumptions  are  more  universally 
applicable  to  the  facts,  than  those  which  that  justly  celebrated  mathema-  I 
tician  has  employed.  I  have  also  attempted  to  throw  some  new  light  on 
the  general  properties  of  matter  in  other  forms ;  and  on  the  doctrine  of 
heat  which  is  materially  concerned  in  them ;  and  to  deduce  some  useful 
conclusions  from  a  comparison  of  various  experiments  on  the  elasticity  of 
steam,  on  evaporation,  and  on  the  indications  of  hygrometers.  I  have 
enumerated,  in  a  compendious  and  systematical  form,  the  principal  facts 
which  have  been  discovered  with  respect  to  galvanic  electricity;  and  I 
have  fortunately  been  able  to  profit  by  Mr.  Davy's  most  important  expe- 
riments, which  have  lately  been  communicated  to  the  Royal  Society,  and 
which  have  already  given  to  this  branch  of  science,  a  much  greater  per- 
fection, and  a  far  greater  extent,  than  it  before  possessed.  The  historical 
part  of  the  work  can  scarcely  be  called  new,  but  several  of  the  circum- 
stances which  are  related,  have  escaped  the  notice  of  former  writers  on  the 
history  of  the  sciences. 

Besides  these  improvements,  if  I  may  be  allowed  to  give  them  that 
name,  there  are  others,  perhaps  of  less  importance,  which  may  still  be 
interesting  to  those  who  are  particularly  engaged  in  those  departments  of 
science,  or  of  mechanical  practice,  to  which  they  relate.  Among  these 
may  be  ranked,  in  the  division  of  mechanics,  properly  so  called,  a  simple 
demonstration  of  the  law  of  the  force  by  which  a  body  revolves  in  an 
ellipsis ;  another  of  the  properties  of  cycloidal  pendulums ;  an  examina- 
tion of  the  mechanism  of  animal  motions ;  a  comparison  of  the  measures 
and  weights  of  different  countries  ;  and  a  convenient  estimate  of  the  effect 
of  human  labour :  with  respect  to  architecture,  a  simple  method  of 
drawing  the  outline  of  a  column  :  an  investigation  of  the  best  forms  for 
arches  ;  a  determination  of  the  curve  which  affords  the  greatest  space  for 
turning  ;  considerations  on  the  structure  of  the  joints  employed  in  car- 
pentry, and  on  the  firmness  of  wedges ;  and  an  easy  mode  of  forming  a 
kirb  roof :  for  the  purposes  of  machinery  of  different  kinds,  an  arrange- 
ment of  bars  for  obtaining  rectilinear  motion  ;  an  inquiry  into  the  most 


x  AUTHOR'S  PREFACE. 

eligible  proportions  of  wheels  and  pinions ;  remarks  on  the  friction  of 
wheel  work,  and  of  balances  ;  a  mode  of  finding  the  form  of  a  tooth  for 
impelling  a  pallet  without  friction  ;  a  chronometer  for  measuring  minute 
portions  of  time ;  a  clock  scapement ;  a  calculation  of  the  effect  of  tem- 
perature on  steel  springs  ;  an  easy  determination  of  the  best  line  of 
draught  for  a  carriage  ;  an  investigation  of  the  resistance  to  be  overcome 
by  a  wheel  or  roller ;  and  an  estimation  of  the  ultimate  pressure  pro- 
duced by  a  blow. 

In  the  hydraulic  and  optical  part,  may  be  enumerated  an  overflowing 
lamp ;  a  simplification  of  the  rules  for  finding  the  velocity  of  running 
water ;  remarks  on  the  application  of  force  to  hydraulic  machines  ;  a 
mode  of  letting  out  air  from  water  pipes  ;  an  analysis  of  the  human 
voice  ;  and  some  arrangements  for  solar  microscopes,  and  for  other  optical 
instruments  of  a  similar  nature. 

In  the  astronomical  and  physical  division  of  the  work,  will  be  found  a 
general  rule  for  determining  the  correction  on  account  of  aberration ; 
a  comparison  of  observations  on  the  figure  of  the  earth ;  a  table  of  the 
order  of  electrical  excitation  ;  a  chart  of  the  variation  of  the  compass,  and 
of  the  trade  winds  :  formulae  for  finding  the  heat  of  summer  and  winter  ; 
remarks  on  the  theory  of  the  winds ;  and  a  comparative  table  of  all  the 
mechanical  properties  of  a  variety  of  natural  bodies. 

A  few  of  these  subjects  have  been  more  fully  discussed  in  the  miscel- 
laneous papers,  which  have  already  been  published,  in  the  Philosophical 
Transactions  and  elsewhere,  and  which  are  now  reprinted  with  corrections 
and  additions ;  others  are  summarily  investigated  in  the  mathematical 
elements,  which  form  a  part  of  the  second  volume,  or  in  the  remarks 
which  are  inserted,  in  their  proper  places,  in  the  catalogue  of  references. 

The  arrangement  of  the  whole  work  is  probably  different  in  many 
respects  from  any  other  that  has  yet  been  adopted ;  the  extent  of  the 
subjects,  which  have  been  admitted,  rendered  it  necessary  to  preserve  a  very 
strict  attention  to  a  methodical  and  uniform  system ;  and  it  is  presumed 
that  this  arrangement  will  be  considered  as  in  itself  of  some  value,  espe- 
cially in  a  work  calculated  to  serve  as  a  key,  by  means  of  which,  access 
may  be  obtained  to  all  the  widely  scattered  treasures  of  science ;  and  which 
will  enable  those,  who  are  desirous  of  extending  their  researches  in  any 
particular  department,  to  obtain  expeditiously  all  the  information  that 
books  can  afford  them. 

It  will  not  be  thought  surprising  that  the  execution  of  this  plan,  allow- 
ing for  some  professional  engagements  of  a  different  kind,  and  for  a 
variety  of  accidental  interruptions,  should  have  occupied  more  than  three 
years,  from  the  resignation  of  the  professorship  to  the  publication  of  the 
work.  Some  part  of  it  is  in  its  nature  incapable  of  permanent  perfection, 
since  the  catalogue  must  require  to  be  continually  extended  by  the 
enumeration  of  new  publications;  and  it  might  perhaps  be  desirable  that 
an  appendix  should  be  added  to  it,  at  least  every  ten  years ;  but  the 
lectures  themselves  may  be  expected  to  remain  tolerably  commensurate 
to  the  state  of  the  sciences  for  a  much  longer  period  ;  since,  in  investiga- 
tions so  intimately  connected  with  mathematical  principles,  the  essential 


AUTHOR'S  PREFACE,  xi 

improvements  will  always  bear  a  very  small  proportion  to  the  number  of 
innovations.  I  do  not,  however,  mean  to  assert,  that  the  catalogue  is  by 
any  means  complete,  even  with  regard  to  older  works,  but  I  believe  that 
the  references  which  it  contains,  are  at  least  sufficient  to  lead  those  who 
may  consult  the  passages  quoted,  to  the  works  of  every  author  of  eminence 
that  has  treated  of  the  respective  subjects.  Nor  do  I  profess  to  have 
excluded  all  references  that  are  of  little  importance  ;  but  I  trust  that  the 
number  which  I  have  admitted  will  be  found  inconsiderable ;  and  it  would 
have  been  very  difficult  to  have  rejected  any  of  them,  without  some 
chance  of  omitting  others  of  greater  value. 

Whatever  the  deficiencies  of  this  work  may  be,  I  think  it  right  to  ob- 
serve, that  my  present  pursuits  will  not  allow  me  to  look  forwards  to  any 
period,  at  which  I  shall  be  able  to  remove  them,  or  even  to  attend  to  the 
correction  of  the  press,  or  the  revision  of  the  engravings,  in  case  of  the 
necessity  of  a  second  edition. 

I  have  already  begun  to  collect  materials  for  a  work,  in  a  form  nearly 
similar,  relating  to  every  department  of  medical  knowledge :  this  work 
will  not,  however,  be  speedily  ready  for  publication  ;  it  will  be  compara- 
tively more  concise  than  these  lectures,  in  proportion  to  what  has  been  said 
and  written  respecting  physic,  but,  I  hope,  much  more  complete,  with 
regard  to  all  that  is  known  with  certainty,  and  can  be  applied  with 
utility. 

WELBECK-STREET,  30th  March,  1807. 


CONTENTS. 


***   The  matter  within  brackets  [  ]  has  been  supplied  by  the  Editor. 


PART   THE    FIRST.  — MECHANICS. 


LECTURE  I. 
INTRODUCTION,  page  1. 

Objects  of  the  Royal  Institution;  Dissemination  of  elementary  knowledge,  I. 
Education  of  females ;  Theory  of  practical  mechanics,  and  of  manufactures,  2. 
Simplicity  of  useful  theory,  3.  Difficulty  of  making  improvements  ;  Repository 
of  the  Institution ;  Library ;  Journals ;  Nature  of  the  lectures,  4.  Merits  of 
English  philosophers,  5.  Delivery  of  the  lectures ;  General  view,  6.  Division 
of  the  lectures  ;  Synthetical  method,  7...  11.  Causation,  11.  Induction;  Erroneous 
inductions;  Newtonian  rules  of  philosophizing,  12.  Their  insufficiency,  13. 

LECTURE  II. 
ON    MOTION,    13. 

Definition  of  motion,  13.  Absolute  and  relative  motion ;  All  motion  relative, 
14.  Quiescent  space ;  Direction  of  motion ;  Laws  of  motion,  15.  Time,  16, 
17.  Composition  of  motion;  Space  in  motion;  Result  of  two  motions,  18. 
Resolution  of  motion ;  General  result  of  a  number  of  motions,  19. 

LECTURE  III. 

ON  ACCELERATING  FORCES,  21. 
Definition  offeree ;  Action  of  force,  21.  Acceleration  and  retardation ;  Velocity 

22.  Uniform  force;  Gravitation;  Laws  of  falling  bodies;    Atwood's  machine, 

23.  Space  described ;  Law  of  Galileo;  General  law  of  velocities,  24.     Ascent; 
Velocity  due  to  a  height,  25. 

LECTURE  IV. 
ON  DEFLECTIVE  FORCES,  26. 

Centrifugal  force ;  Sling ;  Motion  of  a  hoop,  26.  Whirling  table ;  Laws  of 
central  forces,  27;  Keplerian  laws,  28.  Ellipsis;  Projectiles,  29.  Resolution 
of  oblique  motion  ;  Horizontal  range ;  Best  elevation,  30.  Parabolic  path ;  Prac- 
tice of  gunnery ;  Experiments  of  Robins,  31, 32. 

b 


xiv  CONTENTS. 

LECTURE  V. 
ON  CONFINED  MOTION,  32. 

Motion  limited  by  suspension,  or  by  a  smooth  surface  ;  Effect  of  friction  and  of 
rotatory  motion,  32.  Inclined  plane;  Descent  in  the  chords  of  a  circle; 
Velocity  of  descent,  33.  Ascending  force ;  Energy ;  Cycloid ;  Cycloidal  pendulums, 
34.  Laws  of  pendulums  ;  Swiftest  descent,  35.  Circular  pendulums  ;  Pendu- 
lums with  resistance;  Revolving  pendulums,  36.  Composition  of  vibrations; 
Regulator  for  steam  engines;  Circular  road;  Principle  of  the  least  action, 
37,  38. 

LECTURE  VI. 

ON  THE  MOTIONS  OF  SIMPLE  MASSES,  38. 

Definition  of  a  moveable  body,  without  regard  to  its  extension  ;  Inertia  [gravity]  ; 
Centre  of  inertia,  39.  Its  properties ;  Reciprocal  forces  ;  Quantity  of  motion,  40. 
Momentum;  Centre  of  inertia  of  a  system;  Motion  of  the  centre  of  inertia,  41. 
Action  and  reaction,  42.  Newton's  illustrations ;  Magnitude  of  reciprocal  forces, 
43.  Fall  of  a  feather  and  of  a  piece  of  gold ;  Lucretius  ;  Relation  between  forces 
and  distances ;  Displacement  of  the  earth  by  the  effect  of  a  machine,  44. 

LECTURE  VII. 

ON  PRESSURE  AND  EQUILIBRIUM,  45. 

Pressure,  a  force  counteracted  ;  Pressure  and  momentum  incommensurable,  45. 
Laws  of  pressure  included  in  those  of  motion;  Opposition  of  pressures,  46. 
Equilibrium  of  mechanical  powers ;  Centre  of  gravity  ;  Stability  of  equilibrium, 
47.  Stability  independent  of  equilibrium,  48.  Situation  and  motions  of  the 
centre  of  gravity  of  animals,  49.  Levers  of  two  kinds ;  Fundamental  property  of 
the  lever,  50.  Series  of  levers  ;  Bent  levers  ;  Oblique  levers ;  Wheel  and  axis, 
51.  Wheels  and  pinions  ;  Double  axis  ;  Pullies,  52.  Blocks;  Smeaton'spullies; 
Oblique  ropes,  53.  Inclined  plane ;  Wedges,  54.  Props,  or  shores  ;  Screws  ; 
Nuts ;  Hunter's  screw,  55.  Determination  of  mechanical  power  from  virtual 
velocities,  56. 

LECTURE  VIIL 
ON    COLLISION,    57. 

Motions  of  various  bodies  acting  reciprocally ;  Elastic  bodies,  57.  Nature  of 
repulsion  ;  Experiment  on  an  ivory  ball ;  Apparatus  for  experiments  on  collision, 
58.  Inelastic  bodies ;  Energy,  59.  Measure  of  force ;  Relation  of  labour  to 
energy;  Preservation  of  energy;  or  of  ascending  force,  60.  Effect  of  a  blow; 
Rotation,  61.  Billiards ;  Reflection,  62. 

LECTURE  IX. 

ON  THE  MOTIONS  OF  CONNECTED  BODIES,   63. 

!•>    fTf,'",  I 

Rotatory  power;  Consideration  of  the  square  of  the  velocity,  63.  Smeaton's 
apparatus;  Centre  of  gyration  ;  Centre  of  percussion  and  of  oscillation,  64.  Free 
rotation  ;  Motion  of  a  stick  broken  by  a  blow,  65.  Preponderance,  66.  Greatest 


CONTENTS.  xv 

effect  of  machines  ;  Experiments,  67.  Cautions  with  regard  to  the  construction 
of  machines,  68.  Comparison  of  animal  with  inanimate  force;  Regulation  of 
force  ;  Small  momentum  of  machines,  69.  Impossibility  of  a  perpetual 
motion,  70. 

LECTURE  X. 
ON  DRAWING,  WRITING,  AND  MEASURING,  71. 

Subjects  preliminary  to  the  consideration  of  practical  mechanics  ;  Instrumental 
geometry;  Statics;  Passive  strength ;  Friction;  Drawing;  Outline,  71.  Pen; 
Pencil  ;  Chalks  ;  Crayons,  72.  Indian  ink ;  Water  colours ;  Body  colours ; 
Miniatures ;  Distemper ;  Fresco  ;  Oil,  73.  Encaustic  paintings ;  Enamel ; 
Mosaic  work ;  Writing,  74-.  Materials  for  writing ;  Pens,  75.  Inks ;  Use  of 
coloured  inks  for  denoting  numbers ;  Polygraph ;  Telegraph,  76.  Geo- 
metrical instruments  ;  Rulers ;  Compasses,  77.  Flexible  rulers ;  Squares ;  Tri- 
angular compasses ;  Parallel  rulers ;  Marquois's  scales,  78.  Pantograph ; 
Proportional  compasses;  Sector,  79.  Measurement  of  angles;  Theodolites; 
Quadrants ;  Dividing  engine,  80.  Vernier ;  Levelling ;  Sines  of  angles,  81 . 
Gunter's  Scale ;  Nicholson's  circle ;  Dendrometer ;  Arithmetical  machines ; 
Standard  measures,  82.  Quotation  from  Laplace ;  New  measures ;  Decimal 
divisions ;  Length  of  the  pendulum,  and  of  the  meridian  of  the  earth,  83.  Mea- 
sures of  time,  84.  Objections  ;  Comparison  of  measures,  85.  Instruments  for 
measuring  ;  Micrometrical  scales  ;  Log  lines,  86. 

LECTURE  XI. 

ON  MODELLING,  PERSPECTIVE,  ENGRAVING,  AND  PRINTING,  87. 

Copying  a  statue ;  Modelling;  Casting,  87.  Perspective;  Mechanical  perspec- 
tive ;  Geometrical  perspective,  88.  Orthographical  projection,  89.  Projections  of  a 
sphere,  90.  Invention  of  engraving  ;  Wood  cuts  ;  Mode  of  engraving ;  Ruling,  91 . 
Me/zotinto;  Etching,  92.  Aquatinta;  Musical  characters ;  Printing;  Copying 
letters ;  Printing  from  stones,  93.  Letterpress  ;  Stereotype  printing,  94-. 

LECTURE  XII. 
ON  STATICS,  95. 

Weighing ;  English  and  French  weights,  95, 96.  Balances,  96.  False  balances ; 
Weighing  machines ;  Steelyards,  97 ;  Bent  lever  balances ;  Spring  steelyard ; 
Dynamometer ;  Animal  actions ;  Strength  of  muscles,  98.  Instances  of  strength, 
99.  Progressive  motion ;  Running,  100.  Pulling  ;  Sources  of  motion ;  Work 
of  a  labouring  man,  101.  Temporary  exertions ;  Horses,  102.  Wind;  Water; 
Steam;  Gunpowder;  Measurement  of  small  forces,  103,104-. 

LECTURE  XIII. 

ON  PASSIVE  STRENGTH  AND  FRICTION,  104. 

Immediate  effects  of  force  on  a  solid ;  Extension  and  compression ;  Rigidity, 
105.  Measure  of  elasticity,  106.  Detrusion;  Lateral  adhesion;  Flexure,  107. 
Cause  of  irregularities;  stiffness;  Stiffness  of  beams;  Hollow  beams;  Torsion, 
108.  Alteration  ;  Ductility,  109.  Temper  of  metals  ;  Toughness ;  Brittleness ; 

b  2 


xvi  CONTENTS. 

Fracture;  Strength;  Resilience,  110.  Effect  of  velocity;  Limit  of  strength 
or  resilience,  111.  Qualities  of  natural  bodies;  Fracture  by  simple  com- 
pression; Strength  of  lateral  adhesion,  112.  Transverse  force;  Fracture 
by  flexure,  113.  Comparative  strength  and  resilience,  113,  114.  Uses  of 
resistances  of  different  kinds  ;  Coach  springs  ;  Comparison  of  direct  and  trans- 
verse strength,  114.  Beam  cut  out  of  a  tree;  Hollow  masts;  Strongest  forms  of 
beams,  115.  Machine  for  measuring  strength;  Strength  of  different  substances, 

116.  Inconvenience  of  bulk  ;   Friction;  Lateral  adhesion  ;    Uniformity  of  friction, 

117.  Usual  magnitude  of  friction,  118.     Best  direction  for  draught;  Stability 
of  a  wedge  or  nail,  119.     Resistance  to  penetration,  120. 

LECTURE  XIV. 
ON  ARCHITECTURE  AND  CARPENTRY,  121. 

Architecture;  Form  of  a  column,  121.  Eddystone  lighthouse;  Wall,  122. 
Joints;  Mortar;  Arch,  123.  Oblique  pressure  of  earth,  124.  Bridge;  Flat  arch, 
125.  Horizontal  thrust;  Piers;  Blackfriars  bridge;  Dome,  126.  St.  Paul's 
cathedral;  Pantheon;  Orders  of  architecture ;  Gothic  architecture,  127.  Carpen- 
try; Joints,  128.  Scarfing  ;  Joggles  ;  Tenons  ;  Mortises  ;  Straps,  129.  Inconve- 
nience of  transverse  strains  ;  Roofs  ;  Kirb  roof;  Height  of  a  roof,  130.  Wooden 
bridges;  Centres  of  bridges  ;  Furniture;  Parker's  gates,  131. 


LECTURE  XV. 
ON  MACHINERY,  132. 

Application  of  force,  132.  Levers;  Connected  rods;  Hooke's joint;  Cranks, 
133.  Winches;  Rectification  of  circular  motion;  Wheel  work,  134.  Teeth  of 
wheels,  135.  Kinds  of  wheels,  136.  Eccentric  wheels;  Sun  and  planet  wheels; 
Construction  of  wheels ;  Weights  and  springs ;  Fly  wheels,  137.  Air  vessels,  138. 

LECTURE  XVI. 
ON  THE  UNION  OF  FLEXIBLE  FIBRES,  138. 

Chain;  Union  by  means  of  adhesion;  Friction  of  a  rope  on  a  cylinder;  Twist- 
ing; Spinning;  Rope-making,  139.  Materials  of  ropes;  Hemp,  140;  Flax; 
Cotton,  141.  Silk;  Wool;  Weaving,  142.  Crape;  Cloth;  Felts;  Hats,  143. 
Paper,  144. 

LECTURE  XVII. 
ON  TIMEKEEPERS,  144. 

Clepsydrae,  144.  Clocks ;  Fly  clocks,  145.  Balances ;  Chronometer  with  a 
revolving  pendulum,  146.  Measurement  of  minute  intervals  of  time;  Pendulum  ; 
Balance  spring;  Principal  requisites  of  a  timekeeper;  Sustaining  force,  147. 
Equalization  of  the  force  ;  Intermediate  spring  or  wheel;  Scapement ;  Crank,  148. 
Crutch  scapement ;  Common  watch  scapement,  149.  Dead  beat  scapement  and 
horizontal  watch ;  Friction  of  scapements ;  Duplex  scapement ;  Common  scape- 
ment; Scapements  of  Harrison,  Mudge,  150.  Scapements  of  Haley,  Camming, 
Nicholson,  Arnold,  and  Earnshaw;  Isochronism  of  vibrations,  151.  Properties  of 


CONTENTS.  xvii 

springs,  152.  Expansion  of  pendulums  ;  Compensations  for  clocks,  153.  Com- 
pensations for  watches  ;  Resistance  of  the  air,  15*.  Striking  part ;  Supports  of 
clocks ;  Mutual  influence  of  two  clocks,  155. 

LECTURE  XVIII. 
ON  RAISING  AND  REMOVING  WEIGHTS,  156. 

Counteraction  of  gravitation;  Levers,  156.  Perrault's  lever;  Axis  with  a 
winch ;  Water  whimsey ;  Gin,  157.  Capstan  ;  Double  capstan  ;  Wheelvvork ; 
String  of  buckets,  158.  Pullies ;  Inclined  plane;  Duke  of  Bridgwater's  canal,  159. 
Screws  ;  Cranes  ;  Walking  wheels,  160.  White's  crane  ;  Weighing  cranes  ;  Lewis; 
Counterpoise  for  a  chain ;  Removing  weights,  161.  Porters  ;  Distribution  of 
weight:  Simple  dray,  162.  Effect  of  agitation  ;  Oily  substances;  Rollers,  163. 
Friction  wheels  ;  Perrault's  ropes  ;  Wheels  of  carriages,  164- .  Magnitude  of 
wheels,  165.  Line  of  draught;  Conical  wheels;  Effect  of  springs,  166.  Attach- 
ment of  horses ;  Wheel  ways,  167.  String  of  baskets  or  carts,  168. 

LECTURE  XIX. 

ON  MODES  OF  CHANGING  THE  FORMS  OF  BODIES,  169. 

Compression ;  Presses  ;  Effect  of  momentum  ;  Printing  press,  169.  Sugar  mill ; 
Oil  mills  ;  Hammering;  Hydrostatic  press;  Extension;  Laminating  machine,  170. 
Glazier's  vice;  Wire  drawing;  Pottery;  Glassblowing ;  Percussion;  Forges; 
Goldbeating  ;  Coining,  171.  Stamping;  Penetration,  172.  Pile  driving  engine  ; 
Sling;  Bow  and  arrow,  173.  Whip;  Division;  Cutting  instruments;  Slitting 
mill;  Lathes,  174.  Boring;  Agricultural  instruments;  Mining;  Sawing,  175. 
Stonecutting;  Grinding;  Polishing,  176.  Trituration ;  Powder  mills,  177.  Agi- 
tation; Threshing  machines  ;  Corn  mills,  178.  Kneading;  Levigating;  Demoli- 
tion ;  Bolt  drawer;  Burning,  179.  Blasting,  180. 

LECTURE  XX. 
ON  THE  HISTORY  OF  MECHANICS,  180. 

Origin  of  the  Grecian  learning  in  Egypt ;  Thales  ;  Ionian  school ;  Italian  school; 
Pythagoras,  181.  Democritus  ;  Invention  of  the  arch  ;  Archytas  and  Eudoxus, 
182.  Aristotle  ;  Foundation  of  Alexandria ;  Epicurus,  183.  Archimedes  ;  Siege 
of  Syracuse,  184,  185.  Athenaeus ;  Ctesibius,  185.  Vitruvius ;  Middle  ages; 
British  manufactures,  186.  Anglonorman  and  Gothic  architecture,  187.  Roger 
Bacon  ;  Clocks  ;  Engraving  and  Printing,  188.  Leonardo  da  Vinci ;  Bacon  Lord 
Verulam  ;  Galileo;  Napier,  189.  Laws  of  collision;  Hooke  ;  Barrow;  Newton, 
190.  Followers  of  Newton,  191.  Modern  mathematicians  and  mechanics  ;  Time- 
keepers ;  Journals  ;  Royal  Institution,  192.  Future  prospects  ;  Use  of  a  catalogue 
of  references,  193.  Table  of  the  chronology  of  mathematicians  and  mechanics,  ta 
face  p.  194. 


xviii  CONTENTS. 


PART  THE  SECOND.— HYDRODYNAMICS. 


LECTURE  XXI. 
ON  HYDROSTATICS,  195. 

Hydrodynamics  more  dependent  on  experiment  than  mechanics ;  Division  of 
the  subject  into  Hydraulics,  Acustics,  and  Optics,  195.  Hydrostatics ;  Definition 
of  a  fluid  and  a  liquid,  196.  Surface  of  a  gravitating  fluid  horizontal,  197.  Sur- 
face of  a  revolving  fluid ;  Pressure  of  a  fluid  ;  Magnitude  of  hydrostatic  pressure, 
198.  Hydrostatic  paradox,  199.  Blowing  with  the  mouth  and  lungs ;  Pressure 
on  the  bank  of  a  river  ;  Pressure  on  a  concave  surface,  200.  Pressure  of  different 
fluids  ;  Equilibrium  of  fluids  with  solids;  Floating  bodies,  201.  Stability  and  os- 
cillations of  floating  bodies ;  Buoyancy,  202.  Bodies  falling  in  fluids  ;  Hooke's 
hemisphere  ;  Flexible  vessels,  203. 

LECTURE  XXII. 
ON  PNEUMATIC  EQUILIBRIUM,  204. 

Properties  of  the  air,  and  of  gases ;  Mercurial  column,  204.  Steams  and  vapours ; 
Weight  of  the  air  ;  Experiments  with  the  air  pump,  205.  Constitution  of  the  at- 
mosphere ;  Measurement  of  heights ;  Ascent  of  a  balloon,  206.  Pressure  of  the 
atmosphere  ;  Magdeburg  hemispheres ;  Nature  of  suction,  207.  Barometers,  208. 
Compressibility  of  liquids,  209. 

LECTURE  XXIII. 
ON  THE  THEORY  OF  HYDRAULICS,  210. 

General  principle  of  ascending  force,  210.  Bernoulli's  inferences  ;  Velocity 
of  a  jet  of  a  fluid,  211.  Ajutages  of  different  kinds  ;  Contraction  of  a  jet,  212. 
Effect  of  a  short  pipe ;  Diverging  pipe  ;  Experiments  of  Bernoulli,  Venturi,  and 
Matthew  Young;  Discharge  through  large  apertures,  213.  Vessels  emptying 
themselves  ;  Locks,  214.  Siphons ;  Discharge  through  a  vertical  pipe,  215.  Ex- 
planation; Limit  of  velocity;  Whirlpool;  Intermitting  springs,  216.  Ascending 
jets;  Oscillations  of  fluids,  217.  Waves,  218.  Reflection  of  waves ;  Height  of 
waves  ;  Experimental  exhibition  of  waves,  219.  Divergence  of  waves ;  Combina- 
tions of  waves  ;  Applications  ;  Elastic  pipes  ;  Circulation  of  the  blood,  220. 

LECTURE  XXIV. 

ON  THE  FRICTION  OF  FLUIDS,  222. 

Experiments  of  Du  Buat ;  Motions  of  rivers  ;  Friction  and  resistance,  222. 
Examples  of  the  velocity  of  rivers,  223.  Velocity  at  different  depths ;  Weres,  224. 
Changes  and  flexures  of  rivers  ;  Lateral  friction  ;  Venturi's  experiments,  225.  Ball 
supported  by  a  jet ;  Discharge  of  long  pipes,  226.  Bent  pipes ;  Dilatations  of 
pipes  ;  Effect  of  temperature,  227. 


CONTENTS.  xix 

LECTURE  XXV. 

ON  HYDRAULIC  PRESSURE,  228. 

Pressure  of  fluids  in  motion ;  Counterpressure,  228.  Magnitude  of  the  pressure 
and  impulse  of  fluids  ;  Laws  of  hydraulic  pressure,  229.  Particular  case  of  water 
wheels  ;  Oblique  impulse  ;  Distribution  of  pressure,  230.  Elevation  and  depres- 
sion produced  by  the  motion  of  a  floating  body  ;  Form  of  a  ship  ;  Body  moving 
below  the  surface,  231.  Convex  surfaces ;  Hydraulic  pressure  of  the  air,  232. 
Concave  surfaces  ;  Great  effect  of  an  increase  of  velocity ;  Reflection  of  a  ball  or 
stone,  233. 

LECTURE  XXVI. 

ON  HYDROSTATIC  INSTRUMENTS,  AND  HYDRAULIC  ARCHITECTURE,  235. 

Statics  and  architecture  of  fluids;  Hydrostatic  balance,  235.  Hydrometer; 
Glass  globules ;  Specific  gravities  of  particular  substances  ;  Mixtures,  236.  Spirit 
level ;  Hydrostatic  lamps ;  Embankments,  237.  Dikes  ;  Rivers  ;  Reservoirs,  238. 
Flood  gates ;  Strength  of  sluices  and  flood  gates,  239.  Friction  ;  Canals  ;  Piers  ; 
Harbours,  240. 

LECTURE  XXVII. 

ON  THE  REGULATION  or  HYDRAULIC  FORCES,  241. 

Machinery  of  fluids  ;  Water  pipes  ;  Siphons,  241.  Stopcocks  and  valves,  242. 
Pitot's  tube  ;  Hydrometric  fly ;  Captain  Hamilton's  hydraulic  register  ;  Motions 
of  the  air,  243.  Weight  and  impulse  of  fluids ;  Raising  weights  by  the  descent  of 
water;  Effect  of  velocity ;  Overshot  wheel,  244.  Undershot  wheel ;  Mechanical 
power  of  a  stream,  245.  Breast  wheel ;  Second  wheel ;  Oblique  wheels  and  wind- 
mills, 246,  247.  Smoke  jack  ;  Kite,  247.  Parent's  mill ;  Seamanship  ;  Sidewind ; 
Form  and  arrangement  of  a  vessel,  248.  Stability  of  a  ship,  249. 

LECTURE  XXVIII. 

ON  HYDRAULIC  MACHINES,  250. 

Machines  for  raising  water ;  Noria ;  Bucket  wheel ;  Throwing  wheel ;  Rope 
pump,  250.  Venturi's  drain  ;  Spiral  pipes ;  Screw  of  Archimedes ;  Water  screw, 
251.  Wirtz's  spiral  pump,  252.  Centrifugal  pump ;  Pumps;  Plunger  pump, 253. 
Forcing  pump ;  Mixed  pump ;  Pistons ;  Bramah's  press ;  Sucking  pump ;  Bag 
pump,  254.  Lifting  pump  ;  Sucking  and  forcing  pump ;  Air  vessel ;  Fire  engine, 
255.  Roller  pumps  and  slider  pumps ;  Arrangement  of  pipes ;  Bead  pump ;  Cel- 
lular pump;  Chain  pump,  256.  Cranks;  Wheels  and  rollers;  Chinese  walking 
wheels;  Inverted  pump ;  Hydraulic  air  vessels,  257.  Fountain  of  Hero ;  Atmos- 
pheric machines,  258.  Hydraulic  ram,  259. 

LECTURE  XXIX. 
ON  PNEUMATIC  MACHINES,  259. 

Counteraction  and  application  of  pneumatic  forces ;  Torricellian  vacuum ;  Air 
pump;  Double  barrel,  260.  Smeaton's  pump ;  Experiments;  Gages,  261.  Pear 
gage  ;  Condensers ;  Diving  bells ;  Bellows,  262.  Gasometers ;  Shower  bellows ; 


xx  CONTENTS. 

Velocity  of  a  blast,  263.  Ventilation ;  Corn  fan,  264.  Chimnies ;  Furnaces  ; 
Balloons;  Steam  engines;  Savery's  engine,  265.  Newcomen's  arid  Beighton's 
engine ;  Watt's  improvements,  266.  Power  of  Boulton  and  Watt's  machines ; 
Later  alterations,  267.  Gunpowder;  Calculations  of  Bernoulli  and  of  Count 
Rumford  ;  Properties  of  a  gun ;  Bullets ;  Shot,  268.  Air  gun  ;  Improvements 
on  steam  engines ;  Stray  Park  engine ;  Cornish  boiler,  269.  D  valve,  270.  Ap- 
plication of  steam  engine  to  navigation ;  G.  Dodd ;  Explanations ;  Marine  engines, 
271.  High  pressure  engine ;  Young's  formula  for  the  elasticity  of  steam;  For- 
mula of  the  Franklin  Institute ;  Trevithick,  272.  Description  of  the  locomotive 
engine,  272,  273,  274-,  275. 

LECTURE  XXX. 
ON  THE  HISTORY  OF  HYDRAULICS  AND  PNEUMATICS,  275. 

Discoveries  of  Archimedes ;  Ctesibius;  Hero;  Vitruvius,  276.  Canals;  Gun- 
powder; Galileo;  Torricelli;  Castelli,  277.  Mariotte;  Guglielmini;  Guericke; 
Hooke ;  Marquis  of  Worcester,  278.  Huygens  ;  Pardies  :  Renaud ;  James  and 
John  Bernoulli ;  Newton,  279.  Poleni ;  Bouguer ;  D.  Bernoulli,  280.  John 
Bernoulli;  Maclaurin ;  Robins,  281.  Dalembert;  Kaestner;  Euler;  Smeaton ; 
Borda;  Watt,  282.  Specification  of  Mr.  Watt's  patent,  282, 283.  Bossut;  Juan; 
Prony;  Chapman;  Romme;  Hutton;  Rumford, 284.  DuBuat;  Black;  Mont- 
golfier,  285.  Chronological  table,  286. 


LECTURE  XXXI. 

ON  THE  PROPAGATION  OF  SOUND,  287. 

Importance  of  acustics;  Division  of  the  subject;  Definition  of  sound;  Pro- 
pagation of  sound,  287.  Velocity  of  sound ;  Delineation  of  a  sound,  288.  Com- 
pressibility of  hard  bodies ;  Transmission  of  sound  by  different  mediums,  289. 
Correction  on  account  of  heat,  290.  Transmission  in  gases  of  different  kinds ;  In 
liquids;  In  solids,  291.  Divergence  of  sound,  292.  Reflection  of  sound  ;  Illus- 
tration by  waves  of  water;  Speaking  trumpet,  293.  Whispering  gallery;  Invisible 
girl ;  Partial  interception  of  sound ;  Decay  of  sound,  294. 

LECTURE  XXXII. 

ON  THE  SOURCES  AND  EFFECTS  OF  SOUND,  295. 

Origin  of  a  simple  sound;  Of  a  continued  sound;  Musical  sounds  derived 
from  vibrations,  295.  Open  pipes;  Stopped  pipes;  Harmonic  sounds,  296. 
Effect  of  temperature ;  Longitudinal  sounds  of  solids ;  Lateral  vibrations  ;  Flexi- 
ble cords  and  membranes,  297.  Harmonic  sounds  of  cords,  298.  Loaded 
wire  ;  Revolutions  of  cords ;  Vibrations  of  elastic  rods,  299.  Vibrations  of 
plates,  rings,  and  vessels,  300.  Mixed  vibrations  of  solids  and  fluids ;  Sympa- 
thetic sounds;  Hearing,  301.  Description  of  the  ear,  302.  Delicacy  of  the 
ear,  30a 


CONTENTS.  xxi 

LECTURE   XXXIII. 
ON  HARMONICS,  304. 

Theory  of  harmonics;  Combinations  of  sounds,  304.  Beats,  305.  Grave 
harmonics  ;  Concords ;  Melody ;  Rhythm  ;  Simple  compositions,  306.  Diatonic 
scale ;  Half  notes  or  semitones,  307.  Minor  mode  ;  Discords  ;  Rules  of  accom- 
paniment, 308.  Temperament ;  Distinction  of  the  notes,  309. 

LECTURE  XXXIV. 
ON  MUSICAL  INSTRUMENTS,  310. 

Division  of  musical  instruments,  310.  Harp;  Lyre;  Harpsichord;  Spinet; 
Pianoforte;  Dulcimer;  Clavichord;  Guitar,  31 L  Violins  of  different  kinds; 
Vielle ;  Trumpet  Marigni ;  Aeolian  harp  ;  Human  voice,  312.  Drum ;  Stacada, 
313.  Bell;  Harmonica;  Vox  humana  pipe;  Simple  wind  instruments;  Mixed 
wind  instruments,  314.  History  of  Music ;  Lyre;  Hermes;  Terpander;  Pytha- 
goras; Simonides;  Tibia;  Aristotle,  315.  Ctesibius;  Pope  Gregory;  Guido; 
Bacon ;  Galileo ;  Mersenne ;  Kircher ;  Meibomius ;  Wallis  ;  Newton,  316^ 
Brook  Taylor ;  Sauveur  ;  Lagrange ;  Euler ;  Bernoulli ;  Dalembert ;  Sounds  of 
rods  ;  Grave  harmonics  of  Romieu  and  Tartini ;  Sounds  of  pipes,  317.  Chladni; 
Laplace,  318.  Chronological  table,  319. 

LECTURE  XXXV. 
ON  THE  THEORY  OF  OPTICS,  320. 

Importance  of  optics;  Division  of  the  subject;  Definition  of  light;  Ray  of 
light,  320.  Motion  of  light;  Homogeneous  mediums;  Reflection;  Refraction, 
321.  Polished  surfaces,  322.  Return  of  a  ray;  Refractive  density:  Index  of 
refractive  power,  323.  Intermediate  refraction ;  Total  reflection  ;  Dioptrics  and 
catoptrics;  Focus,  324.  Plane  speculum;  Principal  focus;  Convergence  by 
reflection;  Concave  and  convex  mirrors,  325.  Prism;  Multiplying  glass ;  Lens; 
Effects  of  lenses  ;  Focus  of  a  lens,  326.  Joint  focus ;  Image ;  Optical  centre  ; 
Curvature  of  the  image,  327. 

LECTURE  XXXVI. 

ON  OPTICAL  INSTRUMENTS,  328. 

Divergence  of  light,  328.  Photometers  ;  Measurement  of  refractive  densities; 
Instruments  strictly  optical ;  Images  formed  by  lenses  and  mirrors,  329.  Mag- 
nifiers; Simple  microscopes;  Globules;  Illumination  of  an  image;  Burning 
glasses,  330.  Materials  of  lenses  and  mirrors ;  Images  visible  in  every  direction ; 
Camera  obscura,  331.  Solar  microscope,  332.  Lucernal  microscope;  Phantas- 
magoria, 333.  Astronomical  telescope ;  Double  microscope ;  Galilean  telescope ; 
Common  day  telescope;  Dr.  Herschel's  telescope,  334;'  Newtonian  reflector; 
Gregorian  telescope;  Cassegrain's  telescope;  Smith's  microscope;  Curvature  of 
images  in  telescopes,  335.  Magnifying  powers  of  telescopes ;  Field  glass  ;  Dou- 
ble magnifier,  336.  Aberration  from  colour ;  Achromatic  glasses ;  Achromatic 
eye  piece  ;  Micrometers,  337.  Divided  speculum,  338. 


xxii  CONTENTS. 

LECTURE  XXXVII. 
ON  PHYSICAL  OPTICS,  340. 

Sources  of  light ;  Combustion  ;  Slow  decomposition ;  Electricity ;  Friction, 
340.  Solar  phosphori ;  Emission  of  light;  Velocity  of  light,  341.  Apparent 
aberration  ;  Oblique  reflection  ;  Diffraction  ;  Dispersion,  342.  Colour ;  Division 
of  the  spectrum  ;  Light  of  different  kinds,  343.  Mixed  lights  ;  Imitation  of  white 
light ;  Primitive  colours,  344.  Mixture  of  colours  by  rapid  motion ;  Combina- 
tions ;  Atmospherical  refraction,  345.  Horizontal  refraction ;  Rainbows,  346. 
Halos  and  parhelia,  347.  Refraction  of  ice ;  Complicated  halos  ;  Double  refrac- 
tion ;  Iceland  spar,  348.  Second  refraction  ;  Transparent  plates,  349. 

LECTURE  XXXVIII. 
ON  VISION,  350. 

Description  of  the  eye,  350.  Image  on  the  retina ;  Advantages  of  the  arrange- 
ment; Inversion  of  the  image,  351.  Instinct;  Sensibility  of  the  retina,  352. 
Focus  of  the  eye;  Accommodation;  Change  in  the  crystalline  lens,  353.  Uses 
of  the  iris ;  Optometer ;  Myopic  sight,  354.  Presbyopic  sight ;  Single  vision  ; 
Judgment  of  distance,  355.  Apparent  magnitudes  of  the  sun  and  moon ;  Aerial 
perspective  ;  Painting ;  Panorama,  356.  Duration  of  sensations ;  Ocular  spectra, 
357. 

LECTURE  XXXIX. 

ON  THE  NATURE  OF  LIGHT  AND  COLOURS,  359. 

Theories  respecting  the  nature  of  light ;  Simple  propagation,  359.  Transparent 
mediums,  360.  Uniformity  of  velocity ;  Reflection  and  refraction,  361.  Partial 
reflection ;  Total  reflection ;  Sources  of  light,  362.  Aberration ;  Double  refrac- 
tion ;  Dispersion,  363.  Colours  of  thin  plates ;  Alternate  union  and  extinction 
of  colours  ;  Light  admitted  by  two  holes,  364.  Supposed  dimensions  of  undula- 
tions ;  Correction ;  Stripes  in  a  shadow,  365.  Light  passing  through  a  narrow 
aperture ;  Colours  of  striated  surfaces ;  Curved  stripes  of  colours,  366.  Fringes 
near  a  shadow;  Colours  of  thin  plates,  367.  Colours  of  natural  bodies,  368. 
Colours  of  mixed  plates  ;  Supernumerary  rainbows ;  Colours  of  concave  mirrors, 
369.  Agreement  of  the  Huygenian  theory  with  the  phenomena ;  Interference  of 
light,  370.  Phenomena  of  polarized  light;  Double  refraction,  371,  372.  Re- 
ferences, 372. 

LECTURE  XL. 
ON  THE  HISTORY  OF  OPTICS,  374. 

Knowledge  of  the  ancients;  Empedocles;  Aristotle,  374.  Archimedes; 
Euclid;  Ptolemy;  Alhazen;  Vitellio;  R.  Bacon;  Janson,  375.  Galileo, 
Kepler ;  Scheiner ;  Rheita ;  Maurolycus ;  De  Dominis  ;  Snellius  ;  Descartes ; 
Fermat ;  Leibnitz ;  Barrow,  376.  Boyle :  Hooke ;  Newton  ;  Grimaldi,  377.  Bar- 
tholin;  Huygens;  Roemer,378.  Bradley;  Bouguer;  Porterfield;  Jurin;  Smith; 
Dollond  ;  Hall,  379.  Euler;  Lambert,  380.  Mathemetical  opticians  ;  Mazeas ; 
Dutour;  Comparetti ;  Priestley;  Delaval,  381.  R.  Darwin;  Atmospherical 
refraction;  Wollaston ;  Ritter;  Herschel;  Laplace;  Attempts  of  the  author, 
382.  Chronological  table,  385. 


CONTENTS. 


PART   THE  THIRD.— PHYSICS. 


LECTURE  XLI. 

ON  THE  FIXED  STARS,  387. 

Division  of  the  subjects  of  physics ;  Astronomy,  387.  Empty  space,  388. 
Fixed  stars ;  Light  of  the  stars  ;  Figure  ;  Twinkling ;  Number ;  Magnitudes,  389. 
Distances  of  the  stars,  390.  Clusters  or  nebulae ;  Arrangement  of  the  stars 
in  general ;  Milky  way,  391.  Proper  motions  of  the  stars;  Dr.  Herschel's  division 
of  stars  and  nebulae,  392.  Changes  of  the  stars,  393.  Constellations ;  Repre- 
sentations of  the  stars ;  Allocations,  394,  395. 

LECTURE  XLII. 

ON  THE  SOLAR  SYSTEM,  397. 

The  sun  a  star ;  Progressive  motion  of  the  sun,  397.  Orbit  of  the  sun ;  Ro- 
tation ;  Spots,  398.  Solar  heat ;  Sun's  attraction ;  Solar  atmosphere,  399. 
Planets ;  Ecliptics,  400.  Change  of  position  of  the  ecliptic  ;  Nodes ;  Keplerian 
laws,  401.  Rotation  of  the  planets;  Precession  of  the  equinoxes ;  Nutation  of 
the  earth's  axis  ;  Proportional  distances  of  the  planets,  402.  Mercury ;  Venus ;  The 
earth ;  Mars,  403.  Juno ;  Pallas ;  Ceres ;  Vesta ;  Jupiter ;  Saturn,  404.  Georgian 
planet;  Unknown  planets;  Satellites;  Moon,  405.  Satellites  of  Jupiter,  406. 
Ring  of  Saturn;  Comets,  407.  Number  and  orbits  of  the  comets,  408. 

LECTURE  XLIII. 

ON  THE  LAWS  OF  GRAVITATION,  409. 

Newton's  great  discovery,  409.  Attraction  of  spherical  bodies  ;  Extent  of  the 
force  of  gravity,  410.  Sun's  change  of  place ;  Orbits  of  the  planets ;  Keplerian 
laws  ;  Universality  of  gravitation,  411.  Motions  of  the  apsides  and  nodes  ; 
Changes  of  the  ecliptic;  Forms  of  the  planets;  Precession;  Nutation,  412. 
Lunar  motions  ;  Disturbing  force  of  the  sun,  413.  Acceleration  of  the  moon's 
motion  ;  Moon's  rotation  ;  Orbits  of  comets  ;  Predictions  of  Halley  and 
Clairaut,  414,  415. 

LECTURE  XLIV. 

. 
ON  THE  APPEARANCES  OF  THE  CELESTIAL  BODIES,  415. 

Apparent  motions  to  be  described  after  the  real  ones,  415.  Motions  of  the  stars 
and  sun  ;  Motions  of  the  earth  ;  Apparent  revolution  of  the  sun  ;  Sun's  apparent 
diameter,  416.  Length  of  summer  and  winter  ;  Day  and  night  ;  Sun's  apparent 
path;  Centrifugal  force,  417.  Places  of  the  stars  ;  Twilight;  Relative  positions 
and  phases  of  the  planets,  418.  Phases  of  the  moon  ;  Lunar  eclipses ;  Eclipses 
of  the  sun,  419.  Series  of  eclipses,  420.  Harvest  moon;  Eclipses  of  Jupiter's 


xxiv  CONTENTS. 

satellites;  Comets;  Light  of  the  heavenly  bodies,  421.  Planetary  worlds ;  Fon- 
tenelle;  Mercury;  Venus,  422.  Moon;  Mars,  423.  Newly  discovered  planets; 
Jupiter ;  Saturn ;  Georgian  planet,  424,  425. 

LECTURE  XLV. 

ON  PRACTICAL  ASTRONOMY,  425. 

Real  motions  neglected  ;  Situation  of  a  point  in  the  heavens,  425.  Meridian  ; 
Astronomical  instruments;  Time;  Sidereal  day;  Solar  day;  Equation  of  time, 
426.  Dialling  ;  Chronology  ;  Calendar,  427.  Improvement  suggested  ;  Repub- 
lican calendar ;  Metonic  cycle,  428.  Golden  number ;  Epact ;  Moon's  age  ; 
Julian  period  ;  Astronomical  time ;  Quadrants  ;  Transit  instruments,  429. 
Hadley's  quadrant ;  Declinations  ;  Refraction  and  parallax  ;  Latitudes,  430. 
Longitudes  ;  Lunar  observations ;  Distance  of  the  sun,  431.  Transits;  Densities 
of  the  sun  and  planets ;  Artificial  globe,  432.  Planispheres ;  Orreries,  433. 

LECTURE  XLVI. 

ON  GEOGRAPHY,  435. 

Particular  account  of  the  earth ;  Curvature  of  its  surface  ;  Direction  of  the 
plumb  line;  Ellipticity,  435.  Measurements  of  degrees  ;  Zones,  436.  Climates; 
Sea  and  land ;  Continents,  437.  Rivers  ;  Elevations ;  Mountains,  438.  Dif- 
ferent orders  of  mountains,  439.  Internal  parts  of  the  earth  ;  Density  of  the 
earth,  440. 

LECTURE  XL VII. 

ON    THE    TIDES,    441. 

Tides  noticed  by  the  ancients,  441.  Daily  changes  ;  Monthly  changes  ; 
Yearly  changes ;  Connexion  with  the  moon ;  Effect  of  gravitation  on  a  fluid 
sphere,  442.  Primitive  lunar  tides  ;  Comparison  with  a  pendulum  ;  Direct  and 
inverted  tides,  443.  Tides  of  a  lake;  Resistance;  Tides  of  the  Atlantic,  444. 
Particular  modifications,  445.  Tides  of  the  channels  and  of  rivers;  Inferior  and 
superior  tides,  446.  Laws  of  elevation  and  of  depression  ;  Mode  of  observing 
the  tides ;  Solar  tides  ;  Combination  of  tides ;  Retardation  of  spring  and  neap 
tides,  447.  Increased  height  in  converging  channels,  448.  Combinations  in 
particular  ports ;  Currents,  449.  Tides  of  the  atmosphere,  450. 

LECTURE  XLVIII. 

ON  THE  HISTORY  OF  ASTRONOMY,  451. 

Earliest  astronomy;  Signs  of  the  zodiac,  451.  Babylonian  observations  ;  Chal- 
deans; Hermes;  Egyptians;  Chinese;  Indians,  452.  Greeks;  Thales;  Pytha- 
goras, 453.  Meto  ;  Alexandrian  school ;  Eratosthenes  ;  Hipparchus,  454. 
Ptolemy,  455.  Arabians  ;  Persians  ;  Copernicus,  456.  Tycho  Brahe  ;  Kepler, 
457.  Napier  ;  Huygens  ;  Cassini  ;  Gravitation,  458.  Newton's  discoveries  ; 
Extract  from  Pemberton,  459.  British  astronomers ;  Observatory  at  Greenwich, 
460.  Determinations  of  the  longitude;  Late  discoveries,  461,  462.  Chrono- 
logical table,  463. 

. 


CONTENTS.  xxv 

LECTURE  XLIX. 

ON  THE  ESSENTIAL  PROPERTIES  OF  MATTER,  464. 
Importance  of  minute  objects;  Definition  of  matter,  464.  Place  of  the  investiga- 
tion ;  Essential  and  accidental  properties  of  matter ;  Extension ;  Divisibility, 
465.  Actual  division  of  matter,  466.  Impenetrability,  467.  Permeability; 
Orders  of  substances ;  Repulsion ;  Apparent  contact,  468.  Laws  of  repulsion, 
469.  Dalton's  hypothesis ;  Repulsion  of  liquids  and  solids ;  Reciprocality  of 
repulsion ;  Inertia,  470.  Gravitation  ;  Cause  of  gravitation  ;  Mathematical  con- 
ceptions, 471.  Newton's  opinion ;  Constitution  of  a  medium  capable  of  pro- 
ducing gravitation,  472.  Difficulties,  473. 

hits 

LECTURE  L. 
ON  COHESION,  473. 

Accidental  properties  of  matter;  Laws  of  cohesion;  Modification  of  cohesion 
by  heat,  474.  Liquidity;  Superficial  cohesion,  475.  Bubbles;  Form  of  the  surface 
of  a  fluid,  476.  Magnitude  of  the  force  of  cohesion  ;  Ascent  between  two  plates; 
Capillary  tubes,  477.  Horizontal  surface  ;  Detached  portion  of  a  liquid ;  Lyco- 
podium ;  Attractions  and  repulsions  of  floating  bodies,  478.  Apparent  cohesion 
of  plates  ;  Drop  between  plates ;  Oil  spreading  on  water  ;  Sponge ;  Long  column 
supported  by  cohesion,  479.  Cohesion  of  solids;  More  perfect  union  ;  Solidity; 
Cause  of  solidity,  480.  Elasticity,  481.  Stiffness ;  Strength ;  Softness  ;  Ductility; 
Primary  cause  of  cohesion,  482,  483. 

.       . 

LECTURE  LI. 

.ill 
ON  THE  SOURCES  AND  EFFECTS  OF  HEAT,  484. 

Division  of  the  subject  of  heat;  Definition  of  heat  and  cold;  Excitement  of 
heat;  Condensation,  484.  Friction;  Count  Rumford's  experiments,  485. 
Effect  of  velocity;  Pictet's  experiments;  Heat  from  combustion,  486.  Com- 
munication  of  heat;  Conducting  powers;  Fluids,  487.  Radiation  of  heat;  Mr. 
Leslie's  discoveries ;  Differences  of  solar  and  culinary  heat,  488.  Invisible  heat; 
Equilibrium  of  radiant  heat ;  Apparent  reflection  of  cold,  489.  Refrangibility  of 
heat;  Blackening  rays,  490.  Effects  of  heat;  Temporary  effects ;  Expansion  of 
gases;  Condensation;  Expansion  of  fluids,  491.  Diminution  of  cohesive  powers; 
Boiling;  Slow  evaporation  ;  Contraction,  492.  Freezing;  Expansion  of  solids ; 
Liquefaction,  493.  Cracks  from  heat ;  Permanent  effects  of  heat ;  Glass  drops  ; 
Tempering  of  metals,  494,  495. 

:  plli 

LECTURE  LII. 

ON  THE  MEASURES  AND  THE  NATURE  OF  HEAT,  496. 
Measures  of  expansion ;  Pyrometer ;  Scale  of  heat ;  Mixtures ;  Sun's  rays, 
496.  Expansion  of  solids  and  fluids;  Thermometers;  Wedgwood's  thermo- 
meter, 497.  Different  scales  ;  Temporary  change  of  a  thermometer  ;  Air  ther- 
mometers, 498.  Capacities  for  heat ;  Natural  zero,  499.  Theory  of  capacities  ; 
Chemical  effects,  500.  Latent  heat;  Mr.  Davy's  experiments ;  Intimate  nature  of 
heat ;  Theory  of  caloric,  501 .  Confutation ;  Heat  a  quality ;  Newton's  opinion ; 


xxvi  CONTENTS. 

Vibrations  ;  Mechanical  effects  of  vibrations,  502.  Chemical  effects  ;  Comparison 
with  sound,  503.  General  inferences  ;  Additional  remarks  ;  Thermomultiplier ; 
Rock  salt,  504.  Polarization  of  light  and  heat ;  Discoveries  of  Melloni  and 
Professor  Forbes,  505.  Theory  of  Heat ;  References,  506. 


LECTURE  LIIL 
ON  ELECTRICITY  IN  EQUILIBRIUM,  507. 

Utility  of  electrical  hypotheses ;  Division  of  the  subject,  507.  Supposed  elec- 
tric fluid;  Its  attractions  and  repulsions,  508.  Conductors  and  nonconductors; 
Positive  and  negative  electricity ;  Local  electricity,  509.  Distribution  of  electri- 
city; Electricity  of  a  sphere;  Connected  spheres,  510.  Difference  of  hydrostatic 
and  electrical  pressure;  Attractions  and  repulsions,  511.  Induced  electricity; 
Neutral  point ;  Effects  of  attraction  and  repulsion  ;  Currents  of  air ;  Bodies  elec- 
trified in  different  degrees,  512.  Charge;  Discharge;  Shock;  Coated  jar;  Bat- 
tery; Comparison  of  conducting  powers,  513,  514. 

LECTURE  LIV. 
ON  ELECTRICITY  IN  MOTION,  516. 

Effects  and  causes  of  electrical  motions,  and  electrical  apparatus ;  Velocity ; 
Spark,  516.  Perforation  of  a  jar ;  Direction  of  the  motion ;  Opinions  respecting 
positive  and  negative  electricity;  Effects  of  electricity;  Accumulation;  Simple 
current,  517.  Electric  light ;  Heat,  518.  Mechanical  effects  ;  Chemical  effects ; 
Sensible  effects,  519.  Excitation  of  electricity;  Electrics;  Vapours;  Tourmalin, 
520.  Galvanic  electricity ;  Chemical  changes ;  Galvanic  combinations ;  General 
laws,  521.  Particular  facts ;  Pile  of  Volta,  522.  Troughs;  Animal  electricity; 
Mr.  Davy's  discoveries,  523.  Electrical  nature  of  chemical  attractions,  524. 
Theory  of  the  pile ;  Efficacy  of  decomposable  substances ;  Electrical  machines  ; 
Teylerian  machine,  525.  Electrophorus ;  Cendenser ;  Multiplier,  526.  Doublers  ; 
Electrical  balance;  Quadrant  electrometer  ;  Gold  leaf  electrometer,  527.  Lane's 
electrometer ;  General  observations,  528. 

LECTURE  LV. 
ON  MAGNETISM,  531. 

Resemblance  of  magnetism  and  electricity ;  Theory,  531 .  Conducting  powers ; 
Magnetical  substances,  532.  Aurora  borealis  ;  North  and  South  poles  ;  Attrac- 
tions and  repulsions  ;  Polarity,  533.  Arrangement  of  filings ;  Directive  force  ; 
Terrestrial  magnetism  ;  Compass ;  Dipping  needle,  534.  Illustration  ;  Temporary 
magnetism  ;  Natural  magnet ;  Magnetic  poles  of  the  earth ;  Diurnal  changes,  535. 
Variation  of  the  declination ;  Line  of  no  declination  ;  Dip,  53G.  Artificial  mag- 
nets ;  Double  touch,  537.  Magnetic  paste  ;  Division  of  a  magnet ;  Striking  and 
ringing  a  magnet;  Hammering  brass  ;  Solution  in  an  acid,  538.  Resemblance  of 
polarity  to  crystallization  ;  Additional  remarks  ;  Discovery  of  Professor  Oersted  ; 
Electro-magnetism,  539.  Construction  of  the  galvanometer ;  Gumming;  Nobili; 
Action  of  the  voltaic  current,  540.  Electro-magnetic  telegraph  ;  Faraday  ;  Mag- 
neto-electric machine,  541 ;  Arago ;  References,  542. 


CONTENTS.  xxvii 

LECTURE  LVI. 
ON  CLIMATES  AND  WINDS,  544. 

Meteorology ;  Division  of  the  subject ;  Climates ;  Meteorological  thermome- 
ters, 544-.  Immediate  effects  of  the  sun  ;  Prerost's  calculations  ;  Variations  of 
temperature,  545.  Slow  changes  ;  Heat  of  the  sea  ;  Effect  of  freezing  and  thaw- 
ing ;  Heat  of  the  atmosphere,  54*6.  Summer  and  winter ;  Temperatures  of  differ- 
ent places  ;  Local  variations,  547.  Winds  ;  Periodical  winds  ;  Trade  winds  ; 
Hadley  ;  Halley's  theory,  548.  Greater  heat  of  the  northern  hemispheres  ;  West- 
erly winds  ;  Local  modifications  ;  Monsoons,  549.  Land  and  sea  breezes ;  Hur- 
ricanes ;  Variations  of  the  barometer,  550. 

LECTURE  LVII. 

ON  AQUEOUS  AND  IGNEOUS  METEORS,  551. 

Evaporation  and  its  effects  ;  Theory  of  Deluc  and  Dalton  ;  Quantity  of  water 
evaporating,  551.  Precipitation;  Moisture;  Mediterranean,  552.  Currents  at 
the  Straights  ;  Attraction  of  moisture  ;  B.  Prevost ;  Hygrometers,  553.  Natural 
hygrometer;  Water  contained  in  air,  554.  Visible  vapour ;  Dew ;  Mists,  555.  Rain ; 
Indications  of  the  barometer  ;  Effects  of  mountains,  556.  Periodical  rains  ;  Thun- 
der and  lightning ;  Atmospherical  electricity,  557.  Thunder  storms ;  Conduc- 
tors, 558.  Sudden  condensations;  Waterspouts,  559.  Aurora  borealis  ;  Earth- 
quakes and  volcanos ;  Volcanic  countries,  560.  Earthquakes  of  Calabria,  561. 
Eruptions  of  Vesuvius,  562.  Geological  changes  ;  Reality  of  various  changes ; 
Effects  of  rivers  and  of  the  sea,  563.  Shooting  stars ;  falling  stones,  564,  565. 

LECTURE  LVIII. 

ON  VEGETATION,  565. 

Sketch  of  natural  history  ;  Minerals,  565.  Vegetables ;  Animals ;  Distinctions 
of  animals  and  vegetables,  566.  Description  of  a  vegetable ;  Germination,  567. 
Parts  of  plants  ;  Vessels,  568.  Motion  of  the  sap ;  Mr.  Knight's  experiments,  569. 
Grafting;  Diseases  of  plants,  570.  Exposure  to  the  air;  Linnean  system,  571. 
System  of  Jussieu,572. 

LECTURE  LIX. 

ON  ANIMAL  LIFE,  573. 

Classification  of  animals,  according  to  Linne,  573.  Mammalia;  Birds,  574. 
Amphibia;  Fishes;  Insects,  575.  Vermes,  576.  Senses;  Nutrition, 577.  Ner- 
vous system  ;  Nature  of  the  nerves,  578.  Diseases ;  Natural  cures,  579. 


LECTURE  LX. 

ON  THE  HISTORY  OF  TERRESTRIAL  PHYSICS,  580. 

General  retrospect ;  Knowledge  of  the  ancients ;  Chinese ;  Numa,  580.  Thales ; 
Anaximander ;  Anaximenes ;  Pythagoras ;  Anaxagoras ;  Democritus  ;  Heraclitus  ; 
Plato,  581.  Aristotle;  Epicurus,  582.  R.Bacon;  Discovery  of  the  compass  ; 


xxviii  CONTENTS. 

Gesner;  Aldrovandus ;  Gilbert  of  Colchester;  Variation  of  the  compass;  R. 
Bacon,  583.  Opinions  of  heat ;  Drebel ;  Harvey  ;  Circulation  of  the  blood  ;  Baro- 
meter ;  Bauhins,  584.  Ray ;  Willughby ;  Philosophical  societies  ;  Variation  charts ; 
Electricity,  585.  Linnean  system  ;  Discoveries  respecting  heat ;  Theory  of  mag- 
netism and  electricity,  586.  Boscovich  ;  Hygrometry  ;  Galvanism,  587.  Pile  of 
Volta  ;  Mr.  Davy's  experiments  ;  Dalton  ;  Rumford  ;  Leslie,  588.  Herschel ; 
Capillary  tubes  ;  Laplace  ;  Advantages  to  be  expected  from  modern  institutions, 
589,  590.  Chronological  table,  to  face  p.  590. 


ERRATA. 

P.  16,  line  31,  for  "  but  is  "  read  "  but  it  is." 

P.  160,  lines  25,  26,  for  "  immediately  "  read  "  immediately." 

P.  255,  line  29,  for  "  adjutage  "  read  "  ajutage." 

P.  292,  line  4,  for  "  wagon  "  read  "  waggon." 

P.  390,  note,  line  3,  after  "  distances"  insert  "  from  another  star,  of  the  middle 

point." 
P.  396,  Catalogues,  insert  "  Groombridge's  Catalogue  of  Circumpolar  Stars,  4to, 

Lond.  1838." 

P.  404,  line  24,  for  "  asmosphere  "  read  "  atmosphere." 
P.  505,  line  41,  for  "  Franenhofer's  "  read  "  Frauenhofer's." 
P.  582,  Une  33,  for  "  indentical"  read  "identical." 


ON 

NATURAL  PHILOSOPHY 


AND 


THE   MECHANICAL   ARTS. 


LECTURE    I. 


INTRODUCTION. 

IT  is  to  be  presumed,  that  most  of  those  who  honour  the  theatre  of  the 
Royal  Institution  with  their  attendance,  are  already  acquainted  with  the 
nature  of  the  objects  which  its  founders  and  promoters  have  been  endea- 
vouring to  attain :  yet  it  appears  to  be  by  no  means  superfluous  that  I 
should  define  with  accuracy  my  own  views  of  the  utility  that  is  likely  to 
be  derived  from  it,  and  of  the  most  effectual  means  of  accomplishing  its 
purposes  ;  in  order  that  we  may  be  able  to  distinguish,  without  difficulty, 
the  most  eligible  track  for  our  common  progress  through  the  regions  of 
science  ;  and  that  those  who  are  desirous  of  accompanying  me  in  the  jour- 
ney may  know  precisely  what  route  we  are  to  follow,  and  what  depart- 
ments will  more  particularly  arrest  our  attention. 

Societies,  which  are  merely  literary  and  philosophical,  have  in  general 
principally  proposed  to  themselves  to  enlighten  the  understanding  by  the 
discovery  of  unknown  phenomena,  and  to  exercise  the  reasoning  powers  by 
opening  new  fields  for  speculation,  Other  associations  have  been  more 
particularly  intended  for  the  encouragement  of  the  arts,  of  manufactures, 
and  of  commerce.  The  primary  and  peculiar  object  of  the  Royal  Insti- 
tution of  Great  Britain  is  professedly  of  an  humbler,  but  not  of  a  less 
interesting  nature.  It  is  to  apply  to  domestic  convenience  the  improve- 
ments which  have  been  made  in  science,  and  to  introduce  into  general 
practice  such  mechanical  inventions  as  are  of  decided  utility.  But  while 
it  is  chiefly  engaged  in  this  pursuit,  it  extends  its  views,  in  some  measure, 
to  the  promotion  of  the  same  ends  which  belong  to  the  particular  pro- 
vinces of  other  literary  societies  ;  and  it  is  the  more  impossible  that  such 
objects  should  be  wholly  excluded,  as  it  is  upon  the  advancement  of  these 
that  the  specific  objects  of  the  Institution  must  ultimately  depend.  Hence 
the  dissemination  of  the  knowledge  of  natural  philosophy  and  chemistry 
becomes  a  very  essential  part  of  the  design  of  the  Royal  Institution ;  and 


2  LECTURE  I. 

this  department  must,  in  the  natural  order  of  arrangement,  be  anterior  to 
the  application  of  the  sciences  to  practical  uses.  To  exclude  all  know- 
ledge but  that  which  has  already  been  applied  to  immediate  utility,  would 
be  to  reduce  our  faculties  to  a  state  of  servitude,  and  to  frustrate  the  very 

\  purposes  which  we  are  labouring  to  accomplish.     No  ,  discovery,  however 
remote  in  its  nature  from  the  subjects  of  daily  observation,  can  with  rea- 

I  son  be  declared  wholly  inapplicable  to  the  benefit  of  mankind. 

It  has  therefore  always  appeared  to  me,  to  be  not  only  the  best  begin- 
ning, but  also  an  object  of  high  and  permanent  importance  in  the  plan  of 
the  Institution,  to  direct  the  public  attention  to  the  cultivation  of  the 
elementary  doctrines  of  natural  philosophy,  as  well  speculative  as  prac- 
tical. Those  wrho  possess  the  genuine  spirit  of  scientific  investigation,  and 
who  have  tasted  the  pure  satisfaction  arising  from  an  advancement  in 
intellectual  acquirements,  are  contented  to  proceed  in  their  researches, 
without  inquiring  at  every  step  what  they  gain  by  their  newly  discovered, 
,  lights,  and  to  what  practical  purposes  they  are  applicable  :  they  receive  a 
sufficient  gratification  from  the  enlargement  of  their  views  of  the  consti- 
.  tution  of  the  universe,  and  experience,  in  the  immediate  pursuit  of  know- 
ledge, that  pleasure  which  others  wish  to  obtain  more  circuitously  by 
its  means.  And  it  is  one  of  the  principal  advantages  of  a  liberal  educa- 
tion, that  it  creates  a  susceptibility  of  an  enjoyment  so  elegant  and  so 
Irational. 

A  considerable  portion  of  my  audience,  to  whose  information  it  will  be 
my  particular  ambition  to  accommodate  my  lectures,  consists  of  that  sex 
which,  by  the  custom  of  civilized  society,  is  in  some  measure  exempted 
from  the  more  laborious  duties  that  occupy  the  time  and  attention  of  the 
other  sex.  The  many  leisure  hours  which  are  at  the  command  of  females 
in  the  superior  orders  of  society  may  surely  be  appropriated,  with  greater 
satisfaction,  to  the  improvement  of  the  mind  and  to  the  acquisition  of 
knowledge,  than  to  such  amusements  as  are  only  designed  for  facilitating 
the  insipid  consumption  of  superfluous  time.  The  hours  thus  spent  will 
unquestionably  become,  by  means  of  a  little  habit,  as  much  more  agreeable 
at  the  moment,  as  they  must  be  more  capable  of  affording  self-approbation 
upon  reflection.  And  besides,  like  the  seasoning  which  reconciled  the 
Spartans  to  their  uninviting  diet,  they  will  even  heighten  the  relish  for 
those  pursuits  which  they  interrupt :  for  mental  exercise  is  as  necessary  to 
mental  enjoyment  as  corporal  labour  to  corporal  health  and  vigour.  In  this 
point  of  view  the  Royal  Institution  may  in  some  degree  supply  the  place  of 
a  subordinate  university,  to  those  whose  sex  or  situation  in  life  has  denied 
them  the  advantage  of  an  academical  education  in  the  national  seminaries 
of  learning. 

But  notwithstanding  the  necessity  of  introducing  very  copiously  specu- 
lations of  a  more  general  nature,  we  must  not  lose  sight  of  the  original 
objects  of  the  Royal  Institution  ;  and  we  must,  therefore,  direct  our  atten- 
tion more  particularly  to  the  theory  of  practical  mechanics  and  of  manu- 
factures. In  these  departments  we  shall  find  some  deficiencies  which  may 
without  much  difficulty  be  supplied  from  scientific  principles  ;  and  by  an 
ample  collection  and  display  of  models,  illustrative  of  machines  and  of 


INTRODUCTION.  3 

inventions  of  all  kinds,  we  may  proceed  in  the  most  direct  manner  to  con- 
tribute to  the  dissemination  of  that  kind  of  knowledge  which  is  most  parti- 
cularly our  object.  So  that  we  must  be  more  practical  than  academies  of, 
sciences,  and  more  theoretical  than  societies  for  the  improvement  of  arts  ;  | 
while  we  endeavour  at  the  same  time  to  give  stability  to  our  proceedings  by 
an  annual  recurrence  to  the  elementary  knowledge  which  is  subservient  to 
the  purposes  of  both  ;  and,  as  far  as  we  are  able,  to  apply  to  practice  the 
newest  lights  which  may  from  time  to  time  be  thrown  on  particular 
branches  of  mechanical  science.  It  is  thus  that  we  may  most  effectually 
perform  what  the  idolized  sophists  of  antiquity  but  verbally  professed,  to 
bring  down  philosophy  from  the  heavens,  and  to  make  her  an  inhabitant  of 
the  earth. 

To  those  who  are  engaged  in  the  practical  cultivation  of  various  arts 
subservient  to  the  conveniences  of  life,  these  lectures  may  be  of  some 
utility,  by  furnishing  them  with  well  established  principles,  applicable  to 
a  variety  of  cases  which  may  occasionally  occur  to  them,  where  a  little 
deviation  from  the  ordinary  routine  of  their  profession  may  be  necessary. 
Unfortunately,  the  hands  that  execute  are  too  often  inadequately  sup- 
ported by  the  head  that  directs  ;  and  much  labour  is  lost  for  want  of  a 
little  previous  application  to  the  fundamental  doctrines  of  the  mechanical 
sciences.  Nor  is  any  exorbitant  portion  of  time  or  industry  necessary  for 
this  purpose ;  for  it  happens  singularly  enough,  that  almost  all  practical 
applications  of  science  depend  on  principles  easilyjilearnt ;  and,  except  in 
astronomy  only,  it  has  seldom  been  found  that  very  abstruse  investigations 
have  been  of  great  importance  to  society.  Our  most  refined  analytical 
calculations  are  by  far  too  imperfect  to  apply  to  all  possible  cases  of  me- 
chanical actions  that  can  be  proposed  ;  and  those  problems  which  most 
frequently  occur,  may  in  general  be  solved  by  methods  sufficiently 
obvious  ;  although,  from  a  want  of  proper  order  and  perspicuity  in  the 
treatment  of  first  principles,  it  has  often  happened  that  the  most  ele- 
mentary propositions  have  been  considered  as  requiring  great  study  and 
application. 

We  may  also  be  able  to  render  an  important  service  to  society,  and  to 
confer  a  still  more  essential  benefit  on  individuals,  by  repressing  the  pre- 
mature zeal  of  unskilful  inventors.  We  need  only  read  over  the  monthly 
accounts  of  patents,  intended  for  securing  the  pecuniary  advantages  of 
useful  discoveries,  in  order  to  be  convinced  what  expense  of  time  and  for- 
tune is  continually  lavished  on  the  feeblest  attempts  to  innovate  and 
improve.  If  we  can  be  succcessful  in  convincing  such  inconsiderate 
;  enthusiasts  of  their  real  ignorance,  or  if  we  can  shew  them,  that  even  their 
own  fairy  ground  has  been  pre-occupied,  we  may  save  them  from  impending  ; 
ruin,  and  may  relieve  the  public  from  the  distraction  of  having  its  atten- 
tion perpetually  excited  by  unworthy  objects.  The  ridicule  attendant  on 
the  name  of  a  projector  has  been  in  general  but  too  well  deserved  ;  for  few, 
very  few,  who  have  aspired  at  improvement,  have  ever  had  the  patience 
to  submit  their  inventions  to  such  experimental  tests  as  common  sense 
would  suggest  to  an  impartial  observer.  We  may  venture  to  affirm  that 
out  of  every  hundred  of  fancied  improvements  in  arts  or  in  machines, 

B  2 


4  LECTURE  I. 

ninety  at  least,  if  not  ninety-nine,  are  either  old  or  useless  ;  the  object  of 
our  researches  is,  to  enable  ourselves  to  distinguish  and  to  adopt  the  hun- 
dredth. But  while  we  prune  the  luxuriant  shoots  of  youthful  invention, 
we  must  remember  to  perform  our  task  with  leniency,  and  to  show  that  we 
wish  only  to  give  additional  vigour  to  the  healthful  branches,  and  not 
to  extirpate  the  parent  plant. 

The  Repository  of  the  Royal  Institution,  as  soon  as  it  can  be  properly 
furnished,  will  be  considered  as  a  supplementary  room  for  apparatus,  in 
which  the  most  interesting  models,  exhibited  and  described  in  the  lectures, 
will  be  placed  for  more  frequent  inspection,  and  where  a  few  other  articles 
may  perhaps  deserve  admission,  which  will  not  require  so  particular  an 
explanation.  To  those  who  have  profited  by  the  lectures,  or  who  are 
already  too  far  advanced  to  stand  in  need  of  them,  our  rooms  for  reading 
and  for  literary  conversation  may  be  a  source  of  mutual  instruction.  Our 
library  in  time  must  contain  all  those  works  of  importance  which  are  too 
expensive  for  the  private  collections  of  the  generality  of  individuals  ;  which 
are  necessary  to  complete  the  knowledge  of  particular  sciences,  and  to 
which  references  will  occasionally  be  given  in  the  lectures  on  those  sciences. 
Our  journals,  free  from  commercial  shackles,  will  present  the  public, 
from  time  to  time,  with  concise  accounts  of  the  most  interesting  novelties 
in  science  and  in  the  useful  arts  ;  and  they  will  furnish  a  perpetual  incite- 
ment to  their  editors  to  appropriate,  as  much  as  possible,  to  their  own 
improvement,  whatever  is  valuable  in  the  publications  of  their  cotempo- 
raries.  When  all  the  advantages  which  may  reasonably  be  expected  from 
this  institution  shall  be  fully  understood  and  impartially  considered,  it  is 
to  be  hoped  that  few  persons  of  liberal  minds  will  be  indifferent  to  its 
success,  or  unwilling  to  contribute  to  it  and  to  participate  in  it. 

To  that  regulation,  which  forbids  the  introduction  of  any  discussions 
connected  with  the  learned  professions,  I  shall  always  most  willingly  submit, 
and  most  punctually  attend.  It  requires  the  study  of  a  considerable  portion 
jof  a  man's  life  to  qualify  him  to  be  of  use  to  mankind  in  any  of  them  ;  and 
fl  nothing  can  be  more  pernicious  to  individuals  or  to  society,  than  the 
jj  attempting  to  proceed  practically  upon  an  imperfect  conception  of  a  few 
first  principles  only.  In  physic,  the  wisest  can  do  but  little,  and  the  igno- 
rant can  only  do  worse  than  nothing  :  and  anxiously  as  we  are  disposed 
to  seek  whatever  relief  the  learned  and  experienced  may  be  able  to  afford 
us,  so  cautiously  ought  we  to  avoid  the  mischievous  interference  of  the 
half-studied  empiric  :  in  politics  and  in  religion,  we  need  but  to  look  back 
on  the  history  of  kingdoms  and  republics,  in  order  to  be  aware  of  the 
mischiefs  which  ensue,  when  "  fools  rush  in  where  angels  fear  to  tread." 

Deeply  impressed  with  the  importance  of  mathematical  investigations, 
both  for  the  advancement  of  science  and  for  the  improvement  of  the  mind,  1 
thought  it  in  the  first  place  an  indispensable  duty  to  present  the  Royal  Insti- 
tution, in  my  Syllabus,  with  a  connected  system  of  natural  philosophy, 
on  a  plan  seldom,  if  ever,  before  executed  in  the  most  copious  treatises, 
v    ^Proceeding  from  the  simplest  axioms  of  abstract  mathematics,  the  Syllabus 
contains  a  strict  demonstration  of  every  proposition  which  I  have  found  it 
-^>    !   necessary  to  employ  throughout  the  whole  extent  of  natural  philosophy. 


INTRODUCTION. 

I  In  the  astronomical  part  only,  some  obs^rj£atjons  occur,  i 
mathematical  evidence  ;  here,  however,  it  was  as  impracticable  as  ~itl 
would  have  been  useless  to  attempt  to  enter  into  investigations,  which  in 
many  instances  have  been  extended  far  beyond  the  limits  even  of  Newton's 
researches.  But  for  the  sake  of  those  who  are  not  disposed  to  undertake  the 
labour  of  following,  with  mathematical  accuracy,  all  the  steps  of  the 
demonstrations  on  which  the  doctrines  of  the  mechanical  sciences  are 
founded,  I  shall  endeavour  to  avoid,  in  the  whole  of  this  course  of  lectures, 
every  intricacy  which  might  be  perplexing  to  a  beginner,  and  every 
argument  which  is  fitter  for  the  closet  than  for  a  public  theatre.  Here  I 
propose  to  support  the  same  propositions  by  experimental  proofs  :  not  that 
I  consider  such  proofs  as  the  most  conclusive,  or  as  more  interesting  to  a 
truly  philosophic  mind  than  a  deduction  from  general  principles  ;  but  because 
there  is  a  satisfaction  in  discovering  the  coincidence  of  theories,  with 
visible  effects,  and  because  objects  of  sense  are  of  advantage  in  assisting 
the  imagination  to  comprehend,  and  the  memory  to  retain,  what  in  a  more 
abstracted  form  might  fail  to  excite  sufficient  attention. 

This  combination  of  experimental  with  analogical  arguments  constitutes 
the  principal  merit  of  modern  philosophy.  And  here  let  the  citizen  of  the 
world  excuse  the  partiality  of  an  Englishman,  if  I  pride  myself,  and  con- 
gratulate my  audience,  on  the  decided  superiority  of  our  own  country,  in 
the  first  establishment,  and  in  the  subsequent  cultivation,  of  the  true  phi- 
losophy of  the  operations  of  nature.  I  grant  that  we  have  at  times  been 
culpably  negligent  of  the  labours  of  others  ;  that  we  have  of  late  suffered 
our  neighbours  to  excel  us  in  abstract  mathematics,  and  perhaps,  in  some 
instances,  in  patient  and  persevering  observation  of  naked  phenomena.  We 
have  not  at  this  moment  a  taagrauge  or  a  Laplace/:  what  we  have  I  do  not 
think  it  necessary  to  enumerate  :  but  there  is  a  certain  combination  of 
theoretical  reasoning  with  experimental  inquiry,  in  which  Great  Britain, 
from  the  time  of  the  reformation  of  philosophy,  has  never  been  inferior  to 
any  nation  existing.  I  need  only  refer  to  the  Transactions  of  the  Royal 
Society,  for  abundant  instances  of  the  mode  of  investigation  to  which  I 
allude  ;  and  I  will  venture  to  affirm,  that  their  late  publications  are  equal 
in  importance  to  any  that  have  preceded.  It  was  in  England  that  a  Bacon 
| first  taught  the  world  the  true  method  of  the  study  of  nature,  and  rescued 
science  from  that  barbarism'  in  which  the  followers  of  Aristotle,  by  a  too 
servile  imitation  of  their  master,  had  involved  it ;  and  with  which,  even  of 
late,  a  mad  spirit  of  innovation,  under  the  name  of  the  critical  jjhilqsophy, 
has,  in  a  considerable  part  of  Europe,  again  been  threatening  it.  It  was  in 
this  country  that  Newton  advanced,  with  one  gigantic  stride,  from  the  re- 
gions of  twilight  into  the  noon  day  of  science.  A  Boyle  and  a  Hooke,  who 
would  otherwise  have  been  deservedly  the  boast  of  their  century,  served  but 
as  obscure  forerunners  of  Newton's  glories.  After  these,  a  c'ro'wd  of  eminent 
men  succeeded,  each  of  great  individual  merit ;  but,  absorbed  in  the  prose- 
cution of  the  Newtonian  discoveries,  they  chose  rather  to  be  useful  by  their 
humble  industry  than  to  wander  in  search  of  the  brilliancy  of  novelty.  It 
is  difficult  to  judge  of  our  coj,emporaries  ;  but  we  appear  at  present  to  be 
in  possession  of  more  than  one  philosopher,  whose  names  posterity  will  be 


(5  LECTURE  I. 

eager  to  rank  in  the  same  class  with  the  few  that  have  been  enumerated. 
But  it  is  not  our  present  business  to  enter  into  the  history  of  science  ; 
respecting  what  is  supposed  to  be  wholly  unknown  we  can  have  little 
curiosity  :  a  short  sketch  of  the  progress  of  each  branch  of  natural  philoso- 
phy will  be  more  properly  introduced  after  we  have  finished  our  investiga- 
tion of  the  principal  doctrines  belonging  to  it. 

With  regard  to  the  mode  of  delivering  these  lectures,  I  shall  in  general 
intreat  my  audience  to  pardon  the  formality  of  a  written  discourse,  in 
favour  of  the  advantage  of  a  superior  degree  of  order  and  perspicuity.  It 
would  unquestionably  be  desirable  that  every  syllable  advanced  should  be 
rendered  perfectly  easy  and  comprehensible  even  to  the  most  uninformed  ; 
that  the  most  inattentive  might  find  sufficient  variety  and  entertainment 
in  what  is  submitted  to  them  to  excite  their  curiosity,  and  that  in  all  cases 
the  pleasing,  and  sometimes  even  the  surprising-,  should  be  united  with  the 
instructive  and  the  important.  But  whenever  there  appears  to  be  a  real 
impossibility  of  reconciling  these  various  objects,  I  shall  esteem  it  better  to 
seek  for  substantial  utility  than  temporary  amusement ;  for  if  we  fail  of 
being  useful  for  want  of  being  sufficiently  popular,  we  remain  at  least 
respectable  ;  but  if  we  are  unsuccessful  in  our  attempts  to  amuse,  we 
immediately  appear  trifling  and  contemptible.  It  shall,  however,  at  all  times 
be  my  endeavour  to  avoid  each  extreme  ;  and  I  trust  that  I  shall  then  only 
be  condemned  when  I  am  found  abstruse  from  ostentation,  or  uninteresting 
from  supineness.  The  most  difficult  thing  for  a  teacher  is,  to  recollect  how 
much  it  cost  himself  to  learn,  and  to  accommodate  his  instruction  to  the 
apprehension  of  the  uninformed  :  by  bearing  in  mind  this  observation,  I 
hope  to  be  able  to  render  my  lectures  more  and  more  intelligible  and 
familiar  ;  not  by  passing  over  difficulties,  but  by  endeavouring  to  facilitate 
the  task  of  overcoming  them  ;  and  if  at  any  time  I  appear  to  have  failed  in 
this  attempt,  I  shall  think  myself  honoured  by  any  subsequent  inquiries 
that  my  audience  may  be  disposed  to  make. 

We  have  to  extend  our  views  over  the  whole  circle  of  natural  and  arti- 
ficial knowledge,  to  consider  in  detail  the  principles  and  application  of  the 
philosophy  of  nature  and  of  art.  We  are  to  discuss  a  great  number  of 
subjects,  to  each  of  which  a  separate  title  and  rank  among  the  sciences  has 
sometimes  been  assigned  ;  and  it  is  necessary,  in  order  to  obtain  a  distinct 
conception  of  the  foundation  and  relation  of  each  subdivision,  to  pay  par- 
ticular attention  to  the  order  in  which  the  sciences  are  to  be  treated,  and  to 
the  connexion  which  subsists  between  them,  as  well  as  to  the  degree  of 
importance  which  each  of  them  claims,  with  regard  either  to  theory  or  to 
practice.  To  insist  on  the  propriety  of  a  distinct  and  logical  order  is  unne- 
cessary ;  for  however  superfluous  we  may  deem  the  scholastic  forms  of 
rhetoric,  it  is  confessedly  advantageous  to  the  judgment  as  well  as  to  the 
meniQry,  to  unite  those  things  which  are  naturally  connected,  and  to  sepa- 
rate those  which  are  essentially  distinct.  When  a  traveller  is  desirous  of 
becoming  acquainted  with  a  city  or  country  before  unknown  to  him,  he 
naturally  begins  by  taking,  from  some  elevated  situation,  a  distant  view  of 
the  distribution  of  its  parts ;  and  in  the  same  manner,  before  we  enter  on 
the  particular  consideration  of  the  subjects  of  our  researches,  it  may  be  of 


INTRODUCTION.  7 

use  to  form  to  ourselves  a  general  idea  of  the  sciences  and  arts  which  are  to 
be  placed  among  them. 

Upon  the  advantages  of  mathematical  and  philosophical  investigation  in 
general  it  is  unnecessary  to  enlarge,  because  no  liberal  mind  can  require 
any  arguments  to  be  convinced  how  much  the  judgment  is  strengthened,  ! 
and  the  invention  assisted,  by  habits  of  reasoning  with  caution  and  accu- 
racy. The  public  opinion  is  rather,  on  the  contrary,  in  danger,  at  least  in 
some  parts  of  the  world,  of  being  too  exclusively  biassed  in  favour  of 
natural  philosophy  ;  and  has  sometimes  been  inclined  to  a  devotion  too 
much  limited  to  science,  without  a  sufficient  attention  to  such  literature  as 
an  elegant  mind  always  desires  to  see  united  with  it.  As  to  the  practical 
importance  of  philosophical  theories  of  thqf  arts,  it  may  have  been  overrated 
by  some,  but  no  person  is  authorised  to  amrm  that  it  has  been  too  highly 
estimated,  unless  he  has  made  himself  master  of  every  thing  that  theory  is 
capable  of  doing  ;  such  a  one,  although  he  may  in  some  cases  be  obliged  to 
confess  the  insufficiency  of  our  calculations,  will  never  have  reason  to  com- 
plain of  their  fallacy. 

The  division  of  the  whole  course  of  lectures  into  three  parts  was  origi- 
nally suggested  by  the  periodical  succession  in  which  the  appointed  hours 
recur  :  but  it  appears  to  be  more  convenient  than  any  other  for  the  regular 
classification  of  the  subjects.  The  general  doctrines  of  motion,  and  their 
application  to  all  purposes  variable  at  pleasure,  supply  the  materials  of  the 
first  two  parts  ;  of  which  the  one  treats  of  the  motions  of  solid  bodies,  and 
the  other  of  those  of  fluids,  including  the  theory  of  light.  The  third  part 
relates  to  the  particular  history  of  the  phenomena  of  nature,  and  of  the 
affections  of  bodies  actually  existing  in  the  universe,  independently  of  the 
art  of  man  ;  comprehending  astronomy,  geography,  and  the  doctrine  of  the 
properties  of  matter,  and  of  the  most  general  and  powerful  agents  that 
influence  it. 

The  synthetical  order  of  proceeding,  from  simple  and  general  principles, 
to  their  more  intricate  combinations  in  particular  cases,  is  by  far  the  most 
compendious  for  conveying  information  with  regard  to  sciences  that  are  at 
all  referable  to  certain  fundamental  laws.  For  these  laws  being  once 
established,  each  fact,  as  soon  as  it  is  known,  assumes  its  place  in  the 
system,  and  is  retained  in  the  memory  by  its  relation  to  the  rest  as  a  con- 
necting link.  In  the  analytical  mode,  on  the  contrary,  which  is  absolutely 
necessary  for  the  first  investigation  of  truth,  we  are  obliged  to  begin  by 
collecting  a  number  of  insulated  circumstances,  which  lead  us  back  by 
degrees  to  the  knowledge  of  original  principles,  but  which,  until  we  arrive 
at  those  principles,  are  merely  a  burden  to  the  memory.  For  the  pheno- 
mena of  nature  resemble  the  scattered  leaves  of  the  Sibylline  prophecies ; 
a  word  only,  or  a  single  syllable,  is  written  on  each  leaf,  which,  when  sepa- 
rately considered,  conveys  no  instruction  to  the  mind  ;  but  when,  by  the 
labour  of  patient  investigation,  every  fragment  is  replaced  in  its  appropriate 
connexion,  the  whole  begins  at  once  to  speak  a  perspicuous  and  a  harmoni- 
ous language. 

Proceeding,  therefore,   in  the  synthetical  order,  we  set  out  from  the  ' 
abstract  doctrines  of  mathematics,  relating  to  quantity,  space,  and  number, 


8  LECTURE  I. 

which  we  pass  over,  as  supposed  to  be  previously  understood,  or  as  suffi- 
ciently explained  in  the  mathematical  elements,  and  go  on  to  their  imme- 
diate application  to  mechanics  and  hydrodynamics,  or  to  such  cases  of  the 
motions  of  solids  and  fluids  as  are  dependent  on  arbitrary  assumptions,  that 
is,  where  we  do  not  confine  our  inquiries  to  any  particular  cases  of  existing 
phenomena.  By  means  of  principles  which  are  deducible  in  a  satisfactory 
manner  from  mathematical  axioms,  with  the  assistance  only  of  the  general 
logic  of  induction^  we  shall  be  able  to  draw  such  conclusions  as  are  capable 
^of  giving  us  very  important  information  respecting  the  operations  of  na- 
I  ture  and  of  art,  and  to  lay  down  such  laws,  as,  to  an  uninformed  person, 
I  it  would  appear  to  be  beyond  the  powers  of  reason  to  determine  without  the 
/^assistance  of  experiment.  The  affections  of  falling  bodies  and  of  projectiles, 
the  phenomena  of  bodies  revolving  round  a  centre,  the  motions  of  pendu- 
lums, the  properties  of  the  centre  of  gravity,  the  equilibrium  of  forces  in 
machines  of  different  kinds,  the  laws  of  preponderance,  and  the  effects  of 
collision ;  all  these  are  wholly  referable  to  axiomatical  evidence,  and  are 
frequently  applicable  to  important  uses  in  practice.  Upon  these  founda- 
tions we  shall  proceed  ta  the  general  principles  of  machinery,  and  the 
application  of  forces  of  different  kinds :  we  shall  inquire  what  are  the 
principal  sources  of  motion  that  we  can  subject  to  our  command,  and  what 
advantages  are  peculiar  to  each  of  them  :  and  then,  according  to  the 
purposes  for  which  they  are  employed,  we  shall  separately  examine  the 
principal  machines  and  manufactures  in  which  those  forces  are  applied  to 
the  service  of  mankind. 

Such  instruments  and  machines  as  are  more  or  less  immediately  subser- 
vient to  mathematical  purposes  will  be  the  first  in  order,  including  all  the 
mechanism  of  literature,  the  arts  of  writing,  engraving  and  printing,  in 
their  various  branches,  and  the  comparison  of  measures  with  each  other 
and  with  different  standards ;  the  principles  of  perspective  will  also  form  a 
useful  appendage  to  the  description  of  geometrical  instruments.  The  deter- 
mination of  weights,  and  of  the  magnitude  of  moving  forces  of  various 
kinds,  constituting  the  science  of  statics,  will  be  the  next  subject,  and  will 
be  followed  by  the  consideration  of  the  retarding  force  of  friction,  and  of 
the  passive  strength  of  the  various  materials  that  are  employed  in  building 
and  in  machinery. 

All  these  subjects  are  in  part  preparatory  to  the  immediate  examination 
of  the  mechanical  arts  and  manufactures,  which  are  so  numerous  and  com- 
plicated as  not  to  admit  of  regular  arrangement  without  some  difficulty  : 
they  may  howeve^  be  divided  into  such  as  are  principally  employed  for 
resisting,  for  modifying,  or  for  counteracting,  any  motion  or  force  ;  thus 
architecture  and  carpentry  are  chiefly  intended  to  resist  the  force  of  gravi- 
tation :  these  comprehend  the  employments  of  the  mason,  the  bricklayer, 
the  joiner,  the  cabinet  maker,  and  the  locksmith.  In  these  departments  it 
is  often  of  the  utmost  importance  to  the  mechanic  to  recur,  especially  in 
!  works  of  magnitude,  to  philosophical  principles  ;  and  in  many  other  cases, 
fo  where  there  is  no  need  of  much  calculation,  we  may  still  be  of  service,  by 
collecting  such  inventions  of  ingenious  artists  as  are  convenient  and  elegant, 
and  which,  although  simple  in  their  principles,  are  not  obvious  in  their 


INTRODUCTION.  9 

arrangements  ;  and  in  the  same  manner  we  may  be  able,  in  taking-  a  gene- 
ral view  of  other  arts  and  manufactures,  to  explain  their  principles,  where 
theory  is  concerned,  and  to  exhibit  practical  precedents,  where  the  nature 
of  the  subject  requires  no  refined  investigation. 

The  modification  of  motion  and  force  includes  its  communication  and 
alteration,  by  joints  of  various  kinds,  by  wheel  work,  and  by  cordage,  and 
its  equalisation  by  means  of  timekeepers.  The  subject  of  wheelwork  gives 
considerable  scope  for  mathematical  research,  and  requires  the  more  notice, 
as  it  has  often  been  inaccurately  treated  :  the  consideration  of  cordage  leads 
us  to  that  of  union  by  twisting  and  by  intermixture  of  fibres ;  including 
the  important  arts  of  carding,  combing,  spinning,  ropemaking,  weaving, 
fulling,  felting,  and  papermaking  ;  which  constitute  the  employment  of 
many  millions  of  manufacturers  of  all  ages  and  sexes,  in  every  part  of  the 
world,  and  by  which  the  animal  and  vegetable  productions  of  a  large  por- 
tion of  the  surface  of  the  globe  are  made  to  contribute,  as  well  to  the  power 
and  riches  of  the  individuals  who  supply  them,  as  to  the  health  and  comfort 
of  the  public  that  consumes  them.  The  admirable  art  of  the  watch  and 
clock  maker  is  a  peculiarly  interesting  department  of  practical  mechanics  ; 
it  affords  employment  for  mathematical  investigation,  for  experimental 
inquiry,  and  for  ingenious  invention  ;  and  the  perfection  which  it  has 
derived  from  a  combination  of  these  means,  does  honour  as  well  to  the 
nations  who  have  encouraged  it  as  to  the  individuals  who -have  been  en- 
gaged in  it. 

To  counteract  the  powers  of  gravitation  and  of  friction,  is  the  object  of 
such  machines  as  are  used  for  raising  and  removing  weights  :  cranes,  fric- 
tion wheels,  and  carriages  of  all  kinds,  are  referable  to  this  head,  and  some 
of  them  have  been  the  subjects  of  much  speculation  and  experiment. 
Lastly,  to  overcome  and  to  modify  the  corpuscular  forces  of  cohesion  and 
repulsion,  and  to  change  the  external  forms  of  bodies,  is  the  object  of  ma- 
chinery intended  for  compression,  extension,  penetration,  attrition,  tritura- 
tion,  agitation,  and  demolition.  For  these  purposes  we  employ  presses, 
forges,  rolling,  stamping,  coining,  and  milling  machines ;  the  processes  of 
digging,  ploughing,  and  many  other  agricultural  arts  ;  boring,  mining, 
grinding,  polishing,  and  turning ;  mills  of  various  kinds,  threshing  mills, 
corn  mills,  oil  mills,  and  powder  mills  ;  besides  the  chemical  agents  con- 
cerned in  blasting  rocks,  and  in  the  operations  of  artillery.  All  these  arts 
are  comprehended  in  the  department  of  mechanics,  which  constitutes  the 
first  division  of  this  course.  Not  that  we  shall  be  able  to  enter  at  large  faito 
the  detail  of  each  ;  but  having  formed  a  general  outline,  we  may  fill  up  its 
particular  parts  with  more  or  less  minuteness,  as  we  may  find  more  or  less 
matter  of  importance  to  insert  in  each  ;  and  those  who  wish  to  pursue  the 
subjects  further,  will  every  where  be  able  to  derive  great  assistance  from 
the  authors  whose  works  will  be  mentioned. 

The  doctrines  of  hydrodynamics  relate  to  the  motions  and  affections  of 
fluids,  in  which  we  no  longer  consider  each  distinct  particle  that  is  capable 
of  separate  motion,  but  where  we  attend  to  the  effect  of  an  infinite  number 
of  particles,  constituting  a  liquid  or  aeriform  aggregate.  The  general 
theory  of  such  motions  will  be  premised,  under  the  heads  hydrostatics,  or 


10  LECTURE  I. 

the  affections  of  liquids  at  rest ;  pneumatostatics,  or  the  properties  of  elastic 
fluids  at  rest ;  and  hydraulics,  or  the  theory  of  fluids  in  motion.  The 
practical  application  of  this  theory  to  hydraulic  and  pneumatic  machines 
is  of  very  considerable  importance,  and  is  as  interesting  to  the  philosopher 
as  it  is  necessary  to  the  engineer.  The  employment  of  the  force  of  water 
and  wind  to  the  best  advantage,  the  draining  of  lands  and  mines,  the  supply 
of  water  for  domestic  convenience,  the  manoeuvres  of  seamanship,  the  con- 
struction of  the  steam  engine,  are  all  dependent  upon  hydrodynamical 
principles,  and  are  often  considered  as  comprehended  in  the  science  of 
hydraulics.  Harmonics  and  optics,  the  remaining  parts  of  this  division,  are 
more  insulated  :  the  doctrine  of  sound,  the  theory  of  music,  and  the  con- 
struction of  musical  instruments,  are  as  pleasing  to  the  intellect  in  theory, 
as  they  are  gratifying  to  the  senses  in  practice  ;  but  the  science  of  optics  is 
not  less  interesting,  and  at  the  same  time  far  more  useful ;  the  instruments 
which  it  furnishes  are  of  almost  indispensable  necessity  to  the  navigator,  to 
the  naturalist,  to  the  physiologist,  and  even  to  the  man  of  business  or  plea- 
sure. It  is  perhaps  in  this  science  that  many  persons  of  the  greatest 
genius  have  been  the  most  happily  employed.  The  reasons  for  which  it  is 
classed  as  a  division  of  hydrodynamics  will  be  explained  hereafter. 

The  contemplation  of  the  particular  phenomena  of  nature,  as  they  are 
displayed  in  the  universe  at  large,  contributes  perhaps  less  to  the  perfection 
of  any  of  the  arts  which  are  immediately  subservient  to  profit  or  conve- 
nience, than  the  study  of  mechanics  and  hydrodynamics.  But  the  dignity 
and  magnificence  of  some  of  these  phenomena,  and  the  beauty  and  variety 
of  others,  render  them  highly  interesting  to  the  philosophical  mind  ;  at  the 
same  time  that  some  of  them  are  of  the  utmost  importance  in  their  appli- 
cation to  the  purposes  of  life.  In  all  these  respects  the  science  of  astro- 
nomy holds  the  first  rank  ;  its  uses  in  assisting  navigation,  and  in  regulating 
chronology,  are  beyond  all  calculation.  Geography  and  hydrography,  or 
the  particular  histories  of  the  earth  and  sea,  are  immediately  connected 
with  astronomy.  The  discussion  of  the  properties  of  matter  in  general, 
and  of  the  alterations  of  temperature  to  which  all  bodies  are  liable,  has  not 
hitherto  received  a  distinct  appellation  as  a  science  ;  but  both  these  subjects 
require  a  separate  consideration,  and  afford  a  vast  scope  for  speculation 
and  for  observation.  Electricity  and  magnetism  are  partly  referable  to  the 
affections  of  matter,  and  partly  to  the  agency  of  substances  which  appear 
to  agree  with  common  matter  in  some  properties  and  to  differ  from  it  in 
others.  The  phenomena  produced  by  these  agents  are  often  such  as  excite 
a  high  degree  of  curiosity  to  inquire  into  their  causes,  although  the  inquiry 
too  often  terminates  only  in  astonishment  ;  but  we  have  reason  to  expect 
considerable  advancement  in  these  sciences  from  the  singular  discoveries  of 
modern  chemists.  The  utility  of  the  philosophy  of  electricity  is  sufficiently 
exemplified  in  the  general  introduction  of  conductors  for  securing  us 
against  lightning,  to  say  nothing  of  the  occasional  enployment  of  electricity 
in  medicine ;  and  since  the  important  discovery  of  the  compass,  we  have 
only  to  lament  that  the  changeable  nature  of  magnetic  effects  so  much 
limits  the  utility  of  that  instrument  for  nautical  and  geographical  purposes. 
Of  meteorology  and  of  geology  our  knowledge  is  hitherto  very  imperfect. 


INTRODUCTION.  11 

Notwithstanding  many  diffuse  treatises  which  relate  to  them  we  cannot 
boast  of  having  reduced  them  to  any  determinate  laws  ;  and  yet  there  are 
some  meteorological  facts  which  well  deserve  our  attention.  Natural  history 
is  the  last  of  the  sciences  that  it  will  be  necessary  for  us  to  notice.  Some 
may  think  it  superfluous  to  attempt  to  give  so  superficial  a  sketch  of  this 
most  extensive  subject  as  our  plan  will  allow  ;  but  it  is  still  possible  to 
select  some  general  observations  respecting  the  methods  of  classification,  as 
well  as  the  philosophy  of  natural  history,  which,  although  very  concise, 
may  yet  be  in  some  measure  instructive.  This  third  division  of  the  course 
would  properly  include,  together  with  the  general  properties  of  matter  and 
the  particular  actions  of  its  particles,  the  whole  science  of  chemistry  ;  but 
the  variety  and  importance  of  chemical  researches  demand  a  separate  and 
minute  discussion ;  and  the  novelty  and  beauty  of  many  of  the  experi- 
ments with  which  the  labours  of  our  cotemporaries  have  presented  us,  and 
which  will  be  exhibited  in  the  theatre  of  the  Royal  Institution  by  the  pro- 
fessor of  Chemistry,  are  sufficient  to  make  this  department  of  natural  phi- 
losophy the  most  entertaining  of  all  the  sciences. 

Such  is  the  whole  outline  of  our  plan,  and  such  are  the  practical  uses  to 
which  the  arts  and  sciences  comprehended  in  it  are  principally  applicable. 
Before  we  proceed  to  the  examination  of  its  several  parts,  we  must  pause  to 
consider  the  mode  of  reasoning  which  is  the  most  generally  to  be  adopted.  It 
depends  on  the  axiom  which  has  always  been  essentially  concerned  in 
every  improvement  of  natural  philosophy,  but  which  has  been  more  and 
more  employed,  ever  since  the  revival  of  letters,  under  the  name  induction, 
and  which  has  been  sufficiently  discussed  by  modern  metaphysicians. 
That  like  causes  produce  like  effects,  or  that  in  similar  circumstances 
similar  consequences  ensue,  is  the  most  general  and  most  important  law  of 
nature ;  it  is  the  foundation  of  all  analogical  reasoning,  and  is  collected 
from  constant  experience  by  an  indispensable  and  unavoidable  propensity 
of  the  human  mind. 

It  does  not  appear  that  we  can  have  any  other  accurate  conception  of  causa- 
tion, or  of  the  connexion  of  a  cause  with  its  effect,  than  a  strong  impression 
of  the  observation,  from  uniform  experience,  that  the  one  has  constantly 
followed  the  other.  We  do  not  know  the  intimate  nature  of  the  connexion 
by  which  gravity  causes  a  stone  to  fall,  or  how  the  string  of  a  bow  urges 
the  arrow  forwards ;  nor  is  there  any  original  absurdity  in  supposing  it 
possible  that  the  stone  might  have  remained  suspended  in  the  air,  or  that 
the  bowstring  might  have  passed  through  the  arrow  as  light  passes  through 
glass.  But  it  is  obvious  that  we  cannot  help  concluding  the  stone's  weight 
to  be  the  cause  of  its  fall,  and  that  every  heavy  body  will  fall  unless  sup- 
ported ;  and  the  pressure  of  the  string  to  be  the  cause  of  the  arrow's  mo- 
tion ;  and  that  if  we  shoot,  the  arrow  will  fly ;  if  we  hesitated  to  make 
these  conclusions,  we  should  often  pay  dear  for  our  scepticism.  This  ex- 
planation is  sufficient  to  show  the  identity  of  the  two  expressions,  that  like 
causes  produce  like  effects,  and  that  in  similar  circumstances  similar  con- 
sequences ensue.  And  such  is  the  ground  of  argument  from  experience, 
the  simplest  principle  of  reasoning  after  pure  mathematical  truths,  which 
appear  to  be  so  far  prior  to  experience,  as  their  contradiction  always  im- 
plies an  absurdity  repugnant  to  the  imagination. 


12  LECTURE  I. 

In  the  application  of  induction  the  greatest  caution  and  circumspection 
are  necessary  ;  for  it  is  obvious  that,  before  we  can  infer  with  certainty 
the  complete  similarity  of  two  events,  we  must  be  perfectly  well  assured 
that  we  are  acquainted  with  every  circumstance  which  can  have  any  rela- 
tion to  their  causes.  The  error  of  some  of  the  ancient  schools  consisted 
principally  in  the  want  of  sufficient  precaution  in  this  respect ;  for  although 
Bacon  is,  with  great  justice,  considered  as  the  author  of  the  most  correct 
method  of  induction,  yet,  according  to  his  own  statement,  it  was  chiefly  the 
guarded  and  gradual  application  of  the  mode  of  argument  that  he  laboured 
to  introduce.  He  remarks  that  the  Aristotelians,  from  a  hasty  observa- 
tion of  a  few  concurring  facts,  proceeded  immediately  to  deduce  universal 
principles  of  science  and  fundamental  laws  of  nature,  and  then  derived 
from  these,  by  their  syllogisms,  all  the  particular  cases  which  ought  to 
have  been  made  intermediate  steps  in  the  inquiry.  Of  such  an  error  we 
may  easily  find  a  familiar  instance.  We  observe  that,  in  general,  heavy 
bodies  fall  to  the  ground  unless  they  are  supported  ;  it  was  therefore  con- 
cluded that  all  heavy  bodies  tend  downwards  ;  and  since  flame  was  most 
frequently  seen  to  rise  upwards,  it  was  inferred  that  flame  was  naturally 
and  absolutely  light.  Had  sufficient  precaution  been  employed  in  observ- 
ing the  effects  of  fluids  on  falling  and  on  floating  bodies,  in  examining  the 
relations  of  flame  to  the  circumambient  atmosphere,  and  in  ascertaining 
the  specific  gravity  of  the  air  at  different  temperatures,  it  would  readily 
have  been  discovered  that  the  greater  weight  of  the  colder  air  was  the 
cause  of  the  ascent  of  the  flame, — flame  being  less  heavy  than  air,  but  yet 
having  no  positive  tendency  to  ascend.  And,  accordingly,  the  Epicureans, 
whose  arguments,  as  far  as  they  related  to  matter  and  motion,  were  often 
more  accurate  than  those  of  their  cotemporaries,  had  corrected  this  error  ; 
for  we  find  in  the  second  book  of  Lucretius  a  very  just  explanation  of  the 
phenomenon. 

"  See  with  what  force  yon  river's  crystal  stream 
Resists  the  weight  of  many  a  massy  beam. 
To  sink  the  wood  the  more  we  vainly  toil, 
The  higher  it  rebounds,  with  swift  recoil. 
Yet  that  the  beam  would  of  itself  ascend 
No  man  will  rashly  venture  to  contend. 
Thus  too  the  flame  has  weight,  though  highly  rare, 
Nor  mounts  but  when  compelled  by  heavier  air." 

It  may  be  proper  to  notice  here  those  axioms  which  are  denominated  by 
Newton  *  rules  of  philosophizing  ;  although  it  must  be  confessed  that  they 
render  us  very  little  immediate  assistance  in  our  investigations.  The 
first  is,  that  "  no  more  causes  are  to  be  admitted  as  existing  in  nature  than 
are  true  and  sufficient  for  explaining  the  phenomena  to  be  considered :" 
the  second,  "  therefore  effects  of  the  same  kind  are  to  be  attributed,  as  far 
as  is  possible,  to  the  same  causes  :"  thirdly,  "  those  qualities  of  bodies  which 
cannot  be  increased  nor  diminished,  and  which  are  found  in  all  bodies 
within  the  reach  of  our  experiments,  are  to  be  considered  as  general 

*  PHncipia  ;  Introduction  to  Book  III. 


INTRODUCTION.  13 

qualities  of  all  bodies  existing :"  fourthly,  "  in  experimental  philosophy, 
propositions  collected  by  induction  from  phenomena,  are  to  be  esteemed 
either  accurately  or  very  nearly  true,  notwithstanding  any  contrary  hypo- 
thesis, until  other  phenomena  occur  by  which  they  may  either  be  corrected 
or  confuted." 

As  an  illustration  of  the  remark,  that  these  axioms,  though  strictly  true, 
are  of  little  real  utility  in  assisting  our  investigations,  I  shall  give  an  in- 
stance from  the  subject  of  electricity.  Supposing  that  we  wish  to  determine 
whether  or  no  the  electric  fluid  has  weight ;  we  are  to  inquire  whether  or  no 
gravitation  is  one  of  those  properties  which  are  described  in  the  third  rule, 
and  whether  that  rule  will  authorise  us  to  apply  it  to  the  electric  fluid,  as 
one  of  those  qualities  of  bodies  which  cannot  be  increased  nor  diminished, 
which  are  found  in  all  bodies  within  the  reach  of  our  experiments,  and 
which  are,  therefore,  to  be  considered  as  general  qualities  of  all  bodies 
existing.  Now  it  appears  to  be,  in  the  first  place,  uncertain  whether  or  no 
the  increase  and  diminution  of  gravity,  from  a  change  of  distance,  is  strictly 
compatible  with  the  terms  of  the  definition  ;  and,  in  the  second  place,  we 
are  equally  at  a  loss  to  decide,  whether  or  no  the  electric  fluid  can  with 
propriety  be  called  a  body ;  for  it  appears  in  some  respects  to  be  wholly 
different  from  tangible  matter,  while  it  has  other  qualities  in  common  with 
it.  Such  are  the  difficulties  of  laying  down  general  laws  on  so  comprehen- 
sive a  scale,  that  we  shall  find  it  more  secure  to  be  contented  to  proceed 
gradually  by  closer  inductions  in  particular  cases.  We  shall,  however, 
seldom  be  much  embarrassed  in  the  choice  of  a  mode  of  argumentation.  The 
laws  of  motion,  which  will  be  the  first  immediate  subjects  of  discussion, 
have  indeed  sometimes  been  referred  to  experimental  evidence  ;  but  we 
shall  be  able  to  deduce  them  all  in  a  satisfactory  manner,  by  means  of  our 
general  axiom,  from  reasonings  purely  mathematical,  which,  wherever  they 
are  applicable,  are  unquestionably  preferable  to  the  imperfect  evidence  of 
the  senses,  employed  in  experimental  investigations.* 


LECTURE    II. 


ON  MOTION. 

THE  whole  science  of  mechanics  depends  on  the  laws  of  motion,  either 
actually  existing  or  suppressed  by  the  opposition  of  the  forces  which  tend 
to  produce  it.  The  nature  of  motion  requires,  therefore,  to  be  particularly 
examined  at  the  entrance  of  the  science  of  mechanical  philosophy ;  and 
although  the  subject  is  so  abstract  as  to  demand  some  effort  of  the  attention, 
being  seldom  capable  of  receiving  much  immediate  illustration  from  the 
objects  of  sense,  yet  we  shall  find  it  indispensable  to  our  progress  in  the 

*  Consult  Stewart's  Philosophy  of  the  Human  Mind,  2  vols.  1818-21,  v.  2.  Brown 
on  Cause  and  Effect.  Whewell's  Philosophy  of  the  Inductive  Sciences,  2  vols. 
1840. 


14  LECTURE  II. 

investigation  of  many  particular  problems  of  importance,  to  obtain,  in  the 
first  place,  a  clear  conception  of  the  properties  and  affections  of  motions  of 
all  kinds. 

One  of  the  ancient  philosophers,  on  being  asked  for  a  definition  of  motion, 
is  said  to  have  walked  across  the  room,  and  to  have  answered,  you  see  it, 

j  but  what  it  is  I  cannot  tell  you.  It  does  not,  however,  appear  absolutely 
^necessary  to  appeal  to  the  senses  for  the  idea  of  motion  ;  for  a  definition  is 
the  resolution  of  a  complex  idea  into  the  more  simple  elements  which  com- 
pose it ;  and,  in  the  present  instance,  these  elements  are,  the  existence  of 
two  points  at  a  certain  distance,  and,  after  a  certain  interval  of  time, 
the  existence  of  the  same  points  at  a  different  distance  ;  the  difference  of  the 
distances  being  supposed  to  be  ascertained  according  to  that  postulate  of 
geometry  (which  has  in  general  been  tacitly  understood,  but  which  I 
have  expressly  inserted  in  the  geometrical  part  of  my  syllabus),  requiring 
that  the  length  of  a  line  be  capable  of  being  identified,  whether  by  the  effect 
of  any  object  on  the  senses,  or  merely  in  imagination. 

Motion,  therefore,  is  the  change  of  rectilinear  distance  between  two  points.* 
Allowing  the  accuracy  of  this  definition,  it  appears  that  two  points  are 
necessary  to  constitute  motion  ;  that  in  all  cases  when  we  are  inquiring 
whether  or  no  any  body  or  point  is  in  motion,  we  must  recur  to  some 

,  'other  point  which  we  can  compare  with  it,  and  that  if  a  single  atom  existed 
alone  in  the  universe,  it  could  neither  be  said  to  be  in  motion  nor  at  rest. 
This  may  seem  in  some  measure  paradoxical,  but  it  is  the  necessary  con- 
sequence of  our  definition,  and  the  paradox  is  only  owing  to  the  difficulty 
of  imagining  the  existence  of  a  single  atom,  unsurrounded  by  innumerable 
points  of  a  space  which  we  represent  to  ourselves  as  immoveable. 

It  has  been  for  want  of  a  precise  definition  of  the  term  motion,  that 
many  authors  have  fallen  into  confusion  with  respect  to  absolute  and  rela- 
tive motion.  For  the  definition  of  motion,  as  the  change  of  rectilinear 
distance  between  two  points,  appears  to  be  the  definition  of  what  is  com- 
monly called  relative  motion ;  but,  on  a  strict  examination,  we  shall  find, 
that  what  we  usually  call  absolute  motion  is  merely  relative  to  some  space 

,  which  we  imagine  to  be  without  motion,  but  which  is  so  in  imagination 
only.  The  space  which -we  call  quiescent  is  in  general  the  earth's  surface  ; 
yet  we  well  know,  from  astronomical  considerations,  that  every  point  of 
the  earth's  surface  is  perpetually  in  motion,  and  that  in  very  various 
directions  :  nor  are  any  material  objects  accessible  to  our  senses  which  we 
can  consider  as  absolutely  motionless,  or  even  as  motionless  with  regard  to 
each  other ;  since  the  continual  variation  of  temperature  to  which  all  bodies 
are  liable,  and  the  minute  agitations  arising  from  the  motions  of  other 
bodies  with  which  they  are  connected,  will  always  tend  to  produce  some 
imperceptible  change  of  their  distances. 

When,  therefore,  we  assert  that  a  body  is  absolutely  at  rest,  we  only 
mean  to  compare  it  with  some  large  space  in  which  it  is  contained  :  for 
that  there  exists  a  body  absolutely  at  rest,  in  as  strict  a  sense  as  an  abso- 
lutely straight  line  may  be  conceived  to  exist,  we  cannot  positively  affirm  ; 
and  if  such  a  quiescent  body  did  exist,  we  have  no  criterion  by  which  it 
*  See  Descartes  Princip.  Philos.  Part  ii.  §  25. 


ON  MOTION.  16 

could  be  distinguished.  Supposing  a  ship  to  move  at  the  rate  of  three  miles 
in  an  hour,  and  a  person  on  board  to  walk  or  to  be  drawn  towards  the 
stern  at  the  same  rate,  he  would  be  relatively  in  motion  with  respect  to  the 
ship,  yet  we  might  very  properly  consider  him  as  absolutely  at  rest :  but 
he  would,  on  a  more  extended  view,  be  at  rest  only  in  relation  to  the 
earth's  surface  ;  for  he  would  still  be  revolving  round  the  axis  of  the  earth, 
and  with  the  earth  round  the  sun,  and  with  the  sun  and  the  whole  solar 
system,  he  would  be  slowly  moving  among  the  starry  worlds  which  surround 
them.  Now  with  respect  to  any  effects  within  the  ship,  all  the  subsequent 
relations  are  of  no  consequence,  and  the  change  of  his  rectilinear  distance 
from  the  various  parts  of  the  ship  is  all  that  needs  to  be  considered  in  deter- 
mining those  effects.  In  the  same  manner,  if  the  ship  appear,  by  compari- 
son with  the  water  only,  to  be  moving  through  it  with  the  velocity  of 
three  miles  an  hour,  and  the  water  be  moving  at  the  same  time  in  a  con- 
trary direction  at  the  same  rate  in  consequence  of  a  tide  or  current,  the 
ship  will  be  at  rest  with  respect  to  the  shore  ;  but  the  mutual  actions  of  the 
ship  and  the  water  will  be  the  same  as  if  the  water  were  actually  at  rest 
and  the  ship  in  motion. 

It  is  not  sufficient  to  observe  the  increase  or  decrease  of  distance  of  a 
moving  point  from  another  single  point  only ;  we  must  compare  its  succes- 
sive situations  with  many  other  points  surrounding  it ;  and  for  this 
purpose  these  points  must  be  at  rest  among  themselves,  in  order  to  be 
considered  as  belonging  to  a  quiescent  space  or  surface  ;  which  may  be 
denned  as  a  space  or  surface  of  which  all  the  points  remain  always  at  equal 
distances  from  each  other  without  any  external  influence.  In  this  sense 
we  must  call  the  deck  of  the  ship  a  quiescent  surface,  whether  the  ship  be 
at  anchor  or  under  sail ;  but  we  must  not  consider  a  surface  revolving 
round  a  centre  as  a  quiescent  surface,  for  it  will  appear  hereafter  that  no 
such  motion  can  exist  without  the  influence  of  a  centripetal  force  ;  which 
renders  it  improper  for  determining  the  affections  of  a  moving  body. 

When  a  point  is  in  motion  with  respect  to  a  quiescent  space,  it  is  often 
simply  denominated  a  moving  point,  and  the  right  line  joining  any  two 
of  its  places  immediately  contiguous  to  each  other  is  called  its  direction. 
If  it  remains  continually  in  one  right  line  drawn  in  the  quiescent  space, 
that  line  is  always  the  line  of  its  direction ;  if  it  describes  several  right  lines, 
each  line  is  the  line  of  its  direction  as  long  as  it  continues  in  it  ;  but  if  its 
path  becomes  curved,  we  can  no  longer  consider  it  as  perfectly  coinciding  at 
any  time  with  a  right  line,  and  we  must  recur  to  the  letter  of  the  defini- 
tion, by  supposing  a  right  line  to  be  drawn  through  two  successive  points 
in  which  it  is  found,  and  then  if  these  points  be  conceived  to  approach  each 
other  without  limit  we  shall  have  the  line  of  its  direction.  Now  such  a  line 
is  called  in  geometry  a  tangent :  for  it  meets  the  curve  but  does  not  cut  it, 
provided  that  the  curvature  be  continued.  (Plate  I.  ,Fig.  1 — 3.) 

Having  formed  an  accurate  ^idea)  of  the  nature  of  motion,  and  of  the  im- 
port of  the  terms  employed  in  speaking  of  its  properties,  we  may  proceed 
to  consider  the  mechanical  laws  to  which  it  is  subjected,  and  which  are  de- 
rivable from  the  essence  of  tKe~aennitions  that  have  been  premised.  The 
first  is,  that  a  moving  point  never  quits  the  line  of  its  direction  without  a 


16  LECTURE  II. 

II 
disturbing  causej  for  a  right  line  being  the  same  with  respect  to  all  sides, 

no  reason  can  be  imagined  why  the  point  should  incline  to  one  side  more ' 
than  another ;  and  the  general  law  of  induction  requires  that  the  moving 
point  should  preserve  the  same  relations  towards  the  points  similarly 
situated  on  every  side  of  the  line.  This  argument  appears  to  be  sufficiently 
satisfactory  to  give  us  ground  for  asserting  that  the  law  of  motion  here  laid 
down  may  be  considered  as  independent  of  experimental  proof.  It  was  once 
proposed  as  a  prize  question  by  the  Academy  of  Sciences  at  Berlin,  to  determine 
jj  whether  the  laws  of  motion  were  necessary  or  accidental ;  that  is,  whether 
they  were  to  be  considered  as  mathematical  or  as  physical  truths.  Mauper- 
tuis,*  then  president  of  the  Academy,  wrote  an  elaborate  dissertation,  in 
which  he  endeavoured  to  deduce  them  from  a  complicated  principle  of  the 
production  of  every  effect  in  the  manner  which  requires  the  least  possible 
action,  a  principle  which  he  supposes  to  be  most  consistent  with  the  wise 
economy  of  nature.  But  this  principle  has  itself  been  shown  to  be  capable 
/v  of  accommodation  to  any  other  imaginable  laws  of  motion,  and  the  intricacy 
of  the  theory  tends  only  to  envelope  the  subject  in  unnecessary  obscurity  ; 
I  the  laws  of  motion  appear  to  be  easily  demonstrable  from  the  simplest 
mathematical  truths,  granting  only  the  homogeneity  or  similarity  of  matter 
with  respect  to  motion,  and  allowing  the  general  axiom  that  like  causes  pro- 
duce like  effects.  If,  however,  any  person  thinks  differently,  he  is  at  liberty 
to  call  these  laws  experimental  axioms  collected  from  a  comparison  of 
various  phenomena ;  for  we  cannot  easily  reduce  them  to  direct  experi- 
ments, since  we  can  never  remove  from  our  experiments  the  action  of  all 
disturbing  causes;  for  either  gravitation,  or  the  contact  of  surrounding 
^bodies,  will  interfere  with  all  the  motions  which  we  can  examine. 

Having  established  the  rectilinear  direction  of  undisturbed  motion,  we 
come  to  consider  its  uniformity.  Here  the  idea  of  time  enters  into  our  sub- 
ject. To  define  time  in  general  is  neither  easy  nor  necessary  ;  but  we  must 
have  some  measure  of  equal  times.  Our  abstract  idea  of  time  depends  on 
the  memory  of  past  sensations  ;  but  is  obvious  that  the  results  of  an  intel- 
lectual measure  of  the  duration  of  time  would  be  liable  to  the  greatest 
uncertainty.  We  may  observe  that  on  a  journey  the  perpetual  succession 
of  various  objects  will  often  make  a  week  appear,  upon  retrospection,  as 
long  as  a  month  spent  in  a  continuation  of  such  employments  as  are  uni- 
form without  being  laborious  ;  the  multitude  of  new  impressions  not  only 
serving  to  increase  the  apparent  magnitude  of  the  interval,  by  filling  up  its 
vacuities,  but  tending  also  to  dimmish  the  vivacity  of  the  ideas  which  they 
have  superseded,  and  to  give  them  the  character  of  the  fainter  recollections 
of  an  earlier  date.  We  are  therefore  obliged  to  estimate  the  lapse  of  time 
by  the  changes  in  external  objects  ;  of  these  changes  the  simplest  and  most 
convenient  is  the  apparent  motion  of  the  sun,  or  rather  of  the  stars,  derived 

*  Hist,  et  Mem.  de  1'Acad.  de  Berl.  1746,  jp. 267]  Collected  Works  of  Maup., 
4  vols.  Lyons,  1756,  vol.  iv;  p.  31.  Compare  Leibnitz's  Leipsic  Acts,  1682. 
D'Arcy  on  Maupertuis's  Minimum  of  Action.  Hist,  et  Mem.  de  Paris,  1749,  p.  531. 
H.  179,  1752,  p.  503.  Euler  on  the  General  Principles  of  Motion  and  Rest.  Hist, 
et  Mem.  de  1'Acad.  de  Berl.  1751,  pp.  169,  199.  Bertrand  on  the  least  Action,  ib. 
1753,  p.  310.  Malvezio  on  the  Principle  of  Maupertuis,  Com.  Bon.  VI.  Opuscula, 
p.  315.  Euler,  Dissertatio  de  Principio  Min.  Act.  Berl.  1753. 


ON  MOTION.  17 

from  the  actual  rotation  of  the  earth  on  its  axis,  which  is  not,  indeed,  an 
undisturbed  rectilinear  motion,  but  which  is  equally  applicable  to  every 
practical  purpose.  Hence  we  obtain,  by  astronomical  observations,  the 
well-known  measures  of  the  duration  of  time  implied  by  the  terms  day, 
hour,  minute,  and  second. 

Now  the  equality  of  times  being  thus  estimated  from  any  one  motion,  all 
other  bodies  moving  without  disturbance  will  describe  equal  successive  parts 
of  their  lines  of  direction  in  equal  times.  And  this  is  the  second  law  of 
motion,  which,  with  the  former  law,  constitutes  Newton's  first  axiom 
or  law  of  motion  :*  "  that  every  body  perseveres  in  its  state  of  rest  or 
uniform  rectilinear  motion,  except  so  far  as  it  is  compelled  by  some  force  to 
change  it."  It  appears  that  this  second  law  is  strictly  deducible  from  the 
axioms  and  definitions  which  have  been  premised,  and  principally  from  the 
consideration  of  the  relative  nature  of  motion,  and  the  total  deficiency  of  a 
,  criterion  of  absolute  motion.  For,  since  the  velocity  of  a  body  moving 
without  resistance  or  disturbance  is  only  a  relation  to  another  body,  if  the 
second  body  has  no  mechanical  connexion  with  the  first,  its  state  with 
respect  to  motion  can  have  no  effect  on  the  velocity  of  the  first  body,  how- 
ever great  its  comparative  magnitude  may  be  :  and  if  a  body  is  at  rest,  there 
is  nothing  to  determine  it  to  begin  to  move  either  to  the  right  hand  or  to 
the  left ;  if  it  is  at  rest  with  respect  to  any  other  bodies  it  will  remain  in 
the  same  condition,  whatever  the  relative  motions  of  those  bodies  may  be 
when  compared  with  the  surrounding  objects ;  and  these  relations  can  only 
be  preserved  by  its  continuance  in  uniform  rectilinear  motion.  This  law  is 
also  confirmed  by  its  perfect  agreement  with  all  experimental  observations, 
although  it  is  too  simple  to  admit  of  an  immediate  proof.  For  we  can 
never  place  any  body  in  such  circumstances  as  to  be  totally  exempt  from 
the  operation  of  all  accelerating  or  retarding  causes ;  and  the  deductions 
from  such  experiments  as  we  can  make,  would  require  in  general,  for  the 
accurate  determination  of  the  necessary  corrections,  a  previous  knowledge 
of  the  law  which  we  wish  to  demonstrate. 

When,  indeed,  we  consider  the  motion  of  a  projectile,  we  have  only  to 
allow  for  the  disturbing  force  of  gravitation,  which  so  modifies  the  effect, 
that  the  body  deviates  from  a  right  line,  but  remains  in  the  same  vertical 
plane  ;  whence  we  may  infer  that,  in  the  absence  of  the  force  of  gravita- 
tion, the  body  would  continue  to  move  in  every  other  plane  in  which  its 
motion  began,  as  well  as  in  the  vertical  plane  ;  since  in  that  case  all  these 
planes  would  be  indifferent  to  it ;  it  must,  therefore,  remain  in  their  com- 
mon intersection,  which  could  only  be  a  straight  line ;  so  that  by  thus 
combining  arguments  with  observation,  we  may  obtain  a  confirmation  of 
the  law  of  the  rectilinear  direction  of  undisturbed  motion,  partly  founded  on 
direct  experiment.  Its  uniformity  is,  however,  still  less  subjected  to  im- 
mediate examination  :  yet,  from  a  consideration  of  ttye  nature  of  friction 
and  resistance,  combined  with  the  laws  of  gravitation,  we  may  ultimately 
show  the  perfect  coincidence  of  the  theory  with  experiment.  The  ten- 
dency of  matter  to  persevere  in  this  manner  in  the  state  of  rest  or  of 
uniform  rectilinear  motion  is  called  its  inertia. 

*  Principia,  lib.  i. 
c 


18  LECTURE  II. 

In  all  these  cases  it  is  of  importance  to  attend  to  the  composition 
of  motion,  or  the  joint  effect  of  more  than  one  motion  existing  at  the 
same  time.  The  existence  of  two  or  more  motions  at  the  same  time, 
in  the  same  body,  is  not  at  first  comprehended  without  some  difficulty. 
It  is  in  fact  only  a  combination  or  separation  of  relations  that  is  con- 
sidered;  in  the  same  manner  as  by  combining  the  relation  of  son  to 
father,  and  brother  to  brother,  we  obtain  the  relation  of  nephew  to  uncle, 
so,  by  combining  the  motion  of  a  man  walking  in  a  ship,  with  the  motion  of 
the  ship,  we  determine  the  relative  velocity  of  the  man  with  respect  to  the 
earth's  surface.  It  is,  however,  necessary,  for  ascertaining  these  relations, 
to  consider  the  affections  of  a  space  or  surface  in  motion,  and  to  examine 
how  it  may  move  in  the  most  simple  manner  with  respect  to  another  space. 

If  any  number  of  points  move  in  parallel  lines,  describing  equal  spaces 
in  equal  times,  they  are  at  rest  with  respect  to  each  other ;  for  it  may 
easily  be  demonstrated  that  the  rectilinear  distance  of  each,  from  each  of 
the  rest,  remains  unchanged  ;  and  if  all  the  points  of  a  plane  move  in  this 
manner  on  another  plane,  either  plane  may  be  said  to  be  in  rectilinear 
motion  with  respect  to  the  other.  This  is  easily  exemplified  by  causing 
one  plane  to  move  on  another,  so  that  two  or  more  of  its  points  shall 
always  remain  in  a  given  right  line  in  the  second  plane  :  as  when  a  [car- 
penter's] square  is  made  to  slide  along  the  straight  edge  of  a  board,  the 
surface  of  the  square  is  in  rectilinear  motion  with  respect  to  the  board. 
(Plate  I.  Fig.  4.) 

If,  besides  this  general  motion  of  the  plane,  any  point  be  supposed  to 
have  a  particular  motion  in  it,  the  point  will  have  two  motions  with  re- 
spect to  the  other  plane  :  the  one  in  common  with  its  plane,  and  the  other 
peculiar  to  itself ;  and  the  joint  effect  of  these  motions,  with  respect  to  the 
second  plane,  is  called  the  result  of  the  two  motions.  Thus,  when  a  car- 
riage moves  on  a  perfectly  [straight  and]  level  road,  all  its  points  describe 
parallel  lines,  and  it  is  in  rectilinear  motion  with  respect  to  the  road  :  its 
wheels  partake  of  this  motion,  but  have  also  a  rotatory  motion  of  their 
own  ;  and  the  result  of  the  two  motions  of  each  point  of  the  wheels  is  the 
cycloid,  or  trochoid,  that  it  describes  in  a  quiescent  vertical  plane.  (Plate 
I.  Fig.  5.) 

When  an  arm  is  made  to  slide  upon  a  bar,  and  a  thread,  fixed  to 
the  bar,  is  made  to  pass  over  a  pulley  at  the  end  of  the  arm  next  the 
bar,  to  a  slider  which  is  moveable  along  the  arm,  the  slider  moves  on 
the  arm  with  the  same  velocity  as  the  arm  on  the  bar ;  but  if  the  thread, 
instead  of  being  fixed  to  the  slider,  be  passed  again  over  a  pulley  which  is 
attached  to  it,  and  then  brought  back  to  be  fixed  to  the  arm,  the  motion  of 
the  slider  will  be  only  half  that  of  the  arm ;  and  this  will  be  true  in  what- 
ever position  the  arm  be  fixed.  Here  we  have  two  motions  in  the  slider, 
one  in  common  with  the  arm,  and  the  other  peculiar  to  itself,  which  may 
be  either  equal  or  unequal  to  the  first ;  and  by  tracing  a  line  on  a  fixed 
plane,  with  a  point  attached  to  the  slider,  we  may  easily  examine  the  joint 
result  of  both  the  motions.  (Plate  I.  Fig.  6.) 

The  joint  result  of  any  two  motions  is  the  diagonal  of  the  parallelogram 
of  which  the  sides  would  be  described,  in  the  same  time,  by  the  separate  mo- 


ON  MOTION.  .19 

tions,  that  is,  if  we  have  two  lines,  representing  the  directions  and  velocities 
of  the  separate  motions,  and  from  the  remoter  extremity  of  each  draw  a  line 
parallel  to  the  other,  the  intersection  of  these  lines  will  be  the  place  of  the 
moving  body  at  the  end  of  the  given  time.  This  is  the  necessary  consequence 
of  the  co-existence  of  two  motions  in  the  sense  that  has  been  denned  ;  it  is 
also  capable  of  a  complete  illustration  by  means  of  the  apparatus  that  has 
been  described.  (Plate  I.  Fig.  7.) 

Any  given  motion  may  be  considered  as  the  result  of  any  two  or  more 
motions  capable  of  composing  it  in  this  manner.  Thus  the  line  described 
by  the  tracing  point  of  our  apparatus  will  be  precisely  the  same,  whether 
it  be  simply  drawn  along  in  the  given  direction,  or  made  to  move  on  the 
arm  with  a  velocity  equal  to  that  of  the  arm,  or  when  the  arm  is  in  a 
different  position,  with  only  half  that  velocity.  (Plate  I.  Fig.  8.) 

This  principle  constitutes  the  important  doctrine  of  the  resolution  of 
motion.     There  is  some  difficulty  in  imagining  a  slower  motion  to  contain,  \ 
as  it  were,  within  itself,  two  more  rapid  motions  opposing  each  other :  but  ; 
in  fact  we  have  only  to  suppose  ourselves  adding  or  subtracting  mathe- 
matical quantities,  and  we  must  relinquish  the  prejudice,  derived  from  our 
own .feelings,  which  associates  the  idea   of  effort  with   that   of  motion. 
When  we  conceive  a  state  of  rest  as  the  result  of  equal  and  contrary 
motions,  we  use  the  same  mode  of  representation  as  when  we  say  that  a 
cipher  is  the  sum  of  two  equal  quantities  with  opposite  signs ;  for  instance, 
plus  ten  and  minus  ten  make  nothing. 

[  The  law  of  motion  here  established  differs  but  little  in  its  enunciation  I 
1  from  the  original  words  of  Aristotle,  in  his  mechanical  problems.*  He  ' 
says,  that  if  a  moving  body  has  two  motions,  bearing  a  constant  propor- 
tion to  each  other,  it  must  necessarily  describe  the  diameter  of  a  parallelo- 
gram, of  which  the  sides  are  in  the  ratio  of  the  two  motions.  It  is  obvious 
that  this  proposition  includes  the  consideration,  not  only  of  uniform 
motions,  but  also  of  motions  which  are  similarly  accelerated  or  retarded  : 
and  we  should  scarcely  have  expected  that,  from  the  time  at  which  the 
subject  began  to  be  so  clearly  understood,  two  thousand  years  would 
have  elapsed  before  this  law  began  to  be  applied  to  the  determination  of 
the  velocity  of  bodies  actuated  by  deflecting  forces,  which  Newton  has  so 
simply  and  elegantly  deduced  from  it. 

In  the  laws  of  motion,  which  are  the  chief  foundation  of  the  Principia, 
their  great  author  introduces  at  once  the  consideration  of  forces  ;  and  the 
first  corollary  stands  thus  :  "  a  body  describes  the  diagonal  of  a  parallelo- 
gram by  two  forces  acting  conjointly,  in  the  same  time  in  which  it  would 
describe  its  sides  by  the  same  forces  acting  separately."  It  appears,  how- 
ever, to  be  more  natural  and  perspicuous  to  defer  the  consideration  of  force 
until  the  simpler  doctrine  of  motion  has  been  separately  examined. 

We  may  easily  proceed  to  the  composition  of  any  number  of  different 
motions  by  combining  them  successively  in  pairs.     Hence   any  equable 
motions,  represented  by  the  sides  of  a  polygon,  that  is,  of  a  figure  consist- 
ing of  any  number  of  straight  sides,  being  supposed  to  take  place  in  the 
same  moveable  body  in  directions  parallel  to  those  sides,  and  in  the  order 
*  Mech.  Prob.  c.  24.     See  also  Galileo,  Dial.  4,  Prop.  2. 
c2 


20  LECTURE  II. 

of  going  round  the  figure,  destroy  each  other,  and  the  body  remains  at 
rest.  We  may  understand  the  truth  of  this  proposition  by  imagining  each 
motion  to  take  place  in  succession  for  an  equal  small  interval  of  time  ; 
then  the  point  would  describe  a  small  polygon  similar  to  the  original  one,  and 
would  be  found,  at  the  end  of  every  such  interval,  in  its  original  situation. 
When  the  motions  to  be  combined  are  numerous  and  diversified,  it  is 
often  convenient  to  resolve  each  motion  into  three  parts,  reduced  to  the 
directions  of  three  given  lines  perpendicular  to  each  other.  It  is  easy  to 
find  in  this  manner,  by  addition  and  subtraction  only,  the  general  result  of 
any  number  of  motions.  We  may  describe  the  flight  of  a  bird  ascending 
in  an  oblique  direction,  by  estimating  its  progress  northwards  or  south- 
wards, eastwards  or  westwards,  and  at  the  same  time  upwards,  and  we  may 
thus  determine  its  place  as  accurately  as  by  ascertaining  the  immediate 
bearing  and  angular  elevation  of  its  path,  and  its  velocity  in  the  direction 
of  its  motion. 


LECT.  II.— ADDITIONAL  AUTHORITIES. 

Wjallis's  Ph.  Tr.  iii.  864.  Mechanica,  4to,  Lon.  1670.  Opera,  3  vols.  fol.  Oxf.  1713, 
i.  571.  Varignon,  Nouvelle  Mecanique,  2  vols.  4to,  Paris,  1725  (Posthumous).  Hist,  et 
Mem.  de  1'Acad.  de  Paris,  1714,  p.  280,  H.  87  ;  1733,  x.  301.  Roberval,  ibid.  vi. 
1,68.  Joh.  Bernoulli,  Opera,  4  vols.  4to,  Lausanne,  1 742,  iii.  1.  Hermann,  Phoro- 
nomia,  4to,  Amst.  1716.  Courtivron's  Researches,  Hist,  et  Mem.  de  Paris,  1748, 
p.  304  ;  1749,  p.  15.  Kraftii  Mechanik,  2  vols.  4to,  Soroe,  1762-4  ;  also,  4to,  Bat. 
1772,  and  Dresd.  1787.  See  also  LECT.  XIX. 

Elementary  Treatises  on  Mechanics. — Qflohaulti,  Physica  Clarkii,  2  vols.  Lond. 
1799.  Ferguson's  Mechanics,  1799.  Bossut,  Traite  de  Mec.  Paris,  1800.  Eytelwein 
ETaridbuch  der  Mechanik,  Berl.  1801.  Carnot,  Principes  Fondamentaux,  Par. 
1803.  Bezout,  Cours  deMath.  Gregory's  Mechanics,  2  vols.  plates,  1806.  LePriol, 
Introduction,  Strasburg,  1806.  Foucoeur,  Mec.  1800.  Gamier,  Lefons,  1811.  Emer- 
son's Mech.  Venturoli,  Element!  di  Meccanica,  2  vols.  Milan,  1817  ;  translation  by 
Creswell,  Camb.  1822.  Vega  Vorlesungen  iiber  die  Mathematik,  4  vols.  Wien. 
1818-19.  Farrar,  Mech.  Camb.  U.S.  1825.  Boucharlat,  Mec.  1827.  Leslie's  Ele- 
ments of  Natural  Philosophy,  Edin.  1829.  Biot,  Notions  Elementaires  de  Statique, 
1829.  Hachette  (translation  of  Young}  Resume  Complet  de  Mecanique,  32,  Par. 
1829.  Dandelin,  Cours  de  Statique,  Liege,  1830.  Prichard's  Theory  of  Statical 
Couples,  Camb.  1831.  Renwick's  Mechanics,  New  York,  1832.  Poinsot,  Elem.  de 
Statique,  Monge,  TraitS  Elem.  de  Statique,  1834.  Together  with  treatises  by  the 
following  authors,  most  of  which  have  passed  through  several  editions,  and  are  well 
known  : — 

Bridge,  Wood,  Whewell — Mechanical  Euclid,  Statics,  Dynamics,  fyc.  Earn- 
shaw's  Statics,  Dynamics.  Walker,  Young  (J.  R.),  Lardner — (Library  of  Useful 
Knowledge}.  Lardner  and  Kater  (Cabinet  Cyclopaedia),  Eland's  Mechanical  Pro- 
blems. Walton's  Do.  Moseley's  Illustrations  of  Mechanics,  and  Mechanics  applied 
to  the  Arts. 

Treatises  which  embrace  a  wider  range — Laplace,  Traite  de  Mecanique  Celeste, 
5  vols.  4to,  Paris,  1799-1825.  Bowditch's  Translation  of  Laplace's  Celestial  Mecha- 
nics, with  a  Commentary,  3  vols.  4to,  Boston,  U.S.  1829-34./\Lagrange,  Mecanique 
Analytique,  2  vols.  4to,  Paris,  1815.  Prony,  Legons  de  Mecanique  analytique,  2  vols. 
4to,  Paris,  1815.  Poisson,  Traite  de  Mecanique,  2  vols.  Paris,  1833.  Harte's  Trans- 
lation of  Poisson's  Mechanics,  2  vols.  Lond.  1843.  Pontecoulant,  Theorie  Analytique 
du  Systeme  du  Monde,  3  vols.  Paris,  1829-34.  Somerville's  (Mrs.)  Mechanism  of  the 
Heavens,  Lond.  1831.  Pratt,  The  Mathematical  Principles  of  Mechanical  Philoso- 
phy, Camb.  1836. 


LECTURE   III. 


ON  ACCELERATING  FORCES. 

WE  have  hitherto  only  considered  motion  as  already  existing,  without 
any  regard  to  its  origin  or  alteration ;  we  have  seen  that  all  undisturbed 
motions  are  equable  and  rectilinear ;  and  that  two  motions  represented  by 
the  sides  of  a  parallelogram,  cause  a  body  to  describe  its  diagonal  by  their 
joint  effect.  We  are  now  to  examine  the  causes  which  produce  or  destroy 
motion.  Any  cause  of  a  change  of  the  motion  of  a  body  with  respect  to  a 
quiescent  space,  is  called  a  force ;  that  is,  any  cause  which  produces 
motion  in  a  body  at  rest,  or  which  increases,  diminishes,  or  modifies  it  in  a 
body  which  was  before  in  motion.  Thus  the  power  of  gravitation,  which 
causes  a  stone  to  fall  to  the  ground,  is  called  a  force ;  but  when  the  stone, 
after  descending  down  a  hill,  rolls  along  a  horizontal  plane,  it  is  no  longer 
impelled  by  any  force,  and  its  relative  motion  continues  unaltered,  until  it  is 
gradually  destroyed  by  the  retarding  force  of  friction.  Its  perseverance 
in  the  state  of  motion  or  rest  in  consequence  of  the  inertia  of  matter,  has 
sometimes  been  expressed  by  the  term  vis  inertiae,  or  force  of  inertia  ;  but  it 
appears  to  be  somewhat  inaccurate  to  apply  the  term  force  to  a  property 
which  is  never  the  cause  of  a  change  of  motion  in  the  body  to  which  it 
belongs. 

It  is  a  necessary  condition,  in  the  definition  of  force,  that  it  be  the  cause 
of  a  change  of  motior<with  respect  to) a  quiescent  space.  For  if  the  change 
were  only  in  the  relative  motion  of  two  points,  it  might  happen  without 
the  operation  of  any  force  :  thus,  if  a  body  be  moving  without  disturbance, 
its  motion  with  respect  to  another  body,  not  in  the  line  of  its  direction, 
will  be  perpetually  changed :  and  this  change,  considered  alone,  would 
[appear  to]  indicate  the  existence  of  a  repulsive  force ;  and,  on  the  other 
hand,  two  bodies  may  be  subjected  to  the  action  of  an  attractive  force, 
while  their  distance  remains  unaltered,  in  consequence  of  the  centrifugal 
effect  of  a  rotatory  motion.  (Plate  I.  Fig.  9.) 

The  exertion  of  an  animal,  the  unbending  of  a  bow,  and  the  communi- 
cation of  motion  by  impulse,  are  familiar  instances  of  the  actions  of  forces. 
We  must  not  imagine  that  the  idea  of  force  is  naturally  connected  with 
that  of  labour  or  difficulty ;  this  association  is  only  derived  from  habit, 
since  our  voluntary  actions  are  in  general  attended  with  a  certain  effort, 
which  leaves  an  impression  almost  inseparable  from  that  of  the  force  that 
it  calls  into  action. 

It  is  natural  to  inquire  in  what  immediate,  manner>any  force  acts,  so  as 
to  produce  motion  ;  for  instance,  by  what  means  the  earth  causes  a  stone 
to  gravitate  towards  it.  In  some  cases,  indeed,  we  are  disposed  to  imagine 
that  we  understand  better  [tolerably  well]  the  nature  of  the  action  of  a 
force,  as,  when  a  body  in  motion  strikes  another,  we  conceive  that  the 
impenetrability  of  matter  is  a  sufficient  cause  for  the  communication  of 
motion,  since  the  first  body  cannot  continue  its  course  without  displacing 


22  LECTURE  III. 

the  second  ;  and  it  has  been  supposed  that  if  we  could  discover  any  similar 
impulse  that  might  be  the  cause  of  gravitation,  we  should  have  a  perfect 
idea  of  its  operation.  But  the  fact  is,  that  even  in  cases  of  apparent 
jj impulse,  the  bodies  impelling  each  other  are  not  actually  in  contact  j|  and 
if  any  analogy  between  gravitation  and  impulse  be  ever  established,  it  will 
not  be  by  referring  them  both  to  the  impenetrability  of  matter,  but  to  the 
intervention  of  some  common  agent,  perhaps  imponderable.  It  was 
observed  by  Newton,*  that  a  considerable  force  was  necessary  to  bring  two 
pieces  of  glass  into  a  degree  of  contact,  which  still  was  not  quite  perfect ; 
and  Profesor  Robison  t  has  estimated  this  force  at  a  thousand  pounds  for 
every  square  inch.  These  extremely  minute  intervals  have  been  ascer- 
tained by  observations  on  the  colours  of  the  thin  plate  of  air  included 
between  the  glasses ;  and  when  an  image  of  these  colours  is  exhibited  by 
means  of  the  solar  microscope,  it  is  very  easily  shown  that  the  glasses  are 
separated  from  each  other,  by  the  operation  of  this  repulsive  force, 
as  soon  as  the  pressure  of  the  screws  which  confine  them  is  diminished  ; 
the  rings  of  colours  dependent  on  their  distance  contracting  their  dimen- 
sions accordingly.  Hence  it  is  obvious,  that  whenever  two  pieces  of  glass 
strike  each  other,  without  exerting  a  pressure  equal  to  a  thousand  pounds 
on  a  square  inch,  they  may  affect  each  other's  motion  without  actually 
coming  into  contact.  Some  persons  might  perhaps  be  disposed  to  attribute 
this  repulsion  to  the  elasticity  of  particles  of  air  adhering  to  the  glass,  but 
I  have  found  that  the  experiment  succeeds  equally  well  in  the  vacuum  of 
the  air  pump.  We  must,  therefore,  be  contented  to  acknowledge  our  total 
ignorance  of  the  intimate  nature  of  forces  of  every  kind ;  and  we  are 

/  first  to  examine  the  effect  of  forces,  considering  only  their  magnitude  and 

L  direction,  without  any  regard  to  their  origin. 

It  was  truly  asserted  by  Descartes,^  that  the  state  of  motion  is  equally 
natural  with  that  of  rest.  When  a  body  is  once  in  motion,  it  requires  no 
foreign  power  to  sustain  its  velocity.  If,  therefore,  a  moving  body  is  sub- 
jected to  the  influence  of  any  force,  which  acts  upon  it  in  the  line  of  its 
direction,  its  motion  will  be  either  accelerated  or  retarded,  accordingly  as 
the  direction  of  the  force  coincides  with  that  of  the  motion,  or  is  opposed 
to  it.  A  stone,  for  instance,  beginning  to  fall,  or  projected  downwards, 
by  no  means  retains  the  same  velocity  throughout  its  descent,  but  acquires 
more  and  more  motion  every  instant.  We  well  know  that  the  greater 
the  height  from  which  a  body  falls,  the  more  danger  there  is  of  its  destroy- 
ing whatever  opposes  its  progress.  In  the  same  manner,  when  a  ball  is 
thrown  upwards,  it  gradually  loses  its  motion  by  the  operation  of  gravita- 
tion, which  is  now  a  retarding  force,  and  at  last  begins  again  to  descend. 

It  may  here  be  proper  to  inquire  what  is  the  precise  meaning  of  the 
term  velocity  ;  we  appear  indeed  to  understand  sufficiently  the  common  use 
of  the  word,  but  it  is  not  easy  to  give  a  correct  definition  of  it.  The  velocity 
of  a  body  may  be  said  to  be  the  quantity  or  degree  of  its  motion,  indepen- 
dently of  any  consideration  of  its  mass  or  magnitude ;  and  it  might 
always  be  measured  by  the  space  described  in  a  certain  portion  of  time,  for 

*  Optics,  Book  II.     See  also  Huygens,  Ph.  Tr.  No.  86. 
f  Robison's  Mechanical  Philosophy,  Brewster's  Ed.,  i.  250. 
J  Principia  Philos.  Part  ii.  §  26. 


ON  ACCELERATING  FORCES.  23 

instance  a  second,  if  there  were  no  other  motions  than  undisturbed  or 
uniform  motions ;  but  the  velocity  may  vary  very  considerably  within  the 
second,  and  we  must  therefore  have  some  other  measure  of  it  than  the 
space  actually  described  in  any  finite  interval  of  time.  If,  however,  the 
times  be  supposed  infinitely  short,  the  elements  of  space  described  may  be 
considered  as  the 'true  measures  of  velocities.  These  elements,  although 
smaller  than  any  assignable  quantity,  may  yet  be  accurately  compared  with 
each  other ;  and  the  reason  that  they  afford  a  true  criterion  of  the  velo- 
city is  this,  that  the  change  produced  in  the  velocity  during  so  short  an 
interval  of  time,  must  be  absolutely  inconsiderable,  in  comparison  with  the 
whole  velocity,  and  the  element  of  space  becomes  a  true  measure  of  the 
temporary  velocity,  in  the  same  manner  as  any  larger  portion  of  space  may 
be  the  measure  of  a  uniform  velocity. 

When  the  increase  or  diminution  of  the  velocity  of  a  moving  body  is 
uniform,  its  cause  is  called  a  uniform  force ;  the  spaces  which  would  be 
described  in  any  given  time  with  the  actual  velocity  uniformly  continued, 
being  always  equally  increased  or  diminished  by  the  action  of  such  a  force. 
For  example,  if  the  velocities  at  the  beginning  of  any  two  separate 
seconds  be  such  that  the  body  would  describe  one  foot  and  ten  feet  in  the 
respective  seconds,  if  undisturbed,  and  the  spaces  actually  described 
become  two  feet  and  eleven  feet,  each  being  increased  one  foot,  the  accele- 
rating force  must  be  denominated  uniform. 

The  power  of  gravitation,  acting  at  or  near  the  earth's  surface,  may, 
without  sensible  error,  be  considered  as  such  a  force.  Thus,  if  a  body 
begins  to  fall  from  a  state  of  rest,  it  describes  about  16  feet,  or  more  cor- 
rectly 16-jir  in  the  first  second  ;  if  it  begins  a  second  with  a  velocity  of  32 
feet,  it  describes  32  and  16,  or  48  feet  in  this  second.  The  decrease  of  the 
force  of  gravitation,  in  proportion  to  the  squares  of  the  distances  from  the 
earth's  centre,  is  barely  perceptible,  at  any  heights  within  our  reach,  by 
the  nicest  tests  that  we  can  employ. 

The  velocity  produced  by  any  uniformly  accelerating  force,  is  propor- 
tional to  the  magnitude  of  the  force  and  the  time  of  its  operation  con- 
jointly.* When  the  forces  are  the  same,  a  little  consideration  will  convince 
us  that,  since  every  equal  portion  of  time  adds  equally  to  the  velocity,  the 
whole  velocity  produced  or  destroyed  must  be  in  proportion  to  the  whole 
time ;  and  when  the  forces  differ,  the  velocities  differ  in  the  same  ratio ; 
for  the  forces  are  only  measured  by  the  velocities  which  they  generate. 
Thus  a  double  force,  in  a  double  time,  produces  a  quadruple  velocity. 
That  a  force  producing  a  double  velocity  is  properly  called  a  double  force, 
may  be  shown  from  the  laws  of  the  composition  of  motion  ;  for  when  the 
equal  sides  of  a  parallelogram  representing  two  separate  forces  or  motions, 
approach  to  each  other,  and  at  last  coincide  in  direction,  the  diagonal  of 
the  parallelogram,  representing  their  joint  effect,  becomes  equal  to  the  sum 
of  the  sides.  (Plate  I.  Fig.  10.)  t 
,  The  machine  invented  by  Mr.  AtwoodJ  (Plate  I.  Fig.  11)  furnishes  us 

f*S^ 

*  Galileo,  Dialogues  on  Motion,  Dial.  III.  Def. 

f  Halley,  Ph.  Tr.xvi.  0  (1686). 

t  On  the  Rectilinear  Motion,  and  the  Rotation  of  Bodies,  Camb.  1804,  p.  291. 


24  LECTURE  III. 

with  a  very  convenient  mode  of  making  experiments  on  accelerating  forces. 
The  velocity  produced  by  the  undiminished  force  of  gravity,  is  much  too 
great  to  be  conveniently  submitted  to  experimental  examination  ;  but  by 
means  of  this  apparatus  we  can  diminish  it  in  any  degree  -that  is 
required.  Two  boxes,  which  are  attached  to  a  thread  passing  over  a 
pulley,  may  be  filled  with  different  weights,  which  counterbalance  each 
other  and  constitute,  together  with  the  pulley,  an  inert  mass,  which  is  put 
into  motion  by  a  small  weight  added  to  one  of  them.  The  time  of  descent 
is  measured  by  a  second  or  half  second  pendulum,  the  space  described 
being  ascertained  by  the  place  of  a  moveable  stage,  against  which  the  bot- 
tom of  the  descending  box  strikes ;  and  when  we  wish  to  determine  im- 
mediately the  velocity  acquired  at  any  point,  by  measuring  the  space 
uniformly  described  in  a  given  time,  the  accelerating  force  is  removed  by 
means  of  a  ring  which  intercepts  the  preponderating  weight,  and  the  box 
proceeds  with  a  uniform  velocity,  except  so  far  as  the  friction  of  the 
machine  retards  it.  By  changing  the  proportion  of  the  preponderating 
weight  to  the  whole  weight  of  the  boxes,  it  is  obvious  that  we  may  change 
the  velocity  of  the  descent,  and  thus  exhibit  the  effects  of  forces  of  different 
magnitudes.  The  most  convenient  mode  of  letting  the  weights  go,  with- 
out danger  of  disturbance  from  their  vibrations,  is  to  hold  the  lowest 
weight  only,  and  to  allow  it  to  ascend  at  the  instant  of  a  beat  of  the  pen- 
dulum. 

That  the  velocity  generated  is  proportional  to  the  time  of  the  action  of 
the  force,  or  that  the  force  of  gravitation,  thus  modified,  is  properly  called 
a  uniform  accelerating  force,  may  be  shown  by  placing  the  moveable  ring 
so  as  to  intercept  the  same  bar  successively  at  two  different  points  :  thus  the 
space  uniformly  described  in  a  second,  by  the  box  alone,  is  twice  as  great, 
when  the  force  is  withdrawn  after  a  descent  of  ten  half  seconds,  as  it  is  after 
a  descent  of  five.  And  if  we  chose  to  vary  the  weight  of  the  bar,  we  might 
show,  in  a  similar  manner,  that  the  velocity  generated  in  a  given  time  is 
proportional  to  the  force  employed. 

We  are  next  to  determine  the  magnitude  of  the  whole  space  described  in 
a  given  time  with  a  velocity  thus  uniformly  increasing.  The  law  discovered 
by  Galileo,*  that  the  space  described  is  as  the  square  of  the  time  of  descent, 
and  that  it  is  also  equal  to  half  the  space  which  would  be  described  in  the 
same  time  with  the  final  velocity,f  is  one  of  the  most  useful  and  interesting 
propositions  in  the  whole  science  of  mechanics.  Its  truth  is  easily  shown 
from  mathematical  considerations,  by  comparing  the  time  with  the  base, 
and  the  velocity  with  the  perpendicular  of  a  triangle  gradually  increasing, 
of  which  the  area  will  represent  the  space  described  ;  and  we  may  observe, 
by  means  of  Atwood's  machine,  that  a  quadruple  space  is  always  described 
in  a  double  time,  whatever  may  be  the  magnitude  of  the  force.  Of  course, 
if  the  forces  vary,  the  spaces  are  as  the  forces  and  as  the  squares  of  the 
times  conjointly.  (Plate  I.  Fig.  12.) 

It  may  also  be  demonstrated,  that  if  a  body  falls  through  one  foot  in  a 
second  by  means  of  a  certain  force,  it  will  require  a  quadruple  force  to 
make  it  fall  through  the  same  space  in  half  a  second  ;  and  in  general,  where 
*  Dial.  III.  Prop.  2.  f  Ibid.  Prop.  1. 


ON  ACCELERATING  FORCES.  25 

the  spaces  are  equal,  the  forces  are  as  the  squares  of  the  velocities.  Wher- 
ever the  space  and  the  force  remain  the  same,  whether  the  force  be  uniform 
or  not,  the  squares  of  any  two  velocities  with  which  different  bodies  enter 
the  space,  will  receive  equal  additions  while  they  pass  through  it. 

When  a  force  acts  in  a  direction  contrary  to  that  of  the  moving  body,  we 
may  readily  determine  the  retardation  that  it  produces,  by  comparing  the 
motion  with  that  of  a  body  accelerated  by  the  same  force.  For  the  degrees 
by  which  an  ascending  body  loses  its  motion,  are  the  same  as  those  by 
which  it  is  again  accelerated  at  the  same  points  when  it  has  acquired  its 
greatest  height  and  again  descends.  We  may  thus  calculate  to  what  height 
a  body  will  rise  when  projected  upwards  with  a  given  velocity,  and  retarded 
by  the  force  of  gravitation.  Since  the  force  of  gravitation  produces  or  de- 
stroys a  velocity  of  32  feet  in  every  second,  a  velocity  of  320  feet,  for 
instance,  will  be  destroyed  in  10  seconds  ;  and  according  to  what  has  been 
premised,  a  body  will  fall  in  10  seconds  through  a  hundred  times  16  feet, 
or  1600  feet,  which  is  therefore  the  height  to  which  a  velocity  of  320  feet 
in  a  second  will  carry  a  body  moving  without  resistance  in  a  vertical 
direction.  We  may  also  obtain  the  same  result  by  squaring  one  eighth  of 
the  velocity :  thus  one  eighth  of  320  is  40,  of  which  the  square  is  1600, 
the  height  corresponding  to  the  given  velocity  ;  and  this  velocity  is  some- 
times called  the  velocity  due  to  the  height. 


LECT.  III.— ADDITIONAL  AUTHORITIES. 

Galileo,  Discorsi  e  Dimostrazioni  Matematiche  intorno  a  due  Nuove  Scienze,! 
Leyd.  1638.  Riccioli,  Almagestum  Novum,  fol.  1641,  ii.  c.  21.  Mersenni  Cogi- 
tata  Physico-Mathematica,  fol.  Paris,  1644.  Toricellius  de  Motu  Gravium,  4to,  Flor. 
1644.  Hooke  on  Falling  Bodies,  Birch,  i.  195.  Borellus  de  Motionibus  a  Gravi- 
tate dependentibus,  4to,  Reg.  Jul.  1670.  Halley  on  Gravity,  Ph.  Tr.  1686,  xvi.  p.  3. 
Mariotte  on  the  Fall  of  Heavy  Bodies,  Hist,  et  Mem.  de  FAcad.  i.  249.  Varignon, 
ibid.  ii.  96.  See  also  x.  231,  242,  and  an.  1709,  pp.  69,  267,  H.  97  ;  an.  1719, 
p.  195,  H.  77;  an.  1720,  p.  107,  H.  97.  Camus,  an.  1726,  p.  159,  H.  73.  Riccati 
on  the  Effects  of  Attraction,  Comm.  Bon.  ii.  III.  143,  6  O.  138.  Euler,  Me- 
chanics, 1736,  Hist,  et  Mem.  Berlin,  1748,  p.  184.  Nov.  Comm.  Petrop.  ii.  144. 
Cotes  de  Descensu  Gravium,  4to,  Camb.  1770. 

On  the  Laws  of  Motion. — Hooke's  Posthumous  Works,  p.  355.  Euler,  Mec.  i.  8. 
D'Alembert,  Encyc.  au  mot  Force.  Laplace,  Mecanique  Celeste,  liv.  i.  c.  2,  §  5. 
Robison,  Mech.  Ph.  i.  121.  Playfair's  Outlines,  2  vols.  Edin.  1816,  vol.i.  Home 
and  Stewart's  Lit.  and  Phil.  Essays,  i.  Whewell,  Edin.  Journ.  of  Science,  No.  15. 
Trans,  of  the  Cambridge  Philos.  Soc.  V.  Hist,  of  the  Inductive  Sciences,  ii.  Me- 
chanics, Camb.  1828,  3rd  ed.  Poisson,  Mecanique,  i.  278.  Powell,  Nature  and 
Evidence  of  the  Primary  Laws  of  Motion,  Oxf.  1837. 


26 
LECTURE   IV. 

ON  DEFLECTIVE  FORCES. 

IT  has  been  shown  that  the  velocity  generated  by  an  accelerating  force, 
is  proportional  to  the  time  of  its  action,  and  the  space  described  to  the 
square  of  the  time.  We  are  next  to  consider  the  more  complicated  cases  of 
the  action  of  such  forces.  When  they  are  directed  to  a  certain  point  out  of 
the  line  of  the  motion  which  they  affect,  they  become  central  forces,  of 
which  we  have  an  example  in  the  force  of  gravitation,  considered  as  it 
governs  the  planetary  motions  ;  and  when  this  point  becomes  extremely 
distant  in  comparison  with  the  length  of  the  body's  path,  so  that  the  force 
acts  very  nearly  in  parallel  lines,  the  body  comes  under  the  denomination 
of  a  projectile,  as  for  instance  a  cannon  ball  projected  horizontally  or 
obliquely. 

An  accelerating  force,  therefore,  tending  to  a  point  out  of  the  line  of 
direction  of  a  moving  body,*  deflects  it  from  that  line,  and  is  then  usually 
called  a  centripetal  force.  And  the  natural  tendency  of  the  body  to  perse- 
vere in  its  rectilinear  motion,  unless  opposed  by  such  a  force,  is  sometimes 
called  a  centrifugal  force.  How  far  the  term  force  is  properly  applicable 
to  the  perseverance  of  a  body  in  its  rectilinear  motion,  may  perhaps  be 
liable  to  dispute.  If  we  allow  the  propriety  of  the  appellation,  we  must 
.  extend  the  definition  of  the  term  force  to  any  change  of  the  relative  motion 
of  two  points,  and  we  must  also  allow  the  inertia  of  a  body  to  be  justly  deno- 
*;  minated  a  force.  The  fact,  however,  is  certain,  that  all  bodies  revolving 
round  a  centre,  have  a  tendency  to  recede  from  the  centre  in  the  direction 
of  the  tangent,  and  when  this  force  is  counterbalanced  an  equal  centrifugal 
force  must  be  exerted. 

The  effects  of  a  centrifugal  force  may  be  observed  in  the  familiar  instance 
of  a  stone  placed  in  a  sling,  which  may  be  made  to  revolve  in  a  vertical 
direction,  and  even  at  the  upper  part  of  its  orbit,  may  adhere,  as  it  were, 
notwithstanding  its  weight,  to  the  sling  which  is  above  it,  in  consequence  of 
the  excess  of  the  centrifugal  force  above  the  force  of  gravitation. 

It  is  also  a  centrifugal  force  that  is  the  foundation  of  the  amusement  of  a 
boy  driving  a  hoop.  A  hoop  at  rest,  placed  on  its  edge,  would  very  quickly 
fall  to  the  ground  ;  but  when  it  is  moving  forwards,  a  slight  inclination 
towards  either  side  causes  the  parts  to  acquire  a  motion  towards  that  side, 
those  which  are  uppermost  being  most  affected  by  it ;  and  this  lateral 
motion,  assisted  sometimes  by  the  curvature  of  the  surface  of  the  hoop, 
causes  its  path  to  deviate  from  a  rectilinear  direction  ;  so  that  instead  of 
moving  straight  forwards  it  turns  to  that  side  towards  which  it  began  to 
incline ;  and  in  this  position  its  tendency  to  fall  still  further  is  counter- 
acted by  the  centrifugal  force,  and  it  generally  makes  several  complete 
revolutions  before  it  falls.  The  motion  of  a  bowl,  with  its  bias,  is  of  a 
similar  nature  ;  the  centrifugal  force  counteracting  the  tendency  to  curvi- 
*  Galileo,  Dial.  II.  p.  147. 


ON  DEFLECTIVE  FORCES.  27 

linear  motion,  so  as  to  diminish  it  very  considerably,  until  the  velocity  is 
so  much  reduced  as  to  suffer  it  to  describe  a  path  evidently  curved,  and 
becoming  more  and  more  so  as  the  motion  is  slower. 

When  a  body  is  retained  in  a  circular  orbit  by  a  force  directed  to  its 
centre,  its  velocity  is  every  where  equal  to  that  which  it  would  acquire  in 
falling,  by  means  of  the  same  force,  if  uniform,  through  half  the  radius, 
that  is,  through  one  fourth  of  the  diameter.*  This  proposition  affords  a 
very  convenient  method  of  comparing  the  effects  of  central  forces  with 
those  of  simple  accelerating  forces,  and  deserves  to  be  retained  in  memory. 
We  may  in  some  measure  demonstrate  its  truth  by  means  of  the  whirling 
table  :  an  apparatus  which  is  arranged  on  purpose  for  exhibiting  the  pro- 
perties of  central  forces,  although  it  is  more  calculated  for  showing  their 
comparative  than  their  absolute  magnitude  ;  for  accordingly  as  we  place 
the  string  on  the  pullies,  the  two  horizontal  arms  may  be  made  to  revolve 
either  with  equal  velocities,  or  one  twice  as  fast  as  the  other.  The  sliding 
stages,  which  may  be  placed  at  different  distances  from  the  centres,  and 
which  are  made  to  move  along  the  arms  with  as  little  friction  as  possible, 
are  in  a  certain  proportion  to  the  weights,  which  are  to  be  raised  by  means 
of  threads  passing  over  pullies  in  the  centres,  as  soon  as  the  centrifugal 
forces  of  the  stages  with  their  weights  are  sufficiently  great;  and  the 
experiment  is  to  be  so  arranged,  that  when  the  velocity  having  been  gradu- 
ally increased,  produces  a  sufficient  centrifugal  force,  both  stages  may  raise 
their  weights,  and  fly  off  at  the  same  instant.  But,  for  the  present  purpose, 
one  of  the  stages  only  is  required,  and  the  time  of  revolution  may  be  mea- 
sured by  a  half  second  pendulum.  We  may  make  the  force,  or  the  weight 
to  be  raised,  equal  to  the  weight  of  the  revolving  body,  and  we  shall  find 
that  this  body  will  fly  off  when  its  velocity  becomes  equal  to  that  which 
would  be  acquired  by  any  heavy  body  in  falling  through  a  height  equal  to 
half  the  distance  from  the  centre,  and  as  much  greater  as  is  sufficient  for 
overcoming  the  friction  of  the  machine.  (Plate  I.  Fig.  13.) 

From  this  proposition  we  may  easily  calculate  the  velocity  with  which  a 
sling  of  a  given  length  must  revolve,  in  order  to  retain  a  stone  in  its  place 
in  all  positions  ;  supposing  the  motion  to  be  in  a  vertical  plane,  it  is  obvious 
that  the  stone  will  have  a  tendency  to  fall  when  it  is  at  the  uppermost  point 
of  the  orbit,  unless  the  centrifugal  force  be  at  least  equal  to  the  force  of 
gravity.  Thus,  if  the  length  of  the  sling  be  two  feet,  we  must  find  the 
velocity  acquired  by  a  heavy  body  in  falling  through  a  height  of  one  foot, 
which  will  be  eight  feet  in  a  second,  since  eight  times  the  square  root  of  1 
is  eight ;  and  this  must  be  its  velocity  at  the  highest  point ;  with  this 
velocity  it  would  perform  each  revolution  in  about  a  second  and  a  half,  but 
its  motion  in  other  parts  of  its  orbit  will  be  greatly  accelerated  by  the 
gravitation  of  the  stone. 

It  may  also  be  demonstrated,  that  when  bodies  revolve  in  equal  circles, 

their  centrifugal  forces  are  proportional  to  the  squares  of  their  velocities.t 

,  Thus,  in  the  whirling  table,  the  two  stages  being  equally  loaded,  one  of 

them,  which  is  made  to  revolve  with  twice  the  velocity  of  the  other,  will 

lift  four  equal  weights  at  the  same  instant  that  the  other  raises  a  single  one. 

*  Newton,  Principia,  I.  Prop.  4,  Cor.  9.  f  Ibid.  I.  Prop.  4,  Cor.  1. 


28  LECTURE  IV. 

But  when  two  bodies  revolve  with  equal  velocities  at  different  distances, 
the  forces  are  inversely  as  the  distances ;  consequently  the  forces  are,  in  all 
cases,  directly  as  the  squares  of  the  velocities,  and  inversely  as  the  dis- 
tances. 

If  two  bodies  revolve  in  equal  times  at  different  distances,  the  forces  by 
which  they  are  retained  in  their  orbits  are  simply  as  the  distances.  If  one 
of  the  stages  of  the  whirling  table  be  placed  at  twice  the  distance  of  the 
other,  it  will  raise  twice  as  great  a  weight  when  the  revolutions  are  per- 
formed in  the  same  time. 

In  general,  the  forces  are  as  the  distances  directly,  and  as  the  squares  of 
the  times  of  revolution  inversely.*  Thus  the  same  weight  revolving  in  a 
double  time,  at  the  same  distance,  will  have  its  effect  reduced  to  one  fourth, 
but  at  a  double  distance  the  effect  will  again  be  increased  to  half  of  its 
original  magnitude. 

From  these  principles  we  may  deduce  the  law  which  was  discovered  by 
Keplerf  in  the  motions  of  the  planetary  bodies,  but  which  was  first  demon- 
strated by  NewtonJ  from  mechanical  considerations.  Where  the  forces 
vary  inversely  as  the  squares  of  the  distances,  as  in  the  case  of  gravitation, 
the  squares  of  the  times  of  revolution  are  proportional  to  the  cubes  of  the 
distances.  Thus  if  the  distance  of  one  body  be  four  times  as  great  as  that 
of  another,  the  cube  of  4  being  64,  which  is  the  square  of  8,  the  jtime  of  its 
revolution  will  be  8  times  as  great  as  that  of  the  first  body.  It  would  be 
easy  to  show  the  truth  of  this  proposition  experimentally  by  means  of  the 
whirling  table,  but  the  proof  would  be  less  striking  than  those  of  the 
simpler  laws  which  have  already  been  laid  down. 

Hitherto  we  have  supposed  the  orbit  of  a  revolving  body  to  be  a  perfect 
circle  ;  but  it  often  happens  in  nature,  as  for  instance  in  all  the  planetary 
motions,  that  the  orbit  deviates  more  or  less  from  a  circular  form  ;  and  in 
such  cases  we  may  apply  another  very  important  law  which  was  also 
discovered  by  Kepler  ;§  that  the  right  line  joining  a  revolving  body  and  its 
centre  of  attraction,  always  describes  equal  areas  in  equal  times,  and  the 
velocity  of  the  body  is  therefore  always  inversely  as  the  perpendicular 
drawn  from  the  centre  to  the  tangent.  (Plate  I.  Fig.  14.) 

The  demonstration  of  this  law  invented  by  Newton,  ||  was  one  of  the  most 
elegant  applications  of  the  geometry  of  infinites  or  indivisibles  ;  a  branch  of 
mathematics  of  which  Archimedes  laid  the  foundations,  which  Cavalleri** 
and  Wallistt  greatly  advanced,  and  which  Newton^  brought  near  to  per- 
fection. Its  truth  may  be  in  some  measure  shown  by  an  experiment  on  the 
revolution  of  a  ball  suspended  by  a  long  thread,  and  drawn  towards  a  point 
immediately  under  the  point  of  suspension  by  another  thread,  which  may 

*  Principia,  I.  Prop.  4,  Cor.  2.  f  Harmonice  Mundi,  lib.  v.  cap.  3,  §  8. 

J  Principia,  I.  Prop.  4,  Cor.  6;  and  Prop.  15. 

§  On  the  Motion  of  Mars,  1609,  p.  194.         ||  Principia,  I.   1. 

**  Exercitationes  Geometricse,  Bonon.  1647. 

ft  Arithmetica  Innnitorum,  Op.  fol.  Ox.  1699,  v.  i.  p.  365. 

JJ  Fluxions,  Trans,  by  Colson,  4to,  1736,  Ph.  Trans.  No.  432.  Consult  also 
Taylor,  Methodus  Incrementorum,  4to,  1715.  Maclaurin's  Fluxions,  2  vols.  4  to, 
Lond.  1742.  Euler,  Calculus  Dif.  et  int.  4  vols.  4to,  Pet.  1792.  Lacroix,  Traitc 
du  Calcul  Dif.  3  vols.  4to,  Paris.  Lagrange,  Calcul  des  Fonctions. 


ON  DEFLECTIVE  FORCES.  29 

either  be  held  in  the  hand,  or  have  a  weight  attached  to  it.  The  ball  being 
made  to  revolve,  its  motion  becomes  evidently  more  rapia  when  it  is  drawn 
by  the  horizontal  thread  nearer  to  the  fixed  point,  and  slower  when  it  is 
suffered  to  fly  off  to  a  greater  distance.  (Plate  II.  Fig.  15.) 

It  was  also  discovered  by  Kepler*  that  each  of  the  planets  revolves  in  an 
ellipsis,  of  which  the  sun  occupies  one  of  the  foci.  It  is  well  known  that  an 
ellipsis  is  an  oval  figure,  which  may  be  described  by  fixing  the  ends  of  a 
thread  to  two  points,  and  moving  a  tracing  point  so  that  it  may  always  be 
at  the  point  of  the  angle  formed  by  the  thread  ;  and  that  the  two  fixed 
points  are  called  its  foci.  The  inference  respecting  the  force  by  which  a 
body  may  be  made  to  revolve  in  an  ellipsis,  was  first  made  by  Newton  ;t 
that  is,  that  the  force  directed  to  its  focus  must  be  inversely  as  the  square 
of  the  distance.  We  have  no  other  experimental  proof  of  this  theorem  than 
astronomical  observations,  which  are  indeed  perfectly  decisive,  but  do  not 
i  require  to  be  here  anticipated.  (Plate  II.  Fig.  16.) 

There  is  another  general  proposition  which  is  sometimes  of  use  in  the 
comparison  of  rectilinear  and  curvilinear  motions.  Two  bodies  being  at- 
tracted in  the  same  manner  towards  a  given  centre,  that  is,  with  equal 
forces  at  equal  distances,  if  their  velocities  be  once  equal  at  equal  distances, 
they  will  remain  always  equal  at  equal  distances  whatever  be  their  direc- 
tions. J  For  instance,  if  one  cannon  ball  be  shot  obliquely  upwards,  and 
another  perpendicularly  upwards  with  the  same  velocity,  the  one  will 
describe  a  curve,  and  the  other  a  straight  line,  but  their  velocities  will 
always  remain  equal,  not  at  the  same  instants  of  time,  but  at  equal  distances 
from  the  earth's  centre,  or  after  having  ascended  through  equal  vertical 
heights,  although  in  different  directions.  This  proposition  has  usually 
been  made  a  step  in  the  demonstration  of  the  law  of  the  force  by  which  a 
body  is  made  to  revolve  in  an  ellipsis,  but  there  is  a  much  simpler  method 
of  demonstrating  that  law,  by  means  of  some  properties  of  the  curvature  of 
the  ellipsis. 

In  treating  of  the  motion  of  projectiles,  the  force  of  gravitation  may, 
without  sensible  error,  be  considered  as  an  equable  force,  acting  in  parallel 
lines  perpendicular  to  the  horizon.  In  reality,  if  we  ascend  a  mile  from 
the  earth's  surface,  the  actual  weight  of  a  body  is  diminished  about  a  two 
thousandth  part,  or  three  grains  and  a  half  for  every  pound  ;  and  we  may 
discover  this  inequality  by  means  of  the  vibrations  of  pendulums,  which 
become  a  little  slower  when  they  are  placed  on  the  summits  of  very  high 
mountains.  On  the  other  hand,  a  body  not  specifically  heavier  than  water 
gains  more  in  apparent  weight  on  account  of  the  diminished  density  of  the 
atmosphere  at  great  elevations,  than  it  loses  by  the  increase  of  its  distance 
from  the  earth.  But  both  these  differences  may,  in  all  common  calcula- 
tions, be  wholly  disregarded.  The  direction  of  gravity  is  always  exactly 
perpendicular  to  the  horizon,  that  is,  to  the  surface  of  the  earth,  which  is 
somewhat  curved,  on  account  of  the  earth's  spheroidical  figure ;  but  any 
small  portion  of  this  surface  may  be  practically  considered  as  a  plane,  and 
the  vertical  lines  perpendicular  to  it  as  parallel  to  each  other. 

*  On  the  Motion  of  Mars,  c.  58.  f  Principia,  I.  11. 

J  Prop.  40. 


30  LECTURE  IV. 

The  oblique  motion  of  a  projectile  may  be  the  most  easily  understood  by 
resolving  its  velocity  into  two  parts — the  one  in  a  horizontal,  the  other  in  a 
vertical  direction.  It  appears  from  the  doctrine  of  the  composition  of 
motion,  that  the  horizontal  velocity  will  not  be  affected  by  the  force  of 
gravitation  acting  in  a  direction  perpendicular  to  it,  and  that  it  will,  there- 
fore, continue  uniform  ;  and  that  the  vertical  motion  will  also  be  the  same 
as  if  the  body  had  no  horizontal  motion.  Thus,  if  we  let  fall  from  the 
head  of  the  mast  of  a  ship  a  weight  which  partakes  of  its  progressive 
motion,  the  weight  will  descend  by  the  side  of  the  mast  in  the  same  manner 
and  with  the  same  relative  velocity  as  if  neither  the  ship  nor  the  weight 
had  any  horizontal  motion. 

We  may,  therefore,  always  determine  the  greatest  height  to  which  a  pro- 
jectile will  rise,  by  finding  the  height  from  which  a  body  must  fall  in  order 
to  gain  a  velocity  equal  to  its  vertical  velocity,  or  its  velocity  of  ascent ; 
that  is,  by  squaring  one  eighth  of  the  number  of  feet  that  it  would  rise  in  the 
first  second  if  it  were  not  retarded.  For  example,  suppose  a  musket  to  be  so 
elevated  that  the  muzzle  is  higher  than  the  but-end  by  half  of  the  length, 
that  is,  at  an  angle  of  30° ;  and  let  the  ball  be  discharged  with  a  velocity 
of  1000  feet  in  a  second  ;  then  its  vertical  velocity  will  be  half  as  great,  or 
500  feet  in  a  second  ;  now  the  square  of  one  eighth  of  500  is  3906,  conse- 
quently the  height  to  which  the  ball  would  rise,  if  unresisted  by  the  air,  is 
3906  feet,  or  three  quarters  of  a  mile.  But,  in  fact,  a  musket  ball  actually 
shot  upwards,  with  a  velocity  of  1670  feet  in  a  second,  which  would  rise 
six  or  seven  miles  in  a  vacuum,  is  so  retarded  by  the  air,  that  it  does  not 
attain  the  height  of  a  single  mile. 

We  may  easily  find  the  time  of  the  body's  ascent  from  its  initial  velocity ; 
for  the  time  of  ascent  is  directly  proportional  to  the  velocity,  and  may  be 
found  in  seconds  by  dividing  the  vertical  velocity  in  feet  by  32  ;  or  if  we 
divide  by  16  only  we  shall  have  the  time  of  ascent  and  descent ;  and  then 
the  horizontal  range  may  be  found,  by  calculating  the  distance  described 
in  this  time  with  the  uniform  horizontal  velocity.  Thus,  in  the  example 
that  we  have  assumed,  dividing  500  by  16  we  have  31  seconds  for  the 
whole  time  of  the  range  ;  but  the  hypotenuse  of  our  triangle  being  1000, 
and  the  perpendicular  500,  the  base  will  be  886  feet ;  consequently  the  hori- 
zontal range  is  31  times  886,  that  is,  nearly  28,000  feet,  or  above  5  miles. 
But  the  resistance  of  the  air  will  reduce  this  distance  also  to  less  than  one 
mile. 

It  may  be  demonstrated  that  the  horizontal  range  of  a  body,  projected 
with  a  given  velocity  is  always  proportional  to  the  sine  of  twice  the  angle 
of  elevation  :  that  is,  to  the  £sine  of  the  angle  of]  elevation  of  the  muzzle  of 
the  piece  in  a  situation  twice  as  remote  from  a  horizontal  position  as  its 
actual  situation.  Hence  it  follows,  that  the  greatest  horizontal  range  will 
be  when  the  elevation  is  half  a  right  angle  ;*  supposing  the  body  to  move 
in  a  vacuum.  But  the  resistance  of  the  air  increases  with  the  length  of 
the  path,  and  the  same  cause  also  makes  the  angle  of  descent  much  greater 
than  the  angle  of  ascent,  as  we  may  observe  in  the  track  of  a  bomb.  For 
both  these  reasons,  the  best  elevation  is  somewhat  less  than  45°,  and  some- 
*  Galileo,  Dial.  IV.  Prop.  7,  cor. 


ON  DEFLECTIVE  FORCES.  SI 

times,  when  the  velocity  is  very  great,  as  little  as  30°.  But  it  usually 
happens,  in  the  operations  of  natural  causes,  that  near  the  point  where  any 
quantity  is  greatest  or  least,  its  variation  is  slower  than  elsewhere  ;  a  small 
difference,  therefore,  in  the  angle  of  elevation,  is  of  little  consequence  to  the 
extent  of  the  range,  provided  that  it  continue  between  the  limits  of  45°  and 
35°  ;  and  for  the  same  reason,  the  angular  adjustment  requires  less  accuracy 
in  this  position  than  in  any  other,  which,  besides  the  economy  of  powder, 
makes  it  the  best  elevation  for  practice.  (Plate  II.  Fig.  17,  18.) 

The  path  of  a  projectile,  supposed  to  move  without  resistance,  is  always 
a  parabola.  This  interesting  proposition  was  first  discovered  by  Galileo  :* 
it  follows  very  readily  from  the  doctrine  of  the  composition  of  motion,  com- 
bined with  the  laws  which  that  philosopher  established  concerning  the  fall 
of  heavy  bodies.  If  from  any  points  of  a  given  right  line,  as  many  lines  be 
drawn,  parallel  to  each  other,  and  proportional  to  the  squares  of  the  corre- 
sponding segments  of  the  first  line,  the  curve  in  which  all  their  extremities 
are  found,  is  a  parabola.  Now  supposing  the  first  line  to  be  placed  in  the 
direction  of  the  initial  motion  of  a  projectile,  and  parallel  vertical  lines  to  be 
drawn  through  any  points  of  it,  proportional  to  the  squares  of  the  segments 
which  they  cut  off,  these  lines  will  represent  the  effect  of  gravitation,  during 
the  times  in  which  the  same  segments  would  have  been  described,  by  the 
motion  of  projection  alone ;  consequently  the  projectile  will  always  be 
found  at  the  extremity  of  the  vertical  line  corresponding  to  the  time 
elapsed,  and  will  therefore  describe  a  parabola.  (Plate  II.  Fig.  17, 19.) 

It  is  easy  to  show  by  experiment,  that  the  path  of  a  projectile  is  a  para- 
bola :  if  we  only  let  a  ball  descend  from  a  certain  point,  along  a  grobve,  so 
as  to  acquire  a  known  velocity,  we  may  trace  on  a  board  the  parabola  which 
it  will  afterwards  describe  during  its  free  descent ;  and  by  placing  rings  at 
different  parts  of  the  curve,  we  may  observe  that  it  will  pass  through  them 
all  without  striking  them.  (Plate  II.  Fig.  19.) 

In  practical  cases,  on  a  large  scale,  where  the  velocity  of  a  projectile  is 
considerable,  the  resistance  of  the  atmosphere  is  so  great  as  to  render  the 
Galilean  propositions  of  little  or  no  use  ;  and  a  complete  determination  of 
the  path,  including  all  the  circumstances  which  may  influence  it,  is  attended 
with  difficulties  almost  insuperable.  It  appears  from  Robins's  experi- 
ments, that  the  resistance  of  the  air  to  an  iron  ball  of  4|  inches  in  diameter, 
moving  at  the  rate  of  800  feet  in  a  second,  is  equal  to  four  times  its  weight, 
and  that  where  the  velocity  is  much  greater  the  resistance  increases  far 
more  rapidly.t  But  what  must  very  much  diminish  the  probability  of  our 
deriving  any  great  practical  advantage  from  the  theory  of  gunnery,  is  an 
observation,  made  also  by  Mr.  Robins,  that  a  ball  sometimes  deviates  three 
or  four  hundred  yards  laterally,  without  any  apparent  reason  ;  J  so  that  we 
cannot  be  absolutely  certain  to  come  within  this  distance  of  our  mark  in  any 
direction.  The  circumstance  is  probably  owing  to  an  accidental  rotatory  mo- 
tion communicated  to  the  ball  in  its  passage  through  tKe  piece,  causing  after- 
wards a  greater  friction  from  the  air  on  one  side  than  on  the  other ;  and  it  may 
'in  some  measure  be  remedied  by  employing  a  rifle  barrel,  which  determines 

*  Dialogues  on  Motion,  Dial.  IV. 
f  Mathematical  Tracts,  2  vols.  1761,  i.  131.  J  Ibid.  p.  150. 


32  LECTURE  V. 

the  rotation  of  the  ball  in  such  a  manner  that  its  axis  coincides  at  first  with 
the  path  of  the  ball,  so  that  the  same  face  of  the  ball  is  turned  in  succession 
every  way.  For  the  ordinary  purposes  of  gunnery,  an  estimation  governed 
by  experience  is  found  to  be  the  best  guide ;  at  the  same  time  there  is  no 
doubt  but  that  some  assistance  may  be  obtained  from  theory  and  from  ex- 
periment. Those  who  are  desirous  of  pursuing  the  subject  may  find  much 
information  relating  to  it,  collected  by  Professor  Robison,  in  the  article 
'Projectile'  of  the  Encyclopaedia  Britannica. 


LECT.  IV.— ADDITIONAL  AUTHORITIES. 

Central  Forces. — Hooke,  Birch's  History  of  the  Royal  Society,  ann.  1664-6,  ii. 
69,  90.  Huygens  de  vi  centrifuga,  Op.  post ;  de  causa  gravitatis,  1690.  Keill,  Ph. 
Tr.  1708,  p.  174;  1714,  p.  91.  Demoivre,  Ph.  Tr.  1717,  p.  622.  Maclaurin, 
Geom.  Organ.  4to,  1720.  Louville,  Hist,  et  Mem.  de  1'Acad.  de  Paris,  1720.  Mau- 
pertuis,  ibid.  1732,  p.  343,  H.  112.  Montigny,  1741,  p.  280,  H.  143.  Bosco- 
vich,  Com.  Bon.  II.  iii.  262.  Waring,  Ph.  Tr.  1788,  p.  67.  Manchester  Memoirs, 
iv.  369  ;  v.  101.  Trembley,  Hist,  et  Mem.  de  1'Acad.  de  Berlin,  1797,  p.  36. 
Brinkley,  Trans,  of  the  Royal  Irish  Academy,  viii.  215.  Lagrange,  Miscellanea 
Taurinensia,  ii.  II.  and  iv.  IV.  Airy  on  Gravitation,  1834. 

On  Projectiles  and  Gunnery. — Frisius,  Cosmographia,  iv.  Antwerp,  1584.  Digges 
on  the  Art  of  Great  Artillery,  4to,  1624.  Halley,  Ph.  Tr.  1686,  p.  3  ;  1695,  p.  68. 
Bernoulli,  Comm.  Physico-Math.  Paris,  1710.  Keill,  Ph.  Trans.  1715,  p.  91. 
T.  Simpson,  ibid.  1748,  p.  137.  Robins,  ibid.  1743,  xlii.  437;  and  Mathematical 
Tracts,  2  vols.  1761.  Borda,  Hist,  et  Mem.deFAcad.  de  Paris,  1769,  p.  247,  H.  116. 
Glenie,  History  of  Gunnery,  Edin.  1776.  Brown,  The  True  Principles  of  Gunnery, 
4to,  1777  (partly  a  translation  from  Euler).  Hutton,  Ph.Tr.  1778,  p.  50  ;  Tracts,  4to, 
1786,  v.  3.  Pringle,  A  Discourse  on  the  Theory  of  Gunnery,  4to,  1778.  Thompson 
(Count  Rumford),  Ph.  Tr.  1781,  p.  229  ;  1797,  p.  222.  Inman,  An  Introduction  to 
Naval  Gunnery,  Portsea,  1828. 


LECTURE   V. 


ON  CONFINED   MOTION. 

WE  have  hitherto  considered  the  principal  cases  of  motion,  either  un- 
disturbed, or  simply  subjected  to  the  action  of  an  accelerating,  retarding,  or 
deflective  force.  We  now  proceed  to  examine  the  effects  of  an  additional 
modification,  which  is  introduced  when  the  motion  is  limited  to  a  given 
line  or  surface  of  any  kind  ;  the  body  either  being  supposed  to  slide  on  the 
surface  of  a  solid  actually  extended,  or  being  confined  to  an  imaginary  sur- 
face by  its  attachment  to  a  thread,  or  still  more  narrowly  restricted  by 
means  of  two  threads,  which  allow  it  to  move  only  in  a  given  line.  Sus- 
pension is  the  most  convenient  mode  of  making  experiments  on  confined 
motion  ;  but  it  is  not  always  easy  to  cause  the  body  to  remain  in  the  sur- 
face that  is  required  ;  and  to  confine  it  in  this  manner  to  a  perfectly  plane 
surface  is  impossible.  When  we  suffer  a  body  to  slide  along  any  surface, 
there  is  a  loss  of  force  from  friction,  from  the  production  of  rotatory 
motion,  or  from  both  these  causes  combined.  The  effect  of  friction  is 


ON  CONFINED  MOTION.  33 

obvious  and  well  known  ;  and  we  may  be  convinced  of  the  retardation  at- 
tendant on  the  production  of  rotatory  motion,  by  allowing  two  cylinders, 
of  equal  dimensions,  to  roll  down  an  inclined  plane  :  the  one  being  covered 
with  sheet  lead,  the  other  having  an  equal  weight  of  lead  in  its  axis,  and 
being  covered  with  paper,  and  both  having  similar  projecting  surfaces  at 
the  ends, which  come  into  contact  with  the  plane,  we  may  easily  observe  that 
in  the  first  cylinder,  much  more  of  the  force  is  consumed  in  producing 
rotatory  motion,  than  in  the  second,  and  that  it  therefore  descends  much 
more  slowly.  (Plate  II.  Fig.  20.) 

When  a  body  is  placed  on  an  inclined  plane,  the  force  urging  it  to 
descend,  in  the  direction  of  the  plane,  is  to  the  whole  force  of  gravity  as 
the  height  of  the  plane  is  to  its  length.  This  is  demonstrable  from  the  prin- 
ciples of  the  composition  of  motion,  and  may  also  be  shown  experimentally 
with  great  accuracy,  when  we  consider  the  doctrine  of  the  equilibrium  of 
forces.  But  the  interference  of  friction  will  only  allow  us  to  observe,  with 
respect  to  the  velocities  produced,  that  they  nearly  approach  to  those  which 
the  calculation  indicates.  Thus,  if  a  plane  be  inclined  one  inch  in  32,  a 
ball  will  descend  on  it  in  two  seconds,  instead  of  64  feet,  somewhat  less 
than  two  feet. 

It  may  be  deduced  from  the  laws  of  accelerating  forces,  that  when 
bodies  descend  on  any  inclined  planes  of  equal  heights,  but  of  different  in- 
clinations, the  times  of  descent  are  as  the  lengths  of  the  planes,  and  the 
final  velocities  are  equal.  Thus  a  body  will  acquire  a  velocity  of  32  feet  in  a 
second,  after  having  descended  16  feet  either  in  a  vertical  line,  or  in  an  oblique 
direction  ;  but  the  time  of  descent  will  be  as  much  greater  than  a  second  as 
the  oblique  length  of  the  path  is  greater  than  16  feet.  This  may  be  shown 
by  experiment,  as  nearly  as  the  obstacles  already  mentioned  will  permit, 
the  times  being  measured  by  a  pendulum  or  by  a  stop  watch.  (Plate  II. 
Fig.  21.) 

There  is  an  elegant  proposition,  of  a  similar  nature,  which  is  still  more 
capable  of  experimental  confirmation ;  that  is,  that  the  times  of  falling 
through  all  chords  drawn  to  the  lowest  point  of  a  circle  are  equal.  If  two 
or  more  bodies  are  placed  at  different  points  of  a  circle,  and  suffered  to 
descend  at  the  same  instant  along  as  many  planes  which  meet  in  the  lowest 
point  of  the  circle,  they  will  arrive  there  at  the  same  time.  (Plate  II. 
Fig.  22.) 

The  velocity  of  a  body  descending  along  a  given  surface,  is  the  same  as 
that  of  a  body  falling  freely  through  an  equal  height,  not  only  when  the 
surface  is  a  plane,  but  also  when  it  is  a  continued  curve,  in  which  the 
body  is  retained  by  its  attachment  to  a  thread,  or  is  supported  by  any 
regular  surface,  supposed  to  be  free  from  friction.*  We  may  easily  show, 
by  an  experiment  on  a  suspended  ball,  that  its  velocity  is  the  same  when 
it  descends  from  the  same  height,  whatever  may  be  the- form  of  its  path,  by 
observing  the  height  to  which  it  rises  on  the  opposite  side  of  the  lowest 
point.  We  may  alter  the  form  of  the  path  in  which  it  descends,  by  placing 
pins  at  different  points,  so  as  to  interfere  with  the  thread  that  supports  the 
ball,  and  to  form  in  succession  temporary  centres  of  motion  ;  and  we  shall 
*  Principia,  i.  40. 

D 


34  LECTURE  V. 

find,  in  all  cases,  that  the  body  ascends  to  a  height  equal  to  that  from 
which  it  descended,  with  a  small  deduction  on  account  of  friction.  (Plate 
II.  Fig.  23.) 

Hence  is  derived  the  idea  conveyed  hy  the  term  living  or  ascending  force ; 
for  since  the  height  to  which  a  body  will  rise  perpendicularly,  is  as  the 
square  of  its  velocity,  it  will  preserve  a  tendency  to  rise  to  a  height  which 
is  as  the  square  of  its  velocity  whatever  may  be  the  path  into  which  it  is 
directed,  provided  that  it  meet  with  no  abrupt  angle,  or  that  it  rebound  at 
each  angle  in  a  new  direction  without  losing  any  velocity.  The  same  idea 
is  somewhat  more  concisely  expressed  by  the  term  energy,  which  indicates 
the  tendency  of  a  body  to  ascend  or  to  penetrate  to  a  certain  distance,  in 
opposition  to  a  retarding  force. 

The  most  important  cases  of  the  motion  of  bodies,  confined  to  given  sur- 
faces, are  those  which  relate  to  the  properties  of  pendulums.  Of  these 
the  simplest  is  the  motion  of  a  body  in  a  cycloidal  path.  The  cycloid 
is  a  curve  which  has  many  peculiarities  ;  we  have  already  seen  that  it  is 
described  by  marking  the  path  of  a  given  point  in  the  circumference  of  a 
circle  which  rolls  on  a  right  line.  [p.  19.]  Galileo  was  the  first  that  con- 
sidered it  with  attention,  but  he  failed  in  his  attempts  to  investigate  its 
properties.*  It  is  singular  enough,  that  the  principal  cause  of  his  want  of 
success  was  an  inaccurate  experiment :  in  order  to  obtain  some  previous 
information  respecting  the  area  included  by  it,  he  cut  a  board  into  a 
cycloidal  form,  and  weighed  it,  and  he  inferred  from  the  experiment  that 
the  area  bore  some  irrational  proportion  to  that  of  the  describing  circle, 
while  in  fact  it  is  exactly  triple.  In  the  same  manner  it  has  happened  in 
later  times,  that  Newton,  in  his  closet,  determined  the  figure  of  the  earth 
more  accurately  than  Cassini  from  actual  measurement.t  It  was  Huygens  ^ 
that  first  demonstrated  the  properties  of  the  cycloidal  pendulum,  which  are 
of  still  more  importance  in  the  solution  of  various  mechanical  problems, 
than  for  the  immediate  purposes  of  timekeepers,  to  which  that  eminent 
philosopher  intended  to  apply  them.  (Plate  I.  Fig.  5.) 

If  a  body  be  suspended  by  a  thread  playing  between  two  cycloidal 
cheeks,  it  will  describe  another  equal  cycloid  by  the  evolution  of  the 
thread,  and  the  time  of  vibration  will  be  the  same,  in  whatever  part  of  the 
curve  it  may  begin  to  descend. §  Hence  the  vibrations  of  a  body  moving 
in  a  cycloid  are  denominated  isochronous,  or  of  equal  duration.  This 
equality  may  be  shown  by  letting  go  two  pendulous  balls  at  the  same  in- 

*  On  the  authority  of  Toricelli,  Op.  1644.  Consult  Wallis,  Op.  3  vols.  fol.  Oxf. 
1699,  i.  543,  and  Ph.  Tr.  xix.  Ill,  561.  The  cycloid  was  known  to  Cusanus  1454, 
and  to  Bovillus  1500,  a  century  before  it  was  considered  by  Galileo.  See  Leibnitz, 
Op.  iii.  95,  and  British  Magazine  for  1800. 

f  Cassini,  from  his  father's  and  M.  Picard's  measurements,  proved  that  the  earth 
must  be  a  spheroid,  whose  axis  is  greater  than  its  equatorial  diameter.  Newton  de- 
duced the  contrary  from  theory;  and  it  is  so  in  fact.  See  Mem.  de  1'Acad.  1713, 
1718.  Newton's  Principia,  and  Ph.  Tr.  1725,  pp.  33,  201,  239,  277,  344.  Against 
Mairan,  Mem.  de  1'Acad.  1720. 

J  Horologium  Oscillatorium,  fol.  Paris,  1673. 

§  Ibid.  Compare  Part  I.  with  Prop.  25,  Part  II.  In  Birch's  History  of  the 
Royal  Soc.  is  found  an  investigation  of  the  same  property  by  Lord  Brouncker, 
registered  Jan.  22,  1662.  The  president  was  ordered  to  send  a  copy  of  it  to  Huy- 
gens. 


ON  CONFINED  MOTION.  35 

slant,  at  different  points  of  the  curve,  and  observing  that  they  meet  at  the 
lowest  point.     (Plate  II.  Fig.  24.) 

The  absolute  time  of  the  descent  or  ascent  of  a  pendulum,  in  a  cycloid, 
is  to  the  time  in  which  any  heavy  body  would  fall  through  one  half  of  the 
length  of  the  thread,  as  half  the  circumference  of  a  circle  to  its  diameter.* 
It  is,  therefore,  nearly  equal  to  the  time  required  for  the  descent  of  a 
body  through  -|  of  the  length  of  the  thread  ;  and  if  we  suffer  the  pendulum 
to  descend,  at  the  same  moment  that  a  body  falls  from  a  point  elevated 
one  fourth  of  the  length  of  the  thread  above  the  point  of  suspension,  this 
body  will  meet  the  pendulum  at  the  lowest  point  of  its  vibration.  (Plate 
II.  Fig.  24.) 

Hence  it  may  readily  be  inferred,  that  since  the  times  of  falling  through 
any  spaces  are  as  the  square  roots  of  those  spaces,  the  times  of  vibration 
of  different  pendulums  are  as  the  square  roots  of  their  lengths.  Thus,  the 
times  of  vibration  of  pendulums  of  1  foot  and  4  foot  in  length,  will  be  as 
1  to  2  :  the  time  of  vibration  of  a  pendulum  39-rW  inches  in  length  is  one 
second  ;  the  length  of  a  pendulum  vibrating  in  two  seconds  must  be  four 
times  as  great. 

The  velocity  with  which  a  pendulous  body  moves,  at  each  point  of  a 
cycloidal  curve,  may  be  represented,  by  supposing  another  pendulum  to 
revolve  uniformly  in  a  circle,  setting  out  from  the  lowest  point,  at  the  same 
time  that  the  first  pendulum  begins  to  move,  and  completing  its  revolution 
in  the  time  of  two  vibrations  ;  then  the  height,  acquired  by  the  pendulum 
revolving  equably,  will  always  be  equal  to  the  space  described  by  the 
pendulum  vibrating  in  the  cycloid.  (Plate  II.  Fig.  24.) 

It  may  also  be  shown,  that  if  the  pendulum  vibrate  through  the  whole 
curve,  it  will  everywhere  move  with  the  same  velocity  as  the  point  of  the 
circle  which  is  supposed  to  have  originally  described  the  cycloid,  pro- 
vided that  the  circle  roll  onwards  with  an  equable  motion. 

All  these  properties  depend  on  this  circumstance,  that  the  relative  force, 
urging  the  body  to  descend  along  the  curve,  is  always  proportional  to  the 
distance  from  the  lowest  point ;  and  it  happens  in  many  other  instances  of 
the  action  of  various  forces,  that  a  similar  law  prevails  :  in  all  such  cases, 
the  vibrations  are  isochronous,  and  the  space  described  corresponds  to  the 
versed  sine  of  a  circular  are  increasing  uniformly,  that  is  to  the  height  of 
any  point  of  a  wheel  revolving  uniformly  on  its  axis,  or  rolling  uniformly 
on  a  horizontal  plane. 

The  cycloid  is  the  curve  in  which  a  body  may  descend  in  the  shortest 
possible  time,  from  a  given  point  to  another  obliquely  below  it.t  It  may 
easily  be  shown  that  a  body  descends  more  rapidly  in  a  cycloid  than  in  the 
right  line  joining  the  two  points.  This  property  is  of  little  practical 
utility  ;  the  proposition  was  formerly  considered  as  somewhat  difficult  to 
be  demonstrated,  but  of  late,  from  the  invention  of  new  modes  of  calcula- 

,  *  Huyg.  Horol.  Oscil.  Part  II.  Prop.  25. 

t  Jo.  Bernoulli,  Acta  Erudit.  Lips.  1696,  p.  269.  Ja.  Bernoulli,  ibid.  1697,  p. 
211,  and  Opera,  ii.  768.  Euler,  Acta  Petrop.  1733,  &c.  &c.  Lagrange,  Miscella- 
nea Taurinensia,  vols.  i.  and  ii.  Consult  Woodhouse's  Isoperimetrical  Problems, 
Camb.  1810  ;  or  the  article  Variations  in  the  Encyc.  Brit. 

D  2 


3G  LECTURE  V. 

tion,  theorems  of  a  similar  nature  have  been  much  extended  with  great 
facility.  The  experiment  naturally  suggests  a  familiar  proverb,  which 
cautions  us  against  being  led  away  too  precipitately  by  an  appearance  of 
brevity  and  facility.  (Plate  II.  Fig.  25.) 

It  has  been  found  that  the  inconveniences,  resulting  from  the  compli- 
cated apparatus  necessary  to  introduce  a  cycloidal  motion  for  the  pen- 
dulums of  clocks,  are  more  than  equivalent  to  the  advantage  of  perfect 
isochronism  in  theory.  For  since  in  small  cycloidal  arcs  the  curvature  is 
nearly  constant,  the  time  of  vibration  of  a  simple  circular  pendulum  must 
be  ultimately  the  same  as  that  of  a  cycloidal  pendulum  of  the  same  length ; 
but  in  larger  arcs,  the  time  must  be  somewhat  greater,  because  the  circular 
arc  falls  without  the  cycloidal,  and  is  less  inclined  to  the  horizon  at 
equal  distances  from  the  lowest  point.  This  may  be  shown  by  a  compa- 
rison of  two  equal  pendulums,  vibrating  in  arcs  of  different  extent :  it 
may  also  be  observed,  by  an  experiment  with  two  simple  pendulums  of 
different  lengths,  that  their  times  of  vibration,  like  those  of  cycloidal 
pendulums,  are  proportional  to  the  square  roots  of  their  lengths ;  a  half 
second  pendulum  being  only  one  fourth  as  long  as  a  pendulum  vibrating 
seconds. 

We  have  been  obliged  to  suppose  the  weight,  as  well  as  the  inertia,  of  a 
pendulum,  to  be  referred  to  one  point,  since  we  are  not  at  present  prepared 
to  examine  the  effect  of  the  slight  difference  between  the  situations  and  the 
velocities  of  the  different  parts  of  the  substances,  employed  in  our  experi- 
ments. The  nature  of  rotatory  motion  requires  to  be  more  fully  under- 
stood, before  we  can  attend  to  the  determination  of  the  centres  of  oscillation 
of  bodies  of  various  figures,  that  is,  of  the  points  in  which  their  whole  weight 
may  be  supposed  to  be  concentrated,  with  regard  to  its  effect  on  the  times 
of  their  vibrations. 

It  is  remarkable  that  the  isochronism  of  pendulums,  which  is  a  property 
so  important  in  its  application,  may  still  be  preserved,  notwithstanding 
the  interference  of  a  constant  retarding  force,  such  as  the  force  of  friction 
is  in  many  cases  found  to  be.  It  has  been  shown  by  Newton,*  that  each 
complete  vibration  of  a  cycloidal  pendulum,  retarded  by  a  resistance  of 
this  nature,  will  be  shorter  than  the  preceding  one  by  a  certain  constant 
space,  but  that  it  will  be  performed  in  the  same  time. 

There  is  a  great  analogy  between  the  vibrations  of  pendulums,  and  the 
revolution  of  balls  suspended  from  a  fixed  point.  If  a  body,  suspended 
by  a  thread,  revolve  freely  in  a  horizontal  circle,  the  time  of  revolution 
will  be  the  same,  whenever  the  height  of  the  point  of  suspension  above  the 
plane  of  revolution  is  the  same,  whatever  be  the  length  of  the  thread. 
Thus,  if  a  number  of  balls  are  fixed  to  threads,  or  rather  wires,  connected 
to  the  same  point  of  an  axis,  which  is  made  to  revolve  by  means  of  the 
whirling  table,  they  will  so  arrange  themselves  as  to  remain  very  nearly  in 
the  same  horizontal  plane.  (Plate  II.  Fig.  26.) 

The  time  of  each  revolution  of  the  balls  is  equal  to  the  time  occupied  by 
a  double  vibration  of  a  pendulum,  of  which  the  length  is  equal  to  the 
height  of  the  point  of  suspension  above  the  plane  in  which  they  revolve  ; 
*  Principia,  Book  II.  sec.  6. 


ON  CONFINED  MOTION.  37 

consequently  all  the  revolutions  will  be  nearly  isochronous,  while  the 
threads  or  wires  deviate  hut  little  from  a  vertical  situation.*  In  fact,  we 
may  imagine  such  a  revolution  to  be  composed  of  two  vibrations  of  a 
simple  pendulum,  existing  at  the  same  time,  in  directions  at  right  angles 
to  each  other  ;  for  while  a  pendulum  is  vibrating  from  north  to  south,  it 
is  liable  to  the  impression  of  any  force,  capable  of  causing  a  vibration  from 
east  to  west ;  and  the  joint  result  of  both  vibrations  will  be  a  uniform 
revolution  in  a  circle,  if  the  vibrations  are  equal  and  properly  combined  ; 
but  if  they  are  unequal,  the  joint  vibration  will  be  ultimately  an  ellipsis, 
the  joint  force  being  directed  to  its  centre,  and  always  proportional  to 
the  distance  from  that  centre.  (Plate  II.  Fig.  27.) 

The  near  approach  of  these  revolutions  to  isochronism  has  sometimes 
been  applied  to  the  measurement  of  time,  but  more  frequently,  and  more 
successfully  to  the  regulation  of  the  motions  of  machines.  Thus  in  Mr. 
Watt's  steam  engines,  two  balls  are  fixed  at  the  ends  of  rods  in  continual 
revolution,  and  as  soon  as  the  motion  becomes  a  little  too  rapid,  the  balls 
rise  considerably,  and  turn  a  cock  which  diminishes  the  quantity  of  steam 
admitted.  (Plate  II.  Fig.  28.) 

The  same  laws  are  applicable  to  many  other  cases  of  rotatory  motion  ; 
for  instance,  if  we  wish  to  determine  the  height,  at  which  a  ball,  revolving 
with  a  given  velocity,  will  be  retained  in  a  spherical  bowl,  or  the  incli- 
nation of  a  circular  road,  capable  of  counteracting  the  centrifugal  force  of 
a  horse,  running  round  [in]  it;  (for  the  horse,  like  the  ball  of  the 
revolving  pendulum,  has  a  centrifugal  tendency,  which  is  greater  as  his 
velocity  is  greater;)  this  centrifugal  force,  combined  with  the  force  of 
gravity,  composes  a  result,  which,  in  the  case  of  the  pendulum,  is  com- 
pletely counteracted  by  the  force  of  the  thread  or  wire,  and  must  there- 
fore be  in  the  direction  of  the  thread,  and  which  obliges  the  horse  to 
place  his  legs  in  a  similar  direction,  proceeding  from  an  imaginary 
point  of  suspension  above  ;  since  he  would  otherwise  be  liable  to  fall  out- 
wards, if  his  velocity  were  sufficiently  great.  But  in  order  to  withstand 
the  pressure  of  the  horse's  legs,  the  road  must  be  in  a  direction  perpendi- 
cular to  them  ;  otherwise  its  materials  will  naturally  be  forced  outwards, 
until  they  produce  an  elevation  sufficient  to  give  the  road  the  required 
form.  Thus,  if  the  diameter  of  the  ring  were  40  feet,  and  the  horse 
moved  at  the  rate  of  12  miles  an  hour,  he  would  perform  about  500  revo- 
lutions in  an  hour,  and  half  a  revolution  in  three  seconds  and  a  half. 
Now  the  length  of  a  pendulum  vibrating  in  &J  seconds,  must  be  39  inches 
multiplied  by  the  square  of  3^,  or  a  little  more  [less]  than  80  [40]  feet : 
the  road  must,  therefore,  be  perpendicular  to  the  direction  of  a  line  drawn 
to  it  from  a  point  80  [40]  feet  above  the  centre  of  the  ring ;  and  its 
external  circumference  must  be  higher  than  its  internal  circumference  by 
one  fourth  [half]  of  its  breadth.  It  would,  however,  be  improper  to  have 
a  road  of  this  form  in  a  manege,  since  the  horse  must  be  taught  to  perform 
all  his  evolutions  on  a  perfect  plane. 

There  is  a  general  principle  of  curvilinear  motion,  which  is  in  itself  of 

*  Euler  on  a  Rotatory  Pendulum,  Acta  Petr.  1780,  pp.  133,  164. 


88  LECTURE  VI. 

little  importance  or  practical  utility,  but  which  so  far  deserves  to  be 
noticed,  as  it  has  been  magnified  by  some  philosophers  into  a  fundamental 
law  of  nature.  Among  all  the  curves  that  a  body  can  describe,  in  moving 
from  one  point  to  another,  it  always  selects  that,  in  which,  if  its  velocity 
be  supposed  to  be  everywhere  multiplied  by  the  distance  that  it  describes, 
the  sum  of  the  infinitely  small  products  will  be  a  minimum,  that  is,  less 
than  in  any  other  path  that  the  body  could  take.  For  example,  if  a  body 
move  freely,  and  therefore  with  a  uniform  velocity,  in  any  regular  curved 
surface,  it  will  pass  from  one  part  of  the  surface  to  another  by  the  shortest 
possible  path.  This  has  been  called  the  principle  of  the  least  possible 
action  ;  it  is,  however,  merely  a  mathematical  inference  from  the  simpler 
laws  of  motion,  and  if  those  laws  were  even  different  from  what  they  are, 
the  principle  would  be  true  in  another  form,  and  in  another  sense  of  the 
word  action.* 


LECT.  V.— ADDITIONAL  AUTHORITIES. 

Confined  Motion,  Pendulum,  Sfc. — Becherus  de  Nova  Temporis  Dimetiendi  Ra- 
tione,  4to,  Lond.  1680.  Brook  Taylor,  Ph.  Tr.  xxviii.  11.  Graham  and  Camp- 
bell's Experiments  to  determine  the  Difference  in  the  Length  of  Isochronal  Pendu- 
lums at  different  Places,  Ph.  Trans.  1733,  p.  302.  Courtivron  on  a  Circular  Pendu- 
lum, Hist,  et  Mem.  de  1'Acad.  de  Paris,  1744,  p.  384,  H.  30.  Lagrange  on  Iso- 
chronous Curves,  Mem.  de  1'Acad.  de  Berlin,  1765,  p.  361;  1770,  p.  97.  D'Alem- 
bert,  ibid.  1765,  p.  381.  Landen  on  Circular  Pend.  Ph.  Tr.  1771,  p.  308  ;  1775, 
p.  287.  Maseres,  ibid.  1777,  p.  215.  Legendre,  on  do.  Hist,  et  Mem.  de  1'Acad. 
de  Paris,  1786,  pp.  30,  637.  Biot,  on  Tautoch.  Curves,  Bulletin  dela  Soc.  Philo- 
matique,  No.  73.  Carlini  sulla  Lunghezza  del  Pendolo,  Cesaris  Effemeridi, 
1827,  Milan.  Bessel  Untersuchungen  tiber  das  Secunden  Pendul,  4to,  Berl.1828. 
Piola  sulla  Teoria  del  Pen.  Ces.  EfFem.  1831-2. 

Confined  Motion  with,  Resistance. — Krafft  on  the  Inclined  Plane,  Com.  Petr.  xii. 
261 ;  xiii.  100.  Euler,  ibid.  xiii.  197.  Kastner,  ibid.  Leips.  Mag.  ii.  1.  Euler 
on  a  Rotatory  Pendulum  with  Res.  A.  Petr.  1780,  IV.  ii.  164.  Airy,  Transactions 
of  the  Cambridge  Philosophical  Society,  III.  111.  Plana  sur  le  Mouvement  d'un 
Pendule  dans  un  milieu  resistant,  4to,  Turin,  1835.  Challis.  Trans,  of  the  Camb. 
Phil.  Soc.  vii.  333. 

Properties  of  the  Cycloid.— Pascal,  Histoire  de  la  Roulette.  Carlo  Dati,  Let- 
tera  della  vera  Storia  della  Cicloide,  4to,  Firenze,  1663.  Groningius,  Historia  Cy- 
cloidis.  Lalouere,  Geometria  Promota,  4to,  Tolosae,  1660.  Young,  An  Essay 
on  Cycloidal  Curves,  4to,  1800.  Peacock's  Examples  to  the  Diff.  Calc.  I.  Gre- 
gory's Do.  134. 


LECTURE   VI. 


ON  THE  MOTIONS  OF  SIMPLE  MASSES. 

HITHERTO  we  have  considered  the  motions  of  one  or  more  single  points 
or  atoms  only,  without  any  regard  to  the  bulk  or  mass  of  a  moveable  body  : 
but  it  now  becomes  necessary  to  attend  also  to  the  difference  of  the  masses 

*  See  p.  16.*  Consult  also  Ampere  sur  1' Application  du  Calcul  des  Variations 
aux  Prop,  de  Mec.  4to,  Par.  1809. 


ON  THE  MOTIONS  OF  SIMPLE  MASSES.  39 

of  bodies  in  motion.  This  may  however  be  done,  without  considering  the 
actual  magnitude  or  extent  of  the  body.  We  may  easily  conceive  different 
masses  or  bulks  to  be  concentrated  in  a  mathematical  point ;  and  it  is  most 
convenient  to  define  a  moveable  body,  as  a  moveable  point  or  particle  com- 
posed of  other  elementary  particles,  differing  only  in  number,  and  thus 
constituting  the  proportionally  different  mass  or  bulk  of  the  body. 

Although  in  our  experiments  on  motion  we  are  obliged  to  have  recourse 
to  material  bodies,  and  although  such  bodies  differ  considerably  from  this 
definition  of  a  single  moveable  body,  yet  they  serve  sufficiently  well  to 
represent  such  bodies,  especially  when  they  are  small  and  regularly  formed ; 
and  we  are  here  considering  the  doctrine  of  motion  rather  in  a  mathe- 
matical than  in  a  physical  sense ;  so  that  we  are  able  to  neglect  all  such 
properties  of  matter  as  are  not  immediately  necessary  to  our  purpose.  In- 
deed though  the  general  properties  of  matter  are  usually  placed  at  the 
entrance  of  elementary  works  on  mechanics,  it  has  yet  been  found 
necessary  to  omit  the  consideration  of  their  effects,  in  examining  the  laws 
and  affections  of  motion.  The  forces  of  cohesion  and  repulsion,  for  exam- 
ple, act,  in  general,  in  a  very  complicated  manner,  in  almost  all  cases  of 
the  communication  of  motion  ;  but  to  consider  these  operations  minutely 
in  treating  of  collision,  would  be  to  involve  the  subject  in  very  great 
and  very  unnecessary  difficulties  ;  and  the  complete  investigation  of  these 
properties  of  matter  would  require  the  employment  of  various  branches  of 
mechanical  and  hydrodynamical  science.  We  may  therefore  take  a  much 
simpler  course,  by  deferring  entirely  all  theoretical  consideration  of  actual 
matter  ;  but  in  the  mean  time  we  must  have,  for  our  experimental  illustra- 
tions, some  measure  of  the  mass  or  bulk  as  here  defined.  We  might  employ 
spherical  bodies,  composed  only  of  homogeneous  substances,  that  is,  of  sub- 
stances of  the  same  kind,  and  we  might  estimate  the  mass  by  the  compara- 
tive magnitude,  imagining  all  the  particles  of  each  sphere  to  be  united  in 
its  centre.  But  it  is  more  convenient  to  anticipate,  from  the  gravitation  of 
matter,  a  measure  of  the  mass  derived  from  the  weight :  since  it  can  be 
proved  that  the  weight  of  a  body  is  proportional  to  its  absolute  quantity  of 
matter,  supposing  all  matter  to  be  alike  in  its  affections  relative  to  motion. 
So  that  instead  of  numbering  the  particles  of  each  body,  the  same  purpose 
is  answered  by  determining  their  comparative  weight. 

Inertia,  or  a  tendency  to  persevere  in  a  state  of  rest,  or  of  uniform  recti- 
linear motion,  is  a  property  attached  to  all  matter,  and  may  be  considered 
as  proportional  to  the  mass  or  weight  of  a  body.  When  the  motions  of  a 
system  of  bodies  are  considered,  their  inertia  may  in  some  respects  be 
referred  to  a  single  point,  which  is  called  the  centre  of  inertia.  [See  the 
next  paragraph.]  The  centre  of  inertia  of  two  bodies  is  that  point,  in  the 
right  line  joining  them,  which  divides  it  into  two  such  portions,  that  the 
one  is  to  the  other  as  the  mass  of  the  remoter  body  tp  that  of  the  adjacent 
body.  For  instance,  if  one  body  weighs  a  pound,  and  another  two  pounds, 
and  their  distance  is  a  yard,  then  the  centre  of  inertia  is  at  the  distance  of 
two  feet  from  the  smaller  body,  and  one  foot  from  the  larger  :  and  the  dis- 
tance of  each  is  to  the  whole  distance,  as  the  weight  of  the  other  to  the 
whole  weight.  Also  the  products  obtained  by  multiplying  each  weight  by 


40  LECTURE  VI. 

its  distance  are  equal :  thus  two  multiplied  by  one  is  equal  to  one  multi- 
plied by  two.  (Plate  II.  Fig.  29.) 

This  point  is  most  commonly  called  the  centre  of  gravity ;  it  has  also 
sometimes  been  denominated  the  centre  of  position.  Since  it  has  many 
properties  independent  of  the  consideration  of  gravity,  it  ought  not  to  derive 
its  name  from  gravitation,  [but  as  custom  has  familiarized  the  term,  we 
deem  it  better  to  retain  it.] 

The  centre  of  inertia  [gravity]  of  any  two  bodies  initially  at  rest,  remains 
at  rest,  notwithstanding  any  reciprocal  action  of  the  bodies  ;  that  is,  not- 
withstanding any  action  which  affects  the  single  particles  of  both  equally, 
in  increasing  or  diminishing  their  distance.  For  it  may  be  shown,  from 
the  principles  of  the  composition  of  motion,  that  any  force,  acting  in  this 
manner,  will  cause  each  of  the  two  bodies  to  describe  a  space  proportional 
to  the  magnitude  of  the  other  body  :  thus  a  body  of  one  pound  will  move 
through  a  space  twice  as  great  as  a  body  of  two  pounds  weight,  and  the 
remaining  parts  of  the  original  distance  will  still  be  divided  in  the  same 
proportion  by  the  original  centre  of  inertia  [gravity],  which  therefore  still 
remains  the  centre  of  inertia  [gravity],  and  is  at  rest.  And  it  follows  also, 
that  if  the  centre  of  inertia  [gravity]  is  at  first  in  motion,  its  motion  will 
not  be  affected  by  any  reciprocal  action  of  the  bodies. 

This  important  property  is  very  capable  of  experimental  illustration ; 
first  observing,  that  all  known  forces  are  reciprocal,  and  among  the  rest  the 
action  of  a  spring  ;  we  place  two  unequal  bodies  so  as  to  be  separated  when 
a  spring  is  set  at  liberty,  and  we  find  that  they  describe,  in  any  given 
interval  of  time,  distances  which  are  inversely  as  their  weights  ;  and 
that  consequently  the  place  of  the  centre  of  inertia  [gravity]  remains  un- 
altered. They  may  either  be  made  to  float  on  water,  or  may  be  suspended 
by  long  threads ;  the  spring  may  be  detached  by  burning  a  thread  that 
confines  it,  and  it  may  be  observed  whether  or  no  they  strike  at  the  same 
instant  two  obstacles,  placed  at  such  distances  as  the  theory  requires  ;  or  if 
they  are  suspended  as  pendulums,  the  arcs  which  they  describe  may  be 
measured,  the  velocities  being  always  nearly  proportional  to  these  arcs,  and 
accurately  so  to  their  chords.  (Plate  II.  Fig.  30.) 

The  same  might  also  be  shown  of  attractive  as  well  as  of  repulsive  forces. 
For  instance,  if  we  placed  ourselves  in  a  small  boat,  and  pulled  a  rope  tied 
to  a  much  larger  one,  we  should  draw  ourselves  towards  the  large  boat  with 
a  motion  as  much  more  rapid  than  that  of  the  large  boat,  as  its  weight  is 
greater  than  that  of  our  own  boat ;  and  the  two  boats  would  meet  in  their 
common  centre  of  inertia  [gravity],  supposing  the  resistance  of  the  water 
inconsiderable. 

Having  established  this  property  of  the  centre  of  inertia  [gravity]  as  a 
law  of  motion,  we  may  derive  from  it  the  true  estimate  of  the  quantity  of 
motion  in  different  bodies,  in  a  much  more  satisfactory  manner  than  it  has 
usually  been  explained.  For  since  the  same  reciprocal  action  produces,  in 
a  body  weighing  two  pounds,  only  half  the  velocity  that  it  produces  in 
a  body  weighing  one  pound,  the  cause  being  the  same,  the  effects  must  be 
considered  as  equal,  and  the  quantity  of  motion  must  always  be  measured 
by  the  joint  ratio  of  mass  to  mass,  and  velocity  to  velocity  ;  that  is,  by  the 


ON  THE  MOTIONS  OF  SIMPLE  MASSES.  41 

ratio  of  the  products,  obtained  by  multiplying  the  weight  of  each  body 
by  the  number  expressing  its  velocity ;  and  these  products  are  called 
the  momenta  of  the  bodies.  We  appear  to  have  deduced  this  measure  of 
motion  from  the  most  unexceptionable  arguments,  and  we  shall  have  occa- 
sion to  apply  the  momentum  thus  estimated  as  a  true  measure  of  force  ;  at 
the  same  time  that  we  allow  the  practical  importance  of  considering,  in 
many  cases,  the  efficacy  of  forces,  according  to  another  criterion,  when  we 
multiply  the  mass  by  the  square  of  the  velocity,  in  order  to  determine  the 
energy :  yet  the  true  quantity  of  motion,  or  momentum,  of  any  body,  is 
always  to  be  understood  as  the  product  of  its  mass  into  its  velocity.  Thus 
a  body  weighing  one  pound,  moving  with  the  velocity  of  a  hundred  feet  in 
a  second,  has  the  same  momentum  and  the  same  quantity  of  motion  as  a 
body  of  ten  pounds,  moving  at  the  rate  of  ten  feet  in  a  second. 

We  may  also  demonstrate  experimentally,  by  means  of  Mr.  Atwood's 
machine  [Plate  I.  Fig.  11],  that  the  same  momentum  is  generated,  in  a 
given  time,  by  the  same  preponderating  force,  whatever  may  be  the  quan- 
tity of  matter  moved.  Thus,  if  the  preponderating  weight  be  one  sixteenth 
of  the  whole  weight  of  the  boxes,  it  will  fall  one  foot  in  a  second  instead  of 
16,  and  a  velocity  of  two  feet  will  be  acquired  by  the  whole  mass,  instead 
of  a  velocity  of  32  feet,  which  the  preponderating  weight  alone  would  have 
acquired.  And  when  we  compare  the  centrifugal  forces  of  bodies  revolving 
in  the  same  time  at  different  distances  from  the  centre  of  motion,  we  find 
that  a  greater  quantity  of  matter  compensates  for  a  smaller  force  ;  so  that 
two  balls  connected  by  a  wire,  with  liberty  to  slide  either  way,  will  retain 
each  other  in  their  respective  situations  when  their  common  centre  of 
inertia  [gravity]  coincides  with  the  centre  of  motion  ;  the  centrifugal  force 
of  each  particle  of  the  one  being  as  much  greater  than  that  of  an  equal 
particle  of  the  other,  as  its  weight  or  the  number  of  the  particles  is  smaller. 

But  it  is  not  enough  to  determine  the  centre  of  inertia  [gravity]  of  two 
bodies  only,  considered  as  single  points ;  since  in  general  a  much  greater 
number  of  points  is  concerned  :  we  must  therefore  define  the  sense  in  which 
the  term  is  in  this  case  to  be  applied.  We  proceed  by  considering  the  first 
and  second  of  three  or  more  bodies,  as  a  single  body  equal  to  both  of  them, 
and  placed  in  their  common  centre  of  inertia  [gravity], ;  determining  the 
centre  of  inertia  [gravity]  of  this  imaginary  body  and  the  third  body,  and 
continuing  a  similar  process  for  all  the  bodies  of  the  system.  And  it 
matters  not  with  which  of  the  bodies  we  begin  the  operation,  for  it  may  be 
demonstrated  that  the  point  thus  found  will  be  the  same  by  whatever  steps 
it  be  determined.  When  we  come  to  consider  the  properties  of  the  same 
point  as  the  centre  of  gravity  [weight]  we  shall  be  able  to  produce  an  ex- 
perimental proof  of  this  assertion,  since  it  will  be  found  that  there  is  only 
one  point  in  any  system  of  bodies  which  possesses  these  properties.  (Plate 
III.  Fig.  31.) 

We  may  always  represent  the  motion  of  the  centre  of  inertia  [gravity] 
of  a  system  of  moving  bodies,  by  supposing  their  masses  to  be  united  into 
one  body,  and  this  body  to  receive  at  once  a  momentum  equal  to  that  of 
each  body  of  the  system,  in  a  direction  parallel  to  its  motion.  This  may' 
often  be  the  most  conveniently  done  by  referring  all  the  motions  of  this 


42  LECTURE  VI. 

imaginary  body  to  three  given  directions,  and  collecting  all  the  results  into 
three  sums,  which  will  represent  the  motion  of  the  centre  of  inertia 
[gravity]  of  the  system. 

We  have  already  presupposed  this  proposition,  when  we  have  employed 
material  bodies  of  finite  magnitude,  that  is,  systems  of  material  atoms,  to 
represent  imaginary  bodies  of  the  same  weight  condensed  into  their  centres  ; 
and  it  now  appears  that  the  velocity  and  direction  of  the  motions  of  such 
bodies  as  we  have  employed,  agree  precisely  with  those  of  our  imaginary 
material  points.  We  cannot  attempt  to  confirm  this  law  by  experiment, 
because  the  deductions  from  the  sensible  consequences  of  an  experiment 
would  require  nearly  the  same  processes  as  the  mathematical  demonstration. 

It  is  obvious  that  the  result  of  any  number  of  uniform  and  rectilinear 
motions  thus  collected,  must  also  be  a  uniform  and  rectilinear  motion. 
The  centre  of  inertia  [gravity]  of  a  system  of  bodies  moving  without  dis- 
turbance, is,  therefore,  either  at  rest,  or  moving  equably  in  a  right  line. 

The  mass,  or  weight,  of  each  of  any  number  of  bodies,  being  multiplied 
by  its  distance  from  a  given  plane,  the  products,  collected  into  one  sum, 
will  be  equal  to  the  whole  weight  of  the  system,  multiplied  by  the  distance 
of  the  common  centre  of  inertia  [gravity]  from  the  same  plane.  And  the 
proposition  will  be  equally  true,  if,  instead  of  the  shortest  distances,  we 
substitute  the  distances  from  the  same  plane,  measured  obliquely,  in  any 
directions  always  parallel  to  each  other.  This  property  is  peculiarly  appli- 
cable to  the  consideration  of  the  centre  of  gravity  [weight],  and  affords  also 
the  readiest  means  of  determining  its  place  in  bodies  of  complicated  forms. 
(Plate  III.  Fig.  32.) 

We  have  already  seen  that  the  place  of  the  centre  of  inertia  [gravity]  of 
two  bodies  is  not  affected  by  any  reciprocal  action  between  them  ;  and  the 
same  is  true  of  the  actions  of  a  system  of  three  or  more  bodies.  We  might 
easily  apply  our  experiment  on  the  reciprocal  action  of  two  bodies  to  a 
greater  number,  but  we  should  throw  no  further  light  on  the  subject,  and 
the  mode  of  obtaining  the  conclusion  would  be  somewhat  complicated. 

All  the  forces  in  nature,  with  which  we  are  acquainted,  act  reciprocally 
between  different  masses  of  matter,  so  that  any  two  bodies  repelling  or  at- 
tracting each  other,  are  made  to  recede  or  approach  with  equal  momenta. 
This  circumstance  is  generally  expressed  by  the  third  law  of  motion,  that 
action  and  reaction  are  equal.  There  would  be  something  peculiar,  and 
almost  inconceivable,  in  a  force  which  could  affect  unequally  the  similar 
particles  of  matter ;  or  in  the  particles  themselves,  if  they  could  be  pos- 
sessed of  such  different  degrees  of  mobility  as  to  be  equally  moveable  with 
respect  to  one  force,  and  unequally  with  respect  to  another.  For  instance, 
a  magnet  and  a  piece  of  iron,  each  weighing  a  pound,  will  remain  in  equi- 
librium when  their  weights  are  opposed  to  each  other  by  means  of  a 
balance ;  they  will  be  separated  with  equal  velocities,  if  impelled  by  the 
unbending  of  a  spring  placed  between  them,  and  it  is  difficult  to  conceive 
that  they  should  approach  each  other  with  unequal  velocities  in  consequence 
of  magnetic  attraction,  or  of  any  other  natural  force.  The  reciprocality  of 
force  is  therefore  a  necessary  law  in  the  mathematical  consideration  of 
mechanics,  and  it  is  also  perfectly  warranted  by  experience.  The  contrary 


ON  THE  MOTIONS  OF  SIMPLE  MASSES.  43 

supposition  is  so  highly  improbable,  that  the  principle  may  almost  as 
justly  be  termed  a  necessary  axiom,  as  a  phenomenon  collected  from 
observation. 

Sir  Isaac  Newton  *  observes,  in  his  third  law  of  motion,  that  "  reaction 
is  always  contrary  and  equal  to  action,  or,  that  the  mutual  actions  of  two 
bodies  are  always  equal,  and  directed  contrary  ways."  He  proceeds,  "  if 
any  body  draws  or  presses  another,  it  is  itself  as  much  drawn  or  pressed. 
If  any  one  presses  a  stone  with  his  finger,  his  finger  is  also  pressed  by  the 
stone.  If  a  horse  is  drawing  a  weight  tied  to  a  rope,  the  horse  is  also 
equally  drawn  backwards  towards  the  weight :  for  the  rope,  being  dis- 
tended throughout,  will,  in  the  same  endeavour  to  contract,  urge  the  horse 
towards  the  weight  and  the  weight  towards  the  horse,  and  will  impede  the 
progress  of  the  one  as  much  as  it  promotes  the  advance  of  the  other."  Now 
although  Newton  has  always  applied  this  law  in  the  most  unexceptionable 
manner,  yet  it  must  be  confessed  that  the  illustrations  here  quoted  are 
clothed  in  such  language  as  to  have  too  much  the  appearance  of  paradox. 
When  we  say  that  a  thing  presses  another,  we  commonly  mean,  that  the 
thing  pressing  has  a  tendency  to  move  forwards  into  the  place  of  the  thing 
pressed,  but  the  stone  would  not  sensibly  advance  into  the  place  of  the 
finger,  if  it  were  removed  ;  and  in  the  same  manner  we  understand  that  a 
thing  pulling  another  has  a  tendency  to  recede  further  from  the  thing 
pulled,  and  to  draw  this  after  it ;  but  it  is  obvious  that  the  weight  which 
the  horse  is  drawing  would  not  return  towards  its  first  situation,  with  the 
horse  in  its  train,  although  the 'exertion  of  the  horse  should  entirely  cease  ; 
in  these  senses,  therefore,  we  cannot  say  that  the  stone  presses,  or  that  the 
\veight  pulls,  and  we  have  no  reason  to  offend  the  just  prejudices  of  a  be- 
ginner, by  introducing  paradoxical  expressions  without  necessity.  Yet  it  is 
true  in  both  cases,  that  if  all  friction  and  all  connexion  with  the  surround- 
ing bodies  could  be  instantaneously  destroyed,  the  point  of  the  finger  and 
the  stone  would  recede  from  each  other,  and  the  horse  and  the  weight  would 
approach  each  other  with  equal  quantities  of  motion.  And  this  is  what  we 
mean  by  the  reciprocality  of  forces,  or  the  equality  of  action  and  reaction. 

The  quantity  of  action  of  two  attractive  or  repulsive  bodies  on  each 
other  is  partly  dependent  on  their  magnitude.  When  the  bodies  are  of  the 
same  kind,  their  mutual  action  is  in  the  compound  ratio  of  their  bulks  ; 
that  is,  in  the  ratio  of  the  products  of  the  numbers  expressing  their  bulks. 
For  instance,  if  two  bodies,  each  containing  a  cubic  inch  of  matter,  attract 
or  repel  each  other  with  a  force  of  a  grain,  and  there  be  two  other  bodies, 
the  one  containing  two  inches,  the  other  ten,  of  the  same  matter,  then  the 
mutual  attraction  or  repulsion  of  these  will  be  expressed  by  twenty  grains ; 
for  each  of  the  10  inches  is  attracted  by  each  of  the  two  with  a  force  of  a 
grain.  And  the  mutual  action  of  3  and  10  will  be  30,  of  4  and  10,  40  ;  so 
that  when  one  of  the  bodies  remains  the  same,  the, attraction  will  be 
simply  as  the  bulk  of  the  other.  Hence  the  quantity  of  matter,  in  every 
body  surrounding  us,  is  considered  as  proportional  to  its  weight ;  for  it  is 
inferred  from  experiment  that  all  material  bodies  are  equally  subject  to  the 
power  of  gravitation  towards  the  earth,  and  are,  in  respect  to  this  force,  of 
*  Principia,  Lib.  I. 


44  LECTURE  VI. 

the  same  kind.  For  the  apparent  difference  in  the  velocity  with  which 
different  substances  fall  through  the  atmosphere,  is  only  owing  to  the 
resistance  of  the  air,  as  is  sometimes  shown  by  an  experiment  on  a  feather 
and  a  piece  of  gold  falling  in  the  vacuum  of  an  air  pump  ;  but  the  true 
cause  was  known  long  before  the  invention  of  this  machine,  and  it  is  dis- 
tinctly explained  in  the  second  book  of  Lucretius  : 
"  In  water  or  in  air  when  weights  descend, 

The  heavier  weights  more  swiftly  downwards  tend. 

The  limpid  waves,  the  gales  that  gently  play, 

Yield  to  the  weightier  mass  a  readier  way, 

But  if  the  weights  in  empty  space  should  fall, 

One  common  swiftness  we  should  find  in  all." 

We  are  therefore  to  suppose,  that  the  different  weights  of  equal  bulks  of 
different  substances  depend  merely  on  the  greater  or  less  number  of  parti- 
cles contained  in  a  given  space,  independently  of  any  other  characters  that 
may  constitute  the  specific  differences  of  those  substances. 

In  some  cases  it  is  necessary  to  consider  the  sum  of  the  masses  of  two 
bodies,  in  order  to  estimate  their  mutual  action  ;  that  is,  when  we  wish  to 
know  the  whole  relative  motion  of  two  bodies  with  respect  to  each  other  ; 
for  here  we  must  add  together  their  single  motions  with  respect  to  the 
centre  of  inertia  [gravity],  which  are  inversely  in  the  same  ratio.  This 
consideration  is  sometimes  of  use  in  determining  the  action  of  the  sun  on 
the  several  planets. 

If  two  bodies  act  on  each  other  with  forces  proportional  to  any  power  of 
their  distance,  for  instance  to  the  square  or  the  cube  of  the  distance,  the 
forces  will  also  be  proportional  to  the  same  power  of  either  of  their  dis- 
tances from  their  common  centre  of  inertia  [gravity].  Thus,  in  the 
planetary  motions,  when  one  body  performs  a  revolution  by  means  of  the 
attractive  force  of  another,  this  other  cannot  remain  absolutely  at  rest ;  but 
because  it  is  more  convenient  to  determine  the  effect  of  the  attraction  as 
directed  to  a  fixed  point,  we  consider  the  force  as  residing  in  the  common 
centre  of  inertia  [gravity]  of  the  two  bodies,  which  remains  at  rest,  as  far  as 
the  mutual  actions  of  those  bodies  only  are  concerned,  and  it  may  be  shown, 
that  the  force  diminishes  as  the  square  of  the  distance  of  the  bodies,  either 
from  this  point  or  from  each  other,  increases.  The  reciprocal  forces  of  two 
bodies  may  therefore  be  considered  as  tending  to  or  from  their  common 
centre  of  inertia  [gravity]  as  a  fixed  point ;  but  it  often  happens  that  the 
difference  of  magnitude  being  very  great,  the  motion  of  one  of  the  bodies 
may  be  disregarded.  Thus  we  usually  neglect  the  motion  of-  the  sun,  in 
treating  of  the  planetary  motions  produced  by  his  attraction,  although,  by 
means  of  very  nice  observations,  this  motion  becomes  sensible.  But  it  is 
utterly  beyond  the  power  of  our  senses  to  discover  the  reciprocal  motion  of 
the  earth  produced  by  any  terrestrial  cause,  even  by  the  most  copious  erup- 
tion of  a  volcano,  although,  speaking  mathematically,  we  cannot  deny  that 
whenever  a  cannon  ball  is  fired  upwards,  the  whole  globe  must  suffer  a 
minute  depression  in  its  course.  The  boast  of  Archimedes  was  therefore 
accompanied  by  an  unnecessary  condition :  "  give  me,"  said  he,  "  but  a 
firm  support,  and  I  will  move  the  earth  ;"  but,  granting  him  his  support, 


ON  PRESSURE  AND  EQUILIBRIUM.  45 

he  could  only  have  displaced  the  earth  insensibly  by  the  properties  of  his 
machines ;  and  without  any  such  support,  when  he  threw  rocks  upon  the 
ships  of  Marcellus,  he  actually  caused  the  walls  of  Syracuse  and  the  island 
of  Sicily  to  move  northwards,  with  as  much  momentum  as  carried  his  pro- 
jectiles southwards  against  the  Roman  armaments. 


LECT.  VI.— ADDITIONAL  AUTHORITIES. 

Centre  of  Gravity.  — Wallis  de  Centre  Gravitatis  Hyperbolae,  Ph.  Tr.  1672,  p. 
5074.  Roberval  on  the  Centres  of  Gravity  of  Solids,  Hist,  et  Mem.  de  Par.  vi.  270, 
282.  Lahireon  the  Motion  of  the  Centre  of  Inertia,  ibid.  ix.  175.  Laura  Bassion 
ditto,  Com.  Bon.  iv.  O.  74.  Varignon  on  the  Centre  of  Gravity  of  Spheres, 
Hist,  et  Mem.  de  Paris,  x.  508.  Clairaut  on  Finding  the  Centre  of  Gravity,  ibid. 
1731,  p.  159.  Bossut  on  the  Centres  of  Gravity  of  Cycloidal  Surfaces  and  Solids, 
Mem.  Presentes,  Paris,  iii.  603.  Gr.  Fontana  on  the  Axis  of  Equilib.  and  the 
Centre  of  Gr.  Atti  dell'  Academia  di  Siena,  4to,  vi.  177.  L'Huillier's  Theorem 
respecting  the  Centre  of  Gravity,  Nov.  Act.  Petrop.  1786,  4to,  H.  39.  Kramp  on 
the  Centre  of  Gravity  of  Sph.  Triangles,  Hindenburg's  Archiv.  ii.  296. 


LECTURE    VII. 


ON  PRESSURE  AND  EQUILIBRIUM. 

WE  have  now  examined  the  principal  cases  in  which  a  simple  force  is 
employed  in  the  production  of  motion  ;  it  is  of  equal  consequence  to  attend 
to  the  opposition  of  forces,  where  they  prevent  each  other's  action.  A 
force  counteracted  by  another  force,  so  that  no  motion  is  produced,  becomes 
a  pressure  :  thus  we  continually  exert  a  pressure,  by  means  of  our  wreight, 
upon  the  ground  on  which  we  stand,  the  seat  on  which  we  sit,  and  the  bed 
on  which  we  sleep  ;  but  at  the  instant  when  we  are  falling  or  leaping,  we 
neither  exert  nor  experience  a  pressure  on  any  part. 

It  was  very  truly  asserted  by  the  ancients,  that  pressure  and  motion  are 
absolutely  incommensurable  as  effects ;  for  according  to  the  definition  of 
pressure,  the  force  appears  to  be  what  is  called  in  logic  a  potential  cause, 
which  is  not  in  a  state  of  activity  :  and  since  an  interval  of  time  must  elapse 
after  the  removal  of  the  opposite  force,  before  the  first  force  can  have 
caused  any  actual  motion,  this  effect  of  a  finite  time  cannot  with  justice  be 
conceived  to  bear  any  proportion  to  the  pressure,  which  is  as  it  were  a 
nascent  effect  only.  It  is  true  that  a  large  weight  pressing  on  a  spring, 
may  keep  it  bent,  in  exactly  the  same  place  into  which  a  smaller  weight, 
falling  on  it  with  a  certain  velocity,  would  inflect  'it  :  but,  to  retain  a 
spring  in  a  certain  position,  and  to  bend  it  into  that  position,  are  effects 
absolutely  incommensurable  ;  the  one  being  a  measure  of  the  constant 
repulsive  force  of  the  spring,  bent  to  a  certain  point,  the  other  of  the  sum  of 
the  effects  of  the  same  spring  in  various  degrees  of  flexure,  for  a  certain 


46  LECTURE  VII. 

time.  Hence  the  smallest  possible  momentum  is  said  to  be  more  than 
equivalent  to  the  greatest  possible  pressure :  a  very  light  weight,  falling 
from  a  very  minute  distance,  will  force  back  a  very  strong  spring,  although 
often  through  an  imperceptible  space  only.  But  the  impulse  of  a -stream  of 
infinitely  small  particles,  like  those  of  which  a  fluid  is  supposed  to  consist, 
striking  an  obstacle  in  a  constant  succession,  may  be  counteracted  by  a 
certain  pressure,  without  producing  any  finite  motion. 

Nothing,  however,  forbids  us  to  compare  two  pressures,  by  considering 
the  initial  motions  which  they  would  produce,  if  the  opposition  were 
removed  ;  nor  is  there  any  difficulty  in  extending  the  laws  of  the  composi- 
tion of  motion  to  the  composition  of  pressure.  For  since  we  measure 
forces  by  the  motions  which  they  produce,  it  is  obvious  that  the  composi- 
tion of  forces  is  included  in  the  doctrine  of  the  composition  of  motions  ; 
and  when  we  combine  three  forces  according  to  the  laws  of  motion,  there 
can  be  no  question  but  that  the  resulting  motion  is  truly  determined  in  all 
cases,  whatever  may  be  its  magnitude  ;  nor  can  any  reason  be  given  why 
it  should  be  otherwise,  when  this  motion  is  evanescent,  and  the  force 
becomes  a  pressure.  The  case  is  similar  to  that  of  a  fraction,  which  may 
still  retain  a  real  value,  when  both  its  numerator  and  denominator  become 
less  than  any  assignable  quantity.  Some  authors  on  mechanics,  and 
indeed  the  most  eminent,  Bernoulli,*  Dalembert,1*  and  Laplace,^  have 
deduced  the  laws  of  pressure  more  immediately  from  the  principle  of  the 
equality  of  the  effects  of  equal  causes  ;  and  the  demonstration  may  be 
found,  in  an  improved  form,  in  the  article  Dynamics  of  the  Supplement 
of  the  Encyclopaedia  Britannica  ;  but  its  steps  are  still  tedious  and  intri- 
cate. 

We  are,  therefore,  to  consider  the  momentum  or  quantity  of  motion 
which  would  be  produced  by  any  force  in  action,  as  the  measure  of  the 
pressure  occasioned  by  it  when  opposed  ;  and  to  understand  by  equal  or  pro- 
portionate pressures,  such  as  are  produced  by  forces  which  would  generate 
equal  or  proportionate  momenta  in  a  given  time.  And  it  may  be  inferred 
that  two  contrary  pressures  will  balance  each  other,  when  the  momenta 
which  the  forces  would  separately  produce  in  contrary  directions,  are 
equal ;  and  that  any  one  pressure  will  counterbalance  two  others,  when  it 
would  produce  a  momentum  equal  and  contrary  to  the  momentum  which 
would  be  derived  from  the  joint  result  of  the  other  forces.  For,  supposing 
each  [either]  of  two  forces  opposed  to  each  other  to  act  for  an  instant,  and  to 
remain  inactive  for  the  next  equal  instant  while  the  other  force  is  exerted, 
it  is  obvious  that  these  effects  will  neutralise  each  other,  so  that  the  body 
on  which  they  are  supposed  to  operate  will  retain  its  situation  ;  but  such 
an  action  is  precisely  half  of  the  continued  action  of  each  force  ;  conse- 
quently, since  the  halves  completely  counteract  each  other,  the  wholes  will 
do  the  same.  And  a  similar  mode  of  reasoning  may  be  extended  to  any 
number  of  forces  opposed  to  each  other. 

*  Com.  Petrop.  I.  126. 

f  On  the  Principles  of  Mechanics,  Hist,  et  Mem.  de  1'Acad.  1769,  p.  278,  and 
Opuscula,  I.  and  VI. 

t  Mecanique  Celeste.  See  also  Celestial  Mechanics  of  Laplace  (by  Young), 
p.  87. 


ON  PRESSURE  AND  EQUILIBRIUM.  47 

It  follows  from  the  laws  of  the  composition  of  motion,  that  the  result  of 
two  pressures,  expressed  by  the  sides  of  a  parallelogram,  will  be  repra- 
sented  by  its  diagonal,*  and  that,  if  a  body  remain  at  rest  by  means  of 
three  pressures,  they  must  be  related  to  each  other  in  magnitude  as  the 
sides  of  a  triangle  parallel  to  their  directions.  This  may  be  very  com- 
pletely shown  by  experiment.  We  attach  three  weights  to  as  many 
threads,  united  in  one  point,  and  passing  over  three  pullies  ;  then  by 
drawing  any  triangle,  of  which  the  sides  are  in  the  directions  of  the 
threads,  or  in  parallel  directions,  we  may  always  express  the  magnitude  of 
each  weight  by  the  length  of  the  side  of  the  triangle  corresponding  to  its 
thread.  (Plate  III.  Fig.  33.) 

The  most  important  of  the  problems  relating  to  equilibrium  are  such  as 
concern  the  machines  which  are  usually  called  mechanical  powers.  We  are 
not,  however,  to  enter  at  present  into  all  the  properties  and  uses  of  these 
machines  ;  we  have  at  first  only  to  examine  them  in  a  state  of  rest,  since  the 
determination  of  their  motion  requires  additional  considerations,  and  their 
application  to  practice  belongs  to  another  subdivision  of  our  subject. 

There  is  a  general  law  of  mechanical  equilibrium,  which  includes  the 
principal  properties  of  most  of  these  machines.  If  two  or  more  bodies, 
connected  together,  be  suspended  from  a  given  point,  they  will  be  at  rest 
when  their  centre  of  inertia  [gravity ]  is  in  the  vertical  line  passing  through 
the  point  of  suspension.  The  truth  of  this  proposition  may  easily  be 
illustrated  by  the  actual  suspension  of  any  body,  or  system  of  bodies, 
from  or  upon  a  fixed  point ;  the  whole  remaining  in  equilibrium,  when 
the  centre  of  inertia  [gravity]  is  either  vertically  below  the  point  of  sus- 
pension, or  above  the  point  of  support,  or  when  the  fixed  point  coincides 
with  the  centre  of  inertia  [gravity].  And  whatever  may  be  the  form  of  a 
compound  body,  it  may  be  considered  as  a  system  of  bodies  connected 
together,  the  situation  of  the  common  centre  of  the  inertia  [gravity]  deter- 
mining the  quiescent  position  of  the  body.  (Plate  III.  Fig.  34  . .  38.) 

Hence  the  centre  of  inertia  is  called  the  centre  of  gravity  ;  and  it  may 
be  practically  found,  by  determining  the  intersection  of  two  lines  which 
become  vertical  in  any  two  positions  in  which  the  body  is  at  rest.  Thus, 
if  we  suspend  a  board  of  an  irregular  form  from  any  two  points  succes- 
sively, and  mark  the  situation  of  the  vertical  line  in  each  position,  we  may 
find  by  the  intersection  the  place  of  the  centre  of  gravity  :  and  it  will 
appear  that  this  intersection  will  be  the  same  whatever  positions  we 
employ.  (Plate  III;  Fig.  39.) 

The  consideration  of  the  degree  of  stability  of  equilibrium  is  of  material 
importance  in  many  mechanical  operations.  Like  other  variable  quanti- 
ties, the  stability  may  be  positive,  negative,  or  evanescent.  The  equili- 
brium is  positively  more  or  less  stable,  when  the  centre  of  gravity  would 
be  obliged  to  ascend  more  or  less  rapidly  if  it  quitted  the  vertical  line  : 
the  equilibrium  is  tottering,  and  the  stability  is  negative,  when  the  centre 
of  gravity  would  descend  if  it  were  displaced  ;  but  when  the  centre  of 

*  Seepage  19  and  last  page.  For  demonstrations  of  this  property  consult  also 
Poisson,  Traite  de  Mecanique,  i.  43.  Duchayla,  extracted  in  Pratt's  Mec.  p.  7, 
note ;  and  WhewelTs  Mechanics. 


48  LECTURE  VII. 

gravity  coincides  with  the  centre  of  motion,  or  when  its  path  would  be  a 
horizontal  right  line,  the  equilibrium  has  been  called  insensible,  but  may 
more  properly  be  termed  neutral,  and  the  body  will  rest  in  any  position, 
without  tending  either  to  fall  or  to  return  to  its  original  situation.  It  is 
obvious  that  the  centre  of  gravity  cannot  move  without  descending,  when 
it  is  vertically  over  the  fixed  point,  nor  without  ascending,  when  it  is 
immediately  below  it ;  so  that  in  the  one  case  the  equilibrium  is  tottering, 
and  in  the  other  stable.  Hence  we  may  understand  the  reason  of  fixing 
the  moveable  handles  of  a  vessel  of  any  kind  at  its  upper  part,  in  order  that 
the  centre  of  suspension  may  be  always  above  the  centre  of  gravity.  If 
they  be  fixed  too  low,  the  vessel  will  be  liable  to  overset,  unless  there  be 
sufficient  friction  to  retain  it  in  its  proper  situation.  (Plate  III.  Fig.  40.) 

An  oval  surface,  placed  on  a  horizontal  plane,  is  capable  of  a  stable 
equilibrium,  when  it  rests  on  its  side,  or  on  the  extremity  of  its  lesser  axis, 
and  of  a  tottering  equilibrium,  when  it  stands  on  the  extremity  of  its 
greater  axis.  But  the  equilibrium  of  a  circle  or  a  sphere  is  always  neutral, 
for,  when  disturbed,  it  neither  recovers  its  first  position,  nor  deviates 
further  from  it. '  A  flat  body,  resting  on  a  sphere,  will  have  its  equilibrium 
tottering  or  stable,  accordingly  as  its  centre  of  gravity  is  more  or  less  than 
the  semidiameter  of  the  sphere  above  the  point  of  contact.  (Plate  III.  Fig. 
41,  42.) 

The  stability  of  a  body  supported  on  a  flat  basis  of  a  given  extent,  is  of  a 
different  kind,  and  is  independent  of  equilibrium.  For  here,  if  the  centre 
of  gravity  move  either  way,  it  must  begin  its  motion  in  an  inclined  direc- 
tion, instead  of  describing  a  curve  which  is  initially  horizontal.  The 
stability  of  such  a  body  becomes  less  and  less  as  it  is  more  and  more 
inclined,  till,  when  the  centre  of  gravity  is  vertically  over  the  margin  of 
the  basis,  there  is  a  tottering  equilibrium ;  and  if  the  inclination  be  still 
further  continued,  the  body  will  faU.  (Plate  III.  Fig.  43.) 

The  broader  the  basis  and  the  lower  the  centre  of  gravity,  the  steeper 
must  the  path  of  that  centre  be,  and  consequently  the  greater  the  stability. 
Thus  the  disposition  of  the  weight  in  a  carriage  may  considerably  affect  its 
stability  by  altering  the  place  of  the  centre  of  gravity.  A  waggon  loaded 
with  iron  is  much  less  easily  overturned  than  when  it  is  loaded  with  an 
equal  weight  of  hay ;  supposing  the  inequality  of  the  road  or  any  acci- 
dental obstacle,  to  elevate  one  side  of  the  waggon,  it  will  always  recover  its 
position,  provided  that  the  centre  of  gravity  remain  within  the  vertical  line 
passing  through  the  point  of  contact  of  the  lower  wheel  and  the  ground  ; 
and  it  is  obvious  that  the  higher  the  centre  of  gravity  is  situated  the  sooner 
it  passes  this  line.  If  the  velocity  of  the  motion  were  very  great,  the  wheel 
which  is  elevated  might  be  lifted  off  the  ground  by  the  momentum,  and  the 
centre  of  gravity  might  thus  be  carried  beyond  the  vertical  line,  by  means 
of  an  obstacle  which  would  not  have  overset  the  waggon,  if  it  had  been 
moving  slowly.  (Plate  III.  Fig.  44.) 

If  a  person  be  sitting  or  standing  in  a  carriage,  the  part  of  the  carriage 
on  which  he  sits  or  stands  may  be  considered  as  representing  the  place  of 
his  weight,  provided  that  his  situation  be  always  perpendicular  ;  but  if  the 
motion  be  rapid  he  will  not  be  able  to  remain  constantly  in  a  posture  per- 


ON  PRESSURE  AND  EQUILIBRIUM.  49 

fectly  erect,  and  the  centre  of  gravity  of  the  carriage  with  its  passengers, 
will  be  somewhat  more  elevated  than  it  would  be  on  this  supposition. 

The  direction  of  the  initial  motion  of  the  centre  of  gravity  readily  ex- 
plains the  suspension  of  a  weight  or  a  bucket  of  water,  on  a  rod  resting  on 
the  end  of  a  table,  when  another  rod  is  employed  to  keep  the  bucket  at 
such  a  distance  from  the  end  of  the  first,  that  the  centre  of  gravity  may  be 
under  the  table ;  for  although  the  bucket  seems  suspended  by  its  handle, 
yet  if  the  handle  began  to  descend,  the  centre  of  gravity  would  be  obliged 
to  rise  ;  consequently  the  whole  will  retain  its  position,  and  remain  at  rest. 
(Plate  III.  Fig.  45.) 

The  apparent  ascent  of  a  loaded  cylinder  on  an  inclined  plane,  and  the 
motion  of  a  roller  composed  of  two  united  cones  with  a  common  axis,* 
resting  on  the  edge  of  a  triangle  which  is  inclined  to  the  horizon,  may  be 
easily  understood  from  the  same  consideration.  (Plate  III.  Fig.  46.) 

We  may  also  observe  in  the  equilibrium  of  animals  many  circumstances 
illustrative  of  the  properties  of  the  centre  of  gravity.  When  a  person  stands 
on  one  foot  and  leans  forwards,  in  the  attitude  which  is  usually  exhibited 
in  the  statues  of  Mercury,  the  other  foot  is  elevated  behind,  in  order  to 
bring  back  the  centre  of  gravity  so  as  to  be  vertically  over  some  part  of  the 
foot  on  which  he  stands.  But  on  account  of  the  convex  and  irregular  form 
of  the  foot,  the  basis  that  it  affords  is  really  very  narrow ;  hence,  wheji  we 
attempt  to  stand  on  one  foot,  we  find  it  often  necessary  to  use  a  muscular 
exertion,  in  order  to  bring  the  point  of  support  to  that  side  towards  which 
we  are  beginning  to  fall ;  and  when  the  basis  is  still  more  contracted,  the 
body  never  remains  at  rest,  but,  by  a  succession  of  actions  of  this  kind, 
sometimes  too  minute  to  be  visible,  it  is  kept  in  a  state  of  perpetual  vibra- 
tion, without  ever  attaining  such  a  position  as  would  give  it  any  degree  of 
positive  stability  ;  and  thus  it  may  be  conceived  to  be  supported  even  on  a 
single  point,  recovering  its  position  from  time  to  time  by  means  of  a  slight 
degree  of  rotatory  motion,  which  is  produced  by  its  flexure  and  by  the 
changes  of  the  position  of  the  extremities  :  hence,  by  habit,  the  arts  of 
rope-dancers  and  balancers  are  acquired.  Sometimes,  however,  the  position 
of  the  balancer  is  not  so  difficult  to  be  preserved  as  it  appears,  the  curva- 
ture of  the  wire  in  contact  with  the  foot  tending  materially  to  assist  him. 

When  we  attempt  to  rise  from  a  seat,  we  generally  draw  our  feet  inwards, 
in  order  to  bring  the  point  of  support  into,  or  near,  the  vertical  line  passing 
through  the  centre  of  gravity,  and  to  create  a  tottering  equilibrium,  which 
is  favourable  for  the  beginning  of  motion.  And  before  we  rise,  we  bend 
the  upper  part  of  the  body  forwards,  in  order  to  procure  a  momentum, 
capable  of  carrying  the  centre  of  gravity  beyond  the  vertical  line  passing 
through  the  point  of  support. 

When  a  horse  is  walking,  the  centre  of  gravity  is  sometimes  supported 
only  by  two  feet  of  the  same  side,  yet  for  a  time  so  short  that  its  declension 
towards  the  other  side  is  easily  recovered,  after  the  legs  on  that  side  have 

*  Krafft  on  the  apparent  Ascent  of  a  Double  Cone,  Nov.  Com.  Petrop.  vi.  389. 
Kastner  on  a  Cylinder  appearing  to  roll  upwards.  Deutsche  Schriften  Soc.  Gott.  1 13. 
On  the  motion  of  a  double  cone,  see  also  Kostonov.  Nov.  Act.  Petr.  1789,  vii.  229. 
Brunings  Hind.  Arch.  ii.  321. 


50  LECTURE   VII. 

resumed  their  activity.  Some  authors  have  thought  it  impossible  that  a 
quadruped  should  stand  for  an  instant  with  both  feet  of  the  same  side 
raised  from  the  earth  ;  but  when  a  horse  is  walking  fast,  it  may  very  often 
be  observed  that  the  print  of  the  hind  foot  is  considerably  more  advanced 
than  that  of  the  fore  foot,  which  has  been  raised  to  make  way  for  it. 

From  the  general  law  of  the  equilibrium  of  the  centre  of  gravity,  we 
may  deduce  the  properties  of  levers  of  all  kinds.  It  follows,  from  the  defi- 
nition of  this  point,  that  if  two  bodies  be  attached  to  a  straight  rod  of  in- 
considerable weight,  they  may  be  sustained  in  equilibrium  by  a  fixed 
point  or  fulcrum,  which  divides  their  distance  into  portions  which  are  in- 
versely as  their  weights.  And  it  is  obvious  that  if  any  other  equivalent 
forces  be  substituted  for  weights,  acting  at  the  same  distance  from  the 
fulcrum,  and  with  the  same  inclination  to  the  rod  or  lever,  the  conditions 
of  equilibrium  will  be  precisely  the  same.  Also,  if  either  of  the  forces  be 
transferred  to  an  equal  distance  on  the  other  side  of  the  fulcrum,  and  act 
there  in  a  contrary  direction,  the  equilibrium  will  still  remain.  Hence  we 
have  two  principal  kinds  of  levers  ;  the  first,  in  which  the  fixed  point  or 
fulcrum  is  between  the  points  at  which  the  forces  or  weights  are  applied  ; 
the  second,  where  the  forces  are  applied  in  contrary  directions,  on  the 
same  side  of  the  fulcrum.  (Plate  III.  Fig.  47.) 

The  demonstrations  of  the  fundamental  property  of  the  lever  have  been 
very  various.  Archimedes  himself  has  given  us  two.*  Huygens,t  Newton,^ 
Maclaurin,§  Dr.  Hamilton,  ||  and  Mr.  Vince,1T  have  elucidated  the  same 
subject  by  different  methods  of  considering  it.  The  demonstration  of 
Archimedes,  as  improved  by  Mr.  Vince,  is  ingenious  and  elegant,  but  it  is 
neither  so  general  and  natural  as  one  of  Dr.  Hamilton's,  nor  so  simple  and 
convincing  as  Maclaurin's,  which  it  may  be  worth  our  while  to  notice.  Sup- 
posing two  equal  weights,  of  an  ounce  each,  to  be  fixed  at  the  ends  of  the 
equal  arms  of  a  lever  of  the  first  kind  ;  in  this  case  it  is  obvious  that  there 
will  be  an  equilibrium,  since  there  is  no  reason  why  either  weight  should 
preponderate.  It  is  also  evident  that  the  fulcrum  supports  the  whole 
weight  of  two  ounces,  neglecting  that  of  the  lever  ;  consequently  we  may 
substitute  for  the  fulcrum  a  force  equivalent  to  two  ounces,  drawing  the 
lever  upwards  ;  and  instead  of  one  of  the  weights,  we  may  place  the  end 
of  the  lever  under  a  firm  obstacle,  and  the  equilibrium  will  still  remain, 
the  lever  being  now  of  the  second  kind.  Here,  therefore,  the  weight  re- 
maining at  the  other  end  of  the  lever  counterbalances  a  force  of  two 
ounces,  acting  at  half  the  distance  from  the  new  fulcrum  ;  and  we  may 
substitute  for  this  force  a  weight  of  two  ounces,  acting  at  an  equal  distance 
on  the  other  side  of  that  fulcrum,  'supposing  the  lever  to  be  sufficiently 
lengthened,  and  there  will  still  be  an  equilibrium.  In  this  case  the  fulcrum 
will  sustain  a  weight  of  three  ounces,  and  we  may  substitute  for  it  a  force 
of  three  ounces  acting  upwards,  and  proceed  as  before.  In  a  similar 


*  Archimedes  de  ^Equiponderantibus,  and  de  Planorum 

t  Demonstratio  ^Squilibrii  Bilancis,  Hist,  et  Mem.  Paris,  1693. 

J  Principia,  Laws  of  Motion,  cor.  2.  §  View  of  Newton's  Philosophy. 

(I  The  Properties  of  the  Mechanic  Powers  Demonstrated,  Ph.  Tr.  1763,  liii.  103. 

«||  Ph.  Tr.  1794,  Ixxxiv.  33.     Philosophical  Essays,  12mo,  Lond.  1767. 


ON  PRESSURE  AND  EQUILIBRIUM.  .  51 

manner  the  demonstration  may  be  extended  to  any  commensurable  propor- 
tion of  the  arms,  that  is,  any  proportion  that  can  be  expressed  by  numbers ; 
and  it  is  easy  to  show  that  the  same  law  must  be  true  of  all  ratios  what- 
ever, even  if  they  happen  to  be  incommensurable,  such  as  the  side  of  a 
square  compared  to  its  diagonal,  which  cannot  be  accurately  expressed  by 
any  numbers  whatever  ;  the  forces  remaining  always  in  equilibrium  when 
they  are  to  each  other  inversely  as  the  distances  at  which  they  are  applied. 

It  is  sometimes  more  convenient  to  have  a  series  of  levers  acting  on  each 
other  with  a  moderate  increase  of  power  in  each,  than  to  have  a  single 
lever  equivalent  in  its  effect.  We  may  also  bend  either  arm  of  a  lever  in 
any  manner  that  we  please,  without  altering  its  power,  provided  that  the 
direction  of  the  force  be  perpendicular  to  the  line  drawn  to  the  fulcrum ; 
or  if  the  force  be  applied  obliquely,  it  may  always  be  imagined  to  act  at 
the  end  of  a  lever  equal  in  length  to  the  perpendicular  let  fall  from  the  ful- 
crum on  the  direction  of  the  force.  Thus,  if  two  levers  are  connected  by  a  rope 
or  bar,  when  the  direction  of  one  of  them  nearly  coincides  with  that  of  the 
rope,  a  force  applied  transversely  to  the  lever  acts  with  a  great  mechanical 
advantage  against  the  rope  ;  but  as  the  inclination  increases,  the  advantage 
gradually  diminishes,  and  changes,  at  last,  to  an  equal  advantage  on  the 
side  of  the  rope  and  the  other  lever  to  which  it  is  attached.  When,  there- 
fore, a  great  force  is  required  in  the  beginning  of  the  motion,  and  after- 
wards a  much  smaller  force  with  a  greater  velocity,  this  apparatus  may  be 
extremely  convenient :  thus,  in  opening  a  steam  valve,  the  pressure  of  the 
steam  is  at  first  to  be  overcome,  and  after  this,  little  or  no  additional  force 
is  required  ;  and  Mr.  Watt  has  very  ingeniously  applied  this  arrangement 
of  levers  to  the  purpose  in  his  steam  engines.  In  the  same  manner,  it  is 
necessary  that  the  platten  of  a  printing  press,  or  the  part  which  presses  the 
paper  on  the  types,  should  descend  from  a  considerable  height,  but  it  is 
only  at  the  instant  of  taking  off  the  impression  that  a  great  force  is  re- 
quired ;  and  both  these  ends  are  obtained  by  similar  means  in  a  press 
lately  invented  by  Lord  Stanhope.  (Plate  III.  Fig.  48,  49.) 

The  wheel  and  axis  bear  a  very  strong  resemblance  to  the  lever.  If  two 
threads,  or  perfectly  flexible  and  inextensible  lines,  be  wound  in  contrary 
directions  round  two  cylinders,  drums,  or  rollers,  moveable  together  on 
the  same  axis,  there  will  be  an  equilibrium  when  the  weights  attached  to 
the  threads,  or  the  forces  operating  on  them,  are  inversely  as  the  radii  of 
the  cylinders,  or  as  the  diameters  of  which  they  are  the  halves.  It  may 
easily  be  understood  that  the  weights  have  the  same  power  in  turning 
round  the  cylinders,  as  if  they  were  immediately  attached  to  the  arms  of  a 
lever  equal  in  length  to  their  semidiameter,  and  that  the  conditions  of 
equilibrium  will  be  the  same.  The  demonstration  may  also  be  more  im- 
mediately deduced  from  the  position  of  the  centre  of  gravity  immediately 
below  the  axis  of  the  cylinders,  which  requires,  the  weights  to  be  inversely 
as  the  radii.  With  respect  to  stability,  the  equilibrium  is  neutral,  and  the 
cylinders  will  remain  at  rest  in  any  situation.  A  single  cylinder  is  also 
often  combined  with  a  lever  or  winch,  and  in  this  case  the  radius  of  the 
cylinder  is  to  be  compared  with  the  length  of  the  lever  or  winch.  (Plate 
III.  Fig.  50.) 

E2 


52  LECTURE  VII. 

Systems  of  wheels  and  pinions  of  various  kinds  resemble,  in  their  mecha- 
nical properties,  either  a  series  of  levers,  or  the  combination  of  cylinders 
which  constitutes  the  wheel  and  axis  ;  but  the  form  of  the  teeth  may  pro- 
duce a  difference  in  their  action,  which  will  be  mentioned  when  the  prac- 
tical construction  of  wheelwork  is  discussed. 

Sometimes  the  axis  connected  with  a  winch  is  composed  of  two  cylinders, 
one  end  of  the  rope  being  uncoiled  from  the  smaller,  while  the  other  end 
winds  round  the  larger  ;  the  weight  being  supported  by  a  pulley  running 
in  its  angle.  Here  the  conditions  of  equilibrium  are  easily  determined 
from  the  place  of  the  centre  of  gravity,  and  the  effect  of  the  machine  is  the 
same  as  if  the  weight  were  attached  to  a  rope  coiled  round  a  simple 
cylinder,  of  a  diameter  equal  to  half  the  difference  of  the  diameters  of  the 
double  axis.  The  machine  is,  however,  much  stronger  than  such  a 
cylinder  would  be,  and  does  not  require  so  great  a  curvature  in  the  ropes 
employed.  (Plate  IV.  Fig.  51.) 

The  laws  of  the  equilibrium  of  pullies  have  been  referred,  by  some 
writers  on  mechanics,  to  those  of  the  lever  ;  but  the  comparison  is  both 
unnecessary  and  imperfect ;  in  the  simple  case  of  two  equal  weights  at- 
tached to  a  thread  passing  over  a  single  pulley,  which  is  the  only  one  that 
allows  us  to  recur  to  the  properties  of  the  lever,  the  conditions  of  equili- 
brium are  axiomatically  evident,  without  any  further  reasoning  ;  and  in 
more  complicated  cases  the  calculations  proceed  on  perfectly  different 
grounds.  We  are,  therefore,  to  consider  a  pulley  as  a  cylinder,  moving 
on  an  axis,  merely  in  order  to  change  the  direction  of  a  thread,  without 
friction  ;  for  whatever  is  demonstrable  of  pullies  or  their  combinations, 
would  be  equally  true  of  as  many  perfectly  smooth  grooves,  which  do  not 
bear  the  most  distant  analogy  to  the  lever. 

Now  when  the  direction  of  a  thread  is  altered,  by  passing  over  any  per- 
fectly smooth  surface,  it  communicates  the  whole  force  acting  on  it ;  for 
the  resistance  of  a  surface,  without  friction,  can  only  be  in  a  direction 
perpendicular  to  itself  and  to  the  thread,  and  the  operation  of  any  force 
remains  undisturbed  by  a  resistance  which  is  always  in  a  direction  per- 
pendicular to  it. 

A  fixed  pulley,  therefore,  has  no  effect  in  gaining  a  mechanical  ad- 
vantage ;  but  by  means  of  a  moveable  pulley  it  is  obvious  that  a  weight 
may  be  supported  by  two  forces,  each  equivalent  to  half  the  weight, 
applied  in  a  vertical  direction  to  the  extremities  of  the  thread  ;  and  these 
forces  may  be  derived  from  two  weights,  if  the  thread  be  made  to  pass  over 
two  fixed  pullies  in  a  proper  position  ;  and  if  one  of  the  ends  be  attached 
to  a  fixed  point,  and  the  other  remain  connected  to  its  weight,  the  equi- 
librium will  continue  unimpaired,  each  portion  of  the  thread  still  support- 
ing one  half  of  the  original  weight ;  so  that,  by  means  of  a  single  moveable 
pulley,  one  body  may  retain  in  equilibrium  another  of  double  its  weight. 
(Plate  IV.  Fig.  52,  53.) 

The  modes  of  arranging  pullies  are  very  various,  but  the  advantage 
which  they  procure  may  always  be  estimated,  from  the  consideration  that 
every  part  of  the  same  thread  must  be  equally  stretched  ;  and  where  there 
is  only  one  thread,  the  weight  will  be  divided  equally  among  all  the  por- 


ON  PRESSURE  AND  EQUILIBRIUM.  53 

tions  which  help  to  support  the  moveable  block,  each  of  them  bearing  a 
weight  equivalent  to  the  force  which  is  applied  at  the  end  of  the  thread. 
In  the  common  ship's  blocks,  the  pullies  or  shieves  are  equal  in  magni- 
tude, and  placed  side  by  side  ;  here  their  number  cannot  conveniently 
exceed  two  or  three,  without  causing  an  obliquity  in  the  block,  when  the 
force  is  applied  to  the  rope.  Mr.  Smeaton,*  for  this  reason,  invented  a 
system  of  pullies,  arranged  in  two  rows  in  each  block,  one  larger,  and  the 
other  smaller  :  the  force  being  applied  in  the  middle,  the  rope  passes  on  the 
larger  pullies  till  it  arrives  at  the  last,  then  returns  through  the  whole  of 
the  smaller  series  to  the  opposite  side,  and  comes  back  again  on  the  larger, 
to  be  finally  attached  in  the  middle.  (Plate  IV.  Fig.  54... 56.) 

If  the  diameters  of  all  the  pullies  in  both  blocks  be  taken  in  the  ratio  of 
the  number  of  portions  of  the  thread  intervening  between  them  and  the 
fixed  extremity,  their  angular  velocity  will  be  equal,  each  of  them  turning 
on  its  axis  in  the  same  time.  They  may  therefore  be  fixed  to  a  single  axis 
in  each  block  ;  and  in  this  case  the  axis  being  longer,  there  will  be  less 
accidental  friction  from  its  want  of  steadiness,  and  even  the  necessary  fric- 
tion may,  perhaps,  be  somewhat  diminished.  (Plate  IV.  Fig.  57.) 

If  one  end  of  a  thread  supporting  a  moveable  pulley  be  fixed,  and  the 
other  attached  to  another  moveable  pulley,  and  the  threads  of  this  pulley 
be  similarly  arranged,  the  weight  will  be  counterpoised  by  a  ppwer  which 
is  found  by  halving  it  as  many  times  as  there  are  moveable  pullies  ;  for  it 
is  obvious  that  each  of  these  pullies  doubles  the  effect  of  the  power. 
(Plate  IV.  Fig.  58.) 

There  are  also  other  arrangements,  by  which  the  effect  of  pullies  may  be 
increased  or  diversified  :  for  instance,  where  one  end  of  each  rope  is  attached 
to  the  weight  to  be  moved  ;  or  where  two  of  the  pullies  are  connected  by  a 
rope  passing  over  a  third  ;  but  these  methods  are  of  little  practical  utility. 
(Plate  IV.  Fig.  59,  60.) 

We  have  hitherto  supposed  the  ropes  passing  over  the  pullies  to  be  either 
perfectly  or  very  nearly  parallel  to  each  other ;  but  when  their  directions 
are  oblique  the  forces  applied  to  them  require  to  be  modified  accordingly. 
Thus,  if  two  threads  be  attached  to  a  weight,  and  passed  over  two  pullies 
fixed  at  a  distance  from  each  other,  so  that  two  equal  weights  may  be 
attached  to  their  extremities,  the  depression  of  the  first  weight  below  either 
pulley  will  be  to  its  distance  from  the  pulley,  in  the  same  proportion  as 
half  of  the  weight  to  either  of  the  other  weights  ;  and  if,  instead  of  having 
a  weight  attached  to  it,  one  end  of  the  thread  be  fixed  to  a  firm  obstacle, 
the  effect  will  be  precisely  the  same.  A  machine  of  this  kind  is  sometimes 
called  a  swig,  perhaps  by  corruption  from  swing.  (Plate  IV.  Fig.  61.) 

If  all  the  weights  are  unequal,  we  must  draw  a  triangle  of  which  the 
three  sides  are  in  the  same  proportions  as  the  weights ;  and  we  may  deter- 
mine the  directions  of  the  threads  by  placing  such  a  triangle,  with  the  side 
representing  the  middle  weight  in  a  vertical  position. 

A  force  may  also  be  applied  obliquely  to  a  wheel  and  axis.  Supposing  a 
'rope  to  be  coiled  obliquely  round  the  axis,  it  will  require,  in  order  to  pre- 
serve the  equilibrium,  a  force  as  much  greater  than  would  be  sufficient,  if 
*  Ph.Tr.  1752,  xlvii.  404. 


54  LECTURE  VII. 

it  were  simply  applied  in  the  direction  of  the  motion,  as  the  length  of  any 
part  of  the  rope  uncoiled  is  greater  than  the  perpendicular  distance  of  its 
extremity  from  the  axis.  So  that  when  the  rope  becomes  very  oblique,  a 
great  force  is  required,  in  order  to  counteract  a  much  smaller  one-  acting 
perpendicularly.  This  remark  may  be  in  some  measure  illustrated  by 
considering  the  method  used  by  joiners  and  stone  cutters  for  keeping  a  saw 
straight :  two  ropes  or  braces  are  twisted  together  by  means  of  a  pin  or 
lever  passing  between  them,  and  serve  each  other  in  place  of  an  axis,  round 
which  they  are  coiled  obliquely,  so  that  they  act  with  great  force,  when 
they  are  sufficiently  tight  and  not  too  much  twisted.  (Plate  IV.  Fig.  62.) 

It  appears  from  the  laws  which  have  already  been  laid  down,  respecting 
the  motions  of  bodies  on  inclined  surfaces,  that  a  weight  acting  vertically 
will  hold  in  equilibrium  another  weight  resting  on  an  inclined  plane,  with- 
out friction,  when  the  first  is  to  the  second  as  the  height  of  the  plane  to  its 
oblique  length.  The  pressure  on  the  plane  is  in  this  case  to  the  weight 
resting  on  it,  as  the  horizontal  length  of  the  plane  is  to  its  oblique  length. 
This  pressure  may  be  measured  experimentally,  by  substituting  for  the 
resistance  of  the  plane  that  of  a  thread  perpendicular  to  it.  (Plate  IV. 
Fig.  63.) 

The  same  principles  are  applicable  to  the  equilibrium  of  the  wedge.  A 
wedge  is  a  solid  which  has  three  plane  faces  inclined  to  each  other,  and 
two  triangular  ends  ;  and  we  suppose  the  faces  perfectly  polished,  so  as  to 
be  free  from  friction,  and  that  no  force  can  act  on  them  otherwise  than  in 
a  perpendicular  direction.  Now  in  order  that  three  forces,  acting  on  the 
faces  or  sides  of  a  wedge,  may  hold  each  other  in  equilibrium,  each  of  them 
must  be  in  proportion  to  the  length  of  the  side  on  which  it  acts  :  they  must 
also  be  applied  at  such  parts  that  their  directions  may  meet  in  one  point ; 
for  otherwise  they  will  not  be  completely  opposed  to  each  other,  and  a 
rotatory  motion  will  be  produced.  (Plate  IV.  Fig.  64.) 

If  each  face  of  the  wedge  were  conceived  to  be  capable  of  receiving  a 
pressure,  not  only  in  a  perpendicular  direction,  but  in  any  other  direction 
at  pleasure,  as  some  authors  have  supposed,  the  instrument  would  lose  its 
essential  character  as  a  wedge ;  but  in  such  cases  the  proportion  of  the 
forces  required  for  the  state  of  equilibrium  may  always  be  determined  by 
drawing  a  triangle  with  its  sides  parallel  to  their  directions.* 

It  happens,  however,  not  uncommonly,  that  the  force  actually  operating 
on  the  wedge  is  derived  from  another  force  acting  in  a  direction  more  or 
less  oblique,  as  when  a  heavy  body  rests  on  one  of  the  faces  of  the  wedge 
which  is  inclined  to  the  horizon,  the  body  being  retained  in  its  situation  by 
an  obstacle  or  a  thread  which  confines  it  to  a  vertical  line,  and  the  sliding 
away  of  the  wedge  being  prevented  by  a  horizontal  force.  A  wedge  so 
situated,  and  supposed  to  be  capable  of  sliding  without  friction  on  a  hori- 
zontal surface,  is  sometimes  called  a  moveable  inclined  plane,  and  it  will 
support  the  weight  resting  on  it,  if  the  horizontal  force  be  to  the  weight  as 
the  height  of  the  plane  is  to  its  horizontal  length.  If  the  thread  or  the 
obstacle  helping  to  support  the  weight  be  placed  in  any  other  direction,  the 

*  See  Whewell's  Mechanics. 


ON  PRESSURE  AND  EQUILIBRIUM.  55 

magnitude  of  the  forces  must  be  determined  from  the  general  law  of  the 
composition  of  three  pressures.  (Plate  V.  Fig.  65.) 

If  a  prop  or  bar,  leaning  against  a  smooth  vertical  surface  or  wall,  be 
employed  to  support  or  to  raise  a  weight,  by  means  of  a  force  which  draAvs 
its  base  along  a  smooth  horizontal  surface,  the  horizontal  force  must  be  to 
the  weight  as  the  distance  of  the  bottom  of  the  prop  from  the  wall  to  its 
perpendicular  height.  And  from  similar  principles,  the  conditions  of  the 
equilibrium  of  arches,  domes,  and  roofs  may  be  determined.  (Plate  V. 
Fig.  66,  67.) 

The  action  of  a  screw  depends  on  the  same  principles  as  that  of  an 
inclined  plane  ;*  for  by  rolling  a  thin  and  flexible  wedge,  for  instance  a 
triangular  piece  of  card,  round  a  cylinder,  we  form  a  screw.  We  may 
consider  the  force  tending  to  turn  the  screw  round  its  axis,  as  applied  hori- 
zontally to  the  base  of  the  wedge,  and  the  weight  which  is  to  be  raised  as 
acting  vertically  on  its  inclined  surface  :  the  circumference  of  the  cylinder 
will  represent  the  horizontal  length  of  the  wedge,  and  the  distance  between 
the  threads,  measured  in  the  direction  of  the  axis,  will  be  its  height,  pro- 
vided that  the  threads  be  single  ;  consequently,  the  forces  required  for  the 
equilibrium  are  to  each  other  as  the  height  of  one  spire  to  the  circumference 
of  the  screw.  But  besides  these  forces,  it  is  necessary  that  some  obstacle 
be  present,  which  may  prevent  the  body  on  which  the  screw  acts  from 
following  it  in  its  motion  round  its  axis  ;  otherwise  there  can  be  no  equi- 
librium. (Plate  V.  Fig.  68.) 

The  cylinder,  which  is  the  foundation  of  a  screw,  may  be  either  convex 
or  concave,  making  a  cylindrical  or  a  tubular  screw,  and  these,  when  fitted 
together,  are  sometimes  called  a  screw  and  a  nut.  The  nut  acts  on  the 
screw  with  the  same  mechanical  power  as  a  single  point  would  do,  since  it 
only  divides  the  pressure  among  the  different  parts  of  the  spire.  In  general 
the  screw  is  applied  in  combination  with  a  lever,  in  order  to  procure  an 
advantage  in  overcoming  the  friction,  which  is  always  considerable  in  the 
simple  screw  and  nut,  and  which  would  resist  a  force  applied  immediately 
at  the  circumference,  without  any  diminution  of  its  power.  Sometimes  the 
spires  of  a  screw  are  made  to  act  on  the  teeth  of  a  wheel,  when  a  very  slow 
motion  of  the  wheel,  or  a  very  rapid  motion  of  the  screw,  is  required  for 
the  purposes  of  the  machine.  (Plate  V.  Fig.  69,  70.) 

The  power  of  screws  may  be  increased,  in  a  great  proportion,  by  means 
of  an  arrangement  invented  by  Mr.  Hunter  ;t  which  is  somewhat  similar, 
in  its  operation,  to  the  double  axis  already  described.  A  cylindrical  screw 
is  bored,  and  made  at  the  same  time  a  tubular  screw,  with  a  little  difference 
in  the  distances  of  the  threads  ;  so  that  when  it  is  turned  within  a  fixed  nut 
it  rises  or  sinks  a  little  more  or  less  than  the  internal  screw  which  perfo- 
rates it  would  rise  or  sink  by  the  action  of  its  own  threads,  and  a  weight 
attached  to  this  internal  screw  ascends,  in  each  revolution,  only  through  a 
space  equal  to  the  difference  of  the  height  of  the  two  coils.  Here  the  ma- 

**  Leupold.  Theat.  Machin.  t.  6,  7.  Com.  Bon.  iii.  131,  304.  Kastner  on  the 
Screw.  Commentationes  Soc.  Gott.  4to,  1795,  xiii.  M.  i.  47,  1797,  xiv.  M.  3. 
Ibid,  de  Theoria  Cochlese.  Diss.  VI.  38.  Nicholson's  Jour.  i.  158. 

f  Essay  on  a  New  Method  of  applying  the  Screw,  Ph.  Tr.  1781,  Ixxi.  58. 


56  LECTURE  VII. 

chine  is  analogous  to  a  very  thin  wedge,  of  which  the  thickness  is  only 
equal  to  the  difference  of  the  distances  of  the  threads,  and  which  of  course 
acts  with  a  great  mechanical  advantage.  It  might  in  some  cases  be  more 
convenient  to  make  two  cylindrical  screws,  of  different  kinds,  at,  different 
parts  of  the  same  axis,  rather  than  to  perforate  it.  The  friction  of  such 
machines  is,  however,  a  great  impediment  to  their  operation.  (Plate  V. 
Fig.  71.) 

In  all  the  kinds  of  equilibrium  that  we  have  considered,  and  in  all  other 
cases  that  can  be  imagined,  it  will  be  found  that  the  forces,  or  rather 
weights,  opposed  to  each  other,  are  so  arranged  that  if  they  were  put  in 
motion,  their  momenta  in  the  direction  of  gravity  would,  in  the  first 
instance,  be  equal  and  contrary,  the  velocity  being  as  much  greater  as  the 
magnitude  of  the  weight  is  smaller.*  Thus,  if  an  ounce  weight,  placed  on 
a  lever,  at  the  distance  of  four  feet  from  the  fulcrum,  counterpoise  a  weight 
of  four  ounces  at  the  distance  of  one  foot,  the  velocity  with  which  the 
ounce  would  descend,  if  the  lever  were  moved,  would  be  four  times  as 
great  as  that  with  which  the  weight  of  four  ounces  would  descend.  A 
single  moveable  pulley  ascends  with  half  the  velocity  of  the  end  of  the  rope 
which  is  drawn  upwards,  and  acts  with  a  force  twice  as  great ;  a  block  of 
three  shieves  enables  a  weight  to  sustain  another  six  times  as  great ;  but 
the  velocity  with  which  this  weight  ascends,  is  only  one  sixth  of  that  with 
which  the  smaller  weight  must  descend.  When  a  weight  rests  on  an  in- 
clined plane,  of  wrhich  the  height  is  one  half  of  the  length,  it  may  be 
retained  by  the  action  of  a  weight  of  half  its  magnitude,  drawing  it  up 
the  plane  by  means  of  a  thread  passing  over  a  pulley.  Here  if  the  weight 
ascended  or  descended  along  the  oblique  surface,  its  velocity,  reduced  to  a 
vertical  direction,  would  be  half  as  great  as  that  of  the  smaller  weight 
which  balances  it. 

Some  authors  have  considered  this  law  as  affording  a  fundamental  de- 
monstration of  the  conditions  of  equilibrium  in  all  possible  cases.t  For 
since,  wherever  two  weights  are  in  equilibrium,  if  one  of  them  descended, 
the  other  must  ascend  with  an  equal  quantity  of  motion,  it  appears  absurd 
to  suppose  that  the  force  of  gravitation  could  produce  these  two  equal  and 
contrary  effects  at  the  same  time.  But  it  is  more  satisfactory  to  trace,  in 
every  case,  the  steps  by  which  the  immediate  actions  of  the  different 
weights  are  enabled  to  oppose  each  other  ;  and  the  general  law  may  then 
be  inferred,  by  induction,  from  the  agreement  of  the  particular  results,  in 
confirmation  of  the  general  reasoning  which  tends  to  establish  its  truth. 


LECT.  VII.— ADDITIONAL  AUTHORITIES. 

Mechanical  Powers. — Roberval's  Paradox,  Leupold,  Theatrum  St.  4  t.  17.  Lud- 
lam's  Essays,  1770. 

Equilibrium. — Varignon  on  Composition  of  Forces,  Hist.  etMem.  de  Paris,  1714, 
280,  H.  87.  Riccati,  Comm.  Bon.  ii.  II.  305  ;  III.  215  ;  v.  II.  186.  Foncenex, 
Miscel.  Taurin.  ii.  II.  299.  Euler,  Hist,  et  Mem.  de  1'Acad.  de  Berlin,  1762,  p.  265. 

*  Varro  de  Motu,  Geneva,  1584,  Th.  1. 

f  Lagrange,  Mecanique  Analytique,  4to,  1788,  and  2  vols.  4to,  1811. 


ON  COLLISION.  57 

Acta  Petrop.  iii.  II.  106.     Belidor,    Ingenieur  Fran?ais.      Fuss,  Nova   Acta  Pe- 
trop.  1788,  vi.  197.     Nicholson's  Journal,  iv.  443. 

Virtual  Velocities. — Galileo,  Dial.  1592.  De  Caus,  les  Raisons  des  Forces  Mou- 
vantes,  Antwerp.  Bp.  Wilkins's  Mathematical  Magic,  1648.  J.  Bernoulli,  in  Va- 
rignon's  Mec.  1717.  D'Alembert,  Hist,  et  Mem.  1769,  p.  278.  Lagrange  on  a 
Property  of  the  Centre  of  Gravity,  Ac.  Berl.  1783,  p.  290.  Do.  on  Virtual  Velo- 
cities, Journal  Poly  technique,  ii.  V.  115.  Fossombroni  sul  Principio  delle  Velocita 
Virtuali,  4to,  Flor.  1796.  Essay  on  Virtual  Velocities,  Journal  de  Physique,  xlviii. 
210.  Fourrier  and  Prony  on  Do.  Journal  Poly  technique,  ii.  V.  20, 191.  Buquoy, 
Analytische  Bestimmung  des  Gesetzes  der  Virtuellen  Geschwindigkeiten,  Leips. 
1812.  Do.  Weitere  Entwickerung,  do.  1814.  Do.  Exposition  d'un  Nouveau 
Principe  General  de  Dynamique,  dont  le  Principe  des  v.  v.  n'est  q'un  cas  particulier, 
4to,  Paris,  1815.  Pagani,  Mem.  de  1'Acad.  de  Bruxelles,  1825,  iii.  Gauss  in 
Crelle's  Journal,  Band  4.  Mobius  Lehrbuch  der  Statik,  Leipz.  1837. 


LECTURE   VIII. 


ON  COLLISION. 

HAVING  inquired  into  the  laws  and  properties  of  the  motions  and  rest  of 
single  bodies  under  the  operation  of  one  or  more  forces,  and  into  the  equi- 
librium of  these  forces  in  different  circumstances,  we  are  next  to  examine 
some  simple  cases  of  the  motions  of  various  moveable  bodies  acting  recipro- 
cally on  each  other.  In  all  problems  of  this  kind,  it  is  of  importance  to 
recollect  the  general  principle  already  laid  down  respecting  the  centre  of 
inertia  [gravity]  that  its  place  is  not  affected  by  any  reciprocal  or  mutual 
action  of  the  bodies  constituting  the  system. 

Whenever  two  bodies  act  on  each  other  so  as  to  change  the  direction  of 
their  relative  motions,  by  means  of  any  forces  which  preserve  their 
activity  undiminished  at  equal  distances  on  every  side,  the  relative  veloci- 
ties with  which  the  bodies  approach  to  or  recede  from  each  other,  will 
always  be  equal  at  equal  distances.  For  example,  the  velocity  of  a  comet, 
when  it  passes  near  the  earth  in  its  descent  towards  the  sun,  is  the  same 
as  its  velocity  of  ascent  in  its  return,  although  at  different  distances  its 
velocity  has  undergone  considerable  changes.  In  this  case,  the  force  acts 
continually,  and  attracts  the  bodies  towards  each  other  ;  but  the  force 
concerned  in  collision,  when  a  body  strikes  or  impels  another,  acts  only 
during  the  time  of  more  or  less  intimate  contact,  and  tends  to  separate  the 
bodies  from  each  other.  When  this  force  exerts  itself  as  powerfully  in 
causing  the  bodies  to  separate  as  in  destroying  the  velocity  with  which  they 
meet  each  other,  the  bodies  are  called  perfectly  elastic  :  when  the  bodies 
meet  each  other  without  a  re-action  of  this  kind,  they  are  called  more  or 
less  inelastic.  Ivory,  metals,  and  elastic  gum,  are  highly,  and  almost 
perfectly  elastic  :  clay,  wax  mixed  with  a  little  oil,  and  other  soft  bodies, 
are  almost  inelastic  :  and  the  effects  of  inelastic  bodies  may  be  imitated  by 
elastic  ones,  if  we  cause  them  to  unite  or  adhere  after  an  impulse,  so  as 
to  destroy  the  effect  of  the  repulsive  force  which  tends  to  separate  them. 


58  LECTURE  VIII. 

When  two  bodies  approach  to  each  other,  their  form  is  in  some  degree 
changed,  and  the  more  as  the  velocity  is  greater.  In  general,  the  repulsive 
force  exerted  is  exactly  proportional  to  the  degree  in  which  a  body  is  com- 
pressed ;  and  when  a  body  strikes  another,  this  force  continues  to  be 
increased  until  the  relative  motion  has  been  destroyed,  and  the  bodies  are 
for  an  instant  at  rest  with  respect  to  each  other  ;  the  repulsive  action  then 
proceeds  with  an  intensity  which  is  gradually  diminished,  and  if  the 
bodies  are  perfectly  elastic  they  re-assume  their  primitive  form,  aud  separate 
with  a  velocity  equal  to  that  with  which  they  before  approached  each  other. 
Strictly  speaking,  the  repulsion  commences  a  little  before  the  moment  of 
actual  contact,  but  only  at  a  distance  which  in  common  cases  is  imper- 
ceptible. The  change  of  form  of  an  elastic  substance,  during  collision,  is 
easily  shown  by  throwing  a  ball  of  ivory  on  a  slab  of  marble  or  a  piece  of 
smooth  iron,  coloured  with  black  lead  or  printing  ink  ;  or  by  suffering  it 
to  fall  from  various  heights  :  the  degree  of  compression  will  then  be  indi- 
cated by  the  magnitude  of  the  black  spot  which  appears  on  the  ball.  It 
may  be  shown,  from  the  laws  of  pendulums,  that,  on  the  supposition  that 
the  force  is  proportional  to  the  degree  of  compression,  its  greatest  exertion 
is  to  the  weight  of  a  striking  body,  as  the  height  from  which  the  body 
must  have  fallen,  in  order  to  acquire  its  velocity,  to  half  the  depth  of  the 
impression. 

For  making  experiments  on  the  phenomena  of  collision,  it  is  most  con- 
venient to  suspend  the  bodies  employed  by  threads,  in  the  manner  of 
pendulums  ;  their  velocities  may  then  be  easily  measured  by  observing  the 
chords  of  the  arcs  through  which  they  descend  or  ascend,  since  the  veloci- 
ties acquired  in  descending  through  circular  arcs  are  always  proportional 
to  their  chords  ;  and  for  this  purpose,  the  apparatus  is  provided  with  a 
graduated  arc,  which  is  commonly  divided  into  equal  parts,  although  it 
would  be  a  little  more  correct  to  place  the  divisions  at  the  ends  of  arcs,  of 
which  the  chords  are  expressed  by  the  corresponding  numbers.  (Plate  V. 
Fig.  72.) 

The  simplest  case  of  the  collision  of  elastic  bodies  is  when  two  equal 
balls  descend  through  equal  arcs,  so  as  to  meet  each  other  with  equal 
velocities.  They  recede  from  each  other  after  collision  with  the  same 
velocities,  and  rise  to  the  points  from  which  they  before  descended,  with  a 
small  deduction  for  the  resistance  of  the  surrounding  bodies. 

When  a  ball  at  rest  is  struck  by  another  equal  ball,  it  receives  a  velocity 
equal  to  that  of  the  ball  which  strikes  it,  and  this  ball  remains  at  rest. 
And  if  two  equal  balls  meet  or  overtake  each  other  with  any  unequal 
velocities,  their  motions  will  be  exchanged,  each  rising  to  a  height  equal 
to  that  from  which  the  other  descended. 

The  effect  of  collision  takes  place  so  rapidly,  that  if  several  equal  balls 
be  disposed  in  a  right  line  in  apparent  contact  with  each  other,  and  another 
ball  strike  the  first  of  them,  they  will  all  receive  in  succession  the  whole 
velocity  of  the  moving  ball  before  they  begin  to  act  on  the  succeeding  ones  ; 
they  will  then  transmit  the  whole  velocity  to  the  succeeding  balls,  and 
remain  entirely  at  rest,  so  that  the  last  ball  only  will  fly  off. 

In  the  same  manner,  if  two  or  more  equal  balls,  in  apparent  contact,  be 


ON  COLLISION.  59 

in  motion,  and  strike  against  any  number  of  others  placed  in  a  line,  the 
first  of  the  moving  balls  will  first  drive  off  the  most  remote,  and  then  the 
second  the  last  but  one,  of  the  row  of  balls  which  were  at  rest :  so  that 
the  same  number  of  balls  will  fly  off  together  on  one  side,  as  descended  to 
strike  the  row  of  balls  on  the  other  side  ;  the  others  remaining  at  rest. 

If  the  line  of  balls,  instead  of  being  loosely  in  contact,  had  been  firmly 
united,  they  would  have  been  impelled  with  a  smaller  velocity,  and  the 
ball  striking  them  would  have  been  reflected.  For  when  a  smaller  elastic 
body  strikes  a  larger,  it  rebounds  with  a  velocity  less  than  its  first  velocity, 
and  the  larger  body  proceeds  also  with  a  less  velocity  than  that  of  the 
body  striking  it.  But  if  a  larger  body  strikes  a  smaller,  it  still  proceeds 
with  a  smaller  velocity,  and  the  smaller  body  advances  with  a  greater. 

The  momentum  communicated  by  a  smaller  elastic  body  to  a  larger  one 
is  greater  than  its  own,  and  when  the  first  body  is  of  a  magnitude  compa- 
ratively inconsiderable,  it  rebounds  with  a  velocity  nearly  as  great  as  the 
velocity  of  its  impulse,  and  the  second  body  acquires  a  momentum  nearly 
twice  as  great  as  that  of  the  first.  When  a  larger  body  strikes  a  smaller 
one,  it  communicates  to  it  only  as  much  momentum  as  it  loses. 

In  the  communication  of  motion  between  inelastic  bodies,  the  want  of  a 
repulsive  force,  capable  of  separating  them  with  an  equal  relative  velocity, 
is  probably  owing  to  a  permanent  change  of  form ;  such  bodies  receiving  and 
retaining  a  depression  at  the  point  of  contact.  When  the  velocity  is  too 
small  to  produce  this  change  of  form,  the  bodies,  however  inelastic,  may 
usually  be  observed  to  rebound  a  little. 

Bodies  which  are  perfectly  inelastic,  remain  in  contact  after  collision ; 
they  must  therefore  proceed  with  the  same  velocity  as  the  centre  of  inertia 
[gravity]  had  before  collision.  Thus,  if  two  equal  balls  meet,  with  equal 
velocities,  they  remain  at  rest ;  if  one  is  at  rest,  and  the  other  strikes  it, 
they  proceed  with  half  the  velocity  of  the  ball  which  was  first  in  motion. 
If  they  are  of  unequal  dimensions,  the  joint  velocity  is  as  much  smaller 
than  that  of  the  striking  ball,  as  the  weight  of  this  ball  is  smaller  than  the 
sum  of  the  weights  of  both  balls.  And  in  a  similar  manner  the  effects  of 
any  given  velocities  in  either  ball  may  be  determined. 

It  follows  immediately  from  the  properties  of  the  centre  of  inertia  [gra- 
vity] that  in  all  cases  of  collision,  whether  of  elastic  or  inelastic  bodies, 
the  sum  of  the  momenta  of  all  the  bodies  of  the  system,  that  is  of  their 
masses  or  weights  multiplied  by  the  numbers  expressing  their  velocities,  is 
the  same,  when  reduced  to  the  same  direction,  after  their  mutual  collision, 
as  it  was  before  their  collision.  When  the  bodies  are  perfectly  elastic,  it 
may  also  be  shown  that  the  sum  of  their  energies  or  ascending  forces,  in 
their  respective  directions,  remains  also  unaltered. 

The  term  energy  may  be  applied,  with  great  propriety,  to  the  product  of 
the  mass  or  weight  of  a  body,  into  the  square  of  the  number  expressing  its 
velocity.  Thus,  if  a  weight  of  one  ounce  moves  with  the  velocity  of  a  foot 
in  ^a  second,  we  may  call  its  energy  1  ;  if  a  second  body  of  two  ounces 
have  a  velocity  of  three  feet  in  a  second,  its  energy  will  be  twice  the  square 
of  three,  or  18.  This  product  has  been  denominated  the  living  or  ascend- 
ing force  [the  vis  viva],  since  the  height  of  the  body's  vertical  ascent  is  in 


60  LECTURE  VIII. 

proportion  to  it ;  and  some  have  considered  it  as  the  true  measure  of  the 
quantity  of  motion  ;  but  although  this  opinion  has  been  very  universally 
rejected,  yet  the  force  thus  estimated  well  deserves  a  distinct  denomina- 
tion. After  the  considerations  and  demonstrations  which  have  been  pre- 
mised on  the  subject  of  forces,  there  can  be  no  reasonable  doubt  with 
respect  to  the  true  measure  of  motion  ;  nor  can  there  be  much  hesitation  in 
allowing  at  once,  that  since  the  same  force,  continued  for  a  double  time,  is 
known  to  produce  a  double  velocity,  a  double  force  must  also  produce  a 
double  velocity  in  the  same  time.  Notwithstanding  the  simplicity  of  this 
view  of  the  subject,  Leibnitz,*  Smeaton,t  and  many  others  have  chosen  to 
estimate  the  force  of  a  moving  body  by  the  product  of  its  mass  into  the 
square  of  its  velocity ;  and  though  we  cannot  admit  that  this  estimation 
of  force  is  just,  yet  it  may  be  allowed  that  many  of  the  sensible  effects  of 
motion,  and  even  the  advantage  of  any  mechanical  power,  however  it  may 
be  employed,  are  usually  proportional  to  this  product,  or  to  the  weight  of 
the  moving  body,  multiplied  by  the  height  from  which  it  must  have  fallen, 
in  order  to  acquire  the  given  velocity.  Thus  a  bullet,  moving  with  a 
double  velocity,  will  penetrate  to  a  quadruple  depth  in  clay  or  tallow  :  a 
ball  of  equal  size,  but  of  one  fourth  of  the  weight,  moving  with  a  double 
velocity,  will  penetrate  to  an  equal  depth  :  and,  with  a  smaller  quantity  of 
motion,  will  make  an  equal  excavation  in  a  shorter  time.  This  appears  at 
first  sight  somewhat  paradoxical :  but,  on  the  other  hand,  we  are  to  con- 
sider the  resistance  of  the  clay  or  tallow  as  a  uniformly  retarding  force, 
and  it  will  be  obvious  that  the  motion,  which  it  can  destroy  in  a  short 
time,  must  be  less  than  that  which  requires  a  longer  time  for  its  destruc- 
tion. Thus  also  when  the  resistance,  opposed  by  any  body  to  a  force  tend- 
ing to  break  it,  is  to  be  overcome,  the  space  through  which  it  may  be  bent 
before  it  breaks  being  given,  as  well  as  the  force  exerted  at  every  point  of 
that  space,  the  power  of  any  body  to  break  it  is  proportional  to  the  energy 
of  its  motion,  or  to  its  weight  multiplied  by  the  square  of  its  velocity. 

In  almost  all  cases  of  the  forces  employed  in  practical  mechanics,  the  labour 
expended  in  producing  any  motion,  is  proportional,  not  to  the  momentum, 
but  to  the  energy  which  is  obtained  ;  since  these  forces  are  seldom  to  be 
considered  as  uniformly  accelerating  forces,  but  generally  act  at  some  dis- 
advantage when  the  velocity  is  already  considerable.  For  instance,  if  it 
be  necessary  to  obtain  a  certain  velocity,  by  means  of  the  descent  of  a 
heavy  body  from  a  height  to  which  we  carry  it  by  a  flight  of  steps,  we 
must  ascend,  if  we  wish  to  double  the  velocity,  a  quadruple  number  of 
steps,  and  this  will  cost  us  nearly  four  times  as  much  labour.  In  the  same 
manner,  if  we  press  with  a  given  force  on  the  shorter  end  of  a  lever,  in 
order  to  move  a  weight  at  a  greater  distance  on  the  other  side  of  the  ful- 
crum, a  certain  portion  of  the  force  is  expended  in  the  pressure  which  is 
supported  by  the  fulcrum,  and  we  by  no  means  produce  the  same  mo- 

*  Acta  Erudit.  Lips.  1686. 

t  Ph.  Tr.  1776,  p.  450,  and  1782,  p.  337.  See  Desaguliers's  Exp.  Ph.  ii.  92 ; 
and  Ph.  Tr.  1723,  xxxii.  269,  285.  Eames  on  the  Force  of  Moving  Bodies,  Ph.  Tr. 
1726,  xxxiv.  188.  Clarke  in  Ph.  Tr.  1728,  xxxv.  381.  Zendrini,  Sulla  Inutilita 
della  Questione  Intorno  alia  Misura  delle  Forze  Vivi,  8vo,  Venezia,  1804. 


ON  COLLISION.  61 

mentum  as  would  have  been  obtained  by  the  immediate  action  of  an  equal 
force  on  the  body  to  be  moved. 

An  elastic  ball  of  2  ounces  weight,  moving  with  a  velocity  of  3  feet  in  a 
second,  possesses  an  energy,  as  we  have  already  seen,  which  may  be  ex- 
pressed by  18.  If  it  strike  a  ball  of  1  ounce  which  is  at  rest,  its  velocity 
will  be  reduced  to  1  foot  in  a  second,  and  the  smaller  ball  will  receive  a 
velocity  of  4  feet :  the  energy  of  the  first  ball  will  then  be  expressed  by  2, 
and  that  of  the  second  by  16,  making  together  18,  as  before.  The  mo- 
mentum of  the  larger  ball  after  collision  is  2,  that  of  the  smaller  4,  and  the 
sum  of  these  is  equal  to  the  original  momentum  of  the  first  ball. 

Supposing  the  magnitude  of  an  elastic  body  which  is  at  rest  to  be 
infinite,  it  will  receive  twice  the  momentum  of  a  small  body  that  strikes 
it ;  but  its  velocity,  and  consequently  its  energy,  will  be  inconsiderable, 
since  the  energy  is  expressed  by  the  product  of  the  momentum  into  the 
velocity.  And  if  the  larger  body  be  of  a  finite  magnitude,  but  still  much 
greater  than  the  smaller,  its  energy  will  be  very  small ;  that  of  the  smaller, 
which  rebounds  with  a  velocity  not  much  less  than  its  original  velocity, 
being  but  little  diminished.  It  is  for  this  reason  that  a  man,  having  a 
heavy  anvil  placed  on  his  chest,  can  bear,  without  much  inconvenience,  the 
blow  of  a  large  hammer  striking  on  the  anvil,  while  a  much  slighter  blow 
of  the  hammer,  acting  immediately  on  his  body  would  have  fractured  his 
ribs,  and  destroyed  his  life.  The  anvil  receives  a  momentum  nearly  twice 
as  great  as  that  of  the  hammer  ;  but  its  tendency  to  overcome  the  strength 
of  the  bones  and  to  crush  the  man,  is  only  proportional  to  its  energy,  which 
is  nearly  as  much  less  than  that  of  the  hammer,  as  four  times  the  weight  of 
the  hammer  is  less  than  the  weight  of  the  anvil.  Thus,  if  the  weight  of 
the  hammer  were  5  pounds,  and  that  of  the  anvil  100,  the  energy  of  the 
anvil  would  be  less  than  [only]  one  fifth  as  great  as  that  of  the  hammer, 
besides  some  further  diminution,  on  account  of  the  want  of  perfect  elas- 
ticity, and  from  the  effect  of  the  larger  surface  of  the  anvil  in  dividing  the 
pressure  occasioned  by  the  blow,  so  as  to  enable  a  greater  portion  of  the 
chest  to  cooperate  in  resisting  it. 

When  a  body  strikes  another  in  a  direction  which  does  not  pass  through 
its  centre  of  gravity,  the  effect  produced  involves  the  consideration  of 
rotatory  motion,  since,  in  this  case,  the  body  is  made  to  revolve  on  an  axis. 
But  this  can  never  happen  when  the  body  is  spherical,  and  its  surface 
perfectly  polished  ;  since  every  impulse  must  then  be  perpendicular  to  the 
surface,  and  must  consequently  be  directed  to  the  centre  of  the  body.  If 
the  motion  of  a  ball  which  strikes  another  is  not  directed  to  its  centre,  the 
surface  of  contact  must  be  oblique  with  respect  to  its  motion,  and  the 
second  ball  will  only  receive  an  impulse  in  a  direction  perpendicular  to 
this  surface,  while  the  first  receives,  from  its  reaction,  an  equal  impulse  in 
a  contrary  direction,  which  is  combined  with  its  primitive  mption.  The 
magnitude  of  this  impulse  may  be  determined  by  resolving  the  motion  of 
the  first  ball  into  two  parts,  the  one  parallel  to  the  surface  of  contact,  and 
the  other  perpendicular ;  the  first  part  remaining  always  unaltered,  the 
second  being  modified  by  the  collision.  If,  for  example,  the  balls  were 
equal,  this  second  part  of  the  motion  would  be  destroyed,  and  the  remain- 


62  LECTURE  VIII. 

ing  motion  would  be  in  the  direction  of  the  surface  of  contact,  and  perpen- 
dicular to  that  of  the  ball  impelled. 

Hence  it  follows,  that  if  we  wish  to  impel  a  billiard  ball  *  in  a  given 
direction,  by  the  stroke  of  another  ball,  we  have  only  to  imagine  a  third 
ball  to  be  placed  in  contact  with  the  first,  immediately  behind  it  in  the 
line  of  the  required  motion,  and  to  aim  at  the  centre  of  this  imaginary  ball ; 
the  first  ball  will  then  be  impelled  in  the  required  direction,  and  the  second 
will  also  continue  to  move  in  a  direction  perpendicular  to  it. 

By  a  similar  resolution  of  the  motion  of  an  elastic  ball,  we  may  deter- 
mine its  path,  when  it  is  reflected  from  a  fixed  obstacle.  That  part  of  the 
motion,  which  is  in  a  direction  parallel  to  the  surface  of  the  obstacle,  re- 
mains undiminished  :  the  motion  perpendicular  to  it  is  changed  for  an 
equal  motion  in  a  contrary  direction,  and  the  joint  result  of  these  consti- 
tutes a  motion,  in  a  direction  which  is  equally  inclined  to  the  surface  with 
the  first  motion,  but  on  the  opposite  side  of  the  perpendicular.  Of  this  we 
have  also  a  familiar  instance  in  the  motions  of  billiard  balls  ;  for  we  may 
observe,  that  a  ball  rebounds  from  the  cushion  in  an  angle  equal  to  that  in 
which  it  arrives  at  it ;  and  if  we  wish  that  our  ball,  after  reflection,  should 
strike  another  placed  in  a  given  situation,  we  may  suppose  a  third  ball  to 
be  situated  at  an  equal  distance,  on  the  other  side  of  the  cushion,  and  aim 
at  this  imaginary  ball :  our  ball  will  then  strike  the  second  ball,  after  re- 
flection, with  a  direct  impulse.  We  here  suppose  the  reflection  to  take 
place  when  the  centre  of  the  ball  arrives  at  the  cushion,  while  in  fact  the 
surface  only  comes  into  contact  with  it ;  if  we  wish  to  be  more  accurate, 
we  may  place  the  imaginary  ball  at  an  equal  distance  beyond  the  centre  of 
a  ball  lying  in  contact  with  the  nearest  part  of  the  cushion,  instead  of 
measuring  the  distance  from  the  cushion  itself.  (Plate  V.  Fig.  73.) 

When  the  number  of  bodies,  which  meet  each  other,  is  greater,  and  their 
magnitudes  and  motions  are  diversified,  the  calculation  of  the  effects  of 
collision  becomes  very  intricate,  and  the  problem  is  scarcely  applicable  to 
any  practical  purpose.  Those  who  are  desirous  of  pursuing  the  investiga- 
tion as  a  mathematical  amusement,  will  find  all  the  assistance  that  they 
require  in  the  profound  and  elegant  works  of  Maclaurin. 


LECT.  VIII.— ADDITIONAL  AUTHORITIES. 

Galileo,  Op.  i.  957,  ii.  479.  Wallis,  Wren,  Huygens,  in  Ph.  Tr.  1668-69-71.  In 
the  last,  Wallis  gives  a  correct  view  of  momentum.  Mariotte,  Traite  de  la  Percussion 
des  Corps,  12mo,  Par.  1673.  Borellus  de  vi  Percussionis,  4to,  Lugd.  1686.  Saulmon 
— Mairan— Molieres,  Hist.et  Mem.  de  Paris,  1721, pp.  23 ;  1722,  p.  23,  38,40  ;  1726. 
Gravesande,  Essai  d'uneNouvelleTheoriedu  Choc  des  Corps  fondee  sur  1' Experience, 
12mo,  La  Haye,  1722.  Maclaurin's  Fluxions,  2  vols.  4to,  1742.  Milner,  Ph.  Tr. 
1788,  p.  344.  Euler,  Comm.  Petr.  v.  159  ;  ix.  50.  N.  Comm.  Petr.  xv.  414  ;  xvii. 
315.  Mem.  de  Berl.  1745,  p.  21.  Theoria  Motus  Corporum  Solid.  &c.  &c. 

*  BiUiards,  Encyclopedic  Methodique,  pi.  4  ;  Art.  Pausmerie,  pi.  4,  5  ;  Art. 
Amusemens  de  Mecanique.  Coriolis,  Theorie  Mathematique  du  Jeu  de  Billiard,  8vO. 


63 


LECTURE    IX 


ON  THE  MOTIONS  OF  CONNECTED  BODIES. 

THE  motions  of  single  bodies,  acting  in  any  manner  on  each  other,  which 
we  have  been  considering,  as  far  as  they  belong  to  the  effects  of  collision, 
are  of  less  importance  to  practical  mechanics,  than  the  affections  of  such 
bodies  as  are  united,  so  as  either  to  revolve  round  a  common  centre,  or  to 
participate  in  each  other's  motions  by  any  kind  of  machinery. 

It  is  only  within  half  a  century,  that  the  phenomena  and  effects  of  rota- 
tory motion  have  been  sufficiently  investigated.  Newton  committed  a 
mistake,  which  is  now  universally  acknowledged,  in  his  computation  of  the 
precession  of  the  equinoxes,  for  want  of  attending  sufficiently  to  the  subject ; 
and  it  is  of  importance  in  the  calculation  of  many  of  the  effects  of  me- 
chanical arrangements,  that  it  should  be  treated  in  an  accurate  manner. 

The  effect  of  a  moving  body  in  producing  motion  in  any  other  bodies,  so 
connected  as  to  be  capable  of  turning  freely  round  a  given  centre,  is  jointly 
proportional  to  its  distance  from  that  centre,  and  to  its  momentum  in  the 
direction  of  the  motion  to  be  produced.  Thus  a  body,  of  one  pound  weight, 
moving  with  a  velocity  of  one  foot  in  a  second,  will  have  three  times  as 
great  an  effect  on  a  system  of  bodies,  to  which  its  whole  force  is  communi- 
cated, at  the  distance  of  one  yard  from  the  centre  of  their  motion,  as  if  it 
acted  only  at  the  distance  of  a  foot,  on  the  same  system  of  bodies :  a  double 
weight,  or  a  double  velocity,  would  also  produce  a  double  effect.  For, 
supposing  two  unequal  bodies  to  be  connected  by  an  inflexible  line,  and  to 
move  with  equal  velocities  in  a  direction  perpendicular  to  that  of  the  line, 
it  is  demonstrable,  from  the  principles  of  the  composition  of  motion,  that 
they  may  be  wholly  stopped  by  an  obstacle  applied  to  the  centre  of  gravity, 
consequently  their  effects  in  turning  the  line  round  this  point  are  equal ; 
here  the  momenta  are  proportional  to  the  weights,  but  the  products  obtained 
by  multiplying  them  by  the  distances  from  the  centre,  at  which  they  act, 
are  equal :  these  products  therefore  represent  the  rotatory  power  of  the 
respective  bodies.  Hence  in  a  connected  system  of  bodies,  revolving  round 
a  given  point,  with  equal  angular  velocities,  the  effect  produced  by  the 
rotatory  motion  of  each  body,  as  well  as  the  force  which  is  employed  in 
producing  it,  is  expressed  by  the  product  of  the  mass  multiplied  by  the 
square  of  the  velocity,  since  the  velocity  is  in  this  case  proportional  to  the 
distance  from  the  centre  ;  and  this  product  is  the  same  that  I  have  denomi- 
nated the  energy  of  a  moving  body. 

These  propositions  are  of  great  use  in  all  inquiries  respecting  the  opera- 
tions of  machines  ;  and  it  is  of  importance  to  bear  in  mind,  that  although 
the  equilibrium  of  a  system  of  bodies  is  determined  by  the  equality  of  the 
products  of  their  weights  into  their  effective  distances  on  each  side  of  the 
centre,  yet  that  the  estimation  of  the  mechanical  power  of  each  body,  when 
once  in  motion,  requires  the  mass  to  be  multiplied  by  the  square  of  the 
distance,  or  of  the  velocity.  For  this  reason,  together  with  some  others, 


64  LECTURE  IX. 

which  have  been  already  mentioned,  some  have  considered  the  square  of  the 
velocity  as  affording  the  true  measure  of  force  ;  but  the  properties  of 
motion,  concerned  in  the  determination  of  rotatory  power,  are  in  reality 
no  more  than  necessary  consequences  of  the  simpler  laws  on  which  the 
whole  theory  of  mechanics  is  founded. 

The  effects  of  rotatory  motion  may  be  very  conveniently  examined,  by 
means  of  an  apparatus  similar  to  that  which  was  employed  for  the  same 
purpose  by  Mr.  Smeaton.*  A  vertical  axis  is  turned  by  a  thread  passing 
over  a  pulley,  and  supporting  a  scale  with  weights ;  the  thread  may  be 
applied  at  different  parts  of  the  axis,  having  different  diameters,  and  the 
axis  supports  two  arms,  on  which  two  leaden  weights  are  fixed,  at  distances 
which  may  be  varied  at  pleasure.  The  same  force  will  then  produce,  in 
the  same  time,  but  half  the  velocity,  in  the  same  situation  of  the  weights, 
when  the  thread  is  applied  to  a  part  of  the  axis  of  half  the  diameter :  and 
if  the  weights  are  removed  to  a  double  distance  from  the  axis,  a  quadruple 
force  will  be  required,  in  order  to  produce  an  equal  angular  velocity  in  a 
given  time.  (Plate  V.  Fig.  74.) 

When  a  number  of  connected  bodies,  or  a  single  body  of  considerable 
magnitude,  is  made  to  revolve  round  a  centre,  it  is  sometimes  necessary  to 
inquire  into  what  point  their  masses  might  be  supposed  to  be  concentrated 
so  as  to  preserve  the  same  rotatory  power  with  the  same  angular  velocity. 
This  point  is  called  the  centre  of  gyration.  In  a  circle,  or  any  portion  of  a 
circle,  turning  round  its  centre,  the  square  of  the  distance  of  this  point  from 
the  centre,  is  half  the  square  of  the  semidiameter  ;  and  the  whole  effect  of 
the  momentum  of  the  circle  upon  an  obstacle  at  its  circumference,  is  exactly 
half  as  great  as  that  of  an  equal  quantity  of  matter,  striking  the  obstacle 
with  the  velocity  of  the  circumference. 

There  is  another  point,  of  which  the  determination  is  of  considerable 
utility  in  many  mechanical  problems :  this  is  the  centre  of  percussion  ;  or 
the  point  at  which  an  obstacle  must  be  applied,  in  order  to  receive  the  whole 
effect  of  a  stroke  of  a  body  which  is  revolving  round  a  given  centre,  with- 
out producing  any  pressure  or  strain  on  the  centre  or  axis  of  motion.  In 
a  straight  line,  or  a  slender  rod  fixed  at  one  extremity,  the  distance  of  this 
point  from  the  centre  of  motion  is  two  thirds  of  the  whole  length.t 

The  same  point  is  also  the  centre  of  oscillation,  the  distance  of  which 
determines  the  time  of  oscillation  or  vibration  of  the  body,  suspended  as 
a  pendulum  upon  the  given  centre  of  motion.^  It  may  easily  be  shown 
that  a  rod  a  yard  long,  and  of  equable  thickness,  suspended  at  one  ex- 
tremity, vibrates  in  the  same  time  as  a  ball  suspended  by  a  thread  of  which 
the  length  is  two  feet.  But  if  the  rod  were  suspended  on  a  centre  at  some 
point  within  its  extremities,  the  time  of  its  vibration  would  be  prolonged, 
so  as  to  become  equal  to  that  of  a  simple  pendulum  of  much  greater  length. 

*  Ph.  Tr.  1776,  Ixvi.  450,  and  plate.  See  an  examination  of  this  paper  in 
Atwood,  p.  382. 

t  Lahire,  Hist,  et  Mem.  Paris,  ix.  175.  Parent,  ibid.  1700,  H.  149.  Bernoulli, 
ibid.  1703,  pp.  78,  272,  H.  114  ;  1704,  p.  136,  H.  89.  Clairaut,  ibid.  1735,  p.  281, 
H.  92. 

J  Huygens,  Hist,  et  Mem.  de  1'Acad.  x.  446,  462,  and  Hor.  Osc.  121.  John  Ber- 
noulli de  Natura  Centri  Oscil.  1714.  Taylor,  Ph.  Tr.  1713. 


ON  THE  MOTIONS  OF  CONNECTED  BODIES.  65 

This  may  be  illustrated  by  two  balls  fixed  at  the  end  of  a  rod,  with  a  centre 
of  suspension  moveable  to  any  part  of  the  rod,  for  as  the  centre  approaches 
the  middle  of  the  rod,  the  vibrations  are  rendered  extremely  slow.  (Plate  V. 
Fig.  75.) 

The  rotatory  motion  of  bodies  not  fixed  on  an  axis  might  be  considered 
in  this  place,  but  the  subject  involves  in  its  whole  extent  some  intricacy  of 
calculation,  and,  except  in  astronomy,  the  investigation  is  scarcely  ap- 
plicable to  any  problems  which  occur  in  practice.  We  may,  however, 
examine  a  few  of  the  simplest  cases.  If  two  bodies  be  supposed  to  be  con- 
nected by  an  inflexible  line,  and  to  be  moving  with  equal  velocities  in 
parallel  directions  ;  if  an  immoveable  obstacle  be  applied,  so  as  to  form  a 
fulcrum,  at  the  common  centre  of  gravity,  they  will,  as  we  have  already 
seen,  be  wholly  stopped  ;  but  if  the  fulcrum  be  applied  to  any  other  part  of 
the  line,  one  of  the  bodies  will  move  forwards,  and  the  other  backwards,  with 
a  velocity  which  may  easily  be  determined  by  calculating  their  rotatory 
power  with  respect  to  the  fulcrum.  If  the  fulcrum  be  applied  at  a  point 
of  the  line  continued  beyond  the  bodies,  the  one  will  lose  and  the  other 
gain  velocity ;  since  the  quantity  of  rotatory  power  will  always  remain 
unaltered  :  that  point  only  which  is  denominated  the  centre  of  oscillation 
retaining  its  original  velocity.  Now  the  same  inequality  in  the  motion  of 
the  bodies,  and  consequently  the  same  angular  velocity  of  rotation  will  be 
produced,  if  the  connected  bodies  be  initially  at  rest,  and  the  fulcrum  be 
applied  to  them  with  the  same  relative  velocity.  For  example,  if  a  straight 
rod  or  wire  receive  an  impulse  at  one  end  in  a  transverse  direction,  the 
centre  of  oscillation,  which  is  at  the  distance  of  two  thirds  of  the  length 
from  the  end  struck,  will  at  the  first  instant  remain  at  rest,  consequently 
the  centre  will  move  with  one  fourth  of  the  velocity  of  the  impulse,  and 
this  must  be  the  velocity  of  the  progressive  motion  of  the  rod,  since  the 
centre  of  gravity  of  any  body  which  is  at  liberty  moves  always  with  an 
equable  velocity  in  a  right  line,  while  the  whole  rod  will  also  revolve 
equably  round  its  centre,  except  such  retardations  as  may  arise  from 
foreign  causes.  In  a  similar  manner  the  computation  may  be  extended  to 
bodies  of  a  more  complicated  form.  Thus  it  has  been  calculated  at  what 
point  of  each  planet  an  impulse  must  have  operated,  in  order  to  communi- 
cate to  it  at  one  blow  its  rotation  and  its  progressive  motion  in  its  orbit.* 

Those  who  have  asserted  that  the  motion  of  the  centre  of  gravity  of  a 
body  can  only  be  produced  by  an  impulse  which  is  either  wholly  or  partly 
directed  towards  it,  have  obviously  been  mistaken.  The  centre  of  oscilla- 
tion is  the  only  point  which  remains  at  rest  with  regard  to  the  first  effect 
of  the  stroke,  and  the  centre  of  gravity,  which  never  coincides  with  the 
centre  of  oscillation,  moves  in  the  direction  of  the  impulse,  while  the  parts 
beyond  the  centre  of  oscillation  begin  to  move  in  a  contrary  direction. 
Hence  it  is  that  a  thin  stick  may  be  broken  by  a  blow  on  the  middle,  with- 
out injuring  the  glasses  on  which  it  is  supported  :  fo'r  the  ends  of  the  stick, 
instead  of  being  depressed  by  the  stroke,  would  rise  with  half  the  velocity 
of  the  body  which  strikes  them,  if  the  two  portions  were  separated  without 

*  John  Bernoulli,  Op.  vol.  4,  284.     Consult  Whewell,  Dynamics,  1823,  c.  8. 

F 


66  LECTURE  IX. 

the  loss  of  any  force.  But  unless  some  art  has  been  previously  employed 
in  producing  a  partial  separation,  it  will  frequently  be  found  that  the  stick 
has  strength  enough  to  break  the  glasses  before  it  gives  way. 

When  an  insulated  body  revolves  round  an  axis  in  any  direction,  the 
state  of  revolution  cannot  be  permanent,  unless  the  axis  be  so  situated  that 
the  centrifugal  forces  on  each  side  of  it  balance  each  other.*  It  is  obvious 
that  this  must  happen  in  a  homogeneous  sphere,  whatever  may  be  the 
situation  of  the  axis  ;  and  it  has  been  demonstrated,  that  when  the  body 
is  of  an  irregular  form,  there  are  at  least  three  different  axes,  situated  at 
right  angles  to  each  other,  round  which  the  body  may  revolve  in  an  equi- 
librium either  stable  or  tottering.  It  may  also  be  shown  that  if  a  body, 
revolving  round  any  axis,  receive  at  the  same  time  an  impulse  whicli 
would  cause  it  to  revolve  round  a  second  axis  in  another  direction,  the  two 
revolutions  will  be  combined,  and  will  form  a  single  revolution  round  a 
third  axis  in  an  intermediate  position,  which  will  remain  at  rest  until  it  be 
displaced  by  some  new  force,  provided  that  it  be  one  of  the  axes  of  permanent 
revolution  :  so  that  no  body  can  revolve  round  a  moveable  axis  without  a 
continual  disturbing  force.  And  when  an  irregular  body  begins  to  move  on 
an  axis  incapable  of  equilibrium,  its  revolution  will  be  gradually  altered, 
so  as  to  approach  continually  to  a  revolution  round  one  of  the  natural 
axes  ;  but  it  will  never  pass  beyond  the  state  of  equilibrium,  as  in  many 
other  cases  of  deviation  from  such  a  state  ;  since  the  momentum  pro- 
duced by  the  excess  of  centrifugal  force  in  one  part  of  the  revolution  is 
destroyed  in  another.  For  a  similar  reason,  if  a  stick  be  thrown,  in  a 
horizontal  position,  with  a  rotatory  motion,  it  will  fall  in  the  same  position 
much  more  certainly  than  if  it  were  thrown  without  any  rotation ;  for 
any  small  disturbing  force,  which  might  be  sufficient  to  turn  it  into  a  verti- 
cal position  during  the  course  of  its  path,  will  only  produce,  when  com- 
bined with  the  rotatory  motion,  a  slight  change  of  the  direction  of  the  rota- 
tion, which  will  confine  the  deviation  of  the  stick  from  a  horizontal  posi- 
tion within  narrow  limits. 

The  subject  of  preponderance,  or  of  the  action  of  wreights  or  forces  coun- 
teracted by  other  forces  and  incumbered  with  foreign  matter  to  be  put  in 
motion,  requires  for  its  discussion  a  previous  knowledge  of  the  simple 
operation  of  forces,  of  the  conditions  of  equilibrium,  and  of  the  estimation 
of  rotatory  power.  The  consideration  of  the  effects  of  preponderance 
enables  us  to  determine,  in  some  circumstances,  the  best  possible  propor- 
tions of  the  powers  of  machines  for  producing  the  required  effects  in  the 
most  advantageous  manner.  For,  in  order  that  motion  may  be  produced,  it 
is  not  sufficient  that  there  be  an  equilibrium,  in  procuring  which  a  part  only 
of  the  power  is  expended,  but  there  must  be  an  excess  of  force  above  that 
which  would  be  necessary  for  the  equilibrium;  and  it  is  often  of  con- 
sequence to  know  what  portion  of  the  power  must  be  employed  in  each 
wray,  in  order  that  the  greatest  effect  may  be  produced  in  a  given  time. 
We  are  sometimes  told,  that  what  we  gain  in  power  we  lose  in  time.  t  In 

*  Segner,  de  Motu  Turbinum,  Halle,  1755,  first  pointed  out  the  three  natural 
axes  of  rotation  of  all  bodies.  Their  existence  was  demonstrated  by  Eujer  in  1760. 
See  Hist,  et  Mem.  de  1'Acad.  1758,  p.  154;  1760,  p.  176. 


ON  THE  MOTIONS  OF  CONNECTED  BODIES.  67 

one  sense  indeed  the  remark  is  true  ;  thus  one  man  can  do  no  more  by  a 
powerful  machine  in  ten  hours,  than  ten  men  can  do  by  a  weaker  machine 
in  one  hour  ;  but  in  other  senses  the  assertion  is  often  erroneous  ;  for  by 
increasing  the  mechanical  advantage  to  a  given  degree  we  may  in  some 
cases  considerably  increase  the  performance  of  a  machine  without  adding 
to  the  force. 

According  to  the  nature  of  the  force  employed,  and  to  the  construction 
of  the  machine,  a  different  calculation  may  be  required  for  finding  the  best 
proportions  of  the  forces  to  be  employed  ;  but  a  few  simple  instances  will 
serve  to  show  the  nature  of  the  determination.  Thus,  in  order  that  a 
smaller  weight  may  raise  a  greater  to  a  given  vertical  height,  in  the 
shortest  time  possible,  by  means  of  an  inclined  plane,  the  length  of  the  plane 
must  be  to  its  height  as  twice  the  greater  weight  to  the  smaller,*  so  that  the 
acting  force  may  be  twice  as  great  as  that  which  is  simply  required  for 
the  equilibrium.  This  may  be  shown  experimentally,  by  causing  three 
equal  weights,  supported  on  wheels,  to  ascend  at  the  same  time  as  many 
inclined  planes  of  the  same  height  but  of  different  lengths,  by  means  of 
the  descent  of  three  other  equal  weights,  connected  with  the  former  three 
by  threads  passing  over  pullies.  The  length  of  one  of  the  planes  is  twice 
its  height,  that  of  another  considerably  more,  and  that  of  a  third  less  :  if 
the  weights  begin  to  rise  at  the  same  time,  the  first  will  arrive  at  the  top 
before  either  of  the  others.  (Plate  V.  Fig.  76.) 

If  a  given  weight,  or  any  equivalent  force,  be  employed  to  raise  another 
equal  weight  by  means  of  levers,  wheels,  pullies,  or  any  similar  powers, 
the  greatest  effect  will  be  produced  if  the  acting  weight  be  capable  of  sus- 
taining in  equilibrium  a  weight  about  twice  and  a  half  as  great  as  itself. 
This  proposition  may  be  very  satisfactorily  illustrated  by  an  experiment. 
Three  double  pullies  being  placed,  independently  of  each  other,  on  an  axis, 
round  which  they  move  freely,  the  diameters  of  the  two  cylindrical  por- 
tions which  compose  the  first  being  in  the  ratio  of  3  to  2,  those  of  the 
second  as  5  to  2,  and  those  of  the  third  as  4  to  1,  six  equal  weights  are 
attached  to  them  in  pairs,  so  that  three  may  be  raised  by  the  descent  of  the 
other  three,  on  the  principle  of  the  wheel  and  axis.  If  then  we  hold  the 
lower  weights  by  means  of  threads  or  otherwise,  and  let  them  go,  so  that 
they  may  begin  to  rise  at  the  same  instant,  it  will  appear  evidently  that 
the  middle  pulley  raises  its  wreight  the  fastest ;  and  consequently,  that  in 
this  case,  the  ratio  of  5  to  2  is  more  advantageous  than  either  a  much  less 
or  a  much  greater  ratio.  If  the  weight  to  be  raised  were  very  great  in  pro- 
portion to  the  descending  weight,  the  arrangement  ought  to  be  such  that  this 
weight  might  retain  in  equilibrium  a  weight  about  twice  as  great  as  that 
which  is  actually  to  be  raised.  If  the  descending  weight  were  a  hundred 
times  as  great  as  the  ascending  weight,  the  greatest  velocity  would  be 
obtained  in  this  case,  by  making  the  descending  weight  capable  of  holding 
in  equilibrium  a  weight  one  ninth  as  great  as  itself.  (Plate  VI.  Fig.  77.) 

The  proportion  required  for  the  greatest  effect  is  somewhat  different, 

when  the  heights  through  which  both  the  weights  are  to  move  are  limited, 

as  they  usually  must  be  in  practical  cases.     Here,  if  we  suppose  the  opera- 

*  Whewell's  Dyn.  c.  4,  §  4. 

F2 


68  LECTURE  IX. 

tion  to  be  continually  repeated,  the  effect  will  be  greatest  in  a  given  time, 
when  the  ascending  weight  is  between  two  thirds  and  one  half  of  the  exact 
counterpoise  to  the  descending  weight:  If,  however,  the  force  were  accu- 
mulated during  the  action  of  the  machine,  there  would  be  no  limit  to  the 
advantage  of  a  slow  motion.  Thus,  if  we  have  a  stream  of  water  filling  a 
single  reservoir,  which  is  to  raise  a  weight  by  means  of  its  descent,  the 
proportion  here  assigned  will  be  the  best  for  performing  the  most  work  in 
a  given  time  ;  but  if  we  chose  to  double  our  machine,  so  that  one  reservoir 
should  be  filled  during  the  descent  of  another,  it  would  be  proper  to  pro- 
portion the  weights  in  such  a  manner  that  the  whole  time  required  for 
filling  one  of  the  reservoirs  should  be  occupied  in  the  descent  and  the  re- 
ascent  of  the  other. 

In  all  these  cases,  if  great  accuracy  were  required,  it  would  be  necessary 
in  the  calculation  to  add  to  the  mass  to  be  moved  the  quantity  of  moveable 
matter  in  the  machine,  reduced  to  a  mean  distance  from  the  fulcrum  or 
centre,  according  to  its  rotatory  power,  in  the  same  manner  as  the  centre  of 
gyration  is  determined.  But  there  is  seldom  occasion  for  such  a  degree  of 
precision.  The  magnitude  of  the  pressure  which  is  exerted  on  the  fulcrum 
during  the  motion  of  the  connected  bodies  may  always  be  determined,  by 
comparing  the  actual  velocity  of  the  centre  of  gravity  with  that  of  a  body 
descending  without  resistance. 

These  propositions  and  experiments  must  be  allowed  to  require  an  atten- 
tive consideration  from  those  who  are  engaged  in  practical  mechanics  ;  and 
it  is  natural  to  suppose  that  the  proportions  laid  down  may  be  adopted  with 
safety,  and  employed  with  success,  and  that  we  may  sometimes  derive 
important  advantages  from  their  application.  But  on  more  mature  consi- 
deration, we  shall  find  some  practical  reasons  for  caution  in  admitting  them 
without  material  alterations.* 

If  a  machine  were  constructed  for  raising  a  solid  weight,  and  so  arranged 
as  to  perform  its  office  in  the  shortest  possible  time  with  a  given  expense  of 
power,  the  weight  would  still  possess,  when  it  arrived  at  the  place  of  its 
destination,  a  considerable  and  still  increasing  velocity  :  in  order  that  it 
might  retain  its  situation,  it  would  be  necessary  that  this  velocity  should 
be  destroyed  ;  if  it  were  suddenly  destroyed,  the  machinery  would  undergo 
a  strain  which  might  be  very  injurious  to  it ;  and  if  the  velocity  were 
gradually  diminished,  the  time  would  no  longer  be  the  same  as  is  supposed 
in  the  calculation.  In  the  second  place,  the  forces  generally  employed  are 
by  no  means  uniformly  accelerating  forces,  like  that  of  gravitation,  to  which 
the  propositions  which  we  have  been  considering  are  adapted :  they  are  not 
only  less  active  when  a  certain  velocity  has  once  been  attained,  but  they  are 
often  capable  of  a  temporary  increase  or  diminution  of  intensity  at  pleasure. 
We  have  seen  the  inconvenience  of  producing  a  great  final  velocity,  on  ac- 
count of  its  endangering  the  structure  of  the  machine  :  if  therefore  our  per- 
manent force  be  calculated  according  to  the  common  rule,  so  as  to  be  able 
to  maintain  the  equilibrium,  and  overcome  the  friction,  the  momentum  or 
inertia  of  the  weights,  when  once  set  in  motion,  will  be  able  to  sustain  that 

*  Consult  S,  Gravesande's  Nat.  Ph.  i.  c.  21.      Euler,   Ac.  Berl.  1748.     Blake, 
Ph.  Tr.  1759. 


ON  THE  MOTIONS  OF  CONNECTED  BODIES.  69 

motion  equably  ;  and  it  will  not  be  difficult  to  give  them  a  sufficient  mo- 
mentum, by  a  greater  exertion  of  the  moving  force  for  a  short  space  of 
time,  at  the  beginning :  and  this  is  in  fact  the  true  mode  of  operation  of 
many  machines  where  animal  strength  is  employed.  Other  forces,  for 
instance  those  of  wind  and  water,  regulate  themselves  in  some  measure,  at 
least  with  respect  to  the  relative  velocity  of  the  sails  and  the  wind,  or  the 
floatboards  and  the  water  ;  for  we  may  easily  increase  the  resistance  until 
the  most  advantageous  effect  is  produced.  Many  authors,  considering  the 
pressure  of  a  stream  of  water  as  analogous  to  the  impulse  of  a  number  of 
unconnected  particles  striking  the  floatboards  and  then  ceasing  to  produce 
any  further  effect,  have  inferred  that  the  force  obtained  by  such  an  impulse 
must  be  as  the  square  of  the  relative  velocity,  and  that  the  effect  of  an 
undershot  wheel  must  be  the  most  advantageous  when  its  velocity  is  one 
third  of  that  of  the  stream  :  but  it  will  hereafter  appear,  that  this  estima- 
tion of  hydraulic  force  is  by  no  means  accurate.  If  we  compare  the 
greatest  velocity  with  which  a  man  or  a  horse  can  run  or  walk  without 
fatigue,  to  the  velocity  of  the  stream,  and  the  actual  velocity  of  that  part  of 
the  machine  to  which  the  force  is  applied,  to  the  velocity  of  the  floatboards 
of  a  water  wheel,  the  strength  which  can  be  exerted  may  be  represented, 
according  to  the  experiments  of  some  authors,  by  the  impulse  of  the  stream 
as  supposed  to  be  proportional  to  the  square  of  the  relative  velocity  ;  con- 
sequently the  same  velocity  would  be  most  advantageous  in  both  cases,  and 
the  man  or  horse  ought,  according  to  these  experiments,  to  move,  when  his 
force  is  applied  to  a  machine,  with  one  third  of  the  velocity  with  which  he 
could  walk  or  run  when  at  liberty.  This,  for  a  man,  would  be  about  a 
mile  and  a  half  an  hour  ;  for  a  horse,  two  or  three  miles  :  but  in  general 
both  men  and  horses  appear  to  work  most  advantageously  with  a  velocity 
somewhat  greater  than  this. 

Where  a  uniformly  accelerating  force,  like  that  of  gravitation,  is  em- 
ployed in  machines,  it  might  often  be  of  advantage  to  regulate  its  opera- 
tion, so  that  it  might  act  nearly  in  the  same  manner  as  the  forces  that  we 
have  been  considering  ;  at  first  with  greater  intensity,  and  afterwards  with 
sufficient  power  to  sustain  the  equilibrium  and  overcome  the  friction  only. 
This  might  be  done  by  means  of  a  spiral  barrel,  like  the  fusee  of  a  watch  ; 
and  a  similar  modification  has  sometimes  been  applied  by  causing  the 
ascending  weight,  when  it  arrives  near  the  place  of  its  destination,  to  act 
on  a  counterpoise,  which  resists  it  with  a  force  continually  increasing,  by 
the  operation  of  a  barrel  of  the  same  kind,  so  as  to  prevent  the  effect  of 
the  shock  which  too  rapid  a  motion  would  occasion. 

On  the  whole,  we  may  conclude,  that  on  account  of  the  limited  velocity 
which  is  usually  admissible  in  the  operation  of  machines,  a  very  small 
portion  of  the  moving  force  is  expended  in  producing  momentum  ;  the 
velocity  of  3  miles  an  hour  would  be  generated  in  a  heavy  body,  descend- 
ing by  its  own  weight,  in  one  seventh  of  a  second,  and  a  very  short  time  is 
generally  sufficient  for  obtaining  as  rapid  a  motion  as  the  machine  or  the 
nature  of  the  force  will  allow  ;  and  when  this  has  been  effected,  the  whole 
force  is  employed  in  maintaining  the  equilibrium  and  overcoming  the 
resistance  :  so  that  the  common  opinion,  which  has  probably  been  formed 


70  LECTURE  IX. 

without  entering  minutely  into  the  consideration  of  the  subject,  and  which 
appears,  when  first  we  examine  its  foundation  with  accuracy,  to  lead  to 
material  errors,  is  in  great  measure  justified  by  a  more  profound  investi- 
gation. 

To  seek  for  a  source  of  motion  in  the  construction  of  a  machine,  betrays 
a  gross  ignorance  of  the  principles  on  which  all  machines  operate.  The 
only  interest  that  we  can  take  in  the  projects  which  have  been  tried  for 
procuring  a  perpetual  motion,  must  arise  from  the  opportunity  that  they 
afford  us  to  observe  the  weakness  of  human  reason  ;  to  see  a  man  spending 
whole  years  in  the  pursuit  of  an  object  which  a  week's  application  to 
sober  philosophy  might  have  convinced  him  was  unattainable.  The  most 
satisfactory  confutation  of  the  notion  of  the  possibility  of  a  perpetual 
motion,  is  derived  from  the  consideration  of  the  properties  of  the  centre  of 
gravity  :  we  have  only  to  examine  whether  it  will  begin  to  descend  or  to 
ascend,  when  the  machine  moves,  or  whether  it  will  remain  at  rest.  If  it 
be  so  placed,  that  it  must  either  remain  at  rest  or  ascend,  it  is  clear,  from 
the  laws  of  equilibrium,  that  no  motion  derived  from  gravitation  can  take 
place  :  if  it  may  descend,  it  must  either  continue  to  descend  for  ever  with 
a  finite  velocity,  which  is  impossible,  or  it  must  first  descend  and  then 
ascend  with  a  vibratory  motion,  and  then  the  case  will  be  reducible  to 
that,  of  a  pendulum,  where  it  is  obvious  that  no  new  motion  is  generated, 
and  that  the  friction  and  resistance  of  the  air  must  soon  destroy  the 
original  motion.  One  of  the  most  common  fallacies,  by  which  the  super- 
ficial projectors  of  machines  for  obtaining  a  perpetual  motion  have  been 
deluded,  has  arisen  from  imagining  that  any  number  of  weights  ascending 
by  a  certain  path  on  one  side  of  the  centre  of  motion,  and  descending  in 
the  other  at  a  greater  distance,  must  cause  a  constant  preponderance  on 
the  side  of  the  descent :  for  this  purpose  the  weights  have  either  been  fixed 
on  hinges  which  allow  them  to  fall  over  at  a  certain  point  so  as  to  become 
more  distant  from  the  centre,  or  made  to  slide  or  roll  along  grooves  or 
planes  which  lead  them  to  a  more  remote  part  of  the  wheel,  from  whence 
they  return  as  they  ascend  :  but  it  will  appear,  on  the  inspection  of  such  a 
machine,  that  although  some  of  the  weights  are  more  distant  from  the 
centre  than  others,  yet  there  is  always  a  proportionally  smaller  number  of 
them  on  that  side  on  which  they  have  the  greatest  power ;  so  that  these 
circumstances  precisely  counterbalance  each  other.  (Plate  VI.  Fig.  78.) 


LECT.  IX.— ADDITIONAL  AUTHORITIES. 

Lagrange,  Hist,  et  Mem.  de  Berlin,  1773,  p.  85.  Landen,  New  Theory  of  Ro- 
tatory Motion,  Ph.  Tr.  1777,  p.  266  ;  1785,  p.  311.  Vince,  Ph.  Tr.  1780,  p.  546. 
Robison,  Encyc.  Brit.  Art.  Rotation.  Fra^ais  sur  le  Rotat.  d'un  Corps,  4to,  Par. 
1813.  Raeb,  De  Motu  Gyratorio,  Trajecti  adRhenum,  1834. 

Rotation  with  Progression,  D.  Bernoulli,  Comm.  Petr.  xiii.  94.  Euler,  xiii.  220, 
and  Acta  Petr.  ii.  II.  162  ;  1781,  v.  II.  131 ;  1782,  vi.  I.  117,  II.  107  ;  1783,  I. 
119  ;  1787,  v.  149.  Fuss,  ibid.  176,  and  1788,  vi.  172.  Prony  sur  le  Mouvement 
d'un  Corps  sollicite  par  des  Puissances  quelconques,  4to,  1800. 


71 


LECTURE    X. 


ON  DRAWING,  WRITING,  AND  MEASURING. 

HAVING  investigated  all  the  general  principles  and  laws  of  motion,  and 
of  mechanical  power,  we  may  now  proceed  to  the  consideration  of  parti- 
cular departments  of  practical  mechanics.  But  before  we  can  satisfactorily 
compare  the  various  forces  which  we  are  to  employ  or  to  oppose,  we  must 
have  some  mode  of  determining  their  magnitude  ;  and  we  must  begin  by 
examining  the  spaces  which  are  measures  of  their  action  :  a  knowledge  of 
the  instruments  employed  for  delineation,  and  of  the  rules  of  perspective 
projection,  is  also  necessarily  required  as  a  previous  step  in  the  study  of 
practical  mechanics.  We  have  therefore  to  consider,  as  preliminary 
subjects,  first,  the  arts  which  may  be  expressed  by  the  terms  instrumental 
geometry,  or  the  geometry  of  mechanics :  secondly,  statics,  or  the  mode 
of  ascertaining  the  magnitude  of  weights  and  of  other  active  forces  ;  and 
thirdly,  the  examination  of  the  passive  strength  of  materials  of  various 
kinds,  and  of  the  negative  force  of  friction. 

The  art  of  drawing  can  scarcely  be  distinguished  by  any  correct  defini- 
tion from  painting.  In  its  simplest  state,  when  we  merely  imitate  an 
original  laid  before  us,  it  is  called  copying  ;  and  in  writing,  we  only  copy 
the  letters  of  the  alphabet.  If  we  proceed  in  a  mathematical  manner  in 
the  operation  of  drawing,  we  require  a  number  of  geometrical  instruments, 
which  are  still  more  necessary  for  the  first  construction  of  diagrams  or 
figures.  In  modelling  and  sculpture,  a  solid  is  simply  imitated ;  but  when  a 
solid  is  represented  on  a  plane,  the  principles  of  perspective  are  employed  in 
determining  the  position  of  the  lines  which  are  to  form  the  picture.  The 
productions  of  the  arts  of  drawing  and  writing  are  multiplied  and  per- 
petuated by  means  of  engraving  and  printing  ;  inventions  which  have  been 
the  sources  of  inestimable  advantage  in  the  instruction  and  civilisation  of 
mankind. 

In  drawing,  we  may  employ  the  pen,  the  pencil,  chalks,  crayons,  inks, 
water  colours,  or  body  colours  ;  we  may  paint  in  miniature,  in  distemper, 
in  fresco,  in  oils,  in  varnish,  in  wax,  or  in  enamel ;  and  we  may  imitate 
the  effects  of  painting  by  mosaic  work  or  by  tapestry. 

The  first  step  in  copying  a  drawing  or  in  painting,  is  to  procure  a  correct 
outline  :  a  master  of  the  art  can  do  this  with  sufficient  accuracy,  by  such 
an  estimate  of  the  proportions  of  the  figures  as  the  eye  alone  enables  him 
to  form ;  especially  if  he  be  assisted  by  lines  which  divide  the  original  into 
a  number  of  squares,  and  enable  him  to  transfer  their  contents  to  the  corre- 
sponding squares  of  the  copy,  which  may  in  this  manner  be  reduced  or 
enlarged,  when  it  is  required.  But  a  copy  may  sometimes  be  more  expe- 
ditiously  made  by  tracing  immediately  from  the  original,  when  the  mate- 
rials employed  are  sufficiently  transparent  to  admit  the  outlines  to  be  seen 
through  them  ;  or,  where  the  original  is  of  no  value,  by  pricking  a  number 


72  LECTURE  X. 

of  points  through  it,  so  as  to  mark  the  copy,  either  at  once,  or  by  means 
of  charcoal  powder  ruhbed  through  the  holes,  which  is  called  stenciling  : 
and  for  this  purpose,  an  intermediate  copy  may  be  formed  on  semi-trans- 
parent paper.  Another  method  is  to  put  a  thin  paper,  rubbed  with  the 
powder  of  black  lead  or  of  red  chalk,  between  the  original  and  the  paper 
intended  for  the  copy,  and  to  pass  a  blunt  point  over  all  the  lines  to  be 
traced,  which  produces  correspondent  lines  on  the  paper ;  this  is  called 
calking.  Where  the  work  is  large,  it  may  be  covered  with  a  thin  gauze, 
and  its  outlines  traced  on  the  gauze  with  chalk,  which  is  then  to  be  placed 
on  the  blank  surface,  and  the  chalk  shaken  off  it  in  the  way  that  a  car- 
penter marks  a  board  with  his  line/" 

The  pen  was  formerly  much  used  for  making  rough  sketches,  and  it  is 
still  sometimes  employed  for  the  same  purpose,  as  weh1  as  for  assisting  the 
effect  of  the  pencil.  The  appearances  of  uniform  lights  and  shades  must 
necessarily  be  imitated  in  drawings  with  the  pen,  as  well  as  engravings,  by 
a  mixture  of  the  whiteness  of  the  paper  with  the  blackness  or  colour  of 
the  ink,  the  eye  being  too  remote  to  distinguish  minutely  the  separate  lines 
by  which  the  effect  is  produced,  although  they  do  not  entirely  escape  its 
observation.  In  this  respect,  drawings  in  pencils  and  chalks  have  an 
advantage  over  engravings  ;  these  substances,  after  being  laid  on  in  lines, 
are  spread,  by  means  of  rubbers  or  stumps,  of  paper,  leather,  or  linen,  so 
as  to  produce  a  greater  uniformity  of  tint.  Some,  indeed,  are  of  opinion 
that  engravings  derive  a  great  brilliancy  from  the  hatches  that  are 
employed  in  shading  them,  and  that  minute  inequalities  of  colour  make 
every  tint  more  pleasing.  In  drawings  with  chalk,  however,  the  advan- 
tage of  rubbers  is  unquestionable.  The  lines  of  a  drawing  may  be  made 
to  have  an  appearance  of  greater  freedom  than  those  of  an  engraving ; 
they  should  be  parallel,  and  when  they  are  crossed  [the  different  sets 
should  be]  moderately  oblique  to  each  other  ;  their  direction  should  be 
governed  by  that  of  the  outline.  Engravings  in  mezzotinto  exhibit  no 
lines  :  but  they  are  deficient  in  spirit  and  precision  :  the  effect  of  aqua  tinta 
approaches  much  nearer  to  that  of  drawing,  and  it  has  a  similar  advan- 
tage in  the  mode  of  producing  its  lights  and  shades.  (Plate  VI.  Fig.  79.) 

It  is  well  known,  that  the  best  pencils  are  made  of  English  black  lead, 
or  plumbago.  Of  black  chalks,  the  Italian  is  harder  and  more  generally 
useful  than  the  French  :  red  chalk  has  the  disadvantage  of  not  being 
easily  removed,  either  by  bread  or  by  Indian  rubber,  without  leaving  a 
brownish  mark.  All  these  chalks  are  of  the  nature  of  a  soft  schistus  or 
slate  :  they  may  be  made  to  adhere  firmly  to  the  paper  by  dipping  the 
drawings  in  milk  freed  from  cream,  or  even  in  water  only,  which  dissolves 
the  size  or  gum  of  the  paper.  Sometimes  a  grey  paper  is  used,  which 
serves  for  a  middle  tint,  and  lessens  the  labour,  the  lights  and  shades  only 
being  added  in  white  and  black  chalks. 

Crayons  consist  of  colours  mixed  up  with  gum  water,  or  other  adhesive 
substances,  and  usually  also  with  some  chalk,  plaster,  or  pipe  clay,  so  as 
to  be  of  a  proper  consistence  for  working  in  the  manner  of  chalks.  The 

*  Imison's  Elements,  ii.  240,  327. 


ON  DRAWING,  WRITING,  AND  MEASURING.  73 

principal  inconvenience  attending  them  is  their  want  of  adhesion  to  the 
paper  :  the  paper  must  therefore  not  be  too  smooth.* 

For  drawings  washed  in  light  and  shade  only,  the  material's  employed 
are  Indian  ink,  the  black  liquor  of  the  cuttle  fish,  or  bistre  which  is  ex- 
tracted from  soot :  both  these  last  produce  a  browner  and  richer  tint  than 
the  Indian  ink.t  In  using  these  washes,  as  well  as  water  colours,  there  is 
a  great  diversity  in  the  methods  of  different  artists  :  some  work  with  a  dry 
pencil,  others  with  a  full  one  :  some  begin  all  their  coloured  drawings  in 
black  only,  others  use  colours  from  the  beginning.  When  a  full  pencil  is 
used,  care  must  be  taken  that  no  part  of  the  same  tint  dry  sooner  or  later 
than  the  rest.  When  body  colours  are  employed,  there  is  less  difficulty  in 
producing  a  uniformity  of  tint  than  with  water  colours,  each  coat  of  the 
colour  being  laid  on  in  sufficient  quantity  to  cover  all  that  is  below  it  without 
mixing :  hence  it  becomes  easier  to  make  any  alterations  that  may  be  re- 
quired. For  water  colours  of  all  descriptions  a  certain  quantity  of  gum  is 
used,  and  sometimes  a  size  made  of  isinglass  with  a  little  sugar  candy.  Body 
colours  contain  less  gum  than  other  water  colours. :£  Besides  paper,  wood, 
silk  and  cotton  velvet  are  sometimes  used  for  drawings  in  water  colours. 

In  miniatures,  the  most  delicate  tints  are  laid  on  in  points  with  simple 
water  colours;  but  for  the  draperies  body  colours  are  sometimes  used. 
They  are  commonly  executed  on  ivory. 

For  painting  in  distemper  the  colours  are  mixed  with  a  size  made  by 
boiling  shreds  of  untanned  leather  or  of  parchment,  for  several  hours  :  this 
method  is  chiefly  employed  for  colouring  walls  or  paper,  but  sometimes  for 
painting  on  cloth.  For  delicate  purposes,  the  size  may  be  made  with 
isinglass. 

When  a  wall  or  ceiling  is  painted  in  fresco,  the  rough  coat  of  the  plaster 
is  covered  with  a  coat  of  fine  sand  and  lime  as  far  as  it  can  be  painted  before 
it  is  dry,  the  colours  being  partly  imbibed  by  this  coat,  and  thus  becoming 
durable.  When  they  have  been  once  laid  on,  no  alteration  can  be  made, 
without  taking  off  the  last  coat  of  plaster,  and  each  part  must  be  completed 
at  once  ;  it  is  therefore  always  necessary  to  have  a  finished  drawing  for  a 
copy  ;  this  is  usually  executed  on  paper,  and  is  called  a  cartoon.  The 
colours  can  be  only  of  earths  or  metallic  oxids  ;  they  are  prepared  as  for 
painting  in  distemper.  The  only  paintings  of  the  ancients,  which  have 
been  preserved,  were  executed  in  fresco. 

The  art  of  painting  in  oil  was  first  discovered  by  Van  Eyck  of  Bruges,  § 
towards  the  end  of  the  14th  century :  it  has  now  become  almost  the  only 
manner  in  which  paintings  of  magnitude  are  performed.  The  colours  are 
mixed  with  linseed  or  nut  oil,  and  sometimes  with  oil  of  poppy  seed,  together 
with  a  small  portion  of  oil  of  turpentine  to  assist  in  drying  them,  and  with 

*  Russel  on  Painting  in  Crayons,  4to.  Encyclop.  Meth.  Arts  et  Metiers  vi.  Art. 
Pastel.  Contes  Crayons,  Ann.  de  Chimie,  xx.  370.  Lomet,  ibid.  xxx.  284.  Nich. 
Jour.  iii.  216. 

f  Gill  on  Indian  Ink,  Ph.  Mag.  xvii.  210. 

%    t  Handmaid  to  the  Arts,  1758,  Field's  Chromatography.     Mrs.  Callcott's  Es- 
says towards  a  History  of  Painting,  1836. 

§  On  the  authority  of  Vasari,  c.  21  ;  but  it  is  probably  incorrect.  Consult 
James's  Flemish  and  Dutch  Schools  of  Painting,  or  Haydon's  Lectures,  1844,  p. 
265.  Cennini,  translated  by  Mrs.  Merriefield,  1844  ;  Tambroni's  Preface,  p.  49. 


74  LECTURE  X. 

the  occasional  addition  of  other  oily  and  resinous  substances.  The  work 
may  be  executed  on  wood,  cloth,  silk,  paper,  marble,  or  metals  :  these  sub- 
stances being  first  washed  with  size,  and  then  primed  with  an  oil  colour, 
which  is  usually  white,  but  sometimes  dark.  Some  painters  have,  however, 
preferred  a  ground  of  distemper.  The  glare  of  the  oil  colours  or  of  the  var- 
nish, which  is  added  in  order  to  give  them  brilliancy,  is  considered  as  an 
inconvenience  attending  oil  paintings  ;  and  some  of  the  colours  are  too 
liable  to  fade  or  to  blacken  by  the  effect  of  time. 

The  encaustic  paintings  of  the  ancients  were  imperfect  approximations 
to  the  art  of  painting  in  oil.  Wax  or  resins  were  employed  for  retaining 
the  colours  in  their  places  ;  and  they  were  applied  by  means  of  a  moderate 
heat.*  An  effect  nearly  similar  is  produced  by  dissolving  the  resins  in 
spirits  of  wine,  as  is  done  in  painting  in  varnish.  A  much  greater  degree 
of  heat  is  required  for  paintings  in  enamel :  for  this  purpose  the  colours  are 
mixed  with  a  glass  of  easy  fusion,  and,  when  finely  powdered,  they  are 
usually  applied  with  oil  of  turpentine,  or  sometimes  oil  of  lavender,  to  a 
ground  of  metal  or  porcelain ;  they  are  afterwards  fixed  and  vitrified  by 
exposure  to  the  heat  of  a  furnace. 

Mosaic  work  is  performed  by  putting  together  small  pieces  of  stone  or 
baked  clay  of  various  colours,  so  as  to  imitate  the  effects  of  painting  ;t  in 
tapestry  and  in  embroidery,  the  same  is  done  by  weaving,  or  working  in 
threads  of  different  kinds. 

The  art  of  writing  is  of  great  antiquity,  but  it  is  probably  in  all  coun- 
tries, and  certainly  in  some,  of  a  later  date  than  that  of  drawing  represent- 
ations of  nature.  The  Mexicans,  at  the  first  arrival  of  the  Spaniards  in 
South  America,  are  said  to  have  employed  drawings  as  a  mode  of  conveying 
intelligence :  some  of  them  simply  resembling  the  objects  to  which  they 
related,  others  intended  as  hieroglyphics  ;  that  is,  like  the  ancient  Egyptian 
characters,  of  a  nature  intermediate  between  drawing  and  writing.;};  The 
Chinese  have  always  used  arbitrary  marks  to  represent  whole  words  or  the 
names  of  external  objects,  not  resembling  the  objects  to  which  they  relate, 
nor  composed  of  letters  appropriated  to  constituent  parts  of  the  sound, 
although  they  are  said  to  be  combined  from  a  few  hundred  radical  charac- 
ters expressive  of  the  most  simple  ideas.  The  art  of  writing  with  alpha- 
betical letters  must  have  been  sufficiently  understood  in  the  age  of  Moses, 
to  serve  the  purpose  of  the  promulgation  of  laws  and  of  religion ;  it  is 
generally  supposed  to  have  been  invented  by  the  Phenicians.  Among  the 
Greeks  it  was  in  a  very  imperfect  state  until  the  time  of  the  siege  of  Troy, 
or  about  3000  years  ago.  The  Chinese-  write  from  above  downwards, 
beginning  on  the  right  side  ;  the  other  eastern  nations  have  always  written 
from  right  to  left.  The  most  ancient  Greek  inscriptions  are  turned  alter- 
nately backwards  and  forwards,  the  letters  being  reversed  in  the  lines 
which  begin  on  the  right  side  ;  but  the  Greeks  soon  confined  themselves  to 

*  Pliny,!.  35,  c.  11.  Vitruvius,  Architectura,  1.  7,  c.  9,  de  Minii  Temperatura. 
Colebrooke,  Ph.  Tr.  1759,  p.  40.  Caylus  on  Encaustic  Painting,  Lond.  Fabbroni 
on  Do.  Ph.  M.  i.  23,  141.  Gilbert's  Annalen,  v.  357. 

t  Ph.  Mag.  ix.  289. 

t  See  the  plate  of  Aztec  Chronology  from  Carreri,  in  Encyc.  Metr.  vol.  xix,  pi. 
28.  Robertson's  Hist,  of  America,  ii.  284,  480.  Humboldt,  Voyage  de  Cordilleras. 


ON  DRAWING,  WRITING,  AND  MEASURING.  75 

that  mode,  which  has  been  since  adopted  by  all  European  nations,  and 
which  appears  to  be  in  itself  the  most  natural,  at  least  for  writing  with  a 
pen,  and  with  the  right  hand.* 

The  earliest  methods  of  writing  were  probably  such  as  rather  deserve  the 
name  of  engraving ;  the  letters  being  cut  in  stone,  in  wood,  on  sheets  of 
lead,  on  bark,  or  on  leaves.  For  temporary  purposes,  they  were  formed  on 
tablets  of  wax,  with  a  point  called  a  stile,  and  this  practice  was  long  con- 
tinued for  epistolary  correspondence,  and  was  not  wholly  out  of  use  in  the 
fourteenth  century.  The  stile  was  made  of  metal  or  of  bone ;  its  upper 
extremity  was  flattened  for  the  purpose  of  erasing  what  had  been  written. 
The  Egyptian  papyrus  is  said  by  Varro  to  have  been  first  used  for  writing 
at  the  time  of  the  foundation  of  Alexandria  ;  the  leaves  of  palms,  the  inner 
bark  of  trees,  or  sometimes  linen  cloth,  having  been  before  employed.  The 
exportation  of  the  papyrus  was  forbidden  by  Ptolemy,  and  in  consequence 
of  this  prohibition,  skins  of  parchment  or  of  vellum  were  first  applied 
to  the  purpose  of  writing  at  Pergamus,  for  the  library  of  king  Eumenes, 
whence  they  were  called  membrana  pergamena.  To  make  the  best  paper, 
the  widest  and  finest  leaves  of  the  papyrus  were  matted  together,  united  by 
a  vegetable  glue,  and  pressed  till  they  became  sufficiently  smooth  ;  the 
coarser  kinds  were  not  used  for  writing,  but  for  commercial  purposes.  In 
China,  paper  is  sometimes  made  of  a  thin  and  almost  transparent  mem- 
brane taken  from  the  bark  of  a  tree.  Paper  of  cotton  was  introduced  into 
Europe  from  the  east  in  the  middle  ages  :  it  has  been  since  superseded  by 
that  which  is  made  of  linen  rags,  and  which  is  also  an  eastern  invention  ; 
but  for  coarse  and  strong  paper,  old  ropes  of  hemp  are  also  used ;  and 
sometimes  many  other  vegetable  substances  have  been  employed.  The 
strength  and  consistence  of  paper  is  owing  to  the  lateral  adhesion  derived 
from  the  intermixture  of  the  fibres,  assisted  by  the  glutinous  size,  which  is 
also  of  use  in  obviating  the  bibulous  quality  of  the  paper,  by  filling  up  its 
pores.t 

Ivory,  and  prepared  ass's  skin,  are  sometimes  employed  for  writing  with 
a  black  lead  pencil ;  for  slates,  a  pencil  of  a  softer  kind  of  slate  is  used. 
The  ancient  mathematicians  usually  constructed  their  diagrams  on  sand 
for  the  instruction  of  their  pupils. 

Pens  of  goose  quills,  swan's  quills,  or  crow  quills,  were  known  as  early 
as  the  seventh  century  :  in  Europe  they  have  generally  superseded  the 
reeds  which  were  employed  for  writing  by  the  ancients  :  but  in  India, 
reeds,  canes,  and  bamboos,  are  still  in  use.  In  China  a  hair  pencil  is 
used  instead  of  a  pen. 

*  As  Dr.  Young  distinguished  himself  by  his  researches  on  hieroglyphical  writing, 
we  subjoin  the  following  references  to  his  works  : — Museum  Criticum,  8vo,  Camb. 
vol.  ii.  pp.  125,  329.  Hieroglyphics,  fol.  Lond.  by  the  Egyptian  and  Royal  Societies 
of  Literature.  Supp.  to  Ency.  Brit.  vol.  iv.  38.  Discoveries  in  Hier.  Lit.  8vo.  Lond. 
1823.  A  sketch  of  the  discoveries  will  be  found  in  the  Quarterly  Review,  vol.  xliii. 
p.  112;  or  in  Ency.  Metr.  Art.  Hieroglyphics.  See  also  J.  F.  Champollion, 
L'Egypte  sous  les  Pharaons,  2  vols.  8vo.  Par.  1814.  Lettre  a  M.  Dacier  relative  a 
*!' Alphabet  des  Hieroglyphics,  8vo,  Par.  1822.  Precis  du  Systeme  Hierog.  8vo. 
Par.  1824  and  1828.  Lettres  relatives  au  Musee  Royal  Egyptien  de  Turin,  Par. 
1824  and  1826. 

f  Rombold  on  Paper,  Berl.  1744.  Lalande,  L'Art  de  faire  le  Papier,  fol.  Par. 
1761. 


76  LECTURE  X. 

The  inks  of  the  ancients  are  said  to  have  been  made  of  a  carbonaceous 
substance,  and  the  modern  Indian  ink  owes  its  blackness  to  similar  materials. 
Common  writing  ink  consists  of  a  gallate  of  iron,  suspended  by  means  of 
a  little  gum  ;  the  sulfuric  acid,  which  remains  mixed  with  it,  is  probably 
of  no  consequence  to  its  blackness.  It  has  been  observed,  that  an  abun- 
dance of  the  gallic  acid  produces  a  much  blacker  colour  than  is  obtained 
where  this  acid  is  used  in  a  smaller  proportion.  Mr.  Ribaucourt's  method 
of  making  ink,*  is  to  boil  eight  ounces  of  galls,  and  four  of  logwood,  in 
twelve  pounds  of  water,  until  the  quantity  is  reduced  to  one  half ;  and,  hav- 
ing strained  the  decoction,  to  add  to  it  four  ounces  of  sulfate  of  iron,  one  of 
sulfate  of  copper,  three  of  gum  arabic,  and  one  of  sugar  candy.  But  for 
ordinary  purposes,  it  is  sufficient  to  infuse  three  ounces  of  galls  for  a  day  or 
two  in  a  pint  of  water,  and  to  add  to  it  an  ounce  of  gum  arabic,  half  an 
ounce  of  green  sulfate  of  iron,  or  copperas,  and  a  drachm  of  sulfate  of  cop- 
per, or  blue  vitriol,  or  even  a  much  smaller  quantity  of  gum  and  of  copperas, 
if  a  very  fluid  ink  is  required.  The  sulfate  of  copper  produces  a  durable 
stain,  but  it  does  not  immediately  add  to  the  blackness  of  the  ink  :  its 
principal  use  is  to  counteract  the  tendency  of  the  ink  to  become  mouldy. 
Sometimes  a  mercurial  salt  is  employed  for  the  same  purpose,  and  a  little 
cotton,  if  the  inkstand  is  too  open,  is  also  useful  in  preserving  the  ink  ; 
but  the  addition  of  spirits  is  often  insufficient,  and  is  liable  to  make  the 
ink  run. 

It  has  been  proposed  to  use  inks  of  different  colours  for  indicating 
different  numbers  ;  so  that  by  ten  kinds  of  ink  applied  in  different  ways, 
any  numbers  at  pleasure  might  be  expressed.  Thus,  in  making  an  index 
of  the  words  of  an  author,  each  page  might  be  readily  covered  with  lines 
of  different  colours  drawn  in  different  directions,  so  that  each  word,  when 
cut  out,  might  indicate  the  page  to  which  it  belongs. 

An  ingenious  instrument  has  lately  been  constructed,  by  means  of 
which  copies  may  be  multiplied  with  great  facility ;  it  is  called  the  poly- 
graph, and  consists  of  two  or  more  pens,  so  connected  by  frames  and 
springs,  as  to  move  always  in  parallel  directions,  each  having  an  inkstand 
and  a  sheet  of  paper  for  itself.t  In  this  manner  five  copies  may  be  made 
at  once  with  tolerable  facility,  and  the  method  may  perhaps  hereafter  be 
extended  to  a  much  greater  number. 

A  mode  of  writing,  perfectly  different  from  any  of  those  which  have 
been  mentioned,  is  performed  by  means  of  the  telegraph,  which  is  justly 
considered  as  the  invention  of  the  ingenious  Dr.  Hooke.:};  The  ancients 
had  attempted  something  similar,  by  the  exhibition  of  torches  on  elevated 
situations ;  but  Dr.  Hooke  observes,  that  the  addition  of  the  telescope  is 
absolutely  necessary  for  the  practical  success  of  the  process;  and  the 
directions  which  he  gives  for  its  performance  differ  very  little  from  the 
plan  which  has  since  been  generally  adopted,  first  in  France,  and  after- 
wards, with  some  variations,  in  this  country.  Dr.  Hooke  proposed  the 

*  Repertory  of  Arts,  ix.  125. 

f  Cotteneuve,  Mem.  de  1'Acad.  Paris,  1763,  H.  147. 

J  Ph.  Tr.  1684.  Philosoph.  Exp.  and  Obs.  bv  Hooke,  edited  by  Derham, 
p.  142. 


ON  DRAWING,  WRITING,  AND  MEASURING.  77 

employment  of  alphabetical  and  other  arbitrary  characters  ;  at  present  it 
is  usual  to  have  six  boards,*  each  turning  011  its  axis  so  as  to  appear  or 
disappear  at  pleasure  :  these  admit  of  sixty-four  combinations,  which  are 
sufficient,  besides  indicating  the  letters  of  the  alphabet,  for  every  other 
purpose  that  can  be  required.  (Plate  VI.  Fig.  80,  81.) 

Pens  for  drawing  lines  and  figures  differ  sometimes  from  those  which 
are  used  for  writing  ;  they  are  made  of  two  plates  of  steel  inclined  to  each 
other,  and  adjusted  by  a  screw ;  or  sometimes  of  a  plate  of  tin  folded  up, 
so  as  to  include  a  receptacle  for  the  ink  ;  or  of  a  glass  tube  drawn  to  a 
very  fine  point,  and  still  remaining  perforated.  In  all  these  pens,  as  well 
as  in  common  pens,  the  ink  is  retained  by  its  cohesion,  and  by  the 
capillary  attraction  of  the  pen  ;  and  it  attaches  itself  to  the  paper  by  the 
operation  of  similar  powers. 

It  is  by  no  means  easy  to  comply  strictly  with  that  postulate  of  geometry 
which  requires  us  to  draw  a  straight  line  from  one  point  to  another.  The 
edge  of  a  ruler  is  made  straight  by  the  instrument  called  a  plane,  which  is 
worked  with  a  considerable  velocity,  and  therefore  naturally  tends  to 
move  in  a  right  line,  besides  that  it  is  guided  by  the  flatness  of  its  lower  sur- 
face. We  judge  of  the  straightness  of  a  line,  by  means  of  the  well  known 
property  of  light,  which  moves  only  in  right  lines,  so  that  if  we  look  along 
the  edge  of  a  ruler,  we  easily  discover  its  irregularities ;  and  this  may  be 
done  with  still  greater  accuracy,  if  we  look  through  a  small  hole  made 
with  a  pin  in  a  card.  Rulers  of  silver,  brass,  or  ivory,  have  a  material 
advantage  over  those  of  wood,  as  they  are  not  liable  to  be  spoilt  by  warp- 
ing. A  pen  filled  with  ink  cannot  be  applied  close  to  the  edge  of  a  ruler 
without  inconvenience  ;  it  is  therefore  best,  for  diagrams  which  require 
great  accuracy,  to  draw  the  lines  first  with  a  steel  point,  or  a  very  hard 
black  lead  pencil,  and  to  finish  them  with  ink  if  necessary.  The  paper 
should  also  be  fixed  on  a  drawing  board  ;  and  plates  of  lead  or  copper  may 
be  employed,  instead  of  paper,  for  very  delicate  purposes.  The  carpenter's 
chalk  line  is  a  useful  instrument  for  supplying  the  place  of  a  very  long 
ruler  ;  it  becomes  straight  when  it  is  stretched,  because  a  right  line  is  the 
shortest  distance  between  any  two  points. 

For  drawing  a  circle  of  a  given  radius  we  use  compasses,  with  one  point 
generally  of  metal,  the  other  of  various  descriptions,  t  Compasses  are 
sometimes  made  with  a  spring  instead  of  a  joint,  and  opened  or  shut  by  a 
screw :  sometimes  a  graduated  arc  is  fixed  in  one  leg,  and  passes  through 

*  This  species  of  telegraph  was  invented  in  1695,  by  Lord  G.  Murray ;  it  was 
adopted  by  the  Admiralty  until  the  end  of  the  late  war,  when  it  was  discontinued, 
and  the  semaphore,  consisting  of  two  arms  projecting  from  an  upright 
post,  and  working  about  pivots,  was  substituted  in  its  place.  In  this 
instrument  each  arm  has  seven  different  positions,  which  afford  by 
their  combinations  forty-nine  different  arrangements.  Consult  Edge- 
worth,  Trans.  Roy.  Irish  Ac.  vi.  95,  319.  Nicholson's  Journal,  ii.  319. 
Chappe,  Breguet  and  Betancourt,  Bulletin  de  la  Soc.  Ph.  n.  16. 
Mem.  de  1'Institut  III.  H.  22.  Ph.  Mag.  i.  312.  Nocturnal  Tele- 
graph, Rep.  of  Arts.  x.  28.  Boaz's  Patent  Tel.  ibid.  xvi.  223.  Ph. 
Mag.  xii.  84.  Ency.  Brit.  Art.  Tel.  Pasley,  Description  of  the  Uni- 
versal Telegraph,  1823.  Chappe,  Histoire  dela  Telegraphe,  2  vols.  Paris,  1824. 

f  Duval's  New  Compasses,  Mem.  Paris,  1717,  H.  83.  Leup.  Th.  Art.  t.  20, 
a.  b. 


78  LECTURE  X. 

the  other ;  and  when  great  accuracy  is  required,  hair  compasses  may  be 
employed,  having  a  joint  with  a  spring  in  one  of  the  legs,  which  is  bent  a 
little  by  means  of  a  fine  screw.  Beam  compasses*  are  useful  for  drawing 
circles  of  larger  radii :  they  have  also  the  advantage  of  being  steadier  than 
the  common  compasses,  and  of  admitting  readily  the  application  of  a  gra- 
duated scale,  so  as  to  indicate  the  measure  of  the  radius  of  the  circle  which 
is  described.  Sometimes,  for  drawing  portions  of  very  large  circles,  two 
wheels,  differing  a  little  in  diameter,  are  fixed  on  a  common  axis,  and  thus 
made  to  revolve  round  a  point,  which  is  more  or  less  distant,  accordingly 
as  the  wheels  are  set  at  a  greater  or  less  distance  on  the  axis,  the  surface 
of  the  wheels  tracing  the  circles  on  the  paper  ;  or  two  rulers  joined  toge- 
ther, so  as  to  form  an  angle,  are  made  to  slide  against  two  points,  or 
edges,  projecting  from  a  third  ruler ;  so  that  the  angular  point  remains 
always  in  the  arc  of  a  circle.  The  same  effect  may  be  produced,  somewhat 
more  commodiously,  by  means  of  a  thin  piece  of  elastic  wood,  which 
is  made  to  assume  any  required  curvature  by  the  action  of  screws 
applied  to  different  parts  of  its  concavity :  it  would,  however,  be  more 
simple  and  accurate  to  employ  only  one  screw,  in  the  middle  of  the  arc, 
and  to  make  the  flexible  ruler,  or  bow,  every  where  of  such  a  thickness  as 
to  assume  a  circular  form  in  its  utmost  state  of  flexure  :  it  would  then 
retain  the  circular  form,  without  a  sensible  error,  in  every  other  position. 
(Plate  VI.  Fig.  82... 85.) 

For  drawing  a  line  perpendicular  to  another,  we  often  employ  a  square  ; 
and  if  we  use  a  rectangular  drawing  board,  there  is  an  additional  conve- 
nience in  making  the  square  to  slide  on  its  margin.  Rulers  also,  of  various 
descriptions,  are  commonly  made  rectangular,  in  order  to  answer  occasion- 
ally the  same  purpose. 

Triangular  compasses  are  sometimes  used  for  laying  down  a  triangle 
equal  to  a  given  triangle  ;t  and  by  repeating  the  operation,  any  figure 
which  can  be  divided  into  triangles,  may  be  copied  without  the  intersection 
of  arcs  ;  but  the  same  end  is  more  commonly  obtained  by  pricking  off  the 
figure  with  a  steel  point.  (Plate  VI.  Fig.  86.) 

Various  properties  of  parallel  lines  are  employed  in  constructing  parallel 
rulers  :  a  parallelogram  with  jointed  angles  is  the  most  commonly  used  ; 
two  equal  rulers  being  united  by  equal  cross  bars  placed  in  an  oblique 
position,  and  turning  on  pins  fixed  in  the  rulers  :  the  instrument  is  much 
improved  by  adding  a  third  ruler,  similarly  united  to  the  second,  for  then 
the  obliquity  of  one  of  the  two  motions  may  be  made  to  correct  that  of  the 
other.  A  simple  cylinder,  or  a  round  ruler,  answers  the  purpose  in  a  rough 
manner,  and  two  small  rollers,  fixed  on  the  same  axis,  are  also  sometimes 
attached  to  a  flat  ruler,  and  cause  it  to  move  so  as  to  be  always  in  parallel 
positions.  A  very  useful  instrument  for  drawing  parallel  lines,  at  any 
given  distances,  is  now  generally  known  by  the  name  of  Marquois's  scales, 
although  it  is  by  no  means  of  late  invention  ;£  by  sliding  a  triangle  along 
a  graduated  ruler,  we  read  off  the  divisions  on  an  amplified  scale  with  great 

*  Shuckburgh,  Ph.  T.  1798. 
f  Leupold,  Th.  Art.  t.  28.  J  Ibid.  t.  21,  a. 


ON  DRAWING,  WRITING,  AND  MEASURING.  79 

accuracy ;  but  where  the  distances  of  the  lines  are  great,  the  obliquity  of 
this  motion  is  a  considerable  inconvenience.  The  ruler  or  square  of  the 
drawing  board  affords  us  lines  parallel  to  each  other,  in  a  certain  position  ; 
and  if  it  be  made  with  a  joint,  or  as  the  workmen  call  it,  bevilled,  it  may 
be  employed  for  the  same  purpose  in  all  other  directions.  The  systems  of 
lines,  on  which  music  is  written,  are  drawn  at  one  stroke  by  a  pen  with 
five  orifices,  usually  made  of  brass.  It  was  long  since  proposed  to  rule  a 
whole  page  at  once,  with  a  more  complicated  pen  of  the  same  kind,  and 
the  greatest  part  of  the  paper  on  which  music  is  written  in  this  country, 
is  actually  ruled  by  such  a  machine,  for  which  a  patent  has  been  taken 
out.  (Plate  VI.  Fig.  87,  88.) 

The  pantograph  is  used  for  copying  figures,  and  at  the  same  time 
reducing  or  enlarging  them  ;  it  consists  of  four  rulers,  two  of  them 
united  by  a  joint  at  the  extremities,  and  receiving  at  the  middle  the  other 
two,  which  are  but  half  as  long,  and  are  also  united  together  so  as  to  form 
with  the  others  a  jointed  parallelogram,  of  which  two  of  the  sides  are 
produced  beyond  the  angles  ;  if  holes  be  made  in  these,  and  in  one  of 
the  shorter  rulers,  so  situated  as  to  be  in  the  same  right  line  in  any 
position  of  the  instrument,  they  will  remain  in  a  right  line  in  any  other 
position,  and  they  will  always  divide  this  line  in  the  same  proportion  :  so 
that  if  one  of  the  holes  be  placed  on  a  fixed  axis  or  pin,  a  tracing  point 
inserted  in  another,  and  a  pencil  in  the  third,  any  figure  delineated  by 
the  pencil  will  be  similar  to  that  which  is  described  by  the  tracing 
point.  And  instead  of  holes  in  the  rulers,  they  may  be  furnished  with 
sliding  sockets,  to  receive  the  axis,  the  point,  and  the  pencil.  (Plate  VI. 
Fig.  89.)* 

Proportional  compasses  are  also  of  great  use  in  reducing  lines  and 
figures  to  a  different  scale.t  This  instrument  consists  of  two  legs,  pointed 
at  each  end,  and  turning  on  a  centre  which  slides  in  a  groove  common  to 
both  legs,  and  is  furnished  with  an  index.  The  divisions  of  the  scale  are 
so  laid  down  that  the  centre  may  divide  the  length  of  the  legs  from 
point  to  point  in  a  given  proportion  ;  hence  by  the  properties  of  similar 
triangles,  when  the  legs  are  opened  to  any  extent,  the  intervals  between 
each  pair  of  points  must  be  to  each  other  in  the  same  ratio  as  the  por- 
tions of  the  legs.  Sometimes  a  screw  is  added,  for  the  sake  of  adjusting 
the  centre  with  greater  accuracy ;  and  it  is  usual  to  lay  down  scales  for 
dividing  the  circumference  of  a  circle  into  a  given  number  of  parts,  and 
for  some  other  purposes  ;  but  the  instrument  might  be  much  improved 
by  inserting,  in  the  common  scale,  fractional  or  decimal  divisions  between 
the  whole  numbers,  so  that  the  legs  might  be  divided,  for  example,  in 
the  ratio  of  2  to  3,  3  to  4,  or  4  to  5,  or  of  10  to  11,  12  or  13,  at  pleasure. 
(Plate  VI.  Fig.  90.) 

The  use  of  the  sector  depends  also  on  the  properties  of  similar  triangles. 

*  Leup.  Th.  Art.  t.  26.  Langlois's  Pantograph :  Machines  Approuves  par  1'Ac. 
7  vols.  4to,  1735-1777,  vii.  207.  Sike's  Pantograph,  Mem.  Par.  1778,  invented  by 
Sclieiner,  who  describes  it  in  his  Pantographice.  An  improved  instrument  for  the 
same  purpose  is  described  by  Prof.  Wallace,  in  the  Trans,  of  the  Roy.  Soc.  of  Edin. 
vol.  xiii.  and  termed  by  him  the  Eidograph. 

f  Leon,  da  Vinci  MSS.     Leup.  Th.  Ar.  121. 


80  LECTURE  X. 

The  scale  of  equal  parts,  which  is  laid  down  on  each  leg,  beginning  from 
the  centre,  serves  to  determine  the  length  of  the  legs  of  two  equilateral 
triangles,  in  any  required  proportion  to  each  other,  according  to  the 
division  which  we  mark,  and  the  transverse  distances  from  the  corre- 
sponding points  are  necessarily  in  the  same  proportion.  Thus,  if  we  have 
any  line  in  a  figure  which  we  wish  to  call  three  feet,  or  three  inches,  we  may 
take  the  interval  with  a  pair  of  common  compasses,  and  open  the  sector  to 
such  an  angle,  that  it  may  extend  from  the  third  division  of  one  leg  to 
that  of  the  other  ;  then  all  the  other  divisions  of  the  scale  will  furnish  us 
with  the  lengths  corresponding  to  any  distances  that  we  may  wish  to  lay 
down.  The  other  scales  usually  engraved  on  the  sector  are  principally 
intended  for  trigonometrical  calculations  on  similar  principles.  (Plate  VII. 
Fig.  91.) 

The  magnitude  of  angles  admits  an  easy  determination  and  description, 
by  the  comparison  of  the  respective  arcs  with  a  circle,  or  with  a  right  angle. 
We  may  divide  an  angle  geometrically,  by  continual  bisection,  into  parts 
as  small  as  may  be  required,  and  by  numbering  these  parts  we  may 
define  any  angle,  with  an  error  smaller  than  any  assignable  quantity. 
Bisections  of  this  kind  are  sometimes  actually  employed  in  the  construc- 
tion of  instruments  ;  for  instance,  in  one  of  the  arcs  of  the  mural  quad- 
rant of  the  observatory  at  Greenwich,  the  right  angle  is  divided  into  96 
parts,  by  the  continual  bisection  of  one  sixth  of  the  circle.  There  are 
also  some  practical  methods  of  dividing  angles  into  three  or  more  equal 
parts,  which  are  sufficiently  accurate  for  many  purposes, .  although  it  is 
well  known  that  in  theory  the  perfect  trisection  of  an  angle  is  beyond  the 
reach  of  plane  geometry.  This  trisection  is  necessary  in  the  common 
division  of  the  circle  into  360  degrees,  a  number  which  was  probably 
chosen  because  it  admits  a  great  variety  of  divisors,  and  because  it  nearly 
represents  the  diurnal  and  annual  motion  of  the  sun  among  the  stars. 
The  circle  being  divided  into  6  parts,  the  chord  of  each  of  which  is  equal 
to  the  radius,  these  parts  are  divided  into  60  degrees,  each  degree  into  60 
minutes,  and  each  minute  into  60  seconds  :  further  than  this  we  cannot 
easily  carry  the  accuracy  of  our  determination,  although  in  calculations 
we  sometimes  descend  as  far  as  tenths  or  even  hundredths  of  a  second. 
The  decimal  division  of  a  right  angle,  which  has  been  lately  adopted  in 
France,  appears  to  have  very  little  advantage  for  the  purposes  of  calcula- 
tion, beyond  the  common  method,  and  its  execution  in  practice  must  be 
much  more  difficult. 

Whole  circles,  or  theodolites,  divided  into  degrees  and  their  parts,  quad- 
rants and  sextants,  are  usually  employed  in  measuring  angles  ;  and  protrac- 
tors, semicircles,  and  lines  of  chords,  in  laying  them  off.  The  most  convenient 
of  quadrants  for  general  use  is  Hadley's  reflecting  instrument,*  which  is  in 
fact  an  octant  or  a  sextant,  but  in  which,  for  reasons  depending  on  optical 
principles,  each  degree  of  the  arc  is  reckoned  for  two. 

For  the  graduation  of  all  instruments  of  this  kind,  of  moderate  dimen- 
sions, Mr.  Ramsden's  dividing  engine  is  of  great  utility  ;t  the  instrument 

.      *  Ph.  Tr.  1731,  p.  147.  f  Description,  4to,  1787.     Rozier,  i.  147. 


ON  DRAWING,  WRITING  AND  MEASURING.  81 

being  fixed  on  the  revolving  plate  of  the  engine,  its  arc  is  made  to  advance 
under  the  cutting  tool  by  very  minute  steps,  regulated  by  the  turns  of  a 
screw,  of  which  each  revolution  is  divided  into  a  considerable  number  of 
equal  parts.  The  largest  and  finest  instruments  are,  however,  still  usually 
divided  by  hand  ;  that  is,  by  means  of  compasses.  Some  artists  have  first 
divided  a  straight  plate,  and  then  made  a  hoop  of  it,  which  has  served  as 
a  standard  for  further  processes.  An  arc  of  7°  10',  of  which  the  chord  is 
one-eighth  of  the  radius,  may  be  employed  as  a  test  of  the  accuracy  of  the 
work.  A  micrometer  screw  is  often  used  in  large  instruments  as  a  substi- 
tute for  the  minutest  divisions  ;  *  a  moveable  part  of  the  index  being 
brought  to  coincide  with  the  nearest  point  marked  in  the  arc,  by  turning 
the  screw  through  a  part  of  its  revolution,  which  is  measured  by  means  of 
a  graduated  circle.  But  a  simpler  method  of  reading  off  divisions  with 
accuracy  in  common  instruments,  is  the  application  of  a  vernier,  an  appa- 
ratus so  called  from  its  inventor.  The  space  occupied  by  eleven  divisions 
of  the  scale  being  divided  into  ten  parts  on  the  index,  the  coincidence  of 
any  of  the  divisions  of  the  index  with  those  of  the  scale,  shows,  by  its 
distance  from  the  end,  the  number  of  tenths  that  are  to  be  added  to  that  of 
the  entire  divisions.  (Plate  VII.  Fig.  92.) 

There  are  several  ways  of  measuring  the  angular  elevation  of  an  object 
above  the  horizon ;  at  sea,  the  apparent  horizon,  formed  by  the  surface 
of  the  water,  affords  the  most  convenient  determination ;  but  since  the 
spectator  is  somewhat  elevated  above  the  convex  surface  of  the  sea,  the 
apparent  horizon  is  necessarily  lower  than  the  true  horizon,  and  a  correc- 
tion is  therefore  required  according  to  the  height.  In  the  open  sea  this 
correction  may  be  determined  by  measuring  the  whole  angle  above  and 
below  the  apparent  horizon  [respectively],  and  taking  one  fourth  of  the 
difference  for  the  dip  or  depression.  On  shore,-  a  plumb  line  is  the  simplest 
instrument  for  determining  the  situation  of  the  horizon,  and  its  accidental 
vibrations  may  be  prevented  by  suspending  the  weight  in  water  or  in  oil. 
For  small  instruments,  a  spirit  level,  of  which  the  operation  depends  on 
hydrostatical  principles,  is  capable  of  greater  delicacy  than  a  plumb  line. 
It  readily  indicates,  when  well  made,  an  error  of  a  single  second ;  but  it 
requires  some  attention  to  avoid  inequalities  of  temperature,  which  would 
tend  to  disturb  its  figure.  Well  rectified  ether  is  found,  on  account  of  its 
perfect  fluidity,  to  be  the  best  liquid  for  a  spirit  level.  An  artificial  hori- 
zon is  a  reflecting  surface  employed  for  obtaining  an  image  as  much  below 
the  horizon  as  the  object  is  above  it,  and  for  measuring  the  angular  dis- 
tance of  this  image  from  the  object:  sometimes  a  plane  speculum  of  glass 
or  metal  is  used  for  this  purpose,  being  previously  adjusted  by  a  spirit 
level ;  and  sometimes  the  surface  of  mercury,  treacle,  or  tar,  protected  from 
the  wind  by  a  vessel  with  holes  in  it,  or  by  a  glass  cover,  either  detached,  or 
simply  floating  on  the  mercury,  when  this  liquid  is  employed. 

It  is  in  many  cases  simpler  and  more  convenient  to  estimate  angles,  not 
by  the  arcs  subtending  them,  but  by  their  sines,  or  the  perpendiculars 
falling  from  one  leg  on  the  other.  Thus,  it  is  usual  among  miners,  to  say 

*  Hooke's  Lectures,  Lambert  iiber  die  Branderschen  micrometer,  12  Aug.  1769. 
Hornblower,  in  Nich.  Jour.  vi.  247. 


82  LECTURE  X. 

that  the  ground  rises  or  falls  one  foot,  or  one  yard,  in  ten,  when  the  sine  of 
the  angle  of  its  inclination  to  the  horizon  is  one  tenth  of  the  radius.  Angles 
of  different  magnitudes  are  indeed  proportional  to  the  arcs,  and  not  to  the 
sines,  so  that  in  this  sense  the  sine  is  not  a  true  measure  of  the  comparative 
magnitude  of  the  angle  ;  but  in  making  calculations,  we  are  more  frequently 
obliged  to  employ  the  sine  or  cosine  of  an  angle  than  the  angle  or  arc 
itself.  It  is,  however,  easy  to  pass  from  one  of  these  elements  to  the  others, 
by  means  either  of  trigonometrical  tables,  or  of  the  scales  engraved  on  the 
sector. 

The  sines,  tangents,  and  secants  laid  down  on  the  sector,  may  be  em- 
ployed according  to  the  properties  of  similar  triangles,  in  the  computation 
of  proportions.  The  same  purpose  is  answered  by  Gunter's  scale,  by  the 
sliding  rule,  and  by  the  logarithmic  circles  of  Clairaut  and  of  Nicholson,* 
which  are  employed  mechanically  in  the  same  manner  as  a  table  of  loga- 
rithms is  used  arithmetically,  the  proportion  of  any  two  numbers  to  each 
other  being  determined  by  the  distance  of  the  corresponding  divisions  on 
the  scale  ;  so  that  if  we  wish  to  double  or  to  halve  a  number,  we  have  only 
to  find  the  distance  from  1  to  2,  and  to  lay  it  off  from  the  given  number 
either  way.  (Plate  VII.  Fig.  93,  94.) 

The  measurement  of  angles  is  at  once  applied  to  the  estimation  of  dis- 
tances in  the  dendrometer  or  engymeter  ;t  a  part  of  the  instrument  forms  a 
base  of  known  dimensions,  and  the  angle  at  each  extremity  of  this  base 
being  measured  with  great  accuracy,  the  distance  of  the  object  may  be 
inferred  from  an  easy  calculation,  or  from  a  table.  The  most  complete 
instruments  of  this  kind  have  twTo  speculums  for  measuring  the  difference 
of  the  angles  at  once,  in  the  manner  of  Hadley's  quadrant.  Telescopic 
scales  or  micrometers  are  also  sometimes  used  for  measuring  angles  sub- 
tended by  distant  objects,  of  which  the  magnitude  is  known  or  may  be 
estimated,  for  example,  by  the  height  of  a  rank  of  soldiers,  and  inferring 
at  once  the  distance  at  which  they  stand. 

Arithmetical  and  even  algebraical  machines,  of  a  much  more  complicated 
nature,  have  been  invented  and  constructed  with  great  labour  and  ingenuity ; 
but  they  are  rather  to  be  considered  as  mathematical  toys,  than  as  instru- 
ments capable  of  any  useful  application.^ 

An  angle,  when  once  measured,  can  be  verbally  and  numerically  de- 
scribed, by  reference  to  the  whole  circle  as  a  unit :  but  for  the  identification 
of  the  measure  of  a  right  line,  we  have  no  natural  unit  of  this  kind,  and  it 
is  therefore  necessary  to  establish  some  arbitrary  standard  with  which  any 
given  lengths  and  surfaces  may  be  compared.  It  might  be  of  advantage  in 
the  communication  between  different  countries  to  fix  one  single  standard  to 
be  employed  throughout  the  world,  but  this  does  not  appear  to  be  practi- 

*  Hist,  et  Mem.  de  Paris,  1727,  H.  142.  Nich.  Journal,  v.  40.  Ph.  Tr.  1753, 
p.  96  ;  1787,  p.  246. 

f  Pitt's  Dendrometer,  Repertory  of  Arts,  ii.  238.  Fallen's  Engymeter,  Zach. 
Monatliche  Correspondenz,  vi.  46. 

J  Napier's  Reckoning  Rods,  Leup.  Th.  Ar.  t.  13.  Robertson  on  GunCer's 
Scale,  Ph.  Tr.  1753,  p.  96.  Nicholson's  Logistic  Circle  and  Scales,  Ph.  Tr.  1787, 
p.  246  ;  Herschel's  Description  of  Babbage's  Calculating  Machine,  Transactions  of 
the  Cambridge  Philosophical  Society,  iv.  425. 


ON  DRAWING,  WRITING,  AND  MEASURING.  83 

cally  possible,  even  if  it  were  determined  what  the  standard  ought  to  be. 
"  The  observation  of  the  isochronism  of  the  small  vibrations  of  a  pendulum, 
and  the  ease  and  certainty  with  which  the  length  of  a  pendulum  vibrating 
seconds  may  be  ascertained,  have  suggested,"  says  Mr.  Laplace,*  in  his 
account  of  the  system  of  the  world,  "  the  idea  of  employing  this  length 
as  a  universal  measure.  We  cannot  reflect  on  the  prodigious  number  of 
measures  in  use,  not  only  among  different  nations,  but  even  in  the  same 
country,  their  capricious  and  inconvenient  divisions,  the  difficulty  of  deter- 
mining and  comparing  them,  the  embarrassment  and  the  frauds  which  they 
occasion  in  commerce,  without  regarding,  as  one  of  the  greatest  benefits 
that  the  improvements  of  the  sciences,  and  the  ordinances  of  civil  govern- 
ments can  render  to  humanity,  the  adoption  of  a  system  of  measures  of 
which  the  divisions  being  uniform,  may  be  easily  employed  in  calculations, 
and  which  may  be  derived,  in  a  manner  the  least  arbitrary,  from  a  funda- 
mental magnitude  indicated  by  nature  itself.  A  nation  that  would  intro- 
duce such  a  system  of  measures,  would  unite  to  the  advantage  of  reaping 
the  first  fruits  of  the  improvement,  the  pleasure  of  seeing  its  example 
followed  by  other  countries,  of  which  it  would  thus  become  the  benefactor : 
for  the  slow  but  irresistible  empire  of  reason  must  at  length  prevail  over 
national  jealousies,  and  over  all  other  obstacles  that  are  opposed  to  a  mea- 
sure of  which  the  convenience  is  universally  felt.  Such  were  the  motives 
that  determined  the  constituent  assembly  to  intrust  the  Academy  of  Sciences 
with  this  important  charge.  The  new  system  of  weights  and  measures  is 
the  result  of  the  labours  of  the  Committee,  seconded  by  the  zeal  and  infor- 
mation of  several  members  of  the  national  representation.'!* 

"  The  identity  of  the  calculation  of  decimal  fractions  and  of  whole 
numbers,  leaves  no  doubt  with  respect  to  the  advantage  of  the  division  of 
measures  of  all  kinds  into  decimal  parts  :  it  is  sufficient,  in  order  to  be 
convinced  of  this,  to  compare  the  difficulty  of  compound  multiplication  and 
division,  with  the  facility  of  the  same  operations  where  whole  numbers  only 
are  concerned,  a  facility  that  becomes  still  greater  by  means  of  logarithms, 
of  which  the  use  may  also  be  rendered  extremely  popular  by  simple  and 
cheap  instruments.  The  decimal  division  was  therefore  adopted  without 
hesitation  ;  and  in  order  to  preserve  the  uniformity  of  the  whole  system,  it 
was  resolved  to  deduce  every  thing  from  the  same  linear  measure  and  its 
decimal  divisions.  The  question  was  then  reduced  to  the  choice  of  this 
universal  measure,  to  which  the  name  of  metre  was  to  be  given. 

"  The  length  of  the  pendulum,  and  that  of  a  meridian  of  the  earth,  are 
the  two  principal  standards  that  nature  affords  us  for  fixing  the  unit  of 
linear  measures.  Both  of  these  being  independent  of  moral  revolutions, 
they  cannot  experience  a  sensible  alteration  without  very  great  changes  in 
the  physical  constitution  of  the  earth.  The  first  method,  which  is  of  easy 
execution,  has  the  inconvenience  of  making  the  measuf e  of  length  depend 
on  two  elements,  heterogeneous  with  respect  to  itself  and  to  each  other, 
gravitation,  and  time  ;  besides  that  the  division  of  time  into  small  portions 

*  Systeme  du  Monde,  liv.  i.  c.  12. 

f  Report  on  the  choice  of  a  unit  of  measure,  by  Borda,  Lagrange,  Laplace, 
Monge,  and  Condorcet,  Mem.  de  1'Acad.  Paris,  1788.  H.  7-17. 

G2 


84  LECTURE  X. 

is  wholly  arbitrary.  It  was  resolved,  therefore,  to  employ  the  second 
method,  which,"  says  Mr.  Laplace,  "  appears  to  he  of  very  high  antiquity ; 
it  is  so  natural  to  man  to  refer  measures  of  distance  to  the  dimensions  of 
the  globe  which  he  inhabits,  in  order  that,  in  transporting  himself  from 
place  to  place,  he  may  know,  by  the  denomination  of  the  space  passed 
through  alone,  the  relation  of  this  space  to  the  entire  circumference  of  the 
earth.  This  method  has  also  the  advantage  of  making  nautical  measures 
correspond  at  once  with  celestial  ones.  The  navigator  has  often  occasion 
to  compare  with  each  other  the  distance  that  he  has  passed  over,  and  the 
arc  of  the  heavens  corresponding  to  that  distance  ;  it  is  therefore  of  conse- 
quence that  these  measures  should  be  readily  obtained  from  each  other,  by 
altering  only  the  place  of  the  units.  But,  for  this  purpose,  the  funda- 
mental unit  of  linear  measures  must  be  an  aliquot  part  of  the  terrestrial 
meridian,  which  must  correspond  to  one  of  the  divisions  of  the  circum- 
ference of  a  circle.  Thus  the  choice  of  the  metre  was  reduced  to  that  of 
the  unit  of  angular  measure,  and  the  right  angle,  as  constituting  the  limit 
of  the  inclination  of  two  lines  to  each  other,  was  considered  as  entitled  to 
the  preference. 

"  The  arc,  which  was  measured  in  1740,  from  Dunkirk  to  the  Pyren- 
nees,  might  have  served  for  finding  the  magnitude  of  the  quadrant  of  the 
meridian  ;  but  a  new  and  more  accurate  measurement  of  a  larger  arc  was 
more  likely  to  excite  an  interest  in  favour  of  the  new  measures.  Delambre 
and  Mechain  were  therefore  intrusted  with  the  direction  of  the  operations 
for  measuring  an  arc  from  Dunkirk  to  Barcelona,*  and  after  making  a 
proper  correction  for  the  ellipticity  of  the  earth,  according  to  the  measure- 
ment of  the  arc  in  Peru,  the  quadrant  was  determined  to  be  equal  to 
5,130,740  of  the  iron  toise  used  at  the  equator,  its  temperature  being  61^°  of 
Fahrenheit :  the  ten-millionth  part  of  this  quadrant  was  taken  for  the  unit 
or  metre.  A  standard  was  deposited  in  the  custody  of  the  legislative  body, 
adjusted  at  the  temperature  of  melting  ice.  In  order  to  be  able  always  to 
identify  this  length,  without  recurring  to  an  actual  measurement  of  the  arc, 
it  was  of  importance  to  compare  it  very  accurately  with  that  of  the  pen- 
dulum vibrating  seconds,  and  this  has  been  done  with  great  care  by 
Borda,  at  the  observatory  of  Paris.  The  unit  of  measures  of  land  is  the 
are,  or  100  square  metres :  a  cubic  metre  of  wood  is  called  a  stere,  and  a 
cubic  decimetre,  or  a  cube  of  which  the  side  is  one  tenth  of  a  metre,  is  a 
litre,  or  measure  of  fluids. 

"  Uniformity  appeared  to  require  that  the  day  should  be  divided  into  ten 
hours,  the  hour  into  a  hundred  minutes,  and  the  minute  into  a  hundred 
seconds.  This  division,  useful  as  it  will  be  to  astronomers,  is  of  less 
advantage  in  civil  life,  where  arithmetical  operations  are  seldom  performed 
on  the  parts  of  time ;  and  the  difficulty  of  adapting  it  to  clocks  and 
watches,  together  with  our  commercial  relations  with  foreign  countries, 

*  Delambre,  Base  du  Systeme  Metrique,  3  vols.  4to,  Paris.  A  fourth  volume,  the 
work  of  MM.  Biot  and  Arago,  was  added  in  1821.  They  extended  the  survey  tojthe 
island  of  Formentera.  Consult  also  Reports  to  the  National  Institute.  Rozier's 
Journal,  xliii.  169.  Jour,  de  Phys.  xliv.  (1),  81.  Bulletin  de  la  Soc.  Phil.  n.  28. 
Nich.  Jour.  iii.  316.  Ph.  Mag.  i.  269  ;  and  the  article,  Figure  of  the  Earth,  by 
Airy,  in  the  Encyclopaedia  Metropolitana. 


ON  DRAWING,  WRITING,  AND  MEASURING.  35 

have  suspended  its  introduction  for  the  present.  We  may,  however, 
expect  that  it  will  ultimately  be  brought  into  general  use." 

Such  is  Mr.  Laplace's  account  of  the  new  system  of  measures,  the  result 
of  the  joint  labours  of  many  of  the  ablest  mathematicians  on  the  continent. 
There  is  not  at  present  any  great  probability  that  it  will  ever  be  employed 
in  this  country.  It  is  of  little  consequence  from  what  the  original  unit  has 
been  derived,  unless  we  can  with  ease  and  accuracy  recur  to  its  origin  : 
and  whether  a  standard  has  been  first  adjusted  according  to  the  circum- 
ference of  the  globe,  or  to  the  foot  of  an  individual  hero,  the  facility  of 
comparing  other  measures  with  it  is  the  same.  It  is  confessed  that  the 
pendulum  affords  the  readiest  method  of  recovering  the  standard  when 
lost ;  and  if  it  was  necessary  for  the  Committee  of  the  French  Academy 
to  determine  a  unit  absolutely  new,  it  would  perhaps  have  been  more 
eligible  to  fix  on  one  which  was  independent  of  any  ulterior  comparison, 
than  to  seek  for  an  ideal  perfection  in  attempting  to  copy  from  a  more 
magnificent  original ;  to  say  nothing  of  the  uncertainty  with  regard  to  the 
ellipticity  of  the  earth,  and  the  probable  irregularity  of  its  form  in  various 
respects.  On  the  other  hand,  it  must  be  allowed,  that  the  correct  deter- 
mination of  the  length  of  the  pendulum  has  sometimes  been  found  more 
difficult  than  Mr.  Laplace's  statement  would  lead  us  to  suppose  it,  and  we 
cannot  depend  on  any  measurement  of  it  as  totally  exempt  from  an  error 
of  the  ten  thousandth  part  of  the  whole. 

The  metre,  as  definitively  established  by  the  government  of  France,  is 
equal  to  39-nyVV  English  inches,  measured,  as  it  has  been  usual  in  this 
country,  on  a  standard  scale  of  brass,  at  the  temperature  of  62°  of  Fah- 
renheit; while  the  French,  on  the  contrary,  reduce  the  length  of  their 
measures  to  that  which  they  would  acquire  at  the  freezing  point.  Hence 
ten  thousand  inches  are  nearly  254  metres,  a  thousand  feet  305  metres. 
The  length  of  the  pendulum  vibrating  seconds  in  London,  was  found  by 
George  Graham,  from  a  mean  of  several  experiments,  all  agreeing  very 
nearly  together,  to  be  39-rVo-  inches.  This  is  also  nearly  a  mean  between 
the  length  which  may  be  deduced,  with  proper  corrections,  from  Borda's 
experiments  at  Paris,*  and  Mr.  Whitehurst's  experiments  made  in  Lon- 
don, t  with  the  apparatus  invented  by  Mr.  Hatton,;};  where  the  length 
ascertained  is  the  difference  between  the  lengths  of  two  pendulums  vibrat- 
ing in  different  times.  Mr.  Whitehurst's  measures,  however,  require  some 
corrections,  which  Mr.  Nicholson  has  pointed  out.  The  fall  of  a  heavy 
body  in  the  first  second  appears,  from  this  determination  of  the  length  of 
the  pendulum,  to  be  sixteen  feet  one  inch  and  a  tenth. 

Of  the  old  French  measure,  15  inches  made  nearly  16  English,  and  76, 
very  exactly  81 ;  the  toise  was  76T%3A  inches.  In  Germany  the  Rhinland 
foot  is  generally  used  ;  100  of  these  feet  make  103  English. 

A  wine  gallon  contains  231  cubic  inches ;  an  ale  gallon  is  the  content  of 
10  yards  of  a  cylindrical  inch  pipe. 

^  See  Base  du  Systeme  Metrique,  vol.  iii. 

f  Whitehurst's  Attempt  to  obtain  Measures  of  Length  from  the  Measurement  of 

Time,  4to,  Lond.  1787.     Do.  on  Pendulums,  1792. 

I  Hatton's  Machine  for  finding  a  Standard.  Trans,  of  the  Soc.  of  Arts,  I.  238. 


86  LECTURE  X. 

A  variety  of  instruments  are  used  for  the  immediate  comparison  of  the 
standard  measure  or  its  parts,  with  other  lengths  or  distances.  Such  are 
scales,  simple  and  diagonal,*  verniers,  micrometer  screws,  beam  compasses, 
rods,  lines,  chains,  and  measuring  wheels.  The  greatest  accuracy  has 
generally  been  supposed  to  be  obtained,  in  large  distances,  by  means  of 
rods,  made  of  glass  or  of  platina,  in  order  to  be  less  susceptible  of  such 
changes  as  are  produced  by  variations  of  temperature ;  General  Roy,t  how- 
ever, found  that  a  steel  chain  was  as  little  liable  to  error,  as  any  mode 
that  he  could  employ  ;  and  those  who  have  continued  the  extensive  survey 
which  he  began,  even  prefer  it  to  every  other.  J  For  the  comparison  of 
standards,  and  for  determining  small  distances  with  great  precision,  beam 
compasses,  or  scales  with  sliding  indices,  furnished  with  microscopes  and 
cross  wires,  have  been  constructed  by  the  artists  of  this  country:  in 
France  a  lever  has  sometimes  been  introduced,  its  longer  arm  having  an 
ample  range  of  motion,  corresponding  to  a  very  minute  difference  in  the 
length  of  the  substance  which  acts  on  the  shorter  arm.  But  for  common 
purposes  the  diagonal  scale  is  sufficiently  accurate,  and  may  be  applied 
without  the  error  of  the  thousandth  of  an  inch :  in  cases  where  a  very 
delicate  vernier  or  a  micrometer  screw  is  applied,  a  magnifier  is  usually 
required.  Mr.  Coventry  has,  however,  succeeded  in  making  simple  scales 
which  are  accurate  enough  to  measure  the  ten  thousandth  of  an  inch. 
He  draws  parallel  lines  on  glass,  at  this  distance,  which  are  in  some  parts 
sufficiently  regular,  although  they  can  only  be  seen  by  the  help  of  a  power- 
ful microscope  :  but  those  which  are  at  the  distance  of  the  five  thousandth 
of  an  inch  are  much  more  correct  and  distinct.  For  dividing  rectilinear 
scales  of  all  kinds,  Mr.  Ramsden  §  constructed  a  machine  which  acts  by 
the  turns  of  a  screw  :  others  have  employed  an  apparatus  resembling  Mar- 
quois's  parallel  rulers.  (Plate  VII.  Fig.  95... 97.) 

The  motion  of  a  ship  at  sea  is  measured  by  a  log  line,  or  a  rope  divided 
by  knots  into  equal  parts,  and  attached  to  a  log,  which  is  retained  nearly 
at  rest  by  the  resistance  of  the  water.  Attempts  have  also  been  made  to 
cause  a  little  waterwheel  to  turn  by  the  motion  of  the  ship,  and  to  measure 
both  the  rate  and  the  distance  run  ;  and  an  instrument  has  been  invented 
for  doing  the  same  upon  hydraulical  principles  ;  raising  the  water  of  a  gage 
to  different  heights,  by  means  of  the  pressure  occasioned  by  the  relative 
motion  of  the  ship  and  the  water,  and  discharging  at  the  same  time  a 
small  stream  into  a  reservoir,  with  a  velocity  proportional  to  that  of  the 
ship. 

LECT.  X.— ADDITIONAL  AUTHORITIES. 

Drawing  and  Painting. — Leonardo  da  Vinci,  Trattato  della  Pittura,  4to,  Rome, 
1817;  Translation  by  Rigaud.  Junii  de  Pictura  Veterum,  fol.  Rotterd.  1694.  Du- 
fresnoy,  Art  of  Painting.  De  Piles,  Do.  1706.  Bardwell,  Do.  4to,  Lond.  1706. 

*  Hooke  on  Diagonal  Divisions,  Animad.  on  Hevelius.  Wallis  on  Do.  Phil. 
Tr.  1674,  ix.  243. 

f  Roy's  Account  of  the  Measurement  of  a  Base  on  Hounslow  Heath,  Ph.  Tr. 
1785,  Ixxv.  385. 

J  Ramsden's  Steel  Chain,  Ph.Tr.  1785,  p.  394. 

§  Ramsden's  Description  of  an  Inst.  for  dividing  Lines,  4to,  1779. 


I 

MODELLING,  PERSPECTIVE,  ENGRAVING,  PRINTING.      87 


Lahire,  Hist,  et  Mem.  ix.  405,  431,  464.  Reynolds's  Discourses,  Burnet's  ed. 
4to,  1842.  Cooper  on  the  Painting  of  the  Ancients,  Manch.  Mem.  iii.  510.  Ra- 
phael Mengs  Obras,  4to,  Madrid,  1780.  In  Italian,  by  D'Arezza.  Wincklemann, 
Histoire  del' Art  chez  les  Anciens  (Trad,  de  VAllemande),  3  vols.  4to,  Paris,  1790- 
1803.  Burnet' s  Hints  on  Composition,  4to,  1827.  Lanzi,  Storia  Pittorica,  Trans, 
by  Roscoe,  1828.  Rosini,  Storia  della  Pittura  Italiana,  4  vols.  8vo.  already  pub- 
lished, with  plates  fol. 

Writing. — Nouveau  Traite  de  Diplomatique,  6  vols.  4to,  Paris,  1750-65.  Butt- 
ner  on  the  Alphabets  of  all  Nations,  Nov.  Com.  Gott.  1776,  p.  106.  Astle's  Origin 
and  Progress  of  Writing,  4to,  Lond.  1803. 

Measuring  Instruments,  8?c.— Bion  on  Math.  Insts.  1723,  and  4to,  Paris,  1752. 
Adams's  Essays,  Lond.  1797.  Smeaton  on  the  Graduation  of  Insts.  Ph.  Tr.  1786, 
p.  1.  Ludlam  do.  4to,  1786.  Gounella  do.  Pistoia,  1816. 

Modes  of  obtaining  a  Standard,  fyc. — Condamine  on  an  Invariable  Measure, 
Hist,  et  Mem.  de  Paris,  1747,  p.  489,  H.  83.  Remarks  on  Experiments  with 
Pendulums.  Nich.  Journ.  iii.  29. 

Comparison  of  Measures. — Comparison  of  French  and  English  Measures,  Ph. 
Tr.  1742,  p.  185.  Of  English  Standards,  Ph.  Tr.  1743,  p.  541.  Gray  on  the 
Measures  of  Scotland,  Ed.  Ess.  i.  200.  Shuckburgh  on  a  Standard  of  Weights  and 
Measures,  Ph.  Tr.  1798,  p.  133.  Kater,  Ph.  Tr.  1818-19-21.  Hall  and  Foster, 
Ph.  Tr.  1823.  Sabine,  Ph.  Tr.  1828-29.  Baily,  Report  on  the  New  Standard  Scale 
of  the  Astronomical  Society,  Trans.  Royal  Astr.  Soc.  1836,  ix.  See  also  Lect.  XII. 


LECTURE    XI. 


ON  MODELLING,  PERSPECTIVE,  ENGRAVING,  AND  PRINTING. 

WE  have  examined  the  principal  instruments  and  materials  employed 
for  drawing  and  for  measuring ;  we  are  now  to  consider,  first,  the  methods 
of  copying  solids,  and  of  projecting  their  images  011  a  plane  surface  ;  and 
secondly,  the  arts  of  perpetuating  the  works  of  the  pen  and  of  the  pencil 
by  engraving  and  printing. 

When  it  is  required  to  make  a  copy  of  a  solid  of  an  irregular  form,  as  for 
example  of  a  statue,  we  must  determine  the  situation  of  a  sufficient  num- 
ber of  points  to  guide  us  in  our  work  with  accuracy,  by  means  of  an 
instrument  capable  of  being  fixed  in  any  required  situation ;  so  that  the 
extremity  of  a  sliding  bar  or  pin  may  be  in  contact  with  each  point  in  the 
original,  and  then  removed  to  a  similar  part  of  another  frame,  on  which  the 
copy  is  placed,  a  perforation  being  made,  by  degrees,  in  the  block,  so  as  to 
suffer  the  pin  to  arrive  at  its  proper  place,  at  which  it  stops.  (Plate  VII. 
Fig.  98.) 

The  model  of  a  statue  is  generally  first  made  of  clay,  and  a  cast  of  this 
taken  immediately  in  plaster  of  Paris,  since  the  clay  would  crack  and 
change  its  form  in  drying.  This  mode  of  copying  by  means  of  plaster  is 
exceedingly  useful  in  various  departments  of  the  mechanical  arts :  the 
original  is  well  oiled  and  placed  in  a  proper  vessel ;  a  mixture  of  prepared 
plaster  and  water,  of  the  consistence  of  cream,  is  then  poured  on  it ;  this 
in  a  short  time  hardens,  and  is  divided  into  several  parts,  in  such  a  manner 
as  not  to  injure  the  original  figure  in  its  removal.  These  pieces,  being 
again  united,  form  a  mould  for  the  ultimate  cast.  Sometimes  a  small 


88  LECTURE  XI. 

figure  is  first  modelled  in  a  mixture  of  wax,  turpentine,  and  oil ;  and  a 
mould  being  formed  on  this,  the  ultimate  cast  is  made  either  of  plaster,  or 
of  a  composition  of  wax  with  white  lead  and  a  little  oil,  which  serves  as 
an  imitation  of  marble. 

We  have,  however,  much  less  frequent  occasion  to  make  an  exact  copy 
of  a  solid  of  any  kind,  than  to  represent  its  appearance  by  means  of  per- 
spective delineation.  Supposing  ourselves  provided  with  proper  materials 
for  drawing,  we  may  easily  imitate,  with  the  assistance  of  a  correct  eye, 
and  a  hand  well  exercised,  the  figures  and  relative  positions  of  objects 
actually  before  us,  by  delineating  them  in  the  same  form  as  they  would 
appear  to  be  projected  on  a  transparent  surface  placed  before  the  eye. 
Considering  the  simplicity  of  this  process,  it  is  almost  surprising  that  the 
doctrine  of  perspective  should  have  been  supposed  to  require  a  very  serious 
study,  and  that  material  errors  should  have  been  committed  with  respect 
to  it,  by  men  whose  general  merit  in  other  departments  of  painting  is  by 
no  means  contemptible.  But  it  must  be  confessed,  that  when,  instead  of 
imitating  objects  immediately  before  us,  the  pencil  is  employed  in  embody- 
ing imaginary  forms,  calculated  either  for  beauty  or  for  utility,  a  great 
degree  of  care  and  attention  may  be  necessary  in  order  to  produce  a  true 
representation  of  objects,  which  are  either  absent,  or  have  no  existence : 
and  here  memory  and  fancy  only  will  scarcely  ever  be  sufficient,  without  a 
recurrence  to  mathematical  principles.  To  architects  therefore,  and  to 
mechanics  in  general,  a  knowledge  of  perspective  is  almost  indispensable, 
whenever  they  wish  to  convey  by  a  drawing  an  accurate  idea  of  their 
projected  works. 

If  any  assistance  be  required  for  the  delineation  of  an  object  actually 
before  us,  it  may  easily  be  obtained  in  a  mechanical  manner,  by  means  of 
a  frame  with  cross  threads  or  wires  interposed  between  the  eye  and  the 
object.  The  eye  is  applied  to  an  aperture,  which  must  be  fixed,  in  order 
to  preserve  the  proportions  of  the  picture ;  and  which  must  be  small,  in 
order  that  the  threads  and  the  more  distant  objects  may  be  viewed  at  the 
same  time  with  sufficient  distinctness.  The  paper  being  furnished  with 
corresponding  lines,  we  may  observe  in  what  division  of  the  frame  any 
conspicuous  point  of  the  object  appears,  and  may  then  represent  its  image 
by  a  point  similarly  situated  among  the  lines  drawn  on  our  paper ;  and 
having  obtained,  in  this  manner,  a  sufficient  number  of  points,  we  may 
complete  the  figures  by  the  addition  of  proper  outlines.  Sometimes,  for  the 
delineation  of  large  objects  requiring  close  inspection,  it  has  been  found 
useful  to  employ  two  similar  frames,  the  one  a  little  smaller  than  the 
other,  and  placed  at  a  certain  distance  from  it ;  so  that  every  part  of  the 
object,  when  seen  through  the  corresponding  divisions  of  both  frames, 
appears  in  the  same  manner  as  if  the  eye  were  situated  at  a  very  remote 
point.  It  was  in  this  manner  that  the  elegant  anatomical  figures  of  Albinus 
were  executed.  (Plate  VII.  Fig.  99.) 

But  if  it  be  required  to  lay  down,  in  the  plane  of  a  picture,  the  projection 
of  an  object  of  which  the  actual  dimensions  and  situation  are  given,  we 
may  obtain  the  requisite  measures  from  the  properties  of  similar  triangles, 
and  the  consideration  of  the  rectilinear  motion  of  light.  We  may  consider 


MODELLING,  PERSPECTIVE,  ENGRAVING,  PRINTING.     .89 

our  picture  as  a  reduced  copy  of  a  projection  formed  on  an  imaginary  plane, 
which,  as  well  as  the  picture,  is  generally  supposed  to  he  in  a  vertical  situa- 
tion, and  which  stands  on  the  horizontal  plane,  at  the  point  where  the 
ohjects  to  be  represented  hegin.  In  order  to  find  the  position  of  the  image 
of  a  given  right  line,  we  must  determine  the  point  in  which  a  line  parallel 
to  it  passing  through  the  place  of  the  eye  cuts  the  plane  of  the  picture  ;  this 
is  called  the  vanishing  point  of  the  given  line  and  of  all  other  lines  parallel 
to  it,  since  the  image  of  any  such  line,  continued  without  limit,  will  he  a 
right  line  directed  to  this  point,  hut  never  passing  it.  When  the  lines  to  he 
represented  are  parallel  to  the  picture,  the  distance  of  their  vanishing  point 
becomes  infinite,  and  their  images  are  also  parallel  to  the  lines  and  to  each 
other.  The  centre  of  the  picture,  or  that  point  which  is  nearest  to  the  eye, 
is  the  vanishing  point  of  all  lines  perpendicular  to  the  picture  ;  through 
this  point  it  is  usual  to  draw  a  horizontal  and  a  vertical  line  :  we  may  then 
lay  off  downwards  on  the  vertical  line  the  distance  of  the  eye  from  the 
picture,  in  order  to  find  the  point  of  distance,  which  serves  to  determine 
the  position  of  any  oblique  lines  on  a  horizontal  plane  :  for  if  we  draw  a 
ground  plan  of  any  object,  considering  the  picture  as  a  horizontal  surface, 
we  may  find  the  vanishing  point  of  each  of  its  lines,  by  drawing  a  line 
parallel  to  it  through  the  point  of  distance  until  it  meets  the  horizontal 
vanishing  line.  (Plate  VII.  Fig.  100,  101.) 

In  order  to  find  the  position  of  the  image  of  a  given  point  of  a  line,  we 
must  divide  the  whole  image  in  such  a  manner  that  its  parts  may  be  to  each 
other  in  the  same  proportion  as  the  distance  of  the  given  point  and  of  the 
eye,  from  the  plane  of  projection.  This  may  be  readily  done,  when  a 
ground  plan  has  been  first  made,  by  drawing  a  line  "from  any  point  in  the 
plan  to  the  point  of  distance,  which  will  cut  the  whole  image  of  the  line  ia 
the  point  required.  (Plate  VII.  Fig.  102.) 

When  it  is  required  to  determine  a  point  in  a  line  parallel  to  the  picture, 
we  may  suppose  a  line  to  be  drawn  through  it  perpendicular  to  the  picture, 
and,  by  finding  the  image  of  this  line,  we  may  intersect  the  former  image 
in  the  point  required.  It  is  thus  that  the  height  of  any  number  of  columns 
or  figures,  at  different  distances,  may  be  readily  determined.  (Plate  VIII. 
Fig.  103.) 

The  projection  of  curvilinear  figures  is  most  conveniently  effected  by 
drawing  across  them  parallel  lines,  which  form  small  squares  or  rectangles, 
throwing  these  divisions  into  perspective,  and  tracing  a  curve  through  the 
corresponding  points.  There  are  also  methods  of  determining  mathemati- 
cally, or  of  drawing  mechanically  the  ellipsis,  which  results  from  the 
projection  of  a  circle,  in  a  given  position,  but  they  are  considerably  intri- 
cate, and  a  steady  hand  is  seldom  in  want  of  them.  (Plate  VIII.  Fig.  104.) 

This  system  of  perspective  must  necessarily  be  employed  when  we  wish 
to  represent  objects  which  appear  to  us  under  angles  of  considerable  mag- 
nitude, and  to  give  them  as  much  as  possible  the  appearance  of  an  imitation 
o£  nature.  But  for  almost  all  purposes  of  science,  and  of  mechanical 
practice*  the  most  convenient  representation  is  the  orthographical  projection, 
where  the  distance  of  the  eye  from  the  plane  is  supposed  to  be  increased 
without  limit,  and  the  rays  of  light  passing  to  the  eye  to  be  parallel  to  each 


90  LECTURE  XL 

other.  In  order  to  represent  any  object  in  this  manner,  we  must  assume 
one  line  for  the  direction  of  the  centre  of  the  picture,  to  which  the  images 
of  all  lines  perpendicular  to  the  plane  of  projection  must  he  parallel,  and 
another  for  that  of  the  point  of  distance,  hy  means  of  which  we  may 
measure  the  first  lines,  #s  if  that  point  were  actually  within  reach  ;  and  in 
this  manner  we  may  determine  the  place  of  any  number  of  points  of  the 
object  to  be  delineated.  (Plate  VIII.  Fig.  105.) 

If  we  wish  to  apply  the  mechanical  method  of  drawing  by  the  assistance 
of  a  frame  to  this  mode  of  representation,  instead  of  a  fixed  aperture  for  a 
sight,  or  a  second  frame  of  smaller  dimensions,  we  must  employ  a  second 
frame  of  the  same  magnitude  with  the  first,  in  the  manner  which  has 
already  been  described.  Professor  Camper*  has  censured  Albinus  for  not 
adopting  this  method  in  his  figures  :  but  subjects  so  large  as  those  which 
he  has  represented  would  have  had  less  of  the  appearance  of  nature,  if  they 
had  been  projected  orthographically,  nor  would  such  projections  have  been 
materially  more  instructive. 

It  frequently  happens,  that  in  geographical  and  astronomical  drawings 
we  have  occasion  to  represent,  on  a  plane,  the  whole  or  a  part  of  a  spherical 
surface.  Here,  if  we  employ  the  orthographical  projection,  the  distortion 
will  be  such  that  the  parts  near  the  apparent  circumference  will  be  so  much 
contracted  as  to  render  it  impossible  to  exhibit  them  with  distinctness.  It 
is,  therefore,  more  convenient,  in  this  case,  to  employ  the  stereographical 
projection,  where  the  eye  is  supposed  to  be  at  a  moderate  distance  from  the 
object.  The  place  of  the  eye  may  be  assumed  either  within  or  without  the 
sphere  at  pleasure  ;  and  according  to  the  magnitude  of  the  portion  which 
we  wish  to  represent,  the  point,  from  which  the  sphere  may  be  viewed  with 
the  least  distortion,  may  be  determined  by  calculation.  But  in  these  cases 
all  circles  obliquely  situated  on  the  sphere  must  be  represented  by  ellipses  : 
there  is,  however,  one  point  in  which  the  eye  may  be  placed,  which  has  the 
peculiar  and  important  advantage,  that  the  image  of  every  circle,  greater  or 
lesser,  still  remains  a  circle.  This  point  is  in  the  surface  itself,  at  the 
extremity  of  the  diameter  perpendicular  to  the  plane  of  projection ;  and 
this  is  the  point  usually  employed  in  the  stereographical  projection  of  the 
sphere,  which  serves  for  the  geometrical  construction  of  problems  in  spheri- 
cal trigonometry.  The  projection  of  the  whole  surface  of  the  sphere  would 
occupy  an  infinite  space,  but  within  the  limits  of  the  hemisphere,  the 
utmost  distortion  of  the  linear  measure  is  only  in  the  proportion  of  2  to  1, 
each  degree  at  the  circumference  of  the  figure  occupying  a  space  twice  as 
great  as  at  the  centre.  The  angles,  which  the  circles  form  in  crossing  each 
other,  are  also  correctly  represented.  (Plate  VIII.  Fig.  106.) 

For  projecting  figures  on  curved  or  irregular  surfaces,  the  readiest  method 
is  to  trace  cross  lines  on  them,  with  the  assistance  of  such  a  frame  as  has 
been  described  for  drawing  in  perspective,  representing  the  appearance  of 
uniform  squares  or  rectangles,  and  to  delineate  in  each  of  these  the  corre- 
sponding parts  of  the  object,  or  of  the  drawing  which  serves  as  a  copy.  . 

The  arts  of  writing  and  drawing,  in  all  their  varieties,  are  extended  in 

*  Cogan's  Translation  of  Camper,  on  the  connection  between  Anatomy  and  the 
Arts  of  Painting,  Sculpture,  &c.  4to,  Lend.  1794. 


MODELLING,  PERSPECTIVE,  ENGRAVING,  PRINTING.      91 

their  performance,  and  perpetuated  in  their  duration,  by  means  of  en- 
graving and  printing.  If  there  is  any  one  circumstance  to  which  we  can 
peculiarly  attribute  the  more  rapid  progress  of  general  civilisation  in  mo- 
dern than  in  ancient  times,  it  is  the  facility  of  multiplying  copies  of  literary 
productions  of  all  kinds,  by  the  assistance  of  these  arts.  The  distinguishing 
character  of  printing  consists  in  the  employment  of  moveable  types  :  the  art 
of  engraving  is  more  simple,  and  in  some  of  its  forms  more  ancient.  The 
Romans  were  in  the  habit  of  using  seals  and  stamps,  for  marking  letters 
and  words  oh  wax  and  on  pottery;  it  was  usual  in  the  middle  ages  to 
employ  perforated  plates  of  metal  as  patterns  for  guiding  a  brush,  by  means 
of  which  the  capital  letters  were  inserted  in  some  manuscripts,  and  the 
Chinese  are  said  to  have  been  long  in  possession  of  the  art  of  printing  books 
from  wooden  blocks.*  It  was  in  this  form  that  printing  was  first  intro- 
duced into  Europe,  in  the  beginning  of  the  fifteenth  century.  There  seems 
to  have  been  formerly  a  method  of  engraving  on  wood  with  greater  ease 
and  accuracy  than  is  now  practised  ;  the  hatches  may  be  observed  in  old 
wooden  cuts  to  cross  each  other  more  frequently  and  with  greater  freedom, 
than  in  modern  works,  although  some  have  conjectured,  with  considerable 
appearance  of  probability,  that  these  old  engravings  were  in  reality  etched 
in  relief  on  metal.  The  art  of  engraving  on  wood  is,  however,  at  present 
in  a  high  degree  of  perfection  in  this  country,  and  blocks  are  still  frequently 
used  for  mathematical  diagrams  and  other  simple  figures  :  for  although 
they  are  somewhat  more  expensive  than  copper  plates,  they  wear  much 
longer,  and  they  have  the  advantage  of  being  printed  off  at  the  same  time 
with  the  letter  press,  and  of  being  included  in  the  same  page  with  the  text 
to  which  they  belong,  since  the  ink  is  applied  to  the  projecting  parts  only, 
both  of  these  cuts  and  of  the  common  printing  types.f 

The  method  of  engraving  on  plates  of  pewter  or  of  copper,  and  of  taking 
impressions,  by  means  of  the  portion  of  ink  retained  in  the  furrows  cut  by 
the  graver,  was  also  introduced  in  the  fifteenth  century.  For  dry  engraving, 
the  drawing,  if  it  is  not  executed  in  black  lead,  is  generally  prepared  by 
passing  a  pencil  over  its  principal  features,  and  the  outline  is  transferred  to 
the  plate,  which  has  a  thin  coat  of  white  wax  laid  on  it,  by  placing  the 
drawing  on  it,  and  rubbing  it  with  a  burnisher ;  sometimes  a  drawing  in 
Indian  ink,  especially  if  freed  from  a  part  of  its  gum,  may  be  transferred 
in  this  manner  without  the  application  of  a  pencil.  When  written  charac- 
ters are  to  be  engaved,  the  plate  is  laid  on  a  cushion,  so  as  to  be  readily 
turned  under  the  graver,  which  is  a  great  convenience  in  forming  curved 
lines. 

In  laying  on  equable  shades  of  considerable  extent,  much  labour  is  saved 
by  the  use  of  a  ruling  machine,  which  enables  us  to  draw  lines,  at  any  re- 
quired distance,  very  accurately  parallel,  and  either  straight,  or  following 
each  other's  gentle  undulations,  in  order  to  avoid  Jhe  appearance  of  stiffness. 

,  *  Du  Halde,  Description  de  1'Empire  de  la  Chine,  4to,  1736.  Zani,  Material! 
per  Servire  alia  Storia  dell'  Incisione  in  Rame  ein  Legno,  Parma,  1802. 

f  An  account  of  the  re-discovery  of  the  mode  of  decarbonizing  steel  so  as  to  ren- 
der it  capable  of  being  engraved  on,  will  be  found  in  the  Tr.  of  the  Soc.  of  Arts, 
vol.  xli. 


92  LECTURE  XI. 

This  machine,  like  the  dividing  engine,  is  sometimes  adjusted  by  the  revolu- 
tions of  a  screw,  and  sometimes  by  the  oblique  motion  of  a  triangular 
slider.  Besides  the  cutting  graver,  which  is  of  a  prismatic  form,  terminated 
by  an  oblique  surface,  other  instruments  are  occasionally  employed  ;  the 
dry  needle  makes  a  very  fine  line,  and  leaves  the  metal  that  it  has  displaced 
to  be  rubbed  off  by  another  tool.  Sometimes  a  number  of  detached  exca- 
vations are  formed  by  a  pointed  instrument,  and  the  projections  are  after- 
wards removed  ;  this  is  called  stippling.  A  burnisher  and  some  charcoal 
are  required  for  erasing  the  strokes  of  the  graver,  when  it  is  necessary,  and 
for  polishing  the  surface.  It  is  seldom,  however,  that  a  plate  is  begun  and 
completed  by  dry  engraving  only. 

For  engraving  in  mezzotinto,  the  plate  is  roughened,  by  scraping  it  in 
every  direction  with  a  tool  made  for  the  purpose,  so  that  an  impression 
from  it,  in  this  state,  would  be  wholly  dark  ;  the  lights  are  then  inserted, 
by  removing  the  inequalities  of  the  surface,  in  particular  parts,  by  means 
of  a  smooth  scraper  and  a  burnisher.  As  the  plate  wears  in  printing,  some 
of  these  parts  are  liable  to  have  the  grain  a  little  raised  again,  so  that  the 
lights  are  less  clear  in  the  later  impressions  than  in  the  proofs.  It  is  well 
known,  that  in  common  engravings  the  proofs  are  usually  the  darkest 
throughout. 

The  most  expeditious  and  most  generally  useful  mode  of  working  on 
copper,  is  the  process  of  etching.  The  plate,  being  covered  with  a  proper 
varnish,  is  usually  blackened  with  smoke,  and  the  drawing  is  placed  on  it, 
with  the  interposition  of  a  paper  rubbed  over  with  red  chalk,  which,  when 
the  drawing  is  traced  with  a  wooden  point,  adheres  to  the  varnish,  in  the 
form  of  the  outline :  or  if  it  is  required  that  the  ultimate  impression  be 
turned  the  same  way  as  the  drawing,  an  intermediate  outline  must  be 
procured  in  the  same  manner  on  a  separate  paper,  and  then  transferred  to 
the  plate.  All  the  outlines  thus  marked  are  traced  with  needles,  which 
make  as  many  furrows  in  the  varnish,  and  leave  the  copper  bare :  the 
shades  are  inserted  with  the  assistance  of  the  ruling  machine,  wherever 
parallel  lines  can  be  employed.  The  plate  thus  prepared,  and  furnished 
with  an  elevated  border  of  a  proper  consistence,  is  subjected  to  the  action 
of  the  diluted  nitric  acid,  until  all  the  parts  are  sufficiently  corroded,  care 
being  taken  in  the  mean  time  to  sweep  off  the  air  bubbles  as  they  collect, 
and  to  stop  out,  or  cover  with  a  new  varnish,  the  lighter  parts,  which  are 
soonest  completed.  When  the  varnish  is  removed,  the  finishing  touches 
are  added  with  the  graver  :  and  if  the  plate  requires  further  corrosion,  the 
varnish  may  sometimes  be  replaced,  without  filling  up  the  lines,  by  apply- 
ing it  on  a  ball  or  cushion,  taking  care  to  avoid  any  oblique  motion.  It  is 
said  that  the  acid  sometimes  operates  so  as  to  undermine  the  metal  on  each 
side,  and  to  render  the  furrows  wider  as  they  become  deeper,  and  that  for 
this  reason  in  etchings,  as  well  as  in  mezzotintos,  the  latter  impressions 
are  sometimes  darker  than  the  proofs  ;  but  this  is  by  no  means  universally 
true.  It  is  well  known  to  chemists,  that  glass  may  be  corroded  in  a  similar 
manner  by  means  of  the  fluoric  acid. 

An  etching  may  also  be  expeditiously  executed  by  using  a  varnish 
mixed  with  mutton  fat,  and  drawing  upon  a  paper  laid  on  the  plate  ;  the 


MODELLING,  PERSPECTIVE,  ENGRAVING,  PRINTING.      93 

varnish  then  adheres  to  the  hack  of  the  paper,  under  the  lines  which  are 
drawn,  and  is  immediately  removed  when  the  paper  is  taken  off,  without 
the  use  of  needles.  Sometimes  the  outlines  only  are  etched,  and  the  plate 
is  finished  in  mezzotinto. 

In  the  mode  of  engraving  called  aqua  tinta,  the  outline  having  heen  first 
etched,  the  shades  are  also  produced  by  corrosion,  the  parts  being  prepared 
by  various  methods,  so  as  to  be  partially  protected  from  the  action  of  the 
acid.  Sometimes  a  little  resin,  very  finely  powdered,  is  sifted  on  the  plate, 
which  is  then  sufficiently  warmed  to  make  the  particles  adhere  to  it ;  some- 
times it  is  varnished  with  a  spirituous  solution  of  resin,  which  cracks 
throughout  in  drying  :  and  if  a  strong  line  be  any  where  required,  it  may 
be  traced  with  a  mixture  of  whiting  with  some  adhesive  substance,  before 
the  varnish  is  laid  on  ;  this  will  cause  it  to  break  up  at  that  part ;  or  the 
varnish  may  be  partially  removed,  by  rubbing  it  with  spirits  or  with  an 
essential  oil.  The  lighter  parts  may  be  covered,  during  the  corrosion,  with 
a  second  varnish,  which  defends  them  from  the  acid.  This  mode  of  en- 
graving succeeds  very  well  in  imitating  the  effect  of  drawings,  but  the 
plates  are  soon  worn  out.  In  order  to  judge  of  the  state  of  the  work,  an 
impression  of  any  part  of  the  plate  may  be  taken  off,  by  pouring  on  it  a 
little  plaster  of  Paris  mixed  with  water. 

Musical  characters  are  usually  stamped  with  punches  ;  in  this  country, 
on  plates  of  pewter,  but  in  France  generally  on  copper.  Mr.  Rochon  * 
has  invented  a  machine  for  stamping  letters  on  copper,  instead  of  printing, 
but  the  method  does  not  appear  to  have  been  practically  employed. 

In  whatever  way  the  plate  may  have  been  engraved,  when  an  impression 
is  to  be  taken  from  it,  it  is  covered  with  printing  ink  of  the  finest  kind,  by 
means  of  stuffed  balls,  and  then  wiped,  chiefly  with  the  hand,  so  that  the 
ink  is  wholly  removed  from  the  polished  surface :  it  is  then  placed,  with 
the  moistened  paper,  on  a  board,  between  flannels,  and  strongly  pressed 
in  passing  between  two  wooden  rollers.  By  frequent  use  the  plate  loses  its 
sharpness,  and  sometimes  requires  to  be  retouched ;  hence  arises  the 
greater  value  of  first  impressions  ;  but  by  proper  precautions  in  cleaning 
the  plate,  its  delicacy  may  be  preserved  for  a  long  time. 

An  impression,  while  it  is  moist,  may  be  reversed,  by  passing  it  through 
the  press  with  another  paper.  And  by  writing  with  a  peculiar  ink,  even 
common  letters  may  be  thus  copied  on  thin  paper,  and  the  impression  will 
be  legible  on  the  opposite  side.  Mr.  Montbret  proposes  to  put  some  sugar 
candy  into  the  ink,  and  to  take  a  copy  on  unsized  paper  by  means  of  a 
hot  iron.f 

A  simple  and  elegant  method  of  multiplying  drawings  has  been  lately 
introduced  by  Mr,  Andre.  The  drawings  are  made  with  an  unctuous  com- 
position, in  the  form  of  a  crayon  or  of  an  ink,  on  a  soft  stone  of  a  calca- 
rious  nature,  somewhat  like  a  stone  marie.  When  the  drawing  is  finished, 
the  stone  is  moistened,  and  imbibes  so  much  Svater  that  the  [unctuous] 
printing  ink  will  not  adhere  to  it,  except  at  the  parts  where  the  crayon  or 
tne  ink  has  been  applied  [for  neither  will  water  adhere  to  grease  nor  grease 
to  water]  ;  and  in  this  manner  an  impression  is  procured,  which  has  much 
*  Nich.  Jour.  4to,  Ui.  61.  f  Ibid.  8vo,  i.  147. 


94  LECTURE  XI. 

of  the  freedom  and  spirit  of  an  original  drawing.  When  the  ink  is  used, 
a  little  acid  is  afterwards  applied  to  the  stone,  in  order  to  corrode  its  inter- 
mediate parts  ;  and  the  bold  style  of  the  impression  much  resembles  that  of 
the  old  wooden  cuts. 

The  art  of  printing  with  separate  types  was  invented  soon  after  the 
introduction  of  wooden  blocks  into  Europe.*  The  improvement  was  great 
and  important.  The  year  1443,  or  1444,  is  considered  as  the  date  of  the 
oldest  printed  book  ;  but  the  precise  time  and  place  of  the  invention  remain 
somewhat  doubtful:  the  art,  however,  advanced  towards  perfection  by 
very  rapid  steps.  The  letters  are  first  cut,  in  a  reversed  form,  on  steel 
punches  ;  with  these  a  matrix  of  copper  is  stamped,  and  the  matrix  forms 
the  lower  part  of  the  mould  in  which  the  types  are  cast ;  the  metal  is  a 
composition  of  lead  and  antimony,  which  is  easily  fusible.  Thus  the 
printed  sheet  is  the  fourth  form  of  the  letter,  reckoning  from  the  original 
engraving  on  the  punch :  in  the  stereotype  printing,  lately  invented,  or 
rather  improved  and  revived,  it  is  the  sixth.  In  this  method,  when  a  form 
for  the  side  of  a  sheet  has  been  composed,  made  up,  corrected,  and  locked 
up  by  wedges  in  the  chase  or  iron  frame  which  confines  it,  a  mould  of  the 
whole  is  formed  in  fine  plaster,  and  as  many  repetitions  of  it  may  be  cast 
very  thin,  in  type  metal,  as  will  serve  to  print  for  the  use  of  a  century, 
without  the  expense  of  keeping  a  large  quantity  of  types  made  up,  or  of 
providing  paper  for  a  numerous  impression  at  once. 

The  modes  of  arranging  the  types  in  boxes  or  cases,  of  composing  the 
separate  lines  on  the  stick,  and  making  them  up  by  degrees  into  pages  and 
forms,  of  correcting  the  press,  of  applying  the  ink,  and  taking  off  the 
impression,  are  entirely  calculated  for  the  simplicity  and  convenience  of 
the  manual  operations  concerned,  and  require  little  or  no  detailed  expla- 
nation. 


LECT.  XL—ADDITIONAL  AUTHORITIES. 

Sculpture,  Painting,  Sfc. — Behnes's  Machine  for  Sculpture,  Tr.  of  the  Soc.  of 
Arts,  XXXVII.  Jesuit's  Perspective,  4to.  Brook  Taylor's  Linear  Perspective 
1715  and  1811.  Monge  Geometric  Descriptive,  4to,  Paris.  Edwards's  Perspec- 
tive, 4to,  1803.  Creswell's  Perspective,  Camb.  1812.  Courtonne,  Deidier,  Laine, 
Ozanam,  Faucaud,  Lavit,  Traites  de  Perspective.  Laurent,  Theorie  de  la  Peinture, 
1827.  Montabert,  Dessein  Lineaire  enseigne  aux  Ouvriers,  1831.  Bardwell, 
1834.  Rider,  1836.  Hall,  Practical  Geometry,  &c.  1841.  A  brief  Elementary 
Treatise  on  Projections  is  given  in  the  Appendix  to  Maddy's  Astronomy,  Camb. 
1826. 

Engraving. — Evelyn's  Art  of  Engraving,  1662.  Papillon,  Traite  Historique  de 
laGravure  en  Bois,  1766.  Lowry's  Ruling  Machine,  Nich.  Jour.  ii.  523.  Accum 
on  Etching  on  Glass,  ibid.  iv.  1.  Bartsch  Peintre  Graveur,  21  vols.  Vienna, 
1808.  Ottley's  Hist,  of  Engraving,  2  vols.  4to,  1816.  Hullmandel's  Manuel  of 
Lithography,  1820.  Englemann,  Manuel  du  Dessinateur  Lithographique,  Par.  1824. 
Bregault,  do.  1827. 

The  inventor  of  Lithography  was  Alois  Senefelder,  of  Munich.  Andre  was  asso- 
ciated with  Senefelder,  but  has  no  claim  to  the  invention.  A  patent  for  fifteen  years 
was  granted  to  Senefelder  in  1799.  The  art  has  now  arrived  at  a  high  state  of  per- 
fection. 

*  Consult  Hansard's  Typographia,  1825. 


95 


LECTURE   XII, 


ON  STATICS. 

THE  examination  of  the  magnitude  of  the  various  forces  employed  in 
practical  mechanics,  constitutes  the  doctrine  of  statics.  The  term  statics, 
in  a  strict  sense,  implies  the  determination  of  weights  only;  hut  it  may 
without  impropriety  be  extended  to  the  estimation  of  forces  of  all  kinds, 
especially  active  forces,  that  can  be  compared  with  weights,  in  the  same 
manner  as  the  term  hydrostatics  comprehends  every  thing  that  relates  to 
the  equilibrium  of  fluids.  The  measurement  of  the  passive  strength  of  the 
materials  employed,  the  changes  produced  in  them  by  the  forces  which  they 
resist,  and  the  laws  of  the  negative  force  of  friction,  are  also  subjects  imme- 
diately introductory  to  the  particular  constructions  and  uses  of  machinery, 
and  nearly  connected  with  the  department  of  statics. 

The  art  of  weighing  is  peculiarly  important,  as  it  furnishes  us  with  the 
only  practical  mode  of  determining  the  quantity  of  matter  in  a  given  body. 
We  might  indeed  cause  two  bodies  to  meet  each  other  with  known  veloci- 
ties, and  from  the  effects  of  their  collision  we  might  determine  their  com- 
parative momenta,  and  the  proportion  of  their  masses  ;  but  it  is  obvious 
that  this  process  would  be  exceedingly  troublesome,  and  incapable  of  great 
accuracy ;  we  therefore  recur  to  the  well  known  law  of  gravitation,  that 
the  weight  of  every  body  is  proportional  to  the  quantity  of  matter  that  it 
contains,  and  we  judge  of  its  mass  from  its  weight.  If  all  bodies  were  of 
equal  density,  we  might  determine  their  masses  from  their  external  dimen- 
sions ;  but  we  seldom  find  even  a  single  body  which  is  of  uniform  density 
throughout ;  and  even  if  we  had  such  a  body,  it  would  in  general  be  much 
easier  to  weigh  it  correctly  than  to  measure  it. 

The  weight  of  a  body  is  commonly  ascertained,  by  comparing  it  imme- 
diately with  other  weights  of  known  dimensions  ;  but  sometimes  the 
flexure  of  a  spring  is  employed  for  the  comparison.  Standard  weights 
have  generally  been  deduced  from  a  certain  measure  of  a  known  substance, 
and  in  particular  of  water.  According  to  the  most  accurate  experiments, 
when  the  barometer  is  at  30  inches,  and  Fahrenheit's  thermometer  at  62°, 
12  wine  gallons  of  distilled  water  weigh  exactly  100  pounds  avoirdupois, 
each  containing  7000  grains  troy  ;  and  a  cubic  inch  weighs  252  £  grains. 
A  hogshead  of  water,  wine  measure,  weighs,  therefore,  525  pounds,  and  a 
tun  2100  pounds,  which  is  nearly  equal  to  a  ton  weight.  Mr.  Barlow  * 
supposes  that  the  tun  measure  of  water  contained  originally  32  cubic  feet, 
and  weighed  2000  pounds,  which  was  also  called  a  ton  weight,  the  gallon 
being  somewhat  smaller  than  it  is  at  present,  and  the  cubic  foot  weighing 
exactly  1000  ounces,  or  62£  pounds.  A  quarter'  of  wheat  weighed  about 
a  quarter  of  a  ton,  and  a  bushel  as  much  as  a  cubic  foot  of  water.  A 
chaldron  of  coals  was  also  considered  as  equivalent  to  a  ton,  although  it 

*  On  the  analogy  between  English  weights  and  measures  of  capacity,  Ph.  Tr. 
1740,  p.  457. 


96  LECTURE  XII. 

now  weighs  nearly  half  as  much  more.  But  at  the  mean  temperature  of  this 
climate,  or  52°,  a  cubic  foot  of  distilled  water  weighs  only  998  ounces. 
The  avoirdupois  ounce  appears  to  agree  very  nearly  with  the  ancient  Roman 
ounce.  Of  the  old  French  weight,  100  pounds  made  108  English  pounds 
avoirdupois.  The  gramme  of  the  new  weights  is  a  cubic  centimetre  of 
pure  water  at  its  greatest  density,  that  is  about  the  temperature  of  39°  of 
Fahrenheit ;  it  is  equal  to  15£  English  grains  :  hence  the  chiliogramme  is 
2£  pounds,  and  five  myriogrammes  are  nearly  a  hundred  weight.  Five 
grammes  of  silver,  including  one  tenth  of  alloy,  make  a  franc,  which  is  one 
eightieth  better  than  the  old  franc  or  livre,  and  is  intrinsically  worth  nearly 
ninepence  three  farthings  English. 

The  instruments  usually  employed  for  the  comparison  of  weights  are 
either  balances  or  steelyards.  In  the  common  balance,  the  weights  of  the 
substances  compared  are  equal ;  in  a  compound  weighing  machine,  we  use 
weights  which  are  smaller,  in  a  certain  proportion,  than  those  which  they 
represent:  in  the  steelyard,  a  single  weight  acquires  different  values  at 
different  parts  of  the  arm,  and  in  the  bent  lever  balance  the  position  of 
the  arms  determines  the  magnitude  of  the  counterpoise.  The  spring  steel- 
yard measures  the  weight,  by  the  degree  of  flexure  that  it  produces  in  a 
spring. 

The  beam  of  a  common  balance  must  have  its  arms  precisely  equal. 
The  scales,  being  freely  suspended  from  fixed  points  in  the  beam,  act  on 
them  always  in  the  direction  of  gravity ;  and  the  effect  is  the  same  as 
if  the  whole  weight  were  concentrated  in  those  points.  The  beam  sup- 
ports the  scales,  and  is  itself  supported  by  means  of  fine  edges  of  hard 
steel,  working  on  steel,  agate,  or  garnet,  in  order  that  the  motion  may  be 
free,  and  the  distances  of  the  points  precisely  defined.  The  best  beams  are 
made  of  two  hollow  cones  of  brass,  united  at  their  bases  ;  they  are  lifted 
off  their  supports  when  the  balance  is  not  used,  in  order  to  avoid  accidental 
injuries  ;  the  scales  also  are  supported,  so  as  not  to  hang  from  the  beam, 
until  they  have  received  their  weights.  According  to  the  position  of  the 
fulcrum,  with  respect  to  the  points  of  suspension  of  the  scales,  the  equili- 
brium of  the  balance  may  be  either  stable,  neutral,  or  tottering  ;  or  if  the 
beam  be  too  flexible,  it  may  pass  from  one  of  these  states  to  the  other  by 
the  effect  of  the  weights.  The  stable  equilibrium  is  the  most  usual  and  the 
best,  because  it  gives  us  an  opportunity  of  determining  the  degree  of  in- 
equality of  the  weights,  by  the  position  in  which  the  centre  of  gravity 
rests,  or  by  the  middle  point  of  the  vibrations  of  the  beam,  which  are 
sometimes  measured  by  an  index  pointing  to  a  graduated  arc.  If,  how- 
ever, the  fulcrum  be  too  much  elevated  above  the  centre  of  gravity,  the  equi- 
librium may  be  too  stable,  and  may  require  too  great  an  inequality  in  order 
to  produce  a  sensible  preponderance.  If,  on  the  contrary,  by  the  elevation 
of  the  points  of  suspension  of  the  scales,  the  equilibrium  be  rendered  tot- 
tering the  lower  scale  will  not  rise,  even  if  it  be  somewhat  less  loaded  than 
the  upper ;  and  steelyards  of  this  construction  have  sometimes  been  em- 
ployed, in  order  to  impose  on  the  purchaser  by  the  appearance  of  an  ample 
weight.  It  is  necessary,  where  great  accuracy  is  desired,  to  bring  the 
equilibrium  very  near  the  state  of  neutrality,  and  to  make  the  vibrations 


ON  STATICS.  ^97 

of  the  beam  slow  and  extensive,  whether  the  scales  have  weights  in  them 
or  not :  for  this  purpose  a  small  weight  is  sometimes  inclosed  within  the 
beam,  which  is  raised  or  depressed  at  pleasure  by  a  screw,  so  as  to  bring 
the  centre  of  gravity  of  the  whole  moveable  apparatus  as  near  to  the  ful- 
crum as  may  be  required  for  the  occasion.  Mr.  Ramsden's  balance,  made 
for  the  Royal  Society,  is  capable  of  weighing  ten  pounds,  and  turns  with 
one  ten  millionth  part  of  the  weight.*  (Plate  VIII.  Fig.  107... 109.) 

The  arms  of  a  balance  have  sometimes  been  made  unequal  for  fraudulent 
purposes,  the  weight  being  placed  nearer  to  the  fulcrum  than  the  substance 
to  be  weighed.  It  is  obvious  that  the  fraud  may  be  detected,  by  changing 
the  places  of  the  contents  of  the  two  scales.  In  such  a  case,  if  a  counter- 
poise to  the  same  weight  be  determined  in  each  situation,  the  sum  of  both 
will  be  greater  than  twice  the  weight ;  and  the  purchaser  would  be  sure  of 
having  even  more  than  his  due,  by  requesting  the  seller  to  weigh  half  in 
the  one  scale  and  half  in  the  other.  For  example,  if  one  arm  of  the  beam 
were  only  three  fourths  as  long  as  the  other,  the  counterpoise  to  a  weight 
of  twelve  ounces  would  be  nine  ounces  in  one  scale,  and  sixteen  in  the 
other,  making  together  twenty  five  instead  of  twenty  four  ounces,  (Plate 
VIII.  Fig.  110.) 

Supposing  the  beams  of  a  balance  to  be  accidentally  unequal,  either  in 
length  or  in  weight,  we  may  still  weigh  in  it  with  accuracy,  by  making  a 
perfect  counterpoise  of  any  kind  to  a  weight,  and  then  removing  the 
weight  and  putting  in  its  place  as  much  of  the  substance  to  be  weighed  as 
is  sufficient  to  restore  the  equilibrium. 

The  weights  may  also  be  reduced,  or  increased,  in  proportion  to  the 
length  of  the  arms,  if  they  differ  from  each  other,  care  being  taken  to  put 
the  weights  always  into  the  same  scale.  This  is  actually  performed  in 
weighing  machines,  where  a  composition  of  levers  is  employed,  in  order  to 
enable  us  to  determine  the  weight  of  large  masses  by  means  of  weights  of 
moderate  dimensions.  (Plate  IX.  Fig.  111.) 

When  the  effective  lengths  of  one  or  both  arms  of  the  beam  are  capable 
of  being  varied  by  changing  the  points  of  suspension  according  to  the 
divisions  of  a  scale,  the  instrument  is  called  a  steelyard.  Where  one 
weight  only  is  used,  it  is  not  necessary  that  the  two  arms  should  exactly 
balance  each  other,  since  the  divisions  may  be  so  placed  as  to  make  the 
necessary  adjustment ;  but  it  is  sometimes  convenient  to  have  two  or  three 
weights  of  different  magnitudes,  and  for  this  purpose  the  instrument 
should  be  in  equilibrium  without  any  weight.  In  such  cases,  great  accu- 
racy may  be  obtained  by  applying  a  small  weight  at  the  end,  in  the  form 
of  a  micrometer  screw.  (Plate  IX.  Fig.  112.) 

The  arms  of  a  balance,  though  constant  in  length,  may  vary  in  effect 
without  limit,  if  they  can  sufficiently  alter  their  inclination  to  the  horizon ; 
for  no  weight,  however  great,  acting  on  the  arm  of  a  bent  lever,  can  make 
it  perfectly  vertical,  since,  in  this  position,   the  weight  may  be   over- 
powered by  the  minutest  counterpoise  acting  on  the  other  arm.     The  centre 
of1  gravity  being,  in  the  common  balance,  very  nearly  in  a  right  line 
between  the  weights,  in    order   that   it  may  be   immediately  below  the 
*  Rozier's  Journal,  xxxiii.  144. 
H 


98  LECTURE  XII. 

fulcrum,  the  arm  must  have  a  very  considerable  angular  motion  for  a 
slight  inequality  of  the  weights ;  but  in  the  bent  lever  balance,  the  centre 
of  gravity  is  at  such  a  distance  from  the  fulcrum,  that  a  moderate  motion 
of  the  arms  may  bring  it  into  the  vertical  line.  This  motion  is  measured 
by  an  index  on  a  graduated  arc,  which  gives  the  instrument  a  considerable 
range  ;  and  where  expedition  is  particularly  desired,  it  may  often  be  used 
with  advantage ;  but  if  the  weights  to  be  determined  are  large,  the  scale 
becomes  very  much  contracted,  and  the  instrument  requires  to  be  levelled 
with  great  accuracy.  A  counterpoise  acting  on  a  spiral  or  conical  barrel 
has  also  been  applied  to  a  similar  purpose  ;  it  is  capable  of  a  scale  some- 
what more  extended  than  a  bent  lever  balance,  but  it  is  less  simple,  and 
scarcely  more  accurate.  (Plate  IX.  Fig.  113.) 

A  spring,  which  is  usually  of  a  spiral  form,  being  made  to  support  a 
hook  by  the  intervention  of  a  graduated  bar,  the  divisions  of  this  bar, 
which  are  drawn  out  beyond  the  fixed  point,  indicate  the  weight  sup- 
ported by  the  hook.  This  instrument  is  called  a  spring  steelyard.  Mr. 
Hanin's  *  spring  steelyard  has  a  long  index,  which  revolves  on  a  centre, 
and  shows  at  once  the  weight  according  to  the  standards  of  different  coun- 
tries. The  divisions  of  the  scales  in  moderate  flexures  of  the  spring  are 
nearly  equal :  hence  it  may  be  inferred,  that  the  space  through  which  a 
spring  is  bent,  and  consequently  its  curvature  or  change  of  curvature,  is 
simply  proportional  to  the  force  which  acts  on  it,  and  that  the  vibrations  of 
a  weight  supported  by  a  spring,  must,  like  those  of  a  cycloidal  pendulum, 
be  performed  in  equal  times,  whatever  may  be  their  magnitude.  The 
strength  of  all  springs  is  somewhat  diminished  by  heat,  and  for  each  degree 
of  Fahrenheit  that  the  temperature  is  raised,  we  must  deduct  about  one 
part  in  five  thousand  from  the  apparent  weight  indicated  by  the  spring 
steelyard.  (Plate  IX.  Fig.  114.) 

The  spring  steelyard  affords  us  the  most  convenient  method  of  measur- 
ing the  immediate  intensity  of  the  forces  exerted  by  animals  of  different 
kinds,  in  the  labour  which  they  perform.  When  it  is  adapted  for  this 
purpose,  it  is  sometimes  called  the  dynamometer.  We  may  also  estimate 
the  force  of  an  animal  which  is  employed  in  drawing  a  distant  boat  or  car- 
riage, by  the  inclination  of  the  rope  or  chain  to  the  horizon,  compared 
with  the  weight  of  that  portion  of  it  which  the  animal  supports,  that  is,  of 
the  part  which  extends  to  the  point  where  the  curve  becomes  horizontal.*!* 

All  animal  actions,  or,  at  least,  all  the  external  actions  of  animals,  are 
ultimately  dependent  on  the  contractions  and  relaxations  of  the  fleshy 
parts,  which  are  called  muscles.  The  operation  of  the  particular  muscles 
belongs  properly  to  the  science  of  physiology  ;  but  their  mechanism  may 
in  general  be  understood  from  the  properties  of  the  lever  and  of  the 
^  centre  of  gravity.  The  bones  are  the  levers,  the  joints  the  fulcrums,  and 
the  force  is  applied  by  the  muscles,  which  are  usually  attached  to  the  bones 
by  the  intervention  of  tendinous  cords.  When  a  muscle  contracts  in  the 
direction  of  its  fibres,  it  becomes  at  the  same  time  thicker,  and  its  total  bulk 

*  Hist.  etMem.  de  Paris,  1765,  H.  135. 

•f  Consult  Morin,  Description  des  Appareils  Chronometriques,  et  des  Ap.  Dyna- 
mometriques.  Metz,  1838. 


ON  STATICS.  99 

is  little  if  at  all  diminished  :  when  it  relaxes  itself,  it  is  merely  passive,  for 
the  fibres,  being  extremely  flexible,  can  have  little  or  no  efl&ct  in  separating 
the  parts  to  which  they  are  attached  ;  this  separation  is  generally  performed 
by  the  action  of  other  muscles  which  are  called  the  antagonists  of  the  first, 
but  sometimes  by  elastic  ligaments,  or  by  other  means.  The  bone  forms  a 
lever  of  the  second  kind,  where  the  two  forces  opposing  each  other  are  on 
the  same  side  of  the  fulcrum.  In  general  the  insertion  of  a  muscle  is  much 
nearer  to  the  fulcrum  than  the  point  of  action,  and  the  obliquity  of  its 
direction  gives  it  a  still  greater  mechanical  disadvantage  with  regard  to 
rotatory  power  ;  but  it  is  more  convenient  in  the  animal  economy  to  pro- 
duce a  great  contractile  force  than  a  great  extent  in  the  original  motion. 
For  instance,  when  the  arm  is  raised  by  the  exertion  of  the  deltoid  muscle 
of  the  shoulder,  a  very  strong  contraction  takes  place  in  the  muscle,  but 
the  action  is  only  continued  through  a  short  space ;  had  the  contractile 
power  been  weaker  and  more  extensive,  the  shoulder  must  have  been  made 
higher,  in  order  to  give  it  sufficient  purchase,  and  the  projection  would 
have  been  inconvenient. 

Borelli*  has  calculated  that  the  immediate  force  of  the  biceps,  or  double- 
headed  muscle  which  bends  the  arm,  is  equivalent  to  about  300  pounds,  and 
that  of  the  muscles  which  raise  the  lower  jaw,  above  500  in  man,  but  in 
beasts  of  prey  far  greater.  It  is  obvious  that  in  muscles  of  the  same  kind 
the  strength  must  be  as  the  number  of  fibres,  or  as  the  extent  of  the  surface 
which  would  be  formed  by  cutting  the  muscle  across ;  and  it  is  not  im- 
probable that  the  contractile  force  of  the  muscles  of  a  healthy  man  is 
equivalent  to  about  500  pounds  for  each  square  inch  of  their  section.  The 
weakest  man  can  lift  with  his  hands  about  125  pounds,  a  strong  man  400. 
Topham,  a  carpenter,  mentioned  by  Desaguliers,  could  lift  800  pounds. 
He  rolled  up  a  strong  pewter  dish  with  his  fingers  ;  he  lifted  with  his  teeth 
and  knees  a  table  six  feet  long,  with  a  half  hundred  weight  at  the  end. 
He  bent  a  poker,  three  inches  in  circumference,  to  a  right  angle,  by  striking 
it  upon  his  left  fore  arm  ;  another  he  bent  and  unbent  about  his  neck  ;  and 
snapped  a  hempen  rope  two  inches  in  circumference.  A  few  years  ago 
there  was  a  person  at  Oxford  who  could  hold  his  arm  extended  for  half  a 
minute,  with  half  a  hundred  weight  hanging  on  his  little  finger.  A  young 
gentleman,  who  has  distinguished  himself  as  a  pedestrian  by  going  90  miles 
in  19  hours,  has  also  lifted  two  hundred  weights,  one  in  each  hand,  and 
made  them  meet  over  his  head. 

Sometimes  feats  of  strength  apparently  extraordinary  have  been  ex- 
hibited by  men  who  have  not  really  been  possessed  of  any  material  supe- 
riority. Desagulierst  relates,  that  one  of  them  used  to  withstand  the  force 
of  two  horses  drawing  at  a  girdle  passed  round  his  middle,  while  his  feet 
acted  on  a  firm  obstacle.  By  falling  suddenly  backwards,  in  an  oblique 
position,  he  broke  a  rope  which  was  fixed  a  little  before  his  feet.  He 
supported  one  or  two  men  by  forming  his  body  into  an  arch  ;  and  by  a 
harness  fitted  to  his  hips,  he  sustained  a  cannon  weighing  two  or  three 

*  De  Motu  Animalium,  4to,  Lugd.  Batav.  1710,  p.  30  et  seq. 
f  Course  of  Experimental  Philosophy,  2  vols.  8vo,  Lond.  1763,  i.  266,  &c. 

H2 


100  LECTURE  XII. 

thousand  pounds.  In  all  these  cases  the  muscles  principally  employed  are 
the  extensors  of  ^he  legs  and  thighs,  hut  the  passive  strength  of  the  hones  is 
more  concerned  than  the  active  force  of  the  muscles.  In  the  instance, 
mentioned  by  Lahire,*  of  a  young  man  who  raised  an  ass  from  the  ground 
by  cords  tied  to  the  hair  of  his  head,  the  sensibility  of  the  nerves  of  the 
skin  must  have  been  diminished  by  habit,  so  as  to  allow  the  hair  to  be  thus 
forcibly  extended  without  immoderate  pain. 

The  application  of  animal  force  is  usually  performed  by  means  of  a 
progressive  motion.  The  muscles  employed  in  this  process  are  in  general, 
if  not  always,  the  strongest  of  the  body,  both  by  nature  and  by  habit ;  so 
that  when  force  alone  is  required,  it  is  most  advantageously  obtained  from 
their  exertions.  In  walking,  the  centre  of  gravity  is  moved  forwards  with 
a  velocity  nearly  uniform.  If  the  legs  were  perfectly  inflexible,  the  centre 
of  gravity  would  describe,  in  succession,  portions  of  circles,  of  which  each 
leg  would  alternately  be  the  radius  :  but  if  the  velocity  were  great  enough 
to  create  a  centrifugal  force  more  than  equivalent  to  the  force  of  gravity, 
the  pressure  would  be  removed  from  each  leg  after  the  first  instant  of  its 
touching  the  ground  ;  the  path  would  become  parabolic  instead  of  circular, 
and  the  walking  would  be  converted  into  running :  for  the  difference  be- 
tween walking  and  running  is  this,  that  in  running,  one  foot  is  removed 
from  the  ground  before  the  other  touches  it ;  while  in  walking,  the  hind- 
most foot  is  only  raised  after  the  foremost  has  touched  the  ground.  Now 
supposing  the  length  of  the  inflexible  leg  three  feet,  the  centrifugal  force 
would  become  equal  to  the  weight,  with  a  velocity  which  would  be  acquired 
by  a  heavy  body  in  falling  through  a  foot  and  a  half,  that  is,  near  10  feet 
in  a  second,  or  7  miles  an  hour ;  and  this  is  the  utmost  velocity  with 
which  it  would  be  mechanically  possible  to  walk  with  inflexible  legs.  But 
the  flexibility  of  the  legs  makes  the  progressive  motion  much  more  uni- 
form, by  softening  the  angles  of  the  path  which  the  centre  of  gravity 
describes,  and  rendering  it  either  more  or  less  curved  at  pleasure  ;  so  that 
it  becomes  mechanically  if  not  physically  possible,  to  walk  with  a  velocity 
somewhat  greater  than  7  miles  an  hour,  and  to  run  or  dance  with  as  small 
a  velocity  as  we  please,  since  we  may  make  the  path  of  the  centre  of  gravity 
somewhat  less,  or  much  more  curved,  than  a  circle  described  on  the  point 
of  the  foot  as  a  centre.  (Plate  IX.  Fig.  115,  116.) 

The  flexions  and  extensions  of  the  legs  are  also  almost  the  only  means 
by  which  an  impulse  is  given  to  the  body ;  if  the  legs  were  perfectly 
inflexible,  it  would  be  extremely  difficult,  although  not  absolutely  impos- 
sible, to  obtain  a  progressive  motion.  The  centre  of  gravity  is  principally 
impelled  forwards  in  the  beginning  of  the  ascending  part  of  the  curve 
which  it  describes  in  walking,  by  the  action  of  the  leg  which  is  left  behind, 
but  in  running  or  hopping,  by  that  of  the  only  foot  which  touches  the 
ground  at  any  one  time.  When  we  thrust  against  any  obstacle,  or  draw  a 
rope  in  a  horizontal  or  in  a  descending  direction,  the  body  is  inclined 
forwards,  and  in  some  cases  its  action  is  limited  by  the  effect  of  the  weight 
of  the  body  reduced  to  the  direction  of  the  line  of  draught :  but  we  much 

*  Hist,  et  Mem.  de  1'Acad.  1699,  p.  153,  H.  96. 


ON  STATICS.  101 

more  usually  draw  or  pull  in  an  ascending  direction,  so  that  our  whole 
muscular  force  may  be  exerted  without  any  limit  of  this  kind.* 

It  happens,  however,  very  frequently,  that  we  have  occasion  for  motions 
of  such  a  nature  as  to  be  more  conveniently  performed  by  the  hands  and 
arms  than  by  the  action  of  walking  or  running  ;  and  where  delicacy  is 
required  rather  than  strength,  the  form  of  the  hand  and  fingers  gives  the 
human  species  a  great  superiority  over  all  other  animals,  although  by  no 
means,  as  some  authors  have  supposed,  an  advantage  equivalent  to  that  of 
the  higher  perfection  of  the  intellectual  powers.  It  is  true,  as  we  may 
observe  in  the  manufactories  of  this  country,  that  machinery  has  been 
invented  by  which  a  power  of  any  kind  may  be  converted  to  purposes 
seemingly  the  most  intricate  and  refined  ;  and  after  all  that  has  been  done 
by  a  Watt  and  an  Arkwright,  it  is  difficult  to  determine  a  positive  limit  to 
the  ingenuity  of  mechanical  invention. 

It  is  necessary  to  consider,  in  examining  the  different  sources  of  motion, 
not  only  the  immediate  magnitude  of  the  forces  which  they  produce,  but 
also  the  velocity  with  which  they  are  capable  of  acting,  and  the  time  for 
which  that  action  can  be  continued.  The  daily  work  of  a  labouring  man, 
of  middle  age,  and  in  good  health,  will  serve  as  a  convenient  unit  for  the 
comparison  of  moving  powers  of  all  kinds.  It  may  be  most  easily  remem- 
bered in  this  form  :  a  man  can  raise  a  weight  of  10  pounds  to  the  height  of 
10  feet  in  a  second,  and  can  continue  this  labour  for  10  hours  a  day.  The 
actual  velocity  of  the  man's  motion  must  vary  according  to  the  mode  in 
which  his  force  is  applied  ;  but  we  suppose  that  velocity  to  be  such  as  to 
give  the  greatest  effect  under  the  circumstances  of  the  machine.  This  is  a 
moderate  estimate  of  the  work  of  a  labourer,  without  any  deduction  for 
friction.  Desagulierst  states  the  performance  of  a  man  working  at  a 
winch,  with  the  assistance  of  a  fly,  as  considerably  greater,  but  he  does  not 
allege  any  correct  experiments  in  support  of  his  estimate.  Professor 
Robison,  however,  mentions  a  hydraulic  machine  in  which  the  effect  was 
actually  more  than  one  tenth  greater,  without  making  any  allowance  for 
friction  ;  so  that  it  is  probable,  considering  the  loss  both  from  friction  and 
from  the  momentum  with  which  the  water  must  have  been  disengaged, 
that  the  immediate  performance  was  at  least  one  third  more  than  this 
unit :  the  machine  was  worked  by  a  light  man  carrying  a  weight,  and 
walking  backwards  and  forwards  on  a  lever.  According  to  Mr.  Bucha- 
nan's J  experiments,  an  action  like  that  of  ringing  bells  produced  an  effect 
about  one  third  greater  than  turning  a  winch,  and  the  action  of  rowing,  an 
effect  four  ninths  greater ;  but  it  does  not  appear  that  these  experiments 
were  continued  for  a  whole  day  ;  and  the  greatest  number  of  observations 
make  the  daily  performance  of  workmen  considerably  less.  It  is  indeed 
seldom  that  the  muscles  employed  in  progressive  motion  are  so  much 
exerted  as  in  the  arrangement  described  by  Professor  Robison.  A  Chinese, 
in  the  operation  called  sculling,  is  said  to  beat  a  European  at  his  oar. 
•For  a  short  time  a  much  greater  effect  than  this  may  be  produced  by  a 

*  See  Mairan  on  the  position  of  the  legs  in  walking,  Hist,  et  Mem.  de  Par.  1721, 
t  Desaguliers,  vol.  i.  pp.  254,  255.  J  Repertory  of  Arts,  xv.  319. 


102  LECTURE  XII. 

great  exertion  :*  thus  a  man  weighing  above  160  pounds  can  ascend  by 
means  of  steps  at  the  rate  of  more  than  three  feet  in  a  second,  for  a  quarter, 
or  perhaps  half  a  minute  ;  and  this  is  an  effort  five  times  as  great  as  that 
which  can  be  continued  for  a  day.  Usually,  however,  where  the  hands  are 
chiefly  employed,  whether  in  turning  a  winch,  or  in  pumping,  it  is  only 
possible  to  exert  a  double,  or  at  most  a  triple  action,  for  a  minute  or  two  : 
thus,  although  a  machine  may  only  enable  a  man  to  raise  a  hogshead  of 
water  in  a  minute  to  the  height  of  ten  feet  for  a  whole  day,  yet  it  is  easy 
to  work  it  so  rapidly  for  a  single  minute  as  to  raise  double  the  quantity,  or 
to  raise  a  single  hogshead  to  a  height  of  twenty  feet.  The  whole  exertion 
of  force  must  be  a  little  greater  than  that  which  is  thus  estimated,  because 
a  certain  degree  of  superfluous  momentum  must  be  generated  in  removing 
weights  from  one  situation  to  another  :  but  this  loss  is  usually  incon- 
siderable. 

The  action  of  carrying  a  load  horizontally  requires  an  exertion  of  a 
different  kind,  and  admits  of  no  direct  comparison  with  the  application  of 
a  constant  force  to  overcome  the  gravitation  of  a  weight,  or  any  other 
immediate  resistance.  The  work  of  a  labourer  thus  employed  is  however 
confined  within  moderate  limits.  A  strong  porter  can  carry  200  pounds  at 
the  rate  of  three  miles  an  hour  ;  and,  for  a  short  distance,  even  300  pounds  : 
a  chairman  carries  150  pounds,  and  walks  four  miles  an  hour  :  and  in 
Turkey  it  is  said  that  there  are  porters,  who,  by  stooping  forwards,  and 
placing  the  weight  very  low  on  their  backs,  are  enabled  to  carry  from  700 
to  900  pounds.  The  subjects  of  Mr.  Coulomb's t  experiments  appear  to 
have  been  either  weaker  or  more  inactive  than  the  generality  of  porters  in 
this  country:  he  calculates  that  the  most  advantageous  load  for  a  man  of 
common  strength  is  about  a  hundred  weight ;  or,  if  he  is  to  return  without 
a  burden,  135  pounds. 

The  daily  work  of  a  horse  is  equal  to  that  of  five  or  six  men  :  its  imme- 
diate force  is  something  greater,  but  it  cannot  support  the  labour  of  more 
than  8  hours  a  day,  when  drawing  with  a  force  of  200  pounds,  or  of  6 
hours  when  with  a  force  of  240,  walking  two  miles  and  a  half  an  hour.  It 
is  generally  supposed  that  in  drawing  up  a  steep  ascent  a  horse  is  only 
equivalent  to  3  or  4  men,  and  the  employment  of  horses  in  walking  wheels, 
where  the  action  is  similar  to  that  of  ascending  a  hill,  has  for  this  reason  been 
condemned.  For  men,  on  the  contrary,  an  ascent  of  any  kind  appears  to 
afford  a  favourable  mode  of  exertion.  But,  perhaps,  the  weight  of  the 
carriage,  and  of  the  horse  itself,  has  not  always  been  sufficiently  considered 
in  the  comparison.  The  strength  of  a  mule  is  equal  to  that  of  three  or  four 
men.  The  expense  of  keeping  a  horse  is  in  general  about  twice  or  three 
times  as  great  as  the  hire  of  a  day  labourer ;  so  that  the  force  of  horses 
may  be  reckoned  about  half  as  expensive  as  that  of  men.  The  horse 
Childers  is  said,  although,  perhaps,  without  sufficient  authority,  to  have 
run  an  English  mile  in  a  single  minute ;  his  velocity  must  in  this  case 
have  been  88  feet  in  a  second,  which  would  have  been  sufficient  to  carry 

*  See  Amontons,  Hist,  et  Mem.  de  1'Acad.  1703. 

t  On  the  Daily  Labour  of  Men,  Nich.  Jour.  iii.  416. 


I 
ON  STATICS.  i03 

him  on  an  inclined  plane  without  friction,  or  in  a  very  long  sling,  to  the 
perpendicular  height  of  120  feet.* 

A  large  windmill,  on  which  Mr.  Coulombt  made  many  experiments,  was 
capable,  on  an  average,  of  working  eight  hours  a  day ;  its  whole  perform- 
ance was  equivalent  to  our  estimate  of  the  daily  labour  of  34  men ;  25 
square  feet  of  the  sails  doing  the  work  of  one  labourer.  The  expense  of 
the  machinery,  with  its  repairs,  would  probably  amount  to  less  than  half 
the  expense  of  a  number  of  horses  capable  of  exerting  the  same  force. 
Where  a  stream  of  water  can  be  procured,  its  force  is  generally  more  con- 
venient, because  more  regular,  than  that  of  the  wind. 

A  steam  engine  of  the  best  construction,  with  a  thirty  inch  cylinder  has 
the  force  of  forty  horses  ;  and,  since  it  acts  without  intermission,  will  per- 
form the  work  of  120  horses,  or  of  600  men,  each  square  inch  of  the 
piston  being  nearly  equivalent  to  a  labourer.  According  to  Mr.  Boulton, 
the  consumption  of  a  bushel,  or  84  pounds  of  coals,  will  raise  48,000  cubic 
feet  of  water  10  feet  high,  which  is  equivalent  to  the  daily  labour  of  8^ 
men,  or  perhaps  more  :  the  value  of  this  quantity  of  coals  is  seldom  more 
than  that  of  the  work  of  a  single  labourer  for  a  day ;  but  the  expense  of 
the  machinery  generally  renders  a  steam  engine  somewhat  more  than  half 
as  expensive  as  the  number  of  horses  for  which  it  is  substituted.  Accord- 
ing to  other  accounts,  a  24  inch  cylinder,  being  equivalent  to  about  72 
horses,  requires  only  a  chaldron  of  coals  in  a  day,  each  bushel  doing  the 
work  of  ten  men. 

The  force  of  gunpowder  is  employed  with  advantage  where  a  very 
powerful  action  is  required  for  a  short  space,  as  in  dividing  rocks,  or  in 
generating  a  great  velocity  in  a  projectile.  As  a  source  of  momentum  or 
energy  only,  this  power  is  by  no  means  economical,  the  daily  labour  of  a 
man  being  equivalent  to  the  effect  of  about  40  pounds  of  powder ;  but  the 
advantage  of  artillery  consists  in  having  the  force  communicated  by  means 
of  an  elastic  fluid  extremely  rare,  which  is  capable  of  generating  a  very 
great  velocity  in  the  ball  only,  without  any  waste  of  power  in  producing  a 
useless  momentum  in  any  other  substance. 

The  comparative  force  of  different  kinds  of  gunpowder  is  determined  by 
an  eprouvette  or  powder  proof;  the  effect  is  measured  by  the  angular 
motion  of  a  little  wheel,  a  projecting  part  of  which  is  impelled  by  the 
explosion  of  a  small  quantity  of  the  powder,  while  the  friction  of  a  spring 
or  a  weight  creates  a  resistance  which  may  be  varied  if  it  be  required.  The 
absolute  force  of  a  given  quantity  of  powder  may  be  ascertained  either  by 
suspending  a  cannon  as  a  pendulum,  and  measuring  its  angular  recoil ;  or 
by  shooting  into  a  large  block,  and  finding  the  velocity  which  is  imparted 
to  it  by  the  ball.^ 

For  measuring  very  small  attractive  or  repulsive  forces,  with  great  accu- 

*  Messrs.  Boulton  and  Watt  caused  experiments  to  be  made  with  the  strong 
horses  used  in  the  breweries  in  London,  and  from  the  result  of  their  trials,  they 
assigned  33,0001bs.  raised  one  foot  per  minute,  as  the  value  of  a  horse's  power.  This 
is  the  unit  of  engine  power  now  universally  adopted. — Lardner  on  the  Steam  Engine, 
1840,  p.  288. 

f  Hist,  et  Mem.  1781,  p.  65.     Theorie  des  Machines  Simples,  4to,  1821. 

j  See  the  latter  part  of  Lect.  IV. 


104 


LECTURE  XIII. 


racy,  the  most  convenient  test  is  furnished  by  the  effects  of  twisting.  An 
arm  or  beam  is  suspended  horizontally  by  a  long  wire,  and  the  force 
required  to  cause  the  beam  to  make  one  or  more  revolutions  being  ascer- 
tained, we  may  divide  the  circle  described  by  its  extremities  into  as  many 
parts  as  we  think  proper,  and  the  force  required  to  bring  the  beam  into 
any  position  will  always  be  proportional,  without  a  sensible  error,  to  the 
magnitude  of  the  part  of  the  circle  intercepted  between  the  given  position, 
and  that  in  which  the  arm  would  naturally  rest.  When  the  force  is  of 
such  a  nature  as  to  be  capable  of  producing  a  vibration,  the  body  on 
which  it  acts  being  suspended  by  the  thread  of  a  silkworm  or  of  a  spider, 
we  may  compare  its  magnitude  with  that  of  gravitation,  by  observing  the 
time  required  for  each  vibration,  and  determining  the  operation  of  the  force 
according  to  the  laws  of  pendulums.  It  is  in  this  manner  that  the  forces 
concerned  in  the  effects  of  electricity  and  of  magnetism  have  been  measured 
by  Mr.  Coulomb. 


LECT.  XII.— ADDITIONAL  AUTHORITIES. 

Balances. — Lahire,  Hist,  et  Mem.  de  1'Acad.  ii.  9 ;  ix.  42.  Roberval's  New 
Balances,  ibid.  x.  343.  Emerson's  Mechanics.  Troughton's  Balance,  Nich. 
Jour.  iii.  233. 

Steelyard.— Hooke's  Steelyard,  Birch's  History,  iv.  242.  Roemer's  Danish 
Steelyard.  Machines  Approuvees,  i.  79.  Pictet  on  Paul's  Steelyard,  Ph.  Mag. 
iii.  408. 

Weights  and  Measures. — Whitehurst,  An  Attempt  to  obtain  an  invariable  Stand- 
ard of  Length,  &c.  4to,  1787.  Adams  (John  Quincey),  Report  on  Weights  and 
Measures.  Washington,  U.S.  1821.  Hassler  on  Do.  Wash.  1832.  Report  of  the 
Franklin  Institute  on  Do.  1834.  Pasley  on  the  expediency  of  simplifying  Weights, 
&c.  Lond.  1834.  Clark  on  Weights  and  Measures,  Westminster  Review,  No.  31. 
Parliamentary  Reports,  fol.  1758,  1759,  1814,  1819,  1820,  1821. 

Animal  Mechanics,  &fc. — Perrault  on  Animal  Mechanics,  Hist,  et  Mem.  de  Paris, 
i.  181.  Parent  on  Do.  ibid,  1702,  H.  95.  Amontons  on  Moving  Powers,  ibid.  1703. 
D.  Bernoulli  on  the  Muscles  and  Nerves,  Com.  Petr.  i.  297.  Ray,  The  Wisdom  of 
God  manifested  in  the  Works  of  Creation.  Derham,  Physico -Theology.  1712. 
Paley's  Natural  Theology.  Cuvier,  Regne  Animale.  Bell,  Animal  Mechanics,  Lib. 
Useful  Knowledge.  Do.  Bridgewater  Treatise  on  the  Hand. 

Inanimate  Force.— Smeaton  on  the  Effect  of  Wind  and  Water,  Ph.  Tr.  1759, 
p.  100.  Reprinted,  8vo,  Lond. 


LECTURE   XIII. 


ON   PASSIVE  STRENGTH  AND  FRICTION. 

THE  passive  strength  of  the  materials  employed  in  the  mechanical  ails 
depends  on  the  cohesive  and  repulsive  forces  of  their  particles,  and  on  the 
rigidity  of  their  structure.  The  consideration  of  the  intimate  nature  c>f 
these  forces  belongs  to  the  discussion  of  the  physical  properties  of  matter  ; 
but  the  estimation  of  their  magnitude,  and  of  their  relative  value  in  various 
circumstances,  is  of  undeniable  importance  to  practical  mechanics,  and 


ON  PASSIVE  STRENGTH  AND  FRICTION.  105 

requires  to  be  examined  as  a  continuation  of  the  subject  of  statics.  The 
retarding  force  of  friction  is  very  nearly  allied  to  some  kinds  of  passive 
strength,  and  may  be  in  great  measure  explained  from  similar  conside- 
rations. 

The  principal  effects  of  any  force  acting  on  a  solid  body  may  be  reduced 
to  seven  denominations ;  extension,  compression,  detrusion,  flexure,  tor- 
sion, alteration,  and  fracture.  When  a  weight  is  suspended  below  a  fixed 
point,  the  suspending  substance  is  extended  or  stretched,  and  retains  its 
form  by  its  cohesion  assisted  by  its  rigidity  :  when  the  weight  is  supported 
by  a  block  or  pillar  placed  below  it,  the  block  is  compressed,  and  resists 
primarily  by  a  repulsive  force,  but  secondarily  also  by  its  rigidity.  The 
effect  here  called  detrusion  is  produced  when  a  transverse  force  is  applied 
close  to  a  fixed  point,  in  the  same  manner  as  the  blades  of  a  pair  of 
scissors  act  on  the  pin,  and  the  force  which  resists  this  operation  is  prin- 
cipally the  rigidity  or  lateral  adhesion  of  the  strata  of  the  substance,  but 
it  could  scarcely  be  effectual  without  some  degree  of  cohesive  and  repul- 
sive force.  When  three  or  more  forces  are  applied  to  different  parts  of 
any  substance  they  produce  flexure,  that  is,  they  bend  it,  some  of  its 
parts  being  extended  and  others  compressed.  In  torsion  or  twisting,  the 
central  particles  remain  in  their  natural  state,  while  those  which  are 
in  opposite  parts  of  the  circumference  are  detruded  or  displaced,  in  op- 
posite directions.  The  operation  of  forces  applied  in  any  of  these  ways 
may  produce  a  permanent  alteration  or  change  of  figure  in  substances 
sufficiently  soft,  and  perhaps,  in  a  certain  degree,  in  all  substances :  this 
change  is  sometimes  called  by  workmen  settling  or  taking  a  set.  But  the 
limit  of  all  these  effects  is  fracture,  which  is  the  consequence  of  the  appli- 
cation of  any  force  capable  of  overcoming  the  strength  of  the  substance, 
and  to  which  the  generality  of  writers  on  mechanics  have  hitherto  confined 
their  attention. 

The  forces  by  which  the  form  of  any  substance  is  changed  may  also  be 
divided  into  two  kinds,  simple  pressure  and  impulse  ;  but  it  is  only  with 
regard  to  fracture  that  it  will  be  necessary  to  take  the  force  of  impulse 
into  consideration. 

Extension  and  compression  follow  so  nearly  the  same  laws,  that  they 
may  be  best  understood  by  comparison  with  each  other.  The  cohesive  and 
repulsive  forces  which  resist  these  effects,  depend  almost  as  much  on  the 
solidity  or  rigidity  of  the  substances,  as  on  the  attractions  and  repulsions 
which  are  their  immediate  causes :  for  a  substance  perfectly  liquid, 
although  its  particles  are  in  full  possession  of  their  attractive  and  repulsive 
powers,  may  be  extended  or  compressed  by  the  smallest  force  that  can  be 
applied  to  it.  It  is  not  indeed  certain  that  the  actual  distances  of  the  par- 
ticles of  all  bodies  are  increased  when  they  are  extended,  or  diminished 
when  they  are  compressed  :  for  these  changes  are  generally  accompanied 
by  contrary  changes  in  other  parts  of  the  same  substance,  although  pro- 
bably in  a  smaller  degree.  We  may  easily  observe  that  if  we  compress  a 
piece  of  elastic  gum  in  any  direction,  it  extends  itself  in  other  directions ; 
and  if  we  extend  it  in  length,  its  breadth  arid  thickness  are  diminished. 

If  the  rigidity  of  a  body  were  infinite,  and  all  lateral  motions  of  its 


106  LECTURE  XIII. 

particles  were  prevented,  the  direct  cohesion  alone  would  be  the  measure 
of  the  force  required  to  produce  extension,  and  the  direct  repulsion,  of  the 
force  required  to  produce  compression ;  in  this  respect  indeed,  the  actual 
rigidity  of  some  substances  may  be  considered  as  infinite,  wherever  the 
extension  or  compression  is  moderate,  and  no  permanent  alteration  of 
form  is  produced  ;  and  within  these  limits  these  substances  may  be  called 
perfectly  elastic.  If  the  cohesion  and  repulsion  were  infinite,  and  the 
rigidity  limited,  the  only  effect  of  force  would  be  to  produce  alteration  of 
form :  and  such  bodies  would  be  perfectly  inelastic,  but  they  would  be 
harder  or  softer  according  to  the  degree  of  rigidity. 

It  is  found  by  experiment,  that  the  measure  of  the  extension  and  com- 
pression of  uniform  elastic  bodies  is  simply  proportional  to  the  force  which 
occasions  it ;  at  least  when  the  forces  are  comparatively  small.  Thus  if  a 
weight  of  100  pounds  lengthened  a  rod  of  steel  one  hundredth  of  an  inch, 
a  weight  of  200  would  lengthen  it  very  nearly  two  hundredths,  and  a 
weight  of  300  pounds  three  hundredths.*  The  same  weights  acting  in  a 
contrary  direction  would  also  shorten  it  one,  two,  or  three  hundredths 
respectively.  The  former  part  of  this  law  was  discovered  by  Dr.  Hooke, 
and  the  effects  appear  to  be  perfectly  analogous  to  those  which  are  more 
easily  observable  in  elastic  fluids. 

According  to  this  analogy,  we  may  express  the  elasticity  of  any  sub- 
stance by  the  weight  of  a  certain  column  of  the  same  substance,  which  may 
be  denominated  the  modulus  of  its  elasticity,  and  of  which  the  weight  is 
such,  that  any  addition  to  it  would  increase  it  in  the  same  proportion  as 
the  weight  added  would  shorten,  by  its  pressure,  a  portion  of  the  sub- 
stance of  equal  diameter.  Thus  if  a  rod  of  any  kind,  100  inches  long, 
were  compressed  1  inch  by  a  weight  of  1000  pounds,  the  weight  of  the 
modulus  of  its  elasticity  would  be  100  thousand  pounds,  or  more  accu- 
rately 99,000,  which  is  to  100,000  in  the  same  proportion  as  99  to  100.  In 
the  same  manner,  we  must  suppose  that  the  subtraction  of  any  weight 
from  that  of  the  modulus  will  also  diminish  it,  in  the  same  ratio  that  the 
equivalent  force  would  extend  any  portion  of  the  substance.  The  height 
of  the  modulus  is  the  same  for  the  same  substance,  whatever  its  breadth 
and  thickness  may  be :  for  atmospheric  air,  it  is  about  5  miles,  and  for 
steel  nearly  1500.  This  supposition  is  sufficiently  confirmed  by  experi- 
ments to  be  considered  at  least  as  a  good  approximation  :  it  follows  that 
the  weight  of  the  modulus  must  always  exceed  the  utmost  cohesive 
strength  of  the  substance,  and  that  the  compression  produced  by  such  a 
weight  must  reduce  its  dimensions  to  one  half :  and  I  have  found  that  a 
force  capable  of  compressing  a  piece  of  elastic  gum  to  half  its  length  will 
usually  extend  it  to  many  times  that  length,  and  then  break  or  tear  it ; 
and  also  that  a  force  capable  of  extending  it  to  twice  its  length  will  only 
compress  it  to  two  thirds.  In  this  substance,  and  others  of  a  similar  nature, 
the  resistance  appears  to  be  much  diminished  by  the  facility  by  which  a 
contrary  change  is  produced  in  a  different  direction  ;  so  that  the  cohesion 
and  repulsion  thus  estimated  appears  to  be  very  weak,  unless  when  the 
rigidity  is  increased  by  a  great  degree  of  cold.  It  would  be  easy  to  ascer- 
*  See  S'Gravesande's  Elem.  Physices,  lib.  i. 


ON  PASSIVE  STRENGTH  AND  FRICTION.  107 

tain  the  specific  gravity  of  such  a  substance  in  different  states  of  tension 
and  compression,  and  some  light  might  he  thrown  by  the  comparison,  on 
the  nature  and  operation  of  the  forces  which  are  concerned.  It  has  indeed 
been  asserted  that  the  specific  gravity  of  elastic  gum  is  even  diminished  by 
tension,  so  that  the  actual  distances  of  the  particles  cannot,  in  this  case,  be 
supposed  to  be  materially  increased. 

It  is  difficult  to  compare  the  lateral  adhesion,  or  the  force  which  resists 
the  detrusion  of  the  parts  of  a  solid,  with  any  form  of  direct  cohesion.  This 
force  constitutes  the  rigidity  or  hardness  of  a  solid  body,  and  is  wholly 
absent  from  liquids,  although  their  immediate  cohesion  appears  to  be  nearly 
equal  to  that  of  solids.  Some  experiments  have  been  made  on  the  fracture 
of  bodies  by  means  of  detrusion,  but  it  does  not  appear  that  the  force 
necessary  to  produce  a  temporary  derangement  of  this  kind  has  ever  been 
examined  :  it  may  be  inferred,  however,  from  the  properties  of  twisted 
substances,  that  the  force  varies  in  the  simple  ratio  of  the  distance  of  the 
particles  from  their  natural  position,  and  it  must  also  be  simply  propor- 
tional to  the  magnitude  of  the  surface  to  which  it  is  applied. 

The  most  usual,  as  well  as  the  most  important  effect  produced  by  the 
application  of  force,  is  flexure.  When  a  force  acts  on  a  straight  column  in 
the  direction  of  its  axis,  it  can  only  compress  or  extend  it  equally  through 
its  whole  substance  ;  but  if  the  direction  of  the  force  be  only  parallel  to 
the  axis,  and  applied  to  some  point  more  or  less  remote  from  it,  the  com- 
pression or  extension  will  obviously  be  partial :  it  may  be  shown  that  in 
a  rectangular  column,  when  the  compressing  force  is  applied  to  a  point 
more  distant  from  the  axis  than  one  sixth  of  the  depth,  the  remoter  surface 
will  no  longer  be  compressed  but  extended  ;  and  it  may  be  demonstrated 
that  the  distance  of  the  neutral  point  from  the  axis  is  inversely  as  that  of 
the  point  to  which  the  force  is  applied.  From  the  effect  of  this  partial 
compression,  the  column  must  necessarily  become  curved  :  and  the  curva- 
ture of  the  axis  at  any  point  will  always  be  proportional  to  its  dis- 
tance from  the  line  of  direction  of  the  force,  not  only  while  the  column 
remains  nearly  straight,  but  also  when  it  is  bent  in  any  degree  that  the 
nature  of  the  substance  will  allow.  If  the  column  was  originally  bent, 
any  force,  however  small,  applied  to  the  extremities  of  the  axis  will 
increase  the  curvature  according  to  the  same  law,  but  if  the  column  was 
originally  straight,  it  cannot  be  kept  in  a  state  of  flexure  by  any  lon- 
gitudinal force  acting  precisely  on  the  axis,  unless  it  be  greater  than  a 
certain  determinate  force  which  varies  according  to  the  dimensions  of  the 
column.  It  is  not  however  true,  as  some  authors  have  asserted,  that  every 
column  pressed  by  such  a  force  must  necessarily  be  bent ;  its  state  when  it 
is  straight  and  submitted  to  the  operation  of  such  a  force  will  resemble  a 
tottering  equilibrium,  in  which  a  body  may  remain  at  rest  until  some 
external  cause  disturbs  it.  The  figure  of  a  cplumn  naturally  straight, 
but  bent  a  little  by  a  longitudinal  force,  will  coincide  with  that  of  the 
harmonic  curve,  in  which  the  curvature  is  as  the  distance  from  the  basis. 
(Plate  IX.  Fig.  117... 121.) 

Considerable  irregularities  may  be  observed  in  all  the  experiments 
which  have  been  made  on  the  flexure  of  columns  and  rafters  exposed  to 


108  LECTURE  XIII. 

longitudinal  forces ;  and  there  is  no  doubt  but  that  some  of  them  were 
occasioned  by  the  difficulty  of  applying  the  force  precisely  at  the  extremi- 
ties of  the  axis,  and  others  by  the  accidental  inequalities  of  the  substances, 
of  which  the  fibres  must  often  have  been  in  such  directions  as  to  constitute 
originally  rather  bent  than  straight  columns. 

When  a  rod,  not  very  flexible,  is  fixed  at  one  end  in  a  horizontal  posi- 
tion, the  curvature  produced  by  its  own  weight  is  every  where  as  the 
square  of  the  distance  from  the  other  end :  and  if  a  rod  be  simply  sup- 
ported at  each  end,  its  curvature  at  any  point  will  be  proportional  to  the 
product  of  the  two  parts  into  which  that  point  divides  it.  But  when  the 
weights  are  supposed  to  be  applied  to  any  given  points  of  the  rod  only,  the 
curvature  always  decreases  uniformly  between  these  points  and  the  points 
of  support.  (Plate  IX.  Fig.  122,  123.) 

The  stiffness  of  any  substance  is  measured  by  the  force  required  to  cause 
it  to  recede  through  a  given  small  space  in  the  direction  of  the  force.  It  is 
only  necessary  to  consider  this  property  with  regard  to  forces  applied 
transversely.  In  such  cases  the  stiffness  is  directly  as  the  breadth  and  the 
cube  of  the  depth  of  the  beam,  and  inversely  as  the  cube  of  its  length.* 
Thus  if  we  have  a  beam  which  is  twice  as  long  as  another,  we  must  make 
it,  in  order  to  obtain  an  equal  stiffness,  either  twice  as  deep  or  eight  times 
as  broad.  The  property  of  stiffness  is  fully  as  useful  in  many  works  of 
art  as  the  ultimate  strength  with  which  a  body  resists  fracture  :  thus  for  a 
shelf,  a  lintel,  or  a  chimney  piece,  a  great  degree  of  flexure  would  be 
almost  as  inconvenient  as  a  rupture  of  the  substance. 

When  a  beam  is  supported  at  both  ends,  its  stiffness  is  twice  as  great  as 
that  of  a  beam  of  half  the  length  firmly  fixed  at  one  end  ;  and  if  both  ends 
are  firmly  fixed  the  stiffness  is  again  quadrupled.  For  if  the  whole  beam 
were  inverted  and  supported  by  a  fulcrum  in  the  middle,  each  half  would 
resemble  a  separate  beam  fixed  at  one  end,  and  the  fulcrum  would  bear 
the  sum  of  two  equal  weights  placed  at  the  extremities,  disregarding  that 
of  the  beam ;  and  consequently  the  same  flexure  will  be  produced  by 
placing  a  double  weight  on  the  middle  of  the  beam  in  an  inverted  position. 
If  both  ends  were  firmly  fixed,  the  curvature  would  be  every  where  as  the 
distance  from  the  middle  of  each  half,  the  whole  being  in  the  same  state 
as  four  separate  beams  fixed  at  their  extremities  :  each  of  these  beams 
would  be  eight  times  as  stiff  as  beams  of  twice  the  length,  and  the  whole 
beam,  in  this  state,  would  be  eight  times  as  stiff  as  if  the  ends  were  simply 
supported.  It  is,  however,  difficult  to  fix  the  ends  of  a  beam  so  firmly  as 
to  increase  its  resistance  in  this  proportion,  unless  it  be  continued  both 
ways  considerably  beyond  the  supports. 

It  is  evident  that  a  tube  or  hollow  beam  of  any  kind,  must  be  much 
stiffer  than  the  same  quantity  of  matter  in  a  solid  form :  the  stiffness  is 
indeed  increased  nearly  in  proportion  to  the  square  of  the  diameter,  since 
the  cohesion  and  repulsion  are  equally  exerted  with  a  smaller  curvature, 
and  act  also  on  a  longer  lever. 

Torsion,  or  twisting,  consists  in  the  lateral  displacement  or  detrusion  of 
the  opposite  parts  of  a  solid,  in  opposite  directions,  the  central  particles 
*  Robison's  Mechanical  Philosophy,  art.  Strength  of  Materials,  §  386. 


ON  PASSIVE  STRENGTH  AND  FRICTION.  109 

only  remaining  in  their  natural  state.  We  might  consider  a  wire  as  com- 
posed of  a  great  number  of  minute  threads,  extending  through  its  length, 
and  closely  connected  together ;  if  we  twisted  such  a  wire,  the  external 
threads  would  be  extended,  and,  in  order  to  preserve  the  equilibrium,  the 
internal  ones  would  be  contracted  ;  and  it  may  be  shown  that  the  whole 
wire  would  be  shortened  one  fourth  as  much  as  the  external  fibres  would 
be  extended  if  the  length  remained  undiminished ;  and  that  the  force 
would  vary  as  the  cube  of  the  angle  through  which  the  wire  is  twisted. 
But  the  force  of  torsion,  as  it  is  determined  by  experiment,  varies  simply 
as  the  angle  of  torsion  ;  it  cannot,  therefore,  be  explained  by  the  action  of 
longitudinal  fibres  only  ;  but  it  appears  rather  to  depend  principally,  if 
not  entirely,  on  the  rigidity  or  lateral  adhesion  which  resists  the  detrusion 
of  the  particles.  If  a  wire  be  twice  as  thick  as  another  of  the  same  length, 
it  will  require  sixteen  times  as  much  force  to  twist  it  once  round ;  the 
stiffness  varying  as  the  fourth  power  of  the  diameter,  that  is,  as  the  square 
of  its  square.  But  if  the  length  vary,  it  is  obvious  that  the  resistance  to 
the  force  of  torsion  will  be  inversely  as  the  length. 

A  permanent  alteration  of  form  is  most  perceptible  in  such  substances  as 
are  most  destitute  of  rigidity,  and  approach  most  to  the  nature  of  fluids. 
It  limits  the  strength  of  materials,  with  regard  to  practical  purposes, 
almost  as  much  as  fracture,  since  in  general  the  force  which  is  capable  of 
producing  this  effect,  is  sufficient,  with  a  small  addition,  to  increase  it  till 
fracture  takes  place.  A  smaller  force  than  that  which  has  first  produced 
an  alteration  of  form,  is  seldom  capable  either  of  increasing,  or  of  removing 
it,  a  circumstance  which  gives  such  materials  as  are  susceptible  of  an  alter- 
ation of  this  kind,  a  great  advantage  for  many  purposes  of  convenience  and 
of  art.  The  more  capable  a  body  is  of  a  permanent  alteration  of  form,  the 
more  ductile  it  is  said  to  be  ;  pure  gold  and  silver,  lead,  annealed  iron  and 
copper,  wax  when  warm,  glass  when  red  hot,  and  clay  when  moist,  possess 
considerable  ductility.  Wood  admits  of  little  permanent  change  of  form, 
except  in  a  green  state,  although  it  sometimes  settles  a  little,  when  it  has 
been  exposed  to  pressure.  Even  stone  will  become  permanently  bent  in 
the  course  of  years,  as  we  may  observe  in  old  marble  chimney  pieces. 
But  the  most  ductile  of  all  solid  substances  appears  to  be  a  spider's  web. 
Mr.  Bennet  twisted  a  thread  of  this  kind  many  thousand  times,  and 
shortened  it  more  than  a  fourth  of  its  length,  yet  it  showed  no  disposition 
to  untwist.* 

A  ductile  substance  acquires  the  same  cohesive  and  repulsive  powers 
with  regard  to  its  new  form,  as  it  possessed  in  its  original  state ;  and  when 
the  alteration  of  form  has  once  commenced,  those  powers  are  neither  in- 
creased nor  diminished  by  continuing  the  operation  ;  the  degree  of  flexure 
or  torsion  required  for  producing  a  further  alteration,  appears  also  to  be 
little  varied  :  thus  if  the  spider's  web  could  at  first  be  twisted  only  one  half 
round,  so  as  to  retain  the  power  of  returning  to  its  original  state,  without 
a,ny  permanent  alteration  of  form,  it  would  never  acquire  the  power  of 
returning  more  than  half  a  revolution,  however  it  might  be  twisted.  From 

*  Experiments  on  a  New  Suspension  of  the  Magnetic  Needle,  Ph.  Tr.  1792, 
Ixxxii.  82. 


110  LECTURE  XIII. 

a  want  of  attention  to  this  consideration,  a  late  respectable  author  has 
called  in  question,  without  sufficient  reason,  the  accuracy  of  Mr.  Bennet's 
experiments. 

A  variation  of  ductility  in  any  substance,  does  not  appear  to  depend  on 
any  change  in  the  magnitude  of  the  ultimate  powers  of  cohesion  and  repul- 
sion. Steel,  whether  perfectly  hard,  or  of  the  softest  temper,  resists  flexure 
with  equal  force,  when  the  deviations  from  the  natural  state  are  small :  but 
at  a  certain  point  the  steel,  if  soft,  begins  to  undergo  an  alteration  of  form  : 
at  another  point  it  breaks  if  much  hardened  ;  but  when  the  hardness  is 
moderate,  it  is  capable  of  a  much  greater  curvature  without  either  perma- 
nent alteration  or  fracture ;  and  this  quality,  which  is  valuable  for  the 
purposes  of  springs,  is  called  toughness,  and  is  opposed  to  rigidity  and 
brittleness  on  the  one  side,  and  to  ductility  on  the  other.  There  may, 
however,  be  an  apparent  difference  in  the  stiffness  of  some  substances  in 
different  states,  arising  from  the  greater  facility  with  which  their  dimen- 
sions are  extended  in  one  direction  while  they  are  contracted  in  another  : 
thus  elastic  gum  appears  to  possess  a  much  greater  degree  of  stiffness  when 
its  hardness  is  increased  by  cold  than  when  it  is  at  a  more  elevated  tempe- 
rature ;  but  the  change  produced  in  this  case  by  heat  is  not  an  increase  of 
that  ductility  which  facilitates  a  permanent  alteration  of  form,  but  rather 
of  the  toughness  which  allows  a  temporary  change  of  figure,  continuing 
only  while  the  force  is  applied.  The  effect  of  forging  and  of  wiredrawing 
tends  to  lessen  the  ductility  of  metals,  and  to  render  them  tough,  and  even 
rigid  :  so  that  in  hammering  copper  and  brass,  and  in  drawing  wire,  it  is 
necessary  to  anneal  the  metals  more  than  once  by  fire,  in  order  to  restore 
their  ductility,  which  is  lessened  by  the  operation.  The  corrosion  of  the 
surface  of  a  metal  by  an  acid  is  also  said  to  render  it  brittle  ;  but  it  is  not 
impossible  that  this  apparent  brittleness  may  be  occasioned  by  some  irre- 
gularity in  the  action  of  the  acid. 

The  last  effect  of  force  on  solid  materials  is  their  fracture,  which,  as  well 
as  the  former  changes,  may  be  produced  either  by  impulse  or  by  pressure 
alone.  The  action  which  resists  pressure  is  called  strength,  and  that  which 
resists  impulse  may  properly  be  termed  resilience.  The  strength  of  every 
body  is  in  the  joint  ratio  of  its  immediate  cohesion  and  repulsion,  or  elas- 
ticity, and  of  its  toughness,  or  the  degree  in  which  it  may  be  extended, 
compressed,  or  otherwise  deranged,  without  a  separation  of  its  parts.  The 
resilience  is  jointly  proportional  to  its  strength  and  its  toughness,  and  is 
measured  by  the  product  of  the  mass  and  the  square  of  the  velocity  of  a 
body  capable  of  breaking  it,  or  of  the  mass  and  the  height  from  which  it 
must  fall  in  order  to  acquire  that  velocity ;  while  the  strength  is  merely 
measured  by  the  greatest  pressure  that  it  can  support  in  a  state  of  rest. 

The  simplest  way  in  which  a  body  can  be  broken  is  by  tearing  it  asunder. 
The  cohesive  force  continues  to  be  increased  as  long  as  the  tenacity  of  the 
substance  allows  the  particles  to  be  separated  from  each  other  without  a 
permanent  alteration  of  form ;  when  this  has  been  produced,  the  same 
force,  if  its  action  is  continued,  is  generally  capable  of  causing  a  total  solu- 
tion of  continuity ;  and  sometimes  a  separation  takes  place  without  any 
previous  alteration  of  this  kind  that  can  be  observed. 


ON  PASSIVE  STRENGTH  AND  FRICTION.  Ill 

It  follows  from  the  nature  of  resilience,  that  a  hody  of  a  pound  weight, 
falling  from  the  height  of  a  yard,  will  produce  the  same  effect  in  breaking 
any  substance,  as  a  body  of  three  pounds  falling  from  the  height  of  a  foot ; 
so  that  here,  as  well  as  in  the  estimation  of  mechanical  power,  it  is  the 
energy  and  not  the  momentum,  that  is  to  be  considered  as  the  measure  of 
the  effect.  If  we  know  the  strength  of  any  substance,  and  the  degree  in 
which  it  is  capable  of  extension,  we  may  easily  determine  its  resilience 
from  a  consideration  of  the  laws  of  pendulums.  For  the  same  weight 
which  would  break  it  by  pressure,  will  acquire  a  sufficient  impulse  for 
breaking  it,  if  it  fall  from  a  height  equal  to  half  the  space  through  which 
the  substance  may  be  extended,  supposing  the  direction  of  the  stroke  to  be 
horizontal,  so  that  its  effect  may  not  be  increased  by  the  force  of  gravity. 
Thus  if  the  pressure  of  a  weight  of  100  pounds  broke  a  given  substance 
after  extending  it  through  the  space  of  an  inch,  the  same  weight  would 
break  it  by  striking  it  with  the  velocity  that  would  be  acquired  by  the  fall 
of  a  heavy  body  from  the  height  of  half  an  inch,  and  a  weight  of  one 
pound  would  break  it  by  falling  from  a  height  of  50  inches. 

It  is  obvious  that  the  cohesive  strength,  as  well  as  the  resilience,  of  any 
substance  must  be  simply  proportional  to  the  magnitude  of  its  transverse 
section,  that  is,  of  the  surface  of  fracture.  Some  experiments  appear  to  show 
that  it  increases  in  a  greater  proportion  than  this  surface,  others  that  it 
increases  in  a  smaller  proportion  ;  but  it  is  probable  that  in  both  cases 
some  accidental  irregularities  must  have  interfered,  and  that  a  wire  two 
inches  in  diameter  is  exactly  four  times  as  strong  as  a  wire  one  inch  in 
diameter.  The  length  has  no  effect  either  in  increasing  or  in  diminishing 
the  cohesive  strength  ;  but  the  resilience  is  proportional  to  the  length,  since 
a  similar  extension  of  a  longer  fibre  produces  a  greater  elongation. 

There  is  however  a  limit  beyond  which  the  velocity  of  a  body  striking 
another  cannot  be  increased  without  overcoming  its  resilience  and  breaking 
it,  however  small  the  bulk  of  the  first  body  may  be,  and  this  limit  depends 
on  the  inertia  of  the  parts  of  the  second  body,  which  must  not  be  dis- 
regarded when  they  are  impelled  with  a  considerable  velocity.  For  it  is 
demonstrable  that  there  is  a  certain  velocity,  dependent  on  the  nature  of  a 
substance,  with  which  the  effect  of  any  impulse  or  pressure  is  transmitted 
through  it ;  a  certain  portion  of  time,  which  is  shorter  accordingly  as  the 
body  is  more  elastic,  being  required  for  the  propagation  of  the  force  through 
any  part  of  it ;  and  if  the  actual  velocity  of  any  impulse  be  in  a  greater 
proportion  to  this  velocity  than  the  extension  or  compression,  of  which  the 
substance  is  capable,  is  to  its  whole  length,  it  is  obvious  that  a  separation 
must  be  produced,  since  no  parts  can  be  extended  or  compressed  which  are 
not  yet  affected  by  the  impulse,  and  the  length  of  the  portion  affected  at 
any  instant  is  not  sufficient  to  allow  the  required  extension  or  compression. 
Thus  if  the  velocity  with  which  an  impression  is  transmitted  by  a  certain 
kind  of  wood  be  15,000  feet  in  a  second,  and  it  f>e  susceptible  of  compres- 
sion to  the  extent  of  ^-y  of  its  length,  the  greatest  velocity  that  it  can  resist 
will  be  75, feet  in  a  second,  which  is  equal  to  that  of  a  body  falling  from  a 
height  of  about  90  feet.  And  by  a  similar  comparison  we  may  determine 
the  velocity  which  will  be  sufficient  to  penetrate  or  to  break  off  a  substance 


112  LECTURE  XIII. 

in  any  other  manner ;  if  we  calculate  the  velocity  required  to  convey  the 
impulse  from  one  part  of  the  substance  to  the  other,  and  ascertain  the 
degree  in  which  it  can  have  its  dimensions  altered  without  fracture. 

It  is  easy  to  understand,  from  this  statement,  the  different  qualities  of 
natural  bodies  with  respect  to  hardness,  softness,  toughness,  and  brittleness. 
A  column  of  chalk,  capable  of  supporting  only  a  pound,  will  perhaps  be 
compressed  by  it  only  a  thousandth  part  of  its  length  ;  a  column  of  elastic 
gum,  capable  of  suspending  a  pound,  may  be  extended  to  more  than  twice 
its  length,  the  elastic  gum  will  therefore  resist  the  energy  of  an  impulse 
incomparably  greater  than  the  chalk.  A  diamond,  so  hard  as  to  resist  an 
enormous  pressure,  may  be  broken  by  a  moderate  blow,  with  a  small 
hammer.  A  weight  of  1000  pounds,  moving  with  a  velocity  of  one  foot  in 
a  second,  and  acting  on  a  small  surface  of  a  board,  may  possess  sufficient 
energy  to  break  or  to  penetrate  it ;  with  a  velocity  of  100  feet  in  second,  a 
weight  of  T^  of  a  pound  will  possess  the  same  energy,  and  produce  the  same 
effect,  if  it  act  on  a  similar  surface ;  but  if  the  wood  be  so  constituted  as 
to  be  wholly  incapable  of  resisting  a  velocity  of  100  feet  in  a  second,  it  may 
be  penetrated  by  a  weight  of  -^-^  of  a  pound  as  well  as  by  one  tenth,  and 
by  a  moderately  soft  body  as  well  as  by  a  harder  one.  The  whole  board, 
however,  if  at  liberty,  would  receive  a  much  greater  momentum  from  the 
impulse  of  the  large  weight,  than  from  that  of  the  small  one,  its  action 
being  continued  for  a  much  longer  time.  And  it  is  for  this  reason  that  a 
ball  shot  by  a  pistol  will  perforate  a  sheet  of  paper  standing  upright  on  a 
table,  without  overturning  it. 

The  strength,  or  rather  hardness,  of  a  substance  exposed  to  the  action  of 
a  force  that  tends  to  compress  it,  must  not  be  confounded  with  its  resistance 
to  a  force  applied  longitudinally  and  tending  to  produce  flexure.  A  slender 
rod  of  wood,  when  it  yields  to  a  longitudinal  pressure,  commonly  bends 
before  it  breaks,  and  gives  way  at  last  to  the  force  by  a  transverse  fracture  ; 
but  a  column  of  stone  or  brick,  and  even  a  thick  pillar  of  wood,  is  crushed 
without  bending,  and  generally  by  a  smaller  force  than  that  which  would 
produce  or  continue  a  flexure.  In  this  case  the  parts  slide  away  laterally, 
and  in  a  rectangular  pillar  ;  if  the  texture  of  the  substance  is  uniform,  and 
not  fibrous,  the  surfaces  of  fracture  will  make  nearly  a  right  angle  with 
each  other,  supposing  the  resistance  arising  from  the  lateral  adhesion  in  the 
direction  of  any  surface  or  section,  to  be  simply  proportional  to  that  sec- 
tion ;  but  if  this  force,  like  that  of  friction,  is  increased  by  a  pressure 
which  tends  to  bring  the  parts  into  closer  contact,  the  angle  left  after  frac- 
ture must  be  more  acute.  (Plate  X.  Fig.  124, 125.) 

The  power  of  the  force  of  lateral  adhesion  in  resisting  fracture,  is  con- 
sidered by  Mr.  Coulomb  as  nearly  equal  to  that  of  the  direct  cohesion  of 
the  same  substance,  or  a  little  greater ;  while  Professor  Robison*  makes  it 
twice  as  great.  If,  however,  this  force  be  supposed  to  be  simply  equal  to 
the  direct  cohesion,  it  may  be  inferred  that  the  strength  of  a  square  bar  in 
resisting  compression  is  twice  as  great  as  its  cohesive  strength,  allowing 
that  the  fracture  takes  place  in  the  surface  of  least  resistance.  It  is,  how- 
ever, seldom  that  the  strength  with  which  a  body  resists  compression,  is  in 
*  Strength  of  Materials,  arts.  372,  373. 


ON  PASSIVE  STRENGTH  AND  FRICTION.  113 

so  great  a  proportion  as  this  to  its  cohesive  strength  ;  and  where  the  sub- 
stance is  in  any  degree  composed  of  fibres,  they  must  naturally  produce 
great  irregularities  by  their  flexure.  The  strength  in  resisting  compression, 
must,  according  to  this  statement,  be  simply  proportional  to  the  magnitude 
of  the  section  of  the  substance,  although  some  experiments  on  freestone 
appear  to  indicate,  that  when  the  section  is  increased,  the  strength  is  in- 
creased in  a  greater  proportion  ;  and  there  is  no  reason  to  suppose  that  it 
can  be  influenced  either  way  by  the  length.  A  cylindrical  or  prismatic 
form  is  therefore  the  best  that  can  be  given  to  materials  of  a  given  bulk,  in 
order  to  enable  them  to  resist  a  force  which  tends  to  crush  them,  except 
that  the  additional  pressure  of  their  own  weight  on  the  lower  parts,  re- 
quires that  those  parts  should  be  a  little  stronger  than  the  upper  parts.  It 
appears,  also,  that  something  is  gained  by  making  the  outline  a  little  con- 
vex externally  ;  for  it  may  be  demonstrated,  that  for  a  column  or  upright 
beam  to  be  cut  out  of  a  slab  of  equable  thickness,  supposing  the  strength 
to  be  independent  of  pressure,  the  strongest  form  is  a  circle.  (Plate  X. 
Fig.  126,  127.) 

When  a  body  is  broken  by  a  transverse  force  applied  very  near  to  a 
fixed  point,  its  lateral  adhesion  is  overpowered  by  the  effect  which  we  have 
called  detrusion,  and  its  strength  in  this  case  is,  therefore,  generally  some- 
what greater  than  its  direct  cohesive  strength.  But  when  the  part  to  which 
the  force  is  immediately  applied  is  at  a  distance  from  the  fixed  point 
greater  than  about  one  sixth  of  the  depth,  the  fracture  is  no  longer  the 
immediate  consequence  of  detrusion,  but  of  flexure. 

Flexure  is  the  most  usual  manner  in  which  fracture  is  produced  ;  the 
superficial  parts  on  the  convex  side  are  most  extended,  and  usually  give 
wray  first,  except  in  soft  fibrous  substances,  such  as  moist  or  green  wood, 
which  is  more  easily  crushed  than  torn  ;  and  in  this  case  the  concave  side 
fails  first,  and  becomes  crippled,  and  the  piece  still  remains  suspended  by 
the  cohesion  of  the  fibres.  After  the  convex  surface  has  been  cracked,  the 
whole  substance  is  usually  separated,  but  not  always  ;  for  example,  a 
triangular  beam,  with  one  of  the  edges  uppermost,  may  be  charged  with 
such  a  weight  that  the  upper  edge  may  be  divided  and  the  lower  part  may 
remain  intire. 

When  a  column  or  rafter  is  broken  by  the  operation  of  a  longitudinal 
pressure,  the  stiffness  of  the  column  being  once  overcome,  a  small  addition 
of  force  is  usually  sufficient  to  produce  fracture,  unless  the  pressure  has 
been  applied  to  a  part  more  or  less  distant  from  the  axis  ;  for  in  this  case 
a  moderate  force  may  produce  a  moderate  flexure,  and  a  much  greater 
force  may  be  required  to  break  the  column.  But  in  general,  the  stiffness 
of  columns  is  of  more  consequence  than  their  strength  in  resisting  trans- 
verse fracture. 

The  strength  of  beams  of  the  same  kind,  and  fixed  in  the  same  manner, 
in  resisting  a  transverse  force,  is  simply  as  their  fcreadth,  as  the  square  of 
their  depth,  and  inversely  as  their  length.*  Thus,  if  a  beam  be  twice  as 
biDad  as  another,  it  will  also  be  twice  as  strong,  but  if  it  be  twice  as  deep, 
it  will  be  four  times  as  strong  ;  for  the  increase  of  depth  not  only  doubles 
*  Robison's  Mech.  Phil.  i.  §  374,  &c. 


114  LECTURE  XIII. 

the  number  of  the  resisting  particles,  but  also  gives  each  of  them  a  double 
power,  by  increasing  the  length  of  the  levers  on  which  they  act.  The 
increase  of  the  length  of  a  beam  must  also  obviously  weaken  it,  by  giving 
a  mechanical  advantage  to  the  power  which  tends  to  break  it ;  and  some 
experiments  appear  to  show  that  the  strength  is  diminished  in  a  proportion 
somewhat  greater  than  that  in  which  the  length  is  increased. 

The  strength  of  a  beam  supported  at  both  ends,  like  its  stiffness,  is  twice 
as  great  as  that  of  a  single  beam  of  half  the  length,  which  is  fixed  at  one 
end  ;  and  the  strength  of  the  whole  beam  is  again  doubled  if  both  the  ends 
are  firmly  fixed. 

The  resilience  of  a  prismatic  beam,  resisting  a  transverse  impulse,  follows 
a  law  very  different  from  that  which  determines  its  strength,  for  it  is 
simply  proportional  to  the  bulk  or  weight  of  the  beam,  whether  it  be 
shorter  or  longer,  narrower  or  wider,  shallower  or  deeper,  solid  or  hollow. 
Thus  a  beam  ten  feet  long  will  support  but  half  as  great  a  pressure,  with- 
out breaking,  as  a  beam  of  the  same  breadth  and  depth,  wThich  is  only  five 
feet  in  length  ;  but  it  will  bear  the  impulse  of  a  double  weight  striking 
against  it  with  a  given  velocity,  and  will  require  that  a  given  body  should 
fall  from  a  double  height  in  order  to  break  it. 

It  is  therefore  of  great  consequence  in  the  determination  of  the  form  and 
quantity  of  the  materials  to  be  employed  for  any  mechanical  purpose,  that 
we  should  consider  the  nature  as  well  as  the  magnitude  of  the  forces  which 
are  to  be  resisted.  Stiffness,  strength,  or  resilience,  may  be  separately  or 
jointly  required  in  various  degrees.  For  a  ceiling,  stiffness  would  be  prin- 
cipally desirable  ;  for  a  door,  strength  ;  for  the  floor  of  a  ball  room,  resi- 
lience ;  for  a  coach  spring,  resilience  and  flexibility,  that  is,  resilience  with- 
out stiffness.  An  observatory  should  be  as  stiff  as  possible,  a  ship  as  strong 
as  possible,  a  cable  as  resilient  as  possible. 

It  is  a  common  remark,  that  a  floor  which  shakes  is  the  strongest ;  and, 
improbable  as  it  appears  at  first  sight,  it  may  perhaps  be  founded  in  truth  ; 
for  if  the  absolute  strength  of  a  stiff  and  a  shaking  floor  were  equal,  the 
shaking  floor  would  bear  the  effects  of  motion  with  the  least  injury.  It  is 
possible  that  a  stiff  floor,  which  would  support  a  numerous  assembly, 
might  give  way  at  a  ball ;  while  a  more  resilient  one,  which  would  be 
suited  for  dancing,  might  be  destroyed  by  a  crowded  concert. 

A  coach  spring,  divided  into  plates,  has  the  same  power  of  resisting, 
without  being  broken,  the  momentum  of  the  carriage,  arising  from  sudden 
elevations  and  depressions,  as  it  would  possess  if  it  formed  one  entire 
mass,  while  its  greater  flexibility  allows  it  to  regulate  these  motions  in  a 
much  more  gradual  and  gentle  manner.  A  single  piece  of  timber  may 
perhaps,  sometimes,  have  too  much  of  the  flexibility  of  a  coach  spring,  its 
strata  sliding,  in  some  degree,  on  each  other ;  in  such  a  case  its  stiffness 
and  strength  may  be  increased  by  binding  it  very  firmly  with  hoops. 

The  transverse  strength  of  a  perfectly  elastic  substance,  fixed  at  one  end, 
is  to  its  direct  cohesive  strength  as  the  depth  of  the  substance  to  six  times 
its  length.  This  proportion  is  equally  applicable  to  such  substances  as  re- 
sist compression  more  strongly  than  extension  ;  for  their  immediate  repul- 
sive force  is  probably  not  greater  than  their  cohesive  force,  when  their 


ON  PASSIVE  STRENGTH  AND  FRICTION.  115 

dimensions  are  equally  changed,  so  that  the  middle  of  the  beam  is  always 
in  its  natural  state  ;  and  when  the  curvature  is  sufficient  to  overcome  the 
cohesive  force,  the  whole  beam  must  give  way.  When,  however,  the  sub- 
stance is  less  capable  of  resisting  compression  than  extension,  the  concave 
surface  gives  way  first,  and  the  strength  depends  immediately  on  the  repul- 
sive strength  of  the  substance.  This  is  perhaps  the  reason  that,  in  experi- 
ments on  beams  of  oak,  the  transverse  strength  has  seldom  been  found  in  a 
greater  ratio  to  the  whole  cohesive  strength  than  that  of  the  depth  to  nine 
times  the  length. 

It  may  be  inferred  from  the  consideration  of  the  nature  of  the  different 
kinds  of  resistance  which  have  been  explained,  that  if  we  have  a  cylindrical 
tree  a  foot  in  diameter,  which  is  to  be  formed  into  a  prismatic  beam  by 
flattening  its  sides,  we  shall  gain  the  greatest  stiffness  by  making  the 
breadth  or  thickness  6  inches,  and  the  depth  10£,  the  greatest  strength  by 
making  the  breadth  7  inches  and  the  depth  9|,  and  the  greatest  resilience 
by  making  the  beam  square.  The  stiffness  and  the  strength  of  the  beam 
may  be  much  increased  by  cutting  the  tree  into  four  pieces,  turning  their 
edges  outwards,  and  uniting  them  so  as  to  make  a  hollow  beam :  but  it 
will  require  great  strength  of  union  to  make  the  whole  act  as  one  piece, 
and  the  resilience  of  the  beam  will  be  rather  diminished  than  increased  by 
the  operation. 

The  adoption  of  the  hollow  masts  and  beams  which  an  ingenious  me- 
chanic has  lately  introduced,  requires,  therefore,  some  caution.  For  where 
an  impulse  is  to  be  resisted,  such  a  mast  is  no  stronger  than  a  solid  mast  of 
the  same  weight,  and  much  weaker  than  a  solid  mast  of  the  same  diameter. 
The  force  of  the  wind  is,  however,  rather  to  be  considered  as  constituting 
a  pressure  than  a  finite  impulse,  except  when  a  sudden  squall  carries  a 
loose  sail  before  it  with  considerable  velocity.  A  similar  caution  may  also 
be  extended  to  some  other  attempts  to  make  improvements  in  naval  archi- 
tecture :  it  is  a  common  opinion,  and  perhaps  a  well-founded  one,  that 
flexibility  is  of  great  advantage  to  a  ship's  sailing  ;  if  therefore  we  sacrifice 
too  much  resilience  to  strength,  and  too  much  of  both  to  stiffness,  we  may 
perhaps  create  greater  evils  than  those  which  we  wish  to  avoid. 

We  have  hitherto  supposed  the  beams  of  which  the  strength  has  been 
compared,  to  be  prismatic,  that  is,  of  equal  breadth  and  thickness  through- 
out, which  is  not  only  the  simplest  form  in  theory  but  the  most  generally 
useful  in  practice.  If,  however,  we  have  the  power  of  giving  any  form 
that  we  please  to  materials  of  a  certain  weight,  which  may  often  be  done 
where  several  smaller  pieces  are  to  be  cut  out  of  a  larger  one,  or  a  larger 
one  to  be  composed  of  several  smaller  ones,  or  where  the  materials  are 
either  ductile  or  fusible,  it  is  frequently  possible  to  determine  a  more  ad- 
vantageous form  than  that  of  an  equable  beam  or  column.  For  since  the 
extension  which  the  parts  of  the  substance  admit  without  giving  way,  is  the 
limit  of  their  strength,  if  the  depth  of  a  beam  be  everywhere  equal,  and  the 
curvature  unequal,  the  fracture  will  first  take  place  where  the  curvature 
is  greatest,  and  the  superfluous  strength  of  the  other  parts  will  be  lost ;  so 
that,  in  order  to  have  the  greatest  strength  that  a  given  quantity  of  mate- 
rials is  capable  of  affording  in  a  beam  of  given  length,  the  form  must  be 

i2 


116  LECTURE  XIII. 

such  that  the  strength  may  be  everywhere  equal,  the  tension  of  the  surface 
being  equal  throughout ;  and  the  depth  must  be  as  much  smaller  as  the  cur- 
vature is  greater.  It  is  also  necessary  to  consider  whether  the  substance  is 
likely  to  be  crushed,  and  whether  it  is  liable  to  be  broken  by  detrusion 
rather  than  by  flexure.  Sometimes  the  depth  of  the  beam  may  be  limited, 
and  sometimes  its  breadth  ;  or  it  may  be  required  that  the  breadth  and 
depth  may  be  always  equal  or  proportional  to  each  other,  and  the  force 
may  be  either  applied  at  one  end  of  the  beam  or  it  may  be  equally  divided 
throughout  its  length  ;  it  may  also  principally  depend  on  the  weight  of  the 
substance  itself  ;  and  the  strongest  form  will  be  different  according  to  the 
different  conditions  of  its  application.  In  the  most  common  cases,  the 
outline  must  be  either  triangular  or  parabolic,  as  if  the  point  of  the  triangle 
were  rounded  off;  but  the  curves  required  are  sometimes  of  much  more 
difficult  investigation.  (Plate  X.  Fig.  128... 147.) 

The  strength  of  bodies  is  sometimes  employed  in  resisting  torsion,  as  in 
the  case  of  the  axles  of  wheels  and  pinions,  rudders  of  ships,  and  screws  of 
all  kinds  :  but  there  is  seldom  occasion  to  determine  their  absolute  strength 
in  resisting  a  force  thus  applied  ;  if  they  are  sufficiently  stiff,  their  parts 
are  not  often  separated  by  any  violent  efforts. 

In  order  to  investigate  the  strength  of  the  various  substances  employed 
for  the  purposes  of  the  mechanical  arts,  it  is  most  convenient  to  use  a 
machine  furnished  with  proper  supports,  and  gripes,  or  vices,  for  holding 
the  materials,  and  with  steelyards  for  ascertaining  the  magnitude  of  the 
force  applied,  while  the  extension  or  compression  is  produced  by  a  screw 
or  a  winch,  with  the  intervention  of  a  wire,  a  chain,  or  a  cord  :  provision 
ought  also  to  be  made  for  varying  the  direction  of  the  force,  when  the 
flexure  of  the  materials  renders  such  a  change  necessary.  (Plate  XI.  Fig. 
148.) 

According  to  the  experiments  of  various  authors,  the  cohesive  strength  of 
a  square  inch  of  razor  steel  is  about  150  thousand  pounds,  of  soft  steel  120, 
of  wrought  iron  80,  of  cast  iron  50,  of  good  rope  20,  of  oak,  beech,  and 
willow  wood,  in  the  direction  of  their  fibres,  12,  of  fir  8,  and  of  lead  about 
3  thousand  pounds :  the  cohesive  strength  of  a  square  inch  of  brick  300, 
and  of  freestone  200.  Teak  wood,  the  tectona  grandis,  is  said  to  be  still 
stronger  than  oak. 

The  weight  of  the  modulus  of  the  elasticity  of  a  square  inch  of  steel,  or 
that  weight  which  would  be  capable  of  compressing  it  to  half  its  dimen- 
sions, is  about  3  million  pounds  ;  hence  it  follows,  that  when  a  square  inch 
of  steel  is  torn  asunder  by  a  weight  of  150,000  pounds,  its  length  is  first  in- 
creased to  one  twentieth  more  than  its  natural  dimensions. 

The  strength  of  different  materials,  in  resisting  compression,  is  liable  to 
great  variation.  In  steel,  and  in  willow  wood,  the  cohesive  and  repulsive 
strength  appear  to  be  nearly  equal.  Oak  will  suspend  much  more  than 
fir ;  but  fir  will  support  twice  as  much  as  oak  ;  probably  on  account  of 
the  curvature  of  the  fibres  of  oak.  Freestone  has  been  found  to  support 
about  2000  pounds  for  each  square  inch,  oak  in  some  practical  cases  more 
than  4000. 

The  strongest  wood  of  each  tree  is  neither  at  the  centre  nor  at  the  cir- 


ON  PASSIVE  STRENGTH  AND  FRICTION.  117 

cumference,  but  in  the  middle  between  both  ;  and  in  Europe  it  is  generally 
thicker  and  firmer  on  the  south-east  side  of  the  tree.  Although  iron  is 
much  stronger  than  wood,  yet  it  is  more  liable  to  accidental  imperfections ; 
and  when  it  fails,  it  gives  no  warning  of  its  approaching  fracture.  The 
equable  quality  of  steel  may  be  ascertained  by  corrosion  in  an  acid  ;  but 
there  is  no  easy  mode  of  detecting  internal  flaws  in  a  bar  of  iron,  and  we 
can  only  rely  on  the  honesty  of  the  workman  for  its  soundness.  Wood, 
when  it  is  crippled,  complains,  or  emits  a  sound,  and  after  this,  although 
it  is  much  weakened,  it  may  still  retain  strength  enough  to  be  of  service. 
Stone  sometimes  throws  off  small  splinters  when  it  is  beginning  to  give 
way  ;  it  is  said  to  be  capable  of  supporting  by  much  the  greatest  weight 
when  it  is  placed  in  that  position,  with  respect  to  the  horizon,  in  which  it 
has  been  found  in  the  quarry. 

It  is  obvious  that  when  the  bulk  of  the  substance  employed  becomes  very 
considerable,  its  weight  may  bear  so  great  a  proportion  to  its  strength  as  to 
add  materially  to  the  load  to  be  supported.  In  most  cases  the  weight  in- 
creases more  rapidly  than  the  strength,  and  causes  a  practical  limitation  of 
the  magnitude  of  our  machines  and  edifices.  We  see  also  a  similar  limit 
in  nature  :  a  tree  never  grows  to  the  height  of  100  yards ;  an  animal  is 
never  strong  enough  to  overset  a  mountain.  It  has  been  observed  that 
whales  are  often  larger  than  any  land  animals,  because  their  weight  is 
more  supported  by  the  pressure  of  the  medium  in  which  they  swim. 

The  force  of  friction  which  resists  the  sliding  of  different  bodies  on  each 
other,  seems  to  be  intimately  connected  with  that  lateral  adhesion  or  ri- 
gidity which  is  opposed  to  the  internal  displacement  of  the  parts  of  a 
single  body,  by  the  effect  which  we  have  denominated  detrusion ;  and 
when  the  friction  is  considered  as  resisting  pressure  rather  than  motion,  it 
approaches  still  more  nearly  to  the  same  force.  It  is  probably  derived  in 
great  measure  from  the  strength  of  the  protuberant  particles,  which  must 
be  broken,  bent,  or  compressed  by  the  motion  of  the  bodies  on  each  other  : 
but  it  is  not  always  that  the  existence  of  such  particles  can  be  asserted, 
much  less  can  they  be  made  perceptible  to  the  senses,  and  we  can  only  ex- 
amine the  effects  which  they  may  be  supposed  to  produce,  by  immediate 
experiments  on  the  forces  required  to  counteract  them.  Such  experiments 
have  been  made  on  a  very  extensive  scale  by  Musschenbroek*  and 
Coulomb,f  and  many  of  their  results  have  been  confirmed  by  Mr.  Vince,J 
in  a  simple  and  elegant  manner. 

With  a  few  exceptions,  the  friction  of  all  solid  bodies  is  either  perfectly, 
or  very  nearly,  a  uniformly  retarding  force,  neither  increasing  nor  di- 
minishing when  the  relative  velocity  of  the  bodies  concerned  is  changed. 
The  friction  of  some  rough  substances  is  a  little  increased  with  the  velocity, 
but,  as  they  become  more  polished,  this  variation  disappears.  When,  how- 
ever, the  motion  is  wholly  extinct,  and  the  bodies  remain  in  contact  with 
each  other,  their  adhesion  is  usually  greater  thkn  the  friction,  and  by  a 
continuation  of  the  contact,  it  may  become  twice  or  even  thrice  as  great, 

*  Introductio  ad  Philosophiam  Naturalem,  2  vols.  4to,  Leyd.  1762,  i.  145. 

f  Mem.  des  Savans  Etrangers,  x.  161. 

£  On  the  Motion  of  Bodies  affected  by  Friction,  Ph.  Tr.  1785,  kxv.  165. 


118  LECTURE  XIII. 

especially  where  the  surfaces  are  large  and  the  substances  but  moderately 
hard. 

The  truth  of  the  assertion,  that  friction  is  a  uniformly  retarding  force, 
may  be  shown  very  conveniently  by  means  of  Atwood's  machine  for  ex- 
periments on  accelerated  motion.  By  suffering  the  axis  of  the  pulley  to 
rest  on  the  surface  of  any  fixed  substance,  we  may  subject  it  to  a  friction 
of  which  the  magnitude  may  be  varied  by  different  methods  ;  and  we  shall 
find  that  the  motions  of  the  boxes  still  indicate  the  action  of  a  uniformly 
accelerating  force,  the  spaces  described  being  always  proportional  to  the 
squares  of  the  times  of  descent ;  it  follows  therefore,  that  since  the  ope- 
ration of  gravity  is  uniform,  that  of  friction  which  is  deducted  from  it  at 
each  instant,  must  also  be  uniform,  in  order  that  the  remaining  acceleration 
may  follow  the  same  law. 

The  uniformity  of  the  force  of  friction  may  also  be  shown  by  the  descent 
of  a  flat  substance  on  an  inclined  plane  :  if  the  body  be  caused  to  begin  its 
descent  with  a  certain  velocity,  it  will  be  retarded  when  the  resistance  is 
greater  than  the  relative  force  of  gravity  :  in  this  case  the  retardation  will 
continue  until  it  is  wholly  stopped,  the  resistance  not  diminishing  with  the 
velocity.  If,  on  the  contrary,  the  relative  weight  overpowers  the  resistance 
at  first,  the  motion  will  be  continually  accelerated,  the  resistance  not  being 
increased  by  the  increase  of  the  velocity.  But  since  every  experiment  of 
this  kind  must  be  performed  in  the  presence  of  the  air,  the  resistance  of 
this  fluid,  which  follows  another  law,  will  in  the  end  prevent  the  ac- 
celeration. 

It  may  in  general  be  asserted,  with  some  exceptions,  that  the  force  of 
friction  is  simply  proportional  to  the  weight  or  pressure  that  brings  the 
substances  concerned  into  contact,  independently  of  the  magnitude  of  their 
surfaces :  but  Mr.  Coulomb  has  observed  that  in  many  cases  there  is, 
besides  this  force,  another  resistance,  amounting  to  several  pounds  for  each 
square  foot  of  the  surface,  which  is  independent  of  the  pressure  ;  and  by 
calculating  these  forces  separately,  we  may  probably  always  ascertain  the 
whole  resistance  with  sufficient  accuracy.  This  constant  portion  is  usually 
much  smaller  than  that  which  varies  with  the  weight,  and  in  all  common 
cases  it  may  be  safely  neglected,  and  the  friction  of  stone  on  stone  may  be 
called  equal  to  one  half  of  the  pressure,  that  of  wood  on  wood  one  third, 
and  that  of  metal  on  metal  one  fourth  ;  and  this  may  serve  as  an  estimate 
sufficiently  accurate  for  calculating  the  effects  of  machines ;  although,  if 
their  parts  were  perfectly  adjusted  to  each  other,  and  all  the  surfaces  well 
polished,  the  friction  would  not  in  general  exceed  one  eighth  of  the 
pressure,  whatever  might  be  the  nature  of  the  materials.  The  application 
of  unctuous  substances  lessens  the  friction  in  the  first  instance  ;  but  unless 
they  are  frequently  renewed,  they  sometimes  tend  rather  to  increase  it. 

The  simplest  mode  of  ascertaining  the  magnitude  of  the  friction  of  two 
bodies,  is  to  incline  their  common  surface  to  the  horizon  until  the  one 
begins  to  slide  on  the  other  :  this  point  determines  the  magnitude  of  their 
adhesion  ;  but  in  order  to  find  that  of  their  friction  when  they  are  in  mo- 
tion, they  must  be  first  separated,  and  then  allowed  to  move  on  each  other, 
while  the  whole  apparatus  is  gently  agitated.  The  friction  will  then  be  to 


ON  PASSIVE  STRENGTH  AND  FRICTION.  119 

the  pressure,  as  the  height  of  the  inclined  plane  to  its  horizontal  length, 
when  the  inclination  is  barely  such  as  to  allow  the  continuance  of  any 
motion  which  is  imparted  to  the  substance  placed  on  the  plane. 

It  follows  from  the  doctrine  of  the  resolution  of  force,  that  when  any 
body  is  to  be  drawn  along  a  horizontal  surface,  which  produces  a  resistance 
proportionate  to  the  pressure,  a  part  of  the  force  may  be  advantageously 
employed  in  diminishing  the  pressure  produced  by  the  weight  of  the  body  ; 
hence,  in  order  for  the  most  advantageous  application  of  the  force,  its  di- 
rection must  be  inclined  to  the  horizon,  and  it  may  be  demonstrated  that 
the  inclination  must  be  the  same  with  that  of  a  plane  on  which  the  relative 
weight  of  the  body  is  precisely  equal  to  the  friction.  Thus,  if  we  can  de- 
termine the  inclination  of  a  road  which  is  barely  sufficient  for  a  carriage  to 
descend  on  it  by  its  own  weight,  the  same  inclination  will  be  the  best  pos- 
sible for  the  application  of  any  force  by  which  the  carriage  is  to  be  drawn 
along  a  horizontal  road  of  the  same  materials. 

It  is  obvious  that  an  inclined  plane  on  which  a  weight  rests  by  means  of 
an  adhesion  proportionate  to  the  pressure,  can  never  be  forced  backwards 
by  any  increase  of  that  pressure,  since  the  resistance  increases  in  the  same 
proportion,  and  continues  always  sufficient  to  prevent  the  relative  motion 
of  the  weight  and  the  inclined  plane.  Two  such  planes,  put  together, 
would  constitute  a  wedge,  which  would  be  equally  incapable  of  giving 
way  to  a  pressure  applied  to  its  opposite  surfaces,  each  of  them  possessing 
similar  properties  with  respect  to  friction.  Thus,  if  the  friction  or  adhe- 
sion were  exactly  one  eighth  of  the  pressure,  the  height  of  the  inclined 
plane  would  be  one  eighth  of  its  length,  and  the  back  of  the  wedge  one 
fourth.  Such  a  wedge  would  therefore  possess  a  perfect  stability  with 
respect  to  any  forces  acting  on  its  inclined  surfaces.  But  the  effects  of 
agitation,  and  the  minute  tremors  produced  by  percussion,  have  a  great 
tendency  to  diminish  the  force  of  adhesion,  by  interrupting  the  intimacy  of 
contact :  and  where  a  pin,  a  nail,  or  a  screw  is  required  to  retain  its 
situation  with  firmness,  the  inclination  of  the  surfaces  must  be  smaller 
than  the  angle  of  such  a  wedge  as  is  barely  capable  of  affording  a  sufficient 
resistance  in  theory. 

It  appears,  therefore,  that  the  force  of  lateral  adhesion,  acting  between 
two  bodies  in  contact,  is  of  great  importance  in  all  mechanical  arts  ;  the 
firmness  of  architecture  and  of  carpentry  depends  in  great  measure  on  it. 
This  kind  of  resistance  being  equally  powerful,  when  the  force  is  applied 
in  the  direction  of  the  surface,  to  whatever  part  of  the  surface  it  may  tend, 
it  follows  that  any  body  which  is  subjected  to  friction  on  all  sides,  will 
retain  its  situation  with  the  same  force  that  was  used  in  overcoming  the 
friction  in  order  to  bring  it  into  that  situation,  or  rather  with  a  greater 
force,  since  the  lateral  adhesion  is  generally  a  little  greater  than  the  fric- 
tion :  so  that  a  cylindrical  wire  cannot  be  withdrawn  from  a  perforation  in 
a  board,  by  any  direct  force  less  than  that  which'was  employed  in  intro- 
ducing it ;  and  this  kind  of  stability,  together  with  that  of  a  wedge  or  nail 
resisting  a  lateral  pressure,  constitutes  the  security  of  the  lighter  structures 
of  carpentry,  while  those  of  architecture  receive  a  great  part  of  their 


120  LECTURE  XIII. 

firmness  from  the  accumulation  of  weight,  which  makes  the  resistance  of 
their  lower  parts  to  any  lateral  motion  almost  insuperable. 

When  a  hard  body  penetrates  another,  or  when  a  substance  is  ground 
away  by  the  attrition  of  another,  the  force  which  opposes  the  motion,  is 
to  be  considered,  like  the  force  of  friction,  as  a  uniformly  retarding  force. 
There  is  no  reason  for  imagining  the  stiffness  of  a  bar,  whether  longer  or 
shorter,  to  depend  on  the  velocity  of  the  body  that  bends  it,  and  the  space 
through  which  it  may  be  bent,  without  breaking,  is  also  limited  only  by 
the  toughness  of  the  materials.  In  the  same  manner,  when  the  internal 
parts  of  a  solid  are  broken  and  displaced  by  the  penetration  of  another,  or 
its  external  parts  abraded  by  its  attrition,  the  resistance  is  the  same,  what- 
ever the  velocity  may  be,  and  the  space  described  by  the  body  before  its 
velocity  is  destroyed,  is  always  proportional  to  the  square  of  that  velocity, 
or  to  the  energy  which  results  from  a  combination  of  the  proportions  of 
the  velocity  and  the  momentum. 


LECT.  XIII.— ADDITIONAL  AUTHORITIES. 

Passive  strength. — Buffinger  on  the  Strength  of  Beams,  Comm.  Petr.  iv.  164. 
Muschenbroek,  Systeme  de  Physique,  par  Lafond,  Par.  1760.  Buffon  on  the 
Strength  of  Timber,  Hist,  et  Mem.  de  Paris,  1738,  p.  169,  H.  54;  1740,  p.  453 ; 
1741,  p.  292.  Duhamel  on  do.  ibid.  1742,  p.  335  ;  1768,  p.  534,  H.  29.  Jurin 
on  the  Elastic  Force  of  Springs,  Ph.  Tr.  1744,  p.  46.  Emerson's  Fluxions,  343, 
Mechanics,  4to,  1758.  Euler,  Novi  Com.  Petr.  1757.  Acta  Petr.  1758.  Belidor, 
Architecture  Hydraulique,  I.  ii.  92.  Jo.  Bernoulli  on  the  Extension  of  Threads, 
&c.  Hist,  et  Mem.  de  Berlin,  1766,  pp.  78,  108.  Coulomb  on  the  Force  of  Tor- 
sion, Hist,  et  Mem.  de  Paris,  1784,  p.  229.  Gauthey  on  the  Strength  of  Stones, 
Rozier's  Journal,  iv.  402.  Dupin  sur  la  Flexibilite,  la  Force,  et  1'Elasticite  des 
Bois,  Journal  de  1'Ecole  Poly  technique,  x.  137.  Rennie,  Ph.  Tr.  1818.  Barlow 
on  the  Strength  of  Timber,  1824  ;  Iron,  1835.  Do.  do.  Second  Report,  1835. 
Tredgold  on  the  Strength  of  Iron,  Lond.  1824.  Hodgkinson's  Memoirs  of  the  Lit. 
and  Phil.  Soc.  of  Manchester,  vols.  iv.  and  v. 

Friction. — Amontons  on  the  Resistance  of  Mach.  Hist,  et  Mem.  1699,  p.  206, 
H.  104  ;  1700,  p.  47  ;  1703,  H.  105  ;  1704,  pp.  173,  206.  Parent,  do.  ibid.  1700, 
H.  149  ;  1704.  Sauveur  on  the  Friction  of  Ropes  coiled  round  a  Cylinder,  ibid. 
1703,  p.  305.  Varignon,  do.  ibid.  1717,  p.  195,  H.  68.  Euler  on  Friction,  Hist, 
et  Mem.  de  Berlin.  1748,  pp.  122,  133.  Novi  Com.  Petrop.  vi.  233;  xx.  304,  327. 
Bernoulli,  ibid.  xiv.  i.  249.  Hedin,  Dissertatio  Physico-Mechanica  de  Frictione,  4to, 
Upsal,  1770.  Ximenes,  Teoria  e  Pratica  delle  Resistenze  de'  Solidi  ne'  loro  Attriti, 
2  vols.  4to,  Pisa,  1782.  Library  of  Useful  Knowledge,  Mechanics,  Third  Treatise. 
Morin,  Nouvelles  Experiences  sur  le  Frottement,  3  vols.  4to,  Paris,  1843.  The 
newest  and  best  authority. 


121 


LECTURE    XIV. 


ON  ARCHITECTURE  AND  CARPENTRY. 

THE  subjects  which  we  have  lately  examined,  are  to  be  considered  as 
preliminary  to  the  particular  departments  of  practical  mechanics.  The 
first  division  of  these  is  to  consist  of  such  as  are  employed  in  resisting 
forces  of  various  kinds,  but  they  may  almost  all  be  referred,  without  in- 
convenience, to  the  general  heads  of  architecture  and  carpentry,  of  which 
the  principal  business  is  to  resist  the  force  of  gravitation.  Architecture, 
in  its  most  extensive  sense,  may  be  understood  as  comprehending  carpen- 
try, but  the  term  is  more  usually  applied  to  the  employment  of  those  ma- 
terials, which  are  only  required  to  resist  the  effects  of  a  force  tending 
principally  to  produce  compression,  while  the  materials  used  by  carpenters 
are  frequently  subjected  to  the  operation  of  a  force  which  tends  to  extend 
or  to  bend  them  :  the  works  of  architects  being  commonly  executed  in  stone 
or  brick,  and  those  of  carpenters  in  wood,  besides  the  occasional  use  of 
iron  and  other  metals,  in  both  cases. 

The  simplest  problem  in  mechanical  architecture  appears  to  be,  to  de- 
termine the  most  eligible  form  for  a  column.  The  length  and  weight  being 
supposed  to  be  given,  it  is  of  importance  to  investigate  the  form  which 
affords  the  greatest  possible  strength ;  but  it  is  somewhat  difficult  to  ascer- 
tain the  precise  nature  and  direction  of  all  the  forces  which  are  to  be 
resisted.  If  we  consider  the  column  as  a  beam  fixed  in  the  ground,  and 
impelled  by  a  transverse  force,  it  ought  to  be  much  tapered,  and  reduced 
almost  to  a  point  at  its  extremity  ;  but  it  is  seldom  that  any  force  of  this 
kind  can  be  powerful  enough  to  do  more  than  overcome  the  weight  alone 
of  the  column,  and  it  is  only  necessary  to  regard  the  load  which  presses 
vertically  on  it ;  and  whether  we  consider  the  force  as  tending  to  bend  or 
to  crush  it,  the  forms  commonly  employed  will  appear  to  be  sufficiently 
eligible.  Lagrange  seems  to  have  been  misled  by  some  intricacies  of  ma- 
thematical investigation,*  too  remote  from  physical  accuracy,  when  he 
calculated  that  a  cylinder  was  the  strongest  form  for  resisting  flexure  ; 
that  form  approaches  in  reality  much  more  nearly  to  an  oblong  spheroid, 
of  which  the  outline  is  elliptical.  The  consideration  of  the  flexure  of  a 
column  is,  however,  of  little  practical  importance  in  architecture,  for 
upon  a  rough  estimate  of  the  properties  of  the  materials  usually  employed, 
it  may  be  computed  that  a  column  of  stone  must  be  about  forty  times  as 
high  as  it  is  thick,  in  order  to  be  capable  of  being  bent  by  any  weight 
which  will  not  crush  it ;  although  a  bar  of  wood  or  of  iron  may  be  bent 
by  a  longitudinal  force,  if  its  length  exceed  about  twelve  times  its  thick- 
ness. The  force  may  therefore  be  considered  as  'tending  only  to  crush  the 
column  ;  and  since  the  inferior  parts  must  support  the  weight  of  the 
superior  parts  in  addition  to  the  load  which  presses  on  the  whole  column, 
their  thickness  ought  be  somewhat  increased  ;  and  it  appears  from  a  con- 
*  Melanges  de  Turin,  v.  ii.  123. 


122  LECTURE  XIV. 

sideration  of  the  direction  in  which  the  fracture  is  most  easily  effected, 
that  the  outline  ought  to  be  made  a  little  convex  externally,  and  more 
curved  above  than  below,  which  is  the  usual,  although  not  the  universal 
practice;  an  elliptic  arc  is  perhaps  the  most  eligible  outline,  or  a  curve 
formed  by  bending  a  ruler  fixed  at  the  summit  of  the  column  ;  sometimes 
the  form  is  made  to  differ  little  from  a  cone,  but  such  a  figure  is  very 
inelegant.  The  diminution  of  the  thickness  amounts  in  general  to  about 
one  sixth  or  one  seventh  of  the  whole,  and  sometimes  to  one  fourth. 
(Plate  XI.  Fig.  149.) 

For  a  light  house,  where  a  great  force  of  wind  and  water  was  to  be 
resisted,  Smeaton  chose  a  curve  with  its  concavity  turned  outwards.*  If 
we  calculated  what  would  be  the  best  form  for  a  wooden  pillar,  intended 
to  remain  always  immersed  in  the  water  to  a  certain  depth,  we  should  find 
that  a  cone  or  pyramid  would  possess  the  greatest  possible  strength  for 
supporting  the  motion  of  the  water ;  and  a  cone  more  acute  than  this 
would  be  equally  capable  of  resisting  the  force  of  the  wind,  supposing  it 
to  be  less  active  than  that  of  the  water  ;  the  part  below  the  water  might, 
therefore,  be  widened  so  as  to  become  a  portion  of  a  more  obtuse  cone,  the 
upper  part  remaining  more  slender  ;  and  the  greatest  agitation  of  the  sea 
being  near  its  surface,  the  basis  of  the  pillar  might  be  a  little  contracted, 
so  as  to  have  the  outline  of  the  lower  part  a  little  convex  outwards,  if  the 
depth  of  the  water  were  considerable.  But  in  the  case  of  a  building  of  stone, 
the  strength  often  depends  as  much  on  the  weight  of  the  materials  as 
on  their  cohesive  power :  and  the  lateral  adhesion,  which  is  materially 
influenced  by  the  weight,  constitutes  a  very  important  part  of  the  strength. 
For  resisting  a  force  which  tends  to  overset  the  building,  the  form  in 
which  the  weight  gives  the  greatest  strength  is  that  of  a  conoid,  or  a  solid 
of  which  the  outline  is  a  parabola,  concave  towards  the  axis  :  and  for  pro- 
curing, by  means  of  the  weight,  a  lateral  adhesion  which  is  everywhere 
proportional  to  the  force,  the  form  must  be  cylindrical.  So  that  in  a 
building  circumstanced  as  we  have  supposed  the  pillar  to  be,  there  ap- 
pears to  be  no  reason  for  making  either  portion  of  the  outline  taken  sepa- 
rately convex  towards  the  axis,  although  the  angular  junction  of  the  two 
portions  of  cones  might  very  properly  be  rounded  off;  and  the  upper 
parts  might  be  a  little  enlarged  if  it  were  desirable  to  reduce  the  thickness 
of  the  walls.  But  the  Eddystone  light  house  is  completely  above  the  level  of 
the  sea,  although  in  stormy  weather  every  part  of  it  is  exposed  to  the  action 
of  the  waves,  the  water  being  sometimes  thrown  up  to  a  much  greater  height 
than  that  of  the  light  house  :  so  that  it  may  be  considered  as  exposed  to 
the  force  of  a  fluid  more  and  more  powerful  as  it  is  nearer  to  the  founda- 
tion ;  and  in  this  point  of  view  its  form  differs  but  little  from  that  which 
the  most  accurate  theory  would  point  out ;  but  it  is  probably  a  little  weaker 
about  the  middle  of  its  height,  or  somewhat  lower,  than  in  any  other  part. 
(Plate  XI.  Fig.  150.) 

A  wall  must  be  reduced  in  thickness  as  it  rises,  for  the  same  reason  as  a 
column  is  diminished  ;  and  if  the  wall  is  a  part  of  a  house,  it  must  Le 
reduced  in  a  still  greater  degree,  since  the  load,  which  is  to  be  supported  by 
*  On  the  Eddystone  Lighthouse,  fol.  Lond.  1791,  PI.  ix. 


ON  ARCHITECTURE  AND  CARPENTRY.  123 

it  at  different  parts  of  its  height,  is  usually  much  varied  by  the  weight  of 
the  floors  and  of  the  contents  of  the  apartments.  But  sometimes  the 
obliquity  of  the  surface  of  the  wall  may  become  inconvenient,  by  promoting 
the  growth  of  moss  and  weeds.  In  building  a  wall,  the  first  precaution 
that  is  required,  is  to  dig  deep  enough  to  ascertain  the  nature  of  the  ground  ; 
the  next,  to  lay  a  sufficiently  extensive  and  firm  foundation  ;  and  it  has 
been  very  properly  recommended  that  where  a  well  is  wanted,  it  should  be 
dug  before  the  foundations  of  the  house  are  laid,  in  order  to  examine  the 
qualities  of  the  different  strata  which  are  to  support  them.  The  disposition 
of  the  stones  or  bricks,  is  not  a  matter  of  indifference  ;  the  strength  is  obvi- 
ously greatest  when  all  the  surfaces  are  either  horizontal  or  vertical ;  for  if 
they  are  oblique,  they  must  have  a  tendency  to  slide  away  laterally,  and  the 
wall  must  be  very  liable  to  crack  :  hence  the  reticulated  walls,  sometimes 
employed  by  the  ancients,  of  which  all  the  joints  were  oblique,  possessed 
but  little  durability.  If  the  materials  are  thrown  together  without  order, 
they  press  on  the  parts  in  contact  with  them  ;  but  occasionally,  as  in  the 
case  of  piers  or  quays,  this  circumstance  may  be  of  some  advantage  in 
opposing  external  pressure  ;  or  at  least  the  effect  of  such  a  pressure  may 
remove  the  inconvenience  which  would  otherwise  arise  from  the  irregularity 
of  the  structure. 

In  some  cases  it  is  necessary  to  unite  the  stones  of  a  building  mechani- 
cally, either  by  cramps  of  iron,  fixed  by  means  of  melted  lead,  or  by  other 
methods,  similar  to  those  which  are  more  usually  employed  in  carpentry. 
Mr.  Smeaton  was  obliged  to  fix  the  stones  of  his  light  house  to  the  rock  and 
to  each  other,  by  dovetail  joints,  and  to  connect  each  horizontal  tier  with 
the  tier  below  it,  by  pins  of  wood  passing  through  the  stones,  with  wedges 
driven  in  at  each  end,  to  make  them  expand,  and  tie  the  stones  fast 
together.  But,  in  general,  it  is  sufficient  to  employ  mortar,  made  of  lime 
or  terras  and  sand,  of  which  the  utility  depends  principally  on  the  firmness 
and  cohesive  strength  that  it  acquires  in  consequence  of  its  chemical  pro- 
perties. Sometimes  the  whole  structure  is  composed  of  a  mass  which  is  at 
first  soft,  but  hardens  as  it  dries  ;  in  this  manner  mud  walls  are  built ;  and 
the  materials  called  pise  are  of  a  similar  nature.  (Plate  XI.  Fig.  151.) 

The  wall  or  column,  when  raised,  must  in  general  help  to  support  a 
single  lintel  or  beam,  an  arch,  a  dome,  or  a  roof  of  carpentry.  The  strength 
of  the  lintel  depends  more  on  the  nature  of  the  substance  than  on  any  art 
employed  in  forming  it,  excepting  the  precaution  to  give  it  as  much  depth 
as  is  convenient,  especially  towards  the  middle,  if  the  depth  be  anywhere 
unequal ;  but  the  construction  of  an  arch  affords  considerable  scope  for  the 
exertion  of  mechanical  science. 

The  simplest  theory  of  the  arch,  supporting  itself  in  equilibrium,  is  that 
of  Dr.  Hooke,*  the  greatest  of  all  philosophical  mechanics.  The  arch, 
when  it  has  only  its  own  weight  to  bear,  may  be  considered  as  the  inversion 
of  a  chain  suspended  at  each  end  ;  for  the  chain  Kangs  in  such  a  form  that 
the  weight  of  each  link  is  held  in  equilibrium  by  the  result  of  the  two  forces 
acting  at  its  extremities  ;  and  these  forces  or  tensions  are  produced,  the  one 

*  Hooke,  De  Potentia  Restitutiva,  1678,  p.  31.  See  Waller's  Life  of  Hpoke, 
prefixed  to  the  edition  of  his  posthumous  Works,  Lond.  1705,  p.  21. 


124  LECTURE  XIV. 

by  the  weight  of  the  portion  of  the  chain  below  the  link,  the  other  by  the 
same  weight  increased  by  that  of  the  link  ;  both  of  them  acting  originally 
in  a  vertical  direction.  Now  supposing  the  chain  inverted,  so  as  to  consti- 
tute an  arch  of  the  same  form  and  weight,  the  relative  situations  of  all  the 
lines,  indicating  the  directions  of  the  forces,  will  remain  the  same,  the 
forces  acting  only  in  contrary  directions,  so  that  they  are  compounded  in  a 
similar  manner,  and  balance  each  other  on  the  same  conditions,  but  with 
this  difference,  that  the  equilibrium  of  the  chain  is  stable,  and  that  of  the 
arch  tottering.  This  property  of  the  equilibrium  renders  an  accurate 
experimental  proof  of  the  proposition  somewhat  difficult ;  but  it  may  be 
shown  that  a  slight  degree  of  friction  is  sufficient  for  retaining  in  equili- 
brium an  arch  formed  by  the  inversion  of  a  chain  of  beads.  The  figure  is 
called  a  catenaria,  when  the  links  are  supposed  to  be  infinitely  small,  and 
the  curvature  is  greatest  at  the  middle  of  the  chain.*  It  is  not  at  all 
necessary  to  the  experiment  that  the  links  of  the  chain  be  equal ;  the  same 
method  may  be  applied  to  the  determination  of  the  form  requisite  for  an 
equilibrium,  whatever  may  be  the  length  or  weight  of  the  constituent  parts 
of  the  arch ;  and  when  the  arch  is  to  be  loaded  unequally  in  different  parts, 
we  may  introduce  this  circumstance  into  the  experiment,  by  suspending 
proportional  weights  from  different  parts  of  the  chain.  Thus  we  may 
employ  wires  or  other  chains  to  represent  the  pressure,  and  adjusting  them 
by  degrees,  till  their  extremities  hang  in  a  given  line,  we  may  find  the  form 
which  will  best  support  the  weight  of  the  materials,  the  upper  surface  or 
extrados  of  the  arch  being  represented  by  the  same  line  in  an  inverted 
position,  while  the  original  chain  shows  the  form  of  the  intrados,  or  of  the 
curve  required  for  the  arch  stones  themselves.  In  common  cases,  the  form 
thus  determined  will  differ  little  from  a  circular  arc,  of  the  extent  of  about 
one  third  of  a  whole  circle,  rising  from  the  abutments  with  an  inclination 
of  30°  to  the  vertical  line,  and  it  never  acquires  a  direction  much  more 
nearly  perpendicular  to  the  horizon.  It  usually  becomes  more  curved  at 
some  distance  below  the  summit,  and  then  again  less  curved.  (Plate  XI. 
Fig.  152... 154.) 

But  the  supposition  of  an  arch  resisting  a  weight  which  acts  only  in  a 
vertical  direction,  is  by  no  means  perfectly  applicable  to  cases  which 
generally  occur  in  practice.  The  pressure  of  loose  stones  and  earth, 
moistened  as  they  frequently  are  by  rain,  is  exerted  very  nearly  in  the  same 
manner  as  the  pressure  of  fluids,  which  act  equally  in  all  directions  :  and 
even  if  they  were  united  into  a  mass,  they  would  constitute  a  kind  of 
wedge,  and  would  thus  produce  a  pressure  of  a  similar  nature,  notwith- 
standing the  precaution  recommended  by  some  authors,  of  making  the 
surfaces  of  the  arch  stones  vertical  and  horizontal  only.  This  precaution 
is,  however,  in  all  respects  unnecessary,  because  the  effect  which  it  is 
intended  to  obviate,  is  productive  of  no  inconvenience,  except  that  of 

*  For  its  properties  see  D.  Gregory,  Ph.  Tr.  xix.  637,  and  xxi.  419.  Clairaut 
on  Catenariae,  Miscellanea,  Berolin,  1743,  vii.  270.  Krafft,  Novi  Com.  Petrop:  v. 
145.  Cantezzani,  Com.  Bon.  vi.  O.  265.  Legendre,  Mem.  de  Paris,  1786,  p.  20. 
Fuss.  N.  A.  Pet.  1794,  xii.  145.  The  elementary  works  of  Poisson,  Traite  de  Me- 
canique,  and  Whewell's  and  Earnshaw's  Mechanics. 


ON  ARCHITECTURE  AND  CARPENTRY.  125 

exercising  the  skill  of  the  architect.  The  effect  of  such  a  pressure  only 
requires  a  greater  curvature  near  the  abutments,  reducing  the  form  nearly 
to  that  of  an  ellipsis,  and  allowing  the  arch  to  rise  at  first  in  a  vertical 
direction. 

A  bridge  must  also  be  so  calculated  as  to  support  itself  without  being  in 
danger  of  falling  by  the  defect  of  the  lateral  adhesion  of  its  parts,  and  in 
order  that  it  may  in  this  respect  be  of  equal  strength  throughout,  its  depth 
at  each  point  must  be  proportional  to  the  wreight  of  the  parts  beyond  it. 
This  property  belongs  to  the  curve  denominated  logarithmic,  the  length 
corresponding  to  the  logarithm  of  the  depth.  If  the  strength  were  af- 
forded by  the  arch  stones  only,  this  condition  might  be  fulfilled  by  giving 
them  the  requisite  thickness,  independently  of  the  general  form  of  the  arch : 
but  the  whole  of  the  materials  employed  in  the  construction  of  the  bridge, 
must  be  considered  as  adding  to  the  strength,  and  the  magnitude  of  the 
adhesion  as  depending  in  great  measure  on  the  general  outline. 

We  must  examine  in  the  next  place  what  is  the  most  advantageous  form 
for  supporting  any  weight  which  may  occasionally  be  placed  on  the  bridge, 
in  particular  at  its  weakest  part,  which  is  usually  the  middle.  Supposing 
the  depth  at  the  summit  of  the  arch  and  at  the  abutments  to  be  given,  it 
may  be  reduced  considerably  in  the  intermediate  parts,  without  impairing 
the  strength,  and  the  outline  may  be  composed  of  parabolic  arcs,  having 
their  convexity  turned  towards  each  other.  This  remark  also  would  be 
only  applicable  to  the  arch  stones,  if  they  afforded  the  whole  strength  of 
the  bridge,  but  it  must  be  extended  in  some  measure  to  the  whole  of  the 
materials  forming  it. 

If  therefore  we  combine  together  the  curve  best  calculated  for  resisting 
the  pressure  of  a  fluid,  which  is  nearly  elliptical,  the  logarithmic,  and  the 
parabolic  curves,  allowing  to  each  its  due  proportion  of  influence,  we  may 
estimate,  from  the  comparison,  which  is  the  fittest  form  for  an  arch  in- 
tended to  support  a  road.  And  in  general,  whether  the  road  be  horizontal 
or  a  little  inclined,  we  may  infer  that  an  ellipsis,  not  differing  much  from 
a  circle,  is  the  best  calculated  to  comply  as  much  as  possible  with  all  the 
conditions.  (Plate  XI.  Fig.  155.) 

The  tier  of  bricks  cut  obliquely,  which  is  usually  placed  over  a  window 
or  a  door,  is  a  real  arch,  but  so  flat  as  to  allow  the  apparent  outline  to  be 
horizontal.  Mr.  Coulomb  observes,  that  the  greatest  strength  is  obtained 
by  causing  all  the  joints  to  tend  to  a  single  point :  *  but  little  dependence 
can  be  placed  on  so  flat  an  arch,  since  it  produces  a  lateral  thrust  which 
may  easily  overpower  the  resistance  of  the  wall.  For  the  horizontal  force 
required  to  support  each  end  of  any  arch,  is  equal  to  the  weight  of  a 
quantity  of  the  materials  which  are  supported  by  its  summit,  supposed  to 
be  continued,  of  their  actual  depth,  to  the  length  of  a  semidiameter  of  the 
circle  of  which  the  summit  of  the  arch  is  a  portion.  This  simple  calcu- 
lation will  enable  an  architect  to  avoid  such  accidents,  as  have  too  often 
happened  to  bridges  for  want  of  sufficient  firmness  in  the  abutments.  The 
equilibrium  of  a  bridge,  so  far  as  it  depends  only  on  the  form  of  the  arch, 
is  naturally  tottering,  and  the  smallest  force  which  is  capable  of  deranging 
*  Theorie  des  Machines  Simples,  4to,  1821,  p.  355  (reprint}. 


126  LECTURE  XIV. 

it  may  completely  destroy  the  structure ;  but  when  the  stones  or  blocks 
composing  it  have  flat  surfaces  in  contact  with  each  other,  it  is  necessary 
that  the  line  expressing  the  direction  of  the  pressure  be  so  much  disturbed, 
as  to  exceed  at  some  part  the  limits  of  these  surfaces,  before  the  blocks  can 
be  displaced.  When  this  curve,  indicating  the  general  pressure  which 
results  from  the  effect  of  a  disturbing  force,  combined  with  the  original 
thrust,  becomes  more  remote  from  the  centre  of  the  blocks  than  one  sixth 
of  their  depth,  the  joints  will  begin  to  open  on  the  convex  side,  but  the 
arch  may  still  stand,  while  the  curve  remains  within  the  limits  of  the 
blocks. 

It  is  desirable  that  the  piers  of  bridges  should  be  so  firm,  as  to  be 
able  not  only  to  support  the  weight  of  half  of  each  adjoining  arch,  but  also 
to  sustain,  in  case  of  the  failure  of  one  of  those  arches,  the  horizontal 
thrust  of  the  other  ;  and  the  same  condition  is  obviously  necessary  for  the 
stability  of  walls  of  any  kind  which  support  an  arched  or  vaulted  roof, 
wherever  there  is  no  opportunity  of  assisting  the  strength  by  ties  or  chains 
of  any  kind.  There  are  two  ways  in  which  such  a  pier  or  wall  may  give 
way  :  it  may  either  be  overset,  or  caused  to  slide  away  horizontally  ;  but 
since  the  friction  or  adhesion  which  resists  the  horizontal  motion  is  usuallv 
greater  than  one  third  of  the  pressure,  it  seldom  happens  that  the  whole 
thrust  of  the  arch  is  so  oblique  as  not  to  produce  a  sufficient  vertical  pres- 
sure for  securing  the  stability  in  this  respect ;  and  it  is  only  necessary  to 
make  the  pier  heavy  enough  to  resist  the  force  which  tends  to  overset  it. 
It  is  not,  however,  the  weight  of  the  pier  only,  but  that  of  the  half  of  the 
arch  which  rests  on  it,  that  resists  any  effort  to  overset  it,  and  in  order  that 
the  pier  may  stand,  the  sum  of  these  weights,  acting  on  the  end  of  a  lever 
equal  to  half  the  thickness  of  the  pier,  must  be  more  than  equivalent  to  the 
horizontal  thrust,  acting  on  the  whole  height  of  the  pier.  The  pier  may 
also  be  simply  considered  as  forming  a  continuation  of  the  arch,  and  the 
stability  will  be  preserved  as  long  as  the  curve,  indicating  the  direction  of 
the  pressure,  remains  within  its  substance. 

The  arches  of  Black  Friars  bridge  are  of  an  oval  form,  composed  of  cir- 
cular arcs,  and  differing  but  little  from  ellipses ;  the  arch  stones  are  so 
large  that  the  pressure  in  any  direction  might  be  very  greatly  increased 
without  causing  the  general  result  to  exceed  the  limits  of  their  magnitude, 
or  even  to  approach  very  near  to  their  surfaces.  (Plate  XII.  Fig.  156.) 

The  construction  of  a  dome  is  less  difficult  than  that  of  an  arch,  since 
the  tendency  of  each  part  to  fall  is  counteracted,  not  only  by  the  pressure 
of  the  parts  above  and  below,  but  also  by  the  resistance  of  those  which  are 
situated  on  each  side.  A  dome  may  therefore  be  erected  without  any 
temporary  support  like  the  centre  which  is  required  for  the  construction 
of  an  arch,  and  it  may  at  last  be  left  open  at  the  summit,  without  standing 
in  need  of  a  keystone,  since  the  pressure  of  the  lower  parts  is  sufficiently 
resisted,  by  the  collateral  parts  of  the  same  horizontal  tier,  to  prevent  the 
possibility  of  their  falling  in,  or  of  their  forcing  out  the  upper  parts.  The 
weight  of  the  dome  may  however  force  out  its  lower  parts,  if  it  rises  irt  a 
direction  too  nearly  vertical;  and  supposing  its  form  spherical,  and  its 
thickness  equable,  it  will  require  to  be  confined  by  a  hoop  or  chain  as  soon 


ON  ARCHITECTURE  AND  CARPENTRY.  127 

as  the  span  becomes  eleven  fourteenths  of  the  whole  diameter.  But  if  the 
thickness  of  the  dome  be  diminished  as  it  rises,  it  will  not  require  to  be 
bound  so  high  :  thus,  if  the  increase  of  thickness  in  descending  begin  at 
about  30  degrees  from  the  summit,  and  be  continued  until,  at  about  60 
degrees,  the  dome  becomes  a  little  more  than  twice  as  thick  as  at  first,  the 
equilibrium  will  be  so  far  secure ;  and  at  this  distance  it  would  be  proper 
to  employ  either  a  chain  or  some  external  pressure,  to  preserve  the  sta- 
bility, since  the  weight  itself  would  require  to  be  increased  without  limit, 
if  it  were  the  only  source  of  pressure  on  the  lower  parts.  (Plate  XII. 
Fig.  157.) 

The  dome  of  St.  Paul's  cathedral  is  elliptical,  and  is  built  of  wood,  and 
confined  by  strong  chains,  consisting  of  iron  bars  ;  that  of  the  Pantheon  at 
Rome  is  nearly  circular,  and  its  lower  parts  are  so  much  thicker  than  its 
upper  parts,  as  to  afford  sufficient  resistance  to  their  pressure  :  they  are 
supported  by  walls  of  great  thickness,  and  furnished  with  many  projections 
which  answer  the  purpose  of  abutments  and  buttresses.  (Plate  XII.  Fig. 
158, 159.) 

A  knowledge  of  the  parts  and  proportions  usually  assigned  to  columns 
and  to  buildings  in  general,  and  of  their  technical  names  and  divisions, 
belongs  rather  to  the  subject  of  ornamental  than  to  that  of  useful  architecture ; 
and  the  consideration  of  symmetry  and  elegance  is  in  great  measure  foreign 
to  that  of  the  mechanical  properties  of  bodies,  which  it  is  our  present 
business  to  investigate.  The  five  orders  of  ancient  architecture  are  found 
to  differ  considerably  in  their  proportions,  in  the  different  remains  of 
Greek  and  Roman  edifices  ;  but  there  always  remain  some  characteristic 
distinctions  :  the  Tuscan  is  known  by  its  strength  and  simplicity,  without 
any  peculiar  ornament ;  the  Doric  by  its  triglyphs,  or  triangular  grooves, 
above  each  column,  imagined  to  represent  the  ends  of  beams  ;  the  Ionic  by 
the  large  volutes,  and  the  Corinthian  by  the  foliage,  respectively  envelop- 
ing their  capitals  ;  and  the  Composite  usually  by  the  combination  of  both 
these  characters  ;  each  order  being  lighter  than  the  preceding,  and  being 
sometimes  employed  with  it  in  the  upper  parts  of  the  same  building.  In 
general,  the  length  of  the  Tuscan  column,  with  its  capital,  is  equal  to  about 
seven  diameters  of  the  base,  that  of  the  Doric  eight,  of  the  Ionic  nine, 
and  of  the  Corinthian  and  Composite  ten  diameters.  (Plate  XII.  Fig. 
160... 164.) 

The  Gothic  architects  appear  to  have  been  superior  to  the  Greeks  in  the 
mechanical  arrangement  of  the  parts  of  their  edifices,  so  as  to  produce  the 
most  advantageous  effect  in  preserving  the  general  equilibrium.  They 
made  every  essential  member  of  their  buildings  a  constituent  part  of  their 
system  of  ornament,  and  even  those  embellishments,  which,  by  a  super- 
ficial observer,  might  be  deemed  useless  or  prejudicial,  are  frequently  cal- 
culated, either  by  their  strength  or  by  their  weight,  to  serve  some  bene- 
ficial purposes.  The  pointed  arch  is  not  in  all  cases  well  calculated  for 
equilibrium,  but  when  it  has  a  pillar  resting  on  its  summit,  it  is  exceedingly 
strong.  The  most  celebrated  of  modern  architects  have  sometimes  been 
less  successful  than  those  of  the  middle  ages  ;  and  for  want  of  paying  suf- 
ficient attention  to  mechanical  principles,  have  committed  such  errors  in 


128  LECTURE  XIV. 

their  attempts  to  procure  an  equilibrium,  as  have  been  followed  by  the 
most  mischievous  consequences.  Examples  of  this  might  be  pointed  out  in 
the  bridges  of  our  own  country  and  the  churches  of  others  ;  but  if  we  are 
masters  of  the  true  theory  of  pressure,  we  shall  be  able  to  avoid  similar 
errors,  without  examining  the  particular  circumstances  which  have  oc- 
casioned these  accidents.  (Plate  XII.  Fig.  165.) 

The  principles  of  equilibrium,  which  are  employed  in  architecture,  are 
equally  applicable  to  many  cases  in  carpentry  ;  and  where  the  work  is 
principally  calculated  to  withstand  a  thrust,  there  is  little  difference  in 
the  operation  of  the  forces  concerned  ;  but  where  a  tie  is  introduced,  that 
is,  a  piece  which  resists  principally  by  its  cohesive  strength,  the  parts  often 
require  to  be  arranged  in  a  different  manner.  The  general  principle,  that 
three  forces,  in  order  to  retain  each  other  in  equilibrium,  must  be  propor- 
tional to  the  sides  of  a  triangle  corresponding  to  their  directions,  is  suf- 
ficient for  determining  the  distribution  of  pressure  in  almost  all  cases  that 
can  occur.  The  conclusions  which  have  been  drawn  from  this  principle, 
and  from  other  similar  considerations,  respecting  the  strength  of  materials, 
will  also  be  of  great  use  in  directing  us  how  to  determine  the  best  forms  for 
beams,  rafters,  and  timbers  of  all  kinds,  and  how  to  arrange  and  connect 
them  in  the  best  manner  with  each  other. 

The  employment  of  the  cohesive  strength  of  materials  in  carpentry  in- 
troduces a  difficulty  which  scarcely  exists  in  architecture.  Two  blocks, 
placed  on  each  other,  resist  the  force  of  a  weight  compressing  them,  as  ef- 
fectually as  if  they  formed  but  one  piece  :  but  they  have  no  sensible  cohe- 
sion to  enable  them  to  withstand  a  force  tending  to  separate  them,  and  if 
they  are  required  to  co-operate  by  their  cohesive  strength,  some  mode  of 
uniting  them  must  be  found.  For  this  purpose,  it  is  generally  necessary  to 
sacrifice  a  considerable  portion  of  the  strength  of  the  materials  employed. 
The  most  usual  mode  is  to  place  the  ends  of  the  pieces  side  by  side,  first 
reducing  their  dimensions,  where  a  regular  outline  is  required  ;  and  to 
procure  a  firm  adhesion  between  them  by  means  of  external  pressure,  or  to 
employ  the  natural  adhesion  of  some  parts  which  are  made  to  project  be- 
yond the  rest  in  each  piece,  and  receive  in  their  interstices  the  correspond- 
ing projections  of  the  other  piece. 

Where  the  adhesion  is  produced  by  external  pressure  only,  it  is  of  ad- 
vantage to  subdivide  the  joints  into  a  considerable  number  of  parts,  as  is 
usually  done  in  the  masts  of  ships,  and  to  make  the  junction  of  any  two 
pieces,  following  each  other  in  the  same  line,  as  distant  as  possible  from 
any  other  junction ;  for  in  this  manner,  the  loss  of  strength  may  be  di- 
minished almost  without  limit,  provided  that  the  distance  between  the 
joints  be  great  enough  to  afford  a  firm  adhesion  to  each  part.  The  junction 
may  also  be  formed  by  an  oblique  line  ;  but  the  obliquity  must  be  so  great 
that  any  lateral  pressure  may  increase  the  stability  of  the  wedge,  the  length 
being  in  a  greater  proportion  to  the  depth  than  the  pressure  to  the  adhesion 
that  it  occasions  ;  and  the  pieces  must  be  pressed  together  very  forcibly  by 
means  of  hoops  or  bolts.  (Plate  XIII.  Fig.  166... 168.) 

Where  the  natural  adhesion  of  some  projecting  parts  in  each  piece  is  em- 
ployed, the  projections  must  be  sufficiently  long  to  secure  their  strength, 


ON  ARCHITECTURE  AND  CARPENTRY.  129 

and  they  must  be  as  little  prominent  as  possible,  partly  because  the  con- 
tiguous piece  must  be  excavated  for  their  reception,  and  partly  because 
their  strength  is  diminished  when  they  project  more  than  one  sixth  of  their 
length.  A  beam  united  to  another  in  this  manner  is  said  to  be  scarfed. 
(Plate  XIII.  Fig.  169.) 

In  order  to  preserve  the  strength  of  a  compound  beam,  intended  to  re- 
sist a  transverse  action  in  a  particular  direction,  it  is  necessary  to  avoid,  as 
much  as  possible,  reducing  the  depth  of  the  beam  in  that  direction,  and  to 
secure  the  union  with  the  greatest  care  on  the  convex  side  of  the  beam, 
which  is  stretched  by  the  operation  of  the  force.  Where  no  inconvenience 
can  result  from  the  projection  of  a  piece  on  one  side,  it  is  easy  to  preserve 
the  strength  unimpaired,  by  splicing  or  fishing  it  on  the  convex  side  ;  and 
if  the  depth  of  the  piece  added  be  only  half  as  great  as  that  of  the  original 
beam,  the  strength  will  be  somewkat  increased  by  the  operation,  supposing 
the  two  ends  to  meet  each  other  without  any  connection.  Such  pieces  re- 
quire, however,  to  be  firmly  united,  either  by  pins  passing  through  them, 
or  by  blocks  or  joggles  let  in  to  a  certain  depth,  in  order  to  prevent  their 
sliding  on  each  other  ;  and  this  mode  of  union  is  stronger  than  scarfing 
them,  because  it  does  not  diminish  the  depth.  (Plate  XIII.  Fig.  170, 171.) 

Where  the  pieces  to  be  connected  together  are  in  different  directions,  the 
end  of  one  of  them  is  usually  reduced  in  its  size,  and  becomes  a  tenon, 
while  a  mortise  is  cut  in  the  other  for  its  reception,  and  the  joint  is  also 
often  secured  still  more  firmly  by  a  strap  of  iron.  If  a  joist  be  let  into  a 
beam,  at  its  upper  edge,  and  made  very  tight  by  wedges,  the  strength  of 
the  beam  will  not  be  materially  diminished  ;  but  the  vicissitudes  of  mois- 
ture and  dryness  may  very  much  impair  the  firmness  of  the  union,  and 
the  end  of  the  joist  may  fail  in  dry  weather  to  afford  sufficient  resistance 
to  the  flexure  of  the  beam  :  so  that  in  some  cases  it  might  be  more  ad- 
visable to  cut  the  mortise  near  the  middle  of  the  depth  of  the  beam.  If 
two  pieces  meet  obliquely,  and  one  of  them  exerts  a  thrust  against  the 
other,  the  simplest  mode  of  opposing  this  thrust  is  to  bind  them  toge- 
ther by  a  strap  of  iron  fixed  to  the  second  piece ;  this  strap  renders  it 
impossible  for  the  first  to  advance  without  having  its  extremity  crushed  ; 
it  is  also  common  to  make  a  mortise  in  the  second  piece,  a  part  of  which 
serves  as  an  abutment  for  the  first ;  and  for  this  purpose  the  piece  must  be 
continued  far  enough  beyond  the  abutment  to  give  the  projection  sufficient 
force  of  adhesion,  a  condition  which  is  the  more  easily  fulfilled  when  the 
action  of  the  strap  produces  a  pressure  on  it.  The  assistance  of  a  strap 
is  still  more  indispensable  where  the  pieces  are  perpendicular  to  each  other, 
and  the  force  tends  to  draw  one  of  them  away  from  the  other  ;  in  this  case 
the  mortise  may  be  made  a  little  wider  at  the  remoter  part,  and  the  end  of 
the  tenon  may  be  made  to  fit  it  by  driving  in  wedges,  in  the  same  manner 
as  Mr.  Smeaton  united  his  blocks  of  stone  ;  but,  a  large  mortise  would 
weaken  the  beam  too  much,  and  a  strong  strap  or  hoop  is  usually  required 
^additional  security.  Such  a  strap  ought  always  to  be  as  straight  as 
possible,  so  as  to  act  only  in  the  direction  of  the  force  to  be  resisted  :  it 
has  been  too  customary  to  accommodate  the  strap  to  the  form  of  the  beams,  or 
to  make  it  deviate  in  other  ways  from  a  right  line  :  but  wherever  a  strap 


130  LECTURE  XIV. 

is  bent  in  any  direction,  to  a  distance  from  a  right  line  equal  only  to  its 
depth  in  that  direction,  its  strength  is  so  reduced,  as  not  to  exceed  one 
seventh  of  what  it  would  have  been  if  it  had  remained  straight.  (Plate  XIII. 
Fig.  172.. .174.) 

It  is  equally  necessary  in  all  other  cases  which  occur  in  carpentry,  to 
avoid  as  much  as  possible  a  transverse  strain,  the  disadvantage  of  which  is 
obvious  from  the  great  inferiority  of  the  strength  of  any  substance,  resisting 
a  transverse  force,  to  its  primitive  cohesive  or  repulsive  strength.  For 
similar  reasons  it  is  proper  to  avoid  employing  a  very  open  angle  at  a  point 
where  a  load  is  supported,  the  great  obliquity  of  the  two  pieces  forming  the 
angle  requiring  them  to  exert  a  great  force  in  order  to  oppose  a  much 
smaller  one.  Allowance  must  also  be  made  for  the  contraction  of  the 
timber,  and  care  must  be  taken  that  it  do  not  so  alter  the  arrangement  of 
the  parts,  as  to  bring  a  disproportionate  strain  on  a  point  not  calculated  to 
support  it.  If  the  two  pieces  forming  an  obtuse  angle  consisted,  either 
wholly  or  partly,  of  wood  cut  across  the  grain,  and  the  piece  joining  their 
extremities  were  cut  in  the  usual  manner,  the  oblique  pieces  would  contract 
considerably  more  as  they  became  drier,  and  the  angle  would  become  more 
obtuse,  so  that  the  strain,  produced  by  a  given  weight,  would  be  greater 
than  in  the  original  state  of  the  triangle.  Sometimes  the  work  is  liable  to 
be  deranged  by  the  operation  of  a  lateral  force,  which  may  have  appeared 
too  trifling  to  produce  any  considerable  effect,  but  which  may  still  destroy 
the  greater  part  of  the  strength,  by  causing  the  resistances  to  deviate  from 
the  plane  of  the  forces  which  they  are  intended  to  oppose. 

The  framing  of  a  roof  is  one  of  the  most  common  and  most  important 
subjects  for  the  employment  of  the  theory  of  carpentry.  If  the  rafters 
were  simply  to  abut  on  the  walls,  they  would  force  them  outwards  ;  a  tie 
beam  is  therefore  necessary,  to  counteract  the  thrust.  In  order  to  enable 
the  tie  beam  to  support  a  weight,  a  king  post  is  suspended  from  the  rafters  ; 
and  frequently  braces  are  again  erected  from  the  bottom  of  the  king  post, 
to  support  the  middle  of  the  rafters.  Sometimes  a  flat  or  less  inclined 
portion  is  placed  in  the  middle,  forming  a  kirb  or  mansard  roof,  somewhat 
resembling  an  arch  ;  this  form  has  the  advantage,  when  it  is  properly  propor- 
tioned, of  lessening  the  transverse  strain  on  the  rafters  by  making  them 
shorter ;  but  this  purpose  is  answered  equally  well  by  the  addition  of  the 
braces  which  have  been  already  mentioned.  A  kirb  roof  affords,  however,  a 
greater  space  within,  than  a  plain  roof  of  the  same  height,  and  produces  also 
somewhat  less  strain  on  the  tie  beam  or  on  the  abutments  :  the  tie  beam  may 
be  suspended  from  it  by  a  king  post  and  two  queen  posts,  descending  perpen- 
dicularly from  the  joints  ;  and  the  place  of  the  king  post  may  be  supplied 
by  a  cross  beam  uniting  the  heads  of  the  queen  posts  and  keeping  them  at 
a  proper  distance ;  this  beam  may  also  be  suspended  by  a  shorter  king- 
post from  the  summit.  Such  a  roof  appears  to  be  more  advantageous 
than  it  has  been  commonly  supposed.  (Plate  XIII.  Fig.  175. ..177.) 

The  angle  of  inclination  of  a  roof  to  the  horizon  usually  varies  in 
different  climates  :  in  Italy  the  height  is  generally  less  than  one  fourtli  of 
the  breadth  ;  in  England  it  was  formerly  three  fourths,  but  it  now  com- 
monly approaches  much  more  to  the  Italian  proportion.  In  northern 


ON  ARCHITECTURE  AND  CARPENTRY.  131 

climates,  a  steep  roof  is  required  on  account  of  falls  of  snow,  which 
greatly  increase  the  lateral  thrust  of  the  rafters  ;  for  the  horizontal  force 
exerted  by  a  roof  is  always  proportional  to  the  length  of  a  line  perpendi- 
cular to  the  rafter,  descending  from  its  extremity  till  it  meets  another 
similar  line  drawn  from  the  opposite  rafter  ;  and  this  perpendicular  is 
obviously  much  increased  when  the  roof  becomes  very  flat.  But  for  bear- 
ing the  transverse  strain  which  tends  to  break  the  rafters  themselves,  a  low 
roof  is  stronger  than  a  high  one,  supposing  the  number  of  braces  and 
queen  posts  equal  on  both ;  for  if  we  have  to  support  a  given  weight  by  a 
beam  or  rafter,  whether  it  be  placed  in  the  middle,  or  equally  divided 
throughout  the  length,  we  neither  gain  nor  lose  force  by  lengthening 
the  beam  and  raising  it  higher,  while  the  horizontal  span  continues  the 
same,  since  the  obliquity  lessens  the  effect  of  the  weight  precisely  in  the 
same  ratio  that  the  length  of  the  beam  diminishes  its  strength ;  but  by 
lengthening  the  beam  we  also  add  to  the  weight  which  is  to  be  supported, 
and  we  thus  diminish  the  strength  of  the  roof.  It  must  be  observed,  in 
calculating  the  strength  of  a  rafter,  that  the  slight  flexure  produced  by 
the  transverse  strain,  has  a  material  effect  in  diminishing  its  strength  in 
resisting  a  longitudinal  force  ;  and  this  diminution  must  be  determined 
according  to  the  principles  that  have  been  laid  down  respecting  the  equili- 
brium of  elastic  substances. 

Wooden  bridges,  and  the  temporary  centres  on  which  arches  of  stone 
are  supported  during  their  construction,  depend  nearly  on  the  same  prin- 
ciples as  roofs :  the  external  parts  usually  support  a  thrust,  and  the 
internal  act  as  ties  ;  but  the  abutments  are  generally  capable  of  withstand- 
ing a  horizontal  thrust  without  inconvenience,  so  that  by  their  assistance 
the  strain  on  the  ties  is  considerably  diminished.  Great  strength  may 
also  be  obtained,  where  it  is  practicable  to  support  each  part  of  the  centre 
by  two  beams,  in  the  direction  of  chords,  bearing  immediately  on  the  abut- 
ments. (Plate  XIV.  Fig.  178,  179.) 

The  various  articles  of  household  furniture  belong  to  subordinate 
branches  of  carpentry,  but  their  form  is  in  general  more  accommodated  to 
convenience  and  elegance  than  to  strength  and  durability.  Yet,  even  in 
making  a  chair,  there  is  room  for  error  and  for  improvement ;  the  same 
principles  that  direct  us  in  framing  a  roof  are  capable  of  application  here  ; 
but  if  they  were  implicitly  followed,  they  would  lead  us  to  the  employ- 
ment of  bars  crossing  each  other  in  an  inelegant  manner.  Doors,  gates, 
locks,  and  hinges,  are  either  parts  of  the  carpenter's  employment,  or 
appendages  to  his  works  ;  and  it  is  possible  that,  by  attentive  considera- 
tion, improvements  might  be  made  in  all  of  them.  Mr.  Parker  has  de- 
voted much  time  and  labour  to  the  subject  of  gates,  with  their  hinges  and 
fastenings,  and  has  presented  to  the  Royal  Institution  a  very  useful  col- 
lection of  models,  which  show  the  result  of  his  investigations.* 

*  Parker  on  Gates,  Lond.  1801,  Rep.  of  Arts,  ii.  II.  50. 


K2 


132  LECTURE  XV. 

LECT.  XIV.— ADDITIONAL  AUTHORITIES. 

Architecture. — Perrault's  Vitruvius,  fol.  Par.  1673.  Newton's  do.  2  vols.  fol. 
1772.  Hall's  Essay,  4to,  1813.  Rickman's  Gothic  Architecture,  1825.  Willis 
on  the  Architecture  of  the  Middle  Ages,  Camb.  1835.  Britton's  Dictionary  of  Archi- 
tecture, 1830-8.  Hope's  Essay,  2  vols.  1835.  Pugin's  various  works. 

Strongest  forms  of  Columns  and  Walls. — Euler  on  the  Strength  of  Columns, 
Hist,  et  Mem.  de  Berlin,  1757,  p.  252.  Acta  Petr.  ii.  I.  121,  146,  163.  Belidor, 
Architecture  Hydraulique,  ii.  I.  420.  Coulomb,  Mem.  des  Savans  Etrangers,  vii. 
Theorie  des  Mach.  Simples,  1821.  Prony  sur  la  Poussee  des  Terres,  4to,  Par. 
1802.  Prony  sur  les  Murs  de  Revetement,  4to,  1802. 

Practical  Architecture. — Rondelet,  L'Art  de  Batir,  3  vols.  4to.  Par.  1804.  Bor- 
gnis,  Traite  Elementaire  de  Construction  appliquee  &  1'Architecture  Civile,  4to,  Par. 
1823.  Chambers's  Civil  Architecture,  by  Gwilt,  2  vols.  1825.  Bullet,  Nouvelle 
Architecture  Pratique,  par  Jay,  2  vols.  1825.  Navier  sur  1'Application  de  la  Me- 
canique  a  1'Etablissement  des  Constructions,  &c.  1833.  Hosking  on  Architecture 
and  Building,  from  Encyc.  Brit.  4to,  1835.  Nicholson's  Principles  and  Practice  of 
Architecture,  3  vols.  1836. 

Carpentry  in  general. — Fuss  on  the  Strains  of  Framed  Carpentry,  Acta  Petr. 
1778,  ii.  I.  194.  Encyclopedic  Methodique,  Arts  et  Metiers,  art.  Charpentier. 
Robison's  Mech.  Phil.  Tredgold's  Principles  of  Carpentry,  1820.  Nicholson's 
Mechanic's  Companion,  1824.  Carpenter's  Guide,  4to,  1828. 

Arches,  Domes,  and  Bridges. — Lahire  on  Arches,  &c.  Hist,  et  Mem.  de  Paris, 
1702,  p.  94,  H.  119;  1712,  p.  69,  H.  74.  Couplet  on  the  Thrust  of  Arches,  do. 
1729,  p.  79  ;  H.  75  ;  1730,  p.  117,  H.  107.  Labelye  on  Westminster  Bridge,  1739. 
Euler  on  the  Strength  of  a  Model,  Nov.  Com.  Petr.  xx.  271.  Belidor,  Arch. 
Hydr.  ii.  II.  415.  Gauthey,  Construction  des  Fonts.  Peronnet  sur  les  Fonts  de 
Neuilly,  d'Orleans,  &c.  fol.  1782-8.  Berard,  Theorie  de  1'Equilibre  des  Voutes, 
4to,  Par.  1810.  Wiebekings'  Wasserbaukunst,  1812.  Ware,  Tracts  on  Vaults  and 
Bridges,  1822.  Barres,  Nouveau  Systeme  des  Fonts  a  Grandes  Portees,  4to,  Paris, 
1827.  Navier,  Memoires  sur  les  Fonts  Suspendus,  4to,  Par.  Belidor,  Science  des 
Ingenieurs,  4to,  Paris,  1830.  (Navier's  Ed.) 

The  student  is  particularly  referred  to  Robison's  Mechanical  Philosophy,  vol.  i. 
p.  369  to  the  end,  for  details  on  the  subjects  discussed  in  this  Lecture. 


LECTURE   XV. 


ON   MACHINERY. 

HAVING  taken  a  general  view  of  those  branches  of  practical  mechanics 
in  which  forces  are  to  be  resisted,  we  are  next  to  consider  the  modifications 
of  forces  and  of  motions  ;  and  in  the  first  place,  the  modes  of  applying 
forces,  of  changing  their  direction  and  intensity,  and  of  communicating 
them  to  different  parts  of  our  machines  by  the  intervention  of  rods,  joints, 
cranks,  wheelwork,  ropes,  or  other  flexible  substances  ;  in  the  second  place, 
the  structure  of  these  substances,  and  the  methods  by  which  the  union  of 
flexible  fibres  in  general  may  be  effected  ;  and  in  the  third  place,  the  regu- 
lation and  equalisation  of  motion,  by  means  of  clocks  and  watches. 

The  modes  of  applying  mechanical  forces  are  almost  as  various  as  .the 
machines  that  are  constructed  and  the  purposes  for  which  they  are  em- 
ployed :  but  in  general,  the  strength  of  men  is  applied  by  means  of  levers 
or  winches,  or  by  walking  wheels  which  slide  beneath  them  as  they  attempt 


ON  MACHINERY.  133* 

to  ascend  ;  and  that  of  other  animals,  by  a  horizontal  arm  projecting  from 
a  vertical  axis  to  which  they  are  harnessed,  and  sometimes  also  by  causing 
them  to  walk  on  or  in  a  moveable  wheel.  Many  of  these  arrangements 
may  however  be  very  conveniently  considered  as  belonging  to  the  particular 
objects  for  which  each  machine  is  constructed,  especially  to  the  modes  of 
raising  weights  by  cranes,  and  of  grinding  substances  by  mills. 

When  motion  is  simply  communicated  to  a  substance  placed  before  the 
moving  body,  such  materials  must  be  employed  as  are  capable  of  exerting 
a  repulsive  force  or  a  thrust ;  and  these  are  generally  of  the  same  kind  as 
are  sometimes  concerned  in  the  operations  of  architecture,  but  more  com- 
monly in  those  of  carpentry,  particularly  metal  and  wood.  But  when  the 
body  to  be  moved  is  behind  the  moving  power,  and  is  pulled  along  by  it, 
chains  or  ropes  are  sometimes  more  convenient.  In  the  union  of  wood  for 
moveable  machinery,  it  is  generally  advisable  to  avoid  employing  pins  or 
bolts  of  metal ;  for  these,  by  their  superior  weight  and  hardness,  sometimes 
injure  the  wood  in  contact  with  them,  and  become  loose. 

When  the  direction  of  the  motion  communicated  is  also  to  be  changed, 
levers  or  cranks  may  be  employed,  united  by  joints  or  hinges  of  various 
kinds.  Sometimes  a  long  series  of  connected  rods  is  suspended  by  other 
rods  or  chains,  so  as  to  convey  the  effect  of  the  force  to  a  considerable  dis- 
tance ;  in  this  case  the  motion  is  generally  alternate,  when,  for  example, 
pumps  are  worked  by  means  of  a  waterwheel  at  a  distance  from  the  shaft 
in  which  the  pumps  are  placed.  In  this  arrangement,  there  is  no  necessary 
loss  on  account  of  the  alternation  of  the  motion  of  the  rods  ;  for  if  they  are 
suspended  at  equal  distances  from  a  number  of  fixed  points,  they  will  move 
backwards  and  forwards  in  the  manner  of  a  single  pendulum  ;  but  the 
magnitude  of  the  friction  is  the  principal  inconvenience  produced  by  the 
weight  of  the  series.  Where  a  lever  is  employed  for  changing  the  direction 
of  a  great  force,  its  strength  may  be  increased  by  the  addition  of  a  frame 
projecting  in  the  direction  of  its  depth;  and  if  the  lever  is  bent,  a  cross 
piece  uniting  its  arms  is  still  more  requisite.  (Plate  XIV.  Fig.  180... 182.) 

For  the  communication  of  a  rotatory  motion,  Dr.  Hooke's  universal  joint* 
is  sometimes  of  use,  especially  when  the  inclination  is  not  required  to 
be  materially  changed ;  but  if  the  obliquity  is  great,  the  rotation  is  not 
communicated  equably  to  the  new  axis  at  all  points  of  its  revolution.  This 
joint  is  formed  by  a  cross,  making  the  diameters  of  two  semicircles,  one  of 
which  is  fixed  at  the  end  of  each  axis.  (Plate  XIV.  Fig.  183.) 

The  best  mode  of  connecting  a  rotatory  motion  with  an  alternate  one 
is,  in  all  common  cases,  to  employ  a  crank,  acting  on  one  end  of  a  long  rod 
which  has  a  joint  at  the  other.  If  the  rotatory  motion  of  the  crank  be 
equable,  the  progressive  motion  of  the  rod  will  be  gradually  accelerated  and 
retarded,  and  for  a  considerable  part  of  the  revoluion  the  force  exerted  will 
be  nearly  uniform  :  but  if  we  attempted  to  communicate  at  once  to  the  rod 
its  whole  velocity  in  each  direction,  as  has  sometimes  been  done  by  inclined 
planes,  or  by  wheelwork,  the  motion  would  become  extremely  irregular, 

*  Hooke,  Animadversions  on  Hevelius'  Machina  Coelestis,  p.  73,  4to,  Lond.  1674  ; 
and  a  Description  of  Helioscopes  and  other  Instruments,  4to,  Lond,  1676,  p.  14. 


134  LECTURE  XV. 

and  the  machinery  would  be  destroyed  by  the  strain.  (Plate  XIV. 
Fig.  184.) 

On  the  other  hand  it  must  be  observed  that  the  force  applied  to  a  ma- 
chine may,  in  general,  be  divided  into  two  portions  ;  the  one  employed  in 
opposing  another  force,  so  as  to  produce  equilibrium  only,  the  other  in 
generating  momentum.  With  respect  to  the  first  portion,  a  single  crank 
has  the  inconvenience  of  changing  continually  the  mechanical  advantage  of 
the  machine  ;  with  respect  to  the  second,  its  motion  in  the  second  quarter 
of  its  revolution  is  accelerated,  instead  of  being  retarded,  by  the  inertia 
which  this  portion  of  the  force  is  intended  to  overcome  :  and  from  a  com- 
bination of  both  these  causes,  the  motion  must  necessarily  be  rendered  very 
irregular.  They  may,  however,  be  completely  removed,  by  employing  always 
cranks  in  pairs,  one  of  them  being  fixed  so  as  to  make  a  right  angle  with 
the  other,  which  is  also  the  best  position  for  two  winches  to  be  turned  by  two 
labourers ;  since  the  point  of  the  circle,  in  which  a  man  can  exert  his 
greatest  strength,  is  nearly  at  the  distance  of  a  right  angle,  or  a  little  more, 
from  the  point  at  which  his  force  is  smallest. 

An  alternate  motion  may  be  communicated  to  a  rod,  so  that  the  force 
may  be  either  uniformly  exerted,  or  varied  according  to  any  given  law,  by 
means  of  an  inclined  surface  formed  into  a  proper  curve,  and  acting  on  a 
friction  wheel  fixed  to  the  rod  ;  and  a  single  plane  surface,  placed  ob- 
liquely, would  answer  sufficiently  well  for  this  purpose.  But  in  such 
cases,  as  well  as  when  a  crank  is  used,  it  is  necessary  to  employ  other 
means  for  supporting  the  rod  in  its  proper  situation  ;  this  may  either  be 
done  by  additional  friction  wheels,  or  in  a  more  elegant  manner,  by  such  an 
arrangement  of  jointed  rods  as  will  cause  the  extremity  of  one  of  them  to 
move  in  a  curve  which  does  not  sensibly  differ  from  a  right  line.  If  we  fix 
two  pins  in  a  beam,  so  as  to  connect  to  it  two  equal  rods,  of  which  the 
extremities  are  joined  by  a  third,  and  the  end  of  this  third  rod  which  is 
nearest  to  the  centre  of  the  beam  be  connected  to  a  second  beam  of  a  proper 
length,  the  opposite  end  of  the  rod  will  initially  describe  a  right  line  ;  and 
for  this  purpose  the  length  of  the  second  beam  must  be  to  the  distance  of 
the  nearest  pin  from  the  centre  as  that  distance  is  to  the  distance  of  the 
pins  from  each  other.  The  same  effect  may  also  be  produced  by  means  of 
a  frame,  made  of  two  pieces,  each  a  yard  long,  united  by  joints  to  each 
other,  and  to  two  other  pieces  of  a  foot  each  ;  one  of  the  first  pieces  being 
fixed,  if  the  shorter  piece  opposite  to  it  be  produced  to  the  length  of  four 
feet,  its  extremity  will  move  at  first  in  a  right  line.  The  proportions  of 
the  rods  may  also  be  made  more  convenient  than  these,  and  others  may  be 
added  to  them,  if  it  be  required,  which  may  make  a  line  move  so  as  to 
remain  always  in  parallel  directions.  (Plate  XIV.  Fig.  185...  188.) 

But  of  all  the  modes  of  communicating  motion,  the  most  extensively 
useful  is  the  employment  of  wheelwork,  which  is  capable  of  varying  its 
direction  and  its  velocity  without  any  limit. 

Wheels  are  sometimes  turned  by  simple  contact  with  each  other ;  some- 
times by  the  intervention  of  cords,  straps,  or  chains,  passing  over  theni  ; 
and  in  these  cases  the  minute  protuberances  of  the  surfaces,  or  whatever 
else  may  be  the  cause  of  friction,  prevents  their  sliding  on  each  other. 


ON  MACHINERY.  135 

Where  a  broad  strap  runs  on  a  wheel,  it  is  usually  confined  to  its  situation, 
not  by  causing  the  margin  of  the  wheel  to  project,  but,  on  the  contrary, 
by  making  the  middle  prominent :  the  reason  of  this  may  be  understood 
by  examining  the  manner  in  which  a  tight  strap  running  on  a  cone  would 
tend  to  run  towards  its  thickest  part.  Sometimes,  also,  pins  are  fixed  in 
the  wheels,  and  admitted  into  perforations  in  the  straps ;  a  mode  only 
practicable  where  the  motion  is  slow  and  steady.  A  smooth  motion  may 
also  be  obtained,  with  considerable  force,  by  forming  the  surfaces  of  the 
wheels  into  brushes  of  hair.  (Plate  XV.  Fig.  189.) 

More  commonly,  however,  the  circumferences  of  the  contiguous  wheels 
are  formed  into  teeth,  impelling  each  other,  as  with  the  extremities  of  so 
many  levers,  either  exactly  or  nearly  in  the  common  direction  of  the  cir- 
cumferences ;  and  sometimes  an  endless  screw  is  substituted  for  one  of  the 
wheels.  In  forming  the  teeth  of  wheels,  it  is  of  consequence  to  deter- 
mine the  curvature  which  will  procure  an  equable  communication  of 
motion,  with  the  least  possible  friction.  For  the  equable  communication 
of  motion,  two  methods  have  been  recommended  ;  one,  that  the  lower  part 
of  the  face  of  each  tooth  should  be  a  straight  line  in  the  direction  of  the 
radius,  and  the  upper  a  portion  of  an  epicycloid,  that  is,  of  a  curve  de- 
scribed by  a  point  of  a  circle  rolling  on  the  wheel,  of  which  the  diameter 
must  be  half  that  of  the  opposite  wheel ;  and  in  this  case  it  is  demonstrable 
that  the  plane  surface  of  each  tooth  will  act  on  the  curved  surface  of  the 
opposite  tooth  so  as  to  produce  an  equable  angular  motion  in  both  wheels  : 
the  other  method  is,  to  form  all  the  surfaces  into  portions  of  the  involutes 
of  circles,  or  the  curves  described  by  a  point  of  a  thread  which  has  been 
wound  round  the  wheel,  while  it  is  uncoiled  ;  and  this  method  appears  to 
answer  the  purpose  in  an  easier  and  simpler  manner  than  the  former.* 
It  may  be  experimentally  demonstrated  that  an  equable  motion  is  pro- 
duced by  the  action  of  these  curves  on  each  other :  if  we  cut  two  boards 
into  forms  terminated  by  them,  divide  the  surfaces  by  lines  into  equal  or 
proportional  angular  portions,  and  fix  them  on  any  two  centres,  we  shall 
find  that  as  they  revolve,  whatever  parts  of  the  surfaces  may  be  in 
contact,  the  corresponding  lines  will  always  meet  each  other.  (Plate  XV. 
Fig.  190... 192.) 

Both  of  these  methods  may  be  derived  from  the  general  principle  that 
the  teeth  of  the  one  wheel  must  be  of  such  a  form  that  their  outline  may 
be  described  by  the  revolution  of  a  curve  upon  a  given  circle,  while  the 
outline  of  the  teeth  of  the  other  wheel  is  described  by  the  same  curve 
revolving  within  a  second  circle.  It  has  been  supposed  by  some  of  the 
best  authors  that  the  epicycloidal  tooth  has  also  the  advantage  of  com- 
pletely avoiding  friction  ;  this  is  however  by  no  means  true,  and  it  is 
even  impracticable  to  invent  any  form  for  the  teeth  of  a  wheel,  which  will 
enable  them  to  act  on  other  teeth  without  friction.  In  order  to  diminish 
it  as  much  as  possible,  the  teeth  must  be  as  small  and  as  numerous  as  is 
consistent  with  strength  and  durability ;  for  the  effect  of  friction  always 
increases  with  the  distance  of  the  point  of  contact  from  the  line  joining 

*  For  a  demonstration  of  these  propositions,  see  Airy  on  the  Teeth  of  Wheels, 
Trans,  of  the  Camb.  Phil.  Soc.  ii.  279. 


13G  LECTURE   XV. 

the  centres  of  the  wheels.  In  calculating  the  quantity  of  the  friction, 
the  velocity  with  which  the  parts  slide  over  each  other  has  generally  been 
taken  for  its  measure  :  this  is  a  slight  inaccuracy  of  conception,  for,  as 
we  have  already  seen,  the  actual  resistance  is  not  at  all  increased  by  in- 
creasing the  relative  velocity  ;  but  the  effect  of  that  resistance  in  retarding 
the  motion  of  the  wheels,  may  be  shown  from  the  general  laws  of 
mechanics,  to  be  proportional  to  the  relative  velocity  thus  ascertained. 
When  it  is  possible  to  make  one  wheel  act  on  teeth  fixed  in  the  concave 
surface  of  another,  the  friction  may  be  thus  diminished  in  the  proportion 
of  the  difference  of  the  diameters  to  their  sum.  If  the  face  of  the  teeth, 
where  they  are  in  contact,  is  too  much  inclined  to  the  radius,  their  mutual 
friction  is  not  much  affected,  but  a  great  pressure  on  their  axes  is  pro- 
duced ;  and  this  occasions  a  strain  on  the  machinery,  as  well  as  an  increase 
of  the  friction  on  the  axes. 

If  it  is  desired  to  produce  a  great  angular  velocity  with  the  smallest  pos- 
sible quantity  of  wheelwork,  the  diameter  of  each  wheel  must  be  between 
three  and  four  times  as  great  as  that  of  the  pinion  on  which  it  acts.  Where 
the  pinion  impels  the  wheel,  it  is  sometimes  made  with  three  or  four  teeth 
only,  but  it  is  much  better  in  general  to  have  at  least  six  or  eight ;  and 
considering  the  additional  labour  of  increasing  the  number  of  wheels,  it 
may  be  advisable  to  allot  more  teeth  to  each  of  them  than  the  number  re- 
sulting from  the  calculation  ;  so  that  we  may  allow  30  or  40  teeth  to  a 
wheel  acting  on  a  pinion  of  6  or  8.  In  works  which  do  not  require  a  great 
degree  of  strength,  the  wheels  have  sometimes  a  much  greater  number  of 
teeth  than  this  ;  and  on  the  other  hand,  an  endless  screw  or  a  spiral  acts  as 
a  pinion  of  one  tooth,  since  it  propels  the  wheel  through  the  breadth  of  one 
tooth  only  in  each  revolution.  For  a  pinion  of  six  teeth,  it  would  be 
better  to  have  a  wheel  of  35  or  37  than  36  ;  for  each  tooth  of  the  wheel 
would  thus  act  in  turn  upon  each  tooth  of  the  pinion,  and  the  work  would 
be  more  equally  worn  than  if  the  same  teeth  continued  to  meet  in  each 
revolution.  The  teeth  of  the  pinion  should  also  be  somewhat  stronger  than 
those  of  the  wheel,  in  order  to  support  the  more  frequent  recurrence  of 
friction.  It  has  been  proposed  for  the  coarser  kinds  of  wheelwork,  to  di- 
vide the  distance  between  the  middle  points  of  two  adjoining  teeth  into 
30  parts,  and  to  allot  16  to  the  tooth  of  the  pinion,  and  13  to  that  of  the 
wheel,  allowing  1  for  freedom  of  motion. 

The  wheel  and  pinion  may  either  be  situated  in  the  same  plane,  both 
being  commonly  of  the  kind  denominated  spur  wheels,  or  their  planes  may 
form  an  angle  :  in  this  case  one  of  them  may  be  a  crown  or  contrate  wheel, 
or  both  of  them  may  be  bevilled,  the  teeth  being  cut  obliquely.  According 
to  the  relative  magnitude  of  the  wheels,  the  angle  of  the  bevil  must  be  dif- 
ferent, so  that  the  velocities  of  the  wheels  may  be  in  the  same  proportion 
at  both  ends  of  their  oblique  faces :  for  this  purpose  the  faces  of  all  the 
teeth  must  be  directed  to  the  point  where  the  axes  would  meet.  (Plate  XV. 
Fig.  193,  194.) 

In  cases  where  a  motion  not  quite  equable  is  required,  as  it  sometimes 
happens  in  the  construction  of  clocks,  but  more  frequently  in  orreries,  the 
wheels  may  either  be  divided  a  little  unequally,  or  the  axis  may  be  placed 


.     ON  MACHINERY.  137 

a  little  out  of  the  centre ;  and  these  eccentric  wheels  may  either  act  on 
other  eccentric  wheels,  or,  if  they  are  made  as  contrate  wheels,  upon  a 
lengthened  pinion.  (Plate  XV.  Fig.  195,  196.) 

An  arrangement  is  sometimes  made  for  separating  wheels  which  are  in- 
tended to  turn  each  other,  and  for  replacing  them  at  pleasure  ;  the  wheels 
are  said  to  he  thrown  by  these  operations  out  of  gear  and  into  gear  again. 

When  a  wheel  revolves  round  another,  and  is  so  fixed  as  to  remain 
nearly  in  a  parallel  direction,  and  to  cause  the  central  wheel  to  turn  round 
its  axis,  the  apparatus  is  called  a  sun  and  planet  wheel.  In  this  case,  the 
circumference  of  the  central  wheel  moves  as  fast  as  that  of  the  revolving- 
wheel,  each  point  of  which  describes  a  circle  equal  in  diameter  to  the  dis- 
tance of  the  centres  of  the  two  wheels  :  consequently,  when  the  wheels  are 
equal,  the  central  wheel  makes  two  revolutions,  every  time  that  the  ex- 
terior wheel  travels  round  it.  If  the  central  wheel  be  fixed,  and  the  ex- 
terior wheel  be  caused  to  turn  on  its  own  centre  during  its  revolution,  by 
the  effect  of  the  contact  of  the  teeth,  it  will  make  in  every  revolution  one 
turn  more  with  respect  to  the  surrounding  objects,  than  it  would  make,  if 
its  centre  were  at  rest,  during  one  turn  of  the  wheel  which  is  fixed  :  and 
this  circumstance  must  be  recollected  when  such  wheels  are  employed  in 
planetariums. 

Wheels  are  usually  made  of  wood,  of  iron,  either  cast  or  wrought,  of 
steel,  or  of  brass.  The  teeth  of  wheels  of  metal  are  generally  cut  by  means 
of  a  machine  ;  the  wheel  is  fixed  on  an  axis,  which  also  carries  a  plate  fur- 
nished with  a  variety  of  circles,  divided  into  different  numbers  of  equal 
parts,  marked  by  small  excavations  ;  these  are  brought  in  succession 
under  the  point  of  a  spring  which  holds  the  axis  firm,  while  the  intervals 
between  the  teeth  are  expeditiously  cut  out  by  a  revolving  saw  of  steel. 
The  teeth  are  afterwards  finished  by  a  file  ;  and  a  machine  has  also  been 
invented  for  holding  and  working  the  file.  (Plate  XV.  Fig.  197.) 

It  is  frequently  necessary  in  machinery  to  protract  the  time  of  ap- 
plication of  a  given  force,  or  to  reserve  a  part  of  it  for  future  use.  This  is 
generally  effected  by  suffering  a  weight  to  descend,  which  has  been  previ- 
ously raised,  or  a  spring  to  unbend  itself  from  a  state  of  forcible  flexure,  as 
is  exemplified  in  the  weights  and  springs  of  clocks  and  watches.  The  com- 
mon kitchen  jack  is  also  employed  for  protracting  and  equalising  the  ope- 
ration of  a  weight  :  in  the  patent  jack  the  same  effect  is  produced  by  an 
alternate  motion,  the  axis  being  impelled  backwards  and  forwards,  as  in 
clocks  and  watches,  by  means  of  an  escapement,  and  the  place  of  a  balance 
spring  being  supplied  by  the  twisting  and  untwisting  of  a  cord. 

In  these  machines,  as  well  as  in  many  others  of  greater  magnitude,  the 
fly  wheel  is  a  very  important  part,  its  velocity  being  increased  by  the  ope- 
ration of  any  part  of  the  force  which  happens  to  be  superfluous,  and  its  ro- 
tatory power  serving  to  continue  the  motion  when  the  force  is  diminished 
or  withdrawn.  Thus,  when  a  man  turns  a  winch,  he  can  exert  twice  as 
much  force  in  some  positions  as  in  others,  and  a  fly  enables  him  in  some 
crises  to  do  nearly  one  third  more  work.  In  the  pile  engine  also,  without 
the  help  of  the  fly,  the  horses  would  fall  for  want  of  a  counterpoise,  as  soon 
as  the  weight  is  disengaged.  Such  a  fly  ought  to  be  heavy,  and  its  motion 


138  LECTURE  XVI. 

must  not  be  too  rapid,  otherwise  the  resistance  of  the  air  will  destroy  too 
much  of  the  motion  ;  but  in  the  kitchen  jack,  as  well  as  in  the  striking 
part  of  a  clock,  where  the  superfluous  force  is  purposely  destroyed,  the  fly 
is  made  light,  and  strikes  the  air  with  a  broad  surface.  An  effect  similar 
to  that  of  a  fly  and  a  spring  is  sometimes  produced  in  hydraulic  machines 
by  the  introduction  of  an  air  vessel,  the  air  contained  in  which  is  com- 
pressed more  or  less  according  to  the  intensity  of  the  force,  and  exerts  a 
more  uniform  pressure  in  expelling  the  fluid  which  is  forced  irregularly 
into  it. 


LECT.  XV.— ADDITIONAL  AUTHORITIES. 

Lahire's  Mech.  Par.  1695.  Maudey's  Mechanical  Powers,  1709.  Leupold,  Thea- 
trum  Machinarum,  9  vols.  fol.  Leipz.  1724. .  . .  Euler  on  the  Theory  of  Machines, 
Com.  Petr.  x.  67.  Nov.  Com.  Petr.  iii.  254  ;  viii.  230.  Hist,  et  Mem.  de  Berlin, 
1747,  1752.  Camus,  Cours  de  Mathematiques,  Par.  1766.  Berthelot,  Mecanique 
appliquee  aux  Arts,  2  vols.  4to,  1773.  Jacobsons  Technologisches  Worterbuch, 
von  Rosenthal,  Berl.  1787.  Person,  Recueil  de  Mecanique,  4to,  Paris,  1802. 
Banks  on  the  Power  of  Machines,  Kendal,  1803.  Guenyveau,  Essai  sur  la  Science 
des  Machines,  Lyons,  1809.  Lippi,  Principj  Pratici  di  Meccanica,  Napoli,  1811. 
Lauz  et  Betancourt,  Essai  sur  la  Composition  des  Machines,  4to,  Par.  1819.  Bprgnis, 
Traite  Complet  de  Mechanique  appliquee  aux  Arts,  7  vols.  4to.  Paris,  1818-20. 
Dictionnaire  de  do.  4to,  1823.  Hachette,  Traite  Elementaire  des  Machines,  1828. 
Robison,  art.  Machinery.  Coriolis,  Calcul  de  1'Effet  des  Machines,  1829.  Navier, 
Resume  des  Lemons  donnees  &  1'Ecole  des  Ponts  et  Chaussees,  1833.  Prony,  Me- 
moire  sur  un  Moyen  de  convertir  les  Mouvemens,  &c.  4to,  1837.  Whewell's  Me- 
chanics of  Engineering,  Camb.  Willis's  Principles  of  Machinery,  Camb.  1841. 
Poncelet,  Introduction  a  la  Mecanique  Industrielle,  Metz  et  Paris,  1841.  Moseley, 
The  Mechanical  Principles  of  Engineering,  1843. 

WheelworJc. — Hooke's  Perfection  of  Wheelwork.  Cutlerian  Lectures,  No.  2, 
Animadversions  on  Hevelius,  4to,  1674,  p.  70.  Lahire  on  the  Teeth  of  Wheels, 
Hist,  et  Mem.  de  Paris,  ix.  90,  283,  292.  Camus  on  do.  ibid.  1733,  p.  117,  H. 
81  ;  and  Cours  de  Mathematiques,  4  vols.  translated,  1806.  Euler  on  do.  Nov.  Com. 
Petr.  v.  299  ;  ii.207.  Ferguson's  Lectures,  by  Brewster,  2  vols.  1806.  Buchanan, 
Essay  on  the  Teeth  of  Wheels,  1808.  Trans,  of  the  Soc.  of  Civil  Engineers,  ii.  89. 


LECTURE   XVI. 


ON  THE  UNION  OF  FLEXIBLE  FIBRES. 

THE  strength  of  cordage,  and  of  other  substances  which  are  employed  in 
the  communication  of  motion  where  flexibility  is  required,  as  well  as  the 
utility  of  other  flexible  materials  which  serve  for  furniture  or  for  clothing, 
depends  principally  upon  the  lateral  adhesion  produced  by  twisting,  or  by 
the  intermixture  of  fibres.  The  union  of  flexible  fibres,  therefore,  being 
frequently  subservient  to  the  communication  of  motion,  and  the  machinery 
usually  employed  for  producing  it,  belonging  immediately  to  the  subject 
of  the  modification  of  motion,  we  may  with  propriety  consider  at'present, 


ON  THE  UNION  OF  FLEXIBLE  FIBRES.  139 

as  far  as  our  plan  will  allow  us,  those  important  branches  of  the  mechanical 
arts,  of  which  the  object  is  to  effect  a  union  of  this  kind. 

When  a  chain  is  made  of  wire,  each  link  is  separately  bent,  and  remains 
united  with  the  neighbouring  links  in  virtue  of  its  rigidity :  but  the  fibres 
of  vegetable  and  of  animal  substances  must  be  united  by  other  means.  For 
this  purpose  we  have  recourse  to  the  force  of  friction,  or  rather  of  lateral 
adhesion,  and  the  fibres  are  so  disposed,  that  besides  the  mutual  pressure 
which  their  own  elasticity  causes  them  to  exert,  any  additional  force 
applied  in  the  direction  of  the  length  of  the  aggregate,  tends  to  bring  the 
parts  into  closer  contact,  and  to  augment  the  adhesion,  in  the  same  manner 
as  we  have  already  seen  that  a  wedge  and  a  screw  may  be  retained  in  their 
situations.  The  simple  art  of  tying  a  knot,  and  the  more  complicated  pro- 
cesses of  spinning,  ropemaking,  weaving,  and  felting,  derive  their  utility 
from  this  principle.  :  .,. 

When  a  line  is  coiled  round  a  cylinder,  for  instance,  in  letting  down  a 
weight  by  means  of  a  rope  which  slides  on  a  post,  or  on  such  a  grooved 
cylinder  as  is  sometimes  employed  to  enable  a  person  to  lower  himself  from 
a  window  in  cases  of  fire,  the  pressure  on  the  whole  circumference  is  to  the 
weight,  as  twice  the  circumference  to  the  diameter  ;  supposing,  for  ex- 
ample, that  the  friction  of  rope  on  metal  were  one  tenth  of  the  pressure, 
then  a  single  coil  of  rope  round  a  cylinder  of  metal  would  support  about 
two  thirds  of  the  weight ;  or  if  the  weights  acting  on  the  different  ends  are 
different,  the  adhesion  may  be  a  little  greater  or  less  than  in  this  proportion, 
according  to  the  manner  in  which  the  rope  is  applied.  If  such  a  rope  made 
two  or  three  coils,  it  would  be  impossible  to  apply  a  force  sufficient  to  cause 
it  to  slide  in  the  grooves. 

From  considering  the  effect  of  a  force  which  is  counteracted  by  other 
forces  acting  obliquely,  we  may  understand  both  the  effect  of  twisting,  in 
binding  the  parts  of  a  rope  together,  and  its  inconvenience,  in  causing  the 
strength  of  the  fibres  to  act  with  a  mechanical  disadvantage.  The  greater 
the  obliquity  of  the  fibres,  the  greater  will  be  their  adhesion,  but  the  greater 
also  will  be  their  immediate  tension,  in  consequence  of  the  action  of  a  given 
force  in  the  direction  of  the  rope :  so  that  after  employing  as  much  ob- 
liquity and  as  much  tension,  as  is  sufficient  to  connect  the  fibres  firmly  in 
all  cases  of  relaxation  and  of  flexure,  and  to  prevent  in  some  measure  the 
penetration  of  moisture,  all  that  is  superfluously  added  tends  to  overpower 
the  primitive  cohesion  of  the  fibres  in  the  direction  of  their  length.* 

The  mechanism  of  simple  spinning  is  easily  understood  ;  care  is  taken, 
where  the  hand  is  employed,  to  intermix  the  fibres  sufficiently,  and  to 
engage  their  extremities  as  much  as  possible  in  the  centre  ;  for  it  is  obvious 
that  if  any  fibre  were  wholly  external  to  the  rest,  it  could  not  be  retained 
in  the  yarn  ;  in  general,  however,  the  materials  are  previously  in  such  a 
state  of  intermixture  as  to  render  this  precaution  unnecessary.  Where 
we  have  a  number  of  single  continuous  fibres,  as-  in  reeled  silk,  they  are 
sufficiently  connected  by  twisting,  and  we  have  no  need  of  spinning.  In 
bc4h  cases  such  machinery  has  been  invented  for  performing  the  necessary 
operations,  as  is  both  honourable  and  lucrative  to  the  British  nation. 
*  See  Hooke's  Experiments  on  Cordage  Birch.,  ii.  393. 


140  LECTURE  XVI. 

A  single  thread  or  yarn,  consisting  of  fibres  twisted  together,  has  a  ten- 
dency to  untwist  itself ;  the  external  parts  are  the  most  strained  in  the 
operation  and  at  first  shorten  the  thread,  until  the  internal  parts  have  no 
longer  room  for  spreading  out  laterally,  as  they  must  necessarily  do  when 
their  length  is  diminished  ;  the  elasticity  of  all  the  parts,  therefore,  resists, 
and  tends  to  restore  the  thread  to  its  natural  state.  But  if  two  such 
threads  are  retained  in  contact  at  a  given  point  of  the  circumference  of 
each,  this  point  is  rendered  stationary  by  the  opposition  of  the  equal  forces 
acting  in  contrary  directions,  and  becomes  the  centre,  round  which  both 
threads  are  carried  by  the  remaining  forces,  so  that  they  continue  to  twist 
round  each  other  till  the  new  combination  causes  a  tension  capable  of 
counterbalancing  the  remaining  tension  of  the  original  threads.  Three, 
four,  or  more  threads  may  be  united  nearly  in  the  same  manner  :  a  strand 
consists  of  a  considerable  number  of  yarns  thus  twisted  together,  generally 
from  sixteen  to  twenty  five,  a  hawser  of  three  strands,  a  shroud  of  four, 
and  a  cable  of  three  hawsers  or  shrouds.  Shroud  laid  cordage  has  the  dis- 
advantage of  being  hollow  in  the  centre,  or  of  requiring  a  greater  change  of 
form  in  the  strands  to  fill  up  the  vacuity,  and  in  undergoing  this  change, 
the  cordage  stretches,  and  is  unequally  strained.  The  relative  position  and 
the  comparative  tension  of  all  the  fibres  in  these  complicated  combinations 
are  not  very  easily  determined  by  calculation ;  but  it  is  found  by  expe- 
rience to  be  most  advantageous  to  the  strength  of  the  ropes  to  twist  the 
strands,  when  they  are  to  be  compounded,  in  such  a  direction  as  to  untwist 
the  yarns  of  which  they  are  formed  ;  that  is,  to  increase  the  twist  of  the 
strands  themselves :  and  probably  the  greatest  strength  is  obtained  when 
the  ultimate  obliquity  of  the  constituent  fibres  is  the  least,  and  the  most 
equable.  This  advantage  is  obtained  in  a  considerable  degree  by  Mr.  Hud- 
dart's*  method  of  adjusting  the  length  of  the  strand  to  its  position  in  the 
rope,  and  his  registered  cordage  appears  to  derive  a  decided  superiority 
from  this  arrangement  of  the  strands.  A  very  strong  rope  may  also  be 
made  by  twisting  five  or  six  strands  round  a  seventh  as  an  axis ;  the  central 
strand,  or  heart,  is  found  after  much  use  to  be  chafed  to  oakum  ;  it  should 
be  more  twisted  than  the  rest,  in  order  to  allow  it  to  extend  a  little  ;  such 
ropes  are,  however,  unfit  for  running  rigging,  or  for  any  use  in  which  they 
are  liable  to  be  frequently  bent. 

Ropes  are  most  commonly  made  of  hemp,  but  various  other  vegetables 
are  occasionally  employed  ;  the  Chinese  even  use  woody  fibres,  and  the 
barks  of  trees  furnish  cordage  to  other  nations  ;  we  have  indeed  in  this 
country  an  example  of  the  use  of  the  bark  of  the  lime  tree,  which  is 
employed  for  garden  matting.  The  finest  hemp  is  imported  from  Riga  and 
St.  Petersburg.  The  male  and  female  flowers  of  hemp  are  on  different 
plants ;  the  male  plants  are  soonest  ripe,  and  require  to  be  first  pulled. 
They  are  prepared  for  dressing  by  being  exposed  to  the  air,  and  the  fibrous 
part  is  separated  from  the  dry  pulp  by  beating  and  hackling.  In  spinning 
the  yarn,  the  hemp  is  fastened  round  the  waist ;  the  wheel  is  turned  by  an 
assistant,  and  the  spinner,  walking  backwards,  draws  out  the  fibres  with 

*  Huddart's  Patent  registered  Cordage,  Rep.  of  Arts,  xii.  80.  Remarks  on  do. 
4to.  1800. 


ON  THE  UNION  OF  FLEXIBLE  FIBRES.  141 

his  hands.  When  one  length  of  the  walk  has  been  spun,  it  is  immediately 
reeled,  to  prevent  its  untwisting.  The  machines  employed  in  continuing 
the  process  of  ropemaking  are  of  simple  construction,  hut  hoth  skill  and 
attention  are  required  in  applying  them  so  as  to  produce  an  equable 
texture  in  every  part  of  the  rope.  The  tendency  of  two  strands  to  twist,  in 
consequence  of  the  tension  arising  from  the  original  twist  of  the  yarns,  is 
not  sufficient  to  procure  an  equilibrium,  because  of  the  friction  and  rigidity 
to  be  overcome  ;  hence  it  is  necessary  to  employ  force  in  order  to  assist  this 
tendency,  and  the  strands  or  ropes  afterwards  retain  spontaneously  the 
form  which  has  thus  been  given  them :  the  largest  ropes  even  require 
external  force  in  order  to  make  them  twist  at  all. 

The  constituent  ropes  of  a  common  cable,  when  separate,  are  stronger 
than  the  cable  in  the  proportion  of  about  4  to  3 ;  and  a  rope  worked  up 
from  yarns  180  yards  in  length  to  135  yards,  has  been  found  to  be  stronger 
than  when  reduced  to  120  yards,  in  the  ratio  of  6  to  5.  The  difference 
is  owing  partly  to  the  obliquity  of  the  fibres,  and  partly  to  the  unequal 
tension  produced  by  twisting.  Mr.  Huddart's  ropes  of  100  yarns  lose 
but  about  one  eighth  of  the  whole  strength  of  the  yarns  ;  and  his  experi- 
ments appear  to  show  that  similar  ropes  made  in  the  common  manner 
retain  only  one  half  of  their  original  strength.  The  tarring  of  ropes, 
although  sometimes  necessary  for  their  preservation  from  decay,  is  found 
to  lessen  their  strength,  probably  because  it  produces  partial  adhesions 
between  some  of  the  fibres,  which  cause  them  to  be  disproportionally 
strained.  A  rope  is  also  said  to  be  weaker  when  wet  than  when  dry, 
perhaps  because  the  water  enables  the  fibres  to  slide  more  readily  on 
each  other,  or  because  the  presence  of  water  is  in  general  favourable  to 
separation  of  any  kind.  A  good  hempen  rope  will  support,  without 
danger,  one  fifth  as  many  tons  as  the  square  of  its  circumference  contains 
inches.* 

Flax  is  weaker  than  hemp,  but  not  less  extensively  useful.  Its  growth 
considerably  exhausts  the  strength  of  the  soil  which  produces  it ;  its 
cultivation  is  encouraged  in  this  country  by  a  bounty  from  government, 
and  a  large  quantity  is  also  imported  from  the  north  of  Europe.  The 
plant,  while  green,  is  laid  in  water  for  ten  days,  and  undergoes  a  chemical 
change,  which  softens  the  pulpy  part,  without  injuring  the  strength  of  the 
fibres,  and  renders  it  more  easy,  when  it  has  been  dried  and  exposed  to 
the  air  for  a  fortnight,  to  separate  the  two  substances  in  the  process  of 
dressing  it.  This  is  performed  by  beating  it  with  the  edge  of  a  flat  piece 
of  wood,  the  stroke  being  oblique,  and  nearly  in  the  direction  of  the  fibres, 
and  afterwards  combing  it,  in  order  to  reduce  the  fibres  into  regular  order, 
and  to  prepare  them  for  spinning.  The  refuse,  consisting  of  the  shorter 
fibres,  is  tow. 

Cotton  is  a  fine  fibrous  substance,  that  envelopes  the  seeds  of  a  plant. 
The  best  is  brought  from  the  isle  of  Bourbon ;  but  by  far  the  greatest 
quantity  from  the  West  Indies,  although  the  Turkish  dominions  as  well  as 
the  East  Indies  furnish  us  with  a  considerable  supply.  It  is  usually 
white,  but  there  is  a  yellow  kind,  which  is  used  for  nankeens.  It  is 
*  See  Duhamel,  Traite  de  la  Corderie  Perfectionne"e,  4to,  Paris. 


142  LECTURE  XVI. 

separated  from  the  seeds  by  means  of  rollers,  between  which  it  passes,  and 
leaves  the  seeds  behind.  It  is  then  beaten,  on  a  flake,  or  a  stool  covered 
with  a  texture  of  cord.  Next,  it  is  carded,  either  by  hand,  the  fibres 
being  drawn  into  regular  order  by  cards,  that  is,  by  brushes  of  fine  pointed 
wire;  or,  more  commonly,  by  machinery,  the  cards  being  disposed  in 
cylinders  which  revolve  nearly  in  contact  with  each  other.  The  drawing 
or  roving  machine  then  draws  it  into  long  flakes,  a  state  preparatory  to 
its  being  spun  by  Sir  Richard  Arkwright's  machines  or  jennies,  which 
form  at  once  forty  threads  by  the  labour  of  one  person. 

The  silkworm  is  bred  in  the  greatest  abundance  in  Italy  and  in  Asia  ; 
it  has  lately  been  introduced  very  successfully  into  the  British  possessions 
in  the  East  Indies.  The  principal  food  of  the  caterpillar  is  the  white 
mulberry  tree,  which  is  too  delicate  to  thrive  well  in  northern  climates  :  in 
Italy  the  trees  are  planted  in  beds,  like  willows,  and  the  foliage  is  cut  as 
it  is  wanted.  The  room  in  which  the  worms  are  fed,  is  kept  at  the  tem- 
perature of  80  degrees  of  Fahrenheit.  The  eggs  of  a  former  year  are 
hatched  either  by  animal  heat,  or  by  that  of  the  sun  ;  at  the  age  of  six 
weeks,  the  caterpillars  begin  to  spin,  first  a  light  external  texture,  which  is 
carded  and  spun  for  coarse  silk,  and  afterwards  a  compact  oval  pod  or 
cocoon,  of  one  continued  thread.  The  threads  of  several  cocoons  are 
reeled  off  at  the  same  time  :  for  this  purpose  they  are  generally  put  into 
warm  water,  which  kills  the  chrysalis  :  but  when  it  is  preserved,  it  soon 
turns  to  a  moth,  which  lives  but  a  few -days,  taking  no  food,  and  dies  after 
producing  eggs  for  the  next  season. 

The  silk  is  either  yellow  or  white,  but  the  white  is  an  accidental  variety 
only.  By  repeated  washings,  the  yellow  silk  is  bleached,  and  that  which 
is  originally  white,  acquires  a  more  perfect  whiteness.  Soap  is  also  used 
for  removing  a  gummy  substance  that  accompanies  the  silk  of  the  cocoons. 

Wool  is  distinguished  into  two  principal  varieties,  long  and  short  wool. 
The  longest  is  from  Lincolnshire ;  it  is  combed,  by  means  of  instruments 
furnished  with  a  double  row  of  long  and  sharp  teeth  of  iron  or  steel ;  it  is 
repeatedly  drawn  from  one  comb  to  the  other,  heat  being  used  in  the  pro- 
cess, and  also  a  little  oil.  The  fleeces  of  long  wool  are  generally  heavier 
than  those  of  short  wool,  but  less  valuable  on  account  of  their  coarseness  ; 
they  are  used  for  worsteds,  and  for  cloths  in  which  the  separate  threads 
remain  visible,  as  stuffs,  shalloons,  serges,  and  tammies.  Short  wool,  on 
the  contrary,  is  carded,  and  is  used  for  cloths  in  which  the  individual 
threads  are  concealed  by  the  projecting  fibres. 

The  principal  use  of  thread  and  yarn,  when  spun,  is  for  the  purpose  of 
weaving.  The  same  force  of  lateral  adhesion  that  retains  the  twisted 
fibres  of  each  thread  in  their  situations,  is  here  also  employed  in  giving 
firmness  to  the  cloth ;  and  this  adhesion  is  generally  increased  by  the 
action  of  any  external  force,  tending  to  strain  the  whole  texture. 

The  first  step  in  weaving  is  to  form  a  warp,  which  consists  of  threads 
placed  side  by  side,  continued  through  the  length  of  the  piece,  and  suffi- 
cient in  number  to  constitute  its  breadth.  This  being  wound  on  a  beam 
or  roller,  in  the  loom,  the  threads  are  drawn  through  a  harness,  consisting 
of  loops  formed  by  twine  fixed  to  bars  or  frames,  which  elevates  and 


ON  THE  UNION  OF  FLEXIBLE  FIBRES.  143 

depresses  the  threads  in  succession  by  means  of  treadles,  moved  by  the 
feet,  in  an  order  which  is  different,  according  to  the  different  nature  of  the 
intended  work ;  the  cross  thread  or  woof,  being  thrown  between  them  at 
each  alternation,  by  means  of  a  shuttle,  and  forced  into  its  place  by  a 
batten  or  comb  made  of  wire  or  reeds,  while  the  piece,  in  proportion  as  it 
is  completed,  is  rolled  upon  a  second  beam  opposite  to  the  first. 

Crape  is  composed  of  threads  which  are  so  strongly  twisted,  as  to  have 
a  disposition  to  curl,  and  in  weaving  it,  moisture  is  sometimes  employed, 
in  order  to  obviate  this  tendency  during  the  process.  Woollen  cloth,  when 
woven,  is  rendered  stronger  and  more  compact  by  means  of  the  fulling 
mill,  in  which  it  is  beaten  by  heavy  hammers  of  wood,  at  the  same  time 
that  fullers'  earth,  or  alcaline  substances  of  animal  origin,  are  applied  in 
order  to  cleanse  it.  In  this  operation  both  its  length  and  breadth  are 
diminished,  and  it  is  reduced  to  a  texture  approaching  to  that  of  felt. 
The  reason  of  the  contraction  is  probably  this,  that  all  the  fibres  are  bent 
by  the  operation  of  the  hammer,  but  not  all  equally,  and  those  which  have 
been  the  most  bent  are  prevented  by  their  adhesion  to  the  neighbouring 
fibres  from  returning  to  their  original  length.  After  fulling,  the  cloth  is 
roughened  by  means  of  teasels,  which  are  cultivated  for  the  purpose  ;  and 
the  most  projecting  fibres  are  cut  away  by  the  operation  of  shearing. 

The  lateral  adhesion  of  fibres  of  various  kinds  gives  strength  also  to 
felted  substances,  assisted,  as  some  assert,  by  minute  barbs,  with  which 
the  fibres  of  furs  are  said  to  be  furnished.  The  whole  strength  is,  how- 
ever, much  inferior  to  that  of  cloth  ;  partly  because  the  fibres  are  in 
general  much  shorter,  and  partly  because  their  arrangement  is  less  accu- 
rately adjusted.* 

The  materials  commonly  used  for  felting  are  the  furs  of  rabbits  and 
beavers,  mixed  with  each  other,  and  with  sheep's  wool,  in  various  pro- 
portions, according  to  the  quality  required.  A  very  fine  fur  has  lately 
been  discovered  on  the  skin  of  a  species  of  seal,  mixed  with  its  hair,  and  it 
has  been  employed  not  only  for  felting,  but  also  for  spinning  and  weaving 
into  a  cloth  resembling  the  shawls  of  the  East  Indies.  The  fur  of  the 
rabbit  is  also  mixed  with  a  coarser  hair,  which  is  separated  from  it,  by 
being  first  pulled  off  from  the  skins,  with  a  sharper  knife.  The  materials 
to  be  felted  are  intimately  mixed  by  the  operation  of  bowing,  which  de- 
pends on  the  vibrations  of  an  elastic  string;  the  rapid  alternations  of 
its  motion  being  peculiarly  well  adapted  to  remove  all  irregular  knots  and 
adhesions  among  the  fibres,  and  to  dispose  them  in  a  very  light  and 
uniform  arrangement.  This  texture,  when  pressed  under  cloths  and 
leather,  readily  unites  into  a  mass  of  some  firmness ;  this  mass  is  dipped 
into  a  liquor  containing  a  little  sulfuric  acid,  and  when  intended  for  a  hat, 
is  moulded  into  a  large  conical  figure,  which  is  reduced  in  its  dimensions 
by  working  it  with  the  hands,  and  is  formed  into  a  flat  surface  with 
several  concentric  folds,  which  are  still  more  compacted  in  order  to  make 
the  brim  and  the  circular  part  of  the  crown,  and  forced  on  a  block  which 
selves  as  a  mould  for  the  cylindrical  part.  The  black  dye  is  composed  of 
*  On  Hatmaking,  see  Nich.  Jour.  4to,  i.  67  ;  iii.  22,  73. 


144  LECTURE   XVII. 

logwood,  sulfate  of  iron,  and  a  little  acetate  of  copper,  or  verdigris ;  and 
the  stiffening  is  a  thin  glue. 

The  texture  of  paper  is  scarcely  different  from  that  of  felt,  except  that 
its  fibres  are  less  visible  to  the  naked  eye.  To  make  white  paper,  linen  rags 
are  ground  with  warm  water  in  a  mill,  into  a  paste  of  the  consistence  of 
cream  :  a  portion  of  the  paste  is  taken  up  in  a  wire  sieve,  which  is  passed 
obliquely  through  it,  and  this,  being  a  little  shaken,  subsides  into  a  sheet, 
which  is  turned  out  on  a  piece  of  flannel ;  a  number  of  sheets  being  thus 
formed,  they  are  then  pressed,  first  writh  the  interposition  of  flannel,  and 
afterwards  alone,  while  they  are  still  moist.  For  thick  paper,  two  or  more 
sheets  are  laid  on  each  other  before  the  first  pressing.  To  fill  up  the  pores 
of  the  paper,  and  to  increase  its  strength,  a  size  is  employed,  which  is 
generally  made  by  boiling  shreds  of  parchment  or  untanned  leather. 
Sometimes  the  size  is  added  after  printing  on  the  paper,  but  this  is  only 
done  in  works  of  inferior  elegance,  and  in  this  country  not  at  all. 

Such  are  the  principal  cases  of  the  union  of  flexible  fibres,  for  the 
different  purposes  of  strength  or  of  convenience.  Their  importance  is  such 
that  they  might  be  esteemed  worthy  of  a  more  detailed  consideration  ;  but 
we  are  not  likely  to  make  any  material  improvements  in  these  departments 
of  mechanical  art  by  the  application  of  theoretical  refinements.* 


LECTURE   XVII. 


ON  TIMEKEEPERS. 

THE  measurement  of  time  by  clocks  and  watches  is  a  very  important 
and  interesting  department  of  practical  mechanics.  The  subject  is  inti- 
mately connected  with  the  consideration  of  astronomical  instruments,  but 
it  is  not  essentially  dependent  on  astronomical  principles. 

Time  is  measured  by  motion ;  but  in  order  that  motion  may  be  a  true 
measure  of  time,  it  must  be  equable.  Now  a  motion  perfectly  free  and 
undisturbed,  and  consequently  uniform,  is  rendered  unattainable  by 
the  resistances  inseparable  from  the  actual  constitution  of  material  sub- 
stances. It  becomes  therefore  necessary  to  inquire  for  some  mode  of 
approximating  to  such  a  motion.  Astronomical  determinations  of  time, 
which  are  the  most  accurate,  can  only  be  made  under  particular  circum- 
stances, and  even  then  they  assist  us  but  little  in  dividing  time  into  small 
portions. 

The  first  timekeepers  somewhat  resembled  the  hour  glasses  which  are  still 
occasionally  employed ;  they  measured  the  escape  of  a  certain  quantity,  not 
of  sand  but  of  water,  through  a  small  aperture.  In  these  clepsydrae,  "it 
*  For  additional  authorities,  see  Lect.  XIX. 


ON  TIMEKEEPERS.  145 

appears  from  Vitruvius's  account  that  wheelwork  was  employed,*  and  the 
hour  was  shown  on  a  graduated  scale  ;  the  graduations  were  also  probably 
so  adjusted  as  to  correct  the  error  arising  from  the  inequality  of  the  velocity 
occasioned  by  the  variation  of  the  height  of  the  water  in  the  reservoir.  This 
inconvenience  was  however  sometimes  wholly  avoided  by  means  of  a  con- 
stant stream,  which  kept  the  vessel  full,  or  still  more  elegantly,  by  the 
siphon  of  Hero,  which  was  a  bent  tube  supported  by  a  float,  so  that  its 
lower  orifice,  at  which  the  water  was  discharged,  was  always  at  a  certain 
distance  below  the  surface.  Dr.  Hooke  proposed  to  keep  the  reservoir  full, 
by  means  of  a  semicylindrical  counterpoise,  t  so  that  the  time  might  be 
determined  either  from  the  measure  or  weight  of  the  quantity  of  water 
discharged,  or  from  the  position  of  the  counterpoise.  Various  other  modes 
might  also  be  devised  for  making  cheap  and  simple  timekeepers  on  similar 
principles,  dependent  on  the  motion  of  various  liquids  or  elastic  fluids  ;  but 
great  accuracy  could  scarcely  be  expected  from  them.  A  candle  sometimes 
serves  as  a  coarse  measure  of  time  ;  and  by  burning  a  thread  which  passes 
through  it,  it  may  easily  be  made  to  answer  the  purpose  of  an  alarm. 

Clocks  and  watches  are  machines  in  which  wheelwork  is  employed  for 
the  measurement  of  time,  being  driven  by  a  weight  or  by  a  spring,  and 
regulated  by  a  pendulum  or  a  balance.  Watches  differ  from  clocks,  in 
being  portable,  and  this  condition  excludes  the  pendulum  and  the  weight 
from  their  construction. 

It  is  conjectured  that  the  Saracens  had  clocks  which  were  moved  by 
weights,  as  early  as  the  eleventh  century.  J  Trithemius  mentions  an  orrery, 
moved  by  a  weight,  and  keeping  time,  which  was  sent,  in  1232,  by  the 
Sultan  of  Egypt,  as  a  present  to  the  Emperor  Frederick  II.  Wallingf ord  ? 
in  1326,  had  made  a  clock  which  was  regulated  by  a  fly.§  The  use  of  such 
a  fly  in  equalising  motion  depends  on  the  resistance  of  the  air,  which 
increases  rapidly  when  the  velocity  is  increased,  and  therefore  prevents  any 
great  inequality  in  the  motion  as  long  as  the  moving  power  varies  but 
little  ;  and  if  the  action  of  the  weight  were  transmitted  with  perfect  regu- 
larity by  the  wheels,  and  the  specific  gravity  of  the  air  remained  unaltered 
by  pressure  or  by  temperature,  a  fly  clock  might  be  a  perfect  machine,  the 
weight  being  always  exactly  counterbalanced  by  the  resistance  of  the  air, 
attending  a  certain  velocity  of  the  fly ;  and  it  might  even  be  possible  to 
regulate  the  inequalities  of  the  action  of  the  weight,  by  causing  the  fly  to 
open  and  shut  or  to  turn  on  an  axis,  by  means  of  a  spring,  according  to  the 
magnitude  of  the  resistance.  The  unequal  density  of  the  air  would  how 
ever  still  remain  uncompensated ;  and  in  this  respect  a  liquid  would  be  a 
better  medium  than  an  elastic  fluid.  For  experiments  which  are  but  of 
short  duration  and  which  require  great  precision,  a  chronometer  regulated 
by  a  simple  fly  is  still  a  useful  instrument.  Mr.  Whitehurst's  ||  apparatus 
for  measuring  the  time  occupied  in  the  descent  of  heavy  bodies,  is  governed 

*  See  Derham,  The  Artificial  Clockmaker,  1696,  p.  85. 
•    f  Lampas,  4to,  1677,  p.  42. 

J  Beckmann,  History  of  Inventions,  4  vols.  translated  by  Johnstone,  vol.  i. 
§  Epitome  Conrardi  Gesneri,  p.  604. 
||  Ph.  Tr.  1794,  p.  2. 


146  LECTURE  XVII. 

by  a  fly  ;  the  index  is  stopped  by  the  machinery,  and  points  out  the  time 
elapsed  without  an  error  of  the  hundredth  part  of  a  second. 

The  alternate  motion  of  a  balance,  thrown  backwards  and  forwards  by 
the  successive  actions  of  a  wheel  impelling  its  pallets,  is  also  capable  of 
producing  a  degree  of  uniformity  in  the  motion  of  the  wheel ;  for  the  force 
operating  on  the  pallet  is  consumed  in  destroying  a  velocity  in  one  direc- 
tion, and  in  generating  a  velocity  in  the  contrary  direction  ;  and  the  space 
in  which  it  acts  being  nearly  the  same  in  all  cases,  the  velocity  generated 
will  also  be  nearly  the  same  at  all  times,  as  long  as  the  force  remains  the 
same.  The  addition  of  a  balance  to  a  clock  was  made  soon  after  the  year 
1400,  for  Arnault*  who  died  in  1465,  describes  a  planisphere  constructed 
by  his  master  De  Fondeur,  which  had  a  balance  with  a  scapement  like  that 
of  a  common  watch,  but  without  a  spring.  Such  a  balance  vibrates  much 
more  slowly  than  a  balance  provided  with  a  spring  ;  if  the  balance  spring 
of  a  common  watch  be  removed,  the  hands  will  pass  over  the  space  of  about 
twenty  eight  minutes  in  an  hour. 

It  is  said  that  before  the  pendulum  was  used,  a  balance  wheel  was  some- 
times suspended  in  a  horizontal  position  by  a  thread  passing  through  its 
axis,  which  coiled  round  it  and  caused  it  to  rise  and  fall  as  it  oscillated 
backwards  and  forwards.  This  mode  of  regulation  differed  but  little  in 
principle  from  the  modern  pendulums,  but  it  was  more  complicated  and 
less  accurate.  Huygens,  in  somewhat  later  times,  constructed  a  clock  with 
a  revolving  weight,  which  rose  higher,  and  increased  the  resistance,  when- 
ever an  augmentation  of  the  force  increased  the  velocity ;  and  he  caused 
the  thread  which  supported  the  weight,  to  bend  round  a  curve  of  such  a 
form  as  to  preserve  the  equality  of  the  revolutions. 

A  chronometer  may  be  constructed  on  this  principle  for  measuring  small 
portions  of  time  which  appears  to  be  capable  of  greater  accuracy  than 
Mr.  Whitehurst's  apparatus,  and  by  means  of  which  an  interval  of  a 
thousandth  part  of  a  second  may  possibly  be  rendered  sensible.  If  two 
revolving  pendulums  be  connected  with  a  vertical  axis,  in  such  a  manner  as 
to  move  two  weights  backwards  and  forwards  accordingly  as  they  fly  off 
to  a  greater  or  smaller  distance,  the  weights  sliding,  during  their  revolution, 
on  a  fixed  surface,  a  small  increase  of  velocity  will  considerably  increase 
the  distance  of  the  weights  from  the  axis,  and  consequently  the  effect  of 
their  friction,  so  that  the  machine  will  be  immediately  retarded,  and 
its  motion  may  thus  be  made  extremely  regular.  It  may  be  turned  by 
a  string  coiled  round  the  upper  part,  and  this  string  may  serve  as  a 
support  to  a  barrel,  sliding  on  a  square  part  of  the  axis,  which  will  conse- 
quently descend  as  it  revolves.  Its  surface,  being  smooth,  may  be  covered 
either  with  paper  or  with  wax,  and  a  pencil  or  a  point  of  metal  may  be 
pressed  against  it  by  a  fine  spring,  so  as  to  describe  always  a  spiral  line  on 
the  barrel,  except  when  the  spring  is  forced  a  little  on  one  side  by  touching 
it  slightly,  either  with  the  hand,  or  by  means  of  any  body  of  which  the 
motion  is  to  be  examined,  whether  it  be  a  falling  weight,  a  vibrating  cord 
or  rod,  or  any  other  moving  substance.  In  this  manner,  supposing  a  bar- 

*  Venturi,  Essai  sur  les  Ouvrages  de  L.  da  Vinci,  p.  28,  quoting  MS.  No.  7295,  in 
the  National  Library  of  Paris. 


ON  TIMEKEEPERS.  147 

rel  a  foot  in  circumference  to  revolve  in  two  seconds,  each  hundredth  of  an 
inch  would  correspond  to  the  six  hundredth  part  of  a  second  ;  and  the  scale 
might  be  still  further  enlarged  if  it  were  necessary.  (Plate  XV.  Fig.  198.) 

By  means  of  this  instrument  we  may  measure,  without  difficulty,  the 
frequency  of  the  vibrations  of  sounding  bodies,  by  connecting  them  with  a 
point,  which  will  describe  an  undulated  path  on  the  roller.  These  vi- 
brations may  also  serve  in  a  very  simple  manner  for  the  measurement  of 
the  minutest  intervals  of  time  ;  for  if  a  body,  of  which  the  vibrations  are 
of  a  certain  degree  of  frequency,  be  caused  to  vibrate  during  the  revolution 
of  an  axis,  and  to  mark  its  vibrations  on  a  roller,  the  traces  will  serve  as  a 
correct  index  of  the  time  occupied  by  any  part  of  a  revolution,  and  the 
motion  of  any  other  body  may  be  very  accurately  compared  with  the 
number  of  alternations  marked  in  the  same  time,  by  the  vibrating  body. 
For  many  purposes,  the  machine,  if  heavy  enough,  might  be  turned  by  a 
handle  only,  care  being  taken  to  keep  the  balls  in  a  proper  position,  and  it 
would  be  convenient  to  have  the  descent  of  the  barrel  regulated  by  the 
action  of  a  screw,  and  capable  of  being  suspended  at  pleasure. 

But  for  the  general  purposes  of  timekeepers,  all  other  inventions  have 
been  almost  universally  superseded  by  the  pendulum  and  the  balance 
spring,  or  pendulum  spring.  About  the  year  1000,  Ibn  Junis,  and 
the  other  Arabian  astronomers  were  in  the  habit  of  measuring  time, 
during  their  observations,  by  the  vibrations  of  pendulums;  but  they 
never  connected  them  with  machinery.  The  equality  of  the  times 
occupied  by  these  vibrations,  whether  larger  or  smaller,  was  known  to 
Galileo*  in  1600,  and  some  time  before  1633,  he  proposed  that  they 
should  be  applied  to  the  regulation  of  clocks.  But  Sanctorius,  in  his 
commentary  on  Avicenna,  describes  an  instrument  to  which  he  had  him- 
self applied  the  pendulum  in  1612.  Huygens  made  the  same  application 
only  in  1658,  which  is  the  date  of  his  work  on  the  subject.  In  the  same 
year,  Hooke  applied  a  spring  to  the  balance  of  a  watch  ;  t  and  soon  after, 
he  conceived  the  idea  of  improving  timekeepers  sufficiently  for  ascertaining 
the  longitude  at  sea,  J  but  he  was  interrupted  in  the  pursuit  of  his  plan. 
Hooke  was  also  probably  the  first  that  employed  for  a  clock  a  heavy 
weight  vibrating  in  a  small  arc  ;  an  arrangement  from  which  the  peculiar 
advantages  of  a  pendulum  are  principally  derived. 

The  objects  which  require  the  greatest  attention  in  the  construction  of 
timekeepers,  are  these ;  to  preserve  the  moving  power  or  sustaining  force 
as  equable  as  possible,  to  apply  this  force  to  the  pendulum  or  balance  in 
the  most  eligible  manner,  and  to  employ  a  pendulum  or  balance  of  which 
the  vibrations  are  in  their  nature  as  nearly  isochronous  as  possible.  In 
clocks,  the  sustaining  force,  being  generally  derived  from  a  weight,  is  al- 
ready sufficiently  equable,  provided  that  care  be  taken  that  the  line  by 
which  it  is  suspended  may  be  of  equal  thickness  throughout,  and  may  act 

*  Mem.  dell'  Acad.  del  Cimento.     The  date  is  there  stated  as  1583. 

t  Cassini  laid  claim  to  this  invention,  in  behalf  of  Huygens,  but  Hooke  proves 
that  he  had  not  only  conceived  it  but  sent  it  to  Huygens  fifteen  years  before,  who 
wrote  a  letter  against  it  as  impracticable.  Philosoph.  Exp.  &c.  by  Hooke,  p.  388. 
The  main  merit  of  the  application  of  the  pendulum  to  clocks  probably  belongs  to 
Huygens.  +  Ibid.  p.  4. 

L2 


148  LECTURE  XVII. 

on  a  perfect  cylinder.  But  in  some  clocks,  and  in  all  watches,  the  moving 
power  is  a  spring.  One  of  the  first  clock  springs  is  said  to  have  been  an 
old  sword  blade  ;  a  clock  with  such  a  spring  was  lately  preserved  at  Brus- 
sels :  the  spring  which  is  at  present  used,  is  a  thin  elastic  plate  of  steel, 
coiled  into  a  spiral  form.  Every  spring  exerts  the  more  force  as  it  is  more 
bent ;  in  order  to  correct  this  inequality,  the  chain  or  cord  by  which  it  acts 
on  the  work  is  wound  on  a  spiral  fusee  ;  so  that  in  proportion  as  the  force 
is  lessened,  it  is  applied  to  a  larger  cylinder  or  a  longer  lever.  The  gene- 
ral outline  of  the  fusee  must  be  nearly  such  that  its  thickness  at  any  part 
may  diminish  in  the  same  proportion  as  it  becomes  more  distant  from  the 
point  at  which  the  force  would  cease  altogether,  the  curve  being  that  which 
is  denominated  a  hyperbola ;  but  the  workmen  have  in  general  no  other 
rule  than  an  habitual  estimation.*  (Plate  XV.  Fig.  199.) 

Notwithstanding  all  possible  precautions  in  the  immediate  application  of 
the  weight  or  spring,  the  irregular  action  of  the  teeth  of  the  wheels,  the  in- 
creasing tenacity  of  the  oil  usually  employed,  and  other  accidental  dis- 
turbances, make  it  still  desirable  to  procure  a  further  equalisation  of  the 
force  ;  which  is  sometimes  obtained  in  clocks  by  raising  the  loaded  arm  of 
a  lever  to  a  given  height  whence  it  may  descend ;  and  in  watches,  by 
bending  a  spring  into  a  given  position  from  which  it  may  return,  so  as  to 
limit  with  great  precision  the  propelling  force  employed  in  each  vibration. 
The  necessity  of  applying  oil  is  sometimes  in  great  measure  removed  by 
jewelling  the  holes  in  which  the  axes  or  verges  run;  a  perforation  being 
made  in  a  plate  of  ruby,  and  a  diamond  applied  upon  this,  in  contact  with 
the  end  of  the  axis  ;  the  hardness  and  high  polish  of  these  stones  tending 
very  considerably  to  diminish  the  friction. 

There  are  also  different  methods  of  continuing  the  action  of  the  force 
while  the  clock  or  watch  is  wound  up  :  a  spring  is  interposed  between  the 
fusee  and  the  wheel  impelled  by  it,  a  little  inferior  in  force  to  the  original 
weight  or  spring,  so  as  to  remain  always  bent,  until,  when  the  pressure  of 
the  main  spring  is  removed,  it  begins  to  act  upon  a  fixed  point  on  one  side, 
and  upon  the  wheel  of  the  fusee  on  the  other,  so  that  it  propels  the  work  for 
a  short  time  with  a  force  nearly  equal  to  that  of  the  main  spring.  Some- 
times also  the  spring  is  wound  up  by  causing  a  small  wheel  to  revolve 
round  the  centre  of  the  fusee,  having  its  teeth  engaged  on  one  side  in  those 
of  a  wheel  which  makes  a  part  of  the  fusee,  and  on  the  other  side  with  the 
internal  teeth  of  a  hoop  connected  with  the  work,  so  that  the  same  pressure 
which  winds  up  the  spring  tends  also  to  turn  the  hoop  round,  and  to  con- 
tinue the  motion.  (Plate  XVI.  Fig.  200.) 

The  scapement,  by  which  the  sustaining  force  is  communicated  to  the 
pendulum  or  balance,  demands  a  greater  exertion  of  skill  and  accuracy 
than  any  other  part  of  a  timekeeper.  Sometimes  the  alternate  motion  of 
the  pendulum  has  been  produced  by  the  action  of  a  crank,  but  this  con- 
struction subjects  it  too  much  to  the  irregularities  of  the  wheel  work,  and 
is  liable  to  several  other  objections.  A  crank  cannot  properly  be  called  a 
scapement,  for  according  to  the  etymology  of  the  term,  the  pendulum  must 

*  Lahire  on  the  Figure  of  Fusees,  Hist,  et  Mem.  de  Paris,  ix.  102.  Varignon 
on  do.  ibid.  1702,  p.  192,  H.  122. 


ON  TIMEKEEPERS.  149 

escape  for  a  time  from  the  action  of  the  wheelwork,  and  in  general,  the 
more  independent  its  motion  is  rendered  the  better  is  the  effect  of  the 
machine.  The  simplest  forms  in  common  use  are  the  crutch  scapement 
for  a  clock,  and  the  pallets  with  a  vertical  wheel  for  a  watch ;  the  dead 
beat  scapement,  and  the  cylinder  with  a  horizontal  wheel,  are  improve- 
ments on  these ;  and  the  detached  scapement  is  a  still  further  refinement. 

The  crutch  scapement,  called  by  the  French  the  anchor  scapement,  is 
an  arch  in  the  plane  of  the  scape  wheel,  and  parallel  to  that  in  which  the 
pendulum  vibrates,  supporting  at  each  extremity  a  pallet,  of  which  the 
face  is  a  plane,  and  which  is  impelled  in  its  turn  by  the  teeth  of  the  scape 
wheel.  The  faces  are  so  inclined  that  the  pallets  are  alternately  forced,  by 
the  action  of  the  teeth,  to  retire  from  the  centre  of  the  wheel :  and  great 
care  is  taken  in  making  the  teeth  exactly  at  equal  distances,  so  that  they 
may  fall  regularly  on  the  pallet,  immediately  after  the  disengagement  of 
the  teeth  on  the  other  side  from  the  opposite  pallet.  (Plate  XVI.  Fig.  201.) 

In  the  common  watch,  the  axis  of  the  balance  is  parallel  to  the  plane  of 
the  scape  wheel,  which  is  a  contrate  or  crown  wheel,  and  the  flat  pallets 
are  fixed  on  the  axis  of  the  balance  at  the  opposite  parts  of  the  circum- 
ference of  the  scape  wheel.  (Plate  XVI.  Fig.  202.) 

In  both  these  cases  the  impulse  given  to  one  pallet  carries  the  opposite 
pallet  with  some  force  against  the  approaching  tooth,  and  drives  the  wheel 
a  little  backwards  with  a  visible  recoil.  Here  the  sustaining  power,  being 
applied  principally  at  the  extremities  of  the  vibrations,  disturbs  their  iso- 
chronism  or  the  equality  of  the  times  in  which  they  are  performed,  by 
partially  increasing  the  force.  We  may  recollect  that,  in  order  that  all 
vibrations,  of  whatever  magnitude  may  be  performed  in  equal  times,  the 
force  must  be  exactly  proportional  to  the  distance  from  a  given  point, 
consequently  if  an  additional  force  be  applied  near  the  extremities  of  the 
vibration  only,  the  longer  vibrations  will  occupy  less  time  than  the  shorter ; 
and  we  may  observe  that,  by  adding  to  the  force  of  the  spring  of  a  common 
watch,  with  the  key,  we  may  accelerate  its  motion,  at  the  same  time  that 
the  angular  magnitude  of  the  vibration  is  increased.  The  motion  of  the 
balance  also,  being  slowest  at  the  extremities  of  its  vibration  where  the 
sustaining  force  is  applied,  is  more  affected  by  the  inequalities  of  this  force 
than  if  it  were  subjected  to  its  action  through  an  equal  space  in  the  middle 
of  the  vibration.  Yet  a  good  clock  on  this  construction  may  keep  time 
without  an  error  of  the  ten  thousandth  part  of  the  whole,  and  a  watch 
within  a  two  thousandth.  In  the  common  watch  scapement  there  is  little 
friction,  for  the  force  acts  almost  perpendicularly  on  the  pallet ;  it  appears 
to  have  been  the  oldest  scapement,  and  was  employed  before  the  applica- 
tion of  springs  to  balances  :  it  requires  a  considerable  extent  of  motion  in 
the  balance,  and  cannot  therefore  well  be  applied  to  clocks  with  such  pen- 
dulums as  vibrate  in  small  arcs.  The  crutch  scapement,  on  the  contrary, 
cannot  be  applied  immediately  to  a  vibration  in  a  very  large  arc  ;  but  by 
the,  interposition  of  a  lever  with  a  roller,  or  of  a  part  of  a  wheel  with  a 
pinion,  it  may  be  adapted  to  the  balance  of  a  watch  ;  and  some  watches 
thus  constructed  by  Emery,  Letherland  and  others,  appear  to  have  suc- 
ceeded very  well. 


150  LECTURE  XVII. 

To  avoid  the  inconveniences  of  the  recoiling  scapements,  Mr.  Graham 
invented  or  introduced  the  dead  beat  for  the  clock,  and  the  cylinder  for 
the  watch.*  In  both  of  these,  the  tooth  of  the  scape  wheel  rests,  during 
the  greater  part  of  the  vibration,  on  a  cylindrical  surface,  and  acts  on  the 
inclined  plane  for  a  short  time  only  in  the  middle  of  each  vibration  ;  so 
that  a  change  of  the  sustaining  power  scarcely  produces  a  sensible  derange- 
ment of  the  isochronism  ;  for  which  ever  way  we  turn  the  key  of  a  hori- 
zontal watch,  as  long  as  it  continues  to  go,  the  frequency  of  its  vibrations 
is  scarcely  affected.  A  good  horizontal  watch  will  keep  time  within  about 
a  ten  thousandth  part,  especially  if  a  little  oil  be  frequently  applied  to  it, 
or  if  the  cylinder  be  made  of  a  ruby  :  and  the  timekeeper  in  the  obser- 
vatory at  Greenwich  with  a  dead  beat  scapement,  made  by  Graham,  varies 
from  true  time  only  two  parts  in  a  million.  (Plate  XVI.  Fig.  203,  204.) 

Still,  however,  the  friction  of  the  teeth  of  the  scape  wheel  on  the  cylin- 
der or  pallet,  and  the  tenacity  of  the  oil,  where  it  is  employed,  may  in- 
terfere in  a  slight  degree  with  the  time  of  vibration,  especially  by  the 
irregularities  to  which  they  are  liable.  Since  friction  is  always  increased 
by  an  increase  of  pressure,  the  effect  of  any  addition  to  the  sustaining 
force  must  tend  in  some  degree  to  retard  the  vibrations,  even  if  the  friction 
be  somewhat  less  increased  than  the  force  propelling  the  balance.  In  order 
to  obviate  this  retardation,  the  surfaces  on  which  the  teeth  rest,  have  some- 
times been  so  formed  as  to  create  a  slight  recoil ;  but  this  construction  does 
not  appear  to  have  been  very  successful  in  practice.  The  friction  may, 
however,  be  considerably  diminished  by  the  duplex  scapement,  apparently 
so  called  from  the  double  series  of  teeth  employed.  The  teeth  of  the  more 
prominent  series  are  detained  on  a  cylinder  so  small  as  to  be  unfit  for  re- 
ceiving an  impulse  from  them,  the  balance  is  therefore  impelled  by  the  other 
series  of  teeth,  acting  on  a  pallet  at  a  greater  distance  from  its  axis.  The 
French  have  sometimes  employed  a  construction  somewhat  similar,  which 
they  call  the  comma  scapement,  the  teeth  first  resting  on  a  small  arch  of 
repose,  and  then  impelling  the  curved  surface  of  a  pallet  extending  to  a 
considerable  distance  beyond  it.  In  both  these  cases  the  single  pallet, 
which  is  impelled  by  a  tooth  of  a  simple  form,  requires  less  labour  in  the 
execution  than  a  number  of  larger  teeth,  each  of  which  is  to  be  finished 
with  great  accuracy :  but  watches  on  these  constructions,  especially  those 
with  the  comma  scapement,  are  too  liable  to  be  stopped  by  any  sudden 
motion,  although  the  duplex  scapement  begins  to  be  frequently  employed 
for  pocket  timekeepers.  (Plate  XVI.  Fig.  205.) 

Mr.  Harrison  avoided  all  friction  on  the  pallet,  by  connecting  it  with 
the  pendulum  by  means  of  a  slender  spring,  so  flexible  as  to  follow  the 
motion  of  the  scape  wheel  to  a  sufficient  extent  without  sliding  on  its 
teeth.  But  the  construction  which  is  most  usually  employed  where  the 
greatest  accuracy  is  required,  is  the  detached  scapement:  in  which  the 
teeth  of  the  scape  wheel  always  rest  on  a  detent,  excepting  a  short  interval 
when  it  is  unlocked  in  order  to  impel  the  pallets.  Mr.  Mudget  employed  a 
detached  scapement  actuated  by  a  subsidiary  spring,  of  which  the  force  is 

*  See  Nich.  Journal,  4to,  ii.  49. 

f  Mudge  on  a  Scapement,  1763.     On  a  Timekeeper,  4to,  1799. 


ON  TIMEKEEPERS.  151 

scarcely  liable  to  any  variation  ;  the  detent  being  unlocked  by  the  motion 
of  the  balance.  Mr.  Haley*  has  refined  still  further  on  this  construction, 
by  causing  the  subsidiary  spring  to  unlock  the  wheel  in  its  return,  so  that 
the  balance  is  relieved  from  this  action,  which  may  sometimes  produce  a 
slight  irregularity.  These  constructions  are,  however,  much  too  delicate 
for  common  pocket  watches.  In  a  clock,  Mr.  Gumming  has  employed  a 
detached  scapement,  in  which  a  lever  is  raised  to  a  certain  height  by  each 
tooth  of  the  scape  wheel,  and  acts  immediately  on  the  pendulum  in  its 
descent  in  the  middle  of  the  vibration.  The  scape  wheel  is  unlocked  by 
the  pendulum  during  its  ascent,  and  a  variation  of  the  pressure  may,  there- 
fore, produce  a  very  slight  inequality  in  the  motion  of  the  pendulum.  Mr. 
Nicholson  has  attempted  to  remove  this  cause  of  error,  by  a  construction 
in  which  the  scape  wheel  only  assists  the  pendulum  in  raising  the  lever  ; 
but  it  depends  on  the  degree  of  force  applied,  to  determine  what  part  of 
the  weight  the  scape  wheel  shall  sustain  ;  this  scapement  cannot,  therefore, 
by  any  means  be  considered  as  detached.  It  is,  however,  easy  to  remove 
the  defect  of  Mr.  Gumming' s  scapement,  if  it  can  be  called  a  defect,  by  a 
method  similar  to  that  which  Mr.  Haley  has  applied  to  watches  ;  each 
tooth  of  the  wheel  being  unlocked  by  the  descent  of  the  lever  on  the  op- 
posite side,  at  the  moment  that  it  ceases  to  act  on  the  pendulum,  and 
remaining  inactive  until  the  pendulum  meets  it.  (Plate  XVI.  Fig.  206,  207.) 

The  detents  of  the  scapements  of  Mudge  and  Gumming  are  parts  of  the 
pallet,  but  in  the  timekeepers  now  commonly  made  by  Arnold,  Earnshaw, 
and  others,  the  tooth  is  detained  by  a  pallet  or  pin  projecting  from  a  lever, 
the  point  of  which  is  forced  back  by  the  balance,  at  the  moment  that  the 
pallet  presents  itself  to  another  of  the  teeth.  Mr.  Arnold  employs  an 
epicycloidal  tooth,  acting  on  a  single  point  of  the  pallet  ;t  Mr.  Earnshaw 
makes  a  flat  surface  of  the  tooth  first  act  on  the  point  of  the  pallet,  and 
then  the  point  of  the  tooth  on  a  flat  surface  of  the  pallet.^  In  other 
respects  there  is  little  difference  in  these  scapements  ;  and  both  the  artists 
have  been  judged  worthy  of  a  public  reward  for  their  success.  (Plate 
XVI.  Fig.  208,  209.) 

The  last  of  the  three  principal  objects,  which  require  the  attention  of  the 
watchmaker,  is  to  employ  a  pendulum  or  balance  of  which  the  vibrations 
are  in  their  nature  perfectly  isochronous.  For  this  purpose  the  weight  of 
the  pendulum  ought  to  move  in  a  cycloidal  arc,  but  the  difficulty  of  pro- 
ducing such  a  motion  in  practice  is  much  greater  than  the  advantage  derived 
from  it,  and  a  circular  vibration,  confined  to  a  small  arc,  is  sufficiently 
isochronous  for  all  practical  purposes.  The  error  of  such  a  vibration  is 
nearly  proportional  to  the  square  of  the  arc  described  by  the  pendulum, 
and  amounts  to  a  second  and  a  half  in  a  day  of  24  hours,  for  a  single  degree 
on  each  side  the  point  of  rest ;  so  that  a  pendulum  keeping  true  time  in 
an  arc  of  three  degrees,  would  gain  13i  seconds  if  the  arc  were  very  much 

*  Haley's  Patent  Timekeeper,  Repertory  of  Arts,  vi.  145. 

•  f  Explanation  of  Mr.  Arnold's  Timekeeper.  Questions  proposed  by  the  Board 
of  Long,  relative  to  the  same,  4to,  1804-5. 

J  Explanation  of  Mr.  Eamshaw's  Timekeeper.  Questions  proposed  by  the 
Board  of  Long,  relative  to  the  same,  4 to,  1804-5. 


152  LECTURE  XVII. 

contracted  or  made  cycloidal,  and  would  lose  10£  seconds  by  having  the 
vibration  extended  to  an  arc  of  four  degrees.  In  order  to  avoid  the  friction 
which  would  be  occasioned  by  the  motion  of  the  pendulum  on  an  axis,  it  is 
usually  suspended  by  a  flexible  spring  which  is  wholly  free  from  friction. 
The  elasticity  of  this  spring  adds  a  minute  force  to  the  power  of  gravitation 
which  acts  on  the  pendulum,  and  this  force  must  be  considered,  when  the 
length  of  a  simple  pendulum  is  compared  with  the  frequency  of  its  vibra- 
tions. It  does  not,  however,  interfere  with  the  equality  of  the  vibrations 
among  each  other ;  for  in  all  springs,  Dr.  Hooke's  general  law,*  that  the 
force  increases  as  the  degree  of  flexure,  is  found  for  moderate  oscillations 
to  be  perfectly  accurate  ;  such  a  force,  therefore,  accelerates  the  larger  and 
the  smaller  vibrations  precisely  in  the  same  degree.  But  in  balances,  it  is 
desirable  to  have  the  velocity  and  the  extent  of  the  vibration  as  great  as 
possible,  in  order  that  the  motion  may  be  the  less  influenced  by  the  ine- 
qualities of  the  sustaining  power ;  and  in  large  excursions,  Dr.  Hooke's 
law  is  not  so  precisely  true ;  there  must  also  necessarily  be  some  inaccuracy 
from  the  loss  of  a  certain  portion  of  the  force  in  generating  the  momentum 
of  the  spring  itself,  which,  when  the  form  is  spiral,  introduces  great  intricacy 
into  the  calculation  of  the  properties  of  the  vibration.  Yet  it  has  been 
found  by  experiment  that  a  certain  kngth  may  be  determined  for  almost 
every  spring,  which  will  afford  vibrations  either  perfectly  or  veiy  nearly 
isochronous.  In  order  that  the  weight  or  inertia  of  the  spring  may  inter- 
fere the  less  with  the  regularity  of  its  motion,  it  is  sometimes  tapered  and 
made  thinner  at  the  extremity:  it  is  now  also  usual  in  the  best  watches  to 
employ  a  spring  coiled  into  a  cylindrical  form,  like  that  of  the  spring  of  a 
bell,  of  which  the  motion  appears  to  be  somewhat  more  regular  than  that 
of  a  flat  spiral.  This  was  indeed  the  original  construction,  but  was  pro- 
bably laid  aside  on  account  of  the  space  which  it  required.  The  balance 
springs  are  made  of  the  finest  steel,  and  the  best  are  manufactured  in  this 
country,  although  the  French  are  said  to  have  the  art  of  making  their  main 
springs  of  a  better  temper  than  ours.  Sometimes  the  balance  spring-  is 
made  of  an  alloy  of  gold  and  copper ;  these  springs  are  very  elastic,  but 
they  are  too  liable  to  break.  Mr.  Earnshaw  observes  that  the  strength  of 
a  spring  always  diminishes  a  little  as  it  wears  ;  and  endeavours  to  derive 
a  compensation  for  this  diminution  of  strength,  by  employing  a  spring  of 
such  a  form,  that  the  vibrations  in  small  arcs  may  be  a  little  more  frequent 
than  in  larger  ones,  in  order  that  when  the  presence  of  dust  and  the 
tenacity  of  the  oil  contract  the  extent  of  the  vibrations,  this  contraction 
may  tend  to  produce  an  acceleration  which  compensates  for  the  diminished 
force  of  the  spring.  But  it  is  perhaps  more  eligible  to  make  every  com- 
pensation, as  far  as  possible,  independent  of  circumstances  foreign  to  the 
cause  of  the  error.  The  strength  of  the  spring  is  found  to  be  less  impaired 
by  use  when  it  is  hardened  than  when  the  steel  is  softer.  It  sometimes 
happens,  that  from  a  sudden  motion,  or  from  some  other  accidental  circum- 
stance, the  balance  of  a  timekeeper  may  be  thrown  beyond  the  point  at 
which  the  pallets  are  impelled  by  the  scape  wheels,  and  the  whole  motioli 

*  Hooke,  De  Potentia  Restitutiva,  4to,  Lond.  1678.     This  law  was  published  by 
him  about  the  year  1660,  in  the  form  of  an  anagram. 


ON  TIMEKEEPERS.  153 

may  from  this  cause  be  interrupted.  To  prevent  this  accident,  a  small  bar 
or  pin  is  usually  fixed  on  the  balance  spring,  which  is  carried  outwards 
when  the  vibration  begins  to  be  extended  too  far,  and  stops  the  further 
progress  of  the  balance  by  intercepting  a  pin  which  projects  from  it.  This 
arrangement  is  called  banking  the  balance. 

We  have  already  seen  that  the  squares  of  the  times  of  vibration  of  two 
pendulums  are  proportional  to  their  lengths  ;  so  that  if  we  add  to  a  pen- 
dulum one  hundredth  part  of  its  length,  we  increase  the  time  of  its  vibration 
very  nearly  one  two  hundredth.  But  since  all  bodies  are  expanded  by  heat, 
the  variable  temperature  of  the  atmosphere  must  necessarily  produce 
changes  of  this  kind  in  the  motions  of  pendulums,  and  it  may  be  observed 
that  a  clock  goes  somewhat  more  slowly  in  summer  than  in  winter.  The 
same  expansion  has  a  similar  effect  in  the  motion  of  a  balance,  and  the 
increase  of  temperature  produces  also  a  diminution  of  the  elastic  force  of 
the  spring  itself.  There  is,  however,  a  great  difference  in  the  expansibilities 
of  various  substances  ;  dry  deal  is  one  of  the  least  expansible,  and  is  there- 
fore often  used  for  the  rods  of  pendulums.  Brass  expands  one  part  in  a 
hundred  thousand  for  every  degree  of  Fahrenheit,  or  a  little  more  or  less 
than  this,  accordingly  as  it  contains  more  or  less  zinc.  Glass  and  platina 
are  less  than  half  as  expansible  as  brass,  iron  about  two  thirds,  and 
mercury  three  times  as  much.  A  pendulum  of  brass  would  therefore 
make  one  vibration  in  ten  thousand  less  at  70°  than  at  50°,  and  would  lose 
8^  seconds  in  a  day :  a  balance  regulated  by  a  spring  would  lose  much 
more ;  for  I  have  observed  that  vibrations  governed  by  the  elasticity  of 
steel  have  lost  in  frequency  as  much  as  one  ten  thousandth  part  for  a 
single  degree  of  Fahrenheit ;  and  Berthoud  informs  us,  that  where  a  clock, 
probably  with  a  pendulum  of  steel,  loses  20  seconds  by  heat,  a  watert  loses 
eight  minutes. 

Mr.  Graham  appears  to  have  been  the  first  that  attempted  to  compen- 
sate for  the  effects  of  temperature  by  the  different  expansibilities  of  various 
substances.  He  employed  for  a  pendulum,  a  tube  partly  filled  with  mer- 
cury ;  when  the  tube  expanded  by  the  effect  of  heat,  the  mercury  expanded 
much  more  ;  so  that  its  surface  rose  a  little  more  than  the  end  of  the  pen- 
dulum was  depressed,  and  the  centre  of  oscillation  remained  stationary.* 
This  mode  of  compensation  is  still  practised  with  success;  but  the 
gridiron  pendulum  is  more  commonly  used  ;  it  was  the  invention,  of 
Harrison,  t  who  combined  seven  bars,  of  iron  or  steel,  and  of  brass,  in  such 
a  manner,  that  the  bars  of  brass  raised  the  weight  as  much  as  the  bars  of 
iron  depressed  it.  At  present  five  bars  only  are  usually  employed,  two  of 
them  being  of  a  mixture  of  zinc  and  silver,  and  three  of  steel.  Mr.  Ellicott$ 
suspended  a  pendulum  at  the  extremity  of  a  lever,  which  was  supported* 
by  a  pillar  of  brass  much  nearer  to  the  fulcrum  ;  as  the  pendulum  ex- 
panded, the  end  of  the  lever  was  raised  in  the  same  degree,  and  the  weight 

*  A  Contrivance  to  avoid  the  Irregularities  of  a  Clock's  Motion,  Ph.  Tf.  1726. 
xxxiv.  40. 

t  In  1726.  An  account  is  to  be  found  in  the  Minutes  of  the  Roy.  Soc.  for  1749, 
and  in  Ph.  Tr.  xlvii.  521.  See  also  Harrison's  work,  with  preface  by  Maskelyne, 
4to,  Lond.  1767. 

J  Ph.  Tr.  1752,  xlvii.  479. 


154  LECTURE  XVII. 

remained  at  its  original  distance  from  the  point  of  suspension,  which  was 
determined  hy  a  fixed  plate,  transmitting  the  slender  spring,  as  usual,  be- 
tween two  opposite  edges.  The  same  effect  is  produced  more  simply  by 
suspending  the  pendulum  from  the  summit  of  a  bar  nearly  parallel  to  it, 
and  of  the  same  substance  with  itself,  resting  on  a  fixed  support,  and  either 
of  the  same  length  with  the  pendulum,  or  a  little  longer,  accordingly  as 
the  distance  of  the  fixed  plate  from  the  point  of  support  of  the  bar,  is 
determined  by  materials  which  may  be  considered  as  nearly  of  an  inva- 
riable length,  or  as  liable  to  a  certain  degree  of  expansion.  (Plate  XVI. 
Fig.  210.) 

All  these  methods  of  compensation  are  peculiar  to  clocks  ;  for  watches, 
it  is  usual  to  unite  together  two  metals  which  differ  in  expansibility,  so  as 
to  form  a  compound  plate  ;  one  side  of  the .  plate  is  commonly  of  steel, 
the  other  of  brass,  and  it  is  obvious  that  any  increase  of  temperature,  by 
causing  the  brass  to  expand  more  than  the  steel,  must  bend  the  whole  plate. 
Such  a  plate  is  variously  applied  ;  the  most  accurate  method,  which  is 
employed  by  Arnold  and  other  modern  artists,  is  to  make  it  a  part  of  the 
balance  itself,  fixing  a  weight  on  its  extremity,  which  is  brought  nearer  to 
the  centre,  by  the  increase  of  curvature  of  the  plate,  whenever  the  ex- 
pansion of  the  arms  of  the  balance  tends  to  remove  it  further  off.  The 
best  way  of  making  the  plate  appears  to  be  to  turn  a  ring  of  steel,  and  to 
immerse  it  in  melted  brass,  and  then  to  turn  away  what  is  superfluous  of 
the  brass.  The  magnitude  of  the  weight,  and  the  length  of  the  plate,  may 
easily  be  so  regulated  as  to  compensate  not  only  for  the  expansion  pro- 
duced by  heat,  but  also  for  the  diminution  of  the  elasticity  of  the  spring. 
Sometimes  also  a  plate  has  been  applied  in  such  a  way  as  to  shorten  the 
spring  when  the  temperature  is  increased,  by  an  operation  similar  to  that 
which  serves  to  regulate  a  common  watch,  the  clip  that  determines  the 
effective  length  of  the  spring,  being  moved  backwards  and  forwards  ;  and 
a  similar  effect  has  also  been  produced  by  dividing  this  clip  into  two  parts, 
one  of  which  is  fixed  to  a  compound  plate,  and  is  made  to  approach  the 
other,  so  as  to  confine  the  spring  more  narrowly  and  thus  diminish  its 
length,  upon  an  increase  of  temperature.  (Plate  XVI.  Fig.  211.) 

The  flexure  of  a  compound  plate  has  also  been  applied  in  a  simple  and 
elegant  manner  by  Mr.  Nicholson  to  the  pendulum  of  a  clock,  by  causing 
it  to  support  the  upper  extremity  of  the  pendulum.  The  plate  is  placed 
horizontally,  the  brass  being  uppermost,  and  carries  the  pendulum  in  the 
middle,  while  the  ends  rest  on  two  fixed  points,  of  which  the  distance  may 
be  adjusted  with  great  accuracy,  so  that  when  the  temperature  is  in- 
creased, the  curvature  of  the  plate  may  raise  the  rod  of  the  pendulum, 
enough  to  keep  the  weight  or  bob  at  a  constant  distance  below  the  fixed 
point,  which  determines  its  upper  extremity.  (Plate  XVI.  Fig.  212.) 

The  resistance,  opposed  to  the  motion  of  a  pendulum  by  the  air,  affects 
in  some  degree  its  velocity,  and  the  variation  of  the  density  of  the  atmo- 
sphere must  therefore  also  produce  some  irregularities  in  timekeepers  : 
they  are,  however,  too  small  to  be  sensible.  Derham*  found  that  fhe 
resistance  of  the  air  accelerated  the  motion  of  a  half  second  pendulum 
*  Ph.  Tr.  1704,  xxiv.  1785, 


ON  TIMEKEEPERS.  155 

about  four  vibrations  in  an  hour,  by  diminishing  the  arc  in  which  it 
vibrated  :  and  when  the  vibrations  were  restored  to  their  original  magni- 
tude, the  resistance  of  the  air  produced  a  retardation  of  eight  vibrations  in 
the  same  time.  But  a  heavy  pendulum,  vibrating  in  a  small  arc,  is  very 
little  affected  by  this  resistance. 

Besides  these  more  essential  parts  of  the  watchmaker's  art,  there  are 
several  subordinate  considerations  which  require  his  attention ;  the  striking 
part  in  particular  occupies,  in  clocks,  and  in  repeating  watches,  no  incon- 
siderable portion  of  the  bulk  of  the  machine.  But  the  apparatus  employed 
on  these  occasions  requires  neither  refinement  of  invention  nor  delicacy  of 
execution.  In  old  clocks,  the  number  of  hours  struck  is  usually  deter- 
mined by  the  revolution  of  a  certain  portion  of  a  wheel,  which  supports  an 
arm,  and  allows  the  hammer  to  strike,  until  at  a  proper  time  it  falls  into 
a  notch.  In  watches,  and  in  more  modern  clocks,  the  same  effect  is  pro- 
duced by  means  of  a  spiral  of  12  teeth,  revolving  once  in  12  hours. 

It  is  of  considerable  importance  to  the  accurate  performance  of  a  good 
clock,  that  it  should  be  firmly  fixed  to  a  solid  support.  Any  unsteadiness 
in  the  support  causes  the  point  of  suspension  to  follow  the  motion  of  the 
pendulum,  and  enlarges  the  diameter  of  the  circle  of  which  the  pendulum 
describes  an  arc  ;  it  must,  therefore,  tend  in  general  to  retard  the  motion  of 
the  clock.  Sometimes,  however,  an  unsteady  support  may  be  of  such  a 
nature  as  to  accelerate  the  motion ;  and  an  observation  of  this  kind,  made 
by  Berthoud,  has  suggested  to  Bernoulli  a  theory  of  compound  vibrations, 
which  may  perhaps  be  true  in  some  cases,  but  is  by  no  means  universally 
applicable  to  every  case.  On  account  of  some  circumstances  of  this  kind, 
it  happens  that  when  two  clocks  are  placed  near  each  other,  and  rest  in 
some  degree  on  the  same  support,  they  have  often  a  remarkable  effect  on 
each  other's  vibrations,  so  as  to  continue  going  for  several  days,  without 
varying  a  single  second,  even  when  they  would  have  differed  considerably 
if  otherwise  situated  :  and  it  sometimes  happens  that  the  clock  which  goes 
the  more  slowly  of  the  two  will  set  the  other  in  motion,  and  then  stop 
itself ;  a  circumstance  which  has  been  explained  from  the  greater  frequency 
of  the  vibrations  of  a  circular  pendulum  when  confined  to  a  smaller  arc,  the 
tendency  of  the  pendulums  to  vibrate  in  the  same  time  causing  the  shorter 
to  describe  an  arc  continually  larger  and  larger,  and  the  longer  to  contract 
its  vibrations,  until  at  last  its  motion  entirely  ceases.*  This  sympathy  has 
some  resemblance  to  the  alternate  vibrations  of  two  scales  hanging  on 
the  same  beam,  one  of  which  may  often  be  observed  to  stop  its  vibrations 
when  the  other  begins  to  move,  and  to  resume  its  motion  when  its  com- 
panion is  at  rest ;  but  it  is  still  more  analogous  to  the  mutual  influence  of 
two  strings,  or  even  two  organ  pipes,  which,  though  not  separately  tuned 
to  a  perfect  unison,  still  influence  each  other's  vibrations  in  such  a  manner 
as  to  produce  exactly  the  same  note  when  they  sound  together. 

*  Ellicott,  Ph.  Tr.  1739,  p.  126,  describes  the  interference  of  two  pendulums— 
tbe  one  set  the  other  in  motion — the  one  stopped  the  other,  &c. 


156  LECTURE  XVIII. 


LECT.  XVII.— ADDITIONAL  AUTHORITIES. 

Cumming's  Elements  of  Clock  and  Watch  Work,  4  to,  Lond.  1766.  Lepaute, 
Traite  d'Horlogerie,  4to,  Par.  1767.  Berthoud's  Works,  viz.  Essai  sur  1'Horlo- 
gerie,  2  vols.  4to,  Paris,  1763.  Traite  des  Horloges  Marines,  4to,  1773.  Surl'In- 
vention,  &c.  des  Machines  proposees  en  France  pour  la  Determination  des  Longi- 
tudes par  la  Mesure  du  Temps,  4to,  1773.  Supplement,  1787.  Trait6  des  Mon- 
tres  a  Longitudes,  4to,  1792.  Suite,  1797.  Supplement,  1807.  Robison,  Mech. 
Phil.  Reid,  Treatise  on  Clock  and  Watch  Work,  Edin.  1826.  Prony,  Note  sur  un 
Nouveau  Moyen  de  regler  la  Duree  des  Oscillations  des  Pendules,  4to,  Paris. 
Jurgensen,  MSmoires  sur  1'Horlogerie  Exacte,  4to,  Paris,  1832. 


LECTURE   XVIII. 


ON  RAISING  AND  REMOVING  WEIGHTS. 

THE  methodical  arrangement  of  our  subject  leads  us,  after  having  con- 
sidered the  modifications  of  force,  to  those  machines  which  are  intended  for 
counteracting  it,  or  for  producing  motion  in  opposition  to  an  existing  force. 
The  simplest  of  the  forces  to  be  counteracted  is  gravitation,  and  it  is  one 
of  the  most  common  employments  of  mechanical  powers  to  raise  a  weight 
from  a  lower  to  a  higher  situation.  This  operation  is  also  intimately 
connected  with  the  modes  of  overcoming  the  corpuscular  force  of  friction  or 
adhesion,  which  constitutes  the  principal  difficulty  in  removing  bodies 
horizontally  from  place  to  place  ;  for  if  we  had  only  to  produce  motion  in 
an  unresisting  mass  of  matter,  a  loaded  waggon  might  in  time  be  drawn 
along  by  a  silk  worm's  thread.  The  raising  and  removing  of  weights, 
therefore,  together  with  the  modes  of  avoiding  friction  in  general,  constitute 
the  first  part  of  the  subject  of  the  counteraction  of  forces,  and  the  remain- 
ing part  relates  to  the  machinery  intended  for  overcoming  the  other  cor- 
puscular powers  of  bodies  by  such  operations  as  are  calculated  to  change 
their  external  forms. 

Machines  for  raising  weights,  which  involve  only  the  mechanics  of  solid 
bodies,  are  principally  levers,  capstans,  wheels,  pullies,  inclined  planes, 
screws,  and  their  various  combinations  in  the  form  of  cranes. 

A  lever  is  a  very  simple  instrument,  but  of  most  extensive  utility  in 
raising  weights  to  a  small  height.  We  may  recollect  that  levers  are  distin- 
guished into  two  principal  kinds,  accordingly  as  the  power  and  weight 
are  on  different  sides  or  on  the  same  side  of  the  fulcrum ;  the  forces 
counteracting  each  other  being  in  the  one  case  in  the  same  direction,  in  the 
other,  in  opposite  directions.  Thus,  when  a  man  lifts  a  stone  by  means  of 
a  lever  of  the  first  kind,  resting  on  a  fulcrum  between  himself  and  the 
stone,  he  presses  down  the  end  of  the  lever,  and  the  utmost  force  that  fre 
can  apply  is  equal  to  the  whole  weight  of  his  body  ;  but  when  he  thrusts 
the  lever  under  the  stone,  so  that  its  extremity  bears  on  the  ground,  it 
becomes  a  lever  of  the  second  kind,  and  in  order  to  raise  the  stone,  he  must 


ON  RAISING  AND  REMOVING  WEIGHTS.  157 

now  draw  the  end  of  the  lever  upwards.  In  this  direction,  a  strong  man 
can  exert  a  force  equivalent  to  twice  his  weight ;  consequently  the  second 
kind  of  lever  possesses  here  a  temporary  advantage  over  the  first  ;  although, 
if  the  operation  were  continued,  the  workman  would  he  more  fatigued  by 
raising  even  the  same  weight  hy  this  method,  than  if  he  could  conveniently 
apply  his  weight  to  a  lever  of  the  first  kind  :  and  for  this  purpose,  cross 
bars  have  sometimes  been  added  to  levers,  in  order  to  enable  several  work- 
men to  stand  on  them  with  advantage  at  once.  A  bent  lever  operates 
precisely  with  the  same  power  as  a  straight  one,  provided  that  the  forces  be 
applied  in  a  similar  manner  with  respect  to  its  arms  :  and  in  all  cases,  the 
forces  capable  of  balancing  each  other  are  inversely  as  the  distances  of  the 
points  of  action  from  the  fulcrum.  Some  addition  of  force  is  necessary  for 
overcoming  the  equilibrium  and  producing  motion,  but  the  velocity  of  the 
motion  being  seldom  of  much  consequence,  a  small  preponderance  is  usually 
sufficient. 

The  principal  inconvenience  of  the  lever  is  the  short  extent  of  its  action  : 
this  may,  however,  be  obviated  by  means  of  the  invention  of  Perrault, 
in  which  two  pins  are  fixed  in  the  lever,  at  a  short  distance  from  each 
other,  sliding  in  two  pairs  of  vertical  grooves  provided  with  ratchets,  so  that 
when  the  long  arm  of  the  lever  is  pulled  by  means  of  a  rope,  the  nearer  pin 
serves  as  a  fulcrum,  and  the  more  distant  one  is  elevated  at  the  same  time 
with  the  weight,  and  is  detained  in  its  place  by  the  click ;  but  when  the 
rope  is  slackened,  the  weight  sinks  a  little,  and  raises  the  pin  which  first 
served  as  a  fulcrum,  to  a  higher  place  in  its  groove.  The  same  effects  may 
also  be  produced  by  catches  or  clicks  resting  upon  ratchets  on  the  opposite 
sides  of  a  single  upright  bar,  which  passes  through  a  perforation  in  the 
lever.  There  must,  however,  be  a  considerable  loss  of  force  from  the  con- 
tinual intermission  of  the  motion.  (Plate  XVII.  Fig.  213.) 

An  axis  with  a  winch,  that  is,  a  lever  bent  at  the  end,  is  known  from 
the  common  machine  for  raising  a  bucket  out  of  a  well.  A  vertical  or 
upright  axis  with  two  or  more  levers  inserted  into  it,  becomes  a  capstan. 
In  these  cases,  if  we  wish  to  estimate  the  force  with  accuracy,  we  must  add 
to  the  radius  of  the  axis  half  the  thickness  of  the  rope,  when  we  compare 
it  with  the  arm  of  the  lever. 

Sometimes  the  weight  of  a  reservoir  or  bucket  of  water  is  employed  for 
raising  another  bucket,  filled  with  coals  or  other  materials,  by  means  of  a 
rope  or  chain  coiled  round  a  cylinder  or  drum,  or  two  drums  of  different 
sizes.  This  machine  is  called  a  water  whimsey :  when  the  bucket  of 
water  has  reached  the  bottom,  a  valve  is  opened  by  striking  against  a  pin, 
and  lets  out  the  water.  In  a  machine  of  this  kind  employed  in  the  Duke 
of  Bridgwater's  coal  works,  the  water  descends  thirty  yards  and  raises  a 
smaller  quantity  of  coals  from  a  depth  of  sixty.  In  such  cases,  supposing 
the  action  to  be  single,  and  the  stream  of  water  to  be  unemployed  during 
the  descent  of  the  reservoir,  a  considerable  preponderance  may  be  advan- 
tageously employed  in  giving  velocity  to  the  weights,  provided  that  the 
machinery  be  not  liable  to  injury  from  their  impulse. 

An  erect  axis  or  drum,  turned  by  the  force  of  horses  walking  in  a  circle, 
is  used  for  raising  coals  and  other  weights,  and  is  called  a  gin,  probably  by 


158  LECTURE  XVIII. 

corruption  from  engine  :  the  buckets  being  attached  to  the  opposite  ends  of 
a  rope  which  passes  round  the  drum,  and  which  is  drawn  by  means  of  its 
adhesion  to  the  drum.  One  of  the  buckets  descends  empty  while  the  other 
is  drawn  up  full,  and  when  the  motions  of  the  buckets  are  to  be  changed, 
the  horses  are  turned,  or  the  wheels  are  made  to  impel  the  axis  in  a  con- 
trary direction  when  any  other  moving  power  is  employed. 

When  a  ship's  anchor  is  weighed,  the  cable  itself  would  be  too  large  to 
be  bent  round  the  capstan  ;  it  is  therefore  connected  with  it  by  means  of  an 
endless  rope,  called  a  messenger.  As  the  messenger  is  coiled  round  the 
lower  part  of  the  capstan,  it  quits  the  upper  part ;  so  that  its  place  becomes 
lower  and  lower,  till  at  last  it  has  no  longer  room  on  the  capstan  ;  it  is 
therefore  necessary  to  force  it  up  from  time  to  time  :  this  is  called  surging 
the  messenger ;  it  is  commonly  done  by  beating  it,  and  to  facilitate  the 
operation,  the  capstan  is  made  somewhat  conical.  It  has  been  proposed  to 
employ  lifters  in  different  parts  of  the  circumference,  which  are  raised 
once  in  each  revolution,  by  passing  over  an  inclined  plane,  with  the  inter- 
position of  friction  wheels  ;  a  patent  has  been  taken  out  for  the  invention, 
and  it  has  already  been  introduced  in  the  navy.  Some  experienced  judges, 
however,  are  of  opinion,  that  it  would  be  better  and  more  simple  to  employ 
a  capstan  so  much  tapered  that  the  tension  of  the  rope  itself,  guided  only 
by  a  pulley,  might  always  be  sufficient  to  bring  the  messenger  into  its 
place.  * 

The  capstan,  which  consists  of  two  cylinders  of  different  sizes,  on  the 
same  axis,  with  a  rope  passing  from  the  smaller  one  over  a  pulley  which  is 
connected  with  the  weight,  and  returning  to  be  wound  up  by  the  larger  one, 
is  very  powerful  in  its  operation  ;  but  it  requires  a  great  length  of  rope  for 
a  small  extent  of  motion.  (Plate  IV.  Fig.  61.) 

Wheelwork  is  employed  in  a  variety  of  ways  for  raising  weights  :  its 
powers  are  in  all  cases  derived  from  the  same  principles  as  the  actions  of 
levers,  each  wheel  and  pinion  being  considered  as  composed  of  a  series  of 
bent  levers  of  which  the  axis  is  the  common  fulcrum,  and  which  act  in  suc- 
cession on  the  teeth  of  the  next  wheel.  The  simplest  combination  of  wheel- 
work  used  for  this  purpose  constitutes  a  jack ;  a  bar  which  is  furnished 
with  teeth  on  one  side,  being  raised  by  the  last  pinion.  Such  instruments 
were  not  unknown  even  to  the  ancients  ;  the  barulcust  described  by  Hero 
was  a  machine  of  this  nature. 

A  series  of  buckets  connected  by  ropes  and  passing  over  a  wheel,  is  often 
employed  for  raising  water  to  a  small  height,  and  sometimes  even  for  solid 
substances  in  the  state  of  powder,  in  particular  for  raising  flour  in  a  corn 
mill ;  and  in  this  case  the  flour  must  be  brought  within  reach  of  the  buckets 
by  means  of  a  revolving  spiral,  which  pushes  it  gradually  forwards. 
When  a  weight  of  any  kind  is  raised  in  buckets  distributed  through  the 
circumference  of  a  wheel,  the  force  required  for  retaining  the  weight  in 
equilibrium,  is  as  much  less  than  the  weight,  as  the  diameter  of  a  circle  is. 
less  than  half  the  circumference,  the  remainder  of  the  weight  being  sup- 
ported by  the  axis  of  the  wheel. 

*  See  Hamilton's  Rep.  of  Arts,  ii.  II.  126. 

f  Brugmans,  Commentat.  Gott.  1784,  vii.  M.  75. 


ON  RAISING  AND  REMOVING  WEIGHTS.  159 

Pullies,  and  their  combinations  in  blocks,  are  universally  employed  on 
board  of  ships.  They  are  very  convenient  where  only  a  moderate  increase 
of  power  is  required  ;  but  in  order  to  procure  a  very  great  advantage,  the 
number  of  separate  pullies  or  sheaves  must  be  very  much  multiplied  ;  a 
great  length  of  rope  must  also  be  employed  ;  and  it  is  said  that  in  a  pair  of 
blocks  with  five  pullies  in  each,  two  thirds  of  the  force  are  lost  by  the  fric- 
tion and  the  rigidity  of  the  ropes.  The  inconvenience  resulting  from  a 
large  number  of  pullies,  may,  however,  as  we  have  already  seen,  be  con- 
siderably lessened  when  they  are  arranged  in  Mr.  Smeaton's  manner,*  the 
acting  rope  being  introduced  in  the  middle,  so  as  to  cause  no  obliquity  in 
the  block.  Tackles,  or  combinations  of  pullies  for  raising  weights,  are 
most  conveniently  supported  on  shore  by  means  of  shears,  which  consist  of 
three  rods  or  poles,  resting  on  the  ground,  and  meeting  each  other  in  the 
point  of  suspension.  For  raising  stones  in  building,  two  poles  are  em- 
ployed, with  a  rope  fixed  to  their  summit  which  keeps  them  in  a  proper 
position ;  their  lower  ends  are  usually  connected  by  a  third  pole  which 
serves  as  an  axis.  (Plate  IV.  Fig.  56.  Plate  XVII.  Fig.  214.) 

Sometimes  a  pulley  is  drawn  horizontally  along  a  frame,  setting  out 
from  the  point  where  the  rope  is  fixed,  so  that  while  the  bucket  is  raised, 
it  is  also  transferred  diagonally  to  the  opposite  end  of  the  scaffolding. 
This  apparatus  is  used  in  some  of  the  Cornish  stream  works,  in  which  the 
earth  of  a  whole  valley  is  raised  in  order  to  be  washed  for  the  separation  of 
tin  ore.  (Plate  XVII.  Fig.  215.) 

A  fixed  inclined  plane  is  often  of  use  in  assisting  the  elevation  of  great 
weights  by  means  of  other  machinery.  It  is  supposed  that  in  all  the 
edifices  of  remote  antiquity,  where  great  masses  of  stone  were  employed, 
as  in  the  pyramids  of  Egypt  and  the  druidical  temples  of  this  country, 
these  vast  blocks  were  elevated  on  inclined  planes  of  earth,  or  of  scaffold- 
ing, with  the  assistance  also  of  levers  and  rollers.  Inclined  planes  are 
frequently  used  for  drawing  boats  out  of  one  canal  into  another ;  and 
sometimes  the  local  circumstances  are  such  that  this  may  be  done  with 
great  convenience,  merely  by  allowing  a  loaded  boat  to  descend  and  to  turn 
the  axis  which  raises  an  empty  one.  An  example  of  this  may  be  seen,  on 
a  large  scale,  in  the  Duke  of  Bridgwater's  canal.1*  This  canal  is  extended, 
above  ground,  for  forty  miles  on  one  level :  an  underground  navigation, 
twelve  miles  long,  joins  it  at  Worsley,  leading  to  the  coal  mines  under 
"Walkden  moor.  At  a  height  of  35£  yards  above  this  is  another  subter- 
raneous portion,  nearly  six  miles  in  length.  The  connection  between  these 
levels  is  formed  by  an  inclined  plane  ;  the  boats  are  let  down  loaded,  and 
proceed  three  miles  along  the  tunnel  into  the  open  canal.  The  inclined 
plane  is  fixed  in  a  stratum  of  stone,  which  fortunately  has  the  most  eligible 
inclination  of  1  in  4,  and  is  33  yards  in  thickness,  affording  the  most  ad- 
vantageous means  of  fixing  every  part  of  the  machinery  with  perfect 
security.  The  whole  length  of  the  plane  is  151  yards,  besides  a  lock  of 
18  yards  at  the  upper  end.  (Plate  XVII.  Fig.  216.) 

^Inclined  planes  are  also  universally  employed  for  facilitating  the  ascent 

*  Ph.  Tr.  1751,  p.  494. 

t  Consult  Tr.  of  the  Soc.  of  Arts,  xviii.  288  ;  Nich.  Jour.  iv.  486. 


160  LECTURE  XVIII. 

of  heights  by  men  or  by  animals  ;  they  may  either  be  uniform,  as  roads, 
or  the  general  inclination  of  the  surface  may  be  superseded  by  the  for- 
mation of  separate  steps  or  stairs.  The  inclination  of  the  surface  may  be 
governed  by  the  proportion  of  the  strength  of  the  animal  to  its  weight, 
the  force  required  to  support  any  weight  on  a  plane  being  to  the  whole 
weight  as  the  height  of  the  plane  to  its  length  ;  and  if  the  plane  be  a  little 
less  inclined  than  the  exact  equilibrium  would  require,  the  animal  will  be 
able  to  acquire  a  sufficient  velocity  at  first  to  carry  it  easily  up  the  ascent 
with  a  motion  nearly  equable.  The  strength  of  a  labourer  may  be  advan- 
tageously employed  in  ascending  a  given  height  by  a  flight  of  steps,  and 
placing  himself  on  a  stage  which  may  raise  a  weight  by  its  descent ;  but 
it  appears  that  the  force  of  other  animals  is  less  calculated  for  exertions 
of  this  kind. 

The  screw  is  not  often  immediately  applied  to  the  elevation  of  weights  ; 
although  sometimes  a  number  of  screws  have  been  used  for  raising  by  slow 
degrees  a  large  and  unmanageable  weight,  for  instance,  that  of  an  obelise : 
and  a  perpetual  screw  is  frequently  employed  in  giving  motion  to  wheel- 
work.  Such  machines  possess  a  considerable  mechanical  advantage,  but 
they  are  subject  to  much  friction,  and  are  deficient  in  durability.  Mr. 
Hunter's  double  screw  might  be  applied  with  advantage,  if  the  extent  of 
the  motion  required  were  extremely  small ;  but  this  limitation  confines  its 
utility  within  very  narrow  bounds. 

A  crane  is  a  machine  for  raising  weights  by  means  of  a  rope  or  chain 
descending  from  an  arm  which  is  capable  of  horizontal  motion,  and  passing 
over  a  pulley  to  be  wound  up  on  an  axis.  The  axis  is  turned,  either  im- 
mediateiy,  or  with  the  interposition  of  wheelwork,  by  a  winch,  by  the 
horizontal  bars  of  a  windlass,  or  by  a  walking  wheel,  and  sometimes  by 
the  force  of  wind,  of  water,  or  of  steam.  A  walking  wheel  is  an  advan- 
tageous mode  of  employing  the  strength  of  a  labourer,  but  the  bulk  of  the 
machine  is  sometimes  inconvenient  and  detrimental  ;  when,  however,  the 
man  walks  upon  the  wheel,  and  not  within  it,  this  objection  is  in  great 
measure  obviated.  A  walking  wheel  requires  to  be  provided  with  some 
method  of  preventing  the  dangerous  consequences  of  the  rapid  descent  of 
the  weight,  in  case  of  an  accidental  fall  of  the  labourer  :  for  this  purpose, 
a  catch  is  usually  employed,  to  prevent  any  retrograde  motion  ;  a  bar  has 
also  sometimes  been  suspended  from  the  axis  of  the  wheel,  on  which  the 
man  may  support  himself  with  his  hands,  and  other  similar  precautions 
have  been  adopted.  Sometimes  the  plane  of  a  walking  wheel  is  but  little 
inclined  to  the  horizon,  and  the  man  walks  on  its  flat  surface.  In 
either  case  the  labour  of  horses,  asses,  or  oxen,  may  be  substituted  for 
that  of  men  :  but  for  cranes  this  substitution  would  be  very  disadvan- 
tageous, since  much  force  would  be  lost  in  stopping  frequently  so  bulky  a 
machine  as  would  be  required.  The  employment  of  a  turnspit  dog  is  an 
humble  example  of  the  same  operation,  and  even  goats  appear  to  have 
been  sometimes  made  to  climb  in  a  similar  manner.  In  a  walking  wheel 
used  for  raising  water  at  Carisbrook  Castle,  in  the  Isle  of  Wight,  the  woik 
was  performed  by  the  same  individual  ass  for  the  whole  of  forty-five  years 
preceding  1771.  Walking  wheels  have  also  been  invented,  on  which  horses 


ON  RAISING  AND  REMOVING  WEIGHTS.  161 

were  to  act  externally  with  their  fore  feet  or  hind  feet  only  ;  but  they 
have  seldom,  if  ever,  been  applied  to  practical  purposes.  In  general  it  is 
advisable  that  walking  wheels  for  quadrupeds  should  present  to  them  a 
path  as  little  elevated  as  possible  ;  and  it  might  probably  be  of  advantage 
to  harness  them  either  to  a  fixed  point  or  to  a  spring  or  weight,  which 
would  enable  them  to  exert  a  considerable  force  even  in  a  horizontal  direc- 
tion ;  but,  probably,  after  all,  they  might  be  more  advantageously  employed 
in  a  circular  mill- walk.  (Plate  XVII.  Fig.  217.) 

Mr.  White's  crane*  affords  a  good  specimen  of  an  oblique  walking 
wheel ;  the  force  may  be  varied  accordingly  as  the  labourer  stands  at  a 
point  more  or  less  distant  from  the  centre  ;  and  in  order  to  avoid  accidents, 
a  break  is  always  acting  on  the  axis  of  the  wheel  by  its  friction,  except 
when  it  is  removed  by  the  pressure  of  the  man's  hand  on  a  lever  upon 
which  he  leans  as  he  walks.  The  force  is  also  varied  in  some  cranes  by 
changing  the  pinion  which  acts  on  the  principal  wheel,  and  an  expanding 
drum  has  been  contrived  for  the  same  purpose,  consisting  of  a  number  of 
bars  moveable  in  spiral  grooves,  so  as  to  form  a  greater  or  smaller  cylinder 
at  pleasure.  In  order  to  place  the  weight  in  any  situation  that  may  be 
required,  the  pulley  may  be  made  to  slide  horizontally  on  the  gib  or  arm. 
(Plate  XVII.  Fig.  218.) 

A  model  of  a  crane  was  exhibited  some  years  ago  to  the  Royal  Society, 
in  which  a  large  wheel  fixed  to  a  short  axis  was  made  to  roll  round  on 
a  plane,  while  the  lower  end  of  its  axis  was  connected  by  a  joint  with 
another  axis  in  a  vertical  position :  then  the  wheel,  having  to  describe  a 
circumference  somewhat  larger  than  its  own,  was  turned  slowly,  and  there- 
fore powerfully,  round  its  axis,  and  the  motion  was  communicated  to  the 
fixed  axis.  The  machine,  however,  appears  to  be  more  curious  than 
useful. 

Sometimes  a  steelyard  has  been  combined  with  a  crane,  for  weighing 
goods  at  the  same  time  that  they  are  raised  by  it.  A  small  crane,  fixed  in 
a  carriage,  is  convenient  for  loading  and  unloading  goods.  In  France,  the 
carts  used  on  the  wharfs  are  generally  so  long  as  to  reach  the  ground  be- 
hind when  depressed,  and  to  furnish  an  inclined  plane,  along  which  the 
goods  are  raised  by  a  lever  and  axis,  or  a  kind  of  capstan,  fixed  in  front. 

For  taking  hold  of  stones  which  are  to  be  raised  by  means  of  a  rope,  a 
hole  is  sometimes  formed  in  them,  wider  within  than  at  its  opening,  and  in 
this  a  lewis  is  inserted,  consisting  of  two  inverted  wedges,  separated  by  a 
plug,  to  which  they  are  fastened  by  a  pin.  (Plate  XVII.  Fig.  219.) 

When  a  rope  or  chain  which  is  to  raise  a  weight,  is  so  long  as  to  require 
a  counterpoise,  the  effect  of  this  may  be  varied  according  to  the  length  of 
the  rope  which  is  unbent,  by  hanging  it  on  a  second  rope  or  chain,  which 
acts  on  a  spiral  fusee,  slowly  turned  by  a  wheel  and  pinion. 

The  use  of  cranes  is  so  extensive  and  so  indispensable,  that  their  forms 
have  been  often  multiplied  on  account  of  local  circumstances,  or  even  from 
caprice  ;  but  the  constructions  which  have  been  described  appear  to  be  of  the 
most  general  utility,  and  from  them  it  will  be  easy  to  judge  of  others. 

When  weights  of  any  kind  are  simply  to  be  removed  from  one  situation 
*  Trans,  of  the  Soc.  of  Arts,  x.  230, 
M 


162  LECTURE  XVIII. 

to  another,  the  most  natural  and  obvious  method,  if  they  are  portable,  is  to 
carry  them.  There  is,  however,  some  scope  for  theory  even  in  this  common 
operation,  and  we  have  seen  that  calculations  have  been  made  in  order  to 
determine  the  most  advantageous  burden  for  a  porter  to  carry,  but  the 
experience  of  a  few  trials  would  in  general  be  a  better  guide.  Some  carry 
weights  on  their  heads,  others  on  their  shoulders,  others  low  down  on  their 
backs  ;  and  according  to  the  situation  of  the  burden,  they  bend  forwards 
or  backwards,  so  that  the  common  centre  of  gravity  of  the  weight  and 
the  body  comes  immediately  or  very  nearly  over  some  part  of  the  ground 
between  their  feet.  The  difficulty  of  carrying  a  weight  at  the  extremity 
of  a  long  rod  is  easily  understood  from  the  properties  of  the  lever,  and 
the  same  principles  will  enable  us  to  determine  the  distribution  of  a  load 
between  two  porters,  in  whatever  way  they  may  carry  it.  Supposing  the 
weight  to  be  placed  on  a  porter's  horse  or  hand  barrow,  and  at  equal  dis- 
tances from  both  extremities,  each  of  the  men  will  support  an  equal  portion 
of  it ;  but  if  it  be  nearer  to  the  one  than  to  the  other,  the  load  will  be  dis- 
tributed in  the  same  proportion  as  the  poles  are  divided  by  the  centre  of 
the  burden.  For  instance,  if  the  weight  were  300  pounds,  and  it  were 
one  foot  distant  from  the  one,  and  two  from  the  other,  the  first  would  have 
to  carry  200  pounds,  and  the  second  100.  If  the  porters  ascend  a  hill,  or 
a  flight  of  steps,  the  distribution  of  the  load  will  remain  the  same,  provided 
that  the  centre  of  the  weight  lie  in  the  plane  of  the  poles.  But  if  the  weight 
consists  of  a  large  body  placed  on  that  plane,  the  centre  of  gravity  being 
above  it,  the  effect  of  an  inclination  to  the  horizon  may  materially  change 
the  distribution  of  the  load,  since  the  pressure  will  always  be  determined 
by  the  distance  of  the  ends  of  the  poles  from  the  line  passing  perpendicu- 
larly through  the  centre  of  gravity  ;  so  that  if  the  elevation  were  sufficient, 
the  whole  burden  might  rest  on  the  lower  porter.  And  in  the  same  manner, 
if  the  weight  were  suspended  below  the  poles,  the  inclination  would  cause 
a  greater  proportion  of  the  load  to  be  borne  by  the  upper  porter.  The  force 
is,  however,  only  thus  distributed  as  long  as  the  arms  of  the  porters  con- 
tinue parallel  to  each  other  ;  but  the  inequality  would  naturally  be  lessened 
by  a  change  of  the  directions  in  which  they  would  act ;  it  would  only  be 
necessary  that  those  directions  should  meet  in  some  part  of  the  vertical  line 
passing  through  the  centre  of  gravity  ;  the  magnitude  of  each  force  would 
then  be  determined  by  the  length  of  the  side  of  a  triangle  corresponding  to 
its  direction,  and  the  load  might  be  either  equally  or  unequally  divided, 
according  to  the  positions  of  the  arms.  (Plate  XVII.  Fig.  220,  221.) 

A  man  can  carry  in  general  a  weight  four  or  five  times  as  great  as  that 
which  he  can  raise  continually  in  a  vertical  direction  with  the  same  velo- 
city :  so  that  we  may  consider  the  resistance  to  be  overcome  as  a  kind  of 
friction  which  amounts  to  about  a  fourth  or  a  fifth  of  the  weight.  If  we 
attempted  to  draw  a  weight  along  a  horizontal  surface,  the  resistance  of 
the  surface  would  often  not  only  impede  the  motion,  but  also  injure  the 
texture  of  the  substance  to  be  moved.  This  injury  may,  however,  be 
avoided  by  the  interposition  of  a  simple  frame  or  dray,  and  the  dray  may 
be  armed  with  a  substance  subject  to  little  friction,  as  with  iron  :  the  fric- 
tion may  also  be  somewhat  further  diminished  by  making  the  outline  of 


ON  RAISING  AND  REMOVING  WEIGHTS.  163 

the  dray  a  little  convex  below,  so  that  a  slight  agitation  may  be  continually 
produced  during  its  motion.  Sometimes  the  simple  expedient  of  placing  a 
load  on  two  poles  of  elastic  wood,  the  thickest  ends  of  which  are  supported 
by  the  horse,  and  the  thinner  drag  on  the  ground,  is  of  use  both  in  dimi- 
nishing the  friction  by  confining  it  to  a  smaller  and  smoother  surface,  and 
in  equalising  the  motion  by  the  flexibility  of  the  poles. 

It  often  happens  that  agitation  of  any  kind  enables  us  to  lessen  consi- 
derably the  friction  between  two  bodies,  especially  when  they  are  elastic. 
If  we  wish,  for  instance,  to  draw  a  ring  along  an  iron  rod,  by  a  thread 
which  is  nearly  perpendicular  to  it,  we  may  exert  all  our  strength  in  vain 
if  we  apply  it  by  slow  degrees,  since  the  increase  of  force  continues  to  in- 
crease the  adhesion.  But  if  we  pull  the  ring  suddenly,  and  then  slacken 
the  thread,  it  rebounds  from  the  rod  by  its  elasticity,  and  in  this  manner  it 
slides  readily  along  by  a  continuance  of  alternations.  In  such  a  case,  how- 
ever, it  would  be  more  natural,  if  the  thread  were  sufficiently  heavy,  to 
give  it  a  serpentine  motion  which  would  draw  the  ring  in  a  more  oblique 
direction.  It  is  said  that  when  a  screw  is  fixed  very  firmly  in  a  piece  of 
iron,  it  may  be  extricated  much  more  easily  while  the  iron  is  filed  in  some 
neighbouring  part.  The  agitation  thus  produced  probably  operates  in  a 
manner  somewhat  similar  to  that  of  the  rod. 

Friction  may  in  general  be  considerably  diminished  by  the  interposition 
of  oily  substances,  where  the  surfaces  are  of  such  a  nature  as  to  admit  of 
their  application.  Thus  common  oil,  tallow,  or  tar,  are  usually  interposed 
between  metals  which  work  on  each  other.  It  is  necessary  to  attend  to 
the  chemical  properties  of  the  oil,  and  to  take  care  that  it  be  not  of  such 
a  nature  as  to  corrode  the  metals  employed,  especially  where  the  work 
requires  great  accuracy.  Tallow  is  liable  to  lose  its  lubricating  quality 
unless  it  be  frequently  renewed.  Between  surfaces  of  wood,  soap  is  some- 
times applied,  but  more  commonly  black  lead  which  becomes  highly 
polished.  The  advantages  of  canals  and  of  navigation  in  general,  are  prin- 
cipally derived  from  the  facility  with  which  the  particles  of  fluids  make 
way  for  the  motion  of  bodies  floating  on  them. 

The  interposition  of  rollers  or  of  balls  bears  some  resemblance  to  the 
application  of  fluids.  Supposing  the  surfaces  to  be  flat  and  parallel,  a 
roller  moves  between  them  without  any  friction :  but  it  has  still  to  over- 
come the  resistance  occasioned  by  the  depression  which  it  produces  in  the 
substance  on  which  it  moves,  and  which  is  greater  or  less  according  to 
the  softness  and  want  of  elasticity  of  the  substance,  If  the  substance  were 
perfectly  elastic,  the  temporary  depression  would  produce  no  resistance, 
because  the  tendency  to  rise  behind  the  roller  would  be  exactly  equivalent 
to  the  force  opposing  its  progress  before ;  and  the  actual  resistance  only 
arises  from  a  greater  or  smaller  want  of  elasticity  in  the  materials  con- 
cerned. The  continued  change  of  place  of  the  rollers  is  often  a  material 
objection  to  their  employment ;  their  action  may  in  some  cases  be  pro- 
longed by  fixing  wheels  on  their  extremities,  as  well  as  by  some  other 
arrangements ;  but  these  methods  are  too  complicated  to  afford  much 
practical  utility.  Rollers  may  also  be  placed  between  two  cylinders,  the 
one  convex  and  the  other  concave,  and  the  friction  may  in  this  manner 

M2 


164  LECTURE  XVIII. 

be  wholly  removed,  whatever  may  be  the  magnitude  of  the  rollers. 
(Plate  XVII.  Fig.  222,  223.) 

The  effect  of  friction  in  any  machine  being  always  diminished,  in  pro- 
portion as  the  velocity  of  the  parts  sliding  on  each  other  is  diminished,  it 
is  obvious  that  by  reducing  the  dimensions  of  the  axis  of  a  wheel  as  much 
as  possible,  we  also  reduce  the  friction.  When  the  pressure  on  the  axis  is 
derived  principally  from  the  weight  of  the  wheel  itself,  the  friction  may 
be  lessened  by  placing  the  wheel  in  a  horizontal  position  and  making  the 
axis  vertical ;  for  in  this  manner  the  weight  may  be  supported  on  an  axis 
ending  in  a  very  small  surface,  and  the  effect  of  the  friction  on  this  surface 
will  be  about  one  third  less  than  if  it  acted  at  the  circumference.  The 
velocity  of  the  parts  sliding  on  each  other  may  be  still  more  reduced  by 
placing  each  extremity  of  the  axis  on  another  wheel,  or  between  two 
wheels,  on  which  the  axis  rolls  as  they  turn  round,  so  that  the  friction  is 
transferred  to  the  axis  of  these  wheels  of  which  the  motion  is  very  slow. 
But  when  a  great  weight  is  to  be  supported,  it  is  necessary  that  the  friction 
wheels  be  very  strong  and  very  accurately  formed  ;  for  if  their  surface 
were  irregular  they  might  stand  still,  and  their  use  would  be  destroyed. 
(Plate  XVIII.  Fig.  224.) 

Perrault*  attempted  to  avoid  all  friction  by  supporting  the  axis  of  a 
wheel  in  the  coil  of  a  rope,  which  allowed  it  to  turn  while  the  whole  wheel 
ascended  and  descended  ;  but  the  stiffness  of  a  rope  occasions  in  general 
even  a  greater  resistance  than  the  friction  for  which  it  is  substituted. 

The  wheels  of  carriages  owe  a  great  part  of  their  utility  to  the  diminu- 
tion of  friction,  which  is  as  much  less  in  a  carriage  than  in  a  dray,  as  the 
diameter  of  the  axle  is  less  than  that  of  the  wheel,  even  supposing  the  dray 
to  slide  on  a  greased  surface  of  iron.  The  wheels  also  assist  us  in  drawing 
the  carriage  over  an  obstacle,  for  the  path  which  the  axis  of  the  wheel 
describes  is  always  smoother  and  less  abrupt  than  the  surface  of  a  rough 
road  on  which  the  wheel  rolls.  It  is  obvious  that  both  these  advantages 
are  more  completely  attained  by  large  wheels  than  by  smaller  ones ;  the 
dimensions  of  the  axis  not  being  increased  in  the  same  proportion  with 
those  of  the  wheel,  and  the  path  of  the  axis,  to  which  that  of  the  centre 
of  gravity  is  similar,  consisting  of  portions  of  larger  circles,  and  conse- 
quently being  less  curved  ;  and  if  the  wheels  are  elastic  and  rebound  from 
an  obstacle,  the  difference  is  still  increased.  It  is,  however,  barely  possible, 
that  the  curvature  of  the  obstacle  to  be  overcome  may  be  intermediate 
between  those  of  a  larger  and  of  a  smaller  wheel ;  and  in  this  case  the 
higher  wheel  will  touch  a  remoter  part  of  the  obstacle,  so  that  the  path 
of  the  axis  will  form  an  abrupt  angle,  while  the  smaller  wheel  follows 
the  curve,  and  produces  a  more  equable  motion ;  this,  however,  is  a  case 
of  rare  occurrence,  and  an  advantage  of  little  importance.  (Plate  XVIII. 
Fig.  225,  226.) 

The  greater  part  of  the  resistance  to  the  motion  of  a  carriage  very 
frequently  arises  from  the  continual  displacement  of  a  portion  of  the 
materials  of  the  road,  which  do  not  react  on  the  wheels  with  perfect  elasfi- 

*  Machines  approuve*es  par  1' Academic,  i.  13.  Leupold,  Th.  Mach.  t.  xiv.  xv. 
Desaguliers  Ph.  Tr.  xxxvi.  222. 


ON  RAISING  AND  REMOVING  WEIGHTS.  165 

city,  but  undergo  a  permanent  change  of  form  proportional  to  the  loss  of 
force.  Hence,  in  a  soft  sand,  although  the  axles  of  the  wheels  may  move 
in  a  direction  perfectly  horizontal,  the  draught  becomes  extremely  heavy. 
The  more  the  wheel  sinks,  the  greater  is  the  resistance,  and  if  we  suppose 
the  degree  of  elasticity  of  the  materials  and  their  immediate  resistance  at 
different  depths  to  be  known,  we  may  calculate  the  effect  of  their  reaction 
in  retarding  the  motion  of  the  carriage.  Thus,  if  the  materials  were 
perfectly  inelastic,  acting  only  on  the  preceding  half  of  the  immersed  por- 
tion of  the  wheel,  and  their  immediate  pressure  or  resistance  were  simply 
proportional  to  the  depth,  like  that  of  fluids  or  of  elastic  substances,  the 
horizontal  resistance  would  be  to  the  weight  nearly  as  the  depth  of  the 
part  immersed  to  two  thirds  of  its  length ;  but  if  the  pressure  increased 
as  the  square  of  the  depth,  which  is  a  more  probable  supposition,  the  re- 
sistance would  be  to  the  weight  as  the  depth  to  about  four  fifths  of  the 
length  ;  the  pressure  may  even  vary  still  more  rapidly,  and  we  may  con- 
sider the  proportion  of  the  resistance  to  the  weight  as  no  greater  than  that 
of  the  depth  of  the  part  immersed  to  its  length,  or  of  half  this  length  to 
the  diameter  of  the  wheel ;  and  if  the  materials  are  in  any  degree  elastic, 
the  resistance  will  be  lessened  accordingly.  But  on  any  of  these  sup- 
positions, it  may  be  shown  that  the  resistance  may  be  reduced  to  one  half, 
either  by  making  a  wheel  a  little  less  than  three  times  as  high,  or  about 
eight  times  as  broad  as  the  given  wheel.  This  consideration  is  of  parti- 
cular consequence  in  soft  and  boggy  soils,  as  well  as  in  sandy  countries  ; 
thus,  in  moving  timber  in  a  moist  situation,  it  becomes  extremely  advan- 
tageous to  employ  very  high  wheels,  and  they  have  the  additional  con- 
venience that  the  timber  may  be  suspended  from  the  axles  by  chains, 
without  the  labour  of  raising  it  so  high  as  would  be  necessary  for  placing 
it  upon  a  carriage  of  any  kind.  (Plate  XVIII.  Fig.  227.) 

But  the  magnitude  of  wheels  is  practically  limited,  by  the  strength  or 
the  weight  of  the  materials  of  which  they  are  made,  by  the  danger  of 
overturning  when  the  centre  of  gravity  is  raised  too  high,  and  in  the  case 
of  the  first  pair  of  wheels  of  a  four  wheeled  carriage,  by  the  inconvenience 
that  would  arise,  in  turning  a  corner,  with  a  wheel  which  might  interfere 
with  the  body  of  the  carriage.  It  is  also  of  advantage  that  the  draught  of 
a  horse  should  be  in  a  direction  somewhat  ascending,  partly  on  account  of 
the  shape  of  the  horse's  shoulder,  and  partly  because  the  principal  force 
that  he  exerts  is  in  the  direction  of  a  line  passing  through  the  point  of 
contact  of  his  hind  feet  with  the  ground.  But  a  reason  equally  strong 
for  having  the  draught  in  this  direction  is,  that  a  part  of  the  force  may 
always  be  advantageously  employed  in  lessening  the  pressure  on  the 
ground  ;  and  to  answer  this  purpose  the  most  effectually,  the  inclination 
of  the  traces  or  shafts  ought  to  be  the  same  with  that  of  a  road  on  which 
the  carriage  would  begin  or  continue  to  descend  by  its  own  weight  only.* 
In  order  to  apply  the  force  in  this  manner  to  both  pairs  of  wheels,  where 
there  are  four,  the  line  of  draught  ought  to  be  directed  to  a  point  half  way 

*  Couplet,  Reflexions  sur  le  Tirage  des  Charrettes,  Hist,  et  Mem.  de  Paris, 
1733,  p.  49,  H.  82.  Deparcieux  sur  le  Tirage  des  Chevaux,  ib.  1760,  p.  263, 
H.  151. 


166  LECTURE  XVIII. 

between  them,  or  rather  to  a  point  immediately  under  the  centre  of  gravity 
of  the  carriage  ;  and  such  a  line  would  always  pass  above  the  axis  of  the 
fore  wheels.  If  the  line  of  draught  pass  immediately  through  this  axis, 
the  pressure  on  the  hind  wheels  will  remain  unaltered  ;  and  if  the  traces 
or  shafts  be  fixed  still  lower,  the  pressure  on  the  hind  wheels  will  even  be 
somewhat  increased  by  the  draught.  It  is  evident,  therefore,  that  this 
advantage  cannot  be  obtained  if  the  fore  wheels  are  very  high ;  we  may 
also  understand  that  in  some  cases  the  common  opinion  of  the  eligibility 
of  placing  a  load  over  the  fore  wheels  rather  than  the  hind  wheels,  may 
have  some  foundation  in  truth.  When  several  horses  are  employed,  the 
draught  of  all  but  the  last  must  be  nearly  horizontal ;  in  this  case  the 
flexure  of  the  chain  brings  it  into  a  position  somewhat  more  favourable 
for  the  action  of  the  horses  ;  but  the  same  cause  makes  the  direction  of  its 
attachment  to  the  waggon  unfavourable;  further  than  this  there  is  no 
absolute  loss  of  force,  but  it  appears  to  be  advisable  to  cause  the  shaft 
horse  to  draw  in  a  direction  as  much  elevated  as  possible ;  and  on  the 
whole  it  is  probable  that  horses  drawing  singly  have  a  material  advantage, 
when  they  do  not  require  additional  attendance  from  the  drivers. 

The  practice  of  making  broad  wheels  conical  has  obviously  the  disadvan- 
tageous effect  of  producing  a  friction  at  each  edge  of  the  wheel,  when  the 
carriage  is  moving  in  a  straight  line  ;  for  such  a  wheel,  if  it  moved  alone, 
would  always  describe  a  circle  round  the  vertex  of  the  cone  to  which  it 
belongs.  When  the  wheels  are  narrow,  a  slight  inclination  of  the  spokes 
appears  to  be  of  use  in  keeping  them  more  steady  on  the  axles  than  if  they 
were  exactly  vertical ;  and  when,  by  an  inclination  of  the  body  of  the 
carriage,  a  greater  proportion  of  the  load  is  thrown  on  the  lower  wheel,  its 
spokes,  being  then  in  a  vertical  position,  are  able  to  exert  all  their  strength 
with  advantage.  The  axles  being  a  little  conical,  in  order  that  they  may 
not  become  loose,  or  may  easily  be  tightened  as  they  wear,  it  is  necessary 
that  they  should  be  bent  down  so  that  their  lower  surfaces  may  be  hori- 
zontal, otherwise  the  wheels  would  press  too  much  on  the  linch  pin.  For 
this  reason,  the  distance  between  the  wheels  should  be  a  little  greater  above 
than  below,  and  their  surfaces  of  course  slightly  conical.  (Plate  XVIII. 
Fig.  228.) 

It  has  been  proposed  to  fix  the  wheels  to  their  respective  axles,  to  con- 
tinue the  axles  as  far  as  the  middle  of  the  carriage  only,  and  to  cause 
them  to  turn  on  friction  wheels  or  rollers ;  a  plan  which  may  succeed  if 
the  apparatus  is  not  too  complicated  for  use  ;  but  in  fact  the  immediate 
friction  on  the  axles  is  not  great  enough  to  render  this  refinement  neces- 
sary. If  both  opposite  wheels  were  fixed  to  a  single  axis,  one  of  them 
would  be  dragged  backwards  and  the  other  forwards,  whenever  the  motion 
deviated  from  a  straight  line  ;  and  a  similar  effect  actually  takes  place  in 
those  carriages  which  are  supported  on  a  single  roller. 

The  effect  of  the  suspension  of  a  carriage  on  springs  is  to  equalise  its 
motion,  by  causing  every  change  to  be  more  gradually  communicated  to  it 
by  means  of  the  flexibility  of  the  springs,  and  by  consuming  a  certaili 
portion  of  every  sudden  impulse  in  generating  a  degree  of  rotatory  motion. 
This  rotatory  motion  depends  on  the  oblique  position  of  the  straps  sus- 


ON  RAISING  AND  REMOVING  WEIGHTS.  167 

pending  the  carriage,  which  prevents  its  swinging  in  a  parallel  direction  ; 
sucli  a  vibration  as  would  take  place  if  the  straps  were  parallel  would  be 
too  extensive  unless  they  were  very  short,  and  then  the  motion  would  be 
somewhat  rougher.  The  obliquity  of  the  straps  tends  also  in  some  mea- 
sure to  retain  the  carriage  in  a  horizontal  position  ;  for  if  they  were 
parallel,  both  being  vertical,  the  lower  one  would  have  to  support  the 
greater  portion  of  the  weight,  at  least  according  to  the  common  mode  of 
fixing  them  to  the  bottom  of  the  carriage ;  the  spring,  therefore,  being 
flexible,  it  would  be  still  further  depressed.  But  when  the  straps  are 
oblique,  the  upper  one  assumes  always  the  more  vertical  position,  and  conse- 
quently bears  more  of  the  load  ;  for  when  a  body  of  any  kind  is  supported 
by  two  oblique  forces,  their  horizontal  thrusts  must  be  equal,  otherwise 
the  body  would  move  laterally  ;  and  in  order  that  the  horizontal  portions 
of  the  forces  may  be  equal,  the  more  inclined  to  the  horizon  must  be  the 
greater :  the  upper  spring  will,  therefore,  be  a  little  depressed,  and  the 
carriage  will  remain  more  nearly  horizontal  than  if  the  springs  were 
parallel.  The  reason  for  dividing  the  springs  into  separate  plates  has 
already  been  explained  :  the  beam  of  the  carriage,  that  unites  the  wheels, 
supplies  the  strength  necessary  for  forming  the  communication  between 
the  axles  :  if  the  body  of  the  carriage  itself  were  to  perform  this  office,  the 
springs  would  require  to  be  so  strong  that  they  could  have  little  or  no  effect 
in  equalising  the  motion,  and  we  should  have  a  waggon  instead  of  a  coach. 
The  ease  with  which  a  carriage  moves  depends  not  only  on  the  elasticity 
of  the  springs  but  also  on  the  small  degree  of  stability  of  the  equilibrium, 
of  which  we  may  judge  in  some  measure,  by  tracing  the  path  which  the 
centre  of  gravity  must  describe  when  the  carriage  swings.  (Plate  XVIII. 
Fig.  229.) 

The  modes  of  attaching  horses  and  oxen  to  carriages  are  different  in 
different  countries,  nor  is  it  easy  to  determine  the  most  eligible  method. 
When  horses  are  harnessed  to  draw  side  by  side,  they  are  usually  attached 
to  the  opposite  ends  of  a  bar  or  lever  ;  and  if  their  strength  is  very  unequal 
the  bar  is  sometimes  unequally  divided  by  the  fulcrum,  the  weaker  horse 
being  made  to  act  on  the  longer  bar,  and  being  thus  enabled  to  counteract 
the  greater  force  of  his  companion.  But  even  without  this  inequality  a 
compensation  takes  place,  for  the  centre  on  which  the  bar  moves  is  always 
considerably  behind  the  points  of  attachment  of  the  horses  ;  and  when  one 
of  them  falls  back  a  little,  the  effective  arm  of  the  lever  becomes  more  per- 
pendicular to  the  direction  of  his  force,  and  gives  him  a  greater  power, 
while  the  opposite  arm  becomes  more  oblique,  and  causes  the  other  horse 
to  act  at  a  disadvantage  ;  so  that  there  is  a  kind  of  stability  in  the  equili- 
brium. If  the  fulcrum  were  further  forwards  than  the  extremity  of  the 
bar,  the  two  horses  could  never  draw  together  with  convenience.  (Plate 
XVIII.  Fig.  230.) 

In  mining  countries  and  in  collieries,  it  is  usual,  for  facilitating  the  mo- 
tion of  the  carriages  employed  in  moving  the  ore  or  the  coals,  to  lay  wheel- 
ways  of  wood  or  iron  along  the  road  on  which  they  are  to  pass  ;  and  this 
practice  has  of  late  been  extended  in  some  cases  as  a  substitute  for  the 
construction  of  navigable  canals.  Where  there  is  a  turning,  the  carnages 


168  LECTURE  XVIII. 

are  usually  received  on  a  frame  supported  by  a  pivot,  which  allows  them 
to  be  turned  with  great  ease.  In  particular  situations,  these  waggons  are 
loaded  by  little  carts,  rolling  without  direction  down  inclined  planes,  and 
emptying  themselves ;  they  are  also  provided  with  similar  contrivances  for 
being  readily  unloaded,  when  they  arrive  at  the  place  of  their  destination. 
The  carriages  used  for  drawing  loaded  boats  over  inclined  planes,  where 
they  have  to  ascend  and  again  to  descend,  are  made  to  preserve  their  level 
by  having  at  one  end  four  wheels  instead  of  two,  on  the  same  transverse 
line  ;  the  outer  ones  as  much  higher  than  the  pair  at  the  other  end,  as  the 
inner  ones  are  lower;  and  the  wheelway  being  so  laid  that  either  the 
largest  or  the  smallest  act  on  it,  accordingly  as  the  corresponding  part  of 
the  plane  is  lower  or  higher  than  the  opposite  end.  It  is  possible  that 
roads  paved  with  iron  may  hereafter  be  employed  for  the  purpose  of  expe- 
ditious travelling,  since  there  is  scarcely  any  resistance  to  be  overcome, 
except  that  of  the  air,  and  such  roads  would  allow  the  velocity  to  be 
increased  almost  without  limit. 

For  removing  earth  from  one  situation  to  another,  a  series  of  baskets  has 
sometimes  been  hung  on  two  endless  ropes,  moving  on  pullies  of  such  a 
form  as  to  suffer  the  bars  supporting  the  baskets  to  pass  freely  over  them  ; 
the  baskets  being  moved  by  means  of  a  winch  acting  on  the  rope  by  a 
wheel  like  one  of  the  pullies.  Sometimes  also  a  series  of  little  carts  has 
been  connected  by  ropes,  and  drawn  in  a  circle  or  oval  up  and  down  an 
inclined  plane.  These  methods  may  be  adopted  in  making  roads  where  a 
hill  is  to  be  levelled,  and  the  materials  are  to  be  employed  in  filling  up  the 
valley  below ;  but  in  such  cases  two  carts,  connected  by  a  cylinder  or 
windlass,  are  generally  sufficient ;  and  they  may  be  arranged  in  the  same 
manner  as  the  carriages  for  removing  boats  on  an  inclined  plane. 


LECT.  XVIII.— ADDITIONAL  AUTHORITIES. 

Machine  employed  for  clearing  the  Port  of  Toulon.  Belidor,  Architecture  Hy- 
draulique,  ii.  II.  pi.  20.  Ferguson  on  a  Crane,  Ph.'  Tr.  1763,  liv.  24.  Redely- 
kheid,  Machine  &  creuser  les  Pores,  fol.  La  Hague,  1774.  Suspended  Scaffolding, 
Encyclopedic  JMethodique,  pi.  iv.  Peintre  en  Batimens.  Hall's  Crane,  Trans,  of 
the  Soc.  of  Arts,  vol.  xii. 

On  Wheel  Carriages.— On  the  Benefit  of  High  Wheels,  Ph.  Tr.  1685,  xv.  856. 
Lahire  on  the  Magnitude  of  Wheels,  Hist,  et  Mem.  de  Paris,  ix.  116.  Parent,  do. 
1712,  p.  96.  Reaumur,  do.  1724.  p.  300.  Dupin  de  Chenonceau,  do.  1753,  H. 
301.  Emerson's  Mech.  p.  194.  Boulard  and  Margueron  on  Broad  Wheels,  Ro- 
zier's  Jour.  xix.  424.  Jacob  on  Wheel  Carriages,  &c.  2  vols.  4to,  1773-4.  Anstice 
on  do.  1790.  Bailey,  Plates  of  Machines  approved  by  the  Society  of  Arts,  2  vols. 
fol.  1782.  Rizzetti,  Riforma  de'  Cam  di  quattro  Ruote,  Trevigi,  1785.  Edgeworth, 
Tr.  R.  Ir.  Aca.  1788,  ii.  73.  Lamber,  Hindenburg's  Archiv,  ii.  51.  Grobert  sur 
les  Voitures  a  deux  Roues,  1797.  A.  Young,  Annals  of  Agriculture,  xviii.  Fuss, 
Versuch  einer  Theorie  des  Widerstandes  zevey-und-vier-radiger  Fuhrwerke.  Co- 
penhag.  1798.  Ph.  Mag.  xiii.  115.  Anderson's  Institutes  of  Physics,  quoted  by 
Cavallo,  Nat.  Ph.  Cumming  on  Conical  Wheels,  4to,  1804.  Board  of  Agriculture, 
ii.  351.  Repertory  of  Arts,  xiii.  256.  Imison's  Elements  of  Science  and  Art, 
2  vols,  1803,  i.  129.  Ferguson's  Lect.  by  Brewster,  ii.  296. 


169 


LECTURE   XIX. 


ON  MODES  OF  CHANGING  THE  FORMS  OF  BODIES. 

THE  corpuscular  forces  by  which  bodies  retain  their  peculiar  forms  of 
aggregation,  require  in  many  cases  to  be  counteracted  or  modified  by 
mechanical  processes :  thus  we  have  frequent  occasion  to  compress  bodies 
into  a  smaller  space,  to  augment  their  dimensions  in  a  particular  direc- 
tion, to  divide  their  substance,  either  partially  or  totally,  in  given  lines  or 
surfaces,  or  to  destroy  their  general  form  by  reducing  them  into  more 
minute  portions  ;  and  we  may  consider  these  subjects  as  principally  refer- 
able to  the  effects  of  compression,  extension,  penetration,  division,  attri- 
tion, digging,  boring,  agitation,  trituration  and  demolition.  The  two  first 
of  these  articles  depend  on  such  a  change  as  we  have  examined  in  consider- 
ing the  strength  of  materials,  under  the  name  of  alteration,  the  remainder 
on  fracture. 

The  instruments  peculiarly  intended  for  compression  are  in  general  of 
the  description  of  presses  ;  and  the  most  common  act  by  means  of  a  screw. 
The  friction  on  the  screw  interferes  considerably  with  the  power  of  the 
machine ;  but  it  is  of  use  in  keeping  the  press  fixed  in  a  situation  into 
which  it  has  been  brought  by  force.  The  screw  is  always  turned  by  a 
lever ;  for  without  this  assistance,  however  powerful  it  might  be,  the  fric- 
tion would  render  it  almost  useless.  When  great  force  is  required,  the 
screw  is  made  as  close  as  is  consistent  with  the  strength  of  its  spires. 
Mr.  Hunter's  double  screw  may  also  be  used  with  advantage,  where  only 
a  small  extent  of  motion  is  required.  The  screw  of  a  printing  press  or  of  a 
stamping  press,  is,  on  the  contrary,  open,  and  it  is  caused  to  descend  with 
considerable  momentum,  the  handle  being  loaded  with  a  weight.  Wher- 
ever a  force  is  so  employed  as  to  produce  an  impulse  which  acts  on  any 
body,  the  momentum  which  is  the  result  of  the  action  of  the  force  for  a 
certain  time,  is  usually  much  more  powerful  than  the  simple  pressure ; 
the  degree  of  its  efficacy  depends,  however,  on  the  degree  of  compressibi- 
lity of  the  substance.  Thus,  if  a  heavy  body  fall  from  a  certain  height  so 
as  to  acquire  a  momentum  in  consequence  of  the  force  of  gravity,  it  will 
ultimately  exert  on  the  substance  upon  which  it  falls  a  force  about  as 
much  greater  than  its  weight,  as  the  space  through  which  the  surface  of 
the  substance  struck  is  depressed,  by  means  of  the  impulse,  is  less  than 
twice  the  height  from  which  the  body  has  fallen ;  and  unless  either  the 
substance  is  very  compressible,  or  the  height  very  small,  this  force  must  be 
incomparably  greater  than  the  pressure  of  the  weight  only. 

For  a  printing  press,  a  single  heavy  roller  is  'sometimes  made  to  pass 
over  the  paper  when  it  has  been  laid  on  the  types ;  and  since  the  whole 
action  of  such  a  roller  is  confined  to  a  small  part  at  any  one  time,  it  is  said 
to  exert  sufficient  force  and  to  perform  its  work  more  equably  than  a 
common  press  ;  but  its  operation  must  be  comparatively  slow.  A  common 


170  LECTURE  XIX. 

mangle  for  linen  acts  nearly  in  a  similar  manner.  In  calendering  mills, 
the  force  of  a  spring  is  employed  for  exerting  a  pressure  on  the  block  with 
which  the  materials  are  glazed. 

The  copper  plate  printing  press,  and  the  machine  for  copying  letters,  are 
composed  of  two  rollers  parallel  to  each  other,  pressing  on  the  substance 
which  is  interposed,  and  which  is  brought  into  its  situation  partly  by  the 
friction  of  the  surface  of  the  roller  and  partly  by  external  force. 

The  rollers  by  which  sugar  canes  are  pressed,  are  in  general  situated 
vertically,  the  middle  one  of  three  being  turned  by  horses,  by  mules,  or  by 
water,  and  the  canes  being  made  to  return  round  it  so  as  to  pass  through 
both  interstices  in  succession.  It  appears  to  be  of  some  advantage  in  presses 
of  this  kind  that  all  the  rollers  should  be  turned  independently  of  their 
action  on  the  materials  interposed,  since  the  friction  of  two  rollers  may 
tend  to  draw  the  materials  into  the  space  between  them,  with  more  regu- 
larity and  greater  force,  than  the  action  of  a  single  roller  would  do.  For 
this  reason,  it  may  be  advisable  to  retain  the  toothed  wheels  turning  the 
rollers,  even  when  their  axes  are  not  firmly  fixed  but  held  together  by 
an  elastic  hoop.  (Plate  XVIII.  Fig.  231.) 

In  oil  mills,  a  still  greater  momentum  is  applied  to  the  purpose  of  com- 
pression than  in  the  printing  press :  hammers,  or  long  wooden  beams  placed 
vertically,  are  raised  by  a  water  wheel,  and  suffered  to  fall  on  wedges 
which  act  very  forcibly  on  the  materials  contained  in  bags  on  each  side. 

Compression  is  also  sometimes  performed  by  the  operation  of  hammer- 
ing :  thus,  cast  brass  is  generally  hammered  before  it  is  used,  in  order  to 
increase  its  strength ;  the  hammer  renders  it  so  much  stiffer,  that  if  it  is 
necessary  to  preserve  its  ductility,  it  must  be  frequently  annealed  by 
exposure  to  heat.  Anvils  and  vices  are  necessary  appendages  to  the 
hammer ;  their  use  depends  principally  on  their  firmness,  which  is  chiefly 
derived  from  weight  in  the  one  case,  and  from  strength  in  the  other ;  and 
pincers  may  be  considered  as  portable  vices. 

For  the  purpose  of  producing  a  continued  pressure  on  such  substances 
as  have  a  tendency  to  contract  their  dimensions  under  the  operation  of  a 
press,  a  spring  has  been  interposed  between  the  press  and  the  materials, 
which  is  capable  of  pursuing  them  with  a  certain  degree  of  force :  the 
utility  of  such  an  arrangement  must,  however,  be  extremely  limited. 
Mr.  Bramah  has  applied  a  well  known  law  of  hydrostatics  to  the  construc- 
tion of  a  very  useful  press,  which  is  simple,  powerful,  and  portable. 

Extension  is  seldom  performed  by  forces  that  tend  immediately  to  in- 
crease the  dimensions  of  the  substance  only :  it  is  generally  procured  by 
reducing  the  magnitude  of  the  substance  in  another  direction,  sometimes 
by  means  of  pressure,  but  more  effectually  by  percussion.  The  rollers  of 
the  press  employed  for  laminating  metals  are  turned  by  machinery,  and 
are  capable  of  being  moved  backwards  and  forwards  in  order  to  repeat  the 
operation  on  the  same  substance ;  their  distance  is  adjusted  by  screws 
which  are  turned  at  once  by  pinions  fixed  on  the  same  axis,  in  order  that 
they  may  be  always  parallel.  In  this  manner  lead,  copper,  and  silver,  ate 
rolled  into  plates,  and  a  thin  plate  of  silver  being  soldered  to  a  thicker  one 
of  copper,  the  compound  plate  is  submitted  again  to  the  action  of  the 


ON  MODES  OF  CHANGING  THE  FORMS  OF  BODIES.    171 

'  press,  and  made  so  thin  as  to  be  afforded  at  a  moderate  expense.  The 
glazier's  vice  is  a  machine  of  the  same  nature  for  forming  window  lead  : 
the  softness  of  the  lead  enables  it  to  assume  the  required  shape,  in  conse- 
quence of  the  pressure  of  the  rollers  or  wheels  ;  and  the  circumference  of 
these  wheels  is  indented,  in  order  to  draw  the  lead  along  by  the  correspond- 
ing elevations.  (Plate  XVIII.  Fig.  232.) 

In  drawing  wire,  the  force  is  originally  applied  in  the  direction  of  the 
extension,  but  it  produces  a  much  stronger  lateral  compression,  by  means  of 
the  conical  apertures  through  which  the  wire  is  successively  drawn.  For 
holding  the  large  wire,  pincers  are  at  first  used,  which  embrace  it  strongly 
while  they  pull,  and  open  when  they  advance  to  a  new  position,  the  inter- 
ruption being  perhaps  of  use,  by  enabling  the  pincers  to  acquire  a  certain 
momentum  before  they  begin  to  extend  the  wire  ;  but  afterwards,  when  the 
wire  is  finer,  it  is  simply  drawn  through  the  aperture  from  one  wheel  or 
drum  to  another.  During  the  operation,  it  requires  frequent  annealing, 
which  causes  a  scale  to  form  on  its  surface  ;  and  this  must  be  removed  by 
rolling  it  in  a  barrel  with  proper  materials ;  for  the  application  of  an  acid 
is  said  to  injure  the  temper  of  the  metal.  Copper  is  sometimes  drawn  into 
wire  so  large  as  to  serve  for  the  bolts  used  in  shipbuilding,  especially  for 
sheathing  ships'  bottoms.  Silver  wire,  thinly  covered  with  gold,  is  ren- 
dered extremely  fine,  and  then  flattened,  in  order  to  be  fit  for  making  gold 
thread :  the  thickness  of  the  gold  is  inconceivably  small,  much  less  than 
the  millionth  part  of  an  inch,  and  sometimes  only  a  ten  millionth. 

In  order  to  form  the  handles  of  vessels  of  earthenware,  the  clay  is  forced 
through  a  hole  of  a  proper  shape  in  an  iron  box.  The  operation  of  the 
potter's  wheel  consists  in  great  measure  of  compression  and  extension,  per- 
formed by  the  hands  ;  the  vessels  are  finished,  when  they  are  partly  dry, 
in  a  lathe,  or  by  other  instruments ;  some  kinds  of  earthenware  are  formed 
in  a  mould  only. 

When  a  thread  or  a  plate  of  glass  is  extended  in  a  semifluid  state,  it  has 
a  tendency  to  preserve  an  equable  thickness  throughout :  this  is  derived 
from  the  effect  of  the  air  in  cooling  it,  the  thinnest  parts  becoming  imme- 
diately a  little  colder  than  the  rest,  and  consequently  harder,  so  that  they 
retain  their  thickness,  until  the  neighbouring  parts  are  brought  into  a 
similar  state. 

Extension  is  performed  by  means  of  percussion,  in  forges  and  in  the 
common  operation  of  the  smith's  hammer.  In  forges,  the  hammers  are 
raised  by  machinery,  and  thrown  forcibly  against  a  spring,  so  as  to  recoil 
with  great  velocity.  With  the  help  of  this  spring,  the  hammer  sometimes 
makes  500  strokes  in  a  minute,  its  force  being  many  times  greater  than 
the  weight  of  the  hammer.  Such  forges  are  used  in  making  malleable 
iron,  in  forming  copper  plates,  and  in  manufacturing  steel.  (Plate  XVIII. 
Fig.  233.) 

Gold  is  beaten  between  the  intestines  of  animals/ on  a  marble  anvil ;  for 
this  purpose  it  is  alloyed  with  copper  or  silver.  It  is  reduced  to  the  thick- 
iies"s  of  little  more  than  the  three  hundred  thousandth  of  an  inch.  Silver 
leaf  is  about  the  hundred  and  sixty  thousandth  :  it  is  made  of  silver  without 
alloy. 

The  operation  of  coining  depends  also  principally  on  an  extension  of  the 


172  LECTURE  XIX. 

metal  into  the  recesses  of  the  die ;  it  is  performed  by  a  strong  pressure,   f 
united  with  a  considerable  impulse,  communicated  by  a  screw  like  that  of 
a  printing  press ;  and  sometimes  the  impression  is  formed  by  the  repeated 
blows  of  a  hammer  only. 

Thin  plates  of  silvered  copper  are  moulded  into  any  figure  that  may  be 
required,  by  being  placed  between  two  corresponding  stamps,  of  which  the 
one  is  fixed,  and  the  other  attached  to  the  bottom  of  a  heavy  hammer.  The 
hammer  is  raised  and  suffered  to  fall  in  a  right  line,  by  means  of  pincers, 
which  open  when  they  have  acquired  a  certain  height.  Sometimes  the 
contact,  produced  by  the  forcible  impulse  of  a  die,  is  sufficiently  intimate  to 
cause  a  thin  plate  of  silver  to  cohere  permanently  with  a  surface  of  iron  ; 
and  this  mode  of  uniting  metals  is  actually  employed  in  some  manu- 
factures. 

The  operations  of  perforating,  cutting,  turning,  boring,  digging,  sawing, 
grinding,  and  polishing,  resemble  each  other,  in  great  measure,  with  respect 
to  the  minute  actions  of  the  particles  of  bodies  which  they  have  to  overcome. 
Penetration  is  generally  performed  in  the  first  instance  by  the  effect  which 
we  have  called  detrusion,  where  the  magnitude  of  the  penetrating  substance 
is  considerable  :  but  when  a  fine  point  or  edge  is  employed,  it  probably  first 
tears  the  surface  where  it  is  most  depressed,  and  then  acts  like  a  wedge  on 
the  portions  of  the  substance  left  on  each  side,  with  a  force  so  much  the 
greater  as  the  edge  is  thinner.  The  resistance  opposed  by  a  solid,  or  even 
by  a  soft  substance,  to  the  motion  of  a  body  tending  to  penetrate  it,  appears 
to  resemble  in  some  measure  the  force  of  friction,  which  is  nearly  uniform, 
whether  the  motion  be  slow  or  rapid,  destroying  a  certain  quantity  of 
momentum  in  a  certain  time,  whatever  the  whole  velocity  may  be,  or  what- 
ever may  be  the  space  described.  Hence  arises  the  advantage  of  giving  a 
great  velocity  to  a  body  which  is  to  penetrate  another,  the  distance  to  which 
a  body  penetrates  being  as  the  square  of  its  velocity,  or  as  its  energy ;  and  a 
certain  degree  of  energy  being  required  in  order  to  make  it  even  penetrate  at 
all.  It  is  true  that  when  we  exchange  a  slow  motion  for  a  more  rapid  one, 
by  the  immediate  action  of  any  mechanical  power,  we  can  only  obtain  the 
same  energy  from  the  same  power,  for  we  must  diminish  the  mass  in  the 
same  proportion  as  the  square  of  the  velocity  is  increased  ;  but  a  very  small 
part  of  the  force  which  is  consumed  in  the  operation  of  a  machine  of  any 
kind,  is  employed  in  generating  momentum  ;  by  much  the  greatest  part  is 
spent  in  overcoming  resistances  which  vary  but  little  with  the  velocity ;  a 
small  portion  only  of  the  resistance  increasing  in  proportion  to  the  square 
of  the  velocity ;  so  that  by  applying  a  triple  force,  we  may  obtain  more 
than  a  double  velocity,  and  more  than  a  quadruple  effect :  and  besides  it 
has  already  been  observed  that  when  the  velocity  begins  to  exceed  a  certain 
limit,  the  effect  is  increased  in  a  much  greater  proportion  than  that  of  its 
square.  The  same  work  is  also  performed  with  less  pressure,  and  less  strain 
on  the  machinery,  where  a  great  velocity  is  employed.  It  is  on  account  of 
the  efficacy  of  velocity  in  facilitating  penetration,  that  soft  substances,  mov- 
ing very  swiftly,  will  readily  perforate  much  harder  ones  ;  and  for  the 
saine  reason  a  gunshot  wound,  and  even  the  loss  of  a  limb,  takes  place  with 
so  little  disturbance  of  the  neighbouring  parts,  that  it  is  sometimes  scarcely 
felt.  The  advantage  of  an  impulse,  however  inconsiderable,  above  a  pres- 


ON  MODES  OF  CHANGING  THE  FORMS  OF  BODIES.    173 

sure,  however  great,  may  be  easily  understood  from  the  ease  with  which  a 
moderate  blow  of  a  hammer  causes  a  nail  to  penetrate  a  substance,  into 
which  the  whole  force  of  the  arm  could  not  have  thrust  it. 

In  the  engine  for  driving  the  piles,  or  upright  beams,  used  for  the  founda- 
tions of  buildings  in  water,  or  in  soft  ground,  the  weight  is  raised  slowly  to 
a  considerable  height,  in  order  that,  in  falling,  it  may  acquire  sufficient 
energy  to  propel  the  pile  with  efficacy.  The  same  force,  if  applied  by  very 
powerful  machinery  immediately  to  the  pile,  would  perhaps  produce  an 
equal  effect  in  driving  it,  but  it  would  be  absolutely  impossible  in  practice 
to  construct  machinery  strong  enough  for  the  purpose,  and  if  it  were  pos- 
sible, there  would  be  an  immense  loss  of  force  from  the  friction.  For  ex- 
ample, supposing  a  weight  of  500  pounds,  falling  from  a  height  of  50  feet, 
to  drive  the  pile  2  inches  at  each  stroke  ;  then,  if  the  resistance  be  con- 
sidered as  nearly  uniform,  its  magnitude  must  be  about  150  thousand 
pounds,  and  the  same  moving  power,  with  a  mechanical  advantage  of  300 
to  1,  would  perform  the  work  in  the  same  time.  But  for  this  purpose  some 
parts  of  the  machinery  must  be  able  to  support  a  strain  equivalent  to  the 
draught  of  600  horses.  In  the  pile  driving  engine,  the  forceps,  or  tongs, 
sometimes  called  the  monkey,  or  follower,  is  opened  as  soon  as  the  weight 
arrives  at  its  greatest  height ;  and  at  the  same  time  a  lever  detaches  the 
drum,  employed  for  raising  the  weight,  from  the  axis  or  windlass,  at  which 
the  horses  are  drawing ;  the  follower  then  descends  after  the  weight,  un- 
coiling the  rope  from  the  drum,  and  the  force  of  the  horses  is  employed  in 
turning  a  fly-wheel,  until  the  connexion  with  the  weight  is  again  restored. 
(Plate  XVIII.  Fig.  284.) 

When  we  throw  a  stone,  or  a  missile  weapon  of  any  kind,  with  the  hand, 
the  stone  can  acquire  no  greater  velocity  than  the  hand  itself,  accompanied 
by  the  neighbouring  part  of  the  arm  ;  so  that  the  whole  velocity  must  be 
produced  in  a  mass  of  matter  comparatively  very  large.  A  sling  enables 
us  to  throw  a  stone  or  a  ball  much  further ;  for  here  the  stone  may  be 
moved  with  a  velocity  far  greater  than  the  hand  that  impels  it,  although 
the  action  of  the  force  on  the  stone  is  indirect,  and  the  resistance  of  the  air 
considerable.  An  elastic  bow,  furnished  with  a  strong  and  light  string, 
enables  us  to  apply  to  an  arrow  or  to  a  ball  the  whole  force  of  our  arms, 
unencumbered  with  any  considerable  portion  of  matter,  that  requires  to  be 
moved  with  the  arrow ;  hence  a  very  great  velocity  may  be  obtained  in 
this  manner.  An  air  gun  possesses  the  same  advantage  in  a  still  greater 
degree,  and  the  force  of  fired  gunpowder  excels  perhaps  all  others  from  its 
concentrating  an  immense  force  in  the  form  of  an  inconceivably  light  elastic 
fluid  ;  of  course  a  ball  impelled  by  this  force,  becomes  a  most  effectual 
instrument  in  penetrating  the  most  refractory  substances.  We  may  easily 
calculate  the  velocity  of  an  arrow,  by  comparing  its  motion  with  that  of  a 
pendulum,  if  we  know  the  proportion  of  its  weight  to  the  force  that  bends 
the  bow ;  including  in  the  weight  a  small  addition  for  the  inertia  of  the 
bow  and  bowstring  ;  the  height  to  which  the  arrow  will  rise,  being  about  as 
much  greater  than  the  space  through  which  the  bowstring  acts  on  it,  as  the 
greatest  force  applied  in  drawing  the  bow  is  greater  than  twice  the  weight 
to  be  moved. 


174  LECTURE  XIX. 

The  action  of  a  whip,  either  on  the  air,  or  on  a  solid  body,  depends  on 
the  increase  of  velocity  occasioned  by  the  successive  transmission  of  the 
motion  from  a  thicker  to  a  thinner  portion  of  its  flexible  substance,  so  that 
at  last,  the  energy  of  the  lash,  and  of  its  knots,  gives  it  a  sufficient  capa- 
bility of  exciting  sound  or  of  inflicting  pain. 

The  instruments  generally  employed  for  the  division  of  solid  bodies,  are 
wedges,  chisels,  knives,  and  scissors  ;  they  sometimes  act  by  pressure  only, 
but  they  are  more  powerful  when  impulse  is  added  to  it.  Hatchets,  planes, 
saws,  and  files,  always  act  with  some  rapidity.  Cutting  instruments  are  in 
general  very  thin  wedges,  but  the  edge  itself  is  usually  much  more  obtuse  ; 
Mr.  Nicholson*  has  estimated  the  angle,  formed  ultimately  by  the  surfaces 
constituting  the  finest  edge,  at  about  56  degrees.  Knives  are  sometimes 
fixed  on  wheels,  so  as  to  revolve  in  a  direction  oblique  to  their  edges,  as  in 
some  machines  for  cutting  chaff,  where  the  straw  is  also  drawn  forwards, 
through  a  space  variable  at  pleasure,  during  each  revolution  of  the  knife. 
An  instrument  of  a  similar  nature  has  also  been  invented  for  the  purpose  of 
cutting  weeds  under  water. 

For  the  edges  of  all  cutting  instruments,  steel  is  principally  employed. 
After  being  hardened,  by  plunging  it  when  red  hot  into  cold  water,  it  is 
tempered,  by  laying  it  on  a  heated  iron,  or  more  accurately,  by  Mr.  Stod- 
art'st  method,  of  immersing  it  in  a  metallic  composition  in  the  state  of 
fusion.  When  its  surface  has  acquired  a  yellow  tinge,  it  is  fit  for  edge  tools, 
and  the  degree  of  heat  proper  for  watch  springs  is  indicated  by  a  blue 
colour.  The  backs  of  knives  are  often  made  of  iron,  which  is  less  brittle 
than  steel :  these  substances  are  generally  welded  together,  by  hammering 
them  when  red  hot ;  but  sometimes,  in  large  instruments,  a  back  of  iron  is 
only  rivetted  on. 

The  iron  employed  for  making  nails  and  other  small  articles,  is  first 
rolled  into  flat  bars,  and  then  cut  into  narrow  rods,  by  causing  it  to  pass 
between  the  cylinders  of  the  slitting  mill,  the  surfaces  of  which  are  formed 
into  rectangular  grooves,  and  which  are  placed  close  to  each  other,  so  that 
the  prominent  parts  of  the  one  are  opposed  to  the  depressions  of  the  other, 
and  the  bars  are  divided  by  the  pressure  of  the  opposite  forces  acting  trans- 
versely at  the  same  points,  so  as  to  separate  them  by  the  effect  which  we 
have  already  considered  under  the  name  detrusion.  The  same  machinery 
also  generally  works  a  pair  of  large  shears  for  cutting  bars  of  any  kind. 
(Plate  XVIII.  Fig.  235.) 

The  lathe  is  an  elegant  instrument,  in  which  a  considerable  relative 
velocity  is  produced  between  the  tool  and  the  substance  to  be  cut,  by  the 
revolution  of  this  substance  on  an  axis,  while  the  tool  is  supported  by  a 
rest.  Ornamental  lathes  admit  of  a  great  variety  of  mechanical  contriv- 
ance, but  they  are  of  little  practical  use,  except  for  amusement.  Picture 
frames  are,  however,  sometimes  turned  in  oval  lathes  ;  and  in  the  manufac- 
ture of  buttons,  machines  of  a  similar  nature  are  occasionally  employed. 
The  effect  of  every  lathe  of  a  complicated  construction  depends  on  a  certain 
degree  of  motion  of  which  its  axis  is  capable  :  if  this  motion  be  governed  by 

*  Nich.  Jour.  8vo,  i.  47,  210. 

f  Nich.  Jour.  4to,  iv.  127.     See  also  i.  380,  468,  575  ;  ii.  64,  102. 


ON  MODES  OF  CHANGING  THE  FORMS  OF  BODIES.    175 

a  screw,  a  screw  of  any  diameter  may  be  turned  by  its  assistance  ;  if  by  a 
frame  producing  an  elliptic  curve,  any  number  of  ovals,  having  the  same 
centre,  may  be  described  at  once  ;  and  if  a  moveable  point  connected  with 
the  work  be  pressed  by  a  strong  spring  against  a  pattern  of  any  kind,  placed 
at  one  end  of  the  axis,  a  copy  of  the  same  form  may  be  made  at  the  other 
end  of  the  axis. 

The  process  of  boring  is  a  combination  of  penetration  and  division,  and 
sometimes  of  attrition.  Awls,  gimlets,  screws,  augers,  and  centrebits,  are 
various  forms  of  borers.  The  drill  has  the  advantage  of  a  rapid  motion, 
communicated  by  the  drill  bow,  which  turns  it  round  by  means  of  a  little 
wheel  or  pulley.  In  boring  cannon,  the  tool  is  at  rest,  while  the  cannon 
revolves,  and  by  this  arrangement  the  bore  of  the  cannon  is  formed  with 
much  more  accuracy  than  according  to  the  old  method  of  putting  the  borer 
in  motion  ;  perhaps  because  the  inertia  of  so  large  a  mass  of  matter  as  con- 
stitutes the  cannon,  assists  in  denning  the  axis  of  revolution  with  more 
accuracy.  The  borer  is  pressed  against  the  cannon  by  a  weight  hung 
on  the  arm  of  a  bent  spring,  and  during  the  operation  the  outside  is  also 
turned  into  its  intended  shape  by  the  application  of  proper  instruments. 
Cylinders  for  steam  engines  are  cast  hollow,  and  afterwards  bored  ;  but  in 
this  case  the  borer  revolves,  and  the  cylinder  remains  at  rest. 

Ploughs,  spades,  pickaxes,  mattocks,  harrows,  and  other  agricultural 
instruments,  resemble  in  their  operation  the  chisel  and  the  wedge :  the 
numerous  diversities  in  their  form  and  the  complications  of  their  structure, 
are  determined  more  by  the  various  modifications  of  their  action,  required 
for  particular  purposes,  than  by  any  material  difference  in  the  mode  of 
application  of  the  principles  on  which  they  depend.  (Plate  XVIII. 
Fig.  236.) 

The  process  of  mining  is  a  combination  of  boring  and  digging.  Shafts 
are  sunk,  levels  are  driven,  and  drains  are  carried  off,  by  the  help  of  picks 
or  pickaxes,  wedges,  and  hammers,  the  rocks  being  also  sometimes  loosened 
by  blasting  with  gunpowder.  In  searching  for  coal,  a  shaft  is  sunk 
through  the  uppermost  soft  strata,  and  the  rock  is  then  bored  by  striking  it 
continually  with  an  iron  borer  terminating  in  an  edge  of  steel,  which  is  in 
the  mean  time  turned  partly  round  ;  and  at  proper  intervals  a  scoop  is  let 
down  to  draw  up  the  loose  fragments.  In  this  manner  a  perforation 
is  sometimes  made  for  more  than  a  hundred  fathoms,  the  borer  being 
lengthened  by  pieces  screwed  on  to  it ;  it  is  then  partly  supported  by  a 
counterpoise,  and  is  worked  by  machinery ;  if  it  happens  to  break,  the 
piece  is  raised  by  a  rod  furnished  with  a  hollow  cone,  like  an  extinguisher, 
which  is  driven  down  on  it.  Sometimes  the  borer  is  furnished  with  knives, 
which  are  made  to  act  on  any  part  at  pleasure,  and  to  scrape  off  a  portion 
of  the  surrounding  substance,  which  is  collected  in  a  proper  receptacle. 

For  sawing  wood  on  a  large  scale,  sawing  mills  are  very  advantageously 
employed,  being  usually  driven  by  water.  Several  saws  are  generally 
fixed  in  a  frame,  parallel  to  each  other  ;  they  are  worked  up  and  down  by 
a  cfank,  and  at  every  alternation,  a  wheel  is  drawn  round  a  little  by  a 
catch,  or  click,  and  moves  forwards  the  frame  which  supports  the  timber. 
When  the  machine  is  employed  for  cutting  the  fellies  which  form  the  cir- 


176  LECTURE  XIX. 

cumference  of  wheels,  the  frame  supporting  the  timber  is  made  to  turn 
round  a  centre.  A  circular  saw  is  used  in  the  construction  of  blocks  and 
pullies  ;  and  in  order  to  make  the  motion  more  secure  from  the  effect  of 
accidental  irregularities,  the  wheels  are  made  to  turn  each  other  by  contact 
only,  without  teeth.  The  machinery  for  making  blocks,  in  the  'Royal 
dock  yard  at  Portsmouth,  has  been  lately  much  improved  and  enlarged  ; 
it  is  worked  by  a  steam  engine,  the  action  of  which  is  applied  to  a  great 
variety  of  purposes.  The  advantage  of  a  saw  which  revolves  continually 
appears  to  be  very  considerable,  since  a  .much  greater  velocity  may  be 
given  to  it  than  can  be  obtained  when  the  motion  is  alternate.  Such  a  saw 
has  also  sometimes  been  applied  to  cutting  off  piles  under  water. 

In  mills  for  sawing  marble  into  slabs,  the  saws  are  drawn  backwards 
and  forwards  horizontally  :  they  are  made  of  soft  iron,  without  teeth  ;  and 
sand  being  applied  to  them,  with  water,  during  the  operation,  the  sand 
is  partly  imbedded  in  the  iron,  and  grinds  away  the  marble. 

Granite  is  worked  by  driving  a  number  of  thin  wedges  very  gradually 
into  it,  at  various  parts  of  the  section  desired  ;  and  sometimes  wedges  of 
wood  are  employed,  which  being  moistened  by  water,  their  expansion 
separates  the  parts  from  each  other.*  It  is  also  said  that  many  stones 
may  be  divided  by  drawing  lines  on  them  with  oil,  and  then  exposing 
them  to  heat.  Perhaps  some  processes  of  this  kind  might  be  performed 
with  advantage  under  water  ;  it  is  well  known  that  glass  may  be  cut  in  a 
rough  manner  under  water,  without  much  difficulty,  by  a  common  pair 
of  scissors. 

For  reducing  the  magnitude  of  a  substance  in  a  particular  part,  instru- 
ments of  attrition  are  used ;  rasps,  files,  grindstones,  and  hones  ;  and  of 
all  these  the  immediate  actions  appear  to  resemble  those  of  chisels  and 
saws.  The  hatches  of  files  are  cut  with  a  hard  chisel  while  the  steel  is 
soft,  and  the  files  are  afterwards  hardened.  In  using  the  grindstone,  water 
is  applied,  in  order  to  avoid  the  inconvenience  produced  by  too  much  heat ; 
and  sometimes  tallow  is  substituted  for  water  with  equal  advantage  :  but  oil 
is  not  found  to  answer  the  same  purpose ;  and  it  has  been  conjectured  that 
the  cold  continually  occasioned  by  the  melting  of  the  tallow  at  the  point 
of  friction,  serves  as  a  substitute  for  the  cooling  effect  of  the  evaporation 
of  the  water.  For  grinding  and  polishing  steel,  the  grindstones  are  made 
to  revolve,  either  vertically  or  horizontally,  with  a  velocity  so  great  as  to 
describe  sometimes  as  much  as  60  feet  in  a  second.  The  steel  is  also  in 
some  cases  drawn  backwards  and  forwards  horizontally  on  a  circular  sur- 
face, and  in  order  that  the  action  may  be  equally  divided  throughout  the 
surface,  it  is  allowed  to  revolve  on  an  axis  by  means  of  the  friction  ;  its 
motion  being  confined  to  one  direction  by  the  action  of  a  catch. 

Various  substances,  chiefly  of  mineral  origin,  are  also  used,  on  account 
of  their  hardness,  as  intermediate  materials  for  grinding  and  polishing 
others.  These  are  diamond  dust,  corundum,  emery,  tripoli,  putty,  glass, 
sand,  flint,  red  oxid  of  iron,  or  crocus  martis,  and  prepared  chalk ;  they 
are  sometimes  applied  in  loose  powder,  and  sometimes  fixed  on  leather, 

*  See  Herschel's  Discourse  on  the  Study  of  Natural  Philosophy,  p.  48. 


ON  MODES  OF  CHANGING  THE  FORMS  OF  BODIES.      177 

wood  or  paper.  Cuttle  fish  bone,  and  seal  skin,  are  furnished  by  the 
animal  kingdom,  and  Dutch  rushes  by  the  vegetable  ;  these  are  employed 
chiefly  in  polishing  wood  or  ivory. 

Marble  is  made  smooth  by  rubbing  one  piece  on  another,  with  the  in- 
terposition of  sand  ;  the  polishing  blocks  are  sometimes  caused  to  revolve 
by  machinery  in  a  trough  in  which  the  marble  is  placed  under  water,  and 
are  drawn  at  the  same  time  gradually  to  and  from  the  centre  ;  or  the  slab 
itself,  with  the  frame  on  which  it  rests,  is  drawn  slowly  backwards  and 
forwards,  while  the  blocks  are  working  on  it.  Granite  is  polished  with 
iron  rubbers,  by  means  of  sand,  emery,  and  putty ;  it  is  necessary  to  take 
care  during  the  operation  that  the  water,  which  trickles  down  from  the 
rubbers,  and  carries  with  it  some  of  the  iron,  may  not  collect  below  the 
columns,  and  stain  them ;  but  this  inconvenience  may  be  wholly  avoided 
by  employing  rubbers  of  glass. 

Optical  lenses  are  fixed  on  blocks  by  means  of  a  cement,  and  ground 
with  emery,  by  a  tool  of  proper  convexity  or  concavity ;  if  they  are  small, 
a  large  number  is  fixed  on  the  blocks  at  the  same  time.  The  tool  is  some- 
times first  turned  round  its  axis  by  machinery,  and  when  the  lenses  are 
to  be  finished,  a  compound  motion  is  given  to  it  by  means  of  a  crank  ;  and 
in  order  to  make  it  more  smooth,  the  wheels  turn  each  other  by  brushes 
instead  of  cogs.  The  point  of  the  lens  where  its  two  surfaces  are  parallel, 
is  determined  by  looking  through  it  at  a  minute  object,  while  it  is  fixed  on 
a  wheel  with  a  tubular  axis,  and  shifting  it,  until  the  object  no  longer  ap- 
pears to  move  ;  a  circle  is  then  described,  as  it  revolves,  in  order  to  mark 
its  outline. 

Machines  for  trituration,  by  means  of  which  the  larger  masses  of  matter 
are  crushed,  broken,  or  ground,  into  smaller  parts,  are  in  general  compre- 
hended under  the  denomination  of  mills.  After  the  pestle  and  mortar, 
the  simplest  machine  of  this  kind  appears  to  be  the  stamping  mill ;  the 
stampers  resemble  the  hammers  of  the  mill  employed  in  the  extraction  of 
oils  from  seeds,  and  the  machine  is  used  for  reducing  to  powder  the  ores  of 
metals,  and  sometimes  also  barks,  and  linseed ;  the  surface  of  the  stampers 
being  armed  Avith  iron  or  steel.  But  barks  and  seeds  are  more  usually 
ground  by  the  repeated  pressure  of  two  wheels  of  stone,  rolling  on  an  axis 
which  is  forced  in  a  horizontal  direction  round  a  fixed  point.  A  noble- 
man of  distinguished  rank  and  talents  has  lately  employed  for  a  mortar 
mill,  a  wheel  of  cast  iron,  formed  of  two  portions  of  cones,  joined  at  their 
bases  :  after  thirty  revolutions,  the  mortar  being  sufficiently  ground,  a  bell 
rings,  and  the  horse  stops. 

The  materials  for  making  gunpowder  are  also  ground  by  a  wheel  re- 
volving in  a  trough :  in  order  to  corn  them,  they  are  moistened,  and  put 
into  boxes  with  a  number  of  holes  in  their  bottoms,  and  these  boxes  being 
placed  side  by  side,  in  a  circular  frame,  suspended  by  cords,  the  frame  is 
agitated  by  a  crank  revolving  horizontally,  and  the  paste  shaken  through 
the  holes  :  the  corns  are  polished  by  causing  them  to  revolve  rapidly  within 
a  barrel. 

A  revolving  barrel  is  used  for  forming  and  polishing  small  round  bodies 
of  different  kinds,  and  it  is  often  employed  in  agriculture  as  a  churn  for 


178  LECTURE  XIX. 

making  butter.  The  purpose  of  agitation  is  perhaps  more  effectually 
answered  by  an  alternate  motion,  which  has  sometimes  been  produced  in  a 
barrel  churn,  by  means  of  a  cord  attached  to  a  heavy  pendulum. 

Threshing  machines  are  of  two  kinds  ;  the  one  consists  of  a  number  of 
flails,  beating  the  corn  nearly  in  the  same  manner  as  they  are  used  by 
labourers:  in  the  other,  which  is  more  commonly  employed  in  this 
country,  the  corn  is  drawn  along  by  two  revolving  rollers,  and  caused  to 
pass  between  a  cylinder  and  its  concave  cover,  while  a  number  of  blocks, 
projecting  from  the  surface  of  the  cylinder,  beat  or  rub  out  the  grains 
very  effectually  from  the  ears  ;  the  corn  falls  out  at  the  lower  part,  and  is 
winnowed  by  a  fan  which  the  machine  turns  at  the  same  time.  In  this 
manner  it  is  said  that  a  horse  will  thresh  about  100  bushels  of  corn  in  a 
day.  It  is  commonly  reckoned  the  work  of  a  labourer  to  thresh  about  six 
bushels  in  a  day.  (Plate  XVIII.  Fig.  237.) 

Some  kinds  of  grain  are  occasionally  ground  in  mills  of  iron  or  steel, 
which  consist  of  a  solid  cylinder  or  cone  turning  within  a  hollow  one,  both 
the  surfaces  being  cut  obliquely  into  teeth.  But  the  common  mill  for 
grinding  corn  is  composed  of  two  circular  stones  of  silicious  grit,  placed 
horizontally ;  the  upper  one  revolves  with  considerable  velocity,  and  is 
supported  by  an  axis  passing  through  the  lower  one,  at  a  distance  variable 
at  pleasure.  When  the  diameter  is  five  feet,  the  stone  usually  makes  about 
90  revolutions  in  a  minute  ;  if  the  velocity  were  greater,  the  flour  would 
be  too  much  heated.  The  corn  is  shaken  out  of  a  funnel  or  hopper,  by 
means  of  projections  from  the  revolving  axis  which  strike  against  the  ori- 
fice ;  it  passes  through  the  middle  of  the  upper  millstone,  and  is  readily 
admitted  between  the  stones ;  the  lower  stone  is  slightly  convex,  and  the 
upper  one  somewhat  more  concave,  so  that  the  corn  passes  over  more  than 
half  the  radius  of  the  stone  before  it  begins  to  be  ground  :  after  being  re- 
duced to  powder,  it  is  discharged  at  the  circumference,  its  escape  being 
favoured  by  the  convexity  of  the  lower  stone,  as  well  as  by  the  centrifugal 
force.  The  surface  of  the  stones  is  cut  into  grooves,  in  order  to  make  them 
act  more  readily  and  effectually  on  the  corn.  The  resistance,  in  grinding 
wheat,  has  been  estimated  at  about  a  thirty-fifth  of  the  weight  of  the  mill- 
stone. The  stones  have  sometimes  been  placed  vertically,  and  the  axis 
supported  on  friction  wheels  :  but  the  common  position  appears  to  be  more 
eligible  for  mills  on  a  large  scale.  It  is  said  that  a  man  and  a  boy  can 
grind  by  a  hand-mill  a  bushel  of  wheat  in  an  hour ;  in  a  watermill,  the 
grinding  and  dressing  of  a  bushel  of  wheat  is  equivalent  to  the  effect  of 
20,160  pounds  of  water  falling  through  a  height  of  10  feet,  which  is  about 
as  much  as  the  work  of  a  labourer  for  a  little  more  than  half  an  hour.  In 
a  windmill,  when  the  velocity  is  increased  by  the  irregular  action  of  the 
wind,  the  corn  is  sometimes  forced  rapidly  through  the  mill,  without  being 
sufficiently  ground.  There  is  an  elegant  method  of  preventing  this,  by 
means  of  the  centrifugal  force  of  two  balls,  which  fly  out  as  soon  as  the 
velocity  is  augmented,  and  as  they  rise  in  the  arc  of  a  circle,  allow  the  end 
of  a  lever  to  rise  with  them,  while  the  opposite  end  of  a  lever  descends  with 
the  upper  millstone,  and  brings  it  a  little  nearer  to  the  lower  one.  The 
bran  or  husk  is  separated  from  the  flour  by  sifting  it  in  the  bolting  mill, 


ON  MODES  OF  CHANGING  THE  FORMS  OF  BODIES.    179 

which  consists  of  a  cylindrical  sieve,  placed  in  an  inclined  position  and 
turned  by  machinery.  (Plate  XVIII.  Fig.  238.) 

When  the  flour  is  made  into  bread,  the  dough  requires  to  be  kneaded  : 
for  this  purpose  a  machine  is  sometimes  used  in  which  four  or  more  bars, 
parallel  to  the  axis  of  motion,  are  turned  round  by  means  of  a  walking 
wheel.  The  dough  is  placed  in  a  circular  trough,  in  which  the  bars 
revolve  not  quite  in  the  middle,  so  as  to  approach  in  each  revolution  to  one 
of  its  sides,  and  thus  the  dough  is  perpetually  compelled  to  change  its 
form. 

A  machine  of  nearly  the  same  construction  is  employed  for  levigating 
flints,  after  they  have  first  been  made  red  hot,  and  plunged  into  cold  water, 
in  order  to  render  them  friable.  They  are  mixed,  when  it  is  necessary, 
with  other  large  stones,  and  the  water,  in  which  the  process  is  performed, 
carries  off  the  powder,  and  deposits  its  coarser  parts  in  a  short  time,  while 
the  finer  remain  much  longer  suspended,  and  are  thus  separated  from  the 
rest. 

When  a  mechanical  structure  is  to  be  demolished,  or  a  natural  substance 
to  be  broken  into  smaller  parts,  we  have  often  occasion  to  employ  the  col- 
lected force  of  men,  the  powers  of  machinery,  or  the  expansive  force  of 
chemical  agents.  Battering  rams,  or  wooden  beams  suspended  by  ropes 
and  armed  with  iron,  which  were  used  by  the  warriors  of  antiquity  in  be- 
sieging a  town,  are  now  generally  superseded  by  the  introduction  of 
artillery,  although  they  may  perhaps  still  afford,  in  some  cases,  a  more 
economical  and  equally  powerful  mode  of  operation.  The  same  mo- 
mentum, and  the  same  energy,  may  be  given  to  a  battering  ram  at  a  less 
expense  than  to  a  cannon  ball ;  but  it  is  probable  that  the  efficacy  of  a 
cannon  ball  is  chiefly  owing  to  the  augmentation  of  its  velocity  beyond 
that  limit,  which  is  the  utmost  that  the  substance  to  be  destroyed  can  sus- 
tain without  giving  way,  independently  of  the  mass  of  the  body  which 
strikes  it. 

For  demolishing  smaller  aggregates,  pincers,  hammers,  and  crows,  are 
generally  sufficient ;  to  these  sometimes  more  complicated  instruments  are 
added.  Thus,  for  example,  several  machines  have  been  invented  for  draw- 
ing out  ship's  bolts.  A  hook  which  grapples  like  the  common  instrument 
for  drawing  teeth,  has  been  applied  for  holding  them  firmly,  and  sometimes 
a  screw,  turned  by  means  of  wheelwork,  has  been  used  for  gaining  a  force 
sufficient  to  overcome  their  adhesion.  In  all  such  cases,  however,  the  effect 
of  percussion  has  a  considerable  advantage ;  and  even  if  other  means  are 
employed,  it  is  of  use  to  begin  with  lessening  the  firmness  of  the  adhesion 
by  the  blows  of  a  hammer  ;  and  in  this  manner  a  screw  may  be  extracted, 
which  is  so  firmly  attached  by  its  rust  as  to  be  immoveable  by  other 
means. 

The  expansive  force  of  heat  is  frequently  of  great  service  in  dividing 
rocks,  or  in  destroying  old  buildings.  This  is  sometimes  done  simply  by 
the  application  of  fire,  as  in  the  mine  of  Rammelsberg  in  the  Hartz,  where 
the  stratum  containing  the  ore  is  of  such  a  nature,  partly,  perhaps,  on  ac- 
count of  the  combustible  matter  which  enters  into  its  composition,  that,  by 
the  effect  of  a  large  quantity  of  fuel  which  is  burnt  in  the  vast  excavation, 

N2     " 


180  LECTURE  XX. 

of  which  it  forms  the  side,  it  is  rendered  so  friable  as  to  be  worked  with 
ease.  More  commonly,  however,  the  force  of  gunpowder  is  employed,  and 
rocks  are  generally  blasted  with  great  convenience  by  an  explosion  of  this 
powerful  agent.  A  hole  being  bored  to  the  depth  of  three  or  four  feet,  the 
powder  is  placed  at  the  bottom,  and  a  wire  being  introduced,  small  stones 
and  sand  are  rammed  round  it,  and  the  wire  is  withdrawn,  leaving  a  com- 
munication for  firing  the  powder  by  means  of  a  train  of  sufficient  length  to 
insure  the  safety  of  the  workman.  It  is  said  that  the  explosion  is  more 
efficacious  when  the  powder  does  not  fill  the  whole  of  the  cavity  ;  this, 
however,  appears  to  require  confirmation.  The  chemical  powers  which  are 
the  ultimate  causes  of  the  operation  of  gunpowder,  belong  to  a  department 
of  philosophy  which  it  is  not  our  business  to  investigate  :  but  the  elasticity 
of  the  gases  and  vapours  which  are  extricated,  as  modified  by  the  heat 
which  accompanies  their  production,  will  be  considered  and  explained  in 
the  subsequent  divisions  of  this  Course  of  Lectures. 


LECT.  XIX.— ADDITIONAL  AUTHORITIES. 

The  subjects  embraced  in  this  Lecture  and  Lecture  XVI.  are  of  so  miscellaneous 
a  nature,  that  a  detailed  list  of  authorities  would  be  very  tedious.  We  refer  for  ge- 
neral information  to  the  Encyclopedic  Methodique  Arts  et  Metiers.  Machines  ap- 
prouvees  par  1' Academic  Royale  des  Sciences,  4to  and  fol.  1735-89.  Bailey's  Plates 
of  Machines,  approved  by  the  Society  of  Arts,  2  vols.  fol.  1782.  Repertory  of  Arts, 
1794 Nicholson's  Journal,  1797 Philosophical  Magazine,  1798 An- 
nals of  Philosophy,  1800 Mechanics'  Magazine.  Newton's  Patents.  Engi- 
neers' and  Architects'  Journal.  The  Encyclopaedias  Britannica  and  Metropolitan, 
&c.  &c. 

Treatises. — Borgnis,  Theorie  de  la  Mecanique  Industrielle,  4to,  Par.  1821.  Du- 
pin,  Introduction  d'un  Nouveau  Cours  de  Geometric  et  de  Mecanique  appliquees 
aux  Arts,  1824.  Second  Discours,  1825.  Geometric  et  Mecanique  appliquees  aux 
Arts,  3  vols.  1825-8.  Christian,  Traite  de  Mecanique  Industrielle,  3  vols.  4to, 
1822-5.  Hachette,  Traite  Elementaire  des  Machines,  4to,  1828.  Barlow  on  Ma- 
nufactures and  Machinery,  4to,  1836.  Ure's  Dictionary  of  Arts,  Manufactures, 
and  Mines,  1839.  Supplement,  1844. 


LECTURE   XX. 


ON  THE  HISTORY  OF  MECHANICS. 

THE  order  which  we  have  pursued  in  considering  the  various  depart- 
ments of  mechanical  science,  has  been  in  great  measure  synthetical,  dic- 
tated by  the  plan  of  proceeding  logically  from  the  most  simple  principles  to 
their  more  complicated  combinations,  so  as  to  build  at  every  step  on  foun- 
dations which  had  been  firmly  laid  before  :  and  this  method  is  unquestion- 
ably the  best  adapted  for  the  expeditious  progress  of  a  student  in  sciences 
with  which  he  is  unacquainted.  But  having  once  acquired  a  certain 
degree  of  knowledge,  he  is  anxious  to  be  informed  by  what  steps  that 
knowledge  was  originally  obtained,  and  to  what  individuals  mankind  is  in- 
debted for  each  improvement  that  has  been  successively  made.  Hence, 


ON  THE  HISTORY  OF  MECHANICS.  181 

although  we  cannot  attempt  to  enter  into  a  complete  history  of  mechanics, 
it  may  still  be  satisfactory  to  take  a  short  retrospect  of  a  few  of  the  most 
remarkable  eras  in  mechanical  philosophy,  and  in  those  parts  of  mathe- 
matics on  which  it  immediately  depends. 

It  is  universally  allowed  that  the  Greeks  derived  the  elements  of  mathe- 
matical, mechanical,  and  astronomical  learning  from  Egypt  and  from  the 
East.*  Diogenes  Laertius,  who  appears  to  be  very  desirous  of  claiming  for 
his  countrymen  the  merit  of  originality,  does  not  deny  that  Thales  and 
Pythagoras  acquired  much  of  their  knowledge  in  their  travels.  Thales  of 
Miletus  is  the  first  that  can  be  supposed  to  have  introduced  these  studies 
into  Greece.  Moeris,  who  was  probably  a  king  of  Egypt,  and  Theuth  or 
Thoth,  a  native  of  the  same  country,  are  mentioned  as  having  laid  the  foun- 
dations of  geometry ;  but  the  science  could  scarcely  have  extended,  in 
those  ages,  further  than  was  barely  necessary  for  the  measurement  of  land : 
since  Thales,  or  even  a  later  philosopher,  is  said  to  have  first  discovered 
that  two  lines  drawn  from  the  extremities  of  the  diameter  of  a  circle,  and 
meeting  in  any  other  part  of  its  circumference  form  with  each  other  a  right 
angle.  Thales  was  one  of  the  seven  whom  antiquity  distinguished  by  the 
appellation  of  wise  men  ;  he  flourished  about  600  years  before  the  Christian 
era,  and  he  was  the  father  of  the  Ionian  school,  the  members  of  which,  in 
subsequent  times,  devoted  themselves  more  particularly  to  the  study  of 
moral  than  of  natural  philosophy. 

The  Italian  school,  on  the  contrary,  which  was  founded  by  Pythagoras, 
appears  to  have  been  more  inclined  to  the  study  of  nature  and  of  its  laws  ; 
although  none  of  the  departments  of  human  knowledge  were  excluded  from 
the  pursuits  of  either  of  these  principal  divisions  of  the  Grecian  sages,  until 
Socrates  introduced  into  the  Ionian  school  a  taste  for  metaphysical  specu- 
lations, which  excluded  almost  all  disposition  to  reason  coolly  and  clearly 
on  natural  causes  and  effects.  To  Pythagoras  philosophy  is  indebted  for 
the  name  which  it  bears  ;  his  predecessors  had  been  in  the  habit  of  calling 
themselves  wise,  he  chose  to  be  denominated  a  lover  of  wisdom  only.  He 
had  studied  under  Pherecydes,  and  Pherecydes  under  Pittacus  :  but  with 
respect  to  mathematical  and  mechanical  researches,  it  does  not  appear  that 
either  of  his  teachers  had  made  any  improvements.  On  his  return  from 
his  travels  in  Egypt  and  the  East,  in  the  time  of  the  last  Tarquin,  about 
500  years  before  Christ,  he  found  his  native  country  Samos  under  the  do- 
minion of  the  tyrant  Polycrates,  and  went  as  a  voluntary  exile  to  seek  a 
tranquil  retreat  in  a  corner  of  Italy.  At  Croto,  says  Ovid,  he  studied  and 
taught  the  laws  of  nature. 

"  From  human  view  what  erst  had  lain  concealed 
His  piercing  mind  to  open  light  revealed ; 
To  patient  toil  his  ardent  soul  constrained, 
Of  Nature's  richest  stores  possession  gained  : 
And  thence,  with  glowing  heart  and  liberal  hand, 
He  dealt  her  treasures  o'er  the  listening  land. 
•  The  wondering  crowd  the  laws  of  nature  hears, 

And  each  great  truth  in  silent  awe  reveres." 

*  See  Kelland's  Lectures  on  Demonstrative  Mathematics,  Edinb.  1843.    Lect.  I. 


182  LECTURE  XX. 

However  erroneous  the  opinion  may  be,  that  Pythagoras  was  acquainted 
with  the  laws  of  gravitation,  it  is  certain  that  he  made  considerable  im- 
provements both  in  mathematics  and  in  mechanics,  and  in  particular  that 
he  discovered  the  well  known  relation  between  the  hypotenuse  and  the 
sides  of  a  right  angled  triangle,  and  demonstrated  that  the  square  of  the 
hypotenuse  is  always  equal  to  the  sum  of  the  squares  of  the  sides.  This 
theorem  is  more  essential  to  the  perfection  of  geometry  than  any  other  pro- 
position that  can  be  named  ;  and  if  we  may  judge  by  the  story  of  his 
having  sacrificed  a  hecatomb  to  the  Muses  on  occasion  of  the  discovery,  he 
seems  to  have  had  a  foresight  of  the  magnificence  of  the  edifice  that  was  in 
subsequent  times  to-be  built  on  this  foundation. 

Democritus  of  Abdera  lived  about  a  century  after  Pythagoras,  whose 
works  he  studied  and  whose  principles  he  adopted.  He  appears  to  have 
been  possessed  of  very  extensive  knowledge  and  profound  learning  ;  but 
little  remains  of  his  works  excepting  their  titles.  Some  have  attributed  to 
him  the  invention  of  the  method  of  arranging  stones  so  as  to  form  an  arch. 
Seneca  thinks  that  so  simple  an  invention  must  have  been  practised  in 
earlier  ages  :  but  Mr.  King  has  endeavoured  to  show  that  its  general  intro- 
duction in  building  was  of  much  later  date.  Architecture  and  other 
mechanical  arts  had  however  been  considerably  advanced  some  time  before 
this  period,  if  it  is  true  that  Ctesiphon  or  Chersiphron,  who  built  the 
temple  of  Ephesus,  was  contemporary  with  Croesus  and  Thales.  It  is  un- 
certain at  what  time  bridges  of  stone  were  first  built ;  and  it  is  doubtful 
whether  the  art  of  building  bridges  of  wood  was  very  well  understood  in 
those  ages  :  for  according  to  Herodotus,  it  was  commonly  believed  that 
Thales  avoided  the  necessity  of  procuring  a  passage  over  the  Halys  for  the 
army  of  Croesus,  by  encamping  them  on  its  banks,  and  cutting  a  channel 
for  the  river  in  their  rear,  although  the  historian  himself  is  of  opinion,  that 
they  passed  over  bridges  which  already  existed.  Curtius  speaks  of  a  bridge 
of  stone  over  the  Euphrates  at  Babylon,  which  appears  to  have  been  built 
long  before  the  time  of  Alexander,  whose  expedition  he  relates  ;  and  it  is 
scarcely  probable  that  a  stone  bridge  could  have  withstood  the  impulse  of 
so  rapid  a  river,  if  it  had  been  supported  by  columns  only,  without  arches, 
since  they  must  have  left  too  small  a  space  for  the  passage  of  the  water.  If 
however,  we  may  believe  Herodotus,  whom  Mr.  King  has  quoted,  this  was 
in  reality  a  kind  of  drawbridge.  According  to  this  author,  it  was  built  by 
Nitocris,  the  immediate  successor  of  Semiramis  :  the  stones  were  united  by 
iron  and  lead,  and  beams  were  laid  across  them  which  were  removed  at 
night,  in  order  to  prevent  the  mutual  depredations  of  the  inhabitants  of  dif- 
ferent parts  of  the  city.  We  are  informed  by  Pliny  that  Ctesiphon  lowered 
his  large  blocks  of  stone  by  placing  them  on  heaps  of  sand  bags,  and 
letting  out  the  sand  by  degrees  ;  it  does  not  appear  how  he  raised  them,  but 
the  inclined  plane  seems  to  afford  the  simplest  and  most  obvious  method. 

Archytas  of  Tarentum  and  Eudoxus  of  Cnidus  were  also  Pythagoreans. 
They  were  the  first  that  attempted  to  make  the  mathematical  sciences 
familiar  by  popular  illustrations  ;  and  Archytas  is  said  by  some  to  have 
invented  the  pulley  and  the  screw.  They  lived  nearly  150  years  after 
Pythagoras,  and  geometry  had  made  in  the  mean  time  very  rapid  advances, 


ON  THE  HISTORY  OF  MECHANICS.  183 

for  the  properties  of  the  conic  sections  were  well  known  to  these  philoso- 
phers. "  The  first  persons,"  says  Plutarch,  "  that  cultivated  the  method 
of  organic  geometry,  were  of  the  school  of  Eudoxus  and  Archytas.  These 
philosophers  introduced  elegance  and  variety  into  science,  by  illustrations 
derived  from  sensible  objects,  and  made  use  of  mechanical  contrivances  for 
expediting  and  familiarising  the  solutions  of  problems,  which,  if  more 
mathematically  treated,  are  complicated  and  difficult :  each  of  them  in- 
vented a  method  of  determining  in  this  manner  the  magnitude  of  two 
mean  proportionals  between  two  given  lines,  by  the  assistance  of  certain 
curves  and  sections.  Plato  by  no  means  approved  of  their  mode  of  pro- 
ceeding, and  reprehended  them  severely,  as  giving  up  and  perverting  the 
most  essential  advantages  of  geometry,  and  causing  the  science  to  revert 
from  pure  and  incorporeal  forms  to  the  qualities  of  sensible  bodies,  sub- 
jected to  narrow  and  servile  restraints.  It  was  for  this  reason  that  practi- 
cal mechanics  were  separated  from  geometry,  and  were  long  neglected  by 
philosophers,  being  considered  as  a  department  only  of  the  art  of  war." 

Aristotle,  who  was  almost  the  last  of  the  Ionian  school,  flourished  a 
little  less  than  half  a  century  after  Archytas  ;  he  was  perhaps  the  author 
of  no  original  discoveries  relating  to  the  principles  of  mechanics,  but  we 
find,  in  his  treatise  on  this  science,  the  law  of  the  composition  of  motion 
very  distinctly  laid  down ;  he  makes,  however,  some  mistakes  respecting 
the  properties  of  levers.  His  general  merit  in  elegant  literature,  as  well  as 
in  natural  history  and  natural  philosophy,  is  too  well  known  to  require 
encomium. 

The  foundation  of  Alexandria  commences  a  period  memorable  for 
science  in  general,  but  more  particularly  for  mathematics  and  astronomy. 
Dinocrates  was  the  architect  whom  Alexander  employed  in  laying  out  and 
in  building  this  celebrated  city.  Among  those  who  studied  in  this  school, 
the  sciences  are  indebted  to  none  more  than  to  Euclid,  who  lived  about  300 
years  before  our  era.  It  is  uncertain  how  much  of  his  Elements  may 
have  been  derived  from  his  own  investigations ;  but  the  masterly  manner 
in  which  this  well  known  work  is  arranged,  and  the  precision  and  accuracy 
which  reign  in  every  part  of  it,  demand  almost  as  great  a  share  of  praise 
as  is  due  to  original  discovery. 

Epicurus  was  a  contemporary  of  Euclid,  and  is  considered  as  the  last  of 
the  Pythagorean  or  Italian  philosophers.  The  penetration  that  he  dis- 
covered in  assigning  the  true  causes  to  many  mechanical  phenomena,  his 
explanations  of  which  are  copied  by  Lucretius,  is  sufficient  to  induce  us 
to  look  forwards  with  impatience  to  the  publication  of  such  of  his  works, 
as  have  lately  been  discovered  among  the  manuscripts  of  Herculaneum. 
Apollonius  of  Perga  lived  about  half  a  century  later ;  the  elegance  and 
extent  of  his  investigations  of  the  most  abstruse  properties  of  the  conic 
sections  left  but  little  to  be  added  to  them  by  more  modern  geometricians. 
The  architect  Philo  appears  to  have  been  more'ancient  than  Apollonius ; 
but  he  is  not  the  Philo  whose  essay  on  warlike  engines  is  published  in  the 
collection  of  the  Ancient  mathematicians  ;  since  this  author  was  a  pupil 
of  Ctesibius. 

For  the  demonstration  of  the  fundamental  properties  of  the  lever  and  of 


184  LECTURE  XX. 

the  centre  of  gravity ;  for  the  discovery  of  the  laws  of  hydrostatics,  and 
of  the  modes  of  determining  the  specific  gravities  of  bodies ;  for  the  con- 
struction of  the  first  cranes  and  of  the  first  planetarium  ;  and  for  those 
improvements  of  the  methods  of  mathematical  investigation  which  have 
been  the  basis  of  every  modern  refinement  in  analytical  calculation ;  for 
all  these  additions  to  our  knowledge  and  our  powers,  we  are  indebted  to 
Archimedes.  On  a  character  so  conspicuous,  we  can  with  pleasure  dwell 
long  enough  to  attend  to  some  particulars  of  his  history,  which  are  related 
by  Plutarch  in  his  account  of  the  siege  of  Syracuse ;  omitting,  however, 
such  details  as  are  evidently  fabulous.  "Archimedes,"  says  Plutarch, 
"  armed  with  his  own  inventions  only,  made  light  of  the  splendour  of  the 
Roman  preparations,  and  of  the  glory  of  the  name  of  Marcellus.  And 
these  were  inventions  that  he  even  considered  as  of  subordinate  value,  as 
geometrical  playthings,  which  had  been  the  amusements  of  his  leisure  hours. 
It  was  king  Hiero  that  first  induced  him  to  transfer  a  portion  of  his  science 
from  intellectual  to  material  objects,  and  to  condescend  in  some  degree  to  the 
comprehension  of  the  multitude,  by  giving  a  sensible  form  to  those  truths 
which  in  their  abstract  state  are  discoverable  only  to  the  reasoning  faculty. 
Archimedes,  who  was  a  friend  and  a  relation  of  Hiero,  had  asserted  that 
any  weight  whatever  might  be  moved  by  any  given  power :  and  depending 
on  the  validity  of  his  arguments,  had  given  scope  to  his  imagination,  and 
boasted  that  if  he  had  another  earth  to  which  he  could  step  over,  he  would 
draw  the  whole  of  the  present  globe  out  of  its  place.  Hiero,  surprised  at 
the  boldness  of  his  assertion,  requested  him  to  give  some  substantial  proof 
of  its  truth,  by  moving  a  great  weight  with  a  small  power ;  upon  this 
Archimedes  procured  a  ship,  which  was  with  great  labour  drawn  up  on  the 
shore,  and  having  completely  manned  and  freighted  her,  he  seated  himself 
at  a  distance,  and  by  lightly  touching  the  first  movement  of  a  machine,  he 
drew  her  along  as  smoothly  and  as  safely  as  if  she  had  been  sailing  in  the 
deepest  water.  Hiero,  full  of  astonishment,  and  admiring  the  powers  of 
mechanical  art,  prevailed  on  Archimedes  to  construct  such  engines  both  of 
defence  and  of  offence,  as  might  be  of  use  to  him  in  case  of  a  siege  :  for 
these,  however,  Hiero,  who  lived  a  life  of  peace  and  prosperity,  was  not  so 
unfortunate  as  to  have  occasion  ;  but  they  now  became  highly  valuable  to 
the  Syracusans,  and  they  were  of  the  more  advantage,  as  their  inventor 
was  present  to  direct  their  use.  And  in  fact  the  whole  people  of  Syracuse 
constituted  but  a  part  of  Archimedes's  corporeal  machinery,  and  he  was 
the  soul  that  moved  and  governed  the  whole.  All  other  arms  were  deserted, 
and  they  employed  his  engines  alone,  both  for  their  own  defence,  and  for  the 
annoyance  of  the  enemy.  In  short  the  Romans  soon  became  so  terrified, 
that  if  they  saw  a  stick  or  a  rope  upon  the  walls,  they  cried  out  that  it  was 
some  machine  of  Archimedes,  and  immediately  fled  ;  so  that  Marcellus 
at  last  determined  to  desist  from  attempting  to  take  the  place  by  assault, 
and  resolved  to  blockade  it  only. 

"  Archimedes,  however,  had  such  depth  of  intellect,  and  such  sublimity 
of  mind,  that  notwithstanding  he  had  obtained  by  these  inventions,  the 
credit  and  glory  of  an  intelligence  rather  divine  than  human,  he  thought  it 
unworthy  of  him  to  leave  any  written  treatise  on  the  subject,  considering 


ON  THE  HISTORY  OF  MECHANICS.  185 

practical  mechanics  and  every  art  that  is  concerned  in  satisfying  the  wants 
of  life,  as  ignoble  and  sordid  ;  and  resting  all  his  hopes  of  fame  on  those 
works,  in  which  the  magnificent  and  the  elegant  are  exhibited  uncontami- 
nated  by  the  imperfections  of  the  material  world  :  works  that  are  com- 
parable to  nothing  else  that  the  mind  of  man  has  produced  ;  in  which  the 
subject  only  contends  with  the  mode  of  treating  it,  the  magnitude  and 
beauty  of  the  one  being  rivalled  by  the  accuracy  and  vigour  of  the  other. 
It  is  impossible  that  propositions  more  difficult  and  important  should  be 
deduced  from  simpler  and  purer  elements.  Some  attribute  this  excellence 
to  his  natural  genius,  others  to  his  indefatigable  application,  which  has 
given  to  every  thing  that  he  has  attempted  the  appearance  of  having  been 
performed  with  ease.  For  we  might  ourselves  search  in  vain  for  a  demon- 
stration of  his  propositions  ;  but  so  smooth  and  direct  is  the  way  by  which 
he  leads  us,  that  when  we  have  once  passed  it,  we  fancy  that  we  could 
readily  have  found  it  without  assistance.  We  may,  therefore,  easily  give 
credit  to  what  is  said  of  him,  that  being  as  it  were  fascinated  by  this 
domestic  syren  that  bore  him  company,  he  often  neglected  his  food  and 
his  clothing  ;  that  when  sometimes  brought  by  compulsion  to  the  baths,  he 
used  to  draw  his  figures  in  the  ashes  of  the  fire  places,  and  to  make  his 
calculations  upon  the  cosmetics  that  were  employed  by  the  attendants ; 
deriving,  like  a  true  votary  of  the  muses,  every  pleasure  from  an  intellec- 
tual origin.  Among  all  his  beautiful  discoveries,  he  is  said  to  have  chosen 
that  of  the  proportion  of  the  sphere  and  cylinder  for  his  sepulchral  honours  ; 
requesting  of  his  friends  that  they  would  place  on  his  tomb  a  cylinder  con- 
taining a  sphere,  and  inscribe  on  it  the  ratio  which  he  had  first  determined. 

"  By  artifice,  and  through  the  thoughtlessness  and  security  of  a  day  of 
festivity,  the  Romans  at  length  obtained  possession  of  Syracuse,  and  in  the 
pillage,  although  orders  had  been  issued  that  the  life  of  Archimedes  should 
be  spared,  he  was  killed  by  a  private  soldier.  His  death  is  variously 
related,  but  all  accounts  agree  that  Marcellus  was  deeply  concerned  for  his 
loss,  that  he  held  his  assassin  in  abhorrence,  and  conferred  distinguished 
favours  on  his  surviving  relations."  This  event  is  supposed  to  have  hap- 
pened about  212  years  before  the  birth  of  Christ ;  and  the  cultivation  of 
mechanical  philosophy,  which  had  been  continued  for  four  hundred  years 
with  increasing  success,  was  almost  wholly  interrupted  for  eighteen  cen- 
turies. 

There  lived,  however,  in  the  mean  time,  some  mathematicians  and 
mechanics  of  considerable  merit.  A  work  on  warlike  machines,  addressed 
to  Marcellus  by  Athenaeus,  is  still  extant,  and  may  be  found  in  the  splendid 
collection  of  writers  on  military  mechanics  entitled  Mathematici  Veteres. 
Ctesibius  of  Alexandria  was  about  a  century  later  than  Archimedes ;  he 
enriched  hydraulics  with  several  valuable  machines  ;  although  he  contri- 
buted little  to  the  advancement  of  theoretical  investigation.  Hero  was  of 
the  same  school,  and  his  pursuits  were  similar  ;  some  of  his  treatises  on 
hydraulics,  pneumatics,  and  mechanics,  are  published  in  the  collection  of 
Ancient  mathematicians,  and  some  others  are  still  extant  in  manuscript. 
We  are  informed  by  Pappus,  that  Hero  and  Philo  had  referred  the  proper- 
ties of  the  lever,  the  wheel  and  axis,  the  pulley,  the  wedge,  and  the  screw, 


186  LECTURE  XX. 

to  the  same  fundamental  principle  ;  so  that  the  theory  of  the  mechanical 
powers  began  at  that  time  to  be  extremely  well  understood.  The  treatises 
of  Hero  on  pneumatics  and  on  automatons  contain  many  very  ingenious 
inventions,  but  they  are  rather  calculated  for  amusement  than  for  utility  ; 
among  them  is  a  cupping  instrument,  which  operates  nearly  in  the  manner 
of  an  air  pump.  A  work  of  Bito,  on  warlike  machinery,  addressed  to 
king  Attalus,  is  included  in  the  same  collection. 

Vitruvius  was  an  author  of  great  general  knowledge  :  he  lived  under 
one  of  the  earliest  of  the  Caesars,  and  the  greatest  part  of  our  information 
respecting  the  mechanics  of  antiquity  has  been  derived  from  his  works. 
Apollodorus  was  employed  by  Trajan,  in  building  a  bridge  over  the 
Danube,  in  the  year  102  ;  he  has  left  a  treatise  on  besieging  a  town,  which 
is  to  be  found  among  the  Ancient  mathematicians.  Diophantus,  Pappus, 
and  Proclus,  were  mathematicians  of  eminence  :  Diophantus  confined  him- 
self in  great  measure  to  arithmetic  and  pure  geometry  ;  but  the  last  book 
of  Pappus's  collections  is  devoted  to  mechanics,  and  Proclus  wrote  a 
treatise  on  motion,  which  is  still  extant.*  The  rudiments  of  algebraical 
notation  and  calculation  may  be  found  in  the  works  of  Diophantus  ;  but 
the  Arabians  appear  to  have  first  practised  the  method  of  denoting  quanti- 
ties in  general  by  literal  characters  ;  they  made,  however,  no  considerable 
advances,  and  mathematics  in  general  remained  nearly  stationary  until  the 
time  of  the  revival  of  letters. 

During  the  long  interval,  in  which  learning  and  science  were  involved 
in  the  darkness  of  the  middle  ages,  the  arts  subservient  to  the  convenience 
of  life  were  also  in  great  measure  neglected.  It  is  evident  from  many 
remains  of  antiquity,  that  various  manufactures  had  attained  in  Greece 
and  at  Rome,  a  high  degree  of  perfection  ;  but  the  irruptions  of  the  bar- 
barians were  as  effectual  in  suppressing  the  refinements  of  civilisation,  as 
in  checking  the  pursuit  of  literary  acquirements :  our  own  country  was 
not  the  earliest  in  recovering  the  arts  which  had  been  lost,  but  it  has 
always  received  with  open  arms  those  who  have  excelled  in  them ; 
and  the  improvements  which  have  been  made,  within  a  few  centuries,  in 
the  British  manufactures,  have  obtained  for  them  a  celebrity  unrivalled  by 
those  of  any  other  nation.  The  ancient  Britons  are  supposed  to  have 
made,  in  common  with  the  other  Celtic  nations,  coarse  cloths  and  felts  of 
wool,  and  perhaps  some  articles  of  linen  ;  their  chariots  of  war,  wrhich  are 
mentioned  by  Caesar,  could  not  have  been  executed  without  some  skill  in 
the  arts  of  the  carpenter  and  the  smith.  The  Romans  introduced  a  certain 
degree  of  civilisation  into  England,  but  it  appears  to  have  been  in  a  great 
measure  forgotten  soon  after  they  left  the  country.  In  the  seventh  cen- 
tury, several  architects  and  workmen  were  brought  from  the  continent  by 
Wilfrid  and  Biscop ;  they  restored  the  practice  of  building  with  stone, 
which  had  been  generally  superseded  by  wood,  and  laid  the  foundation  for 
other  improvements.  In  the  time  of  king  Alfred,  the  English  goldsmiths 
began  to  excel,  and  before  the  conquest,  the  woollen  manufactures  had 
acquired  a  considerable  degree  of  perfection.  The  paper  now  in  use  w»as 
introduced  about  the  year  1100  ;  it  was  probably  imported  from  the  con- 
*  De  Motu  Disputatio,  Basileae,  1531. 


ON  THE  HISTORY  OF  MECHANICS.  187 

tinent,  since  the  linen  manufacture  was  little  advanced  in  England  till  150 
years  later ;  but  embroidery  was  much  practised,  although  in  the  12th 
century  silks  were  principally  woven  in  Sicily.  The  manufactory  of  cloth 
was  considerably  improved,  in  the  14th  century,  by  the  establishment  of 
Kempe  and  other  Flemish  weavers  in  England  :  and  many  of  the  arts 
were  benefited,  about  the  same  time,  by  the  invention  of  the  method  of 
drawing  wire,  which  was  first  introduced  at  Nuremberg.  In  the  succeed- 
ing century,  the  increasing  number  of  hands  employed  in  various  manu- 
factures, suggested  to  some  mind  of  superior  penetration  the  great  principle 
of  the  division  of  labour,  by  which  each  individual  is  enabled  to  acquire 
so  high  a  degree  of  perfection  in  a  very  limited  branch  of  each  manufac- 
ture, that  the  whole  work  is  performed  much  more  perfectly,  as  well  as 
more  expeditiously,  than  if  it  had  been  begun  and  completed  by  any  one 
person,  even  of  greater  abilities  and  experience.  The  invention  of  the 
modern  spinning  wheel  is  attributed  to  Jiirgen  of  Brunswick,  and  the  year 
1530  is  assigned  as  its  date  :  England  soon  profited  by  the  improvement ; 
many  manufacturers  took  refuge  in  this  country  from  the  Duke  of  Alva's 
persecutions  in  Flanders,  and  before  the  end  of  the  century  a  new  modifi- 
cation of  the  art  of  weaving  was  introduced  by  Lee  of  Cambridge,  who 
invented  the  stocking  loom,  imitating  the  texture  of  the  knit  stockings, 
which  were  first  manufactured  in  Spain  about  the  year  1550.  Mills  for 
drawing  wire  and  for  slitting  iron  were  also  first  erected  in  the  sixteenth 
century ;  Birmingham  and  Sheffield  were  even  at  that  time,  according  to 
Camden,  celebrated  for  their  manufactures;  and  the  machinery  which 
has  been  since  introduced  at  different  periods  in  those  places,  affords  a 
facility  and  expedition  which  astonish  every  unexperienced  spectator.  The 
names  of  Watt  and  of  Boulton  have  acquired  a  just  celebrity  from  their 
refined  improvements ;  but  many  other  mechanics  of  inferior  rank  have 
exhibited  a  degree  of  ingenuity  which  would  have  done  honour  to  the 
most  distinguished  talents.  The  manufactures  of  Manchester  are  also  of 
considerable  antiquity ;  but  they  are  very  greatly  indebted  to  the  inven- 
tions of  Ark wright  and  his  followers,  which  have  also  been  introduced  in 
many  other  parts  of  the  united  kingdom.  The  importance  of  these 
improvements  may  be  estimated  from  the  quantity  of  cotton  which  is 
annually  imported  into  Great  Britain  ;  in  1787,  it  amounted  to  23  million 
pounds,  and  gave  employment  to  420  thousand  manufacturers;  in  1791, 
it  was  increased  to  32  millions :  about  one  half  is  consumed  in  white  goods, 
one  fourth  in  fustians,  and  the  remainder  in  hosiery,  mixtures,  and  candle 
wicks.  But  the  woollen  manufactory  affords  a  subsistence  to  above  a 
million  persons,  who  receive  annually  for  their  work  about  nine  millions 
sterling,  and  employ  as  much  wool  as  is  worth  about  three.* 

In  architecture,  the  Anglonorman  style  prevailed  in  this  country  from 
the  conquest  to  the  beginning  of  the  thirteenth  century  ;  the  arch  was  fre- 
quently employed,  and  its  form  was  semicircular.  'The  Gothic  architecture, 
distinguished  by  its  pointed  arches,  which  is  said  to  have  originated  from 
thG  Saracens,  was  first  introduced  into  England  about  the  year  1170,  and 

*  See  Baines's  History  of  the  Cotton  Manufacture,  1835  ;  or  art.  Cotton  Manu- 
facture, Encyc.  Brit. 


188  LECTURE  XX. 

was  more  and  more  generally  adopted  for  about  three  centuries.  Of  the 
architects  of  this  school,  two  of  the  most  celebrated  were  William  of  Sens, 
and  Walter  of  Coventry  :  the  most  elegant  specimen  of  its  performances 
is,  perhaps,  King's  College  Chapel  at  Cambridge,  which  was  founded  by 
Henry  the  Sixth,  and  begun  in  the  year  1441.  The  Cathedral  of  Lincoln 
appears  to  have  been  one  of  the  earliest  Gothic  edifices  :  Westminster  Abbey 
was  finished  about  1285,  the  Minster  of  York  was  begun  a  few  years  after- 
wards ;  and  it  is  difficult  to  determine  which  of  these  three  buildings  most 
deserves  the  attention  of  the  antiquary  and  the  architect,  or  whether  the 
Cathedral  at  Canterbury  may  not  be  equal  to  either  of  them. 

In  the  midst  of  an  age  of  darkness,  an  insulated  individual  arrests  our 
attention  by  merits  of  no  ordinary  kind.  Roger  Bacon  was  born  at 
Ilchester,  in  the  year  1214  ;  it  is  well  known  that  his  experiments  had  led 
him  to  a  discovery  of  the  properties  of  gunpowder,  although  he  humanely 
concealed  the  nature  of  its  composition  from  the  public,  and  described  it 
only  in  an  enigma  :  the  extent  of  his  optical  knowledge  has  been  variously 
estimated,  but  it  was  unquestionably  much  greater  than  that  of  the  ancient 
philosophers.  He  appears,  however,  to  have  had  some  companions  in  his 
mechanical  pursuits ;  he  declares  that  he  had  seen  chariots  which  could 
move  with  incredible  rapidity,  without  the  help  of  animals  ;  he  describes  a 
diving  bell ;  and  he  says  that  he  had  been  informed,  on  good  authority,  that 
machines  had  been  made,  by  the  assistance  of  which  men  might  fly  through 
the  air.  Cimabue,  who  first  began  to  revive  the  long  neglected  art  of 
painting,  was  contemporary  with  Bacon.  The  use  of  oil  in  painting  is 
commonly  supposed  to  have  been  introduced  by  Van  Eyck,  but  there  are 
traces,  in  the  records  of  this  country,  of  its  employment  as  early  as  the 
year  1239.* 

The  clepsydrae  or  water  timekeepers  of  the  ancients  appear  to  have  been 
gradually  transformed,  in  the  middle  ages,  into  the  clocks  of  the  Saracens 
and  of  the  Arabians :  and  these  were  introduced  into  Europe  in  the 
thirteenth  century.  About  the  year  1290,  turret  clocks  were  erected  at 
Westminster  and  at  Canterbury.  The  first  clock,  of  which  we  know  the 
construction,  is  that  which  was  made  by  Wallingford  in  1326,  and  which 
was  regulated  by  a  fly  ;  and  the  second  that  of  Defondeur,  or  Fusorius, 
with  a  simple  balance,  made  about  1400.  But  it  appears  that  some  portable 
watches  had  been  constructed  in  the  beginning  of  the  fourteenth  century  ; 
and  about  the  year  1460,  several  clock  makers  are  said  to  have  come  to 
England  from  Flanders. 

The  art  of  engraving  on  metal,  and  of  printing  with  the  rolling  press,  is 
supposed  to  have  been  invented  in  the  year  1423.  Some  attribute  the  art 
of  printing  with  types,  to  Laurentius  Coster  of  Haerlem,t  who,  as  they 
say,  in  1430,  employed  for  the  purpose  separate  blocks  of  wood,  tied 
together  with  thread.  Gensfleisch,  one  of  his  workmen,  went  to  Mentz, 
and  was  there  assisted  by  Gutenberg,  who  invented  types  of  metal.  But 
the  best  authors  appear  to  disbelieve  this  story ;  and  Gutenberg,  in  partner- 

*  See  Lect.  XI. 

t  Ellis,  Ph.  Tr.  xxiii.  1416.  See  also  Ph.  Tr.  xxiii.  1507,  Boxhoin,  de  Origine 
Artis  Typographicae. 


ON  THE  HISTORY  OF  MECHANICS.  189 

ship  with  Fust  and  Schaeffer,  is  the  first  that  is  universally  allowed  to 
have  practised  the  art.*  It  was  introduced  into  this  country  by  William 
Caxton. 

Leonardo  da  Vinci,  the  most  accomplished  man  of  his  age,  was  born 
about  the  year  1443,  and  excelled  not  only  in  painting  and  poetry,  but 
also  in  architecture,  mathematics,  and  mechanics.  The  state  of  practical 
mechanics  in  this  and  the  subsequent  centuries  may  be  estimated  from 
Ramelli's  collection  of  machines,  which  contains  several  curious  and 
useful  inventions  ;  some  of  them  long  since  forgotten,  and  even  lately 
proposed  again  as  new. 

The  works  of  Bacon,  Lord  Verulam,  although  not  immediately  tending 
to  the  advancement  of  mathematics  or  of  mechanics,  are  universally  allowed 
to  have  conduced  very  materially  to  the  improvement  of  every  branch  of 
science,  by  the  introduction  of  a  correct  and  conclusive  method  of  philo- 
sophical argument  and  inquiry.  Guido  Ubaldi  published,  in  1577,  a 
treatise  on  mechanics,  not  wholly  exempt  from  inaccuracies,  and  in  the 
following  year  a  valuable  commentary  on  the  works  of  Archimedes  :  some 
of  the  properties  of  projectiles  were  about  the  same  time  rather  imagined 
than  demonstrated  by  Tartalea  :  Benedetti  soon  after  began  to  reason 
correctly  respecting  the  principles  of  mechanics  ;  but  it  was  reserved  for 
Galileo  to  lay  the  foundations  of  the  discoveries,  which  have  succeeded 
each  other  with  increasing  rapidity  for  more  than  two  centuries.  He 
investigated,  in  the  year  1589,  the  laws  of  accelerating  forces,  and  showed 
the  nature  of  the  curve  which  is  described  by  a  projectile  ;  he  inferred  from 
observation  the  isochronism  of  the  vibrations  of  a  pendulum,  and  the 
principle  was  soon  after  applied  by  Sanctorius  to  the  regulation  of  time- 
keepers. Stevinus,  a  Dutchman,  was  the  first  that  clearly  stated  the 
important  law  by  which  the  equilibrium  of  any  three  forces  is  determined  ; 
and  the  properties  of  the  centre  of  gravity  were  successively  investigated  by 
Lucas  Valerius,  Lafaille,  and  Guldinus,  who  made  some  additions  to 
the  elegant  propositions  of  Archimedes  which  relate  to  it.t 

The  application  of  the  more  intricate  parts  of  the  mathematics,  to  prac- 
tical purposes  of  all  kinds,  has  become  incomparably  easier  and  more 
convenient  since  the  invention  of  logarithms.  This  important  improvement 
was  made  by  Baron  Napier  ;  his  tables  were  published  in  1614 :  J  and  they 
were  reduced  to  a  still  more  useful  form  by  the  labours  of  Briggs§  and 
of  Gunter.||  Descartes,  about  the  same  time,  was  making  considerable 

*  Fischer  sur  les  Monumens  Typographiques  de  Gutenberg,  4to,  Mentz,  1802. 

f  The  authors  here  mentioned  occupy  a  prominent  position  in  the  History  of  Me- 
chanics. We  therefore  add  a  list  of  their  principal  works.  Lord  Bacon's  Works, 
a  new  edition  by  Basil  Montagu,  14  vols.  1825-31.  Guido  Ubaldi  Mechanicorum 
liber,  fol.  Pesaro.  Tartalea  Nuova  Scienza,  4to,  Venice,  1537.  Quesiti  et  Inventi 
Diversi,  1544.  Benedettus  Diversarum  Speculationum  liber,  fol.  Taurini,  1585. 
Galileo  Opera,  4  vols.  Padova,  1744.  See  Lect.  IV.  Stevinus,  Beghinselen  der 
Waagconst,  1586.  (Euvres  Mathematiques,  2  vols.  fol..  Ley  de.  1634.  Lucas  Va- 
lerius, DeCentro  Gravitate  Solidorum,  4to,  Romse,  1604.  Lafaille,  Theoremata  de 
Centre  Gravitatis,  4to,  Antwerp,  1632.  Guldinus  de  Centro  Gravitatis,  fol. 
Vienna;,  1635. 

J  Mirifici  Logarithmorum  Canonis  Descriptio,  4to,  Edinb.  1614. 

§  Arithmetica  Logarithmica,  fol.  Lond.  1624. 

||  Works,  4to,  1 680.  The  tables  of  logarithms  in  common  use  are,  Taylor's, 
Collet's,  Hutton's,  and  Babbage's. 


190  LECTURE  XX. 

additions  to  the  science  of  algebra,  and  the  mathematics  were  soon  after 
enriched  by  Cavalleri's  invention  of  the  method  of  indivisibles.  This 
method  was  founded  on  the  principles  introduced  by  Archimedes,  it  was 
further  improved  by  Wallis,  and  it  led  to  the  still  more  valuable  invention 
of  the  fluxional  analysis. 

The  laws  of  collision  were  investigated  nearly  at  the  same  time  in  England 
by  Wren  and  Wallis,  and  in  France  by  Huygens.  After  the  discoveries 
of  Archimedes  and  of  Galileo,  those  of  Huygens  hold  the  third  place,  in  the 
order  of  time,  among  the  greatest  benefits  that  have  been  conferred  on 
science.  His  theory  of  cycloidal  pendulums  and  his  doctrine  of  central 
forces  were  the  immediate  foundations  of  Newton's  improvements. 

Hooke  was  as  great  in  mechanical  practice  and  in  ingenious  contrivance, 
as  Huygens  was  in  more  philosophical  theory  ;  he  was  the  first  that  applied 
•.•  the  balance  spring  to  watches,  and  he  improved  the  mode  of  employing 
pendulums  in  clocks ;  the  quadrant,  the  telescope,  and  the  microscope, 
were  materially  indebted  to  him  ;  he  had  the  earliest  suspicions  of  the  true 
nature  of  the  cause  that  retains  the  planets  in  their  orbits  ;  and  the  multi- 
tude of  his  inventions  is  far  too  great  to  be  enumerated  in  a  brief  history  of 
the  progress  of  science. 

The  composition  of  motion,  and  several  other  mechanical  and  optical 
subjects,  are  elegantly  treated  in  the  lectures  published  by  the  learned 
Doctor  Barrow.*  He  was  professor  of  mathematics  at  Cambridge,  and 
voluntarily  resigned  his  chair  to  make  way  for  his  successor,  the  pride  of 
his  country,  and  the  ornament  of  mankind.  Sir  Isaac  Newton  t  was  born 
at  Woolsthorpe  in  Lincolnshire,  on  Christmas  day  in  1642,  the  year  of 
Galileo's  death.  At  the  age  of  12  he  was  sent  to  school  at  Grantham,  and 
at  18  to  Cambridge.  He  made  some  important  improvements  in  algebraical 
analysis,  and  laid  the  foundation  of  his  admirable  method  of  fluxions, 
before  he  was  24  years  old ;  but  his  modesty  prevented  him  from  imme- 
diately publishing  any  work  on  these  subjects.  His  first  optical  experi- 
ments were  also  made  in  the  year  1666,  and  they  were  communicated  to  the 
Royal  Society,  then  in  its  infancy,  on  his  admission  as  a  member  in  1672. 
The  theory  of  gravitation,  and  the  mechanics  of  the  universe,  are  developed 
in  his  Mathematical  Principles  of  Natural  Philosophy,  first  published  in 
1687.  The  following  year  he  was  chosen  representative  of  the  university 
of  Cambridge  in  parliament,  and  in  1696  he  was  placed,  upon  the  recom- 
mendation of  the  Earl  of  Halifax,  in  a  lucrative  situation  in  the  Mint. 
From  1703  until  his  death  in  1727,  he  continued  president  of  the  Royal 
Society,  and  enjoyed,  to  the  age  of  80,  an  uninterrupted  state  of  good 
health.  He  was  knighted  by  Queen  Anne,  in  1705,  and  died  possessed  of  a 
considerable  fortune.  "  He  had  the  singular  happiness,"  says  Mr.  Fonte- 
nelle,  "of  obtaining,  during  his  life,  all  the  credit  and  consideration  to  which 
his  sublime  researches  and  his  fortunate  discoveries  entitled  him.  All  men 
of  science,  in  a  country  which  produces  so  many,  placed  Newton,  by  a  kind 
of  acclamation,  at  their  head  ;  they  acknowledged  him  for  their  chief  and 

*  Lectiones  Mathematics  xxiii.  Lond.  1685. 

f  See  Brewster's  Life  of  Newton.  A  new  edition,  containing  many  important 
facts  hitherto  unknown,  is  anxiously  expected.  Consult  also  Tumor's  Collections 
for  the  History  of  Grantham,  4to,  Lond.  1806. 


ON  THE  HISTORY  OF  MECHANICS.  191 

J  their  master  ;  no  opponent,  nor  even  a  cool  admirer,  dared  to  appear.  His 
philosophy  was  adopted  throughout  England,  and  it  is  supported  in  the 
*  Royal  Society,  and  in  all  the  excellent  productions  of  the  members  of  that 
Society,  with  as  much  confidence,  as  if  it  had  heeii  consecrated  by  the 
respect  of  a  long  course  of  ages."  A  remarkable  instance  of  the  extent  and 
refinement  of  Newton's  mathematical  acquirements  may  be  found  in  a  paper 
of  a  celebrated  modern  mathematician,  on  the  subject  of  atmospherical 
refraction  ;  Mr.  Kramp*  observes,  with  a  mixture  of  surprise  and  doubt, 
that  Newton  appears  to  have  been  acquainted  with  those  methods  of  alge- 
braical calculation  which  he  had  himself  pursued ;  at  the  same  time  he 
says  that  this  is  almost  incredible,  since  "  he  must  have  discovered  certain 
improvements  in  the  higher  analysis  which  were  unknown  even  to  Euler, 
and  to  every  other  mathematician  before  Laplace." 

Although  Newton  was  unquestionably  the  first  inventor  of  the  method  of 
fluxions,  yet  Leibnitz,  whether  he  had  received  any  hints  of  Newton's 
ideas,  as  there  is  some  reason  to  suspect,  or  whether  his  investigations  were 
wholly  independent  of  those  of  Newton,  was  the  first  that  published  any 
work  on  the  subject ;  and  he  extended  its  application  to  many  important 
problems,  earlier,  perhaps,  than  any  English  mathematician.  James  and 
John  Bernoulli  also  pursued  the  same  studies  with  considerable  success, 
and  the  general  laws  of  mechanics  were  very  elegantly  investigated,  and 
successfully  applied  by  these  three  contemporary  philosophers  on  the  con- 
tinent, while  Machin,  Cotes,  Halley,  and  Demoivre,  were  applying  them- 
selves to  similar  pursuits  in  this  country.  Perrault,  Lahire,  Amontons, 
and  Parent,  members  of  the  Parisian  academy  of  sciences,  were  the  authors 
of  many  useful  investigations  relating  to  practical  mechanics  ;  but  few  of 
them  were  made  public  till  after  the  year  1700 ;  some  of  their  inventions 
made  their  appearance  much  later,  in  the  valuable  collection  of  machines 
approved  by  the  academy,  and  some  of  them  have  been  inserted  in  the 
useful  work  published  by  Leupold,  at  Leipzig,  under  the  title  of  a  Theatrum 
Machinarum.  Throughout  the  last  century,  the  transactions  of  various 
societies,  established  for  the  promotion  of  science,  became  every  year  more 
numerous,  and  the  publication  of  the  literary  journals  of  Leipzig  and  of 
Paris  formed  a  mode  of  communication  which  was  extremely  serviceable 
in  facilitating  the  dissemination  of  all  new  discoveries. 

The  philosophy  of  Newton  assumed  also  a  more  popular  and  attractive 
form  in  the  writings  of  Clarke,t  Pemberton,^  Maclaurin,  §  and  Musschen- 
broek,  ||  and  the  lectures  of  S'Gravesande  and  Desaguliers;  at  the  same 
time  that  its  more  refined  investigations  were  pursued  with  success  in  this 
country  by  Maclaurin  and  Simpson,  and  on  the  continent  by  Hermann, 
Daniel  Bernoulli,  Leonard  Euler,  and  Clairaut.  Maclaurin,  Bernoulli, 
and  Euler,  had  the  honour  of  sharing  with  each  other  the  prize,  proposed 
by  the  academy  of  sciences  at  Paris,  for  the  best  essay  on  the  intricate 
subject  of  the  tides;  but  a  premature  death  prevented  Maclaurin  from 

*  Hindenburgs  Archiv.  ii.  380,  499. 

•  f  Demonstration  of  some  Sections  of  Newton's  Prin.  1730. 
t  View  of  Sir  I.  Newton's  Ph.  4to,  1728. 

§  Account  of  Sir  I.  Newton's  Philosophical  Discoveries,  4to,  Lond.  1748. 
||   Introductio  ad  Phil.  Nat.  2  vols.  Leyd.  1762. 


192  LECTURE  XX. 

long  pursuing  the  career  which  he  began  so  successfully.  Bernoulli  and 
Euler  continued  for  many  years  to  vie  with  each  other  for  the  elegance 
and  extent  of  their  researches  :  Euler  appears  to  have  been  the  more  pro- 
found mathematician,  and  Bernoulli  the  more  accurate  philosopher. 

The  latter  half  of  the  eighteenth  century  was  in  many  respects  extremely 
auspicious  to  the  progress  of  the  sciences ;  the  names  of  Dalembert,  Landen, 
Waring,  Frisi,  *  Robison,  Lagrange,  and  Laplace,  deserve  to  be  enumerated 
in  the  first  class  of  mathematicians  and  theoretical  mechanics ;  those  of 
Smeaton,  Wedgwood,  and  Watt  are  no  less  distinguished  for  their  success 
in  improving  the  practice  of  the  useful  arts  and  manufactures.  The  union 
of  all  these  objects,  into  one  system  of  knowledge,  was  effected,  on  a  mag- 
nificent scale,  in  the  Encyclopedic,  a  work  which  does  as  much  honour  to 
the  labour  and  genius  of  some  of  its  authors,  as  it  reflects  disgrace  on  the 
principles  and  politics  of  others.  The  Society  for  the  encouragement  of 
arts,  manufactures,  and  commerce,  was  established  in  London  about  the 
same  time  that  the  Encyclopedic  began  to  appear  at  Paris,  and  its  pre- 
miums and  publications  have,  without  doubt,  excited  a  degree  of  attention  to 
the  subjects  of  practical  mechanics,  and  agricultural,  as  well  as  commercial 
improvements,  which  must  have  been  beneficial  both  to  individuals  and  to 
the  public.  The  academy  of  Paris  began  to  print,  in  1762,  a  collection  of 
the  descriptions  of  arts  and  trades  of  all  kinds,  on  a  still  more  extended 
scale  than  had  been  attempted  in  the  Encyclopedic  ;  the  work  was  carried 
to  a  very  considerable  length,  but  it  by  no  means  comprehends  all  the 
articles  which  were  intended  to  compose  it. 

The  construction  of  watches  has  been  so  much  improved  by  the  artists 
both  of  this  country  and  of  France,  that  they  have  been  rendered  capable 
of  affording  very  essential  service  to  navigation,  especially  since  the  astro- 
nomical methods  of  determining  a  ship's  place  have  been  brought  to  such 
a  degree  of  perfection,  as  greatly  to  facilitate  the  frequent  correction  of 
the  accidental  errors  of  the  timekeeper.  The  first  artist  that  constructed 
watches,  sufficiently  accurate  for  the  determination  of  the  longitude,  was 
William  Harrison,  who  was  indebted  to  himself  alone  for  his  education 
and  his  inventions  ;  in  1765  he  received  for  his  labours,  from  the  Board  of 
Longitude,  the  promised  reward  of  ten  thousand  pounds. 

There  has  scarcely  been  a  period,  in  any  age  of  the  world,  in  which  the 
sciences  and  literature  in  general,  have  been  so  rapidly  promoted  and  so 
universally  disseminated,  as  within  the  last  forty  years.  This  advance- 
ment has  partly  been  the  cause,  and  partly  the  effect,  of  the  great  multi- 
plication of  scientic  journals,  cyclopaedias,  and  encyclopaedias,  which  have 
been  annually  increasing  since  the  beginning  of  the  Journal  de  Physique  in 
1773  ;  supported  by  the  interest  which  they  have  derived,  in  great  measure, 
from  the  new  and  amusing  discoveries  and  improvements  which  have  been 
made  in  chemistry  and  natural  history  :  some  of  the  most  copious  of  these 
works  have  had  a  sale  unprecedented  even  for  books  of  more  moderate 
extent. 

The  charter  of  the  Royal  Institution  is  dated  in  1799 ;  its  foundation 
will  not  perhaps  make  an  era  in  the  history  of  the  refinements  of  science  ; 

*  Pauli  Frisii  Opera,  3  vols.  4to,  Mediolani,  1782-5. 


ON  THE  HISTORY  OF  MECHANICS.  193 

but  if  it  be  hereafter  found  to  have  given  notoriety  to  what  is  useful,  and 
popularity  to  what  is  elegant,  the  purposes  of  those  who  established  it  will 
not  have  been  frustrated. 

After  all  that  has  been  effected  by  the  united  labours  and  talents  of  the 
philosophers  who  have  been  mentioned,  and  of  many  more,  who,  though 
less  fortunate,  have  yet  been  highly  meritorious,  there  is  still  ample  oppor- 
tunity for  the  employment  of  genius  and  industry  in  following  their  steps. 
To  suppose  that  little  or  nothing  remains  to  be  done,  betrays  a  want  either 
of  knowledge,  or  of  courage.  The  experimental  researches  of  some  of  the 
greatest  philosophers  have  been  very  imperfectly  conducted,  and  the  most 
interesting  results  may  be  expected  from  repeating  and  diversifying  them. 
Whatever  advances  our  neighbours  may  have  made  beyond  us,  in  intricate 
calculations  and  combinations,  we  are  still  able  to  vie  with  them,  and  shall 
probably  long  remain  so,  in  the  accuracy  of  our  instruments,  and  in  the 
art  of  using  them  with  precaution  and  with  success. 

When,  however,  we  contemplate  the  astonishing  magnitude  to  which  a 
collection  of  books  in  any  department  of  science  may  even  at  present  be 
extended,  and  the  miscellaneous  nature  of  the  works  in  which  many  of  the 
most  valuable  disquisitions  have  been  communicated  to  the  public,  together 
with  the  natural  disposition  to  indolence,  which  a  high  degree  of  civilisa- 
tion too  frequently  encourages,  there  is  the  greatest  reason  to  apprehend, 
that  from  the  continual  multiplication  of  new  essays,  which  are  merely 
repetitions  of  others  that  have  been  forgotten,  the  sciences  will  shortly  be 
overwhelmed  by  their  own  unwieldy  bulk,  that  the  pile  will  begin  to  totter 
under  its  own  weight,  and  that  all  the  additional  matter  that  we  heap  on 
it,  will  only  tend  to  add  to  the  extent  of  the  basis,  without  increasing  the 
elevation  and  dignity  of  the  fabric.  Having  been  impressed,  from  con- 
tinued experience,  with  the  truth  of  this  observation,  I  have  employed  no 
small  portion  of  time  and  labour,  in  order  to  obtain  an  effectual  remedy 
for  the  evil ;  and  I  trust  that,  in  future,  every  one  who  is  desirous  of  en- 
larging the  sphere  of  our  knowledge,  with  respect  to  any  branch  of  science, 
connected  with  the  subject  of  these  Lectures,  will  find  it  easy,  by  consult- 
ing the  authors  who  will  be  quoted  in  my  catalogue  of  references,  to  collect 
that  previous  knowledge  of  all  that  has  been  already  done  with  the  same 
view,  which,  in  justice  to  himself,  he  ought  to  acquire  before  he  enters  on 
the  pursuit,  or  at  any  rate,  in  justice  to  the  public,  before  he  calls  on  the 
world  at  large  to  participate  in  his  improvements  and  discoveries. 


LECT.  XX.— ADDITIONAL  AUTHORITIES. 

History  of  Mechanics. — P.  Vergilius,  De  Inventpribus  rerum,  Basle,  1521. 
Sprat's  History  of  the  Royal  Society,  4to,  Lond.  1667.x  Histoire  des  Ouvrages  des 
Savans.  Journal  des  Savans,  Sep.  1688.  Harris,  Lexicon  Technicum,  3  vols.  fol. 
1704,  &c.  Pancirollus,  History  of  Memorable  Things,  3  vols.  12mo,  1715.  Reg- 
nault,  Origine  Ancienne  de  la  Physique  Nouvelle,  3  vols.  Amst.  1735.  Goguet, 
Origine  des  Lois,  des  Arts,  et  des  Sciences,  3  vols.  4to,  1755.  Mattaire,  Mar- 

(chand,  Bowyer,  Ames,  Lemoine,  and  Lucombe,  on  the  History  of  Printing.  Birch's 
History  of  the  Royal  Society,  4  vols.  4to,  1756.  Rollin's  History  of  the  Arts  and 
Sciences  of  the  Ancients,  3  vols.  1768.  Priestley's  Chart  of  Biography.  Diction- 


194  LECTURE  XX. 

naire  des  Origines  des  Inventions  Utiles,  6  vols.  12mo.  Par.  1777.  Brugmans  on 
the  Mechanics  of  the  Ancients,  Comm.  Gott.  1784,  vii.  M.  75.  Mongez  on  Ancient 
Coining.  Roz.  Journal  de  Physique,  xl.  426.  Dutens  on  the  Origin  of  Discoveries, 
4to.  Delambre,  Rapport  Historique  sur  les  Progres  des  Sciences  Mathematiques 
depuis  1789.  Beckmann's  Hist,  of  Inventions  (translated  by  Johnstone),  4  vols. 
1797.  Poppe,  Geschichte  der  Uhrmackerkunst,  1801.  Montucla  and  Lalande, 
Histoire  des  Mathematiques,  4  vols.  4to,  Paris,  1802.  Bossut's  History  of  Mathe- 
matics, translated  by  Bonnycastle,  Lond.  1803.  Libes,  Histoire  des  Progres  de  la 
Physique,  4  vols.  1810.  Hutton's  Mathematical  and  Philosophical  Dictionary, 
2  vols.  4to,  1815.  Powell's  History  of  the  Physical  and  Mathematical  Sciences 
(Cab.  Cyc.),  1834.  Whewell's  History  of  the  Inductive  Sciences,  3  vols.  Lond. 
1837. 


T  0 


CHRONOLOGY    OF    MATHEM 


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N. 

[To  face  page  1Q40 


PART     II. 


LECTURE    XXI. 


ON  HYDROSTATICS. 

THE  mechanical  properties  and  affections  of  fluids,  and  the  laws, and 
phenomena  of  their  motions,  are  to  be  the  subjects  of  the  second  division 
of  this  Course  of  Lectures.  Although  these  properties  are  in  reality 
derived  from  the  same  fundamental  principles  as  the  doctrines  of  pure 
mechanics,  they  are  yet  in  great  measure  incapable  of  being  referred,  in  a 
demonstrative  and  accurate  manner,  to  the  operation  of  simple  and  general 
causes.  We  are  therefore  frequently  under  the  necessity  of  calling  in  the 
assistance  of  experimental  determinations ;  and  for  this  reason,  as  well  as 
others,  the  science  of  hydrodynamics  may  with  propriety  hold  a  middle 
rank,  between  mathematical  mechanics  and  descriptive  physics.  In  treat- 
ing of  the  mechanics  of  solid  bodies,  we  are  able  to  begin  with  axioms  or 
self-evident  truths,  almost  inseparable  from  the  constitution  of  the  human 
mind  ;  to  deduce  from  them  the  general  laws  of  motion,  and  to  apply  these 
laws,  with  little  chance  of  error,  to  every  combination  of  circumstances  in 
which  we  have  occasion  to  examine  their  consequences ;  and  it  requires 
only  a  certain  degree  of  attention  and  of  mathematical  knowledge,  to  be 
perfectly  convinced  of  the  justice  of  all  our  conclusions,  without  any 
reference  to  experimental  proof.  But  here  our  abstract  reasonings  begin  to 
fail ;  and  whether  from  the  imperfection  of  our  modes  of  considering  the 
mechanical  actions  of  the  particles  of  fluids  on  each  other,  or  from  the 
deficiencies  of  our  analytical  calculations,  or,  as  there  is  more  reason  to 
suppose,  from  a  combination  of  both  these  causes,  all  attempts  to  reduce 
the  affections  of  fluids  to  a  perfect  mechanical  theory  have  been  hitherto 
unsuccessful.  At  the  same  time  it  will  appear,  that  by  a  proper  mixture 
of  calculation  with  experiment,  we  may  obtain  sufficient  foundations  for 
all  such  determinations  as  are  likely  to  be  of  any  practical  utility. 

The  whole  of  the  subjects,  which  will  be  classed  under  the  denomination 
Hydrodynamics,  may  be  divided  into  three  general  heads  ;  Hydraulics, 
Aoustics,  and  Optics ;  terms  which  are  sufficiently  understood,  as  relating 
to  the  common  properties  of  fluids,  to  sound,  and  to  light ;  but  which  do 
not  allow  of  a  very  strict  definition,  without  a  still  further  division.  The 

o2 


196  LECTURE  XXI. 

first  subdivision  which  we  shall  consider,  will  relate  to  the  laws  of  the 
equilibrium  of  fluids,  or  of  the  opposition  of  forces  acting  on  them  without  | 
producing  actual  motion,  comprehending  hydrostatics,  or  the  doctrine  of  ' 
the  equilibrium  of  liquids,  either  within  themselves  or  with  moveable  bodies  ; 
and  pneumatostatics,  or  the  equilibrium  of  elastic  fluids.  The  actual 
motions  of  fluids  will  be  considered  in  the  second  subdivision  :  and  the 
third  will  relate  to  the  instruments  and  machines  in  which  the  principles 
of  hydrostatics,  hydraulics,  and  pneumatics,  are  applied  to  the  purposes  of 
the  arts  or  of  domestic  convenience.  The  science  of  hydraulics  must  be 
allowed  to  be  of  as  great  importance  to  civil  life,  and  especially  to  a  mari- 
time nation,  as  any  department  of  practical  mechanics.  Let  us  only  reflect 
for  a  moment  to  what  the  metropolis  of  England  would  be  reduced,  if 
deprived  of  pipes  for  the  conveyance  of  water,  of  pumps,  and  of  fire 
engines  ;  and  how  much  the  commerce  of  the  whole  kingdom  has  been 
facilitated  by  the  formation  of  navigable  canals,  and  we  shall  soon  be  con- 
vinced of  the  obligations  that  we  owe  to  the  art  of  modifying  the  motion 
of  water,  and  to  the  principles  of  hydraulics  on  which  that  art  depends. 

The  facts  concerned  in  acustics  and  harmonics,  or  the  doctrine  of  sound 
and  the  science  of  music,  are  not  exclusively  dependent  on  the  characteristic 
properties  of  fluids.  In  these  departments,  although  we  can  by  no  means 
explain  with  precision  the  manner  in  which  every  appearance  is  produced, 
we  shall  still  find  a  variety  of  very  beautiful  phenomena,  which  have 
indeed  been  too  generally  neglected,  and  supposed  to  be  of  the  most 
abstruse  and  unintelligible  nature  ;  but  which,  when  carefully  examined, 
will  appear  to  be  much  more  within  the  reach  of  calculation,  than  the 
simplest  doctrines  of  hydraulics.  We  may  also  apply  some  of  these 
phenomena  to  a  very  complete  explanation  of  an  extensive  class  of  facts 
in  optics,  which,  in  whatever  other  way  they  are  considered,  are  inextri- 
cably obscure.  Whether  this  explanation  may  or  may  not  be  admitted  as 
satisfactory,  it  deserves  at  least  a  fair  examination;  it  would,  therefore, 
be  impossible  to  assign  to  the  science  of  optics  an  earlier  place  in  the  order 
of  the  system,  even  if  we  agree  with  those  who  imagine  that  all  the  pheno- 
mena of  light  depend  on  causes  wholly  deducible  from  the  mechanics  of 
solid  bodies. 

We  must  commence  the  subject  of  hydrostatics,  or  the  doctrine  of  the 
equilibrium  of  liquids,  with  a  definition  of  the  essential  characteristics  of  a 
fluid  substance.  The  most  eligible  definition  appears  to  be,  that  a  fluid  is 
a  collection  of  material  particles,  which  may  be  considered  as  infinitely 
small,  and  as  moving  freely  on  each  other  in  every  direction,  without 
friction.  Some  have  defined  a  fluid  as  a  substance  which  communicates 
pressure  equally  in  all  directions  ;  but  this  appears  to  be  a  description  of  a 
property  derivable  from  the  former  assumption,  which  is  certainly  more 
simple  ;  and  although  it  may  be  somewhat  difficult  to  deduce  it  mathe- 
matically, in  a  manner  strictly  demonstrative,  yet  we  may  obtain  from 
mathematical  considerations  a  sufficient  conviction  of  its  truth,  without 
assuming  it  as  a  fundamental  or  axiomatic  character.*  A  fluid  which  has 

*  See  Miller's  Hydrostatics,  Camb.  1831.  Challis's  Report  on  Hydrostatics  and 
Hydrodynamics,  Brit.  Assoc.  1833,  p.  134. 


ON  HYDROSTATICS.  197 

no  immediate  tendency  to  expand  when  at  liberty,  is  commonly  considered 
as  a  liquid  :  thus  water,  oil,  and  mercury,  are  liquids  ;  air  and  steam  are 
fluids,  but  not  liquids. 

We  shall  for  the  present  consider  a  liquid  as  without  either  compressi- 
bility or  expansibility :  and  we  must  neglect  some  other  physical  properties 
essential  to  liquids,  such  as  cohesion  and  capillary  attraction  ;  although  in 
reality  the  partigles  of  liquids  are  found,  by  very  nice  experiments,  to  be 
subject  to  the  same  laws  of  elasticity  which  we  have  already  examined  with 
regard  to  solids,  and  are  possessed  also  of  cohesive  powers,  which  essentially 
distinguish  them  from  elastic  fluids,  and  which  resist  any  force  tending 
directly  to  separate  the  particles  from  each  other,  while  they  admit  any 
lateral  motion  with  perfect  facility.  In  treating  of  hydrostatics,  therefore, 
we  suppose  the  fluids  concerned  to  be  of  uniform  density  throughout ;  and 
as  far  as  elastic  fluids  agree  with  this  description,  they  are  subject  to  the 
same  laws  with  liquids ;  on  the  other  hand,  all  fluids,  as  far  as  they  are 
compressible,  possess  properties  similar  to  those  which  will  hereafter  be  ex- 
amined, when  we  investigate  the  subject  of  pneumatic  equilibrium. 

The  first  law  of  hydrostatics  which  arrests  our  attention,  is  this,  that  the 
surface  of  every  homogeneous  gravitating  fluid  when  at  rest,  is  horizontal. 
If  any  part  of  the  surface  were  inclined  to  the  horizon,  the  superficial  par- 
ticles would  necessarily  tend  towards  its  lowest  part,  in  the  same  manner 
as  if  they  moved  without  friction  on  the  inclined  surface  of  a  solid.  And 
if  any  two  portions  of  the  surface  of  the  fluid  are  separated,  as  in  two 
branches  of  a  tube  or  pipe,  however  they  may  be  situated,  the  fluid  cannot 
remain  at  rest  unless  the  surfaces  be  in  the  same  level  plane  :  for  if  we 
imagine  such  a  tube,  containing  water,  to  be  made  of  ice,  and  to  be 
immersed  in  a  large  reservoir  of  water,  and  then  thawed,  the  water  will 
make  a  part  of  the  general  contents  of  the  reservoir,  and  consequently  will 
remain  at  rest,  if  its  surfaces  are  level  with  that  of  the  reservoir  :  and  it  is 
obvious  that  the  tube  has  acquired  no  new  power  of  supporting  it  from 
being  thawed  ;  consequently,  the  water  would  have  remained  in  equili- 
brium at  the  same  height  in  the  original  state  of  the  solid  tube.  The 
experimental  proof  of  this  proposition  is  easy  and  obvious,  and  the  property 
affords  one  of  the  most  usual  modes  of  determining  a  horizontal  surface. 
But  when  we  compare  the  heights  of  fluids  occupying  tubes  of  different 
magnitudes,  it  is  necessary,  if  the  tubes  are  small,  to  apply  a  slight  cor- 
rection on  account  of  the  actions  of  the  tubes  on  the  fluids  which  they  con- 
tain, which  are  more  apparent  as  their  diameters  are  smaller.  The  same 
cause  produces  also  a  curvature  in  each  separate  surface,  which  is  always 
visible  at  the  point  of  contact  with  the  tube  or  vessel.  (Plate  XIX.  Fig. 
239.) 

If  several  separate  fluids  of  different  kinds  be  contained  in  the  same 
vessel,  they  will  never  remain  at  rest  unless  all  the  surfaces  intervening 
between  them  be  horizontal ;  and  this  is  in  fact  the  state  of  the  surface  of 
common  liquids,  which  is  exposed  to  the  pressure  of  the  atmosphere. 

The  power  of  gravitation,  strictly  speaking,  does  not  act  precisely  in 
parallel  lines,  so  that  the  surface  of  lakes,  instead  of  being  perfectly  plane, 
becomes,  like  that  of  the  earth,  a  little  convex.  It  is  obvious  that  the  sur- 


198  LECTURE  XXI. 

face  of  a  fluid  must  always  be  perpendicular  to  the  direction  of  the  joint  t 
results  of  all  the  forces  which  act  on  it ;  and  since  the  earth  turns  round 
on  its  axis,  the  centrifugal  force  resulting  from  its  motion  is  combined  with 
that  of  gravity,  in  determining  the  position  of  the  general  surface  of  the 
ocean. 

A  similar  combination  of  a  centrifugal  force  with  gravitation  may  be 
observed  when  a  bucket  is  suspended  by  a  rope,  and  caused  to  turn  round 
on  its  axis  by  twisting  the  rope  :  the  direction  of  the  joint  forces  is  such 
that  the  surface,  in  order  to  be  perpendicular  to  it,  must  assume  a  parabolic 
form.  When  also  any  number  of  different  fluids  are  made  to  revolve  in 
the  same  manner,  or  when  they  are  inclosed  in  a  glass  globe  and  turned  by 
means  of  the  whirling  table,  the  surfaces  which  separate  them,  acquire 
always  the  forms  of  parabolic  conoids,  when  the  axis  remains  in  a  vertical 
position  ;  but  if  the  axis  be  in  any  other  position,  the  situation  of  the  sur- 
face will  be  of  more  difficult  determination.  (Plate  XIX.  Fig.  240.) 

In  all  these  cases  the  equilibrium  is  stable  ;  for  if  any  part  of  the  fluid 
be  raised  above  the  surface,  it  will  immediately  tend  to  return  to  its  level. 
But  if  a  heavier  fluid  were  contained  in  a  bent  tube  or  siphon,  with  its 
legs  or  branches  opening  downwards,  and  immersed  in  a  lighter  fluid,  the 
equilibrium  would  be  tottering,  since,  if  it  were  once  disturbed,  it  would 
never  be  restored.  (Plate  XIX.  Fig.  241.) 

From  these  principles,  we  may  infer  that  the  pressure  of  a  fluid  on  every 
particle  of  the  vessel  containing  it,  or  of  any  other  surface,  real  or  im- 
aginary, in  contact  with  it,  is  equal  to  the  weight  of  a  column  of  the  fluid 
of  which  the  base  is  equal  to  that  particle,  and  the  height  to  its  depth  below 
the  surface  of  the  fluid.  Thus  if  we  have  a  vessel  of  water  one  foot  deep, 
each  square  foot  of  the  bottom  will  sustain  the  pressure  of  a  cubic  foot  of 
water,  or  nearly  1000  ounces  :  if  we  have  a  vessel  of  mercury  an  inch  in 
depth,  each  square  foot  will  sustain  a  pressure  of  one  twelth  part  of  a  cubic 
foot  of  mercury,  or  1130  ounces ;  the  atmosphere  presses  on  each  square 
foot  of  the  earth's  surface  with  a  force  of  about  34,000  ounces,  which  is 
equivalent  to  the  pressure  of  a  column  of  mercury  30  inches  high.  The 
pressure  of  the  water  on  a  small  portion  of  the  lowest  part  of  the  side  of  the 
vessel  containing  it,  is  also  equal  to  the  weight  supported  by  an  equal  por- 
tion of  the  bottom  ;  but  we  cannot  estimate  the  force  sustained  by  any 
large  portion  of  the  side,  without  considering  the  different  depths  below  the 
surface  at  which  its  different  parts  are  situated. 

It  is  obvious  that  if  we  conceive  a  fluid  to  be  divided  by  an  imaginary 
surface  of  any  kind,  the  particles  contiguous  to  it  are  urged  on  either  side 
by  equal  forces,  the  fluid  below  resisting  them,  and  pressing  them  upwards 
with  as  much  force  as  the  fluid  above  presses  them  downwards,  their  own 
weight  being  comparatively  inconsiderable,  for  without  this  equality  of 
pressures  they  could  not  possibly  remain  at  rest.  And  if  we  employ  a 
vessel  of  such  a  form  as  to  occupy  the  place  of  any  superior  portion  of  the 
fluid,  the  pressure  against  that  part  of  the  vessel  which  is  thus  substituted 
will  be  the  same  that  before  supported  the  weight  of  the  fluid  removed  ; 
and  in  order  that  all  may  remain  in  equilibrium,  the  vessel  must  itself 
exert  an  equal  pressure  on  the  fluid  below  it ;  so  that  the  pressure  on  the 


ON  HYDROSTATICS.  199 

bottom  will  be  the  same  as  if  the  vessel  had  remained  in  its  original  state, 
'and  were  filled  to  the  same  height  with  the  fluid.  (Plate  XIX.  Fig.  242.) 

In  order  to  understand  this  the  more  readily,  we  may  suppose  the  portion 
of  the  fluid,  instead  of  being  removed,  to  have  been  congealed  into  a  solid  mass 
of  equal  density ;  it  is  obvious  that  this  congelation  of  the  fluid  would  not 
have  altered  the  quantity  of  its  pressure ;  it  would,  therefore,  have  re- 
mained in  equilibrium  with  the  water  below ;  the  mass  might  also  be 
united  with  the  sides  of  the  vessel,  so  as  to  form  a  part  of  it,  without  in- 
creasing or  diminishing  any  of  the  pressures  concerned :  and  we  should 
thus  obtain  a  vessel  similar  to  that  which  was  the  subject  of  our  investi- 
gation, the  pressure  on  the  bottom  being  always  the  same  as  if  the  mass, 
supposed  to  be  congealed,  had  remained  fluid.  Thus,  the  pressure  on  the 
base  of  a  conical  or  pyramidical  vessel,  full  of  water,  is  three  times  as 
great  as  the  weight  of  the  water,  since  its  content  is  one  third  of  that  of  a 
column  of  the  same  height,  and  standing  on  the  same  base.  (Plate  XIX. 
Fig.  243.) 

In  this  manner  the  smallest  given  quantity  of  any  fluid  contained  in  a 
pipe  may  be  made  to  produce  a  pressure  equivalent  to  any  given  weight, 
however  large,  which  rests  on  the  cover  of  a  close  vessel  communicating 
with  the  pipe,  and  this  may  be  done  either  by  diminishing  the  diameter  of 
the  pipe,  and  increasing  its  height,  while  the  weight  is  supported  by  a  sur- 
face of  a  certain  extent,  or  by  increasing  the  magnitude  of  this  surface, 
without  adding  to  the  height  of  the  pipe  ;  for  in  either  case  the  ultimate 
force  of  the  fluid,  in  supporting  the  weight,  will  be  equal  to  the  weight  of 
a  column  of  the  same  height,  standing  on  the  whole  surface  which  is  sub- 
jected to  its  action.  And  if  the  effect  of  the  column  be  increased  by  any 
additional  pressure,  independent  of  its  weight,  that  pressure  may  be 
represented  by  supposing  the  height  of  the  column  to  be  augmented ;  and 
the  effect  of  the  additional  pressure  will  also  be  increased  in  proportion  to 
the  magnitude  of  the  surface  which  supports  the  weight.  It  is  on  this 
principle  that  the  pressure  of  water  has  been  applied  by  Mr.  Bramah  to 
the  construction  of  a  very  convenient  press.*  (Plate  XIX.  Fig.  244.) 

Although  this  property  of  fluids  is  the  cause  of  some  results  which  would 
scarcely  be  expected  by  a  person  not  accustomed  to  reflect  on  the  subject, 
and  has,  therefore,  not  improperly,  been  called  the  hydrostatic  paradox, 
yet  it  depends  wholly  on  the  general  and  acknowledged  principles  of 
mechanical  forces  ;  nor  can  we  agree  with  those  authors,  who  have  asserted 
that  a  very  small  quantity  of  a  fluid  may,  "  without  acting  at  any  mechani- 
cal advantage  "  whatever,  be  made  to  balance  a  weight  of  any  assignable 
magnitude  :  for  the  immediate  operation  of  the  force  very  much  resembles, 
in  the  most  common  cases,  the  effect  of  a  wedge,  or  of  a  moveable  inclined 
plane ;  thus,  a  wedge  remains  in  equilibrium,  when  the  forces  acting  on 
each  side  are  in  proportion  to  its  length,  like  the  hydrostatic  pressure  on  a 
vessel  of  a  similar  form.  The  conditions  of  the  equilibrium  of  fluids  may 
also  be  determined,  in  all  cases,  from  the  general  law  of  the  descent  of  the 
centre  of  gravity  to  the  lowest  point.  Thus,  it  is  easy  to  show  that  even 
when  two  branches  of  a  tube  are  of  unequal  diameter,  a  fluid  must  stand  at 
*  He  obtained  a  patent  for  this  press  in  1796. 


200  LECTURE  XXI. 

the  same  height  in  both  of  them,  in  order  to  remain  in  equilibrium  :  for  if 
any  portion  be  supposed  to  stand,  in  either  leg,  above  the  surface  of  the 
fluid  in  the  other  leg,  it  is  obvious  that  its  centre  of  gravity  may  be  lowered, 
by  removing  so  much  of  it  as  will  raise  the  fluid  in  the  opposite  leg  to  its 
own  level,  the  situation  of  the  fluid  below  remaining  unaltered  ;  conse- 
quently the  centre  of  gravity  of  the  whole  fluid  can  never  acquire  its  lowest 
situation,  unless  both  the  surfaces  are  in  the  same  level. 

The  air,  and  all  other  elastic  fluids,  are  equally  subject  with  liquids  to 
this  general  law.  Thus,  a  much  greater  force  is  required,  in  order  to 
produce  a  blast  of  a  given  intensity  with  a  large  pair  of  bellows,  than  with 
a  smaller  pair ;  and  for  the  same  reason,  it  is  much  easier  to  a  glassblower, 
when  he  uses  a  blowpipe,  to  employ  the  muscles  of  his  mouth  and  lips, 
than  those  of  his  chest,  although  these  are  much  more  powerful.  If  we 
estimate  the  section  of  the  chest  at  a  foot  square,  it  will  require  a  force  of 
seventy  pounds  to  raise  a  column  of  mercury  an  inch  high,  by  means  of  the 
muscles  of  respiration,  but  the  section  of  the  mouth  is  scarcely  more  than 
eight  or  nine  square  inches,  and  a  pressure  of  the  same  intensity  may  here 
be  produced  by  a  force  of  about  four  pounds.  The  glassblower  obtains, 
besides,  the  advantage  of  being  able  to  continue  to  breathe  during  the 
operation,  the  communication  of  the  chest  with  the  nostrils  remaining 
open,  while  the  root  of  the  tongue  is  pressed  against  the  palate. 

It  is  obvious  that  the  pressure  on  each  square  inch  of  the  side  of  a  vessel, 
or  on  each  square  foot  of  the  bank  of  a  river,  continually  increases  in 
descending  towards  the  bottom.  If  we  wish  to  know  the  sum  of  the 
pressures  on  all  the  parts  of  the  side  or  bank,  we  must  take  some  mean 
depth  by  which  we  can  estimate  it ;  and  this  must  be  the  depth  of  the 
point  which  would  be  the  centre  of  gravity  of  the  surface,  if  it  were 
possessed  of  weight.  Thus,  if  we  had  a  hollow  cube  filled  with  water,  the 
centre  of  gravity  of  each  side  being  in  its  middle  point,  the  pressure  on 
each  of  the  upright  sides  would  be  half  as  great  as  the  pressure  on  the 
bottom,  that  is,  it  would  be  equal  to  half  the  weight  of  the  water  contained 
in  the  cube. 

If,  however,  we  wished  to  support  the  side  of  the  cube  externally  by  a 
force  applied  at  a  single  point,  that  point  must  be  at  the  distance  of  one 
third  of  the  height  only  from  the  bottom.  For  the  pressure  at  each  point 
may  be  represented  by  aline  equal  in  length  to  its  depth  below  the  surface, 
and  a  series  of  such  lines  may  be  supposed  to  constitute  a  triangle,  of 
which  the  centre  of  gravity  will  indicate  the  place  of  the  centre  of  pressure 
of  the  surface  ;  and  the  height  of  the  centre  of  gravity  will  always  be  one 
third  of  that  of  the  triangle.  It  is  easily  inferred,  from  this  representation, 
that  the  whole  pressure  on  the  side  of  a  vessel,  or  on  a  bank,  of  a  given 
length,  is  proportional  to  the  square  of  the  depth  below  the  water  to  which 
it  extends.  (Plate  XIX.  Fig.  245.) 

The  magnitude  of  the  whole  pressure  on  a  concave  or  convex  surface 
may  also  be  determined  by  the  position  of  its  centre  of  gravity  ;  but  such 
a  determination  is  of  no  practical  utility,  since  the  portions  of  the  forcbs 
which  act  in  different  directions  must  always  destroy  each  other.  Thus 
the  perpendicular  pressure  on  the  whole  internal  surface  of  a  sphere  filled 


ON  HYDROSTATICS.  201 

with  a  fluid,  is  three  times  as  great  as  the  weight  of  the  fluid  ;  but  the 
force  tending  to  burst  the  sphere,  in  the  circumference  of  any  vertical 
circle,  is  only  three  fourths  of  that  weight. 

If  two  fluids  are  of  different  specific  gravities,  that  is,  if  equal  bulks  of 
them  have  different  weights,  their  opposite  pressures  will  counterbalance 
each  other,  when  their  heights  above  the  common  surface  are  inversely  as 
their  specific  gravities  ;  for  it  is  obvious  that  the  greater  density  of  the  one 
will  precisely  compensate  for  its  deficiency  in  height.  Thus,  a  column  of 
mercury,  standing  at  the  height  of  30  inches  in  a  tube,  will  support  the 
pressure  of  a  column  of  water,  in  another  branch  of  the  tube,  exactly  34 
feet  high  :  since  the  weight  of  30  cubic  inches  of  mercury  is  equal  to  that 
of  408  cubic  inches  of  water.  (Plate  XIX.  Fig.  246.) 

We  have  hitherto  considered  the  properties  of  fluids  in  contact  with 
solids  which  are  immoveable,  and  of  invariable  form  ;  but  it  often  happens 
that  they  act  on  substances  which  are  moveable  ;  and  they  are  sometimes 
contained  in  vessels  of  which  the  form  is  susceptible  of  variation  ;  in  these 
cases,  other  considerations  are  necessary  for  the  determination  of  the  equi- 
librium of  fluids  and  solids  with  each  other  ;  and  in  the  first  place  the 
properties  of  floating  bodies  require  to  be  investigated. 

When  a  solid  body  floats  in  a  fluid,  it  displaces  a  quantity  of  the  fluid 
equal  to  itself  in  weight ;  and  every  solid  which  is  incapable  of  doing  this, 
must  sink.  For  in  order  that  the  solid  may  remain  at  rest,  the  pressure  of 
the  fluid  below  it,  reduced  to  a  vertical  direction,  must  be  precisely  equal  to 
its  weight ;  but  before  the  body  was  immersed,  the  same  pressure  was 
exerted  on  the  portion  of  the  fluid  which  is  now  displaced,  and  was  exactly 
counterbalanced  by  its  weight ;  consequently  that  weight  was  equal  to  the 
weight  of  the  floating  body. 

Since  the  force  which  supports  the  weight  of  a  floating  body,  is  the  pres- 
sure of  the  fluid  immediately  below  it,  if  this  pressure  be  removed  or 
diminished,  the  body  may  remain  at  rest  below  the  surface  of  the  fluid, 
even  when  it  is  specifically  lighter.  Thus  a  piece  of  very  smooth  wood  wrill 
remain,  for  some  time,  in  contact  with  the  flat  bottom  of  a  vessel  of  water, 
until  the  water  insinuates  itself  beneath  it ;  and  it  will  contimie  at  the 
bottom  of  a  vessel  of  mercury,  without  any  tendency  to  rise,  since  the 
mercury  has  no  disposition  to  penetrate,  like  water,  into  any  minute  inter- 
stices which  may  be  capable  of  admitting  it.  And,  for  a  similar  reason,  if 
the  pressure  of  the  incumbent  fluid  be  removed  from  the  upper  surface  of  a 
solid  substance  wholly  immersed  in  it,  the  solid  may  remain  suspended, 
although  heavier  than  an  equal  bulk  of  the  fluid.  Thus,  if  a  tube  or  vessel 
of  any  kind,  open  above  and  below,  have  a  bottom  of  metal,  ground  so  as  to 
come  into  perfect  contact  with  it,  without  being  fixed,  the  bottom  will 
appear  to  adhere  to  the  vessel  when  it  is  immersed  to  a  sufficient  depth  in 
water,  the  vessel  remaining  empty. 

In  order  that  a  floating  body  may  remain  in  equilibrium,  it  is  also  neces- 
sary that  its  centre  of  gravity  be  in  the  same  vertical  line  with  the  centre  of 
gravity  of  the  fluid  displaced  ;  otherwise  the  weight  of  the  solid  will  not  be 
completely  counteracted  by  the  pressure  of  the  fluid.  The  nature  of  the 
equilibrium,  with  respect  to  stability,  is  determined  by  the  position  of  the 


202  LECTURE  XXI. 

metacentve,  or  centre  of  pressure,  which  may  be  considered  as  a  fixed  point 
of  suspension  or  support,  for  the  solid  body.  It  is  obvious  that  when  the 
lower  surface  of  the  body  is  spherical  or  cylindrical,  the  metacentre  must 
coincide  with  the  centre  of  the  figure,  since  the  height  of  this  point,  as  well 
as  the  form  of  the  portion  of  the  fluid  displaced,  must  remain  invariable  in 
all  circumstances,  and  the  nature  of  the  equilibrium  will  depend  on  the 
distance  of  the  centre  of  gravity  above  or  below  the  centre  of  the  sphere  or 
cylinder.  And  the  place  of  the  metacentre  may  always  be  determined 
from  the  form  and  extent  of  the  surface  of  the  displaced  portion  of  the 
fluid,  compared  with  its  bulk  and  with  the  situation  of  its  centre  of  gravity. 
For  example,  if  a  rectangular  beam  be  floating  on  its  flat  surface,  the 
height  of  the  metacentre  above  the  centre  of  gravity  will  be  to  the  breadth 
of  the  beam,  as  the  breadth  to  twelve  times  the  depth  of  the  part  immersed. 
Hence,  if  the  beam  be  square,  it  will  float  securely  when  either  the  part 
immersed  or  the  part  above  the  surface  is  less  than  TVo-  of  the  whole  ;  but 
when  it  is  less  unequally  divided  by  the  surface  of  the  fluid,  it  will  overset. 
If,  however,  the  breadth  be  so  increased  as  to  be  nearly  one  fourth  greater 
than  the  depth,  it  will  possess  a  certain  degree  of  stability  whatever  its 
density  may  be.  (Plate  XIX.  Fig.  247.) 

When  the  equilibrium  of  a  floating  body  is  stable,  it  may  oscillate  back- 
wards and  forwards  in  the  neighbourhood  of  the  quiescent  position  :  and 
the  oscillations  will  be  the  more  rapid  in  proportion  as  the  stability  is 
greater  in  comparison  with  the  bulk  of  the  body.  Such  oscillations  may 
also  be  combined  with  others  which  take  place  in  a  transverse  direction  :  a 
ship,  for  example,  may  roll  on  an  axis  in  the  direction  of  her  length,  and 
may  pitch,  at  the  same  time,  upon  a  second  axis  in  the  direction  of  the 
beams.  Besides  these  rotatory  vibrations,  a  floating  body  which  is  suffered 
to  fall  into  a  fluid,  will  commonly  rise  and  sink  several  times  by  its  own 
weight  ;  and  in  all  these  cases,  the  vibrations  of  any  one  kind,  when  they 
are  small,  are  performed  nearly  in  equal  times  :  but  various  and  intricate 
combinations  may  sometimes  arise,  from  the  difference  of  the  times  in 
which  the  vibrations  of  different  kinds  are  performed. 

When  a  solid  body  is  wholly  immersed  in  a  fluid,  and  is  retained  in  its 
situation  by  an  external  force,  it  loses  as  much  of  its  weight  as  is  equiva- 
lent to  an  equal  bulk  of  the  fluid.  For,  conceiving  the  fluid  which  is 
displaced  by  the  body,  to  have  been  converted  into  a  solid  by  congelation, 
it  is  obvious  that  it  would  retain  its  situation,  and  the  difference  of  the 
pressures  of  the  fluid  on  its  various  parts  would  be  exactly  sufficient  to 
support  its  weight.  But  these  pressures  will  be  the  same  if  a  body  of  any 
other  kind  be  substituted  for  the  congealed  fluid  ;  their  buoyant  effect  may, 
therefore,  be  always  estimated  by  the  weight  of  a  portion  of  the  fluid  equal 
in  bulk  to  the  solid.  Thus,  when  a  little  figure,  containing  a  bubble  of  air, 
is  immersed  in  a  jar  of  water,  which  is  so  covered  by  a  bladder  that  it  may 
be  compressed  by  the  hand,  the  bulk  of  the  figure  with  its  bubble  is 
diminished  by  the  pressure,  it  is,  therefore,  less  supported  by  the  water,  and 
it  begins  to  sink  ;  and  when  the  hand  is  removed  it  immediately  rises 
again.  (Plate  XIX.  Fig.  248.) 

While  a  body  is  actually  rising  or  sinking  in  a  fluid,  with  an  accelerated 


ON  HYDROSTATICS.  203 

motion,  the  force  of  gravity  being  partly  employed  in  generating  momentum 
either  in  the  fluid  or  in  the  solid,  the  whole  pressure  on  the  bottom  of  the 
vessel  is  necessarily  somewhat  lessened.  Hence  the  apparent  weight  of  a 
jar  of  water  will  suffer  a  slight  diminution,  while  a  bullet  is  descending  in 
it,  or  while  bubbles  of  air  are  rising  in  it,  but  the  difference  can  seldom  be 
great  enough  to  be  rendered  easily  discoverable  to  the  senses. 

It  sometimes  happens  that  a  solid  body  is  partly  supported  by  a  fluid, 
and  partly  by  another  solid ;  of  this  we  have  an  example  in  one  of 
Dr.  Hooke's*  ingenious  inventions  for  keeping  a  vessel  always  full.  A 
half  cylinder,  or  a  hemisphere,  being  partly  supported  on  an  axis,  which  is 
in  the  plane  of  the  surface  of  the  fluid,  its  weight  is  so  adjusted  as  to  be 
equal  to  that  of  a  portion  of  the  fluid  of  half  its  magnitude  :  when  the 
vessel  is  full  it  is  half  immersed,  and  exerts  no  pressure  on  the  axis  :  it 
descends  as  the  fluid  is  exhausted,  and  its  tendency  to  turn  round  its  axis 
can  only  be  counteracted  by  the  pressure  of  the  fluid  on  its  flat  side,  as  long 
as  the  surface  of  the  remaining  portion  of  the  fluid  retains  its  original  level. 
(Plate  XIX.  Fig.  249.) 

When  a  fluid  is  contained  in  a  vessel  of  a  flexible  nature,  the  sides  of  the 
vessel  will  always  become  curved,  in  consequence  of  the  pressure,  and  the 
more  in  proportion  as  the  pressure  is  greater  ;  the  form  of  the  curved  sur- 
face will  also  be  such  that  the  common  centre  of  gravity  of  the  fluid  and 
the  vessel  may  descend  to  the  lowest  point  that  the  circumstances  of  the 
case  allow  ;  this  form  is  generally  of  too  intricate  a  nature  to  be  determined 
by  calculation  :  no  mathematician  has  hitherto  been  able  to  investigate,  for 
example,  the  curvature  which  a  square  or  rectangular  bag  of  leather  will 
assume  when  filled  with  water  or  with  corn.  "When,  indeed,  one  dimension 
only  of  a  vessel  is  considered,  for  instance,  when  the  bottom  of  a  cistern  is 
supposed  to  be  flexible,  and  to  be  fixed  at  two  opposite  sides,  while  the  ends 
are  simply  in  contact  with  upright  walls,  without  allowing  the  water  to 
run  out,  the  nature  of  the  curve  may  be  determined  with  tolerable  facility, 
whether  the  weight  of  the  bottom  itself  be  considered  or  not.  If  the  weight 
be  exactly  equal  to  that  of  the  water,  the  form  of  a  semicircle  will  agree 
with  the  conditions  of  equilibrium,  as  Bernoulli  has  demonstrated,  sup- 
posing the  fixed  points  at  the  distance  of  its  diameter ;  but  if  the  weight  of 
the  bottom  be  neglected,  the  curvature  will  be  everywhere  proportional  to 
the  distance  below  the  surface,  the  form  being  the  same  as  that  of  an  elastic 
rod,  bent  by  two  forces  in  the  direction  of  the  surface.  The  same  principles, 
with  a  slight  difference  in  the  calculations,  will  serve  to  determine  the  forms 
adapted  to  the  equilibrium  of  arches  intended  for  supporting  the  weight  of 
superincumbent  fluids,  or  of  such  soft  materials  as  approach  nearly  in  their 
operation  to  more  perfect  fluids.  (Plate  XIX.  Fig.  250.) 


LECT.  XXI.— ADDITIONAL  AUTHORITIES. 

Works  on  Hydrodynamics,  8fc.  not  referred  to  in  the  Lectures. — Switzer's 
Hydrostatics,  2  vols.  4to,  Loud.  1729.  Wolfius,  Elementa  Matheseos,  5  vols.  4to, 
Geneva,  1732-41.  D'Alembert,  TraitS  de  1'Equilibre  et  du  Mouvement  des  Fluides, 

*  Birch's  History  of  the  Royal  Society,  ii.  155. 


204  LECTURE  XXII. 

4to,  Paris  1744.  Cotes's  Hydrostatical  and  Pneumatical  Lectures,  1747.  Euler 
on  Hydrostatics,  &c.  Hist,  et  Mem.  de  Berlin,  1755,  p.  217,  &c.  Nov.  Com. 
Petr.  xiii.  xiv.  xv.  Lecchi,  Idrostatica  ed  Idraulica,  Milan,  1765.  Kastner,  An- 
fangsgriinde  der  Hydrodynamik,  Gott.  1769.  Bossut,  Traite  d'Hydrodynamique, 
2vols.  1777.  Lambert  on  the  Constitution  of  Fluids.  Hist,  et  Mem.  de  Berlin, 
1784,  p.  299.  Bernard,  Hydraulique,  4to,  Paris,  1787.  Langsdorfs,  Theorie  der 
Hydrodynamischen  Grundlehren,  Frankf.  1787.  Hydraulik,  4to,  Altenb.  1794. 
Parkinson's  Hydrostatics,  4to,  1789.  Burja,  Grundlehren  der  Hydrostatik,  1790. 
Eytelwein's  Handbuch  der  Mechanik  und  Hydraulik,  Berlin,  1801  ;  translated  by 
Nicholson.  Mollet  Hydraulique  Physique,  Paris,  1810.  Raccolta  di  Autori  Ita- 
liani  che  Trattono  del  Moto  dell'  Acque,  19  vols.  4to,  Bologna,  1821-4.  Gauss, 
Principia  Generalia  Theorise,  fig.  Fluid,  in  Statu  yEquilib.  4to,  Gott.  1830. 

Elementary  Treatises  will  be  found  in  many  of  the  works  on  mechanics  already 
mentioned,  besides  which  are  the  following  : — Francoeur,  Paris.  Vince,  Camb.  1812. 
Bland,  Camb.  1824.  Moseley,  Camb.  ;  Miller,  Camb.  1831.  Webster,  Camb. 
Moreau,  4to,  Brest,  1830  ;  together  with  the  treatises  in  Brewster's  Cyclopaedia, 
&c.  &c. 


LECTURE    XXII. 


ON  PNEUMATIC  EQUILIBRIUM. 

THE  laws  of  the  pressure  and  equilibrium  of  liquids,  which  are  the 
peculiar  subjects  of  hydrostatics,  are  also  applicable  in  general  to  fluids  of 
all  kinds,  as  far  as  they  are  compatible  with  the  compressibility  of  those 
fluids,  or  with  their  tendency  to  expand. 

Elastic  fluids  are  distinguished  from  liquids  by  the  absence  of  all  cohesive 
force,  or  by  their  immediate  tendency  to  expand  when  they  are  at  liberty. 
Such  are  atmospheric  air,  steam,  and  gases  of  various  kinds  ;  and  the  consi- 
deration of  these  fluids,  in  the  state  of  rest,  constitutes  the  doctrine  of  pneu- 
matostatics,  or  of  the  equilibrium  of  elastic  fluids. 

That  the  air  is  a  material  substance,  capable  of  resisting  pressure,  is  easily 
shown  by  inverting  an  empty  jar  in  water,  and  by  the  operation  of  trans- 
ferring airs  and  gases  from  vessel  to  vessel,  in  the  pneumatic  apparatus 
used  by  chemists.  The  tendency  of  the  air  to  expand  is  shown  by  the 
experiment  in  which  a  flaccid  bladder  becomes  distended,  and  shrivelled 
fruit  recovers  its  full  size,  as  soon  as  the  external  pressure  is  removed  from 
it,  by  the  operation  of  the  air  pump  :  and  the  magnitude  of  this  expansive 
force  is  more  distinctly  seen,  when  a  portion  of  air  is  inclosed  in  a  glass 
vessel,  together  with  some  mercury,  in  which  the  mouth  of  a  tube  is 
immersed,  while  the  other  end  is  open,  and  without  the  vessel ;  so  that 
when  the  whole  apparatus  is  inclosed  in  a  very  long  jar,  and  the  air  of  the 
jar  is  exhausted,  the  column  of  mercury  becomes  the  measure  of  the  expan- 
sive force  of  the  air.  (Plate  XIX.  Fig.  251.) 

If  the  diameter  of  the  tube,  in  an  apparatus  of  this  kind,  were  very 
small  in  comparison  with  the  bulk  of  the  air  confined,  the  column  of  mer- 
cury would  be  raised,  in  the  ordinary  circumstances  of  the  atmosphere, 
to  the  height  of  nearly  30  inches.  But  supposing  the  magnitude  of  the 


ON  PNEUMATIC  EQUILIBRIUM.  205 

tube  such,  that  the  portion  of  air  must  expand  to  twice  its  natural  bulk, 
•before  the  mercury  acquired  a  height  sufficient  to  counterpoise  it,  this 
height  would  be  15  inches  only.  For  it  appears  to  be  a  general  law  of 
all  elastic  fluids,  that  their  pressure  on  any  given  surface  is  diminished 
exactly  in  the  same  proportion  as  their  bulk  is  increased.  If,  therefore,  the 
column  of  mercury  in  the  vacuum  of  the  air  pump  were  60  inches  high,  the 
air  would  be  reduced  to  half  its  natural  bulk  ;  and  for  the  same  reason,  the 
pressure  of  a  column  of  30  inches  of  mercury  in  the  open  air  will  reduce 
any  portion  of  air  to  half  its  bulk,  since  the  natural  pressure  of  the  atmo- 
sphere, which  is  equal  to  that  of  about  30  inches  of  mercury,  is  doubled  by 
the  addition  of  an  equal  pressure.  In  the  same  manner  the  density  of  the 
air  in  a  diving  bell  is  doubled  at  the  depth  of  34  feet  below  the  surface  of 
the  water,  and  tripled  at  the  depth  of  68  feet.  This  law  was  discovered  by 
Dr.  Hooke  ;*  he  found,  however,  that  when  a  very  great  pressure  had  been 
applied,  so  that  the  density  became  many  times  greater  than  in  the  natural 
state,  the  elasticity  appeared  to  be  somewhat  less  increased  than  the  density; 
but  this  exception  to  the  general  law  has  not  been  confirmed  by  later  and 
more  accurate  experiments,  t 

Not  only  the  common  air  of  the  atmosphere  and  other  permanently  elastic 
gases,  but  also  steams  and  vapours  of  all  kinds,  appear  to  be  equally  subject 
to  this  universal  law :  they  must,  however,  be  examined  at  temperatures 
sufficient  to  preserve  them  in  a  state  of  elasticity  ;  for  example,  if  we  wished 
to  determine  the  force  of  steam  twice  as  dense  as  that  which  is  usually  pro- 
duced, we  should  be  obliged  to  employ  a  heat  30  or  40  degrees  above  that  of 
boiling  water,  we  should  then  find  that  steam  of  such  a  density  as  to  support, 
when  confined  in  a  dry  vessel,  the  pressure  of  a  column  of  30  inches  of 
mercury,  would  be  reduced  to  half  its  bulk  by  the  pressure  of  a  column 
of  60  inches.  But  if  we  increased  the  pressure  much  beyond  this,  the 
steam  would  be  converted  into  water,  and  the  experiment  would  be  at  an 
end. 

That  the  air  which  surrounds  us  is  subjected  to  the  power  of  gravitation, 
and  possesses  weight,  may  be  shown  by  weighing  a  vessel  which  has  been 
exhausted  by  means  of  the  air  pump,  and  then  allowing  the  air  to  enter,  and 
weighing  it  a  second  time.  In  this  manner  we  may  ascertain  the  specific 
gravity  of  the  air,  even  if  the  exhaustion  is  only  partial,  provided  that  we 
know  the  proportion  of  the  air  left  in  the  vessel  to  that  which  it  originally 
contained.  The  pressure  derived  from  the  weight  of  the  air  is  also  the  cause 
of  the  ascent  of  hydrogen  gas,  or  of  another  portion  of  air  which  is  rarefied 
by  heat,  and  carries  with  it  the  smoke  of  a  fire ;  and  the  effect  is  made 
more  conspicuous,  when  either  the  hydrogen  gas,  or  the  heated  air,  is  con- 
fined in  a  balloon.  The  diminution  of  the  apparent  weight  of  a  body  by 
means  of  the  pressure  of  the  surrounding  air,  is  also  shown  by  the  destruc- 
tion of  the  equilibrium  between  two  bodies  of  different  densities,  upon 
their  removal  from  the  open  air  into  the  vacuum  of  an  air  pump.  For 
this  purpose  a  light  hollow  bulb  of  glass  may  be  exactly  counterpoised  in 
tty3  air  by  a  much  smaller  weight  of  brass,  with  an  index,  which  shows, 

*  Birch's  History  of  the  Royal  Society,  1678,  iii.  384,  387. 

t  Rickmann  on  the  Compression  of  the  Air  by  Ice,  Nov.  Com.  Petr.  ii.  162. 


206  LECTURE   XXII. 

on  a  graduated  scale,  the  degree  in  which  the  large  ball  is  made  to  prepon  - 
derate  in  the  receiver  of  the  air  pump,  by  the  rarefaction  of  the  air,  less-1 
ening  the  buoyant  power  which  helps  to  support  its  weight.  (Plate  XIX. 
Fig.  252.) 

From  this  combination  of  weight  and  elasticity  in  the  atmosphere,  it  fol- 
lows, that  its  upper  parts  must  be  much  more  rare  than  those  which  are 
nearer  to  the  earth,  since  the  density  is  everywhere  proportional  to  the 
whole  of  the  superincumbent  weight.  The  weight  of  a  column  of  air  one 
foot  in  height  is  one  twenty  eight  thousandth  of  the  whole  pressure  ;  conse- 
quently that  pressure  is  increased  one  twenty  eight  thousandth  by  the  addi- 
tion of  the  weight  of  one  foot,  and  the  next  foot  will  be  denser  in  the  same 
proportion,  since  the  density  is  always  proportionate  to  the  pressure  ;  the 
pressure  thus  increased  will  therefore  still  be  equal  to  twenty  eight  thousand 
times  the  weight  of  the  next  foot.  The  same  reasoning  may  be  continued 
without  limit,  and  it  may  be  shown,  that  while  we  suppose  the  height  to 
vary  by  any  uniform  steps,  as  by  distances  of  a  foot  or  a  mile,  the  pressures 
and  densities  will  increase  in  continual  proportion  ;  thus,  at  the  height  of 
about  3000  fathoms,  the  density  will  be  about  half  as  great  as  at  the  earth's 
surface  ;  at  the  height  of  6000,  one  fourth  ;  at  9000,  one  eighth  as  great. 
Hence  it  is  inferred  that  the  height  in  fathoms  may  be  readily  found  from 
the  logarithm  of  the  number  expressing  the  density  of  the  air ;  for  the 
logarithm  of  the  number  2,  multiplied  by  10,000,  is  3010,  the  logarithm  of 
4,  6020,  and  that  of  8,  9031 ;  the  corresponding  logarithms  always  in- 
creasing in  continual  proportion,  when  the  numbers  are  taken  larger  and 
larger  by  equal  steps.  (Plate  XIX.  Fig.  253.) 

Hence  we  obtain  an  easy  method  of  determining  the  heights  of  mountains 
with  tolerable  accuracy  :  for  if  a  bottle  of  air  were  closely  stopped  on  the 
summit  of  a  mountain,  and  being  brought  in  this  state  into  the  plain 
below,  its  mouth  were  inserted  into  a  vessel  of  water  or  of  mercury,  a 
certain  portion  of  the  liquid  would  enter  the  bottle  ;  this  being  weighed,  if 
it  were  found  to  be  one  half  of  the  quantity  that  the  whole  bottle  would 
contain,  it  might  be  concluded  that  the  air  on  the  mountain  possessed  only 
half  of  the  natural  density,  and  that  its  height  was  3000  fathoms.  It  ap- 
pears also,  from  this  statement,  that  the  height  of  a  column  of  equal  density 
with  any  part  of  the  atmosphere,  equivalent  to  the  pressure  to  which  that 
part  is  subjected,  is  every  where  equal  to  about  28,000  feet. 

Many  corrections  are,  however,  necessary  for  ascertaining  the  heights  of 
mountains  with  all  the  precision  that  the  nature  of  this  kind  of  measure- 
ment admits ;  and  they  involve  several  determinations,  which  require  a 
previous  knowledge  of  the  effects  of  heat,  and  of  the  nature  of  the  ascent  of 
vapours,  which  cannot  be  examined  with  propriety  at  present. 

We  may  easily  ascertain,  on  the  same  principles,  the  height  to  which  a 
balloon  will  ascend,  if  we  are  acquainted  with  its  bulk  and  with  its  weight : 
thus,  supposing  its  weight  500  pounds,  and  its  bulk  such  as  to  enable  it  to 
raise  300  pounds  more,  its  specific  gravity  must  be  five  eighths  as  great  as 
that  of  the  air,  and  it  will  continue  to  rise,  until  it  reach  the  height  ,at 
which  the  air  is  of  the  same  density :  but  the  logarithm  of  eight  fifths, 
multiplied  by  10,000,  is  2040 ;  and  this  is  the  number  of  fathoms  contained 


ON  PNEUMATIC  EQUILIBRIUM.  207 

in  the  height,  which  will,  therefore,  be  a  little  more  than  two  miles  and  a 
quarter.  It  may  be  found,  by  pursuing  the  calculation,  that  at  the  dis- 
tance of  the  earth's  semidiameter,  or  nearly  4000  miles  above  its  surface, 
the  air,  if  it  existed,  would  become  so  rare,  that  a  cubic  inch  would 
occupy  a  space  equal  to  the  sphere  of  Saturn's  orbit :  and  on  the  other 
hand,  if  there  were  a  mine  about  42  miles  deep,  the  air  would  become  as 
dense  as  quicksilver  at  the  bottom  of  it. 

It  appears,  therefore,  that  all  bodies  existing  on  or  near  the  earth's 
surface  may  be  considered  as  subjected  to  the  pressure  of  a  column  of  air 
28,000  feet  high,  supposing  its  density  everywhere  equal  to  that  which  it 
possesses  at  the  earth's  surface,  and  which  is  usually  such,  that  100  wine 
gallons  weigh  a  pound  avoirdupois,  creating  a  pressure  equal  to  that  of  30 
inches  of  mercury,  or  34  feet  of  water,  and  which  amounts  to  14|  pounds 
for  each  square  inch.  This  pressure  acts  in  all  directions  on  every 
substance  which  is  exposed  to  it :  but  being  counterbalanced  by  the 
natural  elasticity  of  these  substances,  it  produces  in  common  no  apparent 
effects ;  when,  however,  by  means  of  the  air  pump,  or  otherwise,  the  pres- 
sure of  the  air  is  removed  from  one  side  of  a  body  while  it  continues  to 
act  on  the  other,  its  operation  becomes  extremely  evident.  Thus,  when  two 
hollow  hemispheres,  in  contact  with  each  other,  are  exhausted  of  air,  they 
are  made  to  cohere  with  great  force  ;  they  are  named  Magdeburg  hemis- 
pheres, because  Otto  von  Guerike,  of  Magdeburg,*  constructed  two  such 
hemispheres,  of  sufficient  magnitude  to  withstand  the  draught  of  the  em- 
peror's six  coach  horses,  pulling  with  all  their  force  to  separate  them.  By 
a  similar  pressure,  a  thin  square  bottle  may  be  crushed  when  it  is  suf- 
ficiently exhausted,  and  a  bladder  may  be  torn  with  a  loud  noise  :  and 
the  hand  being  placed  on  the  mouth  of  a  vessel  which  is  connected  with  the 
air  pump,  it  is  fixed  to  it  very  forcibly,  when  the  exhaustion  is  performed, 
by  the  pressure  of  the  air  on  the  back  of  the  hand  ;  the  fluids  also,  which 
circulate  in  the  bloodvessels  of  the  hand,  are  forced  towards  its  lower  sur- 
face, and  the  effect  which  is  called  suction  is  produced  in  a  very  striking 
manner.  It  is  on  the  same  principle  that  cupping  glasses  are  employed,  a 
partial  exhaustion  being  procured  by  means  of  the  flame  of  tow,  which 
heats  the  air,  and  expels  a  great  part  of  it :  so  that  the  remainder,  when  it 
cools,  is  considerably  rarefied. 

It  was  Galileo  that  first  explained  the  nature  of  suction  from  the  effects 
of  the  pressure  of  the  atmosphere  ;t  and  his  pupil  Torricelli  J  confirmed  his 
doctrines  by  employing  a  column  of  mercury,  of  sufficient  height  to  over- 
come the  whole  pressure  of  the  atmosphere,  and  to  produce  a  vacuum  in 
the  upper  part  of  the  tube  or  vessel  containing  it.  In  the  operation  of 

*  Schotti,  Mechanica  Hydraulico-Pneumatica,  4to,  1657.  Ottonis  Guericke, 
Experimenta  Nova  Magdeburgica,  fol.  Amst.  1670. 

f  We  may  doubt  whether  this  is  not  saying  too  much.  Galileo  proved  that  the 
air  has  weight,  and  not,  as  was  then  believed,  intrinsic  levity.  He  actually  weighed  a 
portion  in  a  flask,  but  his  determination  of  the  specific  gravity  of  air  is  not,  as  we 
might  conjecture,  very  accurate.  Opere,  iii.  47.  The  gravity  of  air  was,  however, 
knoton  to  the  ancients.  See  Aristotle,  De  Coelo,  lib.  iv. 

J  On  this  subject,  see  Pascal,  Traite  de  rEquilibre  des  Liqueurs,  Par.  1669,  p.  177. 
Cartesii  Opera,  ii.  243,  246  ;  andMontucla  Histoire  des  Mathematiques,  ii.  203. 


208  LECTURE  XXII. 

sucking  up  a  fluid  through  a  pipe,  with  the  mouth  or  otherwise,  the  pres- 
sure of  the  air  is  but  partially  removed  from  the  upper  surface  of  the  fluid, 
and  it  becomes  capable  of  ascending  to  a  height  which  is  determined  by  the 
difference  of  the  densities  of  the  air  within  and  without  the  cavity 
concerned  :  thus,  an  exhaustion  of  one  fourth  of  the  air  of  the  cavity  would 
enable  us  to  raise  water  to  the  height  of  8£  feet,  and  mercury  to  7i  inches, 
above  the  level  of  the  reservoir  from  which  it  rises.  We  can  draw  up  a 
much  higher  column  of  mercury  by  sucking  with  the  muscles  of  the  mouth 
only,  than  by  inspiring  with  the  chest,  and  the  difference  is  much  more 
marked  than  the  difference  in  the  forces  with  which  we  can  blow  :  for  in 
sucking,  the  cavity  of  the  mouth  is  very  much  contracted  by  the  pressure 
of  the  external  air,  and  the  same  force,  exerted  on  a  smaller  surface,  is 
capable  of  counteracting  a  much  greater  hydrostatic  or  pneumatic  pres- 
sure. 

When  a  tube  of  glass  about  three  feet  long,  closed  at  one  end  and  open 
at  the  other,  is  filled  with  mercury,  and  then  immersed  in  a  bason  of  the 
same  fluid,  the  pressure  of  the  atmosphere  is  wholly  removed  from  the 
upper  surface  of  the  mercury  in  the  tube,  while  it  continues  to  act  on  the 
mercury  in  the  bason,  and  by  its  means  on  the  lower  surface  of  the  column 
in  the  tube.  If  such  a  tube  be  placed  under  the  receiver  of  an  air  pump, 
the  mercury  will  subside  in  the  tube,  accordingly  as  the  pressure  of  the 
atmosphere  is  diminished  ;  and  if  the  exhaustion  be  rendered  very  perfect, 
it  will  descend  very  nearly  to  the  level  of  the  open  bason  or  reservoir. 
When  the  air  is  readmitted,  the  mercury  usually  rises,  on  the  level  of  the 
sea,  to  the  height  of  about  30  inches ;  but  the  air  being  lighter  at  some 
times  than  at  others,  the  height  varies  between  the  limits  of  27  and  31 
inches.  This  well  known  instrument,  from  its  use  in  measuring  the  weight 
of  the  air,  is  called  a  barometer.  In  the  same  manner  a  column  of  water 
from  30  to  35  feet  in  height  may  be  sustained  in  the  pipe  of  a  pump  ;  but 
if  the  pipe  were  longer  than  this,  a  vacuum  would  be  produced  in  the 
upper  part  of  it,  and  the  pump  would  be  incapable  of  acting. 

In  order  to  observe  the  height  of  the  mercury  in  the  barometer  with 
greater  convenience  and  accuracy,  the  scale  has  sometimes  been  amplified 
by  various  methods  ;  either  by  bending  the  upper  part  of  the  tube  into  an 
oblique  position,  as  in  the  diagonal  barometer,  or  by  making  the  lower  part 
horizontal,  and  of  much  smaller  diameter  than  the  upper,  or  by  making  the 
whole  tube  straight  and  narrow,  and  slightly  conical,  or  by  placing  a  float 
on  the  surface  of  the  mercury  in  the  reservoir,  and  causing  an  axis  which 
carries  an  index,  to  revolve  by  its  motion.  But  a  good  simple  barometer, 
about  one  third  of  an  inch  in  diameter,  furnished  with  a  vernier,  is  perhaps 
fully  as  accurate  as  any  of  these  more  complicated  instruments.  In  order 
to  exclude  the  air  the  more  completely  from  the  tube,  the  mercury  must  at 
least  be  shaken  in  it  for  a  considerable  time,  the  tube  being  held  in  an 
inverted  position  ;  and  where  great  accuracy  is  required,  the  mercury  must 
be  boiled  in  the  tube.  The  reservoir  most  commonly  employed  is  a  flat 
wooden  box,  with  a  bottom  of  leather  ;  the  cover,  which  is  unscrewejl  at 
pleasure,  being  cemented  to  the  tube.  Sometimes  a  screw  is  made  to  act 
on  the  leather,  by  means  of  which  the  surface  of  the  mercury  is  always 


ON  PNEUMATIC  EQUILIBRIUM.  209 

brought  to  a  certain  level,  indicated  by  a  float,  whatever  portion  of  it  may 
be  contained  in  the  tube ;  but  the  necessity  of  this  adjustment  may  be 
easily  avoided,  by  allowing  the  mercury  to  play  freely  between  two  hori- 
zontal surfaces  of  wood,  of  moderate  extent,  and  at  the  distance  of  one 
seventh  of  an  inch  :  the  height  may  then  be  always  measured  from  the 
upper  surface,  without  sensible  error.  But  if  the  surfaces  were  closer 
than  this,  the  mercury  would  stand  too  high  in  the  tube.  (Plate  XIX. 
Fig.  254.) 

The  same  method  which  is  employed  for  determining  the  relation  be- 
tween the  heights  and  densities  of  elastic  fluids,  may  be  extended  to  all 
bodies  which  are  in  any  degree  compressible,  and  of  which  the  elasticity  is 
subjected  to  laws  similar  to  those  which  are  discoverable  in  the  air  and 
in  other  gases:  and  it  is  not  improbable  that  these  laws  are  generally 
applicable  to  all  bodies  in  nature,  as  far  as  their  texture  will  allow  them  to 
submit  to  the  operation  of  pressure,  without  wholly  losing  their  form. 
Water,  for  example,  has  been  observed  by  Canton*  to  be  compressed  one 
twenty  two  thousandth  of  its  bulk  by  a  force  equal  to  that  of  the  pressure 
of  the  atmosphere  ;  consequently  this  force  may  be  represented  by  that  of 
a  column  of  water  750  thousand  feet  in  height ;  the  density  of  the  water 
at  the  bottom  of  a  lake,  or  of  the  sea,  will  be  increased  by  the  pressure  of 
the  superincumbent  fluid  ;  and  supposing  the  law  of  compression  to 
resemble  that  of  the  air,  it  may  be  inferred  that  at  the  depth  of  100  miles, 
its  density  would  be  doubled  ;  and  that  at  200  it  would  be  quadrupled. 
The  same  measures  would  also  be  applicable  to  the  elasticity  of  mercury. 
But  there  is  reason  to  suppose  that  they  are  in  both  cases  a  little  too 
small. 


LECT.  XXII.— ADDITIONAL  AUTHORITIES. 

Pascal,  Nouvelles  Experiences  touchant  la  Vuide,  4to,  1647.  Tables  of  the  Com- 
pression of  Air  under  Water,  Ph.  Tr.  vi.  2192,  2239.  Sinclair,  Ars  Magna  Gravi- 
tatis  et  Levitatis,  4to,  Rotterd.  1669.  Mariotte,  sur  la  Nature  del' Air,  1676.  Mari- 
otte  and  Homberg  on  the  Weight  of  Air.  Hist,  et  Mem.  de  Paris,  ii.  41.  Homberg, 
ii.  105.  Wallis,  Ph.  Tr.  1685,  p.  1002.  Halley,  ibid.  1686,  p.  106.  Derham,  ibid. 
1698,  p.  2.  Desaguliers,  ibid.  No.  386.  Senguerd  de  Aeris  Natura,  4to,  Lond.  1699. 
Cassini,  Hist,  et  Mem.  de  Paris,  1705,  p.  61.  Lahire,  ibid.  110,  H.  10.  Amontons, 
ibid.  119,  H.  10.  Varignon,  ibid.  1716,  p.  107,  H.  40.  Forssell,  Dissertatio  Physica 
de  Barometro,  4to,  Upsal,  1747.  Scheuchzer,  Ph.  Tr.  xxxv.  537,  577.  De  Luc,  sur 
les  Modifications  de  T  Atmosphere,  1 772.  Shuckburgh,  Observations  made  to  ascertain 
the  Heights  of  Mountains  by  the  Barometer,  Ph.  Tr.  1777,  p.  513  ;  1778,  p.  681. 
Roy,  ibid.  1777,  p.  513.  Playfair,  Ed.  Tr.  i.  87.  Dalton,  Manch.  Mem.  v.  Assier 
Perricat,  Nouveau  Traite  des  Barometres,  1802.  Lindenau,  Tables  Barometriques, 
4to,  Gotha,  1809.  Biot.  do.  1811.  Ramond,  sur  la  Formule  Barometrique  de  la 
Mecanique  Celeste,  4to,  1811.  Winckler,  Tables  Barometriques,  4to,  Halle, 
1820  and  1826.  Carlini's  do.  Milan,  1823.  Duvillard's  do.  Paris,  1826.  Olt- 
mann's  do.  Stuttg.  1830.  Galbraith's  do.  Edinb.  1833. 

*  Phil.  Trans.  1762,  p.  640  ;  1764,  p.  261.  See  also  Perkins,  Ph.  Tr.  1826,  p. 
561  ;  and  (Ersted's  Report  of  the  British  Association  for  1833  ;  Trans,  of  Sections, 
p.  353. 


210 


LECTURE   XXIII. 


ON  THE  THEORY  OF  HYDRAULICS. 

HAVING  considered  the  principal  cases  of  the  equilibrium  of  fluids,  both 
liquid  and  aeriform,  we  proceed  to  examine  the  theory  of  their  motions. 
Notwithstanding  the  difficulties  attending  the  mathematical  theory  of 
hydraulics,  so  much  has  already  been  done,  by  the  assistance  of  practical 
investigations,  that  we  may  in  general,  by  comparing  the  results  of  former 
experiments  with  our  calculations,  predict  the  effect  of  any  proposed 
arrangement,  without  an  error  of  more  than  one  fifth,  or  perhaps  one  tenth 
of  the  whole  :  and  this  is  a  degree  of  accuracy  fully  sufficient  for  practice, 
and  which  indeed  could  scarcely  have  been  expected  from  the  state  of  the 
science  at  the  beginning  of  the  last  century.  Many  of  these  improvements 
have  been  derived  from  an  examination  of  the  nature  and  magnitude  of 
the  friction  of  fluids,  which,  although  at  first  sight  it  might  be  supposed  to 
be  very  inconsiderable,  is  found  to  be  of  so  much  importance  in  the  appli- 
cation of  the  theory  of  hydraulics  to  practical  cases,  and  to  affect  the 
modes  of  calculation  so  materially,  that  it  will  require  to  be  discussed,  here- 
after, in  a  separate  lecture. 

There  is  a  general  principle  of  mechanical  action,  which  was  first 
distinctly  stated  by  Huygens,*  and  which  has  been  made  by  Daniel 
Bernoulli  t  the  basis  of  his  most  elegant  calculations  in  hydrodynamics. 
Supposing  that  no  force  is  lost  in  the  communication  of  motion  between 
different  bodies,  considered  as  belonging  to  any  system,  they  always  acquire 
such  velocities  in  descending  through  any  space,  that  the  centre  of  gravity 
of  the  system  is  capable  of  ascending  to  a  height  equal  to  that  from  which 
it  descended,  notwithstanding  any  mutual  actions  between  the  bodies.  The 
truth  of  this  principle  may  easily  be  inferred  from  the  laws  of  collision, 
compared  with  the  properties  of  accelerating  and  retarding  forces.  Thus, 
if  an  elastic  ball,  weighing  10  ounces,  and  descending  from  a  height  of  1 
foot,  be  caused  to  act  in  any  manner  on  a  similar  ball  of  one  ounce,  so  as 
to  lose  the  whole  of  its  motion,  the  smaller  ball  will  acquire  a  velocity 
capable  of  carrying  it  to  the  height  of  10  feet.  It  is  true  that  some  other 
suppositions  must  be  made,  in  applying  this  law  to  the  determination  of 
the  motions  of  fluids,  and  that  in  many  cases  it  becomes  necessary  to  sup- 
pose that  a  certain  portion  of  ascending  force  or  energy  is  lost  in  conse- 
quence of  the  internal  motions  of  the  particles  of  the  fluid.  But  still,  with 
proper  restrictions  and  corrections,  the  principle  affords  us  a  ready  method 
of  obtaining  solutions  of  problems,  which,  without  some  such  assistance, 
it  would  be  almost  impossible  to  investigate.  The  principal  hypothesis 
which  is  assumed  by  Bernoulli,  without  either  demonstration,  or  even  the 
appearance  of  perfect  accuracy,  is  this,  that  all  the  particles  of  a  flui4  in 

*  Horologium  Oscillatorium,  Pars  4,  Hypoth.  1. 
f  Hydrodynamica,  4to,  Strasb.  1738. 


ON  THE  THEORY  OF  HYDRAULICS.        211 

motion,  contained  in  any  one  transverse  section  of  the  vessels  or  pipes 
'through  which  it  runs,  must  always  move  with  equal  velocities  ;  thus,  if 
water  be  descending  through  a  vessel  of  any  form,  either  regular  or  irre- 
gular, he  supposes  the  particles  at  the  same  height  to  move  with  the  same 
velocity ;  so  that  the  velocity  of  every  particle  in  every  part  of  a  cylindrical 
vessel  10  inches  in  diameter,  through  which  a  fluid  is  moving,  must  be  one 
hundredth  part  as  great  as  in  passing  through  a  circular  orifice,  an  inch  in 
diameter,  made  in  its  bottom.  It  is  evident  that  this  cannot  possibly  be 
true  of  the  portions  of  the  fluid  nearest  the  bottom  of  the  vessel,  since  the 
particles  most  distant  from  the  orifice  must  be  nearly  at  rest,  while  those 
which  are  immediately  over  the  orifice  are  in  rapid  motion ;  but  still  the 
calculations  founded  on  the  hypothesis  agree  tolerably  well  with  experi- 
ments. In  this  case  the  actual  descent,  in  any  instant,  may  be  estimated 
by  the  removal  of  the  quantity  discharged,  from  the  surface  of  the  fluid  to 
the  orifice,  since  the  intermediate  space  remains  always  occupied.  The 
ascending  force  thus  obtained  is  to  be  distributed  throughout  the  fluid, 
according  to  the  respective  velocities  of  its  different  portions  ;  and  it  may 
easily  be  shown,  that  when  the  orifice  is  small,  the  part  which  belongs  to 
the  fluid  in  the  vessel  is  wholly  'inconsiderable  in  comparison  with  the 
ascending  force  required  for  the  escape  of  the  small  portion  which  is  flow- 
ing through  the  orifice,  and  the  whole  ascending  force  may,  therefore,  be 
supposed  to  be  employed  in  the  motion  of  this  portion ;  so  that  it  will 
acquire  the  velocity  of  a  body  falling  from  the  whole  height  of  the  surface 
of  the  reservoir,  or  the  velocity  due  to  that  height.  It  appears,  also,  that 
very  nearly  the  same  velocity  is  acquired  by  almost  the  first  particles  that 
escape  from  the  orifice,  so  that  no  sensible  time  elapses  before  the  jet  flows 
with  its  utmost  velocity. 

This  velocity  may  be  found,  as  we  have  already  seen,  by  multiplying 
the  square  root  of  the  height  of  the  reservoir,  expressed  in  feet,  by  8,  or 
more  correctly,  by  8^ ;  thus,  if  the  height  be  4  feet,  the  velocity  will  be 
sixteen  feet  in  a  second  ;  if  the  height  be  9  feet,  the  velocity  will  be  24, 
the  squares  of  2  and  3  being  4  and  9  ;  and  if  the  height  were  14  feet,  the 
velocity  would  be  80  feet  in  a  second,  and  a  circular  orifice  an  inch  in 
diameter  would  discharge  exactly  an  ale  gallon  in  a  second.  In  the  same 
manner,  the  pressure  of  the  atmosphere  being  equal  to  that  which  would  be 
produced  by  a  column  of  air  of  uniform  density  28,000  feet  high,  the  air 
would  rush  into  a  vacuum  with  a  velocity  of  more  than  1800  feet  in  a 
second. 

The  velocity  is  also  equal,  whatever  may  be  the  direction  of  the  stream  ; 
for  since  the  pressure  of  fluids  acts  equally  in  all  directions  at  equal  depths, 
the  cause  being  the  same,  the  effect  must  also  be  the  same.  And  if  the 
motion  be  occasioned  by  a  pressure  derived  from  a  force  of  any  other  kind, 
the  effect  may  be  found  by  calculating  the  height  of  a  column  of  the  fluid, 
which  would  be  capable  of  producing  an  equal  pressure.  When  also  the 
force  arises  from  the  difference  of  two  pressures,  the  velocity  may  be  deter- 
mined in  a  similar  manner.  Thus,  the  pressure  of  a  column  of  water  1  foot 
in  height,  would  force  the  air  through  a  small  orifice  with  a  velocity  of  230 
feet  in  a  second,  corresponding  to  the  height  of  830  feet ;  a  column  of  mer- 


212  LECTURE  XXIII. 

cury  1  inch  high,  would  produce  the  same  effect  as  a  reservoir  of  water 
more  than  thirteen  times  as  high,  and  the  force  of  the  air  confined  in  a 
closed  bottle  under  the  receiver  of  the  air  pump,  will  cause  a  jet  to  rise  to 
the  same  height  as  a  column  of  mercury  which  measures  the  difference  of 
the  elasticities  of  the  air  in  the  bottle  and  in  the  receiver. 

But  these  calculations  are  only  confirmed  by  experiment  in  cases  when 
the  ajutage  through  which  the  fluid  runs  is  particularly  constructed  ;  that 
is,  when  it  is  formed  by  a  short  tube,  of  which  the  sides  are  so  curved  that 
the  particles  of  the  fluid  may  glide  along  them  for  some  distance,  and  es- 
cape in  a  direction  parallel  to  the  axis  of  the  stream.  A  short  cylindrical 
pipe  is  found  to  answer  this  purpose  in  some  measure  ;  but  the  end  may  be 
more  completely  obtained  by  a  tube  nearly  conical,  but  with  its  sides  a 
little  convex  inwards,  so  as  to  imitate  the  shape  which  a  stream  or  vein  of 
water  spontaneously  assumes  when  it  runs  through  an  orifice  in  a  thin 
plate  :  for  in  such  cases  the  stream  contracts  itself,  after  it  has  passed  the 
orifice,  for  the  distance  of  about  half  its  diameter,  so  that  at  this  point  its 
thickness  is  only  four  fifths  as  great  as  at  its  passage  ;  and  the  quantity 
discharged  is  only  five  eighths  as  great  as  that  which  the  whole  orifice 
would  furnish,  according  to  the  preceding  calculation  :  instead,  therefore, 
of  multiplying  the  square  root  of  the  height  by  8,  we  may  employ  the 
multiplier  5  for  determining  the  actual  discharge.  But  the  velocity,  where 
the  stream  is  most  contracted,  is  only  one  thirtieth  less  than  that  which  is 
due  to  the  whole  height ;  and  when  the  jet  is  discharged  in  a  direction 
nearly  perpendicular,  it  rises  almost  as  high  as  the  surface  of  the  fluid  in 
the  reservoir. 

This  contraction  of  the  stream,  and  the  consequent  diminution  of  the 
discharge,  is  unquestionably  owing  to  the  interference  of  the  particles  of  the 
fluid  coming  from  the  parts  on  each  side  of  the  orifice,  with  those  which 
are  moving  directly  towards  it ;  and  the  effect  is  more  perceptible  when 
the  orifice  is  made  by  a  pipe  projecting  within  the  reservoir,  so  that  some 
of  the  particles  approaching  it  must  acquire  in  their  path  a  motion  contrary 
to  that  of  the  stream.  It  would  be  possible  to  obtain  an  approximate  cal- 
culation of  the  magnitude  of  this  contraction,  from  the  equilibrium  which 
must  subsist  between  the  centrifugal  forces  of  the  particles,  as  they  pass 
out  of  the  orifice,  describing  various  curves,  according  to  their  various 
situations,  and  the  pressure  required  for  the  contraction  of  the  internal 
parts  of  the  stream,  which  obliges  the  particles  to  move  more  rapidly  as 
they  proceed,  and  which  must  be  proportional  to  the  height  required  for 
producing  this  acceleration.  (Plate  XX.  Fig.  255.) 

When  a  short  cylindrical  tube  is  added  to  the  orifice,  it  is  probable  that 
the  motion  of  the  fluid  within  the  tube  is  still  in  some  measure  similar  : 
but  the  vessel  must  now  be  supposed  to  be  prolonged,  and  to  have  a  new 
orifice  at  the  end  of  the  tube,  at  which  the  particles  cannot  arrive  by  any 
lateral  motions,  and  which  will,  therefore,  not  be  liable  to  a  second  con- 
traction :  the  discharge  may,  therefore,  be  estimated  nearly  according  to 
the  true  measure  of  this  orifice  ;  the  original  pressure  of  the  fluid  continuing 
to  act  until  the  stream  escapes. 

The  effect  of  a  short  pipe  in  increasing  the  discharge,  ceases  when  the 


ON  THE  THEORY  OF  HYDRAULICS.  213 

water  separates  from  its  sides,  so  that  it  is  no  longer  filled  by  the  stream  : 
'since  there  is  then  nothing  to  distinguish  its  motion  from  that  of  a  stream 
passing  through  a  simple  orifice  :  but  the  increase  is  not  owing  merely  to 
the  cohesion  of  the  water  to  the  sides  of  the  pipe  ;  for  the  effect,  as  I  have 
found  by  experiment,  is  nearly  the  same  in  the  motion  of  air  as  in  that  of 
water.  The  contraction  caused  by  the  motion  of  the  water  at  the  entrance 
of  the  short  pipe,  may  be  considered  simply  as  a  contraction  in  the  pipe 
itself,  and  the  subsequent  part  of  the  pipe  either  as  cylindrical  or  as  nearly 
conical :  for  in  this  case  it  follows,  from  the  general  law  on  which  Ber- 
noulli's calculations  are  founded,  that  as  long  as  the  fluid  remains  in  one 
mass,  the  discharge  will  be  nearly  the  same,  as  if  the  mouth  of  the  pipe 
were  the  only  orifice,  supposing  that  no  force  is  lost :  and  the  exceptions 
which  Bernoulli  has  made  to  the  general  application  of  the  principle  in 
such  cases,  although  partly  supported  by  experiments,  have  been  extended 
somewhat  further,  both  by  himself  and  by  other  authors,  than  those  ex- 
periments have  warranted.  In  the  case  of  a  diverging  conical  pipe,  or  of  a 
pipe  with  a  conical  termination,  the  discharge  is  found  to  be  considerably 
greater  than  that  which  a  cylindrical  pipe  would  produce,  but  not  quite  so 
great  as  would  be  produced  on  the  supposition  that  no  force  is  lost.  (Plate 
XX.  Fig.  256.) 

This  analogy  between  the  effects  of  a  cylindrical  and  conical  pipe  is 
strongly  supported  by  the  experiments  of  Venturi,*  compared  with  those 
of  Bernoulli.  Bernoulli  found  that  when  a  small  tube  was  inserted  into 
any  part  of  a  conical  pipe,  in  which  the  water  was  flowing  towards  the 
wider  end,  not  only  none  of  the  water  escaped  through  the  tube,  but  the 
water  of  a  vessel,  placed  at  a  considerable  distance  below,  was  drawn  up  by 
it  ;t  Venturi  observed  the  same,  when  the  tube  was  inserted  into  the  side 
of  a  cylindrical  pipe,  near  to  its  origin  ;  and  in  both  cases  air  was  absorbed, 
as  well  as  water,  so  that  cohesion  could  not  be  in  any  manner  concerned.^ 
But  the  pressure  of  the  atmosphere  is  generally  necessary  for  all  effects  of 
this  kind,  and  both  VenturiJ  and  Dr.  Matthew  Young§  have  observed, 
that  a  short  pipe  has  no  effect,  in  increasing  the  discharge  through  an 
orifice,  in  the  vacuum  of  an  air  pump  :  but  even  if  the  difference  were 
sometimes  found  to  exist  in  the  absence  of  atmospherical  pressure,  it  might 
be  produced  by  an  accidental  cohesion,  like  that  which  sometimes  causes  a 
column  of  mercury  to  remain  suspended  in  similar  circumstances.  (Plate 
XX.  Fig.  257.) 

The  effect  of  ajutages  of  different  kinds,  on  the  quantity  of  water  dis- 
charged through  an  orifice  of  a  given  magnitude,  may  be  most  conveniently 
exhibited  by  placing  them  side  by  side  at  the  same  height  in  a  reservoir, 
and  suffering  the  water  to  begin  to  flow  at  the  same  moment  through  any 
two  of  them  ;  the  quantities  discharged  in  a  given  time  will  then  obviously 
indicate  the  respective  velocities.  If  a  very  long  pipe  were  employed,  some 
time  would  be  required  before  the  velocity  became  uniform  ;  but  in  such 

*  Surla  Communication  Laterale  du  Mouvement  dans  les  Fluides,  Par.  1797. 

t  Hydrodyn   p.  47.     See  D'Alembert,  Trait6  des  Fluides,  Art.  149. 

J  Exp.  2  and  7. 

§  Transactions  of  the  Royal  Irish  Academy,  ii.  8}  ;  vii.  53. 


214  LECTURE  XXIII. 

cases  the  retardation  arising  from  friction  is  so  considerable  as  to  cause  a 
still  greater  deviation  from  the  quantity  which  would  be  discharged  by  a' 
shorter  pipe  in  the  same  time. 

When  the  aperture  through  which  a  fluid  is  discharged,  instead  of  being 
every  way  of  inconsiderable  magnitude,  is  continued  throughout  the  height 
of  the  vessel,  and  is  every  where  of  equal  breadth,  the  velocity  must 
be  materially  different  at  different  parts  of  its  height ;  but  we  may  find  the 
quantity  of  the  discharge,  by  supposing  the  whole  velocity  equal  to  two 
thirds  of  the  velocity  at  the  lowest  point.  And  we  may  find  the  quantity 
discharged  by  an  orifice  not  continued  to  the  surface,  but  still  of  consider- 
able height,  by  subtracting  from  the  whole  discharge  of  an  orifice  so 
continued,  that  which  would  have  been  produced  by  such  a  portion  of  it, 
as  must  be  shut  up  in  order  to  form  the  orifice  actually  existing.  But  in 
this  case,  the  result  will  seldom  differ  materially  from  that  which  is  found 
by  considering  the  pressure  on  the  whole  orifice,  as  derived  from  the  height 
of  the  fluid  above  its  centre. 

When  a  cylindrical  vessel  empties  itself  by  a  minute  orifice,  the  velocity 
of  the  surface,  which  is  always  in  the  same  proportion  to  the  velocity  of 
the  fluid  in  the  orifice,  is,  therefore,  uniformly  retarded  and  follows  in  its 
descent  the  same  law  as  a  heavy  body  projected  upwards,  in  its  ascent ; 
consequently  the  space  actually  described,  in  the  whole  time  of  descent,  is 
equal  to  half  of  that  which  would  have  been  described,  if  the  initial  motion 
had  been  uniformly  continued  ;  and  in  the  time  that  such  a  vessel  occupies 
in  emptying  itself,  twice  the  quantity  of  the  fluid  would  be  discharged  if  it 
were  kept  full  by  a  new  supply.  This  may  be  easily  shown,  by  filling  two 
cylindrical  vessels,  having  equal  orifices  in  their  bottoms,  and  while  the  one 
is  left  to  empty  itself,  pouring  into  the  other  the  contents  of  two  other  equal 
vessels  in  succession,  so  as  to  keep  it  constantly  full ;  for  it  will  be  seen 
that  both  operations  will  terminate  at  the  same  instant. 

A  similar  law  may  be  applied  to  the  filling  of  a  lock  from  a  reservoir  of 
constant  height ;  for  in  all  such  cases,  twice  as  long  a  time  is  required  for 
the  effect,  as  would  be  necessary  if  the  initial  velocity  were  continued.  The 
immersion  of  the  orifice  in  a  large  reservoir  has  been  found  to  make  no 
difference  in  the  magnitude  of  the  discharge,  so  that  the  pressure  may 
always  be  estimated  by  the  difference  of  the  levels  of  the  two  surfaces. 
Thus,  when  a  number  of  reservoirs  communicate  with  each  other  by  ori- 
fices of  any  dimensions,  the  velocity  of  the  fluid  flowing  through  each 
orifice  being  inversely  as  the  magnitude  of  the  orifice,  and  being  produced 
by  the  difference  of  the  heights  of  the  fluid  in  the  contiguous  reservoirs,  this 
difference  must  be  every  where  as  the  square  of  the  corresponding  velocity. 
But  if  the  reservoirs  were  small,  and  the  orifices  opposite  and  near  to  each 
other,  a  much  smaller  difference  in  the  heights  of  the  surfaces  would  be 
sufficient  for  producing  the  required  velocity.  The  same  circumstances 
must  be  considered,  in  determining  the  velocity  of  a  fluid  forced  through  a 
vessel  divided  by  several  partitions,  with  an  orifice  in  each ;  if  the  orifices 
are  small  in  proportion  to  their  distance  from  each  other,  and  if  they  &re 
turned  in  different  directions,  each  orifice  will  require  an  additional  pres- 
sure, equivalent  to  the  whole  velocity  produced  in  it :  but  if  the  partitions 


ON  THE  THEORY  OF  HYDRAULICS.        215 

occupy  a  small  part  only  of  the  vessel,  and  are  placed  near  to  each  other, 
'  the  retardation  will  be  much  less  considerable.  Cases  of  this  kind  occur 
very  frequently  in  the  passage  of  water  through  the  pipes  and  valves  of 
pumps,  and  it  is,  therefore,  of  consequence  to  avoid  all  unnecessary  expan- 
sions, as  well  as  contractions,  in  pipes  and  in  canals,  since  there  is  always 
a  useless  expense  of  force  in  restoring  the  velocity  which  is  lost  in  the 
wider  parts. 

When  a  siphon  or  bent  tube  is  filled  with  a  fluid,  and  its  extremities  are 
immersed  in  fluids  of  the  same  kind  contained  in  different  vessels,  if  both 
their  surfaces  are  on  the  same  level,  the  whole  remains  at  rest ;  but  if 
otherwise,  the  longer  column  in  the  siphon  preponderates,  and  the  pressure 
of  the  atmosphere  forces  up  the  fluid  from  the  higher  vessel,  until  the  equi- 
librium is  restored ;  provided,  however,  that  this  pressure  be  sufficiently 
powerful :  for  if  the  height  of  the  tube  were  more  than  34  feet  for  water, 
or  than  30  inches  for  mercury,  the  pressure  of  the  atmosphere  would  be 
incapable  of  forcing  up  the  fluid  to  its  highest  part,  and  this  part  remaining 
empty,  the  fluid  could  no  longer  continue  to  run.  (Plate  XX.  Fig.  258.) 

If  the  lower  vessel  be  allowed  to  empty  itself,  the  siphon  will  continue 
running  as  long  as  it  is  supplied  from  the  upper,  with  a  velocity  nearly 
corresponding  to  the  height  of  that  portion  of  the  fluid  in  the  longer  leg, 
which  is  not  counterbalanced  by  the  fluid  in  the  shorter  :  that  is,  to  the 
height  of  the  surface  of  the  upper  vessel  above  that  of  the  lower  one,  or 
above  the  end  of  the  siphon,  when  it  is  no  longer  immersed  ;  for  the  height 
of  the  pipe  is  in  all  cases  to  be  considered  as  constituting  a  part  of  that 
height  which  produces  the  pressure.  Thus  the  discharge  of  a  pipe,  descend- 
ing from  the  side  or  bottom  of  a  vessel,  is  nearly  the  same  as  from  a  similar 
horizontal  pipe,  inserted  into  a  reservoir  of  the  whole  height  of  the  descend- 
ing pipe  and  of  the  fluid  above  it ;  and  this  is  true  even  when  the  depth  of 
the  vessel  is  inconsiderable  in  comparison  with  the  length  of  the  pipe,  if  its 
capacity  is  sufficient  to  keep  the  pipe  running  full.  It  appears  at  first  sight 
extremely  paradoxical,  that  the  whole  water  discharged,  each  particle  of 
which  is  subjected  to  the  action  of  gravitation  in  a  pipe  16  feet  long,  for 
half  a  second  only,  should  acquire  the  velocity  of  32  feet  in  a  second,  which 
would  require,  in  common  circumstances,  the  action  of  the  same  force  of 
gravitation  for  a  whole  second,  and  this  fact  may  be  considered  as  favour- 
able to  the  opinion  of  those  who  wish  to  estimate  the  magnitude  of  a  force, 
rather  by  the  space  through  which  it  is  continued,  than  by  the  time  during 
which  it  acts  ;  but  if  we  attend  to  the  nature  of  hydrostatical  pressure,  we 
shall  find  that  the  effect  of  the  column  on  the  atmosphere  is  such  as  to  pro- 
duce, or  to  develope,  a  portion  of  accelerating  force  which  is  actually 
greater  than  the  weight  of  the  particles  immediately  concerned.  If  a  doubt 
could  be  entertained  of  the  truth  of  this  theory,  it  might  be  easily  removed 
by  recurring  to  the  general  law  of  ascending  force,  since  it  follows  from 
that  law,  that  each  particle,  which  descends  in  any  manner  through  the 
space  of  16  feet,  must  acquire,  either  for  itself  or  for  some  other  particles, 
af  power  of  ascending  to  the  same  height ;  and  on  the  other  hand,  the  event 
of  the  experiment  confirms  the  general  law.  For  if  we  fix  a  shallow  funnel 
on  a  vertical  pipe,  and  pour  water  into  it,  so  as  to  keep  it  constantly  full, 


216  LECTURE  XXIIT. 

while  the  pipe  discharges  itself  into  a  reservoir  out  of  which  the  water  runs 
through  a  second  pipe,  placed  horizontally,  of  exactly  the  same  dimensions 
with  the  first,  the  height  at  which  the  water  in  the  reservoir  becomes 
stationary,  will  be  very  nearly  equal  to  the  height  of  the  funnel  above  its 
surface,  so  that  the  same  height  produces  the  same  velocity  in  both  cases. 
(Plate  XX.  Fig.  259.) 

We  may  understand  the  action  of  the  forces  immediately  concerned  in 
this  experiment,  by  attending  to  the  mutual  effects  of  the  water  and  of  the 
atmosphere.  The  water  entering  the  orifice  must  immediately  acquire  a 
velocity  equal  to  that  of  the  whole  water  in  the  pipe,  otherwise  there  would 
be  a  vacuum  in  the  upper  part  of  the  pipe,  which  the  pressure  of  the  at- 
mosphere will  not  permit ;  and  this  pressure,  considered  as  a  hydrostatic 
force,  is  equal  to  that  which  would  be  derived  in  any  other  way  from  a 
column  of  the  same  height  with  the  pipe,  since  the  weight  of  the  water  in 
the  pipe  is  wholly  employed  in  diminishing  the  counterpressure  of  the 
atmosphere  below,  not  only  in  the  beginning,  when  it  is  at  rest,  but  also 
while  it  is  in  motion  ;  for  that  motion  being  uniform  throughout  its  descent, 
the  power  of  gravitation  is  expended  in  producing  pressure  only  :  so  that 
the  pressure  of  the  atmosphere  on  the  water  in  the  funnel  becomes  com- 
pletely analogous  to  the  pressure  of  a  reservoir  of  water,  of  the  same  height 
with  the  pipe.  The  circumstance  which  causes  the  appearance  of  paradox 
in  this  experiment,  exists  also  in  the  simplest  case  of  the  discharge  of 
water  ;  for  it  may  be  shown  that  the  portion  of  accelerating  force  actually 
employed  in  generating  the  velocity  with  which  a  stream  is  discharged 
through  a  small  orifice,  is  twice  as  great  as  the  pressure  of  the  fluid  on  a 
part  of  the  vessel  equal  in  extent  to  the  orifice  ;  and  in  the  same  manner  the 
quantity  of  force  exerted  by  the  atmosphere  on  the  water  in  the  funnel,  as 
well  as  that  with  which  the  descending  fluid  impels  the  air  below,  is  equal 
to  twice  the  weight  of  the  quantity  existing  at  any  time  in  the  pipe. 

There  is,  however,  a  limit,  which  the  mean  velocity  in  such  a  pipe  can 
never  exceed,  and  which  is  derived  from  the  magnitude  of  the  pressure  of 
the  atmosphere.  For  the  water  cannot  enter  the  pipe  with  a  greater 
velocity  than  that  with  which  it  would  enter  an  exhausted  pipe,  and  which 
is  produced  by  the  whole  pressure  of  the  atmosphere  ;  and  this  pressure 
being  equivalent  to  that  of  a  column  of  water  34  feet  high,  the  velocity  de- 
rived from  it  is  about  47  feet  in  a  second  :  so  that  if  the  vertical  pipe  were 
more  than  34  feet  long,  there  would  be  a  vacuum  in  a  part  of  it  near  the 
funnel. 

Wherever  a  pipe  of  considerable  length  descends  from  a  funnel,  if  the 
supply  of  the  fluid  be  scanty,  and  especially  if  it  approach  the  orifice  ob- 
liquely, the  pressure  of  the  amosphere,  and  the  centrifugal  force  of  the 
particles  which  must  necessarily  revolve  round  the  orifice,  will  unite  in 
producing  a  vacuity  in  the  centre ;  and  when  this  happens,  the  discharge 
is  considerably  diminished. 

In  order  that  a  siphon  may  run,  it  is  obvious  that  it  must  first  be  filled  ; 
and  when  it  is  once  filled,  it  will  continue  to  run  till  the  reservoir  ia 
exhausted,  as  far  as  the  level  of  its  upper  orifice.  And  from  this  cir- 
cumstance, the  phenomena  of  some  intermitting  springs  have  been  ex- 


ON  THE  THEORY  OF  HYDRAULICS.        217 

plained,*  which  only  begin  to  run  when  the  reservoirs  from  which  they 
originate  have  been  filled  by  continued  rains,  and  then  go  on  to  exhaust 
them,  even  though  the  weather  may  be  dry.  From  a  combination  of 
several  such  siphons  and  reservoirs,  a  great  number  of  alternations  may 
sometimes  be  produced.  (Plate  XX.  Fig.  260.) 

Since  the  velocity  of  a  stream  or  jet  issuing  in  any  direction,  out  of  a 
simple  orifice  or  a  converging  one,  is  nearly  equal  to  that  of  a  heavy  body 
falling  from  the  height  of  the  reservoir,  it  will  rise,  if  directed  upwards, 
very  nearly  to  the  same  height,  excepting  a  slight  difference  occasioned  by 
the  resistance  of  the  air,  and  by  the  force  which  is  lost  in  producing  the  ve- 
locity with  which  the  particles  must  escape  laterally,  before  they  begin  to 
descend.  The  truth  of  this  conclusion  is  easily  confirmed  by  experiment. 
(Plate  XX.  Fig.  261.) 

If  a  jet  issue  in  an  oblique  or  in  a  horizontal  direction,  its  form  will  be 
parabolic,  since  every  particle  tends,  as  a  separate  projectile,  to  describe  the 
same  parabola  in  its  range  :  and  it  may  be  demonstrated,  that  if  it  be 
emitted  horizontally  from  any  part  of  the  side  of  a  vessel,  standing  on  a 
horizontal  plane,  and  a  circle  be  described,  having  the  whole  height  of  the 
fluid  for  its  diameter,  the  jet  will  reach  the  plane,  at  a  distance  from  the 
vessel  twice  as  great  as  the  distance  of  that  point  of  the  circle,  through 
which  it  would  have  passed,  if  it  had  continued  to  move  horizontally. 
And  if  the  jet  rise  in  any  angle  from  the  bottom  of  the  vessel,  the  utmost 
height  of  its  ascent  will  be  equal  to  that  of  the  point  in  which  it  would  meet 
the  same  semicircle,  if  it  continued  to  move  in  a  right  line,  and  the  hori- 
zontal range  will  be  equal  to  four  times  the  distance,  intercepted  between 
the  same  point  and  the  side  of  the  vessel.  This  law  is  equally  true  with 
regard  to  simple  projectiles  :  but  the  experiment  is  most  conveniently  ex- 
hibited in  the  motion  of  a  jet.  (Plate  XX.  Fig.  262.) 

We  have  hitherto  considered  the  motions  of  fluids  as  continued  princi- 
pally in  the  same  direction  ;  but  they  are  frequently  subjected  to  alternations 
of  motion,  which  bear  a  considerable  analogy  to  the  vibrations  of  pendu- 
lums ;  thus,  if  a  long  tube  be  immersed  in  a  fluid,  in  a  vertical  direction, 
and  the  surface  of  the  fluid  within  the  tube  be  elevated  a  very  little,  by 
some  external  cause,  the  whole  contents  of  the  fluid  will  be  urged  down- 
wards by  a  force  which  decreases  in  proportion  to  the  elevation  of  the 
surface  above  the  general  level  of  the  vessel,  and  when  both  surfaces  have 
acquired  the  same  level,  the  motion  \vill  be  continued  by  the  inertia  of  the 
particles  of  the  fluid,  until  it  be  destroyed  by  the  difference  of  pressures, 
which  now  tends  to  retard  it ;  and  this  alternation  will  continue  until  the 
motion  be  destroyed  by  friction  and  by  other  resistances.  It  is  also  obvious, 
that  since  any  two  vibrations  in  which  the  forces  are  proportional  to  the 
spaces  to  be  described,  are  performed  in  equal  times,  these  alternations 
will  require  exactly  the  same  time  for  their  completion,  as  the  vibrations 
of  a  pendulum  of  which  the  length  is  equal  to  that  of  the  whole  tube  ;  for 
the  relative  force  in  the  tube  is  to  the  whole  force  of  gravity  as  the  elevation 

*  Regnault,  Philosophic  Conversations  (English  edition),  ii.  125.  Dechales,  De 
FontibusNaturalibus,  Tr.  7,  Prop.  15.  Desaguliers,  Ph.  Tr.  No.  384.  Atwell,  Ph. 
Tr.  xxxvii.  301. 


218  LECTURE  XXIII. 

or  depression  is  to  the  whole  length  of  the  tube.  Hence  it  follows,  that  if 
two  such  tubes  were  united  below,  so  as  to  form  a  single  bent  tube,  the' 
vibrations  might  take  place  in  the  whole  compound  tube,  in  the  same 
manner,  and  in  the  same  time,  as  in  each  of  the  separate  tubes  ;  nor  would 
the  effects  be  materially  altered  if  any  part  of  the  middle  of  the  tube  were 
in  a  horizontal  or  in  an  oblique  direction,  provided  that  the  whole  length 
remained  unaltered.  In  such  a  tube,  also,  all  vibrations,  even  if  of  con- 
siderable extent,  would  be  performed  in  the  same  time,  and  would  long 
remain  nearly  of  the  same  magnitude  ;  but  in  a  single  tube,  open  below, 
the  vibrations  would  continually  become  less  extensive,  and  their  duration 
would  also  be  altered  as  well  as  their  extent;  besides  the  unavoidable 
resistances,  which  would  in  both  cases  interfere  with  the  regularity  of  the 
effects. 

But  it  does  not  appear  that  the  laws  of  the  vibrations  of  fluids  in  pipes 
will  at  all  serve  to  elucidate  the  phenomena  of  waves.  Sir  Isaac  Newton  * 
has  supposed  that  each  wave  may  be  compared  with  the  fluid  oscillating  in 
a  bent  pipe  ;  but  the  analogy  is  by  far  too  distant  to  allow  us  to  found  any 
demonstration  on  it.  The  motions  of  waves  have  been  investigated  in  a 
new  and  improved  manner  by  Mr.  Lagrange  ;t  and  I  have  given  a  concise 
demonstration  of  a  theorem  similar  to  his,  but  perhaps  still  more  general 
and  explicit.  It  appears  from  these  determinations,  that  supposing  the 
fluids  concerned  to  be  infinitely  elastic,  that  is,  absolutely  incompressible, 
and  free  from  friction  of  all  kinds,  any  small  impulse  communicated  to  a 
fluid,  would  be  transmitted  every  way  along  its  surface  with  a  velocity 
equal  to  that  which  a  heavy  body  would  acquire  in  falling  through  half 
the  depth  of  the  fluid  ;  and  I  have  reason  to  believe,  from  observation  and 
experiment,  that  where  the  elevation  or  depression  of  the  surface  is  con- 
siderably extensive  in  proportion  to  the  depth,  the  velocity  approaches 
nearly  to  that  which  is  thus  determined,  being  frequently  deficient  one 
eighth  or  one  tenth  only  of  the  whole  ;  in  other  cases,  where  a  number  of 
small  waves  follow  each  other  at  intervals  considerably  less  than  the  depth, 
I  have  endeavoured  to  calculate  the  retardation  which  must  be  occasioned 
by  the  imperfect  elasticity  or  compressibility  of  the  fluid  ;  but  it  seems 
probable  that  the  motion  of  small  waves  is  still  much  slower  than  this 
calculation  appears  to  indicate. 

Whatever  corrections  these  determinations  of  the  velocity  of  waves  may 
be  found  to  require,  the  laws  of  their  propagation  may  still  be  safely 
inferred  from  the  investigation.  Thus,  it  may  be  shown,  supposing  the 
waves  to  flow  in  a  narrow  canal  of  equable  depth,  that,  whatever  the 
initial  figure  of  the  waves  may  be,  every  part  of  the  surface  of  the  fluid 
will  assume  in  succession  the  same  form,  except  that  the  original  elevations 
and  depressions,  extending  their  influence  in  both  directions,  will  produce 
effects  only  half  as  great  on  each  side,  and  those  effects  will  then  be  con- 
tinued until  they  are  destroyed  by  resistances  of  various  kinds.  It  may 
also  be  inferred  that  the  surface  of  a  fluid  thus  agitated  by  any  series  of 
impressions,  will  receive  the  effects  of  another  series,  in  the  same  manner 

*  Principia,  Lib.  II.  Prop.  46. 

f  Mecanique  Analytique,  2de  Partie,  §  xi. 


ON  THE  THEORY  OF  HYDRAULICS.  219 

as  a  horizontal  surface,  and  that  the  undulations,  thus  crossing  each  other, 
'will  proceed  without  any  interruption,  the  motion  of  each  particle  being 
always  the  sum  or  difference  of  the  motions  belonging  to  the  separate 
series. 

Supposing  two  equal  and  similar  series  of  waves  to  meet  each  other  in 
such  a  canal,  in  opposite  directions,  the  point  in  which  their  similar  parts 
meet  must  be  free  from  all  horizontal  motion,  so  that  any  fixed  obstacle  in 
an  upright  position  would  have  the  same  effect  on  the  motions  of  the  fluid 
on  either  side  as  the  opposition  of  a  similar  series  ;  and  this  effect  con- 
stitutes the  reflection  of  a  series  of  waves,  which  is  easily  observed,  when 
they  strike  against  a  steep  wall  or  bank  ;  and  when  this  reflection  is 
sufficiently  regular,  it  is  easy  to  show  that  the  combination  of  the  direct 
with  the  reflected  motions  must  constitute  a  vibration  of  such  a  nature, 
that  the  whole  surface  is  divided  into  portions  which  appear  to  vibrate 
alternately  upwards  and  downwards,  without  any  progressive  motion, 
while  the  points  which  separate  the  portions  remain  always  in  their  natural 
level.  (Plate  XX.  Fig.  263.) 

But  those  series  of  waves  which  are  usually  observable  in  any  broad 
surface,  and  which  constitute  a  number  of  concentric  circles,  are  usually 
reflected  in  such  a  manner  as  to  appear  to  diverge  after  reflection  from  a 
centre  beyond  the  surface  which  reflects  them,  and  to  be  subject  to  all  those 
laws,  which  are  more  commonly  noticed  in  the  phenomena  of  reflected  light ; 
but  as  these  laws  are  of  more  practical  importance  in  their  application  to 
optics,  than  to  hydraulics,  it  is  unnecessary  at  present  to  examine  their 
consequences  in  detail.  It  may,  however,  be  easily  understood,  that  a  new 
series  of  waves,  proceeding  from  a  centre  at  the  same  distance  behind  the 
reflecting  surface  as  the  centre  of  the  original  series  is  before  it,  would  pro- 
duce precisely  the  same  effect  as  a  fixed  obstacle  ;  consequently  the  law  of 
reflection  at  equal  angles  is  a  very  simple  inference  from  this  mode  of  rea- 
soning. (Plate  XX.  Fig.  264.) 

When  a  series  of  waves  proceeds  in  an  equable  canal,  it  is  obvious  that 
the  centre  of  gravity  of  the  whole  fluid  neither  rises  nor  falls;  from  this 
analogy,  as  well  as  from  the  general  application  of  the  law  of  ascending 
force,  it  is  probable  that  in  all  cases  of  the  propagation  of  waves,  the  place 
of  the  centre  of  gravity  remains  unaltered  ;  so  that  when  a  circular  wave 
spreads  further  and  further  from  its  centre,  its  height  is  not  diminished  in 
the  same  ratio  as  its  diameter  is  increased,  but  the  square  of  its  height 
only  varies  in  this  proportion ;  that  is,  a  wave  which  is  a  yard  in  diameter, 
and  an  inch  high,  will  retain  a  height  of  half  an  inch,  when  its  diameter  is 
increased  to  four  yards. 

Many  of  the  phenomena  of  waves  may  be  very  conveniently  exhibited, 
by  means  of  a  wide  and  shallow  vessel,  with  a  bottom  of  glass,  surrounded 
by  sides  inclined  to  the  horizon,  in  order  to  avoid  the  confusion  which  would 
arise  from  the  continual  reflections  produced  by  perpendicular  surfaces. 
The  waves  may  be  excited  by  the  vibrations  of  an  elastic  rod  or  wire, 
loaded  with  a  weight,  by  means  of  which  its  motions  may  be  made  more  or 
less  rapid  at  pleasure ;  and  the  form  and  progress  of  the  waves  may  be 
easily  observed,  by  placing  a  light  under  the  vessel,  so  that  their  shadows 


220  LECTURE  XXIII. 

may  fall  on  a  white  surface,  extending  in  an  inclined  position  above.  In 
this  manner  the  minutest  inflections  of  the  surface  of  the  water  may  be 
made  perfectly  conspicuous.  (Plate  XX.  Fig.  265.) 

By  means  of  this  apparatus,  we  may  examine  the  manner  in  which  a 
wave  diverges,  when  a  portion  of  it  has  been  intercepted  on  either  side  or  on 
both  sides.  Thus,  if  a  wave  is  admitted,  by  an  aperture  which  is  very 
narrow  in  proportion  to  its  own  breadth,  into  the  surface  of  a  part  of  the 
water  which  is  at  rest,  it  diverges  from  the  aperture  as  from  a  new  centre  ; 
but  when  the  aperture  is  considerably  wider  than  the  wave,  the  wave  con- 
fines its  motion  in  great  measure  to  its  original  direction,  with  some  small 
divergence,  while  it  is  joined  on  each  side  by  fainter  circular  portions, 
spreading  from  the  angles  only.  (Plate  XX.  Fig.  266.) 

When  two  equal  series  of  circular  wraves,  proceeding  from  centres  near 
each  other,  begin  their  motions  at  the  same  time,  they  must  so  cross  each 
other  in  some  parts  of  their  progress,  that  the  elevations  of  the  one  series 
tend  to  fill  up  the  depressions  of  the  other  ;  and  this  effect  may  be  actually 
observed,  by  throwing  two  stones  of  equal  size  into  a  pond  at  the  same 
instant ;  for  we  may  easily  distinguish,  in  favourable  circumstances,  the 
series  of  points  in  which  this  effect  takes  place,  forming  continued  curves, 
in  which  the  water  remains  smooth,  while  it  is  strongly  agitated  in  the 
intermediate  parts.  These  curves  are  of  the  kind  denominated  hyperbolas, 
each  point  of  the  curve  being  so  situated  with  respect  to  its  foci,  as  to  be 
nearer  to  one  than  the  other  by  a  certain  constant  distance.  (Plate  XX. 

Fig.  267.) 

The  subject  of  waves  is  of  less  immediate  importance  for  any  practical 
application  than  some  other  parts  of  hydraulics ;  but  besides  that  it  is 
intimately  connected  with  the  phenomena  of  the  tides,  it  affords  an  elegant 
employment  for  speculative  investigation,  and  furnishes  us  with  a  sensible 
and  undeniable  evidence  of  the  truth  of  some  facts,  which  are  capable  of 
being  applied  to  the  explanation  of  some  of  the  most  interesting  phenomena 
of  acustics  and  optics. 

It  may  be  shown,  by  steps  nearly  similar  to  those  by  which  the  velocity 
of  the  motions  of  waves  is  investigated,  that  a  fluid  which  is  contained  in  an 
elastic  pipe,  and  which  receives  an  impulse  at  any  part  of  the  pipe,  will 
transmit  its  effects  with  the  same  velocity  as  a  wave  would  have  in  a 
reservoir,  of  that  depth  which  measures  the  elasticity  of  the  pipe,  that  is, 
with  half  the  velocity  which  a  body  would  acquire  in  falling  from  the 
height  at  which  a  portion  of  the  fluid  connected  with  the  contents  of  the 
pipe,  would  stand  in  a  vertical  tube.  It  is  in  this  manner  that  the  blood  is 
transmitted,  by  means  of  the  impulse  given  to  it  by  the  heart  through  the 
blood  vessels ;  the  pulse  moves  on  with  great  rapidity,  the  elastic  force  of 
the  vessels  being  considerably  assisted  by  the  temporary  actions  of  the  mus- 
cular coats  of  the  arteries,  which  cause  a  contraction  more  rapid  than  the 
dilatation ;  while  the  whole  mass  of  the  arterial  blood  continues  at  the  same 
time  to  advance  with  a  much  smaller  velocity  ;  like  the  slow  stream  of  a 
river,  on  the  surface  of  which  undulations  are  continually  propelled  with 
motions  independent  of  its  own. 


ON  THE  THEORY  OF  HYDRAULICS.        221 

LECT.  XXIII.— ADDITIONAL  AUTHORITIES. 

Theory  of  Hydraulics. —  See  Lect.  XXI.  Baliani,  De  Motu  Gravium,  4to, 
Geneva,  1646.  Sturmius  de  Clepsydrarum  Phenomenis  et  Eflfectibus,  4to,  1674. 
Mariotte,  Traite  du  Mouvement  des  Eaux,  Paris,  1686.  Varignon,  Hist,  et  Mem. 
de  Paris,  ii.  162,  1703,  p.  238,  H.  125.  Picard,  ibid.  vii.  323.  Lahire,  ibid.  x. 
162,  264.  Saulmon,  ibid.  1712,  p.  279,  H.77;  1714,  p.  381,  H.  102;  1715,  p.  61, 
H.  61  ;  1716,  p.  244,  H.  68.  Polenus,  De  Motu  Aquae  Mixto,  4to,  Patavii,  1717. 
Da  Castellis  per  quse  Derivantur  Fluviorum  Aquae,  Pat.  1718.  Desaguliers  on  the 
Running  of  Water  in  Pipes,  Ph.  Tr.  1726,  p.  77.  Eames  on  the  Estimation  of 
Force  in  Hydraulic  Experiments,  ibid.  1727,  p.  343.  D.  Bernoulli  on  the  Motion, 
Action,  and  lateral  Pressure  of  Fluids.  Com.  Petr.  ii.  Ill,  304  ;  iv.  194.  Pitot, 
Hist,  et  Mem.  1730,  p.  336,  H.  110.  Guglielmini,  Com.  Bon.  i.  545.  Couplet, 
Hist,  et  Mem.  1732,  p.  113,  H.  107.  Dufay,  ibid.  1736,  p.  191,  H.  118.  Clare 
on  the  Motion  of  Fluids,  1737.  Jo.  Bernoulli  on  the  Motion  of  Water  in  Pipes, 
Com.  Petr.  ix.  3,  19;  x.  Opuscula,  4.  Krafft,  ibid.  x.  207.  Ja.  Bernoulli, 
Opera,  vol.  iv.  Petit  Vandin,  Mem.  des  Savans  Etrangers,  i.  261.  Euler  on  the 
Motion  of  Water  in  Pipes.  Hist.  etMem.  de  Berlin,  1752,  p.  111.  On  the  Re- 
action of  Water  in  Pipes.  Nov.  Com.  Petr.  vi.  312.  Borda  on  the  Discharge  of 
Fluids.  Hist,  et  Mem.  1766,  p.  579,  H.  143.  Kastner,  Nov.  Com.  Gott.  1769, 
i.  45.  Matteuci,  Com.  Bon.  vi.  286  ;  Michelotti,  Sperienze  Idrauliche,  2  vols.  4to. 
Turin,  1771.  D'Alembert,  Opuscules,  vi.  Lagrange,  Hist,  et  Mem.  de  Berlin, 
1781,  p.  151.  Ximenes,  Nuove  Sperienze  Idrauliche.  Riccati,  Memorie  di  Ma- 
tematica  e  Fisica  della  Societa  Italiana,  4to,  Verona,  iii.  238.  Lorgna,  ibid.  iv.  369. 
On  Weres,  ibid.  v.  313.  On  Castelli's  Principle,  ibid.  vi.  218.  Bonati,  ibid.  v.  501. 
Stratico,  ibid.  v.  525.  Girard  on  the  Pressure  of  running  Water,  Journal  de 
Physique,  xlii.  429.  Banks,  Manchester  Mem.  v.  398.  Young  on  the  Discharge  of 
a  vertical  Pipe,  Journal  of  the  Royal  Institution,  vol.  i.  Eytelwein,  Me'm.  de  Berlin, 
1814,  1815.  Prony,  Journal  de  1'Ecole  Poly  technique,  vol.  iii.  Bidone,  Experiences 
sur  la  Forme  et  la  Direction  des  Veines  et  des  Courans  d'Eau.  Mem.  de  Turin, 
1822,  1824,  p.  281  ;  1830,  p.  229 ;  1838,  p.  1  ;  et  Mem.  della  Soc.  Ital.  vol.  xxi. 
D'Aubuisson,  Traite  du  Mouvement  de  1'Eau  dans  les  Tuyaux  de  Conduite,  Paris, 
1827.  Traite  d'Hydraulique  a  TUsage  des  Ingenieurs,  Paris,  1834.  Annales  de 
Chimie,  1830,  p.  225.  Corancez,  Theorie  du  Mouvement  de  1'Eau  dans  les  Vases, 
Paris,  1830.  Mallet,  Notices  Historiques,  1830.  Navier,  Mem.  de  1'Acad.  1830, 
vol.  ix.  Hachette,  Experiences  sur  le  Mouvement  des  Fluides,  Paris,  1830. 
Poncelet  et  Lesbros,  Experiences  Hydrauliques  sur  les  Lois  de  1'Ecoulement  de 
1'Eau,  4to,  Paris,  1832.  Savart,  Comptes  Rendus,  1833.  Rennie,  Ph.  Tr.  1831, 
and  Report  of  the  British  Association,  1833,  p.  153. 

Waves. — Laplace,  Mem.  de  1'Acad.  1776.  D'Alembert,  Encyclopedic,  art. 
Onde.  Lagrange,  Mem.  de  1'Acad.  de  Berlin,  1781,  1786,  p.  192.  Flaguergues, 
Journal  des  Savans,  Oct.  1789.  Bremontier,  Recherches  sur  le  Mouvement  des 
Ondes,  Paris,  1809.  Poisson,  Mem.  de  1'Institut,  1816,  vol.  viii.  Cauchy,  Mem. 
des  Savans  Etrangers,  vol.  i.  Bidone,  Mem.  de  Turin,  1826,  p.  195.  Weber, 
Wellenlehre  auf  Experimente  Gegrundet,  Leipz.  1825.  Challis,  Trans,  of  the  Camb. 
Phil.  Soc.  vols.  iii.  and  v.  Earnshaw,  ibid.  vi.  203.  Green,  ibid.  vol.  vi.  Russell, 
Trans,  of  the  Roy.  Soc.  of  Edinb.  v.  xiv.  p.  47.  Kelland,  ibid.  vol.  xiv.  p.  497  ; 
xv.  101.  Report  of  the  British  Assoc.  1837,  p.  417.  Airy  on  Tides  and  Waves, 
Encyc.  Metrop. 


222 


LECTURE  XXIV. 


ON  THE  FRICTION  OF  FLUIDS. 

WE  have  hitherto  considered  the  motions  of  fluids  independently  of  the 
resistance  which  they  undergo  from  the  vessels  containing  them  and  from 
the  surfaces  in  contact  with  them,  as  well  as  from  the  interference  of  the 
neighbouring  particles  with  each  other  ;  there  is,  however,  a  variety  of 
cases  of  very  common  occurrence,  in  which  these  frictions  most  materially 
affect  the  results  of  our  calculations  ;  so  that  before  this  subject  was  labo- 
riously and  judiciously  investigated  by  the  Chevalier  du  Buat,*  it  was 
almost  impossible  to  apply  any  part  of  our  theoretical  knowledge  of  hy- 
draulics to  practical  purposes. 

The  effect  of  friction  is  particularly  exemplified  by  the  motions  of  rivers, 
in  which  almost  the  whole  force  of  gravity  is  employed  in  overcoming  it. 
When  the  inclination  and  the  dimensions  of  a  river  continue  uniform,  the 
velocity  is  also  every  where  equal ;  for  otherwise  the  depth  would  become 
unequal :  here,  therefore,  the  force  of  gravitation  must  be  an  exact  counter- 
poise to  the  resistance  which  is  to  be  overcome,  in  order  that  the  water  may 
flow  with  its  actual  velocity  :  this  velocity  having  been  originally  derived 
from  the  effect  of  a  greater  inclination  near  the  origin  of  the  river.  When 
the  river  is  thus  proceeding,  with  an  equable  motion,  it  is  said  to  be  in  train ; 
and  it  is  obvious  that  no  increase  of  its  length  will  produce  any  alteration 
in  its  velocity.  There  is,  therefore,  a  very  material  difference  between  the 
course  of  a  river,  and  the  descent'  of  a  body,  with  an  accelerated  motion, 
along  an  inclined  surface.  For  when  a  solid  body  is  placed  on  an  inclined 
plane,  the  force  of  friction  is  either  great  enough  to  overpower  its  relative 
weight,  and  to  retain  it  at  rest,  or  else  the  friction  is  constantly  less  than 
the  gravitation,  and  the  motion  is  always  accelerated.  But  the  resistance 
to  the  motions  of  fluids  arises  principally  from  different  causes  ;  not  from 
the  tenacity  of  the  fluids,  which,  where  it  exists,  is  a  force  nearly  uniform 
like  that  of  friction,  but  principally  from  the  irregular  motions  and  mutual 
collisions  of  their  particles;  and  in  this  case,  according  to  the  laws  of 
mechanics,  it  must  vary  nearly  in  proportion  to  the  square  of  the  velocity. 
For  when  a  body  is  moving  in  a  line  of  a  certain  curvature,  the  centrifugal 
force  is  always  as  the  square  of  the  velocity  ;  and  the  particles  of  water  in 
contact  with  the  sides  and  bottom  of  a  river  or  pipe,  must  be  deflected,  in 
consequence  of  the  minute  irregularities  of  the  surfaces  on  which  they  slide, 
into  nearly  the  same  curvilinear  paths,  whatever  their  velocity  may  be,  so 
that  the  resistance,  which  is  in  great  measure  occasioned  by  this  centrifugal 
force,  must  also  vary  as  the  square  of  the  velocity.  Thus  also  the  curva- 
ture assumed  by  the  outline  of  a  stream  of  water  issuing  from  a  simple 
orifice  which  constitutes  the  contraction  already  described,  is  very  nearly 

*  Principes  d'Hydraulique,  1786,  and  Svols.  1816. 


ON  THE  FRICTION  OF  FLUIDS.  223 

the  same,  whatever  the  velocity  may  be  :  nor  does  the  friction  increase  with 
the  pressure,  as  is  demonstrated  by  an  experiment  of  Professor  Robison 
on  the  oscillations  of  a  fluid  through  a  bent  tube,  terminated  by  two  bulbs, 
which  were  performed  in  the  same  time,  whether  the  tube  was  in  a  hori- 
zontal or  in  a  vertical  position.  Mr.  Coulomb  has  also  proved  the  same 
fact  by  experiments  on  the  vibrations  of  bodies  immersed  in  fluids,  and 
suspended  by  twisted  wires  ;  he  finds  that  precisely  at  the  surface,  the 
friction  is  somewhat  greater  than  at  any  depth  below  it :  he  also  considers 
a  certain  part  of  the  friction  as  simply  proportional  to  the  velocity,  and 
a  very  small  portion  only,  in  common  fluids,  as  perfectly  independent 
of  it.* 

It  is  obvious  that  wherever  the  friction  varies  as  the  square  of  the  velo- 
city, or  even  when  it  increases  in  any  degree  with  the  velocity,  there  must 
always  be  a  limit,  which  the  velocity  can  never  exceed  by  means  of  any 
constant  force,  and  this  limit  must  be  the  velocity  at  which  the  resistance 
would  become  equal  to  the  force.  It  is  for  this  reason  that  a  light  body, 
descending  through  the  air,  soon  acquires  a  velocity  nearly  uniform  ;  and 
if  it  be  caused,  by  any  external  force,  to  move  for  a  time  more  rapidly,  it 
will  again  be  speedily  retarded,  until  its  velocity  be  restored  very  nearly  to 
its  original  state.  In  the  same  manner  the  weight  of  the  water  in  a  river, 
which  has  once  acquired  a  stationary  velocity,  is  wholly  employed  in  over- 
coming the  friction  produced  by  the  bottom  and  the  banks. 

From  considering  the  effect  of  the  magnitude  of  the  surface  exposed  to 
the  friction  of  the  water,  in  comparison  with  the  whole  quantity  contained 
in  the  river,  together  with  the  degree  in  which  the  river  is  inclined  to  the 
horizon,  we  may  determine,  by  following  the  methods  adopted  by  Mr. 
Buat,  the  velocity  of  any  river  of  which  we  know  the  dimensions  and  the 
inclination.  Supposing  the  whole  quantity  of  water  to  be  spread  on  a  hori- 
zontal surface,  equal  in  extent  to  the  bottom  and  sides  of  the  river,  the 
height  at  which  it  would  stand,  is  called  the  hydraulic  mean  depth  ;  and 
it  may  be  shown  that  the  square  of  the  velocity  must  be  jointly  propor- 
tional to  the  hydraulic  mean  depth,  and  to  the  fall  in  a  given  length.  If 
we  measure  the  inclination  by  the  fall  in  2800  yards,  the  square  of  the 
velocity  in  a  second  will  be  nearly  equal  to  the  product  of  this  fall  multi- 
plied by  the  hydraulic  mean  depth.  For  example,  in  the  Ganges,  and  in 
some  other  great  rivers,  the  mean  depth  being  about  30  feet,  and  the  fall  4 
inches  in  a  mile,  the  fall  in  2800  yards  will  be  about  6£  inches,  which, 
multiplied  by  360  inches,  gives  2340  inches  for  the  square  of  the  mean  ve- 
locity, and  48  £  inches,  or  about  four  feet,  for  the  mean  velocity  in  a  second, 
that  is,  not  quite  three  miles  an  hour,  which  is  the  usual  velocity  of  rivers 
moderately  rapid.  If,  however,  great  precision  were  required  in  the  deter- 
mination, some  further  corrections  would  be  necessary,  on  account  of  the 
deviation  of  the  resistance  from  the  exact  proportion  of  the  squares  of  the 
velocities ;  since  the  friction,  as  we  have  already  seen,  does  not  increase 
quite  so  fast  as  this. 
Jit  is  obvious  that  the  friction  of  a  fluid,  moving  on  the  surface  of  a  solid 

*  Hist,  et  Mem.  de  Paris,  1784,  p,  229.  Mem.  de  1'Institut,  vol.  Hi.  Phil. 
Mag.  vii.  183. 


224  LECTURE  XXIV. 

alone,  would  not  produce  any  material  retardation  of  its  motion,  if  the  par- 
ticles of  the  fluid  themselves  were  capable  of  moving  on  each  other  without 
the  least  resistance  ;  for  in  this  case  a  small  portion  of  the  fluid,  in  imme- 
diate contact  with  the  solid,  might  remain  at  rest,  and  the  remaining  mass 
of  the  fluid  might  slide  over  this  portion  without  any  retardation.  It  ap- 
pears, however,  that  the  water  in  contact  with  the  bottom  of  a  river  moves 
with  a  very  considerable  velocity,  and  the  water  next  above  this  only  a 
little  faster,  so  that  the  velocity  increases  almost  uniformly  as  we  ascend 
towards  the  surface.  It  follows,  therefore,  that  the  resistance  must  be  much 
greater  where  the  particles  of  water  slide  on  each  other,  than  where  they 
glide  along  the  surface  of  a  solid.  This  internal  friction  operates  gradually 
throughout  the  water  ;  the  surface  being  retarded  by  the  particles  immedi- 
ately below  it,  those  particles  by  the  next  inferior  stratum,  and  each  stra- 
tum being  actuated,  besides  its  own  relative  weight,  by  the  friction  of  the 
water  above,  tending  to  draw  it  forwards,  and  by  that  of  the  water  below 
tending  still  more  to  retard  it ;  the  retardation  being  communicated  from 
below  upwards,  in  such  a  manner  as  to  be  every  where  equivalent  to  the 
relative  weight  of  the  water  above  the  part  considered.  It  appears  from 
observation,  that  when  we  have  determined  the  mean  velocity  in  English 
inches,  we  may  find  the  superficial  velocity,  very  nearly,  by  adding  to  it 
its  square  root,  and  the  velocity  at  the  bottom,  by  subtracting  from  it  the 
same  number :  thus  the  square  root  of  48f  being  nearly  7,  the  superficial 
velocity  of  the  Ganges  will  be  about  55  inches,  or  4  feet  7  inches  in  a 
second,  and  the  velocity  at  the  bottom  41  f.  There  are,  however,  frequent 
irregularities  in  the  proportions  of  the  velocities  at  different  depths,  and  it 
has  sometimes  been  observed,  perhaps  on  account  of  the  resistance  of  the 
air,  that  the  velocity  is  a  little  less  immediately  at  the  surface,  than  a  few 
inches  below  it. 

For  similar  reasons,  the  velocity  of  a  river  is  also  generally  greater  in 
the  middle  than  at  the  sides  ;  and  the  motion  of  the  particles  in  the  middle 
must  be  retarded,  not  only  by  those  which  are  below  them,  but  also  by 
those  on  each  side,  while  these,  on  the  contrary,  are  dragged  on  by  the 
water  in  the  middle :  the  middle  parts  tend,  therefore,  to  draw  the  sides 
towards  them,  which  they  cannot  do,  without  lowering  the  surface  of  the 
fluid  next  to  the  banks  in  such  a  degree  as  to  make  the  difference  of  level 
an  equivalent  to  this  tendency  to  approach  the  middle.  This  appears  to  be 
the  reason  that  the  surface  of  a  large  river  may  generally  be  observed  to 
be  slightly  convex,  or  a  little  elevated  in  the  middle. 

The  course  of  a  river  is  sometimes  interrupted  by  a  were  or  a  fall,  natu- 
ral or  artificial ;  in  such  cases  the  velocity  may  be  calculated  in  the  same 
manner  as  when  a  fluid  is  discharged  from  a  reservoir  through  an  aperture 
of  considerable  height :  supposing  the  whole  section  of  the  were  to  be  such 
an  aperture,  in  a  vessel  so  much  higher,  that  the  velocity  of  a  fluid  issuing 
from  it  at  the  upper  part  of  the  aperture  would  be  precisely  equal  to  the 
actual  velocity  of  the  river.  The  extent  of  the  swell  caused  by  a  were,  or 
by  any  partial  elevation  thrown  across  the  bed  of  a  river,  may  also  'be 
found  by  first  determining  the  height  at  which  the  surface  must  stand 
immediately  above  the  were,  and  then  calculating  the  inclination  of  the 


ON  THE  FRICTION  OF  FLUIDS.  225 

surface  which  will  be  required  for  producing  the  actual  velocity  in  the 
•  river  thus  made  deeper ;  which  of  course  will  determine  the  situation  of 
the  surface  where  the  water  approaches  the  were ;  and  this  surface,  which 
is  more  nearly  horizontal  than  the  general  surface  of  the  river,  will  be  so 
joined  to  it  as  to  have  a  curvature  nearly  uniform  throughout. 

It  appears  from  calculations  of  the  effects  of  various  changes  in  the 
dimensions  of  rivers,  as  well  as  from  immediate  observation,  that  a  con- 
siderable diminution  of  the  breadth  of  a  river  at  a  particular  place,  will 
often  produce  but  a  small  elevation  of  its  surface.  The  velocity,  however, 
may  sometimes  be  considerably  increased  by  such  a  change,  and  where  the 
bottom  is  of  a  loose  nature,  its  particles  may  be  carried  away  by  means  of 
the  increased  velocity,  and  the  bed  of  the  river  may  be  deepened. 

Where  a  river  bends  in  a  considerable  degree,  it  is  generally  remarked 
that  the  velocity  of  the  water  is  greater  near  the  concave  than  the  convex 
side  of  the  flexure,  that  is,  at  the  greatest  distance  from  the  centre  of  its 
curvature.  This  effect  is  probably  occasioned  by  the  centrifugal  force, 
which  accumulates  the  water  on  that  side ;  so  that  the  banks  are  under- 
mined, and  the  channel  is  deepened  by  its  friction.  Some  authors  have 
been  led  to  expect  that  the  velocity  would  be  greater  nearest  to  the  convex 
bank,  because  the  inclination  of  the  surface  must  be  a  little  greater  there ; 
but  the  effect  of  the  accelerating  force  in  any  short  distance  is  inconsiderable, 
and  it  is  more  than  compensated  by  the  want  of  depth.  It  may  easily  be 
understood,  that  all  angles  and  flexures  must  diminish  the  general  velocity 
of  the  river's  motion,  and  the  more  as  they  are  more  abrupt. 

It  has  sometimes  been  imagined,  that  because  the  pressure  of  fluids  is 
propagated  equally  in  all  directions,  their  motions  ought  also  to  diverge  in 
a  similar  manner  ;  but  this  opinion  is  by  no  means  well  founded,  even 
with  respect  to  those  particles  which  receive  their  motions  in  an  unlimited 
reservoir  from  the  impulse  of  a  stream  which  enters  it.  An  experi- 
ment, which  sets  this  fact  in  a  clear  point  of  view,  was  made  long  ago 
by  Hauksbee.  *  He  produced  a  very  rapid  current  of  air,  by  means  of  a 
vessel,  into  which  three  or  four  times  as  much  air  as  it  naturally  con- 
tained had  been  condensed  by  means  of  a  syringe,  and  causing  the  current 
to  pass  through  a  small  box,  in  which  the  bason  of  a  barometer  was 
placed,  the  mercury  was  depressed  more  than  two  inches,  in  consequence 
of  the  rarefaction  which  the  current  produced  in  the  air  of  the  box.  (Plate 
XXI.  Fig.  268.) 

Professor  Venturi  has  also  made  several  experiments  of  a  similar  nature 
on  the  motion  of  water  :  he  observes  that  not  only  the  water  in  contact  with 
a  stream  is  drawn  along  by  it,  but  that  the  air  in  the  neighbourhood  of  a  jet 
is  also  made  to  partake  of  its  motion.  When  the  mouth  of  a  pipe  through 
which  a  stream  of  water  is  discharged,  is  introduced  into  a  vessel  a  little 
below  the  surface  of  the  water  which  it  contains,  and  is  allowed  to  escape 
by  ascending  an  inclined  surface  placed  opposite  to  the  pipe  and  leading 
over  the  side  of  the  vessel,  the  stream  not  only  ascends  this  surface  without 
leaving  any  portion  of  itself  behind,  but  carries  also  with  it  the  whole  of 

*  Hauksbee,  Physico- Mechanical  Experiments,  4to,  Lond.  1709,  p.  89.  See 
Leslie's  examination  of  the  experiment,  art.  Barometer.  Supp.  Encyc.  Brit.  p.  129. 


226  LECTURE  XXIV. 

the  water  of  the  vessel,  until  its  surface  becomes  level  with  the  lowest  part 
of  the  stream.  (Plate  XXI.  Fig.  269.) 

The  effect  of  a  jet  of  water,  in  drawing  towards  it  a  current  of  air,  is  in 
some  measure  illustrated  by  an  experiment  which  is  often  exhibited  among 
the  amusements  of  hydraulics.  A  ball  of  cork,  or  even  an  egg,  being 
placed  in  the  middle  of  a  jet,  which  throws  up  a  pretty  large  stream  to  a 
moderate  height,  the  ball,  instead  of  falling  or  being  thrown  off,  as  it  might 
naturally  have  been  expected  to  do,  remains  either  nearly  stationary  or 
playing  up  and  down,  as  long  as  the  experiment  is  continued.  Besides  the 
current  of  air  which  Venturi  has  noticed,  and  which  tends  to  support  the 
ball  in  a  stable  equilibrium,  the  adhesion  of  the  water,  combined  with  its 
centrifugal  force  in  turning  round  the  ball,  assists  in  drawing  it  back, 
when  it  has  declined  a  little  on  either  side,  so  that  the  stream  has  been 
principally  in  contact  with  the  other  side.  A  similar  effect  may  be  observed 
in  the  motions  of  the  air  only,  as  I  have  shown  by  some  experiments  of 
which  an  account  is  published  in  the  Philosophical  Transactions.*  Thus, 
if  we  bend  a  long  plate  of  metal  into  the  form  of  the  letter  S,  and  sus- 
pend it  in  the  middle  by  a  thread,  so  that  it  may  move  freely  on  its  centre, 
and  if  we  then  blow  on  its  convex  surface  with  a  tube  directed  obliquely 
towards  the  extremity,  instead  of  retreating  before  the  blast,  it  will  on  the 
contrary  appear  to  be  attracted  ;  the  pressure  of  the  atmosphere  being 
diminished  by  the  centrifugal  force  of  the  current,  which  glides  along  the 
convex  surface,  because  it  finds  a  readier  passage  in  the  neighbourhood  of 
the  solid,  towards  which  it  is  urged  by  the  impulse  of  the  particles  of  the 
air  approaching  it  on  one  side,  and  by  the  defect  of  pressure  on  the  other 
side,  occasioned  by  the  removal  of  a  certain  portion  of  the  air  which  it 
carries  with  it.  (Plate  XXI.  Fig.  270,  271.) 

From  considerations  similar  to  those  by  which  the  velocity  of  a  river  is 
determined,  we  may  calculate  the  quantity  of  water  discharged  from  a  pipe 
of  any  given  dimensions,  and  in  any  position.  The  same  expressions  will 
serve  for  estimating  the  magnitude  of  the  friction  in  both  cases  ;  the  pipe 
being  considered  as  a  small  river  of  which  the  mean  depth  is  one  fourth  of 
its  diameter :  but  a  part  only  of  the  force  of  gravity  is  now  expended  in 
overcoming  the  friction,  the  rest  being  employed  in  producing  the  momen- 
tum of  the  water.  We  may  obtain  a  sufficiently  accurate  determination  of 
the  velocity,  by  supposing  the  height  of  the  reservoir  above  the  orifice  of 
the  pipe  to  be  diminished  in  the  same  proportion  as  the  diameter  of  the 
pipe  would  be  increased  by  adding  to  it  one  fiftieth  part  of  the  length,  and 
finding  the  whole  velocity  corresponding  to  four  fifths  of  this  height.  Thus, 
if  the  diameter  of  the  pipe  were  one  inch,  and  its  length  100  inches,  we 
must  suppose  the  effective  height  to  be  reduced  to  one  third  by  the  friction, 
and  the  discharge  must  be  calculated  from  a  height  four  fifths  as  great  as 
this,  which  may  be  considered  as  a  reduction  derived  from  the  interference 
of  the  particles  entering  the  pipe,  with  each  other's  motions.  If  the  diameter 
of  the  pipe  had  been  two  inches,  the  height  must  only  have  been  supposed 
to  be  reduced  to  one  half  by  the  friction ;  such  a  pipe  would,  therefore, 

*  Outline  of  Experiments  and  Inquiries  respecting  Sound  and  Light,  Ph.  Tr. 
1800,  p.  106. 


ON  THE  FRICTION  OF  FLUIDS.  227 

discharge  about  five  times  as  much  water  as  the  former,  although  of  only 
twice  the  diameter  ;  and  this  circumstance  requires  the  attention  of  all  those 
who  are  concerned  in  regulating  the  distribution  of  water  by  pipes-  for 
domestic  use,  or  for  any  other  purpose. 

In  such  cases  it  becomes  also  frequently  necessary  to  attend  to  the  angle 
in  which  a  small  pipe  is  inserted  into  a  larger  ;  whenever  a  pipe  is  bent, 
there  is  a  loss  of  force  according  to  the  degree  of  flexure  and  to  the  velocity 
of  the  water,  which  may  be  calculated,  if  it  be  required  ;  but  if  a  pipe  be 
fixed  into  another  through  which  the  water  is  moving  very  rapidly  in  a 
direction  contrary  to  that  of  the  stream,  its  discharge  will  not  only  be  much 
smaller  than  if  the  directions  more  nearly  coincided,  but  sometimes  such  a 
pipe  will  discharge  nothing  at  all ;  on  the  contrary,  like  the  air  in  Hauks- 
bee's  experiment,  the  water  which  it  contains  may  be  dragged  after  the 
stream  in  the  larger  pipe. 

The  bad  effect  of  unnecessary  dilatations,  as  well  as  contractions,  in  aque- 
ducts and  in  pipes,  may  be  understood  from  what  has  been  already  said  of 
the  loss  of  force  attendant  on  every  change  of  velocity  ;  a  circumstance  of 
a  similar  nature  sometimes  happens  in  the  animal  economy.  When  an 
artery  is  dilated  so  as  to  form  an  aneurism,  it  has  been  observed  that  the 
artery  is  usually  distended  above  the  cavity ;  and  this  effect  is  easily  un- 
derstood from  the  actual  increase  of  resistance  which  the  aneurism  pro- 
duces, united  perhaps  with  the  previous  debility  of  the  artery. 

Mr.  Gerstner*  has  found  by  some  very  accurate  observations  on  the 
motion  of  water  in  very  small  pipes,  that  the  resistance  is  considerably 
affected  by  the  temperature  at  which  the  experiment  is  performed  ;  but  in 
the  cases  of  rivers,  and  of  such  pipes  as  are  commonly  used  in  practice,  no 
variations  of  temperature  to  which  they  can  be  liable,  will  produce  any 
sensible  effects.  His  experiments  indicate  a  resistance,  where  the  tubes  are 
very  small,  which  follows  a  law  so  different  from  that  which  is  observed  in 
more  common  cases,  that  it  appears  to  be  owing  to  some  other  cause  :  this 
cause  is  perhaps  the  capillary  attraction  of  the  open  end  of  the  tube,  and  it 
is  the  more  probable  that  the  resistance  depends  on  some  such  circumstance, 
as  there  is  reason  to  think  that  the  irregularity  may  be  in  great  measure 
removed  by  placing  the  tube  wholly  under  water. 


LECT.  XXIV.— ADDITIONAL  AUTHORITIES. 

Castelli,  della  Mensura  dell'  Acque  correnti,  4to,  Rome,  1628.  Toricellius^  de 
Motu  gravium  naturaliter  accelerate,  1643.  Varennius,  by  Jurin  and  Shaw,  1765. 
Guglielmini,  Aquarum  fluentium  Mensura,  2  vols.  4to,  Bonon,  1690-91.  Epistolse 
duse  Hydrostatics,  4to,  Bonon,  1692.  Della  Naturadi  Fiumi,  2  vols.  Milan,  1821. 
Polenus,  see  Lect.  XXIII.  Jurin,  De  Motu  Aquse  fluentis,  4to,  Venetii,  1724. 
Frisius,  Del  Mododi  regolare  i  Fiumi,  4to,  Lucca,  1762  ;  Paris,  1774  ;  Lond.  1818. 
Lorgna,  Ricerca  intorno  alia  Distribuzione  della  Velocita  nella  Sectione  de' 
Fiumi,  4to,  Verona,  1771.  Stattleri  Physica,  8  vols.  Augsb.  1772.  Euler  on  the 
Motion  of  Rivers.  Hist,  et  Mem.  de  Berlin,  1760,  p.  101.  Ximenes  on  the 
Velocity  of  Rivers.  Atti  dell'  Academia  di  Siena,  iii.  16  ;  vi.  31 ;  vii.  1.  Les- 

*  *  On  the  Discharge  of  Water  at  different  Temperatures.  Abhandlungen  der 
Bohmischen  Gesellschafft  der  Wissenchaften,  4to,  Prag.  1798.  Gilbert's  Journal, 
v.  160. 

Q2 


228  LECTURE  XXV. 

pinasse  and  Frisi  on  do.  Rozier's  Journal,  ix.  145,  398  ,  xi.  58.  Fabre  sur  les 
Torrens  and  les  Rivieres,  4to,  Paris,  1797.  Silberschlag,  Theorie  des  Fleuves.  Ro- 
bison's  Mechanical  Philosophy,  art.  Rivers.  Eytelwein's  Experiments  with  the 
Hydraulic  Quadrant.  Sammlung  zurBaukunst  1799.  Girard,  Essai  sur  le  Mouve- 
ment  des  Eaux  courantes,  1804.  Recherches  sur  les  Eaux  Publiques,  &c.  Prony, 
Mem.  des  Savans  Etrangers,  1815.  Tadini,  Del  Movimento  delle  Acque  correnti, 
4to,  Milan,  1816.  Hachette,  De  1'Ecoulement  des  Fluides  Aeriformes,  Annales  de 
Chimie.  1827,  and  Paris,  1830.  Genieys,  Essai  sur  les  Moyens  de  conduire,  d'ele- 
ver,  et  dedistribuer  les  Eaux,  4to,  1839. 


LECTURE   XXV. 

ON  HYDRAULIC  PRESSURE. 

THE  mutual  effects  of  fluids  and  moveable  solids  on  each  other  depend 
principally  on  the  laws  of  hydraulic  pressure,  and  of  the  resistance  of  fluids, 
which  have  been  considered  by  Bernoulli  as  constituting  a  separate  depart- 
ment of  hydrodynamics,  under  the  name  of  hydraulicostatics,  and  which 
are  of  the  utmost  practical  importance,  since  the  application  of  the  powers 
of  wind  or  water  to  the  working  of  mills,  and  to  the  navigation  of  ships,  are 
wholly  dependent  on  them.  The  impulse  of  a  fluid  differs  very  materially 
from  that  of  a  solid,  for  in  the  motions  of  solids,  the  least  possible  finite 
momentum  must  overpower  the  strongest  possible  pressure;  but  since  the 
particles  of  fluids  are  supposed  to  be  infinitely  small,  the  momentum  of  a 
fluid  stream  may  always  be  balanced  by  a  certain  determinate  pressure, 
without  producing  motion  in  the  solid  opposed  to  it ;  so  that  this  division  of 
the  subject  of  hydraulics  has  nothing  analogous  to  it  in  simple  mechanics. 
It  is  true  that  when  a  certain  quantity  of  a  fluid  is  made  to  concentrate  its 
action  almost  instantaneously,  its  effect  is  nearly  similar  to  that  of  a  solid, 
for  here  the  essential  distinction  derived  from  the  successive  action  of  the 
particles  no  longer  exists.  Thus,  when  a  stream  of  fluid  filling  a  pipe  acts 
suddenly  on  an  obstacle  at  the  end  of  it,  it  requires  to  be  resisted  by  a  force 
far  greater  than  that  which  originally  caused  its  motion,  unless  the  action 
of  the  force  be  continued  through  a  considerable  space  ;  and  for  this  reason 
the  strength  of  the  pipe  ought  to  be  so  calculated  as  to  be  able  to  resist 
this  action  ;  its  intensity  may,  however,  be  easily  diminished  by  means  of 
an  air  vessel  communicating  with  the  pipe,  which  will  allow  the  motion 
to  be  changed  in  a  less  abrupt  manner.  But  in  the  principal  cases  which 
we  are  about  to  consider,  the  action  of  the  fluid  on  the  solid  is  supposed 
to  be  confined  to  such  of  its  particles  as  are  nearly  in  contact  with  the 
surface. 

When  a  part  of  the  weight  of  any  fluid  is  expended  in  producing  a  motion 
in  any  direction,  an  equal  force  is  deducted  from  its  pressure  on  the  vessel 
in  that  direction :  for  the  gravitation  employed  in  generating  velocity, 
cannot  at  the  same  time  be  causing  pressure  ;  and  when  the  motion  produced 
is  in  any  other  direction  than  a  vertical  one,  its  obliquity  must  be  imme- 


ON  HYDRAULIC  PRESSURE.  229 

diately  derived  from  the  reaction  of  the  vessel,  or  of  some  fixed  obstacle  ;  for 
"it  is  obvious  that  a  vertical  force,  like  that  of  gravity,  cannot  of  itself  pro- 
duce an  oblique  or  a  horizontal  motion. 

If  a  small  stream  descends  from  the  bottom  of  a  vessel,  the  weight  expended 
in  producing  its  motion  is  equal  to  that  of  a  column  of  the  fluid  standing 
on  a  base  equal  to  the  contracted  orifice,  and  of  twice  the  height  of  the 
vessel.  Thus,  if  the  vessel  be  16  feet  high,  the  velocity  of  the  stream  will 
be  32  feet  in  a  second,  and  a  column  32  feet  in  length  will  pass  through  the 
orifice  in  each  second,  with  the  whole  velocity  derivable  from  its  weight 
acting  for  the  same  time ;  so  much,  therefore,  of  the  pressure  of  the  fluid  in 
the  reservoir  must  be  expended  in  producing  this  motion,  and  must  of  course 
be  deducted  from  the  whole  force  with  which  the  fluid  acts  on  the  bottom  of 
the  reservoir ;  in  the  same  manner  as  when  two  unequal  weights  are  con- 
nected by  means  of  a  thread  passing  over  a  pulley,  and  one  of  them  begins 
to  descend,  the  pressure  on  the  pulley  is  diminished  by  a  quantity,  which  is 
as  much  less  than  the  sum  of  the  weights,  as  the  velocity  of  their  common 
centre  of  gravity  is  less  than  the  velocity  of  a  body  falling  freely.  If  the 
stream  issue  from  the  vessel  in  any  other  direction,  the  effect  of  the  dimi- 
nution of  the  pressure  in  that  direction  will  be  nearly  the  same  as  if  the 
vessel  were  subjected  to  an  equal  pressure  of  any  other  kind  in  a  contrary 
direction  ;  and  if  the  vessel  be  moveable,  it  will  receive  a  progressive  or 
rotatory  motion  in  that  direction.  Thus,  when  a  vessel  or  pipe  is  fixed  on  a 
centre,  and  a  stream  of  water  is  discharged  from  it  by  a  lateral  orifice,  the 
vessel  turns  round  at  first  with  an  accelerated  motion,  but  on  account  of  the 
force  consumed  in  producing  the  rotatory  motion,  in  successive  portions  of 
the  water,  the  velocity  soon  becomes  nearly  stationary.  (Plate  XXI.  Fig. 
272.) 

From  similar  reasoning  it  appears,  that  the  effect  of  a  detached  jet  on  a 
plane  surface  perpendicular  to  it  must  be  equivalent  to  the  weight  of  a 
portion  of  the  same  stream  equal  in  length  to  twice  the  height  which  is 
capable  of  producing  the  velocity.  And  this  result  is  confirmed  by  expe- 
riments :  but  it  is  necessary  that  the  diameter  of  the  plane  be  at  least  four 
times  as  great  as  that  of  the  jet,  in  order  that  the  full  effect  may  be  produced. 
When  also  a  stream  acts  on  an  obstacle  in  a  channel  sufficiently  closed  on 
all  sides  to  prevent  the  escape  of  any  considerable  portion  of  water,  its 
effect  is  nearly  the  same  as  that  of  a  jet  playing  on  a  large  surface.  But  if 
the  plane  opposed  to  the  jet,  be  only  equal  to  it  in  diameter,  or  if  it  be 
placed  in  an  unlimited  stream,  the  whole  velocity  of  the  fluid  column  will 
not  be  destroyed,  it  will  only  be  divided  and  diverted  from  its  course,  its 
parts  continuing  to  move  on,  in  oblique  directions  ;  in  such  cases  the  pres- 
sure is  usually  found  to  be  simply  equivalent  to  the  weight  of  a  column  equal 
in  height  to  the  reservoir,  the  surface  being  subjected  to  a  pressure  nearly 
similar  to  that  which  acts  on  a  part  of  the  bottom  of  a  vessel,  while  a  stream 
is  descending  through  a  large  aperture  in  another  part  of  it.  (Plate  XXI. 

Fig.  273.) 

*  It  is  obvious  that  in  all  these  cases,  the  pressure  varies  as  the  square  of 

the  velocity,  since  the  height  required  to  produce  any  velocity  is  proper- 


230  LECTURE  XXV. 

tional  to  its  square.  This  inference  was  first  made  in  a  more  simple  man-  < 
ner,  from  comparing  the  impulse  of  a  fluid  on  a  solid  with  that  of  a  number 
of  separate  particles  striking  the  surface  of  the  body,  each  of  which  would 
produce  an  effect  proportional  to  its  velocity,  while  the  whole  number  of 
particles  acting  in  a  given  time,  would  also  vary  in  the  same  ratio.  If  the 
solid  were  in  motion,  and  the  fluid  either  in  motion  or  at  rest,  it  is  obvious 
that  the  relative  velocity  of  the  solid  and  the  fluid  with  regard  to  each  other, 
would  be  the  only  cause  of  their  mutual  effects,  and  that  the  hydraulic 
pressure  or  resistance  must  be  dependent  on  this  velocity  alone,  except  so 
far  as  the  limited  dimensions  of  the  reservoir  containing  the  fluid,  might  pro- 
duce a  difference  in  the  internal  motions  of  its  particles  in  different  cases. 
Thus,  where  the  fluid  is  so  confined  that  the  whole  of  the  stream  acts  on  a 
succession  of  planes,  each  portion  into  which  it  is  divided  may  be  considered 
as  an  inelastic  solid,  striking  on  the  surface  exposed  to  it  with  a  certain 
velocity  ;  and  in  this  case  the  force  must  be  considered  as  simply  propor- 
tional to  the  relative  velocity,  and  not  to  its  square.  For  want  of  this  con- 
sideration, the  effects  of  water  wheels  have  frequently  been  very  erroneously 
stated. 

When  a  jet  strikes  a  plane  surface  obliquely,  its  force,  in  impelling  the 
body  forwards,  in  its  own  direction,  is  found  to  be  very  nearly  proportional 
to  the  height  to  which  the  jet  would  rise,  if  it  were  similarly  inclined  to  the 
horizon.  But  when  a  plane  is  situated  thus  obliquely  with  respect  to  a 
wide  stream,  the  force  impelling  it  in  the  direction  of  the  stream  is  some- 
what less  diminished  by  the  obliquity,  at  least  if  we  make  allowance  for  its 
intercepting  a  smaller  portion  of  the  stream  :  thus,  if  the  anterior  part  of  a 
solid  be  terminated  by  a  wedge  more  or  less  acute,  the  resistance,  according 
to  the  simplest  theory  of  the  resolution  of  forces,  might  be  found  by 
describing  a  circle  on  half  the  base  of  the  wedge  as  a  diameter,  which 
would  cut  off*  a  part  from  the  oblique  side  of  the  wedge  that  would  be  the 
measure  of  the  resistance,  the  whole  side  representing  the  resistance  to  the 
same  solid  without  the  wedge  :  but  the  resistance  is  always  somewhat  more 
than  this,  and  the  portion  to  be  added  may  be  found,  very  nearly,  by 
adding  to  the  fraction  thus  found  one  ten  millionth  of  the  cube  of  the 
number  of  degrees  contained  in  the  external  angle  of  the  wedge.  (Plate 
XXI.  Fig.  274.) 

The  pressure  of  a  fluid  striking  perpendicularly  on  a  plane  surface,  has 
been  found  to  be  very  different  at  different  parts  of  the  surface  ;  being 
greatest  at  the  centre,  and  least  towards  the  edges  ;  so  that  if  an  aperture 
be  made  in  the  centre  of  a  circular  plane,  covering  the  mouth  of  a  bent 
tube,  the  fluid  within  it  will  rise  half  as  high  again  as  if  the  whole  mouth 
were  open.  It  is  also  observable,  that  two  bodies,  equal  and  similar  in  the 
form  of  the  part  meeting  the  fluid,  undergo  very  different  degrees  of 
resistance  according  to  the  forms  of  their  posterior  terminations,  and  that  a 
thin  circular  plate  is  much  more  retarded  than  a  long  cylinder  of  the  same 
diameter.  These  circumstances  are  utterly  inexplicable  upon  the  vague 
approximation  of  supposing  the  resistance  produced  by  the  immediate  im- 
pulse of  separate  particles  of  the  fluid  on  the  solid  ;  but  they  are  no  longer 


ON  HYDRAULIC  PRESSURE.  231 

surprising,  when  we  consider  the  true  mode  of  action  of  continuous  fluids, 
'since  all  the  motion  which  is  produced  by  the  fluid  in  the  solid  or  by  the 
solid  in  the  fluid  is  communicated  much  more  by  means  of  pressure  than 
by  immediate  impulse.     The  minute  operations  of  this  pressure  are  too 
intricate  to  be  accurately  developed,  but  we  may  observe  in  general,  that 
when  a  body  moves  along  the  surface  of  a  resisting  medium  at  rest,  or 
when  an  obstacle  at  rest  is  opposed  to  a  fluid  in  equable  motion,  the  pres- 
sure is  increased  before  the  moving  substance,  and  diminished  behind  it ; 
so  that  the  surface  is  elevated  at  the  one  part  and  depressed  at  the  other, 
and  the  more  as  the  velocity  is  greater.     Now  it  is   obvious  that  the 
pressure  must  be  greatest  where  the  elevation  is  greatest,  and  hence  a 
perforation  at  the  centre  of  the  surface  indicates  a  greater  pressure  than  at 
the  circumference.     Behind  the  body  this  pressure  becomes  negative,  and 
has  sometimes  been  called  nonpressure ;    hence  it  happens  that  a  tube, 
opening  in  the  centre  of  the  posterior  surface,  exhibits  the  fluid  within  it 
depressed  below  the  level  of  the  general  surface  of  the  water.     Thus,  if  we 
suppose  the  velocity  of  a  body,  terminated  by  perpendicular  surfaces,  to  be 
8  feet  in  a  second,  it  will  require  the  pressure  of  about  a  foot,  to  produce 
such  a  velocity,  and  we  may,  therefore,  expect  an  elevation  of  about  a  foot 
before   the  body,  and  an  equal  depression  behind  it ;    consequently  an 
equivalent  difference  must  be  found  in  the  pressure  of  the  water  at  any 
equal  depths  on  the  anterior  and  posterior  surfaces  of  the  body.    The  water 
elevated  before  the  body  escapes  continually  towards  each  side,  and  the 
deficiency  behind  is  also  filled  up  in  some  measure  by  the  particles  rushing 
in  and  following  the  body  :  but  there  is  in  both  cases,  a  certain  quantity  of 
water  which  moves  forwards,  and  constitutes  what  is  called  the  dead  water : 
before,  where  it  is  usually  most  observable,  it  forms  an  irregular  triangle, 
of  which  the  sides  are  convex  inwards.     If  the  posterior  part  of  the  body 
be  formed  like  a  wedge,  the  water  on  each  side  will  be  advancing  to  fill  up 
the  vacuity,  even  while  it  remains  in  contact  with  the  sides,  and  the  nega- 
tive pressure  will  be  considerably  diminished.    For  this  reason  the  bottoms 
of  ships  are  made  to  terminate  behind  in  a  shape  somewhat  resembling  a 
wedge ;  and  the  same  economy  may  be  observed  in  the  forms  of  fishes, 
calculated  by  nature  for  following  their  prey  with  the  greatest  possible 
rapidity.    In  general,  fishes,  as  well  as  ships,  are  of  a  more  obtuse  form 
before  than  behind,  but  it  is  not  certain  that  there  would  be  any  material 
difference  in  the  resistance  in  a  contrary  direction,  although  some  experi- 
ments seem  to  favour  such  an  opinion.     Perhaps  if  the  natural  form  of  the 
dead  water  moving  before  an  obtuse  body,  were  ascertained,  it  might  serve 
to  indicate  a  solid  calculated  to  move  through  the  water  with  the  least 
resistance ;  for  the  water  must  naturally  assume  such  a  form  for  its  own 
motions,  and  the  friction  of  fluids  on  solids  being  less  than  that  of  fluids 
moving  within  themselves,  the  resistance  would  be  diminished  by  substi- 
tuting a  solid  of  the  same  form  for  a  fluid.*     (Plate  XXI.  Fig.  275.) 

Supposing  a  body  to  move  through  a  fluid  at  a  considerable  depth  below 
• 

*  Consult  Russel,  Trans,  of  the  Roy.  Soc.  of  Edin.  vol.  xiv.  p.  47. 


232  LECTURE   XXV. 

its  surface,  there  will  still  be  an  elevation  before  and  a  depression  behind  it, 
the  less  in  height  and  the  greater  in  extent,  as  the  depth  at  which  the  body* 
is  situated  is  greater.     Such  an  elevation  appears  to  be  in  some  measure 
analogous  to  the  effect  of  a  low  were  thrown  across  a  river,  which  raises  its 
surface,  and  produces  a  swell. 

If  two  or  more  bodies  differently  formed,  the  resistances  to  the  motions 
of  which  had  been  ascertained,  were  caused  to  move  through  a  fluid  in 
contact  with  each  other,  it  is  obvious  that  the  paths  described  by  the 
particles  of  the  fluid  in  gliding  by  them,  must  be  very  materially  altered 
by  their  junction ;  and  it  seems  natural  to  expect  that  the  joint  disturbance 
produced  in  the  motions  of  the  fluid,  when  the  surfaces  are  so  united  as  to 
form  a  convex  outline,  would  be  somewhat  less  than  if  each  surface  were 
considered  separately.  Accordingly,  it  is  found  that  no  calculation,  de- 
duced from  experiments  on  the  resistance  opposed  to  oblique  plane  surfaces, 
will  determine  with  accuracy  the  resistance  to  a  curved  surface.  It  appears 
from  experiment  that  the  resistance  to  the  motion  of  a  sphere  is  usually 
about  two  fifths  of  the  resistance  to  a  flat  circular  substance  of  an  equal 
diameter.  The  resistance  to  the  motion  of  a  concave  surface  is  greater 
than  to  a  plane,  and  it  is  easily  understood,  that  since  the  direction  in 
which  the  particles  of  the  fluid  recede  from  the  solid,  must  be  materially 
influenced  by  the  form  of  the  solid  exposed  to  their  action,  their  motion  in 
this  case  must  be  partly  retrograde,  when  they  glide  along  towards  the 
edges  of  the  concave  surface,  and  a  greater  portion  of  force  must  have 
been  employed,  than  when  they  escape  with  a  smaller  deviation  from  their 
original  direction.  (Plate  XXI.  Fig.  276.) 

For  some  reason  which  is  not  well  understood,  the  hydraulic  pressure  of 
the  air  appears  to  be  somewhat  greater  in  proportion  to  its  density,  than 
that  of  water.  It  has  been  found  that  the  perpendicular  impulse  of  the 
air  on  a  plane  surface,  is  more  than  equivalent  to  the  weight  of  a  column 
of  air  of  a  height  corresponding  to  the  velocity,  and  the  excess  is  said  by 
some  to  amount  to  one  third,  by  others  to  two  thirds  of  that  weight.  The 
resistance  appears  also  to  be  a  little  greater  for  a  large  surface,  than  for  a 
number  of  smaller  ones  which  are  together  of  equal  extent. 

The  resistance  or  impulse  of  the  air  on  each  square  foot  of  a  surface 
directly  opposed  to  it,  may  in  general  be  found,  with  tolerable  accuracy, 
in  pounds,  by  dividing  the  square  of  the  velocity  in  a  second,  expressed 
in  feet,  by  500.  Thus,  if  the  velocity  were  100  feet  in  a  second,  the  pressure 
on  each  square  foot  would  be  20  pounds  ;  if  1000  feet,  2000  pounds.  For 
a  sphere  of  a  foot  in  diameter,  we  may  divide  the  square  of  the  velocity 
by  1600.  We  may  also  find,  in  a  similar  manner,  the  utmost  velocity  that 
a  given  body  can  acquire  or  retain  in  falling  through  the  air ;  for  the 
velocity  at  which  the  resistance  is  equal  to  the  weight  must  be  its  limit. 
Thus,  if  a  sphere  one  foot  in  diameter  weighed  100  pounds,  the  square  of 
its  utmost  velocity  would  be  160,000,  and  the  velocity  itself  400  feet  in  a 
second  ;  if  a  stone  of  such  dimensions  entered  the  atmosphere  with  a  greater 
velocity,  its  motion  would  very  soon  be  reduced  to  this  limit ;  and  a  lighter 
or  a  smaller  body  would  move  still  more  slowly.  The  weight  of  Mr. 


ON  HYDRAULIC  PRESSURE.  233 

Garnerin's  parachute,*  with  its  whole  load,  was  about  a  quarter  of  a 
pound  for  each  square  foot,  the  square  of  its  greatest  velocity  must,  there- 
fore, have  been  about  125,  and  the  velocity  11  feet  in  a  second,  which  is  no 
greater  than  that  with  which  a  person  would  ascend,  in  leaping  from  a 
height  of  two  feet,  without  stooping.  Mr.  Garnerin  found  the  velocity 
even  less  than  this,  and  it  is  not  improbable  that  the  concave  form  of  the 
parachute  might  considerably  increase  the  resistance.  Thus,  Mr.  Edge- 
worth  found  that  a  plate  9  inches  long,  when  bent  into  an  arc  of  which 
the  chord  was  7£,  had  the  resistance  increased  more  than  one  seventh,  t 
The  diminution  of  the  resistance  of  the  air  by  the  obliquity  of  the  surface  is 
still  less  than  that  of  the  resistance  of  water  :  thus,  the  resistance  on  the 
oblique  surfaces  of  a  wedge  is  not  quite  so  much  less  than  the  resistance 
on  its  base,  as  its  breadth  is  less  than  the  length  of  those  surfaces. 

When  the  velocity  of  a  body  moving  through  an  elastic  fluid  is  very 
great,  the  resistance  is  increased  in  a  much  greater  proportion  than  the 
square  of  the  velocity  :  thus  the  retardation  of  a  cannon  ball  moving  with 
a  velocity  of  1000  feet  in  a  second,  or  a  little  more,  becomes  suddenly 
much  greater  than  the  calculation  indicates.  The  reason  of  this  change 
appears  to  be,  that  the  condensation  of  the  air  before  the  ball  is  necessarily 
confined  to  a  smaller  portion  which  is  very  intensely  compressed,  because 
the  effect  of  the  impulse  can  only  spread  through  the  air  with  a  certain 
velocity  which  is  not  much  greater  than  that  of  the  ball ;  and  this  smaller 
portion  of  air  must  necessarily  be  much  more  condensed  than  a  larger 
portion  would  have  been.  Thus,  when  a  cannon  ball  moves  slowly,  its 
effect  at  any  instant  is  in  some  degree  divided  throughout  all  that  part  of 
the  atmosphere  which  the  sound  of  the  report  has  reached  ;  and  if  the  ball 
follows  the  sound  very  speedily,  it  is  obvious  that  the  portion  of  the  air 
before  the  ball  which  partakes  of  the  effect,  must  be  very  small.  The 
sound  is  observed  to  be  propagated  with  a  velocity  of  about  1130  feet  in  a 
second,  and  a  cannon  ball  may  be  discharged  with  a  velocity  of  2000  ;  but 
one  half  of  this  is  very  speedily  lost,  so  as  to  be  wholly  useless  with  regard 
to  the  effect  of  the  ball.  If,  therefore,  we  wish  to  increase  the  range  of  a 
cannon  ball,  we  must  increase  its  weight ;  for  the  resistance  increases  only 
in  proportion  to  the  surface  of  the  ball,  while  the  weight  is  determined  by 
its  solid  content. 

It  is  not  easy  to  explain,  in  a  manner  perfectly  satisfactory,  the  reflection 
of  a  cannon  ball,  or  of  a  stone,  which  strikes  the  surface  of  the  sea,  or  of 
a  piece  of  water,  in  an  oblique  direction.  We  may,  however,  assign  some 
causes  which  appear  to  be  materially  concerned  in  this  effect.  In  the  first 
place  the  surface  of  the  water,  acting  at  first  for  some  time  on  the  lower 
part  of  the  ball,  produces,  by  its  friction,  a  degree  of  rotatory  motion,  by 
means  of  which  the  ball,  as  it  proceeds,  acts  upon  the  mass  of  water  which 
is  heaped  up  before  it,  and  is  obliged  by  a  similar  friction  to  roll  upwards, 
so  that  it  mounts  again  to  a  much  greater  height  than  it  could  possibly 

.*  Nich.  Jour.  i.  523,  8vo.  iii.  57.    Gilbert's  Jour.  xvi.  156,  164,  257.    See  the 
article  Aeronautics,  Supp.  to  Encyc.  Brit, 
f  Ph.  Tr.  1783,  kxiii.  136. 


234  LECTURE  XXV. 

have  attained  by  the  mere  hydrostatic  pressure  of  the  water  at  a  depth  so 
inconsiderable.  But  a  more  powerful  cause  than  this  appears  to  be  the* 
continual  succession  of  new  surfaces  which  are  to  be  depressed,  and  which 
may  be  supposed  to  react  on  the  ball,  so  as  to  produce  the  same  effect  as  a 
more  intense  pressure  would  have  done,  if  it  had  continued  stationary  ; 
and  the  mutual  action  of  the  water  and  the  ball  may  be  compared  to  the 
impulse  of  an  oblique  stream,  moving  with  the  velocity  of  the  ball,  which 
would  impel  it  much  more  powerfully  than  the  simple  hydrostatic  pressure 
at  a  much  greater  depth.  It  happens  in  this  case,  as  in  many  others,  that 
the  effects  which  appear  to  be  the  most  familiar  to  us,  do  not  by  any  means 
admit  the  clearest  and  simplest  explanation. 


LECT.  XXV.— ADDITIONAL  AUTHORITIES. 

L'Hopital  on  the  Solid  of  least  Resistance,  Hist,  et  Mem.  de  Paris,  1699,  p.  107, 
H.  95.  Craig  on  do.  Ph.  Tr.  1701,  p.  746.  Varignon  on  Motions  in  a  resisting 
Medium,  Hist,  et  Mem.  1707,  p.  382,  H.  139;  1708,  pp.212,  250,  302,  419,  H. 
123  ;  1709,  1710, 1711,  p.  248,  H.  87.  Desaguliers  on  the  Resistance  of  the  Air, 
from  Exp.  in  St.  Paul's  Cathedral,  Ph.  Tr.  1719,  No.  362.  Pitot  on  the  Oblique 
Impulse  of  Fluids,  Hist,  et  Mem.  1727,  p.  49,  H.  137.  D.  Bernoulli  on  Pres- 
sure and  Resistance,  Com.  Petr.  iii.  214,  iv.  136,  v.  106,  viii.  99,  113.  Euler  on 
Friction  and  Resistance,  Nov.  Com.  Petr.  vi.  338,  viii.  197.  Bouguer  on  the 
Solid  of  least  Resistance,  Hist.  etMem.  1733,  p.  85,  H.  86  ;  1767,  p.  504,  H.  110. 
On  Impulse  of  Fluids,  ibid.  1746,  p.  237,  H.  289.  Manoeuvre  des  Vaisseaux,  4to, 
1757.  Krafft  on  the  Impulse  of  a  Vein  of  Water,  Com.  Petr.  viii.  253  ;  xi.  233. 
D'Alembert,  Essai  sur  la  Resistance  des  Fluides,  4to,  1752.  Silvabelle  on  the 
Solid  of  least  Resistance,  Mem.  des  Savans  Etrangers,  iii.  639.  Borda  on  the  Re- 
sistance of  Fluids,  Hist,  et  Mem.  de  Paris,  1763,  p.  358,  H,  118  ;  1767,  p.  495,  H. 
145  ;  1769,  p.  247.  Lambert,  Hist,  et  Mem.  de  Berlin,  1765,  p.  102.  Don  Jorge 
Juan,  Examen  Maritime,  2  vols.  4to,  Madrid,  1771.  Nouvelles  Experiences  sur  la 
Resistance  des  Fluides,  par  MM.  D'Alembert,  De  Condorcet,  et  Bossut,  1777. 
Bossut's  Experiments,  Hist,  et  Mem.  1778,  p.  353,  H.  38.  Mann's  Experiments 
on  the  Resistance  in  shallow  Canals,  &c.  Ph.  Tr.  1779,  pp.  555,  629.  Euler  on 
the  Impulse  of  a  Vein  of  Fluid,  in  his  Comment  on  Robins,  1783.  Lagrange  on  do. 
Mem.  de  Turin,  1784-5.  Michelotti  on  do.  Melanges  de  Turin,  1788,  App.  121. 
Legendre's  Example  of  the  Solid  of  least  Resistance,  Hist.  etMem.  1786,  p.  21, 
App.  121.  Lorgna,Mem.  della  Soc.  Ital.  4to,  418.  Vince  on  the  Resistance  of  Fluids, 
Ph.  Tr.  1795,  p.  24;  1798,  p.  1.  Gerstner's  Theory  of  the  Impulse  of  Water, 
Abhandlungen  derBomischen  Gesellschaft,  1795.  Experiments  of  the  Society  for  the 
Advancement  of  Naval  Architecture,  4to,  Lond.  Charnock's  Hist,  of  Marine  Ar- 
chitecture, 3  vols.  4to,  1800.  Morosi  on  the  Impulse  of  a  Vein  of  Fluid,  Mem. 
dell'  Institute  Lombardo-Veneto,  1812,  pp.  119,  305.  Brunacci,  Mem.  della  Soc. 
Ital.  1816-17.  Macneill's  Canal  Navigation,  4to,  1833.  Beaufoy's  Nautical  and 
Hydraulic  Experiments,  4to,  1834. 


235 


LECTURE   XXVI. 


ON  HYDROSTATIC  INSTRUMENTS  AND  HYDRAULIC 
ARCHITECTURE. 

WE  have  now  examined  the  fundamental  laws  of  the  principal  depart- 
ments of  hydrodynamics,  which  may  be  considered  as  constituting  the 
theory  of  the  science :  we  are  next  to  proceed  to  the  application  of  this 
theory  to  a  variety  of  practical  purposes.  Following  the  same  general 
order  as  we  have  observed  in  mechanics,  our  first  division  will  be  analogous 
to  the  subject  of  statics,  and  will  relate  to  hydrostatic  instruments  ;  the 
second  to  architecture,  containing  some  particulars  respecting  canals  and 
embankments ;  the  third  to  machinery,  comprehending  the  modification 
and  application  of  the  force  of  fluids  considered  as  inelastic ;  the  fourth 
and  the  fifth  to  the  methods  of  raising  and  removing  weights,  in  which  the 
principal  hydraulic  and  pneumatic  machines  will  be  respectively  explained, 
and,  as  a  part  of  this  subject,  the  application  of  pneumatic  force  will  also 
be  examined. 

The  principles  of  hydrostatics  are  very  frequently  applied  to  the  deter- 
mination of  the  specific  gravities  of  the  various  productions  of  nature  or 
of  art.  The  diminution  of  the  apparent  weight  of  a  solid  body  upon 
immersion  into  a  fluid,  affords  an  easy  method  of  comparing  its  density 
with  that  of  the  fluid.  For  the  weight  of  the  solid  being  previously 
determined,  if  we  examine  how  much  that  weight  is  diminished  by  plung- 
ing the  body  in  pure  water,  we  shall  have  the  weight  of  an  equal  bulk  of 
water:  and  thence  we  may  immediately  obtain  the  proportion  of  the 
specific  gravity  of  the  body  to  that  of  water,  which  is  the  usual 
standard  of  comparison.  And  if  we  weigh  a  solid  of  given  magnitude, 
for  instance,  a  ball  of  glass,  first  in  water,  and  then  in  any  other  fluid,  the 
quantities  of  weight  lost  in  each  case  will  be  in  the  same  proportion  as 
the  specific  gravities  of  the  two  fluids.  A  balance  adapted  for  such  exami- 
nations is  called  a  hydrostatic  balance  ;  on  one  side  it  has  a  scale  as  usual, 
and  on  the  other  a  loop  of  fine  wire  or  of  horse  hair,  for  holding  the  solid 
to  be  weighed,  which  may  be  changed  occasionally  for  a  ball  of  glass, 
suspended  in  a  similar  manner  :  sometimes  also  a  dish  is  added  for  holding 
any  loose  substances  which  will  sink  in  water,  proper  counterpoises  being 
used  as  equivalents  for  the  weight  of  the  dish  either  in  air  or  in  water  ; 
and  when  a  body  lighter  than  water  is  examined,  a  weight  of  known 
magnitude  and  density  is  employed  for  sinking  it.  (Plate  XXI.  Fig.  277.) 

The  specific  gravities  of  any  substances,  and  in  particular  of  such  as  are 
lighter  than  water,  may  also  be  very  conveniently  determined  by  means  of 
a  common  balance,  employing  a  phial  with  a  conical  ground  stopple,  filling 
it  first  with  water,  and  then  either  with  a  given  fluid,  or  with  a  portion  of 
the  solid  of  which  the  weight  has  been  ascertained,  together  with  as  much 
water  as  is  sufficient  to  exclude  all  the  air. 


236  LECTURE  XXVI. 

For  the  speedy  examination  of  a  variety  of  fluids,  differing  but  little  in 
specific  gravity  from  some  known  standard,  an  hydrometer  may  be  very" 
conveniently  employed.  This  instrument  is  said  to  have  been  invented  by 
Archimedes  :  it  consists  of  a  hollow  ball,  with  a  weight  below  it,  and  a 
slender  stem  above,  so  graduated  as  to  express  the  specific  gravity  of  the 
fluid  by  the  degree  to  which  it  sinks.  Sometimes  the  instrument  is  sunk 
to  a  certain  mark,  by  means  of  weights  placed  in  a  dish  at  the  end  of  the 
stem  ;  or  different  weights  are  fixed  to  it  below,  while  the  graduations  of 
the  scale  are  still  observed  ;  and  it  may  even  be  applied  to  finding  the 
specific  gravities  of  solids,  the  solid  being  first  placed  in  the  dish  at  the  end 
of  the  stem,  and  then  in  a  second  dish  which  is  suspended  from  the  bulb 
below  the  water.  (Plate  XXI.  Fig.  278.) 

Another  mode  of  ascertaining  the  specific  gravities  of  fluids  differing  but 
little  from  each  other  in  density,  is  to  have  a  series  of  globules  of  glass,  so 
loaded  as  to  correspond  to  the  specific  gravities  indicated  by  as  many 
numbers,  which  are  marked  on  them  ;  and  throwing  several  of  them 
together  into  the  fluid,  to  observe  which  of  them  remains  nearly  stationary 
without  either  rising  to  the  surface  or  sinking.  This  method,  though  not 
expeditious,  appears  to  be  very  secure  from  error  :  the  globules  are  sold  by 
patent,  adapted  for  the  measurement  of  the  strength  of  spirituous  liquors. 

In  whatever  manner  we  compare  the  specific  gravities  of  bodies  with 
that  of  water,  it  is  necessary,  for  very  accurate  experiments,  either  that  the 
water  be  employed  at  the  temperature  of  the  air  when  moderately  warm, 
or  that  a  proper  correction  should  be  made  for  its  change  of  bulk  at  dif- 
ferent temperatures.  Platina,  the  densest  known  substance,  is  23  times  as 
heavy  as  distilled  water,  gold  19J,  mercury  13|,  lead  11£,  silver  11,  copper 
9,  iron  and  steel  71 ,  stony  substances  usually  about  2£,  rectified  spirits  £, 
naphtha,  the  lightest  liquid,  ^  cork  about  •£,  common  air  -g-j-^,  steam  s  £0  0, 
and  pure  hydrogen  gas  -r^^nr*  From  this  comparison  the  weight  of  a  cubic 
foot  of  any  of  these  substances  may  be  easily  determined  ;  since  a  cubic 
foot  of  water  weighs  nearly  1000  ounces  avoirdupois,  or  more  nearly  998  ; 
thus  a  cubic  foot  of  gold  would  weigh  about  195,000  ounces,  and  be  worth 
above  60,000  pounds  sterling  ;  a  cubic  foot  of  iron  weighs  7750  ounces,  and 
a  cubic  foot  of  common  stone  about  2500. 

The  method  of  measuring  the  bulk  of  solid  bodies  by  immersing  them  in 
a  fluid,  was  applied,  by  its  inventor  Archimedes,  to  the  detection  of  a  fraud 
in  the  composition  of  a  mixed  metal  :*  and  at  present  the  principal  use  of 
hydrometers  is  for  ascertaining,  by  the  specific  gravity  of  a  compound  of 
alcohol  and  water,  the  proportional  quantities  of  its  ingredients.  But  in  all 
experiments  of  this  kind,  it  is  necessary  to  be  aware,  that  a  considerable 
change  of  the  joint  bulk  of  two  substances  is  often  produced  by  their  mix- 
ture :  and  that  in  general  their  dimensions  are  considerably  contracted. 
Thus,  18  gallons  of  water,  and  18  of  alcohol,  instead  of  36  gallons,  make 
only  35,  consequently  the  specific  gravity  of  the  compound  is  one  35th 
greater  than  the  mean  of  the  specific  gravities  of  the  ingredients.  And  in 
some  cases  the  whole  dimensions  of  a  single  substance  may  even  be  co'u- 

*  Vitruvius,  Architect.  1.  ix,  c.  13. 


ON  HYDROSTATIC  INSTRUMENTS,  &c.  237 

traded  by  the  addition  of  another  substance  :  thus  iron,  by  the  addition  of 
erne  eighth  of  its  bulk  of  platina,  becomes  contracted  one  fortieth  of  that 
bulk. 

The  use  of  the  spirit  level  depends  on  the  tendency  of  all  fluids  to  pre- 
serve a  horizontal  surface,  and  the  freedom  with  which  the  particles  of 
fluids  move  on  each  other,  renders  it  an  instrument  capable  of  the  greatest 
delicacy.  A  tube  which  is  very  slightly  curved,  being  nearly  filled  with 
alcohol  or  ether,  and  then  perfectly  closed,  the  bubble  will  always  rise  to 
the  highest  part  of  the  tube,  and  will  never  be  stationary  at  the  point  which 
is  marked  as  its  proper  place,  unless  the  instrument  be  very  accurately 
horizontal,  or  in  the  same  position  in  which  the  mark  was  adjusted.  The 
surface  of  the  bubble,  especially  when  it  is  small,  cannot,  in  a  strict  sense, 
be  called  perfectly  horizontal,  since  its  form  approaches  nearly  to  that  of  a 
sphere  ;  but  in  order  that  the  centre  of  gravity  of  the  water  may  attain  the 
lowest  possible  situation,  the  bubble  must  necessarily  occupy  the  highest 
point  of  the  tube.  (Plate  XXI.  Fig.  279.) 

The  principles  of  hydrostatics  have  been  employed  in  various  ways  for 
supplying  lamps  with  oil.  It  is  found  that  a  lamp  will  burn,  without  con- 
suming any  considerable  portion  of  its  wick,  as  long  as  it  is  amply  supplied 
with  oil ;  hence  it  becomes  desirable  that  it  should  always  be  level  with 
the  surface  of  the  reservoir,  and  this  may  be  effected  sufficiently  well  by 
placing  the  wick  at  the  edge  of  a  very  large  vessel,  or  at  the  end  of  a  tube 
projecting  from  such  a  vessel,  or  from  a  vessel  closed  above,  and  opening 
only  by  an  orifice  below,  which  lets  in  the  air  as  the  oil  escapes  through  it. 
But  all  these  methods  are  often  attended  with  inconveniences  of  various 
kinds,  especially  where  the  lamp  is  to  be  employed  like  a  candle,  and 
placed  on  a  table.  A  French  artist  has  applied  a  little  pump,  which  is 
worked  by  means  of  a  spring,  for  raising  the  oil  from  a  vessel  under  the 
lamp  ;  but  this  refinement  is  too  complicated  to  be  practically  useful.  Mr. 
Keir's  lamp  *  contains  a  divided  cavity,  one  part  of  which  is  filled  with  oil, 
and  the  other  with  a  saline  or  saccharine  fluid  of  greater  density,  so  that 
when  the  oil  contained  in  the  upper  part  of  the  tube  is  exhausted,  its  place 
is  partly  supplied  by  a  fresh  portion,  which  is  forced  up  in  consequence  of 
the  descent  of  the  denser  fluid  in  a  much  larger  vessel.  Still,  however,  the 
surface  must  be  lowered  by  degrees  ;  but  by  combining  the  invention  with 
Dr.  Hooke's  semicylindrical  counterpoise,t  a  little  modified,  the  height  of 
this  fluid  may  be  so  regulated,  that  the  surface  of  the  oil  may  remain 
almost  invariable,  until  the  reservoir  is  quite  exhausted.  For  this  purpose, 
the  centre  of  gravity  of  the  counterpoise  must  be  a  little  higher  than  the 
line  which  bisects  it ;  and  its  specific  gravity  must  be  about  three  fourths 
as  great  as  that  of  the  fluid  ;  and  in  this  manner  it  may  be  made  to  raise 
the  surface  of  the  heavier  fluid,  in  proportion  as  a  greater  quantity  of  it 
escapes,  to  supply  the  place  of  the  oil ;  and  to  keep  it  always  at  a  sufficient 
height  above  the  surface  which  separates  it  from  the  oil,  so  that  the  wick 
may  be  amply  and  almost  uniformly  supplied.  (Plate  XXI.  Fig.  280.) 

•The  art  of  embankment  is  a  branch  of  architecture  entirely  dependent  on 

*  Nich.  Jour.  iii.  467.  t  Lampas,  p.  188. 


238  LECTURE   XXVI. 

hydrostatical  and  hydraulic  principles.  In  Holland  and  in  some  parts  of 
Germany,  this  art  is  indispensable  to  the  existence  of  large  tracts  of 
country  ;  and  even  in  this  island  it  has  heen  of  extensive  utility,  in  gaining 
and  securing  ground  on  the  sea  coast.  The  construction  of  canals,  and 
the  management  of  rivers  and  harbours,  are  also  dependent  on  the -same 
principles  ;  and  these  important  subjects  have  been  discussed  by  various 
writers,  in  many  copious  treatises,  expressly  devoted  to  hydraulic  archi- 
tecture. 

When  a  bank  or  dike  is  to  be  constructed,  it  must  be  composed  of  ma- 
terials capable  of  resisting,  by  their  weight,  the  effort  of  the  fluid  to  over- 
turn them  ;  by  their  lateral  adhesion,  the  force  tending  to  thrust  them  aside 
horizontally ;  and  by  their  density  and  tenacity,  the  penetration  of  the 
water  into  their  substance.  If  the  water  be  in  motion,  they  must  also  be 
able  to  resist  its  friction,  without  being  carried  away  by  it,  and  they  must 
be  arranged  in  such  a  form,  as  to  be  least  liable  to  be  undermined.  For 
many  of  these  reasons,  the  surface  of  the  bank  exposed  to  the  water 
must  be  inclined  to  the  horizon  :  the  line  expressing  the  general  direction 
of  the  pressure  of  the  water  ought  to  be  confined  entirely  within  its  sub- 
stance, so  that  no  force  thus  applied  may  be  able  to  overturn  it  as  a  whole  ; 
and  this  condition  will  always  be  fulfilled,  when  the  sides  of  the  bank  make 
an  angle  with  each  other  not  less  than  a  righl^angle.  The  pressure  acting 
on  a  bank  thus  inclined  will  also  tend  to  condense  the  materials,  and  to 
increase  their  lateral  adhesion,  and  the  particles  will  become  less  liable  to 
crumble  away  by  their  weight,  than  if  the  surface  were  more  nearly  ver- 
tical. For  embankments  opposed  to  the  sea,  a  bank  much  inclined  has  also 
the  additional  advantage  of  breaking  the  force  of  the  waves  very  effectually. 
An  embankment  of  this  kind  is  usually  furnished  with  drains,  formed  by 
wooden  pipes  or  by  brickwork,  closed  by  falling  doors  or  valves,  which 
allow  the  water  to  flow  out  at  low  water,  but  do  not  permit  the  tide  to  enter. 
To  prevent  the  penetration  of  the  water,  clay  is  often  used,  either  mixed 
with  gravel  or  sunk  in  a  deep  trench  cut  on  each  side  of  the  canal  or  re- 
servoir. (Plate  XXI.  Fig.  281.) 

The  greater  or  less  velocity  of  a  river  must  determine  what  substances 
are  capable  of  withstanding  its  tendency  to  disturb  them  ;  some  are  carried 
away  by  a  velocity  of  a  few  inches  in  a  second,  others  remain  at  rest  when 
the  velocity  amounts  to  several  feet.  But  in  general,  the  velocity  of  a  river 
is  sufficient  to  produce  a  gradual  transfer  of  the  particles  of  its  bed,  which 
are  shifted  slowly  downwards,  towards  the  sea,  being  occasionally  deposited 
in  those  parts  where  the  water  has  least  motion,  and  serving  at  last  to  form 
the  new  land,  which  is  always  advancing  into  the  sea,  on  each  side  of  the 
mouth  of  a  large  river.  It  has  been  recommended  as  a  good  form  for  a 
navigable  river  or  canal,  to  make  the  breadth  of  the  horizontal  bottom  one 
fifth  of  that  of  the  surface,  and  the  depth  three  tenths.  (Plate  XXI. 
Fig.  282.) 

If  a  canal  or  a  reservoir  were  confined  by  a  perpendicular  surface  of 
boards,  and  it  were  required  to  support  it  by  a  single  prop,  the  prop  should 
be  placed,  as  we  have  already  seen,  at  the  distance  of  one  third  of  the  whole 
height  from  the  bottom  ;  but  it  would  be  always  more  convenient  in  prac- 


ON  HYDROSTATIC  INSTRUMENTS,  &c.  239 

tice  to  fix  the  side  of  the  reservoir  at  the  bottom,  than  to  allow  the  whole 
pressure  to  be  supported  by  the  prop,  and  it  might  also  be  strengthened  by 
means  of  ribs,  thicker  below  than  above,  so  as  to  produce  an  equal  strength 
throughout,  wherever  the  prop  might  be  placed  ;  but  if  the  side  were 
formed  of  a  single  plank  of  uniform  thickness,  the  strain  would  be  most 
equally  divided  by  placing  the  prop  very  near  the  middle  of  its  height. 

The  strength  of  the  materials  employed  for  flood  gates  and  sluices  requires 
to  be  determined  according  to  the  principles  which  have  been  laid  down, 
in  treating  of  the  passive  strength  of  substances  used  for  purposes  simply 
mechanical ;  but  the  calculations  become  in  this  case  much  more  intricate. 
Thus,  if  we  have  a  circular  plate  or  plank,  of  a  uniform  elastic  substance, 
constituting  the  bottom  of  a  pipe  or  cistern,  and  simply  supported  at  the 
circumference,  a  very  complicated  calculation  is  required  for  determining 
the  proportion  of  its  strength  to  that  of  a  square  plate  of  the  same  breadth, 
supported  only  at  two  opposite  ends,  since  at  each  point  of  the  circular 
piece,  there  are  two  curvatures  which  require  to  be  considered.  The  square 
plate  will  support  a  column  of  fluid  twice  as  heavy  as  the  weight  which 
would  break  it,  if  placed  at  its  centre ;  and  if  I  have  been  correct  in  the 
calculation,  a  circular  plate  will  support  a  height  of  water  nearly  sixteen 
sevenths  as  great  as  a  square  plate.  But  for  ordinary  purposes,  it  will  be 
sufficient  to  consider  the  strength  as  derived  only  from  the  resistance  opposed 
to  the  flexure  in  one  direction,  since  the  additional  strength,  obtained  from  the 
lateral  supports,  may  very  properly  be  neglected,  as  only  assisting  in  afford- 
ing that  additional  security  which  is  always  necessary,  to  compensate  for 
any  accidental  defects  of  the  materials.  It  has  been  asserted  that  the 
strength  of  a  square  plate  is  doubled  when  it  is  supported  on  both  sides  ; 
but  this  appears  to  be  a  mistake. 

We  may,  therefore,  be  contented  with  determining  the  strain  on  the  ma- 
terials in  that  direction  in  which  they  afford  the  greatest  resistance,  either 
from  the  shorter  distance  between  the  supports,  or  by  the  disposition  of  the 
fibres  ;  and  it  will  be  always  most  eligible  to  combine  these  circumstances, 
so  that  the  fibres  of  the  wood  may  be  arranged  in  the  direction  of  the  short- 
est dimensions  of  the  sluice.  If  a  sluice  be  supported  above  and  below 
only,  the  greatest  strain  will  be  at  the  distance  of  about  three  sevenths  of 
its  height  from  the  bottom  ;  and  it  is  at  this  point  that  the  greatest  strength 
is  required.  But  if  the  boards  forming  the  sluice  be  fixed  across  it,  in  hori- 
zontal directions,  their  strength  must  be  greatest  at  the  bottom.  (Plate 
XXI.  Fig.  283.) 

In  the  construction  of  flood  gates,  the  principles  of  carpentry  must  be  ap- 
plied in  a  manner  nearly  similar  to  that  which  serves  for  the  determination 
of  the  best  forms  of  roofs.  The  flood  gates,  if  they  are  double,  without  a 
solid  obstacle  between  them,  must  meet  at  an  angle  :  and  when  this  angle 
is  very  open,  the  thrust  against  the  walls  or  hinges  must  necessarily  be  very 
great.  If,  however,  the  angle  were  too  acute,  the  flood  gates  would  require 
to  be  lengthened,  and  in  this  case  their  strength  would  be  far  more  dimi- 
nj^hed  than  that  of  a  roof  similarly  elevated,  since  the  hydrostatic  pressure 
acts  always  with  full  force  in  a  perpendicular  direction.  The  thickness 


240  LECTURE  XXVI. 

required  for  each  flood  gate  may  be  determined  in  the  same  manner  as  the 
thickness  of  a  sluice. 

Where  a  sluice  board  of  considerable  dimensions  is  to  be  occasionally 
raised,  it  may  be  necessary  to  ascertain  the  force  which  will  be  required  for 
overcoming  its  friction ;  this  friction  is  nearly  proportional  to  the  whole 
pressure  of  the  water,  and  may  be  found,  with  sufficient  accuracy,  in  pounds, 
by  multiplying  the  square  of  the  depth  of  the  sluice,  in  feet,  by  10.  Thus, 
if  the  depth  be  3  feet,  the  friction  or  adhesion  will  be  about  90  pounds  for 
each  foot  of  the  breadth. 

If  the  side  of  a  canal  gives  way,  it  is  sometimes  of  consequence  to  pre- 
vent, as  much  as  possible,  the  escape  of  the  water.  For  this  purpose  it  is 
usual  to  have  doors  or  valves  in  various  parts  of  the  canal,  which,  when  the 
water  is  at  rest,  lie  nearly  flat  at  the  bottom ;  but  when  it  begins  to  run 
over  them,  with  a  considerable  velocity,  they  are  raised  by  its  force,  and 
put  a  stop  to  its  motion. 

The  utility  of  the  introduction  of  canals  into  a  commercial  country  may 
be  estimated  in  some  measure  by  the  effect  of  the  same  labour,  employed  in 
removing  weights  by  land  carriage  and  by  water.  Thus,  a  single  horse  can 
scarcely  draw  more  than  a  ton  weight  on  the  best  road,  but  on  a  canal,  the 
same  horse  can  draw  a  boat  of  30  tons  at  the  same  rate. 

The  construction  of  piers  and  quays,  and  the  management  of  harbours, 
are  also  important  departments  of  hydraulic  architecture  ;  it  often  happens 
that  besides  the  application  of  the  general  principles  of  mechanics  and 
hydrostatics  to  these  purposes,  the  peculiar  circumstances  of  the  case  may 
indicate  to  an  ingenious  artist  a  mode  of  performing  the  required  work  in 
an  effectual  and  economical  manner.  We  may  find  a  good  example  of  such 
an  arrangement,  in  the  account  given,  by  Mr.  Smeaton,  of  the  method 
which  he  adopted  for  the  improvement  of  the  port  of  Ramsgate,*  and  which 
indeed  resembles  some  that  had  been  before  employed  in  similar  cases :  by 
forming  a  large  excavation,  which  is  furnished  with  flood  gates,  and  is  con- 
stantly filled  at  high  water,  he  has  procured  a  number  of  artificial  torrents, 
which  escape  through  the  sluices,  and  become  powerful  agents  for  carrying 
away  the  matter  deposited  by  the  sea,  and  tending  to  impede  the  navigation 
of  the  harbour. 


LECT.  XXVL— ADDITIONAL  AUTHORITIES.     (See  LECT.  XXIV.) 

Specific  Gravities. — Marinus  Ghetaldus,  Promotus  Archimedes,  4to,  Romse, 
1603.  Boyle's  Works,  1772.  Tables  of  Specific  Gravities,  Ph.  Tr.  xv.  927; 
xvii.  694  ;  xxvii.  206,  511 ;  xxxiii.  114  ;  xlv.  416,  the  last  by  Davis.  Brisson,  Pe- 
santeur  Spec,  des  Corps,  4to,  Paris,  1787.  Ramsden  on  the  Sp.  Gr.  of  Fluids,  4to, 
1792.  Atkins  on  Sp.  Gr.  4to,  1803. 

Hydrometers.— Boyle's,  Ph.  Tr.  1675,  p.  329.  Moncorie's,  Birch,  i.  257.  Horn- 
berg's  Areometer,  Hist,  et  Mem.  1699,  p.  46.  Irwin,  Ph.  Tr.  1721,  p.  223. 
Fahrenheit,  Areometri  Descriptio,  ibid.  1724,  p.  140.  Desaguliers  on  Clarke's 
Hydrometer,  ib.  1730,  p.  277.  Gesner  de  Hydroscopico,  Zurich,  1754.  On 
Areometers,  Hist,  et  Mem.  1768,  p.  435  ;  1770,  p.  526  ;  Ph.  Tr.  1778,  p.  509  ; 
1788,  p.  582 ;  1793,  p.  145.  Roz.  Jour,  xxxiii.  241.  Mem.  della  Soc.  Ital.  vii.  79. 
Annales  de  Chimie,  xxi.  3  (Guytoris),  xxvi.  3,  132  ;  xxviii.  3,  282  ;  xxxi.  12^  ; 

*  Smeaton  on  Ramsgate  Harbour,  Lond.  1791. 


ON  THE  REGULATION  OF  HYDRAULIC  FORCES.        241 

xxxiii.  3.  Nicholson's  Journal,  i.  37  (Baume's),  110.  Nicholson's  Hyd.  Manch. 
Mem.  ii.  370.  Nat.  Ph.  ii.  16.  Quin's,  Tr.  Soc.  Arts,  yiii.  198.  Schmidt's, 
Gren's  Journal  der  Physik,  vii.  186.  Charles's  Biot's  Traite  de  Physique,  i.  114; 
Benoit  Theorie  Generale  des  Pese -liqueurs,  1821. 

Hydraulic  Architecture. — Belidor  Sommaired'un  Cours  d' Architecture  Hydrau- 
lique,  Paris,  1720.  Architecture  Hydraulique,  4  vols.  4to,  1737-53.  Erskine,  A 
Dissertation  on  Rivers,  &c.  Loud,  1770.  Prony,  Nouvelle  Architecture  Hydraulique, 
2  vols.  4to,  Paris,  1790-6.  Gilly,  Grundriss  zu  den  Vorlesungen  iiber  Wasserbau- 
kunst,  Berlin,  1795.  Wiebekung,  Wasserbaukunst,  4to,  Darmst.  1798.  Smeaton's 
Reports.  Coulomb  sur  les  Moyens  d'Executer  sous  1'Eautoutes  sortes  de  Travaux 
Hydrauliques  sans  employer  aucun  Epuisement,  1819.  Delaistre,  Science  des  Inge- 
nieurs,  2  vols.  4to,  Paris,  1825.  Crisp,  A  Treatise  on  Marine  Architecture,  1826. 
Aster's  Constructions  Hydrauliques,  fol.  Paris,  1828.  Beaudemoulin,  Recherches 
sur  la  Fondation  des  Ouvrages  Hyd.  4to,  1829. 


LECTURE    XXVII. 


ON  THE  REGULATION  OF  HYDRAULIC  FORCES. 

THOSE  modifications  of  the  motions  of  fluids  which  are  employed  either 
for  conducting  them  from  place  to  place,  or  for  applying  their  powers  to 
the  production  of  mechanical  effects,  may  be  considered  as  constituting  a 
separate  division  of  practical  hydraulics,  which  is  analogous  to  the  subject 
of  general  machinery  in  practical  mechanics. 

A  supply  of  water  may  be  obtained  from  a  reservoir  situated  above  the 
level  at  which  it  is  wanted,  whatever  its  distance  may  be,  either  by  means 
of  open  canals,  or  aqueducts,  or  of  closed  pipes.  Where  an  uninterrupted 
declivity  cannot  be  obtained,  it  is  necessary  to  employ  pipes,  which  may  be 
bent  upwards  or  downwards  at  pleasure,  provided  that  no  part  of  them  be 
more  than  thirty  feet  above  the  reservoir,  and  when  the  pipe  is  once  filled, 
the  water  will  continue  to  flow  from  the  lower  orifice  ;  but  it  is  best  in  all 
such  cases  to  avoid  unnecessary  angles ;  for  when  the  pipe  rises  and  falls 
again,  a  portion  of  the  air,  which  is  always  contained  in  water,  is  frequently 
collected  in  the  angle,  and  very  materially  impedes  the  progress  of  the 
water  through  the  pipe.  When  the  bent  part  is  wholly  below  the  orifices 
of  the  pipe,  this  air  may  be  discharged  by  various  methods.  The  ancients 
used  small  upright  pipes  called  columnaria,  rising  from  the  convexity  of 
the  principal  pipe,  to  the  level  of  the  reservoir,  and  suffering  the  air  to 
escape  without  wasting  any  of  the  water.  It  may  however  frequently  be 
inconvenient  or  impossible  to  apply  a  pipe  of  this  kind  ;  and  the  same  pur- 
pose may  be  answered,  by  fixing  on  the  pipe  a  box  containing  a  small  valve, 
which  opens  downwards,  and  is  supported  by  a  float,  so  as  to  remain  shut 
while  the  box  is  full  of  water,  and  to  fall  open  when  any  air  is  collected  in 
it.  (Plate  XXI.  Fig.  284.) 

J[f  the  pipe  were  formed  into  a  siphon,  having  its  flexure  above  both 
orifices,  it  would  be  necessary  to  bend  it  upwards  at  the  extremities,  in  order 
to  keep  it  always  full ;  but  in  this  case  the  accumulation  of  the  air  would 

R 


242  LECTURE   XXVII. 

be  extremely  inconvenient,  since  it  would  collect  so  much  the  more  copiously 
as  the  water  in  the  upper  part  of  the  pipe  would  be  more  free  from  pres- 
sure, and  neither  of  the  methods  which  have  been  mentioned  would  be  of 
any  use  in  extricating  it.  It  has  been  usual  in  such  cases  to  force  a  quan- 
tity of  water  violently  through  the  pipe,  in  order  to  carry  the  air  with  it ; 
but  perhaps  the  same  effect  might  be  produced  much  more  easily,  by  making 
a  small  airtight  valve  in  the  upper  part  of  the  pipe,  opening  outwards,  and 
a  stopcock  immediately  before  it :  the  stopcock  being  suddenly  turned  as 
often  as  might  be  necessary,  the  momentum  of  the  water  in  the  pipe  would 
probably  carry  it  forwards  with  sufficient  force  to  throw  out  the  air  ;  or  if  it 
were  necessary,  external  pressure  might  be  added,  and  the  air  might  even  in 
this  manner  be  discharged  by  the  valve  much  more  readily  than  without  it. 
But  it  might  be  still  simpler  to  have  a  pretty  large  vessel  of  water  screwed 
on  to  the  pipe,  which  would  not  be  filled  with  air  for  a  considerable  time  ; 
and  which,  when  full,  might  be  taken  off  and  replenished  with  water.  (Plate 
XXI.  Fig.  285.) 

The  diameter  of  a  pipe  required  for  conveying  a  given  quantity  of  water 
to  a  given  distance  may  be  calculated  from  the  experiments  of  Mr.  Buat, 
which  have  been  already  mentioned.  Pipes  are  usually  made  of  wood,  of 
lead,  or  of  cast  iron,  but  most  commonly  of  lead  ;  and  of  late  tinned  copper 
has  been  employed  with  considerable  advantage.  A  pipe  of  lead  will 
bear  the  pressure  of  a  column  of  water  ]  00  feet  high,  if  its  thickness  be 
one  hundredth  of  its  diameter,  or  even  less  than  this  ;  but  when  any 
alternation  of  motion  is  produced,  a  much  stronger  pipe  is  required,  and 
it  is  usual  to  make  leaden  pipes  of  all  kinds  far  thicker  than  in  this  pro- 
portion. 

The  form  and  construction  of  stopcocks  and  valves  are  very  various,  ac- 
cording to  their  various  situations  and  uses.  Stopcocks  usually  consist  of 
a  cylindrical  or  conical  part,  perforated  in  a  particular  direction,  and 
capable  of  being  turned  in  a  socket  formed  in  the  pipe,  so  as  to  open  or  shut 
the  passage  of  the  fluid,  and  sometimes  to  form  a  communication  with  either 
of  two  or  more  vessels  at  pleasure.  A  valve  is  employed  where  the  fluid 
is  to  be  allowed  to  pass  in  one  direction  only,  and  not  to  return.  For 
water,  those  valves  are  the  best  which  interrupt  the  passage  least ;  and  none 
appears  to  fulfil  this  condition  better  than  the  common  clack  valve  of 
leather,  which  is  generally  either  single,  or  divided  into  two  parts ;  but  it 
is  sometimes  composed  of  four  parts,  united  so  as  to  form  a  pyramid,  nearly 
resembling  the  double  and  triple  valves  which  are  formed  by  nature  in  the 
hearts  of  animals.  A  board,  or  a  round  flat  piece  of  metal,  divided  un- 
equally by  an  axis  on  which  it  moves,  makes  also  a  very  good  simple  valve. 
Where  a  valve  is  intended  to  intercept  the  passage  of  steam,  it  must  be  of 
metal ;  such  a  valve  is  generally  a  flat  plate,  with  its  edge  ground  a  little 
conically,  and  guided  in  its  motion  by  a  wire  or  pin.  For  air,  valves  are 
commonly  made  of  oiled  silk,  supported  by  a  perforated  plate  or  grating. 
(Plate  XXI.  Fig.  286,  287.) 

Before  we  consider  the  application  of  the  force  of  fluids  in  motion  to  prac- 
tical purposes,  we  must  attend  to  the  methods  of  measuring  the  velocity  of 
their  motions.  This  may  be  done  either  by  a  comparison  with  linear  mea- 


ON  THE  REGULATION  OF  HYDRAULIC  FORCES.        243 

sures,  or  by  instruments  founded  on  the  laws  of  hydraulic  pressure.  One 
of  the  best  of  such  instruments  is  the  tube  invented  by  Pitot,*  and  improved 
by  Buat.t  A  funnel  is  presented  to  the  stream,  and  the  water  in  a  vertical 
tube  connected  with  it  is  elevated  above  the  level  of  the  river,  nearly  to  the 
height  corresponding  to  the  velocity  :  but  it  is  said  that  the  result  will  be 
less  liable  to  error,  if  the  funnel  be  covered  by  a  plate  with  a  small  orifice  in 
its  centre,  the  elevation  being  in  this  case  always  half  as  great  again  as  the 
height  due  to  the  velocity.  Other  instruments  intended  for  the|same  pur- 
pose, require  some  previous  experiments  for  determining  the  degree  in 
which  they  are  affected  by  different  velocities  ;  in  this  manner  the  hydro- 
metrical  fly  is  adjusted  ;£  the  impulse  of  the  water  on  two  inclined  planes 
turning  an  axis  to  which  they  are  fixed,  and  by  its  means  a  series  of  wheels, 
with  an  index,  which  expresses  the  space  described  during  the  time  of 
observation.  Instruments  similar  to  these  have  also  sometimes  been  em- 
ployed, for  measuring  the  relative  velocity  with  which  a  ship  under  way 
passes  through  the  water  ;  and  an  apparatus,  resembling  Pitot' s,  has  been 
adapted  to  this  purpose  by  Captain  Hamilton,  with  the  addition  of  a  tube 
inserted  into  it  on  a  level  with  the  surface  of  the  water,  which  continually 
discharges  a  small  stream  into  a  reservoir  with  a  velocity  regulated  by  the 
pressure,  and  consequently  equal  or  proportional  to  that  of  the  ship  itself.§ 
In  this  manner  he  obtains  an  accurate  register  of  the  whole  distance 
described,  including  the  effect  of  all  the  variations  of  the  velocity.  If  the 
orifice  be  small,  it  will  be  necessary  to  attend  to  the  temperature  of  the 
water,  since  the  discharge  is  considerably  retarded  by  any  considerable 
degree  of  cold.  But  when  the  aperture  which  determines  the  magnitude 
of  the  discharge  is  wholly  under  water,  as  Captain  Hamilton  has  placed 
it,  this  source  of  error  is  probably  much  diminished.  (Plate  XXII.  Fig. 
288,  289.) 

The  motions  of  the  air  may  also  be  measured  by  instruments  similar  to 
those  which  are  employed  for  determining  the  velocity  of  streams  of  water. 
The  direction  of  the  wind  is  sometimes  indicated  by  a  wind  dial,  consisting 
simply  of  an  index,  connected  by  wheels  with  a  common  vane  or  weather- 
cock. Its  velocity  may  be  found  by  means  of  wind  gages  of  different  kinds  :  || 
these  are  sometimes  constructed  by  opposing  a  flat  surface  to  the  wind,  the 
pressure  being  measured  by  the  flexure  of  a  spring,  or  by  the  winding  up 
of  a  weight  on  a  spiral  barrel  ;  and  sometimes  by  receiving  the  stream  in 
the  mouth  of  a  funnel,  so  as  to  raise  a  column  of  water,  in  a  vertical 
tube,  to  a  height  equivalent  to  the  pressure,  or  to  condense  a  quantity  of 
air  inclosed  in  a  cavity,  to  a  degree  which  is  indicated  by  the  place  of 
a  small  portion  of  mercury,  moving  in  a  horizontal  tube,  which  leads  to 
the  cavity.  A  little  windmill,  like  the  hydrometrical  fly,  may  also  be 


*  Hist,  et  Mem.  del'Acad.  de  Par.  1732,  p.  263,  H.  103. 
f  Principes  d'Hydraulique,  vol.  ii.     See  also 


Langsdorffs  Hydraulik,  PI.  25. 

Brouckner's  Machine,  Hist,  et  Mem.   de  Paris,  1750,  H.  169.     Woltmann, 
Theorie  des  Hydrometrischen  Fliigels,  Hamb.  1790. 
" 


. 

§  "Papers  on  Naval  Architecture,  Repert.  ii.  I.  355. 
||  Such  as  Lind's  Wind-Gage,  Ph.  Tr.  1775,  p.  353. 


R2 


244  LECTURE  XXVII. 

employed  for  measuring  the  velocity  of  the  wind,  with  the  assistance  of 
a  watch.* 

The  principal  methods  of  applying  the  force  of  fluids  to  useful  purposes 
are  to  employ  their  weight,  their  impulse,  or  their  pressure.  The  weight  of 
water  may  be  applied,  by  collecting  it  in  a  reservoir  which  alternately 
ascends  and  descends,  by  causing  it  to  act  within  a  pipe  on  a  moveable 
piston,  or  by  conducting  it  into  the  buckets  of  a  revolving  wheel;  its 
impulse  may  be  directed  either  perpendicularly  or  obliquely  against  a 
moveable  surface ;  and  its  pressure  may  be  obtained,  without  any  imme- 
diate impulse,  by  causing  a  stream  to  flow  horizontally  out  of  a  moveable 
pipe  which  revolves  round  an  axis.  The  force  of  the  air  can  only  be  applied 
by  means  of  its  impulse,  and  this  may  be  employed  either  perpendicularly 
or  obliquely. 

When  water  is  collected  in  a  single  reservoir,  which  serves  to  work  a 
pump  or  to  raise  a  weight,  the  mode  of  its  operation  may  be  determined 
from  mechanical  considerations  only  ;  and  it  is  obvious  that  if  we  are  de- 
sirous of  preserving  the  whole  force  of  the  water,  we  must  employ  a  second 
reservoir  to  be  filled  during  the  descent  of  the  first,  which  may  either 
descend  in  its  turn,  or  empty  itself  into  the  first  when  it  has  ascended 
again  to  its  original  situation.  The  action  of  a  column  of  water  inclosed  in 
a  pipe,  is  of  a  nature  nearly  similar  to  that  of  such  a  reservoir,  excepting 
that  the  apparatus  is  more  liable  to  friction  ;  the  arrangement  of  its  parts  is 
nearly  similar,  although  in  an  inverted  position,  to  that  which  is  more  com- 
monly employed  for  raising  water  by  means  of  pumps.  But  both  these 
methods  of  employing  the  weight  of  water  are  in  great  measure  confined  to 
those  cases  in  which  it  is  to  be  procured  in  a  small  quantity,  and  may  be 
allowed  to  descend  through  a  considerable  height,  and  when  the  circum- 
stances do  not  allow  us  to  employ  machines  which  require  a  greater  space. 

We  have  seen  that  in  order  to  determine  the  effect  of  any  force  employed 
in  machinery,  we  must  consider  not  only  its  magnitude,  but  also  the  velo- 
city with  which  it  can  be  brought  into  action,  and  we  must  estimate  the 
ultimate  value  of  the  power,  by  the  joint  ratio,  or  the  product,  of  the  force 
and  the  velocity.  Thus,  if  we  had  a  corn  mill,  for  example,  in  which  we 
wished  the  millstone  to  revolve  with  a  certain  velocity  and  to  overcome  a 
given  resistance,  and  supposing  that  this  effect  could  be  obtained  by  means 
of  a  certain  train  of  wheels  from  a  given  source  of  motion  ;  if  the  velocity 
of  the  motion  at  its  source  be  reduced  to  one  half,  we  must  double  the 
diameter  of  one  of  the  wheels  by  which  the  force  is  communicated,  in  order 
to  give  the  millstone  the  desired  velocity,  and  thus  we  must  introduce  a 
mechanical  disadvantage,  which  can  only  be  compensated  by  a  double  in- 
tensity in  the  force  at  its  origin. 

If  we  apply  this  estimation  of  effect  to  the  motion  of  an  overshot  wheel, 

*  Huygens,  Mach.  Approuvees,  i.  71.  Sir  C.  Wren's  "Weather-wiser,  Birch's 
Hist,  of  the  Roy.  Soc.  i.  341.  Hookes  in  his  Philos.  Experiments,  &c.  edited  by 
Derham,  p.  41.  Whewell's,  Trans,  of  the  Camb.  Ph.  Soc.  vol.  vi.  Osier's,  Report 
of  the  Br.  Ass.  vol.  vii.  Sections,  p.  33,  and  Description  of  a  Self-registering  Ane- 
mometer, &c.  4to,  Birmingham,  1839. 


ON  THE  REGULATION  OF  HYDRAULIC  FORCES.        245 

we  shall  find  that  the  velocity  of  the  wheel,  and  consequently  its  hreadth, 
and  the  magnitude  of  its  buckets,  is  perfectly  indifferent  with  respect  to  the 
value  of  its  operation  :  for  supposing  the  stream  to  enter  the  buckets  with 
the  uniform  velocity  of  the  wheel,  the  quantity  of  water  in  the  wheel  at  any 
one  time,  and  consequently  the  pressure,  must  be  inversely  as  the  velocity, 
so  that  the  product  of  the  force  into  the  velocity  will  be  the  same,  however 
they  may  separately  vary.  If,  however,  the  velocity  were  to  become  very 
considerable,  it  would  be  necessary  to  sacrifice  a  material  part  of  the  fall, 
in  order  that  the  water  might  acquire  this  velocity  before  its  arrival  at  the 
wheel ;  but  a  fall  of  one  foot,  or  even  less,  is  sufficient  for  producing  any 
velocity  that  would  be  practically  convenient :  and  it  is  obvious,  on  the 
other  hand,  that  a  certain  velocity  may  be  procured  from  a  wheel  moving 
rapidly,  with  less  machinery  than  from  another  which  moves  more  slowly. 
In  general  the  velocity  of  the  surface  of  the  wheel  is  between  two  and  six 
feet  in  a  second  ;*  and  whether  it  be  greater  or  smaller,  the  force  actually 
applied  will  always  be  equal  in  effect  to  the  weight  of  a  portion  of  the 
stream  employed,  equal  in  length  to  the  height  of  the  wheel.  In  order  to 
avoid  the  resistance  which  might  be  occasioned  by  the  stagnant  water  below 
the  wheel,  it  is  a  good  practice  to  turn  the  stream  backwards  upon  its 
nearer  half,  so  that  the  water,  when  discharged,  may  run  off  in  the  general 
direction  of  its  motion.  (Plate  XXII.  Fig.  290.) 

If  we  suffer  the  stream  of  water  to  acquire  the  utmost  velocity  that  the 
whole  fall  can  produce,  and  to  strike  horizontally  against  the  floatboards  of 
an  undershot  wheel,  or  if  we  wish  to  employ  the  force  of  a  river  running  in 
a  direction  nearly  horizontal,  the  wheel  must  move,  in  order  to  produce  the 
greatest  effect,  with  half  the  velocity  of  the  stream.t  For  the  whole  quan- 
tity of  water  impelling  the  floatboards  is  nearly  the  same,  whatever  may  be 
the  velocity,  especially  if  the  wheel  is  properly  inclosed  in  a  narrow  chan- 
nel, and  hence  it  is  easy  to  calculate  that  the  greatest  possible  effect  will  be 
produced  when  the  relative  velocity  of  the  stream,  striking  the  floatboards, 
is  equal  to  the  velocity  of  the  wheel  itself.  The  pressure  on  the  floatboards 
is  equal  to  that  of  a  stream  containing  the  same  quantity  of  water,  and 
striking  a  fixed  obstacle  with  half  the  velocity,  that  is,  such  a  stream  as 
escapes  from  the  wheel,  which  must  be  twice  as  deep  or  twice  as  wide  as 
the  original  stream,  since  its  motion  is  only  one  half  as  rapid  ;  and  a  column 
of  such  a  stream,  of  twice  the  height  due  to  its  velocity,  that  is,  of  half  the 
height  of  the  fall,  being,  as  we  have  already  seen,  the  measure  of  the 
hydraulic  pressure,  this  force  will  be  precisely  half  as  great  as  that  of  a 
similar  column,  acting  on  an  overshot  wheel,  which  moves  with  the  same 
velocity.;}:  But  the  stream  thus  retarded  will  not  retain  the  other  half  of 
its  mechanical  power  ;  since  its  greatest  effect  will  be  in  the  same  propor- 
tion to  that  of  an  equal  stream  acting  on  an  overshot  wheel  with  one  fourth 
of  the  fall  of  the  former  :  and  the  remaining  fourth  of  the  power  is  lost  in 

*  Smeaton,  Ph.  Tr.  1759,  li.  134,  deduces  from  experiments  a  little  more  than 
three  feet  in  a  second,  and  observes,  that  high  wheels  (24  feet,  or  the  like)  may  de- 
viate more  from  this  velocity  than  low,  without  materially  affecting  their  work. 

f  Do.  ibid.  p.  122,  gives  the  best  proportion  as  2  :  5.  Compare  Robison,  Mech. 
Phil.  ii.  625.  J  Ibid.  p.  130. 


246  LECTURE  XXVII. 

producing  the  change  of  form  of  the  water,  and  in  overcoming  its  friction. 
In  whatever  way  we  apply  the  force  of  water,  we  shall  find  that  the  me- 
chanical power  which  it  possesses  must  be  measured  by  the  product  of 
the  quantity  multiplied  by  the  height  from  which  it  descends  :*  for  exam- 
ple, a  hogshead  of  water  capable  of  descending  from  a  height  of  10  feet, 
possesses  the  same  power  as  10  hogsheads  descending  from  a  height  of  one 
foot ;  and  a  cistern  filled  to  the  height  of  10  feet  above  its  orifice  possesses 
100  times  as  much  power  as  the  same  cistern  filled  to  the  height  of  one 
foot  only. 

When,  therefore,  the  fall  is  sufficiently  great,  an  overshot  wheel  is  far 
preferable  to  an  undershot  wheel,  and  where  the  fall  is  too  small  for  an 
overshot  wheel,  it  is  most  advisable  to  employ  a  breast  wheel,  which  par- 
takes of  its  properties,  its  floatboards  consisting  of  two  portions  meeting  at 
an  angle  so  as  to  approach  to  the  nature  of  buckets,  and  the  water  being 
also  in  some  measure  confined  within  them  by  the  assistance  of  a  sweep  or 
arched  channel  which  follows  the  curve  of  the  wheel,  without  coming  too 
nearly  into  contact  with  it  so  as  to  produce  unnecessary  friction.  When 
the  circumstances  do  not  admit  even  of  a  breast  wheel,  we  must  be  con- 
tented with  an  undershot  wheel ;  it  is  recommended,  for  such  a  wheel,  that 
the  floatboards  be  so  placed  as  to  be  perpendicular  to  the  surface  of  the 
water  at  the  time  that  they  rise  out  of  it ;  that  only  one  half  of  each  should 
ever  be  below  the  surface,  and  that  from  three  to  five  should  be  immersed 
at  once,  according  to  the  magnitude  of  the  wheel.  Sometimes,  however,  it 
has  been  thought  eligible  to  employ  a  much  smaller  number ;  thus  the 
water  wheel  which  propels  Mr.  Symington's  steam-boatt  has  only  six 
floatboards  in  its  whole  circumference.  (Plate  XXII.  Fig.  291,  292.) 

Since  the  water  escaping  from  an  undershot  wheel  still  retains  a  part  of 
its  velocity,  it  is  obvious  that  this  may  be  employed  for  turning  a  second 
wheel,  if  it  be  desirable  to  preserve  as  much  as  possible  of  the  force.  In  this 
case,  by  causing  the  first  wheel  to  move  with  two  thirds  of  the  velocity  of 
the  stream,  the  whole  effect  of  both  will  be  one  third  greater  than  that  of  a 
single  wheel  placed  in  the  same  stream ;  but  it  must  be  considered  that 
the  expense  of  the  machinery  will  also  be  materially  increased. 

Considerable  errors  have  frequently  been  made  by  mathematicians  and 
practical  mechanics  in  the  estimation  of  the  force  of  the  wind  or  the  water 
on  oblique  surfaces  ;  they  have  generally  arisen  from  inattention  to  the 
distinction  between  pressure  and  mechanical  power.  It  may  be  demon- 
strated that  the  greatest  possible  pressure  of  the  wind  or  water,  on  a  given 
oblique  surface  at  rest,  tending  to  turn  it  in  a  direction  perpendicular  to 
that  of  the  wind,  is  obtained  when  the  surface  forms  an  angle  of  about  55° 
with  the  wind  ;  but  that  the  mechanical  power  of  such  a  pressure,  which 
is  to  be  estimated  from  a  combination  of  its  intensity  with  the  velocity  of 
the  surface,  may  be  increased  without  limit  by  increasing  the  angle  of 
inclination,  and  consequently  the  velocity.  The  utmost  effect  that  could  be 
thus  obtained  would  be  equal  to  that  of  the  same  wind  or  stream  acting  on 
the  floatboards  of  an  undershot  wheel :  but  since  in  all  practical  cases  the 

*  Smeaton,  Ph.  Tr.  li.  116,  131 ;  and  Ixvi.  450. 
f  See  Journal  of  the  Royal  Institution,  vol.  i. 


ON  THE  REGULATION  OF  HYDRAULIC  FORCES.        247 

velocity  is  limited,  the  effect  will  be  somewhat  smaller  than  this  :  for 
example,  if  the  mean  velocity  of  the  sails  or  floatboards  be  supposed  equal 
to  that  of  the  wind,  the  mechanical  power  will  be  more  than  four  fifths  as 
great  as  that  of  an  undershot  wheel,  that  is,  in  the  case  of  a  windmill, 
more  than  four  fifths  of  the  utmost  effect  that  can  be  obtained  from  the 
wind.  In  such  a  case  Maclaurin  has  shown  that  the  sails  ought  to  make 
an  angle  of  74°  with  the  direction  of  the  wind  :  *  but  in  practice  it  is 
found  most  advantageous  to  make  the  angle  somewhat  greater  than  this, 
the  velocity  of  the  extremities  of  the  sails  being  usually,  according  to 
Mr.  Smeaton,  more  than  twice  t  as  great  as  that  of  the  wind.  It  appears, 
therefore,  that  the  oblique  sails  of  the  common  windmill  are  in  their  nature 
almost  as  well  calculated  to  make  the  best  use  of  any  hydraulic  force  as 
an  undershot  wheel ;  and  since  they  act  without  intermission  throughout 
their  whole  revolution,  they  have  a  decided  advantage  over  such  machines 
as  require  the  sails  or  fans  to  be  exposed  to  a  more  limited  stream  of  the 
wind,  during  one  half  only  of  their  motion,  which  is  necessary  in  the 
horizontal  windmill,  where  a  screen  is  employed  for  covering  them  while 
they  are  moving  in  a  direction  contrary  to  that  of  the  wind  :  and  such 
machines,  according  to  Smeaton,  %  are  found  to  perform  little  more  than 
one  tenth  of  the  work  of  those  which  are  more  usually  employed.  The 
sails  of  a  common  windmill  are  frequently  made  to  change  their  situation 
according  to  the  direction  of  the  wind,  by  means  of  a  small  wheel,  with 
sails  of  the  same  kind,  which  turns  round  whenever  the  wind  strikes  on 
either  side  of  it,  and  drives  a  pinion  turning  the  whole  machinery ;  the 
sails  are  sometimes  made  to  furl  or  unfurl  themselves,  according  to  the 
velocity  of  the  wind,  by  means  of  a  revolving  pendulum,  which  rises  to  a 
greater  or  less  height,  in  order  to  prevent  the  injury  which  the  flour  would 
suffer  from  too  great  a  rapidity  in  the  motion,  or  any  other  accidents  which 
might  happen  in  a  mill  of  a  different  nature.  The  inclination  of  the  axis 
of  a  windmill  to  the  horizon  is  principally  intended  to  allow  room  for  the 
action  of  the  wind  at  the  lower  part,  where  it  would  be  weakened  if  the 
sails  came  too  nearly  in  contact  with  the  building,  as  they  must  do  if  they 
were  perfectly  upright.  When  it  is  necessary  to  stop  the  motion  of  a 
windmill,  a  break  is  applied  to  the  surface  of  a  large*  wheel,  so  that  its 
friction  operates  with  a  considerable  mechanical  advantage.  Water  wheels 
with  oblique  floatboards  are  sometimes  used  with  good  effect  in  China  and 
in  the  south  of  France  :  for  tide  wheels,  such  floatboards  have  the  advan- 
tage that  they  may  be  easily  made  to  turn  on  a  hinge  with  the  stream,  so 
as  to  impel  the  wheel  in  the  same  direction  whether  the  tide  be  flowing  or 
ebbing.  (Plate  XXII.  Fig.  293.) 

A  smoke  jack  is  a  windmill  in  miniature  ;  a  kite  affords  a  very  familiar 
example  of  the  effect  of  the  oblique  impulse  of  the  air,  of  which  the  action 
first  causes  a  pressure  perpendicular  to  the  surface  of  the  kite,  and  this 
force,  combined  with  the  resistance  of  the  string,  produces  a  vertical  result 
capable  of  counteracting  the  weight  of  the  kite.  (Plate  XXII.  Fig.  294.) 

*  Maclaurin's  Account  of  Sir  I.  Newton's  Philos.  Discoveries,  art.  29. 
f  Nearer  three  times.     See  Smeaton,  Ph.  Tr.  1759,  li.  163. 
t  Ibid.  p.  172. 


248  LECTURE  XXVII. 

The  counterpressure  of  the  water,  occasioned  by  the  escape  of  a  stream 
from  a  moveable  reservoir,  was  applied  by  Parent*  to  the  purpose  of  turn- 
ing a  millstone,  and  various  other  authors  have  described  machines  of  a 
similar  nature  :  they  may  be  constructed  with  little  or  no  wheel  work,  and  it 
does  not  appear  to  be  necessary  that  much  of  the  force  of  the  water  sliould  be 
lost  in  their  operation  ;  but  they  have  never  been  practically  employed 
with  success,  nor  have  they  perhaps  ever  had  a  fair  trial. 

The  art  of  seamanship  depends  almost  entirely  on  the  management  of 
the  forces  and  resistances  of  air  and  water,  and  if  the  laws  of  hydraulic 
pressure,  with  respect  to  oblique  and  curved  surfaces,  were  more  completely 
ascertained,  we  might  calculate  not  only  what  the  motions  of  a  ship  would 
be  under  any  imaginable  circumstances,  but  we  might  also  determine  pre- 
cisely what  would  be  the  best  possible  form  of  a  ship,  and  what  the  best 
arrangement  of  her  rigging. 

When  a  ship  is  sailing  immediately  before  the  wind,  little  or  no  art  is 
required  in  setting  her  sails,  and  her  velocity  is  only  limited  by  that  of  the 
wind  and  by  the  resistance  of  the  water  :  but  for  sailing  with  a  side  wind, 
it  becomes  necessary  that  the  immediate  force  of  the  wind  should  be  con- 
siderably modified. 

If  we  had  a  circular  vessel  or  tub,  with  a  single  mast,  and  a  sail  perfectly 
flat,  and  if  the  sail  were  placed  in  a  direction  deviating  but  little  from  that 
of  the  wind,  the  tub  would  begin  to  move  in  a  direction  nearly  at  right 
angles  to  that  of  the  wind,  since  the  impulse  of  the  wind  acts  almost 
entirely  in  a  direction  perpendicular  to  that  of  the  sail :  but  the  slightest 
inequality  of  the  dimensions  of  the  sail,  or  of  the  force  of  the  wind,  would 
immediately  disturb  the  position  of  the  vessel ;  and  in  order  to  avoid  this 
inconvenience,  it  would  be  necessary  to  have  a  moveable  body  projecting 
into  the  water,  so  as  to  create  a  resistance  by  means  of  which  the  vessel 
might  be  steered,  and  the  sail  confined  to  its  proper  place  :  and  this  might 
be  done  more  effectually  by  changing  the  form  of  the  vessel  from  round  to 
oval ;  it  would  then  also  have  the  advantage  of  moving  much  more  easily 
through  the  water  in  the  direction  of  its  length  than  a  circular  vessel  of 
equal  size,  and  of  creating  still  more  resistance  in  a  transverse  direction,  so 
that  when  urged  by  an  oblique  force,  it  would  move  in  some  measure 
obliquely,  but  always  much  more  nearly  in  the  direction  of  its  length  than 
of  its  breadth.  The  angular  deviation  from  the  track  of  the  ship  is  called 
its  lee  way,  and  if  we  know  the  direction  of  the  sails,  and  the  actual  pro- 
portions of  the  resistances  opposed  to  the  ship's  motion  in  different  direc- 
tions, we  may  calculate  from  these  resistances  the  magnitude  of  the  angular 
deviation  or  lee  way :  but  hitherto  such  calculations  have  generally  indi- 
cated a  lee  way  three  or  four  times  as  great  as  that  which  has  been 
observed.  The  use  of  the  keel  is  not  only  to  assist  in  confining  the  motion 
of  the  ship  to  its  proper  direction,  but  also  to  diminish  the  disposition  to 
vibrate  from  side  to  side,  which  would  interfere  with  the  effect  of  the  sails, 
and  produce  many  other  inconveniences.  When  the  principal  force  of  the 
wind  is  applied  to  the  anterior  part  of  the  ship,  her  head  would  be  naturally 

*  Hist,  et  Mem.  de  Paris,  1704.  See  Euler,  Hist,  et  Mem.  de  Berlin,  1750, 
1751,  1752.  Waring,  American  Transactions,  iii.  185. 


ON  THE  REGULATION  OF  HYDRAULIC  FORCES.        249 

turned  from  the  wind  if  the  rudder  were  not  made  to  project  from  the  stern 
in  a  contrary  direction,  and  to  present  the  surface  of  an  inclined  plane  to 
the  water  which  glides  along  the  keel,  so  as  to  preserve  the  ship,  by  means 
of  the  pressure  which  it  receives,  in  any  direction  that  may  be  required  for 
her  manoeuvres.  Commonly,  however,  although  the  sails  may  be  so 
arranged  that  the  principal  force  of  the  wind  appears  to  be  on  the  fore  part 
of  the  ship,  the  curvature  of  the  sails,  or  some  other  cause,  throws  the  pres- 
sure further  backwards,  and  the  action  of  the  rudder  is  necessary  to  prevent 
the  ship's  head  turning  towards  the  wind.  (Plate  XXII.  Fig.  295.) 

When  a  ship  is  steering  in  this  manner  on  a  side  wind,  the  effect  of  the 
wind  has  a  natural  tendency  to  overset  her,  and  if  she  is  too  crank,  that  is, 
deficient  in  stability,  she  cannot  sail  well,  otherwise  than  directly  before  the 
wind.  The  place  of  the  centre  of  gravity,  compared  with  that  of  the  meta- 
centre,  or  imaginary  centre  of  pressure,  determines  the  degree  of  stability, 
and  the  most  general  way  of  increasing  it  is  to  lessen  the  weight  of  the 
upper  part  and  of  the  rigging  of  the  vessel,  to  diminish  her  height,  or  to 
increase  her  breadth,  and  to  stow  the  ballast  as  low  as  possible  in  the  hold. 
Too  little  attention  has  frequently  been  paid  to  this  subject,  as  well  as  to 
many  other  departments  of  naval  architecture  ;  and  although  mere  theore- 
tical investigations  have  hitherto  been  but  of  little  service  to  the  actual 
practice  of  seamanship,  yet  it  cannot  be  doubted  that  an  attention  to  what 
has  already  been  discovered  of  the  laws  of  hydrodynamics,  as  well  as  to  the 
principles  of  mechanics  in  general,  must  be  of  great  advantage  to  the  navi- 
gator, in  enabling  him  to  derive  from  his  own  experience  all  the  benefits 
which  a  correct  mode  of  reasoning  is  capable  of  procuring  him. 


LECT.  XXVII.— ADDITIONAL  AUTHORITIES. 

Force  of  Water. — Segner,  Exercitationes  Hydraulics,  4to,  Gott.  1747.  J.  A. 
Euler,  Enodatio  Qusestionis  de  Molis,  Gott.  1754.  Lambert  on  Mills,  Hist,  et 
Mem.  de  Berlin,  1755.  On  Water-wheels,  ibid.  1755,  pp.  49,  70,  82.  Mallet  on 
do.  Ph.  Tr.  1767,  pp.  57,  372.  Borda  on  do.  Hist.  etMem.  de  Paris,  1767,  p.  270, 
H.  149.  Bossut  on  do.  ibid.  1769,  pp.  288,  477,  H.  121.  Fabre,  Essai  sur  la 
Maniere  la  plus  avantageuse  de  construire  les  Machines  Hydrauliques,  4to,  1783. 
Buchanan  on  Water-wheels,  Ph.  Mag.  x  278  ;  xi.  79.  Essay  on  Millwork,  2  vols. 
1823.  L'Huillier  sur  rArtd'Employerl'Eaucomme  Moteur  des  Roues,  Paris,  1823. 

Force  of  Wind. — Hooke  on  the  Sails  of  Mills  and  Ships,  Philosophical  Collections, 
No.  3,  p.  61.  Lahire  on  Windmills,  Hist,  et  Mem.  de  Paris,  ix.  96.  Euler  on 
do.  Nov.  Com.  Petr.  vi.  41.  Hist,  et  Mem.  de  Berlin,  1756,  p.  165.  Bourrier's 
Horizontal  Mill,  Hist,  et  Mem.  de  Paris,  1762,  H.  190.  Maiziere's  Windmill,  ibid. 
1767,  H.  185.  Coulomb  on  Windmills  and  the  form  of  their  Sails,  ibid.  1781, 
p.  65,  H.  41.  Repertory  of  Arts,  iv.  12  ;  vii.  6,  ii.  I.  II.  13,  Phil.  Mag.  iv.  174.  See 
also  Leupold's  Theatrum  Hydraulicum,  Bailey's  Machines,  Machines  Approuvees, 
Emerson's  Mechanics,  and  Encyclep.  Method,  art.  Meunier. 

Seamanship. — John  Bernoulli's  Theory  of  the  Manoeuvres  of  Ships,  Hist,  et 
Mem.  de  Paris,  1714,  H.  107.  Pitot  on  do.  ibid.  1731,  H.  81.  Bouguer,  ibid. 
1754,  p.  342,  H.  91  ;  1755,  p.  355,  481,  H.  83,  135.  Clairaut,  ibid.  1760,  p.  171, 
H.  141.  Bouguer,  de  la  Manoauvre  des  "Vaisseaux,  4to,  1757.  Euler,  Scientia 
Navalis,  2  vols.  4to,  Petrop.  1749.  Theorie  de  la  Man.  des  Vais.,  Pet.  1773. 
Romme,  Art  de  la  Marine,  4 to,  Paris,  1787.  Hutchison's  Seamanship,  4to,  1794. 
Chapman  on  Canal  Navigation,  4to,  1797.  Bezout,  Traite  de  Navigation,  Paris. 
1814. 

Naval  Architecture. — Meibomius  de  Triremium  Fabrica,  4to,  Amst.  1671.    Du- 


250  LECTURE  XXVIII. 

hamel,  Architecture  Navale,  4to,  Paris,  1758.  Gordon's  Principles  of  Naval  Archi- 
tecture, Lond.  1784.  Chapman,  Traite  de  la  Construction  des  Vaisseaux,  trans- 
lated by  Inman.  Also,  Essays,  in  Papers  on  Naval  Architecture.  Atwood  on  the 
Stability  of  Ships,  Ph.  Tr.  1796,  p.  46;  1798,  p.  201.  Euler  on  the  Construc- 
tion of  Vessels,  by  Sir  G.  Shee.  Trans.  Roy.  Ir.  Acad.  vi.  15.  Watson's  Elements 
of  Naval  Architecture,  fol.  1805. 


LECTURE    XXVIII. 


ON  HYDRAULIC  MACHINES. 

WE  shall  apply  the  denomination  of  hydraulic  machines  to  such  only, 
as  are  intended  for  counteracting  the  gravity  of  water,  that  is,  for  raising  it 
from  a  lower  situation  to  a  higher..  The  simplest  of  these  are  buckets, 
bucket  wheels,  and  friction  ropes  ;  moveable  pipes  are  the  next  in  order  ; 
and  pumps  of  various  kinds  constitute  the  most  extensive  and  the  most 
important  part  of  the  subject.  Besides  these  and  some  other  similar 
machines,  hydraulic  air  vessels  and  artificial  fountains  will  also  require  to 
be  examined. 

A  series  of  earthen  pitchers,  connected  by  ropes,  and  turned  by  trundles 
or  pinions,  over  which  they  pass,  has  long  been  used  in  Spain  under  the 
name  of  noria  :  in  this  country  buckets  of  wood  are  sometimes  employed 
in  a  similar  manner.  A  bucket  wheel  is  the  reverse  of  an  overshot  water- 
wheel,  and  the  water  may  be  raised  by  buckets  nearly  similar  to  those 
which  are  calculated  for  receiving  it  in  its  descent :  sometimes  the  buckets 
are  hung  on  pins,  so  as  to  remain  full  during  the  whole  ascent ;  but  these 
wheels  are  liable  to  be  frequently  out  of  repair.  Sometimes  the  reverse  of 
an  undershot  wheel  or  rather  of  a  breast  wheel,  is  employed  as  a  throwing 
wheel,  either  in  a  vertical  or  in  an  inclined  position.  Such  wheels  are 
frequently  used  for  draining  fens,  and  are  turned  by  windmills  ;  the  float- 
boards  are  not  placed  in  the  direction  which  would  be  best  for  an  undershot 
wheel,  but  on  the  same  principle,  so  as  to  be  perpendicular  to  the  surface 
when  they  rise  out  of  it,  in  order  that  the  water  may  the  more  easily  flow 
offthem.*  (Plate  XXII.  Fig.  296.. .298.) 

Instead  of  a  series  of  buckets  connected  by  ropes  or  chains,  a  similar  effect 
is  sometimes  produced  by  a  simple  rope,  or  a  bundle  of  ropes,  passing  over 
a  wheel  above,  and  a  pulley  below,  moving  with  a  velocity  of  about  8  or  10 
feet  in  a  second,  and  drawing  a  certain  quantity  of  water  up  by  its  fric- 
tion. It  is  probable  that  the  water  commonly  ascends  with  about  half  the 
velocity  of  the  rope,  and  on  this  supposition  we  might  calculate  its  depth  on 
the  rope  by  comparing  its  relative  motion  with  that  of  a  little  river  :  but 
the  rules  which  serve  for  calculating  the  velocity  of  rivers,  do  not  perfectly 
agree  in  this  case  with  the  results  of  direct  experiments  ;  for  the  friction 

*  Vitruvius,  Architecture,  1.  10,  c.  9,  translated  by  Newton,  2  vols.  fol.  London. 


ON  HYDRAULIC  MACHINES.  251 

required  for  elevating  the  quantity  raised  by  such  a  machine,  appears 
from  calculation  to  correspond  to  a  velocity  about  twice  as  great  as  the 
actual  relative  velocity.  While  the  water  is  principally  supported  by 
the  friction  of  the  rope,  its  own  cohesion  is  amply  sufficient  to  prevent 
its  wholly  falling,  or  being  scattered,  by  any  accidental  inequality  of  the 
motion.  (Plate  XXII.  Fig.  299.) 

The  lateral  friction  of  water  has  been  applied  in  a  very  simple  manner 
by  Venturi*  to  the  draining  of  land  by  means  of  a  stream  which  runs 
through  it,  allowing  the  stream  to  acquire  sufficient  velocity  to  carry  it 
over  an  inclined  surface,  and  to  drag  with  it  a  certain  portion  of  water 
from  the  lowest  part  of  this  surface :  but  the  quantity  of  water  raised 
in  this  manner  must  be  very  inconsiderable,  and  the  loss  of  force  by  fric- 
tion very  great. 

A  system  of  spiral  pipes  may  be  placed  in  the  plane  of  a  wheel,  receiving 
the  water  at  its  circumference,  and  raising  it  by  degrees,  as  the  wheel  turns, 
towards  the  axis,  where  it  is  discharged  ;  the  motion  of  the  wheel  being 
usually  derived  from  the  same  stream  which  supplies  the  pipes :  but  the 
height  to  which  the  water  is  raised  by  this  machine  is  very  small  in 
proportion  to  its  bulk.  A  single  pipe  wound  spirally  round  a  cylinder 
which  revolves  on  an  axis  in  an  oblique  situation,  has  been  denominated 
the  screw  of  Archimedes,t  and  is  called  in  Germany  the  water  snail.  Its 
operation,  like  that  of  the  flat  spiral,  may  be  easily  conceived  by  imagining 
a  flexible  pipe  to  be  laid  on  an  inclined  plane,  and  its  lower  part  to  be 
gradually  elevated,  so  that  the  fluid  in  the  angle  or  bend  of  the  pipe  may 
be  forced  to  rise ;  or  by  supposing  a  tube,  formed  into  a  hoop,  to  be  rolled 
up  the  same  plane,  the  fluid  being  forced  by  the  elevation  of  the  tube 
behind  it  to  run  as  it  were  up  hill.  This  instrument  is  sometimes  made  by 
fixing  a  spiral  partition  round  a  cylinder,  and  covering  it  with  an  external 
coating,  either  of  wood  or  of  metal ;  it  should  be  so  placed  with  respect  to 
the  surface  of  the  water  as  to  fill  in  each  turn  one  half  of  a  convolution ; 
for  when  the  orifice  remains  always  immersed,  its  effect  is  much  dimi- 
nished. It  is  generally  inclined  to  the  horizon  in  an  angle  of  between  45 
and  60  degrees  :  hence  it  is  obvious  that  its  utility  is  limited  to  those  cases 
in  which  the  water  is  only  to  be  raised  to  a  moderate  height.  The  spiral 
is  seldom  single,  but  usually  consists  of  three  or  four  separate  coils,  forming 
a  screw  which  rises  slowly  round  the  cylinder.  (Plate  XXII.  Fig.  300, 
301.) 

An  instrument  of  a  similar  nature  is  called  by  the  Germans  a  water 
screw ;  it  consists  of  a  cylinder  with  its  spiral  projections  detached  from 
the  external  cylinder  or  coating,  within  which  it  revolves.  This  machine 
might  not  improperly  be  considered  as  a  pump,  but  its  operation  is  pre- 
cisely similar  to  that  of  the  screw  of  Archimedes.  It  is  evident  that  some 
loss  must  here  be  occasioned  by  the  want  of  perfect  contact  between  the 

*  Prop.  9. 

t  Vitruvius,  1.  10,  c.  11.  Pitot,  Hist,  et  Mem.  de  Paris,  1736,  p.  173,  H.  110. 
TSuler,  Nov.  Com.  Petr.  v.  259.  Hennert,  Dissertation  sur  la  vis  d'Archimede, 
Berl.  1767.  Pattu,  Journal  des  Mines,  1815,  xxxviii.  321.  Gregory's  Mechanics, 
ii.  343. 


252  LECTURE  XXVIII. 

screw  and  its  cover ;  in  general,  at  least  one  third  of  the  water  runs  back, 
and  the  machine  cannot  be  placed  at  a  greater  elevation  than  30° ;  it  is 
also  very  easily  clogged  by  accidental  impurities  of  the  water :  yet  it  has 
been  found  to  raise  more  water  than  the  screw  of  Archimedes,  when  the 
lower  ends  of  both  are  immersed  to  a  considerable  depth ;  so  that  if  the 
height  of  the  surface  of  the  water  to  be  raised  were  liable  to  any  great  vari- 
ations, the  water  screw  might  be  preferable  to  the  screw  of  Archimedes. 
(Plate  XXII.  Fig.  302.) 

When  a  spiral  pipe,  consisting  of  many  convolutions,  arranged  either  in 
a  single  plane,  or  in  a  cylindrical  or  conical  surface,  and  revolving  round  a 
horizontal  axis,  is  connected  at  one  end  by  a  watertight  joint  with  an  as- 
cending pipe,  while  the  other  end  receives  during  each  revolution  nearly 
equal  quantities  of  air  and  water,  the  machine  is  called  a  spiral  pump.  It 
was  invented  about  1746,  by  Andrew  Wirtz,  a  pewterer  at  Zurich,  and  it 
is  said  to  have  been  used  with  great  success  at  Florence  and  in  Russia  :  it 
has  also  been  employed  in  this  country  by  Lord  Stanhope,  and  I  have 
made  trial  of  it  for  raising  water  to  a  height  of  forty  feet.'*  The  end  of  the 
pipe  is  furnished  with  a  spoon,  containing  as  much  water  as  will  fill  half  a 
coil,  which  enters  the  pipe  a  little  before  the  spoon  has  arrived  at  its 
highest  situation,  the  other  half  remaining  full  of  air,  which  communicates 
the  pressure  of  the  column  of  water  to  the  preceding  portion,  and  in  this 
manner  the  effect  of  nearly  all  the  water  in  the  wheel  is  "united,  and  be- 
comes equivalent  to  that  of  the  column  of  wrater,  or  of  water  mixed  with 
air,  in  the  ascending  pipe.  The  air  nearest  the  joint  is  compressed  into  a 
space  much  smaller  than  that  which  it  occupied  at  its  entrance,  so  that 
where  the  height  is  considerable,  it  becomes  advisable  to  admit  a  larger 
portion  of  air  than  would  naturally  fill  half  the  coil,  and  this  lessens  the 
quantity  of  water  raised,  but  it  lessens  also  the  force  required  to  turn  the 
machine.  The  joint  ought  to  be  conical,  in  order  that  it  may  be  tightened 
when  it  becomes  loose,  and  the  pressure  ought  to  be  removed  from  it  as 
much  as  possible.  The  loss  of  power,  supposing  the  machine  well  con- 
structed, arises  only  from  the  friction  of  the  water  on  the  pipe,  and  the 
friction  of  the  wheel  on  its  axis  ;  and  where  a  large  quantity  of  water  is  to 
be  raised  to  a  moderate  height,  both  of  these  resistances  may  be  rendered 
inconsiderable.  But  when  the  height  is  very  great,  the  length  of  the  spiral 
must  be  much  increased,  so  that  the  weight  of  the  pipe  becomes  extremely 
cumbersome,  and  causes  a  great  friction  on  the  axis,  as  well  as  a  strain  on 
the  machinery :  thus,  for  a  height  of  40  feet,  I  found  that  the  wheel 
required  above  100  feet  of  a  pipe  which  was  three  quarters  of  an  inch  in 
diameter  ;  and  more  than  one  half  of  the  pipe  being  always  full  of  water, 
we  have  to  overcome  the  friction  of  about  80  feet  of  such  a  pipe,  which  will 
require  24  times  as  much  excess  of  pressure  to  produce  a  given  velocity,  as 
if  there  were  no  friction.  The  centrifugal  force  of  the  water  in  the  wheel 
would  also  materially  impede  its  ascent  if  the  velocity  were  considerable, 
since  it  would  be  always  possible  to  turn  it  so  rapidly  as  to  throw  the 
whole  water  back  into  the  spoon.  The  machine  which  I  had  erected  being 

*  Sulzer's  Sammlungen  Vermischeln  Schriften,  1754.  Ziegler,  Gesellschaft  zu 
Zurich,  vol.  iii.  Nicander,  Schwed.  Abhand.  1783. 


ON  HYDRAULIC  MACHINES.  253 

out  of  repair,  I  thought  it  more  eligible  to  substitute  for  it  a  common 
'forcing  pump,  than  to  attempt  to  make  any  further  improvement  in  it, 
under  circumstances  so  unfavourable.  But  if  the  wheel  with  its  pipes  were 
entirely  made  of  wood,  it  might  in  many  cases  succeed  better  :  or  the  pipes 
might  be  made  of  tinned  copper,  or  even  of  earthenware,  which  might  be 
cheaper  and  lighter  than  lead.  (Plate  XXII.  Fig.  303.) 

The  centrifugal  force,  which  is  an  impediment  to  the  operation  of 
Wirtz's  machines,  has  sometimes  been  employed,  together  with  the  pressure 
of  the  atmosphere,  as  an  immediate  agent  in  raising  water,  by  means  of  the 
rotatory  pump.  This  machine  consists  of  a  vertical  pipe,  caused  to  revolve 
round  its  axis,  and  connected  above  with  a  horizontal  pipe,  which  is  open 
at  one  or  at  both  ends,  the  whole  being  furnished  with  proper  valves  to  pre- 
vent the  escape  of  the  water  when  the  machine  is  at  rest.  As  soon  as  the 
rotation  becomes  sufficiently  rapid,  the  centrifugal  force  of  the  water  in  the 
horizontal  pipe  causes  it  to  be  discharged  at  the  end,  its  place  being  sup- 
plied by  means  of  the  pressure  of  the  atmosphere  on  the  reservoir  below, 
which  forces  the  water  to  ascend  through  the  vertical  pipe.  It  has  also 
been  proposed  to  turn  a  machine  of  this  kind  by  the  counterpressure  of 
another  portion  of  water,  in  the  manner  of  Parent's  mill,  where  there  is 
fall  enough  to  carry  it  off.*  This  machine  may  be  so  arranged  that, 
according  to  theory,  little  of  the  force  applied  may  be  lost ;  but  it  has 
failed  of  producing  in  practice  a  very  advantageous  effect.  (Plate  XXIII. 
Fig.  304.) 

A  pump  is  a  machine  so  well  known,  and  so  generally  used,  that  the  de- 
nomination has  not  uncommonly  been  extended  to  hydraulic  machines  of 
all  kinds  ;  but  the  term,  in  its  strictest  sense,  is  to  be  understood  of  those 
machines  in  which  the  water  is  raised  by  the  motion  of  one  solid  within 
another,  and  this  motion  is  usually  alternate,  but  sometimes  continued  so  as 
to  constitute  a  rotation.  In  all  the  pumps  most  commonly  used,  a  cavity 
is  enlarged  and  contracted  by  turns,  the  water  being  admitted  into  it  through 
one  valve,  and  discharged  through  another. 

One  of  the  simplest  pumps  for  raising  a  large  quantity  of  water  to  a  small 
height,  is  made  by  fitting  two  upright  beams  or  plungers,  of  equal  thickness 
throughout,  into  cavities  nearly  of  the  same  size,  allowing  them  only  room 
to  move  without  friction,  and  connecting  the  plungers  by  a  horizontal  beam 
moving  on  a  pivot.  The  water  being  admitted,  during  the  ascent  of  each 
plunger,  by  a  large  valve  in  the  bottom  of  the  cavity,  it  is  forced,  when  the 
plunger  descends,  to  escape  through  a  second  valve  in  the  side  of  the  cavity, 
and  to  ascend  by  a  wide  pipe  to  the  level  of  the  beam.  The  plungers  ought 
not  to  be  in  any  degree  tapered,  because  of  the  great  force  which  would  be 
unnecessarily  consumed,  in  continually  throwing  out  the  water,  with  great 
velocity,  as  they  descend,  from  the  interstice  formed  by  their  elevation. 
This  pump  may  be  worked  by  a  labourer,  walking  backwards  and  forwards, 
either  on  the  beam  or  on  a  board  suspended  below  it.  By  means  of  an  ap- 
paratus of  this  kind,  described  by  Professor  Robison,tan  active  man,  loaded 
with  a  weight  of  thirty  pounds,  has  been  able  to  raise  580  pounds  of  water 

*  West  in  Tilloch's  Ph.  Mag.  vol.xi. 

f  Mechanical  Philosophy,  art.  Pump,  ii.  671. 


254  LECTURE  XXVIII. 

every  minute,  to  a  height  of  11^  feet,  for  ten  hours  a  day,  without  fatigue  ; 
this  is  the  greatest  effect  produced  by  a  labourer  that  has  ever  been  correctly 
stated  by  any  author ;  it  is  equivalent  to  somewhat  more  than  1 1  pounds 
raised  through  10  feet  in  a  second,  instead  of  10  pounds,  which  is  a  fair 
estimate  of  the  usual  force  of  a  man,  without  any  deduction  for  friction. 
(Plate  XXIII.  Fig.  305.) 

It  is  obvious  that  if  the  plungers  were  so  well  fitted  to  the  cavity  as  to 
prevent  the  escape  of  any  water  between  them,  the  ascending  pipe  might 
convey  the  water  to  any  required  height ;  the  machine  would  then  become 
a  forcing  pump,  and  the  plungers  might  be  shortened  at  pleasure,  so  as  to 
assume  the  form  of  a  piston  sliding  within  a  barrel.  The  piston  might  also 
be  situated  above  the  level  of  the  reservoir,  and  in  this  case  the  water  would 
be  forced  up  after  it  by  the  pressure  of  the  atmosphere  to  the  height  of 
about  30  feet,  but  not  much  further  :  and  even  this  height  would  be  some- 
what too  great  for  practice,  because  the  water  might  sometimes  follow  the 
piston  in  its  ascent  too  slowly.  Such  a  pump,  partaking  of  the  nature  of  a 
forcing  and  a  sucking  pump,  is  sometimes  called  a  mixed  pump.  In 
Delahire's  pump,  the  same  piston  is  made  to  serve  a  double  purpose,  the  rod 
working  in  a  collar  of  leathers,  and  the  water  being  admitted  and  expelled 
in  a  similar  manner,  above  and  below  the  piston,  by  means  of  a  double  ap- 
paratus of  valves  and  pipes.*  (Plate  XXIII.  Fig.  306.) 

For  forcing  pumps  of  all  kinds,  the  common  piston,  with  a  collar  of 
loose  and  elastic  leather,  is  preferable  to  those  of  a  more  complicated  struc- 
ture :  the  pressure  of  the  water  on  the  inside  of  the  leather  makes  it  suffi- 
ciently tight,  and  the  friction  is  inconsiderable.  In  some  pumps  the  leather 
is  omitted,  for  the  sake  of  simplicity,  the  loss  of  water  being  compensated 
by  the  greater  durability  of  the  pump ;  and  this  loss  will  be  the  smaller 
in  proportion  as  the  motion  of  the  piston  is  more  rapid.  (Plate  XXIII. 
Fig.  307.) 

Mr.  Bramah  has  very  ingeniously  applied  a  forcing  pump,  by  means  of 
the  well  known  properties  of  hydrostatic  pressure,  to  the  construction  of  a 
convenient  and  powerful  press.  The  water  is  forced,  by  a  small  pump,  into 
a  barrel  in  which  it  acts  on  a  much  larger  piston ;  consequently  this  piston 
is  urged  by  a  force  as  much  greater  than  that  which  acts  on  the  first  pump 
rod,  as  its  surface  is  greater  than  that  of  the  small  one.  (Plate  XXIII. 
Fig.  308.) 

In  the  common  sucking  pump,  the  valve  through  which  the  water 
escapes  is  placed  within  the  piston  itself,  so  that  the  same  barrel  serves  for 
the  ascent  of  the  water,  which  rises  in  one  continued  line  while  the  piston 
is  raised,  and  rests  on  the  fixed  valve  while  it  is  depressed.  The  velocity  of 
the  stroke  ought  never  to  be  less  than  4  inches  in  a  second,  nor  greater  than 
two  or  three  feet ;  the  stroke  should  also  be  as  long  as  possible,  in  order  to 
avoid  unnecessary  loss  of  water  during  the  descent  of  the  valves.  The  di- 
ameter of  the  pipe  through  which  the  water  rises  to  the  barrel,  ought  not  to 
be  less  than  two  thirds  of  the  diameter  of  the  barrel  itself.  (Plate  XXIII. 
Fig.  309.) 

A  bag  of  leather  has  also  been  employed  for  connecting  the  piston  of  a 

*   Hist,  et  Mem.  de  1'Acad.  1716,  p.  322. 


ON  HYDRAULIC  MACHINES.  255 

pump  with  the  barrel,  and  in  this  manner  nearly  avoiding  all  friction  :  but 
it  is  probable  that  the  want  of  durability  would  be  a  great  objection  to  such 
a  machine.  (Plate  XXIII.  Fig.  310.) 

Where  the  height,  through  which  the  water  is  to  be  raised,  is  consider- 
able, some  inconvenience  might  arise  from  the  length  of  the  barrel  through 
which  the  piston  rod  of  a  sucking  pump  would  have  to  descend,  in  order 
that  the  piston  might  remain  within  the  limits  of  atmospheric  pressure. 
This  may  be  avoided  by  placing  the  inoveable  valve  below  the  fixed  valve, 
and  introducing  the  piston  at  the  bottom  of  the  barrel.  Such  a  machine  is 
called  a  lifting  pump  :  in  common  with  other  forcing  pumps,  it  has  the 
disadvantage  of  thrusting  the  piston  before  the  rod,  and  thus  tending  to 
bend  the  rod,  and  produce  an  unequal  friction  on  the  piston,  while,  in  the 
sucking  pump,  the  principal  force  always  tends  to  straighten  the  rod. 
(Plate  XXIII.  Fig.  311.) 

The  rod  of  a  sucking  pump  may  also  be  made  to  work  in  a  collar  of 
leather,  and  the  water  may  be  forced  through  a  valve  into  an  ascending 
pipe.  By  applying  an  air  vessel  to  this,  or  to  any  other  forcing  pump,  its 
motion  may  be  equalised,  and  its  performance  improved  ;  for  if  the  orifice 
of  the  air  vessel  be  sufficiently  large,  the  water  may  be  forced  into  it, 
during  the  stroke  of  the  pump,  with  any  velocity  that  may  be  required, 
and  with  little  resistance  from  friction,  while  the  loss  of  force,  from  the 
frequent  accelerations  and  retardations  of  the  whole  body  of  water,  in  a 
long  pipe,  must  always  be  considerable.  The  condensed  air,  reacting  on 
the  water,  expels  it  more  gradually,  and  in  a  continual  stream,  so  that  the 
air  vessel  has  an  effect  analogous  to  that  of  a  fly  wheel  in  mechanics. 
(Plate  XXIII.  Fig.  312.) 

If,  instead  of  forcing  the  water  to  a  certain  height  through  a  pipe,  we 
cause  it  to  form  a  detached  jet,  we  convert  the  forcing  pump  into  a  fire 
engine  :  and  in  general  two  barrels,  acting  alternately,  are  connected,  for 
this  purpose,  with  the  same  air  vessel ;  so  that  the  discharge  is  thus 
rendered  very  nearly  uniform.  The  form  of  the  adjutage,  or  orifice  of  the 
pipe,  is  by  no  means  indifferent  to  the  effect  of  the  machine,  since  the 
height  of  the  jet  may  be  much  increased  by  making  it  moderately  con- 
tracted, and  a  little  conical  rather  than  cylindrical.  When  the  air  vessel 
is  half  filled  with  water,  the  height  of  such  a  jet  will  be  about  30  feet,  when 
two  thirds  filled,  about  60,  the  height  being  always  nearly  proportional  to 
the  degree  of  condensation  of  the  air,  or  to  the  excess  of  its  density  above 
that  of  the  surrounding  atmosphere.  Sometimes  a  double  forcing  pump,  or 
fire  engine,  is  formed  by  the  alternate  rotatory  motion  of  a  flat  piston 
within  a  cylindrical  barrel ;  the  axis  of  its  motion  coinciding  with  that  of 
the  barrel,  and  the  barrel  being  divided  by  a  partition  into  two  cavities, 
which  are  filled  and  emptied  in  the  same  way  as  the  separate  barrels  of  the 
common  fire  engine.  The  mechanical  advantage  of  this  machine  is  nearly 
the  same  as  that  of  the  more  usual  constructions,  but  it  appears  to  be  some- 
what more  simple  than  a  common  engine  of  equal  force.  The  partition 
may  be  extended  throughout  the  diameter  of  the  cylinder,  the  opposite  pairs 
of  cavities  being  made  to  communicate  with  each  other,  and  thus  both  sides 
of  the  piston  may  be  employed  at  once.  (Plate  XXIII.  Fig.  313.) 


256  LECTURE  XXVIII. 

A  piston  placed  in  a  similar  manner  has  sometimes  been  made  to  revolve 
continually,  and  to  force  the  water  through  a  pipe  by  means  of  a  slider  or  A 
spring,  which  intercepts  its  passage  in  any  other  direction.  Machines  of  this 
kind  have  been  invented  and  rein  vented,  by  Ramelli,*  Cavalleri,f  Amontons,J 
Prince  Rupert,t  Dr.  Hooke,  Mr.  Bramah,§  and  Mr.  Gwynn.  Mr.  Gwynn's 
engine,  which  has  been  employed  in  many  cases  with  considerable  success, 
consists  of  a  piston  or  roller  nearly  elliptical,  well  fitted  to  the  cylinder 
within  which  it  revolves,  with  a  valve  pressed  lightly  against  it  by  a  spring, 
which  causes  a  considerable  part  of  the  water  contained  in  the  cylinder  to 
be  forced  in  each  revolution  into  the  pipe  :  the  whole  machine  is  made  of 
brass  ;  the  spring  requires  very  little  force,  for  the  pressure  of  the  water 
on  the  valve  keeps  it  always  close  to  the  roller,  and  the  friction  arising 
from  this  cause  is  even  an  objection  to  the  machine.  The  stream,  although 
never  wholly  intermitted,  is,  however,  by  no  means  uniform  in  its  velocity. 
(Plate  XXIII.  Fig.  314... 317.) 

The  pipes,  through  which  water  is  raised  by  pumps  of  any  kind,  ought 
to  be  as  short  and  as  straight  as  possible  ;  thus,  if  we  had  to  raise  water  to 
a  height  of  20  feet,  and  to  carry  it  to  a  horizontal  distance  of  100  by 
means  of  a  forcing  pump,  it  would  be  more  advantageous  to  raise  it  first 
vertically  into  a  cistern  20  feet  above  the  reservoir,  and  then  to  let  it  run 
along  horizontally,  or  find  its  level  in  a  bent  pipe,  than  to  connect  the 
pump  immediately  with  a  single  pipe  carried  to  the  place  of  its  destination. 
And  for  the  same  reason  a  sucking  pump  should  be  placed  as  nearly  over 
the  well  as  possible,  in  order  to  avoid  a  loss  of  force  in  working  it.  If 
very  small  pipes  are  used,  they  will  much  increase  the  resistance,  by  the 
friction  which  they  occasion. 

Water  has  been  sometimes  raised  by  stuffed  cushions,  or  by  oval  blocks 
of  wood,  connected  with  an  endless  rope,  and  caused  by  means  of  two 
wheels  or  drums,  to  rise  in  succession  in  the  same  barrel,  carrying  the 
water  in  a  continual  stream  before  them  ;  but  the  magnitude  of  the  friction 
of  the  cushions  appears  to  be  an  objection  to  this  method.  From  the  re- 
semblance of  the  apparatus  to  a  string  of  beads,  it  has  been  called  a  bead 
pump,  or  a  paternoster  work.  When  flat  boards  are  united  by  chains, 
and  employed  instead  of  these  cushions,  the  machine  may  be  denominated 
a  cellular  pump  ;  and  in  this  case  the  barrel  is  usually  square,  and  placed 
in  an  inclined  position,  but  there  is  a  considerable  loss  from  the  facility 
with  which  the  water  runs  back.  The  chain  pump  generally  used  in  the 
navy  is  a  pump  of  this  kind,  with  an  upright  barrel,  through  which 
leathers,  strung  on  a  chain,  are  drawn  in  constant  succession  ;  these  pumps 
are  only  employed,  when  a  large  quantity  of  water  is  to  be  raised,  and 
they  must  be  worked  with  considerable  velocity  in  order  to  produce  any 

*  Artificiose  Machine,  fol.  Paris,  1588. 

t  Exercit.  Geomet.  p.  541.     Birch;  i.  285. 

J  Machines  et  Inventions  Approuvees  par  1'Academie,  7  vols.  4to,  1735, v.  i. 

to  which  work  we  refer  for  the  description  of  numerous  hydraulic  machines  by  Per- 
rault,  Cusset,  Joly,  Francini,  Cordamoy,  Gay,  L'  Heureux,  Joue,  Martenot,  Mar- 
chand,  Auger,  Ublemann,  Laesson,  Denisart,  Ledemoust,  Boulogne,  Saulm,  Gallon, 
Deparcieux,  Gensanne,  Dupuy,  Amy,  &c. 

§  Repertory  of  Arts,  ii.  73. 


ON  HYDRAULIC  MACHINES.  257 

effect  at  all.  Mr.  Cole  has  improved  the  construction  of  the  chain  pump, 
so  as  materially  to  increase  the  quantity  of  water  raised  by  it.*  (Plate 
XXIII.  Fig.  318.) 

It  is  frequently  necessary  to  procure  alternate  motion  in  pumps  by 
means  of  wheel-work,  and  for  this  purpose  the  application  of  a  crank  is  the 
most  usual  and  perhaps  the  best  method.  Provided  that  the  bar  by  which 
it  acts  be  sufficiently  long,  very  little  will  be  lost  by  the  obliquity  of  its 
situation,  and  it  is  easy,  by  means  of  rollers,  or  of  a  compound  frame,  to 
confine  the  head  of  the  pump  rod  to  a  rectilinear  motion.  When  any 
other  mode  is  employed,  it  must  be  remembered  that  the  motion  of  the 
pump  rod  ought  always  to  be  slower  at  the  beginning  of  each  alternation, 
since  a  considerable  part  of  the  force  is  consumed  in  setting  the  water  in 
motion,  especially  where  the  pipe  is  long,  and  the  velocity  considerable. 
But  it  may  happen  that,  from  the  nature  of  hydraulic  pressure  under 
other  circumstances,  the  resistance  may  be  nearly  equal  throughout  the 
stroke  :  for  example,  when  the  motion  of  the  piston  is  slow  in  comparison 
of  that  of  the  water  in  the  pipe,  or  when  the  force  employed  in  producing 
velocity  is  inconsiderable,  in  comparison  with  that  which  is  required  for 
counteracting  the  pressure.  In  such  cases  it  may  sometimes  be  eligible  to 
employ  inclined  surfaces  of  such  forms  as  are  best  adapted  to  communicate 
the  most  advantageous  velocity  to  the  pump  rod  by  their  pressure  on  a 
roller,  which  may  be  confined  to  its  proper  direction  by  the  same  means  as 
when  a  crank  is  used.  (Plate  XIV.  Fig.  184...  187.) 

The  Chinese  work  their  cellular  pumps,  or  bead  pumps,  by  walking  on 
bars  which  project  from  the  axis  of  the  wheel  or  drum  that  drives  them, 
and  whatever  objection  may  be  made  to  the  choice  of  the  machine,  the 
mode  of  communicating  motion  to  it  must  be  allowed  to  be  advantageous. 

Pumps  have  sometimes  been  worked  by  means  of  the  weight  of  water 
acting  within  a  barrel,  which  resembles  a  second  pump  placed  in  an  in- 
verted position.  The  only  objection  to  the  machine  appears  to  be  the 
magnitude  of  the  friction,  and  even  this  inconvenience  may  perhaps  be 
inconsiderable.  The  invention  is  by  no  means  modern,t  but  it  is  best 
known  in  Germany  under  the  name  of  HolTs  machine,^  and  it  has  been 
introduced  into  this  country  by  Mr.  Westgarth§  and  Mr.  Trevithick.|| 
A  chain  pump,  or  a  series  of  buckets,  may  also  be  applied,  in  a  manner 
nearly  similar,  to  the  working  of  machinery  of  any  kind.  (Plate  XXIII. 
Fig.  319.) 

The  mediation  of  a  portion  of  air  is  employed  for  raising  water,  not 
only  in  the  spiral  pump,  but  also  in  the  air  vessels  of  Schernnitz.«[  A 
column  of  water,  descending  through  a  pipe  into  a  closed  reservoir  full  of 
air,  obliges  the  air  to  act,  by  means  of  a  pipe  leading  from  the  upper  part 

*  London  Magazine  for  1768,  p.  499. 

t  It  is  figured  in  Fludd's  Naturae  Simia,  Oppenheim,  1618,  p.  467. 
J  Hist.  etMem.  1760,  H.  160. 

§  Bailey's  Machines,    ii.  52.     Smeaton,  Transactions  of  the   Society  of  Arts, 
vol.  v. 
•||  Nich.  Jour.  8vo,  i.  161. 

^  Wolfe's  Description  of  Hero's  Fountain  at  Schemnitz,  Ph.  Tr.  1762,  p.  547. 
Poda's  do.  Prag.  1771.  Nich.  Jour.  iv.  8, 117. 

s 


258  LECTURE  XXVIII. 

of  the  reservoir  or  air  vessel,  on  the  water  in  a  second  reservoir,  at  any 
distance  either  below  or  above  it,  and  forces  this  water  to  ascend  through- 
a  third  pipe  to  any  height  less  than  that  of  the  first  column.  The  air 
vessel  is  then  emptied,  and  the  second  reservoir  filled,  and  the  whole  opera- 
tion is  repeated.  The  air  must,  however,  acquire  a  density  equivalent  to 
the  pressure,  before  it  can  begin  to  act ;  so  that  if  the  height  of  the 
columns  were  34  feet,  it  must  be  reduced  to  half  its  dimensions  before  any 
water  would  be  raised  ;  and  thus  half  of  the  force  would  be  lost ;  in  the 
same  manner,  if  the  height  were  68  feet,  two  thirds  of  the  force  would  be 
lost.  But  where  the  height  is  small,  the  force  lost  in  this  manner  is  not 
greater  than  that  which  is  usually  spent  in  overcoming  friction  and  other 
imperfections  of  the  machinery  employed ;  for  the  quantity  of  water, 
actually  raised  by  any  machine,  is  not  often  greater  than  half  the  power 
which  is  consumed.  The  force  of  the  tide,  or  of  a  river  rising  and  falling 
with  the  tide,  might  easily  be  applied  by  a  machine  of  this  kind,  to  the 
purposes  of  irrigation.  (Plate  XXIII.  Fig.  320,  321.) 

The  fountain  of  Hero  precisely  resembles  in  its  operation  the  hydraulic 
vessels  of  Schemnitz,  which  were  probably  suggested  to  their  inventor  by 
the  construction  of  this  fountain.*  The  first  reservoir  of  the  fountain  is 
lower  than  the  orifice  of  the  jet ;  a  pipe  descends  from  it  to  the  air  vessel, 
which  is  at  some  distance  below,  and  the  pressure  of  the  air  is  communi- 
cated, by  an  ascending  tube  to  a  third  cavity,  containing  the  water  which 
supplies  the  jet.  Many  other  hydraulic  and  pneumatic  instruments,  in- 
tended for  amusement  only,  and  some  of  them  of  much  more  complicated 
structure,  are  also  described  in  the  works  of  Hero.  (Plate  XXIII.  Fig. 
322.) 

The  spontaneous  vicissitudes  of  the  pressure  of  the  air,  occasioned  by 
changes  in  the  weight  and  temperature  of  the  atmosphere,  have  been  ap- 
plied, by  means  of  a  series  of  reservoirs  furnished  with  proper  valves,  to 
the  purpose  of  raising  water  by  degrees  to  a  moderate  height.  But  it 
seldom  happens  that  such  changes  are  capable  of  producing  an  elevation  in 
the  water  of  each  reservoir  of  more  than  a  few  inches,  or  at  most  a  foot  or 
two,  in  a  day  ;  and  the  whole  quantity  raised  must,  therefore,  be  very 
inconsiderable. 

The  momentum  of  a  stream  of  water,  flowing  through  a  long  pipe,  has 
also  been  employed  for  raising  a  small  quantity  of  water  to  a  considerable 
height. 

The  passage  of  the  pipe  being  stopped  by  a  valve,  which  is  raised  by  the 
stream,  as  soon  as  its  motion  becomes  sufficiently  rapid,  the  whole  column 
of  fluid  must  necessarily  concentrate  its  action  almost  instantaneously  on 
the  valve  ;  and  in  this  manner  it  loses,  as  we  have  before  observed,  the  cha- 
racteristic property  of  hydraulic  pressure,  and  acts  as  if  it  were  a  single 
solid  ;  so  that,  supposing  the  pipe  to  be  perfectly  elastic  and  inextensible, 
the  impulse  must  overcome  any  pressure,  however  great,  that  might  be 
opposed  to  it,  and  if  the  valve  open  into  a  pipe  leading  to  an  air  vessel,  a 
certain  quantity  of  the  water  will  be  forced  in,  so  as  to  condense  the  air, 

*  See  Heronis  Spiritalium  Liber,  Lat.  &  F.  Commandino,  4to,  Par.  1583;  or 
Veter.  Math.  Op.  fol.  1693. 


ON  PNEUMATIC  MACHINES.  259 

more  or  less  rapidly,  to  the  degree  that  may  be  required  for  raising  a  por- 
•tion  of  the  water  contained  in  it  to  any  given  height.  Mr.  Whitehurst 
appears  to  have  been  the  first  that  employed  this  method  ;*  it  was  after- 
wards improved  by  Mr.  Boulton  ;t  and  the  same  machine  has  lately  at- 
tracted much  attention  in  France  under  the  denomination  of  the  hydraulic 
ram  of  Mr.  Montgolfier.J  (Plate  XXIII.  Fig.  323.) 


LECT.  XXVIII.— ADDITIONAL  AUTHORITIES. 

Strada,  Wasserkunsten,  fol.  Frankfort,  1617  ;  Cologne,  1623.  De  Caus,  Inven- 
tions Hydrauliques,  translated  into  English  by  Leak,  fol.  1659.  Morland,  Elevation 
des  Eaux,  1685.  Papin's  Engine  for  Raising  Water,  Ph.  Tr.  1686,  p.  283.  Recueil, 
Cassel,  1695.  In  the  vols.  of  the  Hist.  et,Mem.  de  1'  Acad.  de  Paris  are  the  follow- 
ing : — Lafaye's  Hydraulic  Machine,  1717,  p.  67,  H.  70.  Mey  and  Meyer's  do. 
1726,  H.  71.  Lebrun's  do.  1731,  H.  91  ;  his  Piston,  1735,  H.  102.  Drussen's 
Puinp,  ibid.  Renon's  Mach.  ibid.  Bertier's  Mach.  ibid.  Pitot's  Theory  of  Pumps, 
1735,  p.  327,  H.  72  ;  1739,  p.  393  ;  1740,  p.  511.  Camus  on  the  Best  Application 
of  Buckets,  1739,  p.  157,  H.  49  ;  on  the  Best  Proportion  of  Pumps,  1739,  p.  287, 
H.  49.  Gensanne  on  Pumps,  1741,  H.  163.  Geffrier's  Hyd.  Mach.  1743,  H.  168. 
Thillay's  Fire  Engine,  1746,  H.  120.  Bonnet's,  1749,  H.  182.  Jacquet's  Piston, 
1752,  H.  148.  D'Arcy,  1754,  p.  699,  H.  138.  Veltman,  1756,  H.  129.  Varan, 
1760,  H.  162.  Limbourg,  1761,  H.  154.  Loritt's  Endless  Chain,  1761,  H.  161. 
Deparcieux,  1762,  p.  1,  H.  182.  Nollet's  Pumps,  1766,  H.  150,  Borda  on  Pumps, 
1768,  p.  418,  H.  122.  Quentin,  1769,  H.  130.  Bertier,  1770,  H.  117.  Recueil 
d'  Ouvrages  Curieux  de  Math,  et  de  Mec. ;  ou  Description  du  Cabinet  de  M.  Grol- 
lier  de  Serviere  par  son  Petit  Fils,  Lyons,  1719.  Briickmann  and  Weber's  Elemen- 
tar  Maschine,  Cassel,  1720.  Beighton  on  the  Water  Works  at  London  Bridge,  Ph. 
Tr.  1731,  p.  5.  Churchman's  Engine,  Ph.  Tr.  1734,  p.  402.  Weidler,  Tractatus  de 
Mach.  Hydraul.  Leipz.  1728.  Besson's  Theatre,  Lyons,  1579.  Bocker's  Theatrum, 
1661.  Tielen  en  Von  der  Host's  do.  Policy's  do.  Amst.  1737.  Van  Zyl's  do. 
Amst.  1761.  Euler  on  Pumps,  Hist,  et  Mem.  de  Berlin,  1752,  pp.  149,  185. 
Landriani  on  the  Rope  Pump,  Geneva,  1782.  Perronet,  Description  des  Projetsdes 
Fonts  de  Neuilly,  1783.  Baaden,  Theorie  der  Pumpen,  4to,  Bayr,  1797.  Close's 
Method  of  Raising  Water,  Nich.  Jour.  iv.  293,  493,  8vo.  i.  145.  Application  of  the 
Siphon, iv.  547 ;  v.  22,  8vo.  i.  27.  Person,  Recueil  de  Mechanique,  4to,  Paris,  1802. 
Dietot's  Danaide,  Thomson's  Annals  of  Philosophy,  ii.  412.  Ewbank's  Descriptive 
and  Historical  Account  of  Hydraulic  Machines,  New  York,  1842,  very  copious, 
interesting,  and  curious. 


LECTURE    XXIX. 


ON  PNEUMATIC  MACHINES. 

PNEUMATIC  machines  are  such  as  are  principally  dependent,  in  their 
operation,  upon  the  properties  of  elastic  fluids ;  they  may  be  calculated 
either  for  diminishing  or  increasing  their  density  and  pressure,  as  air 
pumps  and  condensers ;  or  for  directing  and  applying  their  force,  as  bel- 
lows, ventilators,  steam  engines,  and  guns. 

.  *  Ph.Tr.  1775,  Ixv.  277. 

f  Repertory  of  Arts,  1798,  vol.  ix. 

J  Journal  de  Physique,  xlvi.  143.  Brunacci,  Trattato  dello  Ariete  Hydraulico, 
4to,  Milan,  1813. 

s2 


2GO  LECTURE  XXIX. 

The  density  and  pressure  of  the  air  may  be  diminished,  or  the  air  may  be 
perfectly  or  very  nearly  withdrawn  from  a  given  space,  either  by  means  of  • 
a  column  of  mercury,  or  by  the  air  pump.  The  ancients  sometimes  ex- 
hausted a  vessel  imperfectly  by  the  repeated  action  of  the  mouth,  and 
preserved  the  rarefaction  by  the  assistance  of  a  stopcock.  The  Torricellian 
vacuum,  obtained  by  inverting  a  receiver  filled  with  mercury,  and  fur- 
nished with  a  descending  tube  at  least  30  inches  long,  is  the  most  perfect 
that  can  be  procured  ;  but  there  is  generally  a  portion  of  air  adhering  to 
the  vessels,  and  mixed  with  the  mercury,  which  may  often  be  considerably 
diminished  by  agitation,  but  can  only  be  completely  expelled  by  boiling 
the  mercury  for  some  time  in  the  vessel  and  its  tube,  previously  to  their 
inversion.  (Plate  XXIV.  Fig.  324.) 

The  construction  of  an  air  pump  greatly  resembles  that  of  a  common 
sucking  pump  for  raising  water  ;  but  the  difference  in  the  operation  to  be 
performed  requires  a  difference  in  several  particular  arrangements.  The 
objects  are,  to  rarefy  or  exhaust  the  air  as  completely,  as  expeditiously,  and 
as  easily,  as  possible.  In  order  that  the  exhaustion  may  be  complete,  it  is 
necessary  that  no  air  remain  in  the  barrel  when  the  valve  is  opened,  and 
that  the  process  be  very  long  continued.  For,  supposing  all  the  parts  of  an 
air  pump  to  be  perfectly  well  fitted,  and  the  exhaustion  to  be  carried  on  for 
any  length  of  time,  the  limit  of  its  perfection  will  be  a  rarefaction  expressed 
by  the  proportion  of  the  air  remaining  in  the  barrel,  when  the  piston  is  down, 
to  the  whole  air  that  the  barrel  is  capable  of  containing ;  for  such  will  be 
the  rarity  of  the  air  in  the  barrel  when  the  piston  is  raised.  It  becomes, 
therefore,  of  consequence  to  lessen  the  quantity  of  this  residual  air  as  much 
as  possible  :  and  at  the  same  time  to  take  care  that  the  valve  may  be  capable 
of  being  accurately  closed  and  easily  opened,  or  that  a  stopcock  may  be 
occasionally  substituted  for  it,  which  may  be  opened  and  shut  by  external 
force,  when  the  elasticity  of  the  air  remaining  is  too  small  to  lift  the  valve. 
In  pumping  water  from  a  well,  we  raise  an  equal  quantity  at  each  stroke, 
but  in  the  air  pump,  we  withdraw  at  most  only  equal  bulks  of  the  air  dif- 
ferently rarefied,  so  that  the  quantity  extracted  is  continually  diminished 
as  the  operation  proceeds.  Thus,  if  one  tenth  of  the  air  were  exhausted  by 
the  first  stroke,  only  nine  tenths  as  much,  that  is,  one  tenth  of  the  remain- 
der, would  be  drawn  out  by  the  second ;  hence,  in  order  that  the  process 
may  be  expeditious,  it  is  of  importance  to  have  the  barrel  as  large  as  pos- 
sible in  proportion  to  the  receiver.  In  cases  where  the  presence  of  aqueous 
vapour  would  be  of  no  consequence,  the  exhaustion  might  be  made  very 
rapidly  by  filling  the  whole  apparatus  with  water,  which  was  the  me- 
thod first  employed  by  Otto  von  Guericke,  the  inventor  of  the  modern 
air  pump. 

In  order  to  lessen  the  labour  of  the  operation,  two  barrels  may  be  em- 
ployed, and  so  connected  as  to  work  alternately  ;  in  this  manner  the 
pressure  of  the  atmosphere,  acting  on  both  pistons  at  once,  opposes  no 
resistance  to  their  motion  in  either  direction.  In  Smeaton's  pump*  a 

*  Ph.  Tr.  1751-2,  xlvii.  415.  See  also  the  Dutch  translation  of  Dr.  Priestley's 
Observations  and  Experiments  on  different  kinds  of  air,  vol.  ii.  1781.  Cavallo,  Ph. 
Tr.1783,  p.  435. 


ON  PNEUMATIC  MACHINES.  261 

single  barrel  has  nearly  the  same  advantage,  the  rod  of  the  piston  working 
'in  a  collar  of  leathers  with  oil,  and  the  air  heing  excluded  from  the  upper 
part  of  the  barrel  by  a  valve,  through  which  the  air  passes  when  the  piston 
is  raised  near  to  the  top  ;  so  that  in  the  descent  of  the  piston  there  is 
a  vacuum  above  it,  and  the  air  below  opens  the  valve  much  earlier,  and 
passes  more  completely  through  it,  than  in  the  common  air  pump  ;  and 
the  piston  is  only  exposed  to  the  whole  pressure  of  the  atmosphere 
during  the  discharge  of  the  air  through  the  upper  valve.  (Plate  XXIV. 
Fig.  325.) 

That  the  air  is  really  removed  by  the  operation  of  the  air  pump,  may  be 
demonstrated  by  various  experiments,  which  show  the  absence  of  its 
resistance,  of  its  buoyant  effect,  and  of  its  pressure  ;  such  are  the  descent  of 
a  guinea  and  a  feather  at  the  same  time,  the  equal  duration  of  the  motion 
of  two  fly  wheels,  with  their  plates  placed  in  different  directions,  the  prepon- 
derance of  the  larger  of  two  bodies  which  balance  each  other  in  the  open 
air,  the  descent  of  mercury  or  of  water  in  a  barometrical  tube,  the  playing 
of  a  fountain  urged  by  the  expansion  of  a  portion  of  confined  air,  and  the 
ebullition  of  ether,  or  of  water  moderately  warm.  (Plate  XXIV.  Fig. 
326,  327.) 

The  degree  of  perfection  of  the  vacuum  formed  by  the  air  pump,  or  the 
rarity  of  the  air  remaining  in  the  receiver,  is  measured  by  gages  of  different 
kinds.  The  simplest  gage  is  a  short  tube  filled  with  mercury,  and  inverted 
in  a  bason  of  the  same  fluid  ;  in  this  the  mercury  begins  to  descend  when 
the  elasticity  of  the  air  becomes  diminished  in  the  proportion  of  the  height 
of  the  gage  to  that  of  the  barometer ;  but  on  account  of  the  capillary  at- 
traction of  the  particles  of  mercury  for  each  other,  there  is  a  depression 
within  the  tube,  differing  in  quantity  according  to  its  magnitude,  which 
renders  it  difficult  to  observe  the  exact  situation  of  the  surface  when  the 
height  of  the  column  is  very  small,  although,  if  that  height  were  correctly 
ascertained,  the  allowance  to  be  made  for  the  depression  might  easily  be 
calculated.  It  is,  however,  more  usual  to  employ  the  long  barometer  gage, 
in  which  the  pressure  is  removed  from  the  upper  surface  of  the  column  of 
mercury  in  proportion  as  the  exhaustion  proceeds,  and  the  height  to  which 
it  is  raised  by  the  pressure  of  the  external  atmosphere,  is  compared  with 
that  of  a  common  barometer,  the  difference  always  indicating  the  density 
of  the  air  left  in  the  receiver.  Sometimes  also  a  bent  tube  is  employed  in- 
stead of  the  short  gage,  the  difference  of  the  height  in  its  two  branches  indi- 
cating the  pressure  ;  and  this  instrument  has  the  advantage  of  requiring  no 
correction  on  account  of  capillary  attraction,  since  the  depressions  of  the 
two  columns  exactly  counterbalance  each  other.  But  in  all  these  cases  the 
mercury  must  be  well  boiled  in  the  tubes ;  and  in  the  bent  tube,  or  siphon 
gage,  the  operation  is  somewhat  difficult. 

The  pressure  indicated  by  a  gage  of  any  kind  depends  on  the  elasticity 
of  the  whole  of  the  fluid  remaining  in  the  receiver  ;  but  this  fluid  is  not 
always  atmospheric  air  alone.  In  all  common  temperatures,  water,  and 
iriany  other  liquids,  have  the  property  of  emitting  a  vapour  which  possesses 
a  very  sensible  degree  of  elasticity  ;  so  that  if  either  water,  or  any  moist 
substance,  be  present  under  the  receiver,  it  will  be  impossible  to  procure  a 


262  LECTURE  XXIX. 

total  absence  of  pressure,  the  short  mercurial  gage  commonly  standing  at 
the  height  of  at  least  half  an  inch,  in  the  best  pumps.  Hence,  the  vacuum 
may  be  made  more  perfect  when  the  receiver  is  ground  to  the  plate  of  the 
pump,  with  the  interposition  of  an  unctuous  substance,  than  when  it  is 
placed  on  wet  leather,  as  it  has  sometimes  been  usual  to  do.  The  quantity 
of  atmospherical  or  incondensable  air  actually  existing  in  the  receiver, 
whether  mixed  with  vapour  or  alone,  is  measured  by  means  of  Smeaton's 
pear  gage,*  which  is  left  open  under  the  receiver  during  the  exhaustion, 
and  having  its  orifice  then  plunged,  by  means  of  a  wire  passing  through  a 
collar  of  leather,  into  a  bason  of  mercury,  receives,  upon  the  readmission 
of  the  air,  as  much  of  the  mercury  as  is  sufficient  to  fill  it,  leaving  only  in 
a  tube  rising  from  the  neck  of  the  gage,  the  small  quantity  of  air  which 
had  before  filled  the  whole  cavity,  so  that  from  the  space  occupied  by  this 
air,  compared,  by  means  of  previous  measurements,  with  the  capacity  of  the 
gage,  the  degree  of  exhaustion  of  the  pump  with  respect  to  air  may  be  es- 
timated. It  is  said  that  in  an  air  pump  of  Cuthbertson's  construction,  such 
a  rarefaction  has  been  procured  that  the  air  sustained  but  one  hundredth 
part  of  an  inch  of  mercury,t  that  is,  it  was  expanded  to  nearly  3000  times 
its  original  bulk.  The  pear  gage  often  indicates  a  much  more  complete 
exhaustion,  but  this  measurement  relates  only  to  the  quantity  of  dry  air 
present.*  (Plate  XXIV.  Fig.  328.) 

A  condenser  is  the  reverse  of  an  air  pump  ;  and  sometimes  the  same 
machine  is  made  to  serve  for  both  purposes ;  but  the  condenser  requires 
more  strength  than  the  air  pump,  and  less  delicacy.  The  gage  for  measur- 
ing the  degree  of  condensation  is  a  small  portion  of  air  contained  in  a  gra- 
duated cylindrical  tube,  the  space  that  it  occupies  being  indicated  by  a  drop 
of  mercury  which  confines  it.  (Plate  XXIV.  Fig.  329.) 

Diving  bells  were  formerly  supplied  with  air  by  means  of  barrels  let 
down  continually  from  the  surface  of  the  water,  and  taken  into  the  bell  by 
the  divers  ;  but  it  is  now  more  usual  to  force  down  a  constant  stream  by 
means  of  a  pump  resembling  a  condenser  in  its  construction  and  operation  ; 
the  heated  air  is  suffered  to  escape  by  a  stopcock  at  the  upper  part  of 
the  bell.  When  proper  care  is  taken  to  lower  the  machine  gradually, 
the  diver  can  support  the  pressure  of  an  atmosphere  of  twice  or  thrice 
the  natural  density.  It  would  be  advisable  that  every  diver  should  be 
provided  with  a  float  of  cork,  or  with  a  hollow  ball  of  metal,  which 
might  be  sufficient  to  raise  him  slowly  to  the  surface,  in  case  of  any 
accident  happening  to  the  bell ;  for  want  of  a  precaution  of  this  kind, 
several  lives  have  been  lost  from  confusion  in  the  signals.  §  (Plate  XXIV. 
Fig.  330.) 

Bellows  are  commonly  made  of  boards  connected  by  leather,  so  as  to 
allow  of  alternately  increasing  and  diminishing  the  magnitude  of  their 
cavities,  the  air  being  supplied  from  without  by  a  valve.  The  blast  must 

*  Ph.  Tr.  1752,  p.  420. 

t  Cuthbertson,  Description  of  an  improved  Air  Pump,  1783,  §38. 

*  See  Nairne's  Account  of  some  Experiments  made  with  an  Air  Pump,  Ph.  Tr. 
1777,  p.  622.     Roz.  Journ.  xi.  159  ;  xxv.  261. 

§  See  Halley's  Art  of  Living  under  Water,  Ph.  Tr.  1716,  p.  492;  1721,  p.  177. 
Healy  on  Diving  Bells,  Ph.  Mag.  xv.  9. 


ON  PNEUMATIC  MACHINES.  263 

be  intermitted  while  the  cavity  is  replenished  ;  and  in  order  to  avoid  this 
inconvenience,  a  second  cavity  is  sometimes  added,  and  loaded  with  a  weight, 
which  preserves  the  continuity  of  the  stream.  If  great  uniformity  be 
required  in  the  blast,  it  will  be  necessary  to  take  care  that  the  cavity  be  so 
formed  as  to  be  equally  diminished  while  the  weight  descends  through  equal 
spaces  ;  but  notwithstanding  this  precaution,  there  must  always  be  an 
additional  velocity  while  the  new  supply  of  air  is  entering  from  the  first 
cavity.  Sometimes  the  construction  of  the  bellows  resembles  that  of  a 
forcing  pump  ;  and  then,  if  the  barrel  is  single,  a  second  barrel,  loaded  with 
a  weight,  must  be  provided,  in  order  to  equalise  the  blast  :  or  a  vessel 
inverted  in  water,  and  either  loaded  or  fixed,  may  supply  the  place  of  the 
second  barrel.  The  first  cavity  may  also  be  formed  of  a  similar  inverted 
vessel,  suspended  to  a  beam,  so  as  to  be  moved  up  and  down  in  the  water, 
and  such  a  machine  is  much  used,  in  large  founderies,  under  the  name  of 
hydraulic  bellows.  The  quantity  of  water  employed  may  be  much  dimi- 
nished, and  the  operation  expedited,  by  introducing,  in  the  centre  of  the 
inverted  vessel,  a  fixed  solid,  or  an  internal  inverted  vessel,  capable  of 
nearly  filling  up  the  cavity  of  the  moveable  vessel  when  it  is  in  its  lowest 
position,  so  that  the  water  only  occupies  a  part  of  the  interstice  between  the 
vessels.  (Plate  XXIV.  Fig.  331.) 

The  gasometer  differs  little  from  the  hydraulic  bellows,  except  that  it  is 
provided  with  stopcocks  instead  of  valves,  and  the  moveable  cylinder  is 
supported  by  a  counterpoise,  which,  in  the  best  kind,  acts  on  a  spiral  fusee, 
calculated  to  correct  the  difference  of  pressure  arising  from  the  greater  or 
less  immersion  of  the  cylinder.  (Plate  XXIV.  Fig.  332.) 

A  shower  of  water,  or  even  an  irregular  stream,  being  conveyed  through 
a  descending  pipe,  plunged  into  the  water  of  a  reservoir,  a  large  quantity  of 
air  is  carried  down  with  the  water,  and  rises  to  the  upper  part  of  an 
inverted  vessel  which  surrounds  the  pipe,  whence  it  may  be  conveyed 
through  another  pipe,  in  a  rapid  stream,  for  any  required  purpose ;  and 
the  water  escapes  at  the  bottom  of  the  air  vessel  into  the  general  reser- 
voir, from  the  surface  of  which  it  runs  off.  The  quantity  of  air  sup- 
plied by  these  shower  bellows  is,  however,  small.  (Plate  XXIV.  Fig. 
333.) 

The  velocity  of  the  blast  produced  by  any  pressure,  forcing  the  air 
through  a  pipe  of  moderate  dimensions,  may  readily  be  determined  from 
the  height  of  a  column  of  air  equivalent  to  the  pressure.  Thus  if  the 
hydraulic  bellows  were  worked  with  a  constant  pressure  of  four  feet  of 
water,  the  velocity  would  correspond  to  a  height  of  about  3300  feet, 
and  the  air  would  move  through  a  space  of  about  460  feet  in  a  second.  But 
in  this  calculation  no  allowance  is  made  for  any  of  the  causes  which 
diminish  in  all  cases  the  discharge  of  fluids,  and  the  velocity  actually 
observed  is  only  five  eighths  as  great  as  that  which  corresponds  to  the 
height ;  that  is,  in  the  example  here  given,  285  feet  in  a  second,  when  the 
air  escapes  through  a  small  orifice  ;  but  when  it  moves  in  a  pipe,  about 
three  fourths,  or  345  feet.  If  the  pipe  were  of  considerable  length,  there 
would  also  be  a  diminution  of  velocity  on  account  of  friction.  In 
some  bellows  actually  employed,  a  pressure  equivalent  to  nine  feet  of 


264  LECTURE   XXIX. 

water  is  applied,  and  in  this  case  the  velocity  must  be  about  500  feet 
in  a  second. 

Bellows  may  be  used  for  the  ventilation  of  a  mine,  either  by  forcing 
air  into  it,  or  by  drawing  it  out  through  a  pipe  connected  with  the  valve. 
The  wind  may  also  be  received  by  the  mouth  of  a  tube  a  little  conical,  and 
may  be  made  to  cause  a  current  where  it  is  conveyed  ;  such  an  instrument 
is  sometimes  called  a  windsail,  or  a  horse  head.  It  has  been  proposed  to 
draw  the  air  up  through  a  pipe  by  the  lateral  friction  of  a  current  of  air 
received  by  such  a  funnel,  but  the  effect  would  probably  be  too  small  to  be 
of  much  practical  utility. 

A  corn  fan  is  turned  by  the  hand  or  by  machinery  ;  its  simplest  opera- 
tion is  to  cause  a  portion  of  air  to  revolve  with  it,  and  to  create  a  wind  in 
the  direction  of  its  circumference.  But  when  a  small  fan  is  made  to  revolve 
with  great  rapidity,  as  in  Papin's  Hessian  bellows,  the  centrifugal  force 
causes  the  air  admitted  at  the  centre  to  rush  towards  the  circumference, 
and  to  pass  with  great  velocity  through  a  pipe  inserted  there.  The  com- 
mon ventilator  placed  in  windows,  which  revolves  in  the  same  manner  as 
a  smoke  jack,  in  consequence  of  the  impulse  of  a  current  of  air,  serves 
only  to  retard  a  little  the  entrance  of  that  current,  to  disperse  it  in  some 
measure  in  different  directions,  and  to  prevent  any  sudden  increase  of  the 
intensity  of  the  draught ;  but  it  has  little  or  no  power  of  acting  on  the  air, 
so  as  to  prevent  the  decrease  of  the  velocity  of  the  current.  (Plate  XXIV. 
Fig.  384.) 

The  operation  of  heat  affords  us  also  a  very  effectual  mode  of  ventilation. 
Its  action  upon  air  at  common  temperatures  occasions  an  expansion  of 
about  T^ly  for  every  degree  that  Fahrenheit's  thermometer  is  raised  ;  the  air 
becomes  in  the  same  proportion  lighter,  and  the  fluid  below  it  is  conse- 
quently relieved  from  a  part  of  its  weight :  the  pressure  of  the  surrounding 
atmosphere,  .therefore,  preponderates,  and  the  lighter  column  is  forced 
upwards.  When  the  shaft  of  a  mine  communicates  with  the  external  air 
at  two  different  heights,  there  is  generally  a  sufficient  ventilation  from  the 
difference  of  the  temperatures  of  the  air  in  the  shaft,  and  of  the  surrounding 
atmosphere:  for  the  temperature  of  the  earth  is  nearly  invariable,  it 
therefore  causes  the  air  in  the  shaft  to  be  warmer  in  winter  than  the 
external  air,  and  colder  in  summer  ;  so  that  there  is  a  current  upwards  in 
winter,  and  downwards  in  summer ;  and  in  the  more  temperate  seasons, 
the  alternations  take  place  in  the  course  of  the  day  and  night.  For  a 
similar  reason  there  is  often  a  current  down  a  common  chimney  in  sum- 
mer ;  but  when  the  fire  is  burning,  the  whole  air  of  the  chimney  is  heated, 
and  ascends  the  more  rapidly  as  the  height  is  greater.  It  would  be  easy, 
from  the  principles  of  hydraulics,  if  the  length  of  the  chimney,  and  the 
mean  temperature  of  the  air  in  it  were  given,  to  calculate  the  velocity  of 
the  draught :  thus  if  the  height  of  the  chimney  were  50  feet,  and  the  air 
contained  in  it  10  degrees  hotter  than  the  external  air,  the  expansion  would 
be  one  fiftieth,  and  the  pressure  of  the  whole  column  being  diminished  one 
fiftieth,  the  difference  would  be  equivalent  to  a  column  of  one  foot  ifc 
height,  and  such  a  column  would  represent  the  pressure  causing  the 
draught,  which  might,  therefore,  be  expected  to  have  a  velocity  of  0  feet 


ON  PNEUMATIC  MACHINES.  265 

in  a  second.  If  the  room  were  perfectly  closed,  the  air  contained  in  it 
would  by  degrees  become  so  much  lighter  than  the  external  air,  as  would 
be  equivalent  to  one  foot  of  the  height  of  the  column  causing  the  pres- 
sure, and  the  current  would  then  stop  ;  if  fresh  air  were  gradually  ad- 
mitted by  a  small  orifice,  the  current  would  again  go  on,  but  the  air  in 
the  room  would  always  remain  somewhat  rarer  than  the  external  at- 
mosphere, unless  a  fresh  supply  were  admitted  through  ample  openings. 

The  object  of  a  chimney  is  not  so  much  to  ventilate  the  room,  as  to  pro- 
vide a  sufficiently  rapid  supply  of  air  for  maintaining  the  process  of  com- 
bustion, and  to  carry  off  the  products  of  that  process :  hence,  it  is  desirable 
to  allow  as  little  air  as  possible  to  enter  the  chimney  without  passing 
through  the  fire  ;  and  this  is  the  best  general  mode  of  avoiding  smoky 
chimnies.  For  wind  furnaces,  the  flue  should  be  as  equable  as  possible, 
throughout  its  height,  or  widened  rather  than  contracted  in  its  ascent,  and 
free  from  any  considerable  angles. 

The  ascent  of  a  balloon  is  an  effect  of  the  same  kind  as  that  of  air  in  a 
chimney,  and  arises  sometimes  from  the  same*  cause,  when  the  air  within  it 
is  expanded  by  heat ;  but  more  commonly  from  the  greater  rarity  of  hydro- 
gen gas,  with  which  the  balloon  is  filled,  and  which,  when  pure,  is  only  one 
thirteenth  as  heavy  as  atmospherical  air,  but  as  it  is  commonly  used,  about 
one  fifth  or  one  sixth. 

The  steam  engine  is  perhaps  the  most  magnificent  effort  of  mechanical 
power  ;  it  has  undergone  successive  changes,  and  it  appears  to  have  been 
brought  very  near  to  perfection  by  the  improvements  of  Mr.  Watt.  The 
pressure  of  steam  was  first  applied  by  the  Marquis  of  Worcester,*  and 
afterwards  by  Savery,f  to  act  immediately  on  the  surface  of  water  contained 
in  a  close  vessel,  and  this  water  was  forced,  by  the  elasticity  of  the  steam,  to 
ascend  through  a  pipe.  But  a  great  degree  of  heat  was  required  for  raising 
water  to  any  considerable  height  by  this  machine  ;  for  in  order  that  steam 
may  be  made  capable  of  supporting,  in  addition  to  the  atmospherical  pres- 
sure, a  column  of  34  feet  of  water,  its  temperature  must  be  raised  to  248° 
of  Fahrenheit,  and  for  a  column  of  68  feet,  to  271°  ;  such  a  pressure,  also, 
acting  on  the  internal  surface  of  the  vessels,  made  it  necessary  that  they 
should  be  extremely  strong  ;  and  the  height  to  which  water  could  be  drawn 
up  from  below,  when  the  steam  was  condensed,  was  limited  to  33  or  34  feet. 
A  still  greater  objection  was,  however,  the  great  quantity  of  steam  neces- 
sarily wasted,  on  account  of  its  coming  into  contact  with  the  cold  water 
and  the  receiver,  the  surfaces  of  which  required  to  be  heated  to  its  own 
temperature,  before  the  water  could  be  expelled  ;  hence  a  tenth  or  a  twen- 
tieth part  only  of  the  steam  produced  could  be  effective  ;  and  there  would 
probably  have  been  a  still  greater  loss,  but  for  the  difficulty  with  which 
heat  is  conducted  downwards  in  fluids.  These  inconveniences  were  in 

*  See  p.  278.  There  is  reason  to  believe  that  Hooke,  in  1678,  was  master  of  the 
principle  ;  for  he  gives  in  a  cypher  the  outline  of  "  a  very  extraordinary  invention  in 
mechanics,  above  the  chimeras  of  perpetual  motion,  for  several  uses."  The  cypher  is 
expressed  by  Pondere  premit  aer  vacuum  quod  ab  igne  relictum  est.  Waller's  Life 
of  Hooke,  p.  21. 

f  Ph.  Tr.  1699,  p.  228,  with  a  plate  of  the  engine.  Improvements  on  it  by  De 
Moura,  Ph.  Tr.  1752,  p.  436. 


266  LECTURE  XXIX. 

great  measure  avoided  in  Newcomen's  engine,*  where  the  steam  was  gra- 
dually introduced  into  a  cylinder,  and  suddenly  condensed  by  a  jet  of 
water,  so  that  the  piston  was  forced  down  with  great  violence  by  the  pres- 
sure of  the  atmosphere,  which  produced  the  effective  stroke :  this  effect 
was,  however,  partly  employed  in  raising  a  counterpoise,  which  descended 
upon  the  readmission  of  the  steam,  and  worked  a  forcing  pump  in  its  re- 
turn, when  water  was  to  be  raised.  The  condensation,  although  rapid,  was, 
however,  neither  instantaneous,  nor  complete,  for  the  water  injected  into 
the  cylinder  had  its  temperature  considerably  raised  by  the  heat  emitted 
by  the  steam  during  its  condensation  ;  it  could  only  reduce  the  remaining 
steam  to  its  own  temperature,  and  at  this  temperature  it  might  still  retain 
a  certain  degree  of  elasticity ;  thus,  at  the  temperature  of  180°  steam  is 
found  to  be  capable  of  sustaining  about  half  the  pressure  of  the  atmosphere, 
so  that  the  depression  of  the  piston  must  have  been  considerably  retarded 
by  the  remaining  elasticity  of  the  steam,  when  the  water  was  much  heated. 
The  water  of  the  jet  was  let  off  when  the  piston  was  lowest,  and  was  after- 
wards pumped  up  to  serve  the  boiler,  as  it  had  the  advantage  of  being 
already  hot.  This  engine,  with  Beighton's  apparatus  for  turning  the  cocks, 
was  until  lately  in  general  use,  and  it  is  still  very  frequently  employed.  In 
this,  as  well  as  in  other  steam  engines,  the  boiler  is  furnished  with  a  safety 
valve,  which  is  raised  when  the  force  of  the  steam  becomes  a  little  greater 
than  that  of  the  atmospheric  pressure  ;  and  it  is  supplied  with  water  by 
means  of  another  valve,  which  is  opened  when  the  surface  of  the  water  within 
it  falls  too  low,  by  the  depression  of  a  block  of  stone  which  is  partly  supported 
by  the  water.  (Plate  XXIV.  Fig.  335,  336.) 

The  cylinder  of  Beighton's  machine  is  necessarily  much  cooled  by  the 
admission  of  the  jet,  and  by  exposure  to  the  air.  Mr.  Watt  has  avoided 
this  inconvenience  by  performing  the  condensation  in  a  separate  vessel,  into 
which  a  small  jet  is  flowing  without  intermission  ;  and  by  introducing  the 
steam  alternately  above  and  below  the  piston,  the  external  air  is  wholly  ex- 
cluded ;  the  piston  rod  working  in  a  collar  of  leathers,  so  that  the  machine 
has  a  double  action,  somewhat  resembling  that  of  Lahire's  double  pump  ; 
and  the  stroke  being  equally  effectual  in  each  direction,  the  same  cylinder, 
by  means  of  an  increased  quantity  of  steam,  performs  twice  as  much  work 
as  in  the  common  engine.  We  might  also  employ,  if  we  thought  proper,  a 
lower  temperature  than  that  at  which  water  usually  boils,  and  work  in  this 
manner  with  a  smaller  quantity  of  steam  ;  but  there  would  be  some  diffi- 
culty in  completely  preventing  the  insinuation  of  the  common  air.  On  the 
other  hand,  we  may  raise  the  fire  so  as  to  furnish  steam  at  220°  or  more, 
and  thus  obtain  a  power  somewhat  greater  than  that  of  the  atmospheric  pres- 
sure ;  and  this  is  found  to  be  the  most  advantageous  mode  of  working  the 
engine  ;  but  the  excess  of  the  force  above  the  atmospheric  pressure  cannot 
be  greater  than  that  which  is  equivalent  to  the  column  of  water  descending 
to  supply  the  boiler,  since  the  water  could  not  be  regularly  admitted  in 
opposition  to  such  a  pressure.  The  steam  might  also  be  allowed  to  expand 
itself  within  the  cylinder  for  some  time  after  its  admission,  and  in  this 
manner  it  appears  from  calculation  that  much  more  force  might  be  obtained 
*  His  patent  is  dated  1705.. 


ON  PNEUMATIC  MACHINES.  267 

from  it  than  if  it  were  condensed  in  the  usual  manner  as  soon  as  its  ad- 
mission ceases  ;  but  the  force  of  steam  thus  expanding  is  much  diminished 
by  the  cold  which  always  accompanies  such  an  expansion,  and  this  method 
would  be  liable  to  several  other  practical  inconveniences. 

The  peculiarities  of  Mr.  Watt's  construction  require  also  some  other  ad- 
ditional arrangements ;  thus,  it  is  necessary  to  have  a  pump,  to  raise  not 
only  the  water  out  of  the  condenser,  but  also  the  air,  which  is  always  ex- 
tricated from  the  water  during  the  process  of  boiling.  If  the  water  em- 
ployed has  been  obtained  from  deep  wells  or  mines,  it  contains  more  air 
than*iisual,  and  ought  to  be  exposed  for  some  time  in  an  open  reservoir  be- 
fore it  is  used ;  for  it  appears  that  the  quantity  of  air,  which  can  be  con^- 
tained  in  water,  is  nearly  in  proportion  to  the  pressure  to  which  it  is  sub- 
jected. The  admission  of  the  steam  into  the  cylinder  is  regulated  by  the 
action  of  a  double  revolving  pendulum.  The  piston  is  preserved  in  a  situ- 
ation very  nearly  vertical  by  means  of  a  moveable  parallelogram,  fixed  on 
the  beam,  which  corrects  its  curvilinear  motion  by  a  contrary  curvature. 
In  the  old  engines,  a  chain  working  on  an  arch  was  sufficient,  because 
there  was  no  thrust  upwards.  When  a  rotatory  motion  is  required,  it  may 
be  obtained  either  by  means  of  a  crank,  or  of  a  sun  and  planet  wheel,*  with 
the  assistance  of  a  fly  wheel ;  this  machinery  is  generally  applied  to  the 
opposite  end  of  the  beam  ;  but  it  is  sometimes  immediately  connected  with 
the  piston,  and  the  beam  is  not  employed.  The  cylinder  is  usually  inclosed 
within  a  case,  and  the  interval  is  filled  with  steam,  which  serves  to  confine 
the  heat  very  effectually.  (Plate  XXIV.  Fig.  337.) 

The  steam  engines  of  Messrs.  Boulton  and  Watt  are  said  to  save  three 
fourths  of  the  fuel  formerly  used  ;  and  it  appears  that  only  one  fourth  of 
the  whole  force  of  the  steam  is  wasted.  Such  a  machine,  with  a  thirty 
inch  cylinder,  performs  the  work  of  120  horses,  working  8  hours  each  in 
the  day. 

When  the  water  producing  the  condensation  is  to  be  raised  from  a  great 
depth,  a  considerable  force  is  sometimes  lost  in  pumping  it  up.  Hence 
Mr.  Trevithick  t  has  attempted,  as  Mr.  Watt  had  indeed  long  before  pro- 
posed, to  avoid  entirely  the  necessity  of  condensation,  by  employing  steam 
at  a  very  high  temperature,  and  allowing  it  to  escape,  when  its  elasticity  is 
so  reduced  by  expansion,  as  only  to  equal  that  of  the  atmosphere :  the  air 
pump  is  also  unnecessary  in  this  construction,  and  for  a  small  machine,  it 
may  perhaps  succeed  tolerably  well.  But  there  must  always  be  a  very 
considerable  loss  of  steam,  and  although  the  expense  of  fuel  may  not  be 
increased  quite  in  the  same  proportion  as  the  elasticity  of  the  steam,  yet 
the  difference  is  probably  inconsiderable.  A  great  number  of  less  essential 
alterations  have  also  been  made  in  Mr.  Watt's  arrangements  by  various 
engineers,  but  they  have  generally  been  calculated  either  for  obtaining  some 
subordinate  purpose  of  convenience,  or  for  imposing  on  the  public  by  a 
fallacious  appearance  of  novelty.  (Plate  XXIV.  Fig.  338.) 

The  force  of  steam,  or  of  heated  vapour,  is  probably  also  the  immediate 
• 

*  After  the  expiry  of  Wasbrough's  patent  for  the  crank,  the  sun  and  planet  wheel 
was  discontinued  in  Watt's  engines,  and  is  now  never  used. 

t  Repertory  of  Arts,  vol.  iv. 


268  LECTURE  XXIX. 

agent  in  the  astonishing  effects  produced  by  the  explosion  of  gunpowder. 
The  initial  elasticity  of  the  fluid  by  which  a  cannon  ball  is  impelled,  ap- 
pears, from  Bernoulli's  calculation,  to  be  at  least  equal  to  ten  thousand 
times  the  pressure  of  the  atmosphere,  and  upon  the  most  moderate  compu- 
tation, from  Count  Rumford's  experiments,  to  be  more  than  three  times  as 
great  as  this.  The  quantity  of  moisture,  or  of  water  of  crystallization,  con- 
tained in  the  powder,  is  certainly  too  small  to  furnish  steam  enough  for  so 
great  an  effect.  We  have  no  reason  to  suppose  that  the  elasticity  of  a  given 
quantity  of  any  aeriform  fluid  or  vapour  is  increased  more  than  about  one 
five  hundredth  for  each  degree  of  Fahrenheit  that  its  temperature  ib  ele- 
vated ;  and  if  we  suppose  the  heat  to  be  raised  to  more  than  5000  degrees, 
the  force  of  each  grain  of  water  converted  into  steam  will  only  be  increased 
tenfold  ;  so  that  if  the  elasticity  were  40  thousand  times  as  great,  the  den- 
sity must  be  4  thousand  times  as  great  as  that  of  ordinary  steam,  and  the 
whole  space  must  be  filled  with  an  aqueous  vapour  almost  twice  as  dense 
as  water  itself.  It  is,  therefore,  probable  that  some  other  parts  of  the 
materials  assume,  together  with  the  water,  the  state  of  vapour,  and  possess 
in  this  form  a  much  greater  elasticity  than  that  of  the  steam  :  for  the  quan- 
tity of  fluids  permanently  elastic,  which  are  extricated,  must  be  allowed  to 
be  wholly  inadequate  to  the  effect. 

The  force  of  fired  gunpowder  is  found  to  be  very  nearly  proportional  to 
the  quantity  employed  ;  consequently,  if  we  neglect  the  consideration  of  the 
resistance  of  the  atmosphere,  the  square  of  the  velocity  of  the  ball,  the  height 
to  which  it  will  rise,  and  its  greatest  horizontal  range,  must  be  directly  as 
the  quantity  of  powder,  and  inversely  as  the  weight  of  the  ball.  Count 
Rumford,*  however,  found  that  the  same  quantity  of  powder  exerted  some- 
what more  force  on  a  large  ball  than  on  a  smaller  one. 

The  essential  properties  of  a  gun  are  to  confine  the  elastic  fluid  as  com- 
pletely as  possible,  and  to  direct  the  motion  of  the  bullet  in  a  rectilinear 
path  ;  and  hence  arises  the  necessity  of  an  accurate  bore.  The  advantage 
of  a  rifle  barrel  is  principally  derived  from  the  more  perfect  contact  of  the 
bullet  with  its  cavity ;  it  is  also  supposed  to  produce  a  rotation  round  an 
axis  in  the  direction  of  its  motion,  which  renders  it  less  liable  to  deviations 
from  its  path  on  account  of  irregularities  in  the  resistance  of  the  air.  The 
usual  charge  of  powder  is  one  fifth  or  one  sixth  of  the  weight  of  the  ball, 
and  for  battering,  one  third.  When  a  24  pounder  is  fired  with  two  thirds 
of  its  weight  of  powder,  it  may  be  thrown  almost  four  miles,  the  resistance 
of  the  air  reducing  the  distance  to  about  one  fifth  of  that  which  it  would 
describe  in  a  vacuum. 

Bullets  of  all  kinds  are  usually  cast  in  separate  moulds:  shot  are 
granulated  by  allowing  the  lead,  melted  with  a  little  arsenic,  to  pass 
through  perforations  in  the  bottom  of  a  vessel,  and  to  drop  in  a  shower 
into  water.  The  patent  shot  fall  in  this  process  through  a  height  of  120 
feet :  the  roundest  are  separated  by  rolling  them  down  an  inclined  plane 
slightly  grooved,  those  which  are  of  an  irregular  form  falling  off  at  the  sides. 

Condensed  air  may  also  be  employed  for  propelling  a  bullet  by  means 

*  New  Experiments  upon  Gunpowder,  by  Benjamin  Thompson,  Ph.  Tr.  1781, 
p.  229.  Consult  Dalton,  Manchester  Memoirs,  vol.  v. 


ON  PNEUMATIC  MACHINES.  269 

of  an  air  gun,  an  instrument  of  considerable  antiquity,  but  of  little  utility. 
It-  is  obvious  that  no  human  force  can  so  far  increase  the  density  of 
air  as  to  make  its  elasticity  at  all  comparable  to  that  of  the  fluid  evolved 
by  fired  gunpowder,  and  even  if  it  were  reduced  to  such  a  state,  its  effects 
would  still  be  far  inferior  to  those  of  gunpowder  :  for  the  utmost  velocity, 
with  which  it  could  expand  itself,  would  not  exceed  1300  feet  in  a  second, 
and  it  would,  therefore,  be  incapable  of  imparting  to  a  ball  a  velocity  even 
as  great  as  this,  while  the  vapour  of  gunpowder  impels  a  heavy  ball  with 
a  velocity  of  more  than  2000  feet  in  a  second.  When,  however,  it  is 
considered  that  by  far  the  greatest  part  of  such  a  velocity  as  this  is  use- 
lessly employed,  and  that  the  mechanical  power  which  is  practically 
obtained  from  gunpowder  is  much  more  expensive  than  an  equivalent 
exertion  of  any  of  the  ordinary  sources  of  motion,  it  must  be  allowed 
that  the  force  of  condensed  air  may  possibly  be  applied  in  some  cases  with 
advantage,  as  a  substitute  for  that  of  gunpowder.  (Plate  XXIV.  Fig.  339.) 

[The  improvements  which  have  been  effected  in  the  construction  of  con- 
densing steam  engines  since  the  time  of  the  publication  of  these  Lectures, 
are  neither  few  nor  unimportant.  As,  however,  most  of  them  are  con- 
nected with  details,  rather  than  with  principles,  it  will  not  be  necessary  to 
give  a  very  specific  account  of  them.  They  consist  of  alterations  in  the 
construction  of  furnaces  and  the  regulation  of  the  fire  ;  better  forms  of  the 
boiler  and  its  appendages  ;  simpler  modes  of  effecting  a  communication 
between  the  boiler,  the  cylinder,  and  the  condenser,  by  a  new  form  of  the 
valves,  and  an  improved  way  of  opening  them  ;  and,  lastly,  more  accurate 
methods  of  fitting  the  different  portions  together,  so  as  to  lose  less  heat  and 
to  waste  less  steam.  Many  of  these  improvements  are  the  results  of  prac- 
tical experience.  About  1811,  the  proprietors  of  some  of  the  Cornish  mines 
established  a  system  of  inspection  of  their  engines,  the  efficacy  of  which  is 
fully  evinced  by  the  work  of  the  registrar  and  inspector,  Captain  Lean. 
He  mentions  the  following  instance  of  it,*  "  relative  to  Stray  Park  engine, 
a  single  engine,  on  Boulton  and  Watt's  construction,  of  sixty-inch  cylinder. 
When  this  engine  was  first  put  on  the  report  in  1811,  its  duty  was  below 
1C  millions  :  during  eight  months,  ending  with  April  1813,  it  had  consumed 
17,633  bushels  of  coal,  performing  the  average  duty  of  21 '5  millions,  and 
worked  at  the  rate  of  5  strokes  per  minute  :  during  eight  months,  ending 
with  April  1814,  it  had  consumed  only  12,671  bushels  of  coal,  performed 
the  average  duty  of  30'5  millions,  and  worked  at  the  rate  of  5'7  strokes  per 
minute."  And  from  the  same  work  it  appears,  that  the  average  duty  had, 
up  to  1834,  increased  from  26'5  to  90  millions ;  the  duty  being  the  number 
of  pounds  which  are  raised  one  foot  high  by  a  bushel  of  coals.  The  eco- 
nomy of  the  Cornish  boiler  and  its  appendages  is  due,  in  a  great  measure, 
to  the  extent  of  surface  which  is  presented  to  the  flame.  This  is  effected 
by  a  number  of  flues,  external  and  internal,  the  latter  somewhat  analogous 
to  those  of  the  locomotive  boiler,  which  will  be  described  presently.  The 
firg  is  laid  on  in  large  masses,  and  allowed  to  consume  slowly,  whilst  the] 

*  Historical  Statements  of  the  Improvements  on  the  Duty  of  Engines  in  Corn- 
wall.    By  T.  Lean  &  Brother,  1836.    Introd.  p.  11. 


270 


LECTURE  XXIX. 


([space  which  the  evolved  gases,  &c.  have  to  travel  before  they  quit  the 
neighbourhood  of  the  water,  enables  them  both  to  be  thoroughly  consumed, 
and  to  part  with  all  their  heat  to  advantage.  The  communications  between 
the  cylinder  and  boiler,  and  cylinder  and  condenser,  are  commonly  made  by 
means  of  a  sliding  valve,  which,  from  its  shape,  is  known  by  the-  name  of 
the  D  valve.  It  is  seen  in  figures  (1)  and  (2), 


Fig.  1. 


Fig.  2 


and  consists  of  nothing  more  than  a  slide  G  of  this  shape, 

placed  in  the  steam  chest,  the  opening  be  being  sufficiently 

wide  to  allow  a  free  communication  between  the  passage 

which  leads  to  the  eduction  pipe  T,  and  one  of  the  passages 

to  the  cylinder,  whilst  it  closes  the  latter  from  the  steam  chest. 

Thus,  in  figure  1,  the  communication  is  between  the  bottom 

of  the  cylinder  and  the  condenser,  whilst  steam  is  entering  to  the  top  of  the 

cylinder.    In  figure  2  it  is  the  reverse. 

The  apparatus  by  which  the  valve  is  slid  up  and  down  is  seen  at 
figure  (3), 


ON  PNEUMATIC  MACHINES.  271 

[the  rod  EF,  which  moves  the  valve,  in  figs.  1  and  2,  being  united  to  it  at  O. 
•I*  is  called  an  eccentric,  and  consists  of  a  hollow  circle  working  on  a  solid 
one,  the  centre  of  motion  of  which  is  not  the  centre  of  the  circle.  As  the 
centres  of  both  circles  always  coincide,  and  that  of  the  solid  circle  revolves 
about  the  centre  of  motion,  the  rod  CM  will  be  moved  forwards  and  back- 
wards, and  consequently  0  will  move  upwards  and  downwards,  and  effect 
the  different  communications  and  interruptions  by  the  aid  of  the  D  valve. 

The  application  of  the  steam  engine  to  navigation,  which  took  place  about 
the  time  of  the  appearance  of  Dr.  Young's  work,  was  a  result  so  obvious  and 
necessary,  that  it  required  the  development  of  no  new  principles,  and  but 
little  refinement  in  the  application  of  those  already  recognised,  to  bring  it 
about.  The  size  and  weight  of  the  machinery  no  doubt  offered  a  considerable 
obstacle  at  first,  inasmuch  as  the  force  obtained  might  bear  too  small  a  pro- 
portion to  the  mass  to  be  moved  and  the  resistance  to  be  overcome,  to  render 
it  economical.  And  this  in  fact  appears  to  have  been  the  case  with  the 
earliest  application  of  steam  power  to  navigation,  that  of  Mr.  Symington. 
But  the  perseverance  of  Fulton,  Henry  Bell,  and  others,  obviated  all  these 
difficulties,  whilst  successive  improvements  both  in  the  arrangements  and 
the  construction  of  the  different  parts  of  the  machinery,  have  rendered 
the  expenditure  of  fuel  very  much  less  than  it  was  a  quarter  of  a  cen- 
tury ago. 

For  a  considerable  time  steam  vessels  plied  only  on  rivers,  not  daring  to 
venture  into  the  open  sea,  and  nautical  men,  for  the  most  part,  entertained 
the  opinion  that  they  were  unfitted  to  brave  it.  George  Dodd,  an  enter- 
prising but  unfortunate  man,  decided  this  point.  He  came  down  to  Glas- 
gow and  fitted  up  a  little  vessel  of  75  tons  burthen,  with  a  steam  engine  of 
14  horse  power,  in  which  he  started  with  a  crew  of  five  seamen,  two  engine 
men,  and  a  boy,  for  London.  Although  the  voyage  was  stormy,  it  was 
safely  performed  in  122  hours  (exclusive  of  stoppages).  Dodd  was  emi- 
nent as  engineer ;  he  projected  Waterloo  Bridge  and  the  Thames  Tunnel,* 
purposing  to  carry  it  across  from  Gravesend  to  Tilbury,  at  the  estimated 
cost  of  under  £16,000  !  t  Yet,  with  talent,  energy,  and  courage,  he  almost 
literally  died  in  the  streets  a  beggar.  His  active  mind  led  him  into  dis- 
astrous schemes — failure  impoverished  him  and  drove  him  to  intempe- 
rance, which  ended  in  destitution  and  premature  death. 

The  adaptation  of  the  steam  engine  to  the  propelling  of  vessels  is  now 
so  universally  known,  that  a  very  brief  description  of  the  mode  of  effecting 
it  will  suffice.  Across  the  deck  of  the  vessel  is  carried  a  shaft,  to  the  ex- 
tremities of  which  paddle  wheels  are  fixed,  the  action  of  which  every  one 
is  familiar  with.  On  this  shaft  two  cranks  are  constructed  at  right  angles 
to  each  other,  on  which  the  connecting  rods  of  the  two  engines  respectively 
work.  By  this  contrivance  a  tolerable  uniformity  of  action  is  produced, 
without  the  aid  of  a  fly  wheel,  the  one  engine  being  in  its  position  of 
greatest  effect  when  the  other  is  in  the  contrary  position.  The  principal 
feature  in  the  construction  of  marine  engines,  as  compared  with  land  ones, 
consists  in  the  reversal  of  the  beam,  to  prevent  the  inconvenience  of  its] 

*  Stuart's  Anecdotes,  p.  534.     Probably  his  father  was  the  projector, 
t  Nicholson's  Journal,  ii.  239,  473. 


272  LECTURE  XXIX. 

[protruding  above  deck.  To  connect  it  with  the  piston  rod,  cross  pieces  are 
attached  to  the  top  of  the  latter,  which  extend  beyond  the  cylinder,  aiid 
are,  on  each  side  of  it,  united  by  parallel  motions  to  connecting  rods  4which 
communicate  with  the  beam. 

In  this  country  the  steam  is  applied  to  marine  engines  at  a  temperature 
not  greatly  exceeding  the  boiling  point  ;  but  in  America  the  case  is  other- 
wise, the  steam  being  often  applied  at  such  a  temperature  as  to  produce 
double  the  pressure  it  does  under  ordinary  circumstances. 

Where  lightness  is  an  object,  the  condensing  apparatus  is  altogether 
done  away  with,  steam  of  a  high  temperature  being  employed,  which  after 
it  has  done  its  work,  is  allowed  to  escape  into  the  air.  An  engine  on  this 
principle  is  designated  a  high  pressure  engine.  The  pressure  of  steam  in- 
creases very  rapidly  with  its  temperature,  because  its  density  increases  at 
the  same  time.  The  law  which  connects  the  two  is  given  empirically  by 
Dr.  Young  (vol.  ii.  p.  398),  as 

d—(l  +  -0029/)7, 

d  being  the  depth  of  mercury  in  atmospheres  of  30  in.  each,  which  would 
press  as  much  as  steam  at  a  temperature  f  of  Fahrenheit  above  212°. 
Thus,  at  212°,  d  =  1  atmosphere  =  weight  of  30  in.  of  mercury  =  about 
15lbs.  per  square  inch;  at  250°,  /=  38,  d=  (1-1102)7  =  a  little  more 
than  2,  or  the  pressure  is  more  than  doubled.  Many  analogous  formulae 
have  been  proposed  at  different  times.  That  of  the  Franklin  Institute  is 


For  the  purpose  of  inland  transport,  the  condensing  engine  is  inappli- 
cable, on  account  of  the  weight  of  the  condensing  apparatus.  As  early  as 
1802,  Mr.  Trevi  thick  constructed  a  high-pressure  engine,  in  which  the 
boiler  and  apparatus  formed  one  machine  ;  but  it  was  soon  found  that  the 
roughness  of  common  roads  prevented  the  use  of  such  an  engine,  and 
finally  destroyed  it.  Mr.  Trevithick  consequently  turned  his  attention 
to  railroads  ;  but  a  difficulty  arose,  which  gave  much  unnecessary  trouble, 
from  the  fact  of  its  being  almost  imaginary.  The  adhesion  of  the  wheels 
was  not  supposed  to  be  sufficient  to  prevent  their  slipping.  To  obviate 
tthis,  various  devices  were  put  in  requisition,*  such  as  rack  work,  pro- 
jecting moveable  feet,  &c.  Experience  finally  taught  that  the  friction  of 
the  driving  wheels  .is  more  than  sufficient,  in  ordinary  cases,  to  prevent 
slipping,  provided  a  considerable  portion  of  the  weight  be  made  to  press 
on  them.  This  being  established,  the  construction  of  the  working  engine 
presents  no  insuperable  difficulties.  The  following  is  a  brief  description 
of  one  of  the  most  approved  forms  of  the  locomotive. 

The  first  thing  to  be  attained  is  the  supply  of  a  large  quantity  of 
steam  at  a  high  temperature,  and  from  a  small  apparatus.  To  effect  this, 
as  large  a  surface  as  possible  must  be  exposed  to  the  action  of  the  fire, 
and  the  fuel  itself  must  be  kept  in  a  vigorous  state  of  combustion  by  a 
great  draught.  These  objects  are  attained  by  perforating  the  boiler,  which 
is  cylindrical,  from  end  to  end,  by  upwards  of  100  hollow  tubes  of  about 
two  inches  diameter.  Through  these  the  flame  and  heated  air  find  their 
way  from  the  grate  to  the  chimney  ;  thus  imparting  heat  to  a  vast  surface] 
*  See  Gordon's  Treatise  on  Elemental  Locomotion,  1832. 


ON  PNEUMATIC  MACHINES. 


273 


[of  water  with  which  they  come  in  contiguity.  To  accelerate  the  draught, 
the  steam  ejected  from  the  cylinder,  which  has  still  considerable  force,  is 
emitttyl  up  the  chimney,  thus  producing  a  rapid  current  in  that  direction. 
A  section  of  the  engine  is  given  in  figure  (4.)* 


*  From  Tredgold's  work  on  the  Steam  Engine,  edited  by  Woolliouse,  2  vols.  4to, 


274  LECTURE  XXIX. 

[It  will  be  seen,  that  by  far  the  larger  part  of  the  machine  is  the  boiling 
apparatus;  the  working  machinery  occupying  only  the  comparative!} 
small  space  below.  That  portion  of  the  boiler  which  contains  water  is 
shaded  in  the  figure  ;  and  the  tubes  are  seen  at  E,  by  which  the  flame 
penetrates  the  whole  body  of  the  boiler  from  the  fire-box  C  to  the 
smoke-box  F.  From  every  part  of  the  surface  of  the  water,  steam  is  rapidly 
and  constantly  emitted;  but  it  has  no  way  of  escape  from  the  boiler, 
except  tjy  ascending  the  steam  dome  T,  in  which  the  mouth  of  the  steam 
pipe  df  Is  situated.  After  entering  the  steam  pipe,  it  has  to  traverse  the 
whole  length  of  the  boiler  d'SS  before  it  reaches  the  cylinder.  The  .object 
of  this  arrangement  is  to  separate  from  the  steam  a  quantity  of  water, 
which,  being  raised  by  the  violence  of  ebullition,  would  otherwise  be 
carried  along  to  the  cylinder.  The  same  arrangement  facilitates  the 
regulation  of  the  steam,  by  bringing  it  into  the  immediate  neighbourhood 
of  the  engine  driver,  who  is  enabled  to  increase  or  diminish  the  supply  which 
is  furnished  to  the  cylinder,  by  means  of  a  winch  hf  acting  on  a  valve  e'. 
As  the  steam  pipe  is  everywhere  inclosed  in  steam,  there  is  no  loss  of  tem- 
perature on  this  account,  except  a  very  trifling  amount  due  to  the  time 
which  elapses  between  the  production  of  the  steam,  and  its  application  to  do 
its  work.  Two  safety  valves  are  placed  in  the  upper  part  of  the  boiler ;  one 
at  0,  loaded  with  a  constant  weight,  and  out  of  the  reach  of  the  conductor  ; 
the  other  at  N. 

In  the  steam  chest  at  U  is  the  D  valve,  admitting  steam  to  the  front  or 
back  of  the  cylinders  W,  which  are  horizontal,  and  alternately  suffering  it 
to  escape  by  the  waste  port  up  the  blast  pipe  />,  to  increase  the  draught  of 
the  chimney,  as  already  mentioned.  The  construction  of  the  working 
machinery  is  of  the  most  simple  kind.  An  axle,  bent  so  as  to  form  two 
cranks,  at  right  angles  to  each  other,  is  attached  to  the  two  driving  wheels. 
These  are  larger  than  the  other  wheels,  of  which  there  are  usually  two 
pair,  provided  with  flanges  or  rims  on  the  inside  of  their  circumference,  for 
the  purpose  of  retaining  the  machine  on  the  rail.  Thus  the  axle  and 
driving  wheels  of  this  engine  are  analogous  to  the  shaft  and  paddle  wheels 
of  the  marine  engine.  There  is  no  beam,  but  the  piston  rods  Y  being  con- 
fined by  guide  bars,  which  allow  them  to  play  backwards  and  forwards 
through  the  space  of  about  18  inches,  are  attached  immediately  at  their 
extremities  to  the  connecting  rods  which  act  on  the  cranks.  These  being 
at  right  angles  to  each  other,  the  force  is  equalised  as  in  the  marine  engine. 
The  valve  machinery  consists,  as  usual,  of  an  eccentric  and  levers,  but  in 
the  locomotive,  each  cylinder  is  provided  with  two  sets  of  eccentrics,  the 
one  being  the  reverse  of  the  other,  that  is,  tending  to  move  the  valve  back 
when  the  other  would  move  it  forwards.  A  lever  is  in  the  direction  of  the 
driver,  by  means  of  which  one  set  may  be  thrown  out  of  gear,  whilst 
the  other  is  thrown  in.  The  rod  of  the  eccentric  which  is  not  in  gear  is 
seen  at/".  It  terminates  in  a  Y,  so  that  when  raised  it  will  readily  catch 
the  working  levers  (at  M,  fig.  3).  By  this  means  the  action  of  the  engine 
can  be  instantaneously  reversed. 

It  will  be  seen  from  this  description  that  the  locomotive  is  by  far  the 
most  simple  form  of  the  steam  engine.  As,  however,  it  is  applied  to  per- 
form work  in  which  great  speed  is  necessary ;  so  much  so  as  to  require  that] 


ON  THE  HISTORY  OF  HYDRAULICS,  &c.  275 

[the  piston  rods  move  backwards  and  forwards  three  or  four  times  in  a 
'second,  and  therefore,  that  each  of  the  cylinders  he  filled  and  emptied  six 
or  eight  times  in  the  same  interval ;  it  is  evident  that  the  utmost  accuracy 
of  workmanship  is  requisite,  not  merely  to  prevent  useless  expenditure  of 
fuel,  but  even  to  keep  the  machine  in  action  at  this  speed  at  all.] 


For  further  information  on  the  Steam  Engine,  consult  Partington's  History  and 
Description  of  the  Steam  Engine,  1822.  Stuart's  Descriptive  History  of  do.  1824. 
Historical  and  Descriptive  Anecdotes  of  Steam  Engines  and  their  Inventors,  2  vols. 
12mo,  1829.  Farey  on  the  Steam  Engine,  4to,  1827.  Gilbert,  Progressive  Improve- 
ment^ on  the  Efficiency  of  Steam  Engines  in  Cornwall,  Ph.  Tr.  1830.  Coriolis, 
Journal  de  1'Ecole  Polytechnique,  vol.  13.  Brewster's  Journal,  Nos.  17  and  19. 
Birkbeck  and  Aldcock  on  the  Steam  Engine.  Renwick  on  do.  New  York,  1830. 
Tredgold  on  do.  a  new  edition  by  Woolhouse,  2  vols.  4to,  1838,  with  various  subse- 
quent appendices.  De  Pambour  on  the  Theory  of  do.  Lardner  on  do.  7th  edition, 
1840.  Russel  on  do.  from  Encyc.  Brit.  The  last  four  treatises  contain  all  that 
could  be  desired  on  this  subject. 

On  its  Applications,  see  Jonathan  Hulls'  Description  of  a  New  Machine,  1737. 
Buchanan  on  Steam  Navigation,  Glasgow,  1816.  Dodd  on  do.  1816.  Wood's 
Practical  Treatise  on  Railways.  Marestier,  Mem.  sur  les  Bateaux  a  Vapeur,  1824. 
Cleland's  Hist.  Account  of  the  Steam  Engine,  and  its  Application  to  propelling 
Vessels,  1825.  Seguin,  Mem.  sur  la  Navigation  a  Vapeur,  1828.  Brees's  Railway 
Practice,  1838. 

LECT.  XXIX.— ADDITIONAL  AUTHORITIES. 

Air  Pumps,  Condensers,  8fc. — Boyle  on  the  Spring  and  Weight  of  the  Air,  4to, 
Oxf.  1663,  and  Opera,  passim.  Varignon  on  an  Air  Pump,  Hist,  et  Mem.  de  Paris, 
x.  285.  Leupolds  Beschreibung  der  Luftpumpe,  4to,  Leipz.  1710-12.  Nollet,  Hist, 
et  Mem.  1740,  pp.  385,  567 ;  1741,  p.  338,  H.  145.  Lowitz  iiber  die  Eigenschaf- 
ten  derLuft,  1754.  Coulomb  on  Condensing  with  an  Air  Pump,  Roz.  Journ.  xvii. 
301.  Ingenhousz  Vermischte  Schriften,  p.  197.  Hindenburg  de  Antlia  Baaderiana, 
4to,  Leipz.  1787.  De  Antlia  Nova,  4to,  Leipz.  1789.  Goth.  Mag.  v.  II.  81. 
Prince's  Air  Pump,  Trans,  of  the  American  Academy,  vi.  235.  Van  Marum's 
Simple  Air  Pump,  Gilb.  Jour.  i.  379.  Mackenzie's  Air  Pump,  Nich.  Jour.  ii.  28. 


LECTURE    XXX. 


ON  THE  HISTORY  OF  HYDRAULICS  AND  PNEUMATICS. 

NOTWITHSTANDING  a  few  observations  and  experiments  made  by 
Aristotle  and  his  predecessors,  the  properties  of  fluids  had  scarcely  been 
the  subjects  of  much  accurate  investigation  before  the  time  of  Archimedes. 
The  progress  which  the  science  of  hydrostatics  in  particular  made  under 
this  eminent  mathematician,  does  the  highest  honour  to  his  genius  and 
penetration.  His  treatise  on  floating  bodies,  although  the  theorems  which 
it  contains  are  not  so  general  as  they  have  been  rendered  since  the  late 
improvements  in  the  methods  of  calculation,  still  affords  us  instances  of 
very  ingenious  determinations  of  the  equilibrium  of  floating  bodies  of 
different  forms,  grounded  on  the  true  principles  of  the  opposition  of  the 
general  directions  of  the  weight  of  the  body  and  of  the  pressure  of  the 
fluid  ;  and  in  this  manner  he  has  shown  in  what  cases  the  equilibrium  of 

T2 


276  LECTURE   XXX. 

conical  and  conoidal  solids  will  be  stable,  and  in  what  cases  unstable. 
Archimedes  was  the  inventor  of  the  mode  of  measuring  the  bulk  of  a  solid 
by  immersing  it  in  a  fluid  :  to  us,  indeed,  there  appears  to  have  beef\  little 
difficulty  in  the  discovery,  but  the  ancients  thought  otherwise.  Vitruvius 
observes  that  this  invention  indicates  a  degree  of  ingenuity  almost  in- 
credible. The  philosopher  himself  is  said  to  have  valued  it  so  highly, 
that  when  it  first  occurred  to  him,  in  a  public  bath,  he  hastened  home  in 
an  ecstasy  without  recollecting  to  clothe  himself,  in  order  to  apply  it  to 
the  determination  of  the  specific  gravity  of  Hiero's  crown  and  to  the 
detection  of  the  fraud  of  the  maker,  who  had  returned  the  crown  'equal 
in  weight  to  the  gold  that  was  given  him,  but  had  adulterated  it  with 
silver,  and  imagined  that  on  account  of  the  complicated  form  of  the  work, 
which  rendered  it  almost  impossible  to  determine  its  bulk  by  calculation, 
he  must  infallibly  escape  conviction.  The  hydrometer,  which  has  some- 
times been  attributed  to  Hypatia,  a  learned  Greek  lady  of  Constantinople, 
is  mentioned  by  Fannius,*  an  early  writer  on  weights  and  measures,  and 
is  ascribed  by  him  to  Archimedes. 

The  forcing  pump,  or  rather  the  fire  engine,  was  the  invention  of 
Ctesibius  of  Alexandria,  the  greatest  mechanic  of  antiquity  after  Archi- 
medes. He  is  also  said  to  have  invented  the  clepsydra,  for  the  hydraulic 
measurement  of  time,  and  Philot  informs  us  that  he  constructed  an  air 
gun,  for  propelling  a  stone,  or  rather  a  ball,  by  means  of  air  previously 
condensed  by  a  syringe.  The  ball  was  not  immediately  exposed  to  the 
action  of  the  air,  but  was  impelled  by  the  longer  end  of  a  lever,  while  the 
air  acted  on  the  shorter.  Ctesibius  is  said  to  have  been  the  son  of  a  barber, 
and  to  have  had  his  attention  turned  to  mechanics  and  pneumatics,  by 
being  employed  to  fit  a  shutter,  with  a  counterpoise  sliding  in  a  wooden 
pipe,  for  his  father's  shop  window.^ 

Hero  was  a  cotemporary,  and  a  scholar  of  Ctesibius  ;  he  describes,  in 
his  treatise  on  pneumatics,  a  number  of  very  ingenious  inventions,  a  few 
of  which  are  calculated  for  utility,  but  the  greater  part  for  amusement 
only  ;  they  are  principally  siphons  variously  concealed  and  combined, 
fountains,  and  water  organs,  besides  the  syringe  and  the  fire  engine.  The 
description  of  this  engine  agrees  precisely  with  the  construction  which  is 
at  this  day  the  most  usual ;  it  consists  of  two  barrels,  discharging  the 
water  alternately  into  an  air  vessel ;  and  it  appears  from  Vitruvius,  that 
this  was  the  original  form  in  which  Ctesibius  invented  the  pump.  Hero 
supposes  the  possibility  of  a  vacuum  in  the  intervals  of  the  particles  of 
bodies,  observing  that  without  it  no  body  could  be  compressible ;  but  he 
imagines  that  a  vacuum  cannot  exist  throughout  a  perceptible  space,  and 
thence  derives  the  principle  of  suction.  The  air  contained  in  a  given 
cavity  may  be  rarefied,  he  says,  by  sucking  out  a  part  of  it,  and  he 
describes  a  cupping  instrument,  which  approaches  very  nearly  to  the 
nature  of  an  imperfect  air  pump.  (Plate  XXIV.  Fig.  324.) 

After  the  time  of  Ctesibius  and  Hero,  the  science  of  hydraulics  made 

*  Rhemnius  Fannius  Palsemon  de  Ponderibus  et  Mensuris. 

f  Duten's  Inquiry  into  the  Origin  of  the  Discoveries  attributed  to  the  Moderns, 
Lond.  1769,  p.  186. 

I  Vitruvius,  ix.  9.     A  figure  of  tbe  clepsydra  is  given  in  Perrault's  translation. 


ON  THE  HISTORY  OF  HYDRAULICS,  &c.  277 

little  further  progress  until  the  revival  of  letters.  The  Romans  had  water 
mills  in  the  time  of  Julius  Caesar,  which  are  described  by  Vitravius ;  and 
it  appears  that  their  aqueducts  were  well  built,  and  their  waterpipes  well 
arranged.  Pipes  of  lead  were,  however,  less  frequent  than  at  present, 
from  an  apprehension  of  the  poisonous  quality  of  the  metal,  which  was 
not  wholly  without  foundation.*  Some  say  that  the  ancients  had  no 
chimnies,  but  whatever  may  be  the  authorities,  the  opinion  is  extremely 
improbable. 

It  was  in  the  middle  ages  that  navigable  canals  began  to  be  considerably 
multiplied,  first  in  China,  and  afterwards  in  other  parts  of  the  world. 
The  canal  from  the  Trent  to  the  Witham,  which  is  the  oldest  in  England, 
is  said  to  have  been  dug  in  1134.  The  date  of  the  earliest  windmills  has 
been  referred  to  the  year  1299.  The  invention  of  gunpowder  possesses 
perhaps  an  equal  claim  with  the  art  of  printing,  to  the  honour  of  being 
considered  as  constituting  the  most  marked  feature  that  distinguishes  the 
character  of  ancient  from  that  of  modern  times ;  its  introduction  must 
necessarily  have  tended  to  produce  material  alterations,  and  perhaps  im- 
provements, in  the  habits  of  nations  and  of  individuals.  It  is  said  to  have 
been  known  long  since  to  the  Chinese,  and  our  countryman,  Roger  Bacon, 
was  evidently  acquainted  with  its  properties  ;  but  it  was  not  actually  em- 
ployed in  Europe  or  in  its  neighbourhood  till  about  the  year  1330  ;  and  the 
earliest  artillery  appears  to  have  been  that  which  was  used  by  the  Moors, 
at  the  siege  of  Algesiras,  in  1334.  King  Edward  had  four  pieces  of  cannon 
at  the  memorable  battle  of  Cressy,  in  1346. 

About  the  year  1600,  Galileo  made  the  important  discovery  of  the  effects 
of  the  weight  and  pressure  of  the  atmosphere,t  in  the  operation  of  suction, 
and  in  various  other  phenomena.  Before  his  time,  it  was  generally  sup- 
posed that  water  was  raised  by  a  sucking  pump,  on  account  of  the  im- 
possibility of  the  existence  of  a  vacuum  :  if,  however,  a  vacuum  had  been 
impossible  in  nature,  the  water  would  have  followed  the  piston  to  all 
heights,  however  great,  but  Galileo  found  that  the  height  of  its  ascent  was 
limited  to  about  34  feet,  and  concluded  that  the  weight  of  a  column  of 
this  height  was  the  measure  of  the  magnitude  of  the  atmospherical  pres- 
sure. His  pupil  Torricelli  afterwards  confirmed  the  explanation,  by 
showing  that  a  column  of  mercury  was  only  supported  when  its  weight 
was  equal  to  that  of  a  column  of  water  standing  on  the  same  base ;  hence 
the  vacuum  obtained  by  means  of  mercury  is  often  called  the  Torricellian 
vacuum.  Torricelli  corrected  also,  in  1644,  the  mistake  of  Castelli  respect- 
ing the  quantities  of  water  discharged  by  equal  orifices,  at  different 
distances  below  the  surface  of  the  water  in  the  reservoir.  Castelli's  ex- 
periments, made  about  1640,  were  the  first  of  the  kind,  and  some  of  them 
really  tended  to  the  improvement  of  the  science  of  hydraulics,  but  others 
appeared  to  show  that  a  double  height  of  the  head  of  water  produced  a 
double  discharge.  Torricelli's  more  accurate  observations  proved  that  a 

*  It  is  an  important  circumstance  in  reference  to  the  action  of  water  on  lead,  that 
it^is  more  injurious  in  proportion  to  the  purity  of  the  water.  That  which  contains 
less  than  gg^th  of  salts  in  solution,  cannot  be  safely  conducted  in  lead  pipes  without 
certain  precautions.  Christison,  Trans.  Roy.  Soc.  Edin.  xv.  265. 

f  See  note,  p.  207.  t 


278  LECTURE  XXX. 

quadruple  height  was  required  in  order  to  produce  a  double  velocity  ;  and 
his  assertions  were  afterwards  fully  confirmed  by  Mariotte  and  by 
Guglielmini.*  j 

A  little  before  the  year  1654,  Otto  von  Guericke,  of  Magdeburg,  first 
constructed  a  machine  similar  to  the  air  pump,  by  inserting  the  barrel  of  a 
fire  engine  into  a  cask  of  water,  so  that  when  the  water  was  drawn  out  by 
the  operation  of  the  piston,  the  cavity  of  the  cask  remained  nearly  void 
of  all  material  substance.  But  finding  that  the  air  rushed  in  between  or 
through  the  staves  of  the  cask,  he  inclosed  a  smaller  cask  in  a  larger  one, 
and  made  the  vacuum  in  the  internal  one  more  complete,  while  the  inter- 
vening space  remained  filled  with  water ;  yet  still  he  found  that  the  water 
was  forced  into  the  inner  cask  through  the  pores  of  the  wood.  He  then 
procured  a  sphere  of  copper,  about  two  feet  in  diameter,  and  was  exhausting 
it  in  the  same  way,  wThen  the  pressure  of  the  air  crushed  it,  with  a  loud 
noise.  This  machine  was  more  properly  a  water  pump  than  an  air  pump, 
but  the  inventor  soon  after  improved  his  apparatus,  and  made  all  the  expe- 
riments which  are  to  this  day  the  most  usually  exhibited  with  the  air 
pump,  such  as  the  apparent  cohesion  of  two  exhausted  hemispheres,  the 
playing  of  a  jet  by  means  of  the  expansion  of  a  quantity  of  air  inclosed  in 
a  jar,  the  determination  of  the  air's  weight,  and  others  of  a  similar 
nature.  He  also  observed  that  for  very  accurate  experiments,  the  valve 
of  the  pump  might  be  raised  at  each  stroke  by  external  force ;  and  he 
particularly  noticed  the  perpetual  production  of  air  from  the  water  that 
he  generally  employed,  which  caused  an  imperfection  in  the  vacuum.  An 
account  of  his  experiments  was  first  published  in  different  works,  by 
Caspar  Schott,t  and  afterwards  by  himself,  in  his  book  entitled  Experimenta 
nova  Magdeburgica,  printed  in  1672  at  Amsterdam. 

In  the  year  1658,  Hooke  finished  an  air  pump  for  Boyle,  in  whose  labo- 
ratory he  was  an  assistant :  it  was  more  convenient  than  Guericke' s,  but 
the  vacuum  was  not  so  perfect ;  yet  Boyle's  numerous  and  judicious  expe- 
riments gave  to  the  exhausted  receiver  of  the  air  pump  the  name  of  the 
Boylean  vacuum,  by  which  it  was  long  known  in  the  greatest  part  of 
Europe.  Hooke' s  air  pump  had  two  barrels,  and  with  some  improvements 
by  Hauksbee,^  it  remained  in  common  use  until  the  introduction  of  Smea- 
ton's  pump,  which,  however,  has  not  wholly  superseded  it.  The  theory  of 
pneumatics  was  also  considerably  indebted  to  Hooke's  important  experi- 
ments on  the  elasticity  of  the  air,  which  were  afterwards  confirmed  and  ex- 
tended by  Mariotte  and  Amontons,  in  France,  by  Hales  in  this  country, 
and  by  Richmann  at  Petersburg. 

About  the  same  time  the  first  steam  engine  was  constructed  by  the  cele- 
brated Marquis  of  Worcester.  Hints  of  the  possibility  of  such  a  machine 
had  been  given  a  hundred  years  before,  by  Matthesius,§  in  a  collection  of 
sermons  entitled  Sarepta,  and  at  a  subsequent  period  by  Brunau;||  but  the 

*  See  authorities  in  Lect.  XXIV. 

f  Magia  Universalis,  4vols.4to,  Wurtzb.  1657.  Mechanica  Hydraulico-pneu- 
matica,  4to,  1657.  Technica  Curiosa,  4to,  Norimbergee,  1664. 

J  Hauksbee,  Physico-Mechanical  Experiments,  4to,  Lond.  1709,  p.  1. 

§  Kepler  in  Bergmannische's  Journal,  1791,  ii.  263. 

||  Hints  towards  a  Steam  Engine,  in  1627,  Nich.  Jour.  vii.  311. 


ON  THE  HISTORY  OF  HYDRAULICS,  &c.  279 

Marquis  of  Worcester  professes  to  have  carried  the  project  into  full  effect, 
as  We  are  informed  by  his  account  of  what  he  called  a  fire  water  work, 
which  fts  one  of  his  Century  of  Inventions,  first  published  in  1663,*  and 
which  is  thus  described  :  "  I  have  taken  a  piece  of  a  whole  cannon,  whereof 
the  end  was  burst,  and  filled  it  three  quarters  full  of  water,  stopping  and 
screwing  up  the  broken  end,  as  also  the  touch  hole  ;  and  making  a  constant 
fire  under  it,  within  24  hours  it  burst,  and  made  a  great  crack  :  so  that 
having  a  way  to  make  my  vessels  so  that  they  are  strengthened  by  the 
force  within  them,  and  the  one  to  fill  after  the  other,  I  have  seen  the  water 
run  l&e  a  constant  fountain  stream  forty  foot  high.  One  vessel  of  water, 
rarefied  by  fire,  driveth  up  forty  of  cold  water  :  and  a  man  that  tends  the 
work  is  but  to  turn  two  cocks,  that  one  vessel  of  water  being  consumed, 
another  begins  to  force  and  refill  with  cold  water,  and  so  successively,  the 
fire  being  tended  and  kept  constant,  which  the  self  same  person  may  like- 
wise abundantly  perform  in  the  interim  between  the  necessity  of  turning 
the  said  cocks."  The  machine  was,  however,  not  at  that  time  prac- 
tically introduced,  and  it  was  soon  forgotten  ;  Savery's  engines  were 
constructed  in  a  manner  precisely  similar,  some  time  before  1700  ;  and 
it  is  uncertain  whether  he  adopted  the  Marquis  of  Worcester's  ideas, 
or  reinvented  a  similar  machine.  About  1710,  the  piston  and  cylinder 
were  invented  by  Newcomen,  and  with  Beighton's  apparatus  for  turning 
the  cocks  by  its  own  motion,  the  engine  remained  nearly  stationary  for 
many  years. 

As  early  as  the  year  1667,  the  pressure  of  fluids  in  motion,  and  the  re- 
sistance opposed  by  fluids  at  rest  to  the  motion  of  solid  bodies,  were  expe- 
rimentally examined  by  Huygens,  and  some  other  members  of  the  Parisian 
Academy.  Pardies,  whose  works  were  published  in  1673,  attempted  to 
determine,  although  upon  some  inaccurate  suppositions,  the  effects  of  the 
wind  on  a  ship's  sails  under  different  circumstances.  His  principles  were 
adopted  by  Renaud,  who  published  a  work  on  the  subject  in  1689.t  Their 
imperfections  were,  however,  soon  after  pointed  out  by  Huygens,  and  by 
James  Bernoulli;  and,  in  1714,  John  Bernoulli  published  an  extensive 
treatise  on  the  manoeuvres  of  ships,  which  at  last  compelled  Renaud  to 
submit  to  so  many  united  authorities. 

It  must  be  confessed  that  the  labours  of  Newton  added  fewer  improve- 
ments to  the  doctrines  of  hydraulics  and  pneumatics  than  to  many  other 
departments  of  science ;  yet  some  praise  is  undeniably  due  both  to  his  com- 
putations and  to  his  experiments  relating  to  these  subjects.  No  person 
before  Newton  had  theoretically  investigated  the  velocity  with  which  fluids 
are  discharged,  and  although  his  first  attempt  was  unsuccessful,  and  the 
method  which  he  substituted  for  it  in  his  second  edition  is  by  no  means  free 
from  objections,  yet  either  of  the  determinations  may  be  considered  in  some 
cases  as  a  convenient  approximation  ;  and  the  observation  of  the  contraction 
of  a  stream  passing  through  a  simple  orifice,  which  was  then  new,  serves  to 
reconcile  them  in  some  measure  with  each  other.  His  modes  of  considering 
the*  resistance  of  fluids  are  far  from  being  perfectly  just,  yet  they  have  led 
to  results  which,  with  proper  corrections,  are  tolerably  accurate  ;  and  his 
*  Invention,  68.  f  Manoeuvres  des  Vaisseaux. 


280  LECTURE  XXX. 

determination  of  the  oscillations  of  fluids  in  bent  tubes,  was  a  good  begin- 
ning of  the  investigation  of  their  alternate  motions  in  general. 

The  accurate  experiments  of  Poleni  were  published  in  1718.  He  has  the 
merit  of  having  first  distinctly  observed  that  the  quantity  of  water  dis- 
charged by  a  short  pipe  is  greater  than  by  a  simple  orifice  of  the  same 
diameter ;  although  there  is  some  reason  to  suppose  that  Newton  was  before 
acquainted  with  the  circumstance. 

In  1 727,  Mr.  Bouguer  received  a  prize  from  the  Academy  of  Paris  for  his 
essay  on  the  masts  of  ships,  which  is  said  to  be  ingenious,  but  by  no  means 
practically  useful.  He  was,  probably,  tempted  by  this  encouragement  to 
continue  his  application  to  similar  studies  ;  and,  about  twenty  years  after- 
wards, he  published  his  valuable  essay  on  the  construction  and  manoeuvres 
of  ships,  which  appears  to  have  superseded  all  that  had  been  done  before 
respecting  the  subjects  of  his  investigation. 

The  first  researches  of  Daniel  Bernoulli  concerning  the  properties  and 
motions  of  fluids,  bear  also  the  date  of  1727.  This  justly  celebrated  man 
was  as  happy  in  his  application  of  mathematics  to  natural  philosophy,  as  he 
was  ready  and  skilful  in  his  calculations.  The  greatest  part  of  his  hydraulic 
theorems  are  founded  on  the  principle  first  assumed  by  Huygens,  and  called 
by  Leibnitz  the  law  of  living  or  ascending  force,  which  is  confessedly  only 
true  where  there  is  no  loss  of  velocity,  from  the  imperfection  of  the  elasticity 
of  the  bodies  concerned  ;  for  it  is  only  with  this  limitation  that  the  motions 
of  any  system  of  bodies  are  always  necessarily  such  as  to  be  capable  of 
carrying  the  common  centre  of  gravity  to  the  height  from  which  it  has  de- 
scended while  the  bodies  have  been  acquiring  their  motions.  This  law  of 
ascending  force  is  of  considerable  utility  in  facilitating  the  solution  of  a  great 
variety  of  problems.  It  is  certain  that  mechanical  power  is  always  to  be 
estimated  by  the  product  of  the  mass  of  a  body  into  the  height  to  which  it 
is  capable  of  ascending  ;  and  whatever  objections  may  have  been  made  to  the 
employment  of  this  product  as  the  measure  of  the  force  of  a  body  in  motion, 
which  is  indeed  an  expression  inconsistent  with  a  correct  definition  of  the 
term  force,  yet  it  must  be  confessed,  on  the  other  hand,  that  some  of  the  best 
English  mathematicians  have  fallen  into  material  errors  for  want  of  paying 
sufficient  attention  to  the  general  principle.  Bernoulli  estimates  very  justly 
in  this  manner  the  mechanical  power  of  a  variety  of  natural  and  artificial 
agents,  and  among  the  rest  he  examines  that  of  gunpowder ;  but,  from  an 
accidental  combination  of  errors,  he  states  the  force  of  a  pound  of  gun- 
powder as  equivalent  to  the  daily  labour  of  100  men,  while,  in  fact,  the 
effect  which  is  actually  obtained  from  two  tons  of  powder  is  no  greater  than 
that  which  is  here  attributed  to  a  pound.  His  calculations  of  the  motions 
of  fluids,  in  some  very  intricate  cases,  are  very  ingenious  and  satisfactory, 
and  they  are  in  general  sufficiently  confirmed  by  well  imagined  experiments. 
He  examines  the  force  of  the  wind  acting  on  the  sails  of  a  windmill,  but  by 
another  mistake  in  calculation,  which  Maclaurin  has  detected,*  of  two 
angles  which  answer  the  conditions  of  the  determination,  he  has  taken  the 
wrong  one,  and  assigned  that  position  of  the  sail  as  the  most  effectual,  which 
produces  absolutely  no  effect  at  all. 

*  Fluxions,  2  vols.  4to,  Edin.  1742,  art.  914. 


ON  THE  HISTORY  OF  HYDRAULICS,  &c.  281 

It  may  be  objected  to  Bernoulli's  calculations,  that  some  of  the  circum- 
stances which  are  necessarily  neglected  in  them,  produce  a  very  material 
effect  in  the  results  of  all  experiments ;  but  it  must  be  allowed  that  the 
corrections  required  on  account  of  this  unavoidable  omission,  may  easily 
be  deduced  from  simple  experiments,  and  then  applied  to  the  most  compli- 
cated cases.  It  is,  however,  a  more  material  objection,  that  the  fundamental 
law  of  the  preservation  of  ascending  force  can  only  be  adopted  with  certain 
limitations  ;  thus,  when  a  small  stream  passes  through  a  large  reservoir,  Ber- 
noulli is  obliged  to  suppose  the  whole  of  its  force  consumed  by  the  resistance 
which  it  meets.  The  immediate  mode,  in  which  the  accelerating  forces  must 
be  supposed  to  act,  remains  also  wholly  undetermined  ;  and  it  was  princi- 
pally for  this  reason,  that  John  Bernoulli  attempted  to  substitute,  for  his 
son's  calculations,  a  method  of  deducing  the  motions  of  fluids  more  imme- 
diately from  the  gravitation  of  their  different  parts.  The  peculiarity  of 
John  Bernoulli's  mode  of  investigation  consists  in  his  imagining  the  weight 
of  each  individual  particle  to  be  transferred  to  the  surface  of  the  fluid, 
causing  there  a  pressure  in  the  direction  of  gravity;  and  he  examines 
the  manner  in  which  this  force  must  operate,  in  order  to  produce  every 
acceleration  which  is  required  for  the  motion  of  fluids  in  vessels  of  all 
imaginable  forms. 

Maclaurm,  in  his  treatise  of  fluxions,  investigated  several  of  the  proper- 
ties of  fluids  in  his  usual  concise  and  elegant  manner.  His  remarks  on  the 
positions  of  the  sails  of  windmills  and  of  ships  are  peciiliarly  interesting  : 
he  added  much  to  what  had  been  done  respecting  the  effects  of  the  wind, 
and  showed  the  possibility  of  arranging  the  sails  of  a  ship  in  such  a  manner 
as  to  make  her  advance  with  a  greater  velocity  than  that  of  the  wind  itself. 
At  that  time,  however,  the  science  of  hydraulics  had  been  too  little  assisted 
by  experiments  to  be  capable  of  affording  determinations  of  all  questions 
which  are  of  very  frequent  occurrence  in  practice.  An  application  was 
made  to  Maclaurin,  and  at  the  same  time  to  Desaguliers,*  a  man  of  con- 
siderable eminence  in  the  mechanical  sciences,  respecting  the  quantity  of 
water  that  might  be  brought,  by  a  train  of  pipes  of  certain  dimensions,  to 
the  city  of  Edinburgh.  The  project  was  executed  with  a  confidence  founded 
on  their  opinions,  but  the  quantity  actually  obtained  was  only  about  one 
sixth  of  Desaguliers's  calculation,  and  one  eleventh  of  Maclaurin' s.  At  a 
still  later  period,  the  French  Academicians  were  consulted  respecting  a 
great  undertaking  of  a  similar  nature ;  and  their  report  was  such  as  to 
dissuade  the  projectors  from  making  the  attempt,  which  was  consequently 
at  the  point  of  being  abandoned,  till  a  celebrated  practical  architect  insisted, 
from  a  rough  estimation,  deduced  from  his  general  experience,  that  more 
than  double  the  quantity  assigned  by  the  Academicians  might  be  obtained  ; 
and  the  event  justified  his  assertion. 

The  experiments  and  calculations  of  Robins,  respecting  the  resistance  of 
the  air  and  the  operation  of  gunpowder,  deserve  to  be  mentioned  with 
commendation  on  account  of  their  practical  utility ;  but  he  appears  to  have 
.been  less  successful  in  his  theoretical  investigations  than  Daniel  Bernoulli 
had  been  a  few  years  before. 

*  Robison's  Mech.  Phil.     See  Desaguliers's  Course  of  Exp.  Ph.  vol.  ii.  p.  126. 


282  LECTURE   XXX. 

Dalembert  attempted,  in  his  treatise  on  the  motions  of  fluids,  which  was 
published  in  1744,  to  substitute  for  the  suppositions  of  John  Bernoulli,  a 
more  general  law,  relating  to  all  changes  produced  in  the  motions  of  a 
system  of  bodies  by  their  mutual  actions  on  each  other ;  but  his  calculations 
are  more  intricate  and  less  easily  understood,  than  some  others  which  are 
capable  of  an  application  equally  extensive.  The  late  Professor  Kaestner 
of  Gottingen  has  defended  Bernoulli  against  Dalembert's  objections  with 
some  success,  and  has  in  many  instances  facilitated  and  extended  Ber- 
noulli's theory;  but  there  is  often  a  singular  mixture  of  acuteness  and 
prolixity  in  this  author's  works.*  By  the  side  of  an  intricate  and  difficult 
fluxional  calculation,  he  inserts  a  long  string  of  logarithms  for  performing 
a  simple  multiplication ;  and  in  a  work  which  comprehends  the  whole 
range  of  the  mathematical  sciences,  he  does  not  venture  to  determine  the 
square  root  of  10  without  quoting  an  authority. 

About  the  same  time,  the  profound  Leonard  Euler  applied  himself,  with 
some  success,  to  the  examination  of  the  motions  of  fluids,  particularly  as 
they  are  connected  with  the  subjects  of  seamanship  and  naval  architecture  ; 
but  the  investigations  of  Euler  are  in  general  more  remarkable  for  mathe- 
matical address  than  for  philosophical  accuracy  and  practical  application  ; 
although  his  calculation  of  the  resistance  of  the  air  to  the  motions  of  pro- 
jectiles may  be  employed  with  considerable  advantage  by  the  gunner. 

The  beginning  of  the  modern  experimental  improvements  in  hydraulics 
may  perhaps  be  dated  from  the  investigations  of  Smeaton  respecting  the 
effects  of  wind  and  water,  which  were  published  in  the  Philosophical 
Transactions  for  1759.  His  observations  are  of  material  importance 
as  far  as  they  are  capable  of  immediate  application  to  practice,  but  he  has 
done  little  to  illustrate  their  connexion  with  the  general  principles  of  me- 
chanics. It  was  Mr.  Borda  that  first  derived  from  a  just  theory,  about  10 
years  after,  the  same  results,  respecting  the  effects  of  undershot  water 
wheels,  as  Smeaton  had  obtained  from  his  experiments.  Before  this  time, 
the  best  essay  on  the  subject  of  water  wheels  was  that  of  Elvius,  published 
in  1742  ;  his  calculations  are  accurate  and  extensive  ;  but  they  are  founded, 
in  great  measure,  on  the  imperfect  suppositions  respecting  the  impulse  of  a 
stream  of  water,  which  were  then  generally  adopted. 

Our  countryman  Mr.  Watt  obtained,  in  1769,  a  patent  for  his  improve- 
ments of  the  steam  engine,  which  includes  almost  every  essential  change 
that  has  been  made  since  the  time  of  Beighton.  On  a  subject  so  important, 
it  cannot  be  superfluous  to  insert  the  words  of  the  inventor,  whose  admirable 
application  of  the  sciences  to  practical  purposes,  most  justly  entitles  him  to 
a  rank  among  philosophical  mechanics,  not  inferior  to  that  of  Ctesibius  and 
Dr.  Hooke, 

"  My  method  of  lessening  the  consumption  of  steam,  and  consequently 
fuel,  in  fire  engines,"  says  Mr.  Watt,  in  his  specification  of  his  patent, 
"consists  of  the  following  principles.  First,  that  vessel  in  which  the 
powers  of  steam  are  to  be  employed  to  work  the  engine,  which  is  called 
the  cylinder  in  common  fire  engines,  and  which  I  call  the  steam  vessel, 
must,  during  the  whole  time  the  engine  is  at  work,  be  kept  as  hot  as  the 
*  Dissertationes  Math,  et  Phys.  4to,  Altenb.  1776. 


ON  THE  HISTORY  OF  HYDRAULICS,  &c.  283 

steam  that  enters  it ;  first,  by  inclosing  it  in  a  case  of  wood,  or  any  other 
•materials  that  transmit  heat  slowly  ;  secondly,  by  surrounding  it  with 
steam  or  other  heated  bodies  ;  and  thirdly,  by  suffering  neither  water,  nor 
any  other  substance  colder  than  the  steam,  to  enter  or  touch  it  during  that 
time.  Secondly,  in  engines  that  are  to  be  worked  wholly  or  partially  by 
condensation  of  steam,  the  steam  is  to  be  condensed  in  vessels  distinct  from 
the  steam  vessels,  or  cylinders,  although  occasionally  communicating  with 
them  ;  these  vessels  I  call  condensers  ;  and,  whilst  the  engines  are  working, 
these  condensers  ought  at  least  to  be  kept  as  cold  as  the  air  in  the  neigh- 
bourhood of  the  engines,  by  application  of  water,  or  other  cold  bodies. 
Thirdly,  whatever  air  or  other  elastic  vapour  is  not  condensed  by  the  cold 
of  the  condenser,  and  may  impede  the  working  of  the  engine,  is  to  be  drawn 
out  of  the  steam  vessels,  or  condensers,  by  means  of  pumps,  wrought  by  the 
engines  themselves,  or  otherwise.  Fourthly,  I  intend,  in  many  cases,  to 
employ  the  expansive  force  of  steam  to  press  on  the  pistons,  or  whatever 
may  be  used  instead  of  them,  in  the  same  manner  as  the  pressure  of  the 
atmosphere  is  now  employed  in  common  fire  engines  :  in  cases  where  cold 
water  cannot  be  had  in  plenty,  the  engines  may  be  wrought  by  this  force 
of  steam  only,  by  discharging  the  steam  into  the  open  air  after  it  has  done 
its  office.  Fifthly,  where  motions  round  an  axis  are  required,  I  make  the 
steam  vessels  in  form  of  hollow  rings  or  circular  channels,  with  proper 
inlets  and  outlets  for  the  steam,  mounted  on  horizontal  axles,  like  the 
wheels  of  a  water  mill ;  within  them  are  placed  a  number  of  valves,  that 
suffer  any  body  to  go  round  the  channel  in  one  direction  only ;  in  these 
steam  vessels  are  placed  weights,  so  fitted  to  them  as  entirely  to  fill  up  a 
part  or  portion  of  their  channels,  yet  capable  of  moving  freely  in  them  by 
the  means  herein  after  mentioned  or  specified.  When  the  steam  is  admitted 
in  these  engines  between  the  weights  and  the  valves,  it  acts  equally  on  both, 
so  as  to  raise  the  weight  to  one  side  of  the  wheel,  and,  by  the  reaction  of 
the  valves,  successively,  to  give  a  circular  motion  to  the  wheel,  the  valves 
opening  in  the  direction  in  which  the  weights  are  pressed,  but  not  in  the 
contrary  ;  as  the  steam  vessel  moves  round,  it  is  supplied  with  steam  from 
the  boiler,  and  that  which  has  performed  its  office  may  either  be  discharged 
by  means  of  condensers,  or  into  the  open  air.  Sixthly,  I  intend,  in  some 
cases,  to  apply  a  degree  of  cold,  not  capable  of  reducing  the  steam  to  water, 
but  of  contracting  it  considerably,  so  that  the  engines  may  be  worked  by 
the  alternate  expansion  and  contraction  of  the  steam.  Lastly,  instead  of 
using  water  to  render  the  piston  or  other  parts  of  the  engines  air  and  steam 
tight,  I  employ  oils,  wax,  resinous  bodies,  fat  of  animals,  quicksilver,  and 
other  metals,  in  their  fluid  state." 

It  is  probable  that  the  rotatory  engines  described  by  Mr.  Watt,  although 
they  appear  to  produce  some  advantage  in  theory,  will  never  be  generally 
introduced,  on  account  of  the  difficulty  of  constructing  steam  vessels  so 
large,  and  of  so  complicated  a  form,  as  would  be  necessary,  in  order  to  give 
full  effect  to  the  machine.  The  term  of  this  patent  was  prolonged  by  act 
o£  parliament  until  the  year  1799  ;  but  although  the  legal  privilege  of  the 
original  manufacturers  is  expired,  yet  the  superiority  of  their  workmanship 
still  gives  their  engines  a  decided  preference. 


284  LECTURE  XXX. 

Much  of  the  labour  of  the  later  writers  on  hydraulics  has  been  em- 
ployed on  the  determination  of  the  resistance  of  fluids  to  bodies  of  different • 
forms  which  move  through  them  ;  a  subject  which  derives  great  importance 
from  its  immediate  application  to  the  manoeuvres  of  ships.  The  most 
extensive  experiments  on  these  subjects  were  made  by  Bossut  and  some 
other  members  of  the  Academy  of  Sciences.  About  the  same  time  Don 
George  Juan,  a  gentleman  who  had  enjoyed  the  best  possible  opportunity 
for  actual  observation  and  practical  study  in  serving  with  Ulloa,  published 
at  Madrid  his  Examen  Maritimo,  which  appears  to  be  the  most  ingenious 
and  useful  treatise  on  the  theory  and  practice  of  seamanship  that  ha«  yet 
appeared.  But  unfortunately  his  deductions,  however  refined  and  diversi- 
fied, are  principally  founded  on  a  mistaken  theory  respecting  the  effects  of 
hydraulic  pressure  ;  since  he  tacitly  assumes,  in  his  fundamental  pro- 
position on  the  subject,  that  a  double  force,  acting  in  a  given  small  space, 
will  produce  a  double  velocity  ;  while  it  is  well  known  that  in  such  cir- 
cumstances a  quadruple  force  would  be  required.  Hence  he  derives  some 
conclusions  which  indicate  that  the  resistance  must  vary  very  materially 
at  different  depths  below  the  surface  of  the  water,  and  alleges  in  support 
of  the  assertion  a  few  imperfect  experiments  of  Mariotte  and  of  his  own, 
in  which  some  accidental  circumstances  not  noticed  may  easily  have  caused 
great  irregularities.  Mr.  Prony,  in  his  Architecture  Hydraulique,  appears 
to  have  followed  Juan ;  and  Professor  Robison  very  justly  observes,  in 
speaking  of  this  work,  that  if  the  pressure  of  the  water  alters  the  magni- 
tude of  the  resistance  at  different  depths,  that  of  the  atmosphere  ought  by 
no  means  to  be  omitted  in  the  calculation.  But  if  a  more  correct  mathe- 
matician and  mechanic  would  take  the  pains  to  model  Juan's  book  anew, 
to  correct  his  errors,  and  to  adapt  his  modes  of  calculation  to  the  laws  of 
resistance  previously  deduced  from  accurate  experiments  rather  than  from 
theory,  there  is  no  doubt  but  that  the  work  thus  modified  might  essentially 
improve  the  science  of  seamanship.  He  alleges  indeed  that  the  results  of  his 
calculations  are  in  almost  every  instance  rigidly  conformable  to  observa- 
tion and  experience,  but  it  is  probable  that  where  such  a  coincidence  really 
exists,  it  must  be  owing  to  some  combination  of  errors  compensating  each 
other ;  and  it  is  indeed  very  possible  that  his  calculations,  with  all  their 
errors,  may  approach  nearer  to  the  truth  than  the  imperfect  approximations 
which  had  been  before  employed.  Juan  has  generally  made  use  of  the 
English  weights  and  measures,  on  account  of  their  convenience  in  compu- 
tations respecting  the  descent  of  falling  bodies  and  the  impulse  of  water. 

The  works  of  Chapman  and  of  Romme,  upon  various  departments  of 
seamanship,  possess  also  considerable  merit.  These  authors  appear  to 
have  avoided  the  errors  of  Juan,  but  without  entering  so  minutely  into  the 
detail  of  nautical  operations  as  he  has  done. 

The  accurate  experiments  of  Dr.  Hutton  and  of  Count  Rumford  on  the 
force  of  fired  gunpowder  and  the  resistance  of  the  air,  deserve  to  be  men- 
tioned as  affording  valuable  materials  to  the  speculative  investigator,  and 
useful  information  to  the  practical  gunner.  Robins  had  very  erroneously 
supposed  that  the  whole  of  the  effects  of  gunpowder  might  be  derived 
from  the  expansive  force  of  fluids  permanently  elastic ;  but  Vandelli  soon 


ON  THE  HISTORY  OF  HYDRAULICS,  &c.  285 

after  maintained  a  contrary  opinion  in  the  commentaries  of  Bologna,*  and 
Count  Rumford  has  very  satisfactorily  shown  the  insufficiency  of  the 
agents  considered  by  Robins,  although  he  has  been  unsuccessful  in  at- 
tempting to  deduce  the  whole  force  from  the  elasticity  of  aqueous  vapour 
alone. 

The  theory  of  practical  hydraulics,  as  affected  by  friction,  may  be  con- 
sidered as  having  been  begun  and  completed  by  the  highly  meritorious 
labours  of  the  Chevalier  du  Buat.  He  had  some  assistance  in  expressing 
the  results  of  his  experiments  by  means  of  general  rules  or  formulae,  and 
these,  although  they  agree  sufficiently  well  with  the  experiments,  have  not 
always  been  reduced  to  the  simplest  and  most  convenient  forms ;  nor  have 
they  been  much  improved  either  by  Langsdorf  or  Eytelwein  in  Germany, 
or  by  Robison  in  this  country,  who  have  gone  over  nearly  the  same  ground 
with  each  other,  and  have  shown  the  way  in  which  the  results  of  Buat's 
investigations  may  be  applied  to  a  variety  ofoases,  which  occur  in  hydrau- 
lic architecture. 

One  of  the  latest  inventions  which  require  to  be  mentioned  in  speaking 
of  the  history  of  pneumatics,  is  that  of  the  aerostatic  globe  or  air  balloon. 
The  suggestions  of  Lohmeier,t  of  Albertus,  and  of  Wilkins,^  respecting 
the  various  modes  of  passing  through  the  air,  had  long  remained  disre- 
garded as  idle  speculations  ;  and  Rosnier,  who,  in  the  17th  century, 
descended  obliquely  over  some  houses,  by  means  of  wings,  was  wholly 
unable  to  employ  them  in  ascending.  §  Dr.  Black  had  exhibited  in  his 
lectures  a  bladder  filled  with  hydrogen  gas,  and  floating  in  the  air  by 
means  of  its  smaller  specific  gravity,  many  years  before  Montgolfier  con- 
ceived the  idea  of  applying  a  similar  machine  to  the  elevation  of  human 
beings  into  the  aerial  regions.  It  was  in  1783  that  this  project  was  first 
executed,  and  persons  of  a  warm  imagination  were  disposed  to  believe  that 
the  discovery  would  be  of  great  importance  to  the  convenience  of  mankind.  || 
But  if  we  coolly  consider  the  magnitude  of  the  force  with  which  the  wind 
unavoidably  impels  a  surface  so  large  as  that  of  a  balloon,  we  shall  be  con- 
vinced of  the  absolute  impossibility  of  counteracting  it,  in  such  a  manner, 
as  to  direct  the  balloon  in  any  course,  materially  different  from  that  of  the 
wind  which  happens  to  blow.  With  this  limitation,  the  invention  may 
still  in  some  cases  be  capable  of  utility,  wherever  we  are  only  desirous 
of  ascending  to  a  great  height,  without  regarding  the  place  in  which  we 
are  to  descend  :  or  where  we  wish  to  attain  only  a  height  so  moderate  that 
the  machine  may  be  kept  by  ropes  in  the  situation  which  is  desired.  In 
France  the  balloon  has  lately  been  employed  with  considerable  success  as 
a  meteorological  observatory;  Mr.  Biot  and  Mr.  Gay  Lussac  having 
ascended  to  a  height  of  above  four  miles,  for  the  laudable  purpose  of  ascer- 
taining some  facts  relating  to  the  constitution  of  the  atmosphere,  and  to 
the  magnetic  properties  of  the  earth. 

*  iii.  92  ;  iv.  106.  f  De  Artificio  Navigandi  per  Aerem,  1676. 

J  Mathematical  Magic,  1680.         §  Hooke,  Ph.  Coll.  No.  1,  p.  15. 
'||  Montgolfier,  Discours  sur  TAerostate,  Paris,  1784.     P.  de  Rozier,  Premiere 
Experience  de  la  Montgolfiere,  4to,  Paris,  1784. 


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LECTURE  XXX. 


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287 


LECTURE   XXXI, 


ON  THE  PROPAGATION  OF  SOUND. 

THE  theory  of  sound,  which  constitutes  the  science  of  acustics,  is  on 
many  accounts  deserving  of  particular  attention,  for  it  not  only  involves 
many  interesting  properties  of  the  motions  of  elastic  substances,  but  it  also 
affords  us  considerable  assistance  in  our  physiological  inquiries  respecting 
the  nature  and  operation  of  the  senses.  The  subject  has  usually  been  con- 
sidered as  exceedingly  abstruse  and  intricate,  but  the  difficulty  has  in  some 
measure  originated  from  the  errors  which  were  committed  in  the  first 
inquiries  respecting  it ;  and  many  of  the  phenomena  belonging  to  it  are  so 
remarkable  and  so  amusing,  as  amply  to  repay  the  labour  of  examining 
them  by  the  entertainment  that  they  afford.  We  shall  consider  first  the 
nature  and  propagation  of  sound  in  general,  secondly,  the  origin  of  par- 
ticular sounds,  and  the  effects  of  single  sounds  ;  thirdly,  the  consequences 
of  the  combinations  of  sounds  variously  related,  constituting  the  doctrine 
of  harmonics,  and  fourthly,  the  construction  of  musical  instruments,  and 
the  history  of  the  science  of  acustics. 

Sound  is  a  motion  capable  of  affecting  the  ear  with  the  sensation  peculiar 
to  the  organ.  It  is  not  simply  a  vibration  or  undulation  of  the  air,  as  it  is 
sometimes  called  ;  for  there  are  many  sounds  in  which  the  air  is  not  con- 
cerned, as  when  a  tuning  fork  or  any  other  sounding  body  is  held  by  the 
teeth :  nor  is  sound  always  a  vibration  or  alternation  of  any  kind ;  for 
every  noise  is  a  sound,  and  a  noise,  as  distinguished  from  a  continued 
sound,  consists  of  a  single  impulse  in  one  direction  only,  sometimes  without 
any  alternation  ;  while  a  continued  sound  is  a  succession  of  such  impulses, 
which,  in  the  organ  of  hearing  at  least,  cannot  but  be  alternate.  If  these 
successive  impulses  form  a  connected  series,  following  each  other  too 
rapidly  to  be  separately  distinguished,  they  constitute  a  continued  sound, 
like  that  of  the  voice  in  speaking  ;  and  if  they  are  equal  among  themselves 
in  duration,  they  produce  a  musical  or  equable  sound,  as  that  of  a  vi- 
brating cord  or  string,  or  of  the  voice  in  singing.  Thus,  a  quill  striking 
against  a  piece  of  wood  causes  a  noise,  but,  striking  against  the  teeth  of  a 
wheel  or  of  a  comb,  a  continued  sound  ;  and  if  the  teeth  of  the  wheel  are 
at  equal  distances,  and  the  velocity  of  the  motion  is  constant,  a  musical 
note. 

Sounds  of  all  kinds  are  most  usually  conveyed  through  the  medium  of 
the  air ;  and  the  necessity  of  the  presence  of  this  or  of  some  other  material 
substance  for  its  transmission  is  easily  shown  by  means  of  the  air  pump  ;* 
for  the  sound  of  a  bell  struck  in  an  exhausted  receiver  is  scarcely  per- 
ceptible. The  experiment  is  most  conveniently  performed  in  a  moveable 
receiver  or  transferrer,  which  may  be  shaken  at  pleasure,  the  frame  which 

*  Hauksbee,  Ph.  Tr.  1705,  xxiv.  1902,  and  xxvi.  367.  Biot,  Mem.  d'Arcueil, 
ii.  97.  See  Tr.  R.  S.  E.  v.  34.  Saussure,  Voyage  dans  les  Alpes,  vii.  377. 


288  LECTURE   XXXI. 

suspends  the  bell  being  supported  by  some  very  soft  substance,  such  as 
cork  or  wool.  As  the  air  is  gradually  admitted,  the  sound  becomes  stronger 
and  stronger,  although  it  is  still  much  weakened  by  the  interposition  of 
the  glass :  not  that  glass  is  in  itself  a  bad  conductor  of  sound,  but  the 
change  of  the  medium  of  communication  from  air  to  glass,  and  again  from 
glass  to  air,  occasions  a  great  diminution  of  its  intensity.  It  is  perhaps  on 
account  of  the  apparent  facility  with  which  sound  is  transmitted  by  air, 
that  the  doctrine  of  acustics  has  been  usually  considered  as  immediately 
dependent  on  pneumatics,  although  it  belongs  as  much  to  the  theory  of  the 
mechanics  of  solid  bodies  as  to  that  of  hydrodynamics.  • 

A  certain  time  is  always  required  for  the  transmission  of  an  impulse 
through  a  material  substance,  even  through  such  substances  as  appear  to 
be  the  hardest  and  the  least  compressible.  It  is  demonstrable  that  all 
minute  impulses  are  conveyed  through  any  homogeneous  elastic  medium, 
whether  solid  or  fluid,  with  » uniform  velocity,  which  is  always  equal  to 
that  which  a  heavy  body  would  acquire  by  falling  through  half  the  height 
of  the  modulus  of  elasticity,  that  is,  in  the  case  of  the  air,  half  the  height 
of  the  atmosphere,  supposed  to  be  of  equal  density  ;  so  that  the  velocity  of 
sound  passing  through  an  atmosphere  of  a  uniform  elastic  fluid  must  be 
the  same  with  that  of  a  wave  moving  on  its  surface.  In  order  to  form  a 
distinct  idea  of  the  manner  in  which  sound  is  propagated  through  an 
elastic  substance,  we  must  first  consider  the  motion  of  a  single  particle, 
which,  in  the  case  of  a  noise,  is  pushed  forwards,  and  then  either  remains 
stationary,  or  returns  back  to  its  original  situation ;  but  in  the  case  of  a 
musical  sound,  is  continually  moved  backwards  and  forwards,  with  a 
velocity  always  varying,  and  varying  by  different  degrees,  according 
to  the  nature  or  quality  of  the  tone  ;  for  instance,  differently  in  the  notes 
of  a  bell  and  of  a  trumpet.  We  may  first  suppose  for  the  sake  of  sim- 
plicity, a  single  series  of  particles  to  be  placed  only  in  the  same  line  with 
the  direction  of  the  motion.  It  is  obvious  that  if  these  particles  were  ab- 
solutely incompressible,  or  infinitely  elastic,  and  were  also  retained  in 
contact  with  each  other  by  an  infinite  force  of  cohesion  or  of  compression, 
the  whole  series  must  move  precisely  at  the  same  time,  as  well  as  in  the 
same  manner.  But  in  a  substance  which  is  both  compressible  and 
extensible  or  expansible,  the  motion  must  occupy  a  certain  time  in  being 
propagated  to  the  successive  particles  on  either  side,  by  means  of  the 
impulse  of  the  first  particle  on  those  which  are  before  it,  and  by  means  of 
the  diminution  of  its  pressure  on  those  which  are  behind ;  so  that  when  the 
sound  consists  of  a  series  of  alternations,  the  motion  of  some  of  the  par- 
ticles will  be  always  in  a  less  advanced  state  than  that  of  others  nearer  to 
its  source,  while  at  a  greater  distance  forwards,  the  particles  will  be  in 
the  opposite  stage  of  the  undulation,  and  still  further  on,  they  will  again 
be  moving  in  the  same  manner  with  the  first  particle,  in  consequence  of 
the  effect  of  a  former  vibration. 

The  situation  of  a  particle  at  any  time  may  be  represented  by  supposing 
it  to  mark  its  path  on  a  surface  sliding  uniformly  along  in  a  transverse  dJ- 
rection.  Thus,  if  we  fix  a  small  pencil  in  a  vibrating  rod,  and  draw  a 
sheet  of  paper  along,  against  the  point  of  the  pencil,  an  undulated  line  will 


ON  THE  PROPAGATION  OF  SOUND.  289 

be  marked  on  the  paper,  and  will  correctly  represent  the  progress  of  the 
vibration.  Whatever  the  nature  of  the  sound  transmitted  through  any 
medium  may  be,  it  may  be  shown  that  the  path  thus  described  will  also 
indicate  the  situation  of  the  different  particles  at  any  one  time.  The 
simplest  case  of  the  motion  of  the  particles  is  that  in  which  they  observe 
the  same  law  with  the  vibration  of  a  pendulum,  which  is  always  found  op- 
posite to  a  point  supposed  to  move  uniformly  in  a  circle  :  in  this  case  the 
path  described  will  be  the  figure  denominated  a  harmonic  curve  ;  and  it  may 
be  demonstrated  that  the  force  impelling  any  particle  backwards  or  for- 
warfls,  will  always  be  represented  by  the  distance  of  the  particle  before  or 
behind  its  natural  place  ;  the  greatest  condensation  and  the  greatest  direct 
velocity,  as  well  as  the  greatest  rarefaction  and  retrograde  velocity,  happen- 
ing at  the  instant  when  it  passes  through  its  natural  place. 

We  are  ready  to  imagine  that  very  hard  bodies  transmit  motion  instan- 
taneously, because  we  have  no  easy  means  of  measuring  the  interval  of 
time  that  elapses  between  the  action  of  pushing  the  end  of  a  rod,  and  the 
protrusion  of  an  obstacle  at  the  other  end,  or  between  the  instant  of  pulling 
a  bell  rope,  and  that  of  the  ringing  of  the  bell.  But  it  is  demonstrable  that 
in  order  to  transmit  an  impulse  in  a  time  infinitely  small,  the  hardness  of 
the  substance  must  be  infinitely  great,  and  it  must  be  absolutely  incom- 
pressible and  inextensible  by  any  force,  which  is  a  property  not  discover- 
able in  any  natural  bodies :  the  hardest  steel  and  the  most  brittle  glass 
being  very  susceptible  both  of  extension  and  compression. 

The  least  elastic  substance  that  has  been  examined,  is  perhaps  carbonic 
acid  gas,*  or  fixed  air,  which  is  considerably  denser  than  atmospheric  air 
exposed  to  an  equal  degree  of  pressure.  The  height  of  the  atmosphere, 
supposed  to  be  homogeneous,  is  in  ordinary  circumstances,  and  at  the  sea 
side,  about  28,000  feet,  and  in  falling  through  half  this  height  a  heavy 
body  would  acquire  a  velocity  of  946  feet  in  a  second.  But  from  a  com- 
parison of  the  accurate  experiments  of  Derham,t  made  in  the  day  time, 
with  those  of  the  French  Academicians,^:  made  chiefly  at  night,  it  appears 
that  the  true  velocity  of  sound  is  about  1130  feet  in  a  second,  which  agrees 
very  nearly  with  some  observations  made  with  great  care  by  Professor 
Pictet.  This  difference  between  calculation  and  experiment  has  long 
occupied  the  attention  of  natural  philosophers,  but  the  difficulty  appears 
to  have  been  in  great  measure  removed  by  the  happy  suggestion  of 
Laplace,§  who  has  attributed  the  effect  to  the  elevation  of  temperature, 
which  is  always  found  to  accompany  the  action  of  condensation,  and  to 
the  depression  produced  by  rarefaction.  It  is  true  that  a  greater  change 
of  temperature  would  be  required  than  Mr.  Dalton's  experiments  on  the 
compression  of  air  appear  to  indicate  ;  but  those  experiments  do  not  per- 

*  It  is  sulphurous  acid,  in  which  the  velocity  is  229 -2  ft.  Rees,  Dissertatio  de 
Celeritate  Soni,  4to.  Trajecti  ad  Rhenum,  1819.  Journal  de  Physique,  1821,  p.  40. 

t  Ph.Tr.  1708,  p.  2,  concludes  that  the  velocity  is  1142ft.  per  second. 

J  Hist.  etMem.  del'Acad.  1738-9.  Here  the  effect  of  the  wind  was  first  taken 
into  account:  vel.  =  1106ft.  at  43°  of  temp.  The  actual  velocity  at  the  freezing 
t&np.  is  about  1090  ft.  per  second.  The  increase  of  velocity  is  1  '136  ft.  for  every 
degree  of  temperature,  on  Fahrenheit's  scale. 

§  See  Poisson,  Journal  de  1'Ecole  Poly  technique,  cah.  xiv.  Biot,  Journal  de  Phy- 
sique, Iv.  173.  Mem.  d'Arcueil,  ii.  94. 


290  LECTURE  XXXI. 

fectly  agree  among  themselves  ;  and  the  observation  which  has  been  made 
in  France,  that  a  heat,  sufficient  to  set  tow  on  fire,  may  be  produced/  by 
the  operation  of  a  condensing  syringe,  seems  to  show  that  Mr.  Dalton's 
results  are  somewhat  below  the  truth.  In  this  manner  the  theory  may 
be  completely  reconciled  with  experiments  ;*  we  may  estimate  the  modulus 
of  the  air's  effective  elasticity,  which  is  the  measure  of  its  immediate 
force,  from  the  velocity  which  is  thus  observed,  and  its  height  will  appear 
to  be  39,800  feet,  instead  of  27,800,  which  is  the  supposed  height  of  the 
atmosphere.  This  velocity  remains  unchanged  by  any  alternation  of  pres- 
sure indicated  by  the  barometer,  but  it  may  be  affected  by  a  change  of 
temperature.  For  when  an  elastic  fluid  is  compressed,  its  elasticity  is 
increased  in  the  same  ratio  as  its  density  ;  and  the  height  of  a  homo- 
geneous atmosphere  equivalent  to  the  pressure,  remains  the  same,  conse- 
quently the  velocity  calculated  from  that  height  remains  unaltered  ;  but 
the  identity  of  the  acceleration,  from  the  effect  of  heat  which  has  been 
mentioned,  can  only  be  inferred  from  observation  :  this  identity  may,  how- 
ever, be  satisfactorily  shown,  by  means  of  experiments  on  the  sounds  of 
organ  pipes,  which  are  intimately  connected  with  the  velocity  of  the 
transmission  of  sound  through  the  air,  and  which  are  found  to  remain 
precisely  the  same,  however  the  air  may  be  rarefied  or  condensed.  The 
Academicians  del  Cimento  inclosed  an  organ  pipe,  with  bellows  worked  by 
a  spring,  in  the  receiver  of  an  air  pump  and  of  a  condenser,  and  they 
found  that,  as  long  as  the  sound  was  audible,  its  pitch  remained  unchanged. 
Papint  screwed  a  whistle  on  the  orifice  which  admits  the  air  into  the 
receiver  of  the  air  pump,  and  I  have  fixed  an  organ  pipe  in  the  same 
manner  ;  and  the  result  agreed  with  the  experiment  of  the  academicians. 
But  if  the  density  of  the  air  is  changed,  while  its  elasticity  remains  unal- 
tered, which  happens  when  it  is  expanded  by  heat,  or  condensed  by  cold, 
the  height  of  the  column,  and  consequently  the  velocity,  will  also  be 
altered  ;  so  that  for  each  degree  of  Fahrenheit's  thermometer  the  velocity 
will  vary  about  one  part  in  a  thousand.  Bianconi  J  has  actually  observed 
this  difference  of  velocity  according  to  the  different  heights  of  the  thermo- 
meter, and  it  may  be  shown  less  directly  by  means  of  the  sounds  of  pipes  ; 
but  it  has  not  been  accurately  determined  whether  or  no  the  correction  on 
account  of  the  effect  of  compression  in  causing  heat,  remains  unaltered, 
although  Bianconi's  experiments  agree  very  well  with  the  supposition  that 
no  material  change  takes  place  in  this  respect.  The  velocity  of  sound 
must  also  be  in  some  measure  influenced  by  the  quantity  of  moisture  con- 
tained in  the  atmosphere  :  it  must  be  a  little  diminished  by  cold  fogs, 
which  add  to  the  density,  without  augmenting  the  elasticity,  and  increased 
by  warm  vapours,  which  tend  to  make  the  air  lighter ;  and  these  two 
opposite  states  are  probably  often  produced  in  succession  in  wind  instru- 
ments blown  by  the  mouth,  the  air  within  them  being  at  first  cold  and 
damp,  and  afterwards  warm  and  moist. 

In  pure  hydrogen  gas,  the  velocity  of  sound  ought,  from  calculation,  to 
be  more  than  three  times  as  great  as  in  common  air,  but  the  difference  does 

*  Clement  and  Desormes,  Journal  de  Physique,  1819,  p.  34. 
t  Birch,  iv.  379.  J  Comm.  Bonon.  ii.  I.  365. 


ON  THE  PROPAGATION  OF  SOUND.  291 

not  appear  to  have  been  so  great  in  any  experiment  hitherto  made  on  the 
soiftids  of  pipes  in  gases  of  different  kinds.  For  such  experiments,  the 
comparative  specific  gravity  of  the  gas  may  be  most  conveniently  ascer- 
tained by  Mr.  Leslie's  method  of  observing  the  time  employed  in  emptying  a 
vessel  through  a  small  orifice,  by  means  of  the  pressure  of  an  equal  column 
of  water ;  according  to  the  simple  theory,  the  velocities  of  the  gas  thus 
discharged  ought  to  be  in  the  same  proportion  as  the  respective  velocities 
with  which  sounds  would  be  transmitted  by  them  ;  and  if  any  variation 
from  this  proportion  were  discovered,  it  must  be  attributed  to  the  different 
degrees  of  heat  produced  by  condensation  in  the  different  fluids.  Steam, 
at  the  temperature  of  boiling  water,  is  only  one  third  as  heavy  as  common 
air  ;  consequently  the  velocity  of  sound  in  steam  must  be  nearly  three 
fourths  greater  than  in  air. 

It  does  not*  appear  that  any  direct  experiments  have  been  made  on  the 
velocity  with  which  an  impulse  is  transmitted  through  a  liquid,  although 
it  is  well  known  that  liquids  are  capable  of  conveying  sound  without  diffi- 
culty ;  Professor  Robison  informs  us,  for  example,  that  he  heard  the  sound 
of  a  bell  transmitted  by  water  at  the  distance  of  1200  feet.  It  is,  however, 
easy  to  calculate  the  velocity  with  which  sound  must  be  propagated  in  any 
liquid  of  which  the  compressibility  has  been  measured.  Mr.  Canton  has 
ascertained  that  the  elasticity  of  water  is  about  22,000  times  as  great  as 
that  of  air  ;  t  it  is,  therefore,  measured  by  the  height  of  a  column  which  is 
in  the  same  proportion  to  34  feet,  that  is  750  thousand  feet,  and  the  velocity 
corresponding  to  half  this  height  is  4900  feet  in  a  second.  In  mercury, 
also,  it  appears  from  Mr.  Canton's  experiments,  J  that  the  velocity  must  be 
nearly  the  same  as  in  water,  in  spirit  of  wine  a  little  smaller.  These 
experiments  were  made  by  filling  the  bulb  of  a  thermometer  with  water, 
and  observing  the  effects  of  placing  it  in  an  exhausted  receiver,  and  in  con- 
densed air  ;  taking  care  to  avoid  changes  of  temperature,  and  other  sources 
of  error :  the  fluid  rose  in  the  tube  when  the  pressure  was  removed,  and 
subsided  when  it  was  increased.  A  slight  correction  is,  however,  required, 
on  account  of  the  expansion  and  contraction  of  the  glass,  which  must  have 
tended  to  make  the  elasticity  of  the  fluids  appear  somewhat  greater  than  it 
really  was. 

It  is  also  well  known  that  solid  bodies  in  general  are  good  conductors  of 
sound  :  thus  any  agitation  communicated  to  one  end  of  a  beam  is  readily 
conveyed  to  the  ear  applied  to  the  other  end  of  it.  The  motion  of  a  troop 

*  Since  the  above  was  written,  experiments  have  been  made  on  the  velocity  of 
sound  in  water,  by  M.  Beudant,  at  Marseilles,  and  MM.  Colladon  and  Sturm, (a)  in 
the  Lake  of  Geneva.  The  care  with  which  the  latter  series  of  experiments  were  con- 
ducted, and  the  distance  to  which  the  sounds  were  transmitted,  amounting  to  about 
four  leagues,  entitles  them  to  confidence.  The  sounds  were  made  by  bells  rung 
under  the  water  on  one  side  of  the  lake,  which  were  heard  on  the  other  side  by  the 
intervention  of  a  tube,  closed  at  one  end  and  open  at  the  other ;  the  closed  end  being 
immersed  in  the  water,  so  that  a  column  of  air  transmitted  the  sound  to  the  ear 
above  the  water.  By  a  great  number  of  experiments,  it  appears  that  the  velocity  is 
4708  feet  per  second,  in  water  of  the  temperature  46'6°  of  Fahrenheit. 

*t  21,740,  according  to  Canton,  Ph.  Tr.  1762,  lii.  640;   1764,  liv.  261. 

J  Ibid.  

(a)  Annales  de  Chimie,  vol.  xxxvi.     Comptes  Rendus,  xiii.  439. 
u2 


292  LECTURE  XXXI. 

of  cavalry  is  said  to  he  perceived  at  a  greater  distance  by  listening  with  the 
head  in  contact  with  the  ground,  than  by  attending  to  the  sound  conveyecl 
through  the  air  ;  and  we  may  frequently  observe  that  some  parts  of  the 
furniture  of  a  house  are  a  little  agitated  by  the  approach  of  a  wagon,  before 
we  hear  the  noise  which  it  immediately  occasions.  The  velocity  with 
which  impulses  are  transmitted  by  solids,  is  in  general  considerably  greater 
than  that  with  which  they  are  conveyed  by  the  air :  Mr.  Wunsch*  has 
ascertained  this  by  direct  observations  on  a  series  of  deal  rods  closely 
united  together,  which  appeared  to  transmit  a  sound  instantaneously,  while 
a  sensible  interval  was  required  for  its  passing  through  the  air :  I  have  also 
found  that  the  blow  of  a  hammer  on  a  wall,  at  the  upper  part  of  a  high 
house,  is  heard  as  if  double  by  a  person  standing  near  it  on  the  ground,  the 
first  sound  descending  through  the  wall,  the  second  through  the  air.  It 
appears  from  experiments  on  the  flexure  of  solid  bodies  of  all  kinds,  that 
their  elasticity,  compared  with  their  density,  is  much  greater  than  that  of 
the  air  :  thus,  the  height  of  the  modulus  of  elasticity  of  fir  wood,  is  found, 
by  means  of  such  experiments,  to  be  about  9,500,000  feet,  whence  the 
velocity  of  an  impulse  conveyed  through  it  must  be  17,400  feet,  or  more 
than  three  miles,  in  a  second.  It  is  obvious,  therefore,  that  in  all  common 
experiments  such  a  transmission  must  appear  perfectly  instantaneous. 
There  are  various  methods  of  ascertaining  this  velocity  from  the  sounds 
produced  under  different  circumstances  by  the  substances  to  be  examined, 
and  Professor  Chladnit  has  in  this  manner  compared  the  properties  of  a 
variety  of  natural  and  artificial  productions. 

We  have  hitherto  considered  the  propagation  of  sound  in  a  single  right 
line,  or  in  parallel  lines  only ;  but  it  usually  happens,  at  least  when  a  sound 
is  transmitted  through  a  fluid,  that  the  impulse  spreads  in  every  direction, 
so  as  to  occupy  at  any  one  time  nearly  the  whole  of  a  spherical  surface. 
But  it  is  impossible  that  the  whole  of  this  surface  should  be  affected  in  a 
similar  manner  by  any  sound,  originating  from  a  vibration  confined  to  a 
certain  direction,  since  the  particles  behind  the  sounding  body  must  be 
moving  towards  the  centre,  whenever  the  particles  before  it  are  retreating 
from  the  centre  ;  so  that  in  one  half  of  the  surface  the  motions  may  be 
called  retrograde  or  negative,  while  in  the  other  they  are  direct  or  positive, 
consequently  at  the  sides,  where  these  portions  join,  the  motions  can  be  nei- 
ther positive  nor  negative,  and  the  particles  must  remain  at  rest ;  the  mo- 
tions must  also  become  gradually  less  and  less  sensible  as  they  approach  to 
the  limit  between  the  two  hemispheres.  And  this  statement  may  be  con- 
firmed by  an  experiment  on  the  vibration  of  a  body  of  which  the  motion  is 
limited  to  a  certain  direction,  the  sound  being  scarcely  audible  when  the  ear 
is  in  a  direction  precisely  perpendicular  to  that  of  the  vibration. 

The  sound  thus  diverging  must  always  be  spread  through  a  part  of  a 
spherical  surface,  because  its  velocity  must  be  equal  in  every  direction,  so 
that  the  impulse  will  always  move  forwards  in  a  straight  line,  passing 
through  the  centre  of  the  sphere,  or  the  vibrating  body.  But  when  a  hemi- 

*  Berlin  Memoirs,  1788,  p.  87. 

f  Traite  d'Acoustique,  Paris,  1809,  p.  319.  See  Herschel's  remark  on  these 
results,  Encyc.  Met.  art.  Sound,  p.  773. 


ON  THE  PROPAGATION  OF  SOUND.  293 

spherical  pulse  arrives  at  the  surface  of  a  plane  solid  obstacle,  it  is  reflected 
precisely  in  the  same  manner  as  we  have  already  seen  that  a  wave  of  water 
is  reflected,  and  assumes  the  form  of  a  pulse  proceeding  from  a  centre  at  an 
equal  distance  on  the  opposite  side  of  the  surface.  This  reflection,  when  it 
returns  back  perpendicularly,  constitutes  what  is  commonly  called  an 
echo  ;  but  in  order  that  the  echo  may  be  heard  distinctly,  it  is  necessary 
that  the  reflecting  object  be  at  a  distance  moderately  great,  otherwise  the 
returning  sound  will  be  confused  with  the  original  one  ;  and  it  must  either 
have  a  smooth  surface,  or  consist  of  a  number  of  surfaces  arranged  in  a 
suitable  form  ;  thus  there  is  an  echo  not  only  from  a  distant  wall  or  rock, 
but  frequently  from  the  trees  in  a  wood,  and  sometimes,  as  it  is  said,  even 
from  a  cloud. 

If  a  sound  or  a  wave  be  reflected  from  a  curved  surface,  the  new  direction 
which  it  will  assume  may  be  determined,  either  from  the  condition  that  the 
velocity  with  which  the  impulse  is  transmitted  must  remain  unaltered,  or 
from  the  law  of  reflection,  which  requires  that  the  direction  of  the  reflected 
pulse  or  wave  be  such  as  to  form  an  angle  with  the  surface,  equal  to  that 
which  the  incident  pulse  before  formed  with  it.  Thus  if  a  sound  or  wave 
proceed  from  one  focus  of  an  ellipsis,  and  be  reflected  at  its  circumference, 
it  will  be  directed  from  every  part  of  the  circumference  towards  the  other 
focus,  since  the  distance  which  every  portion  of  the  pulse  has  to  pass  over 
in  the  same  time,  in  following  this  path,  is  the  same,  the  sum  of  the  lines 
drawn  from  the  foci  to  any  part  of  the  curve  being  the  same  ;  and  it  may 
also  be  demonstrated  that  these  lines  form  always  equal  angles  with  the 
curve  on  each  side.  The  truth  of  this  proposition  may  be  easily  shown  by 
means  of  the  apparatus  already  described  for  exhibiting  the  motions  of  the 
waves  of  water  ;  we  may  also  confirm  it  by  a  simple  experiment  on  a  dish 
of  tea  :  the  curvature  of  a  circle  differs  so  little  from  that  of  an  ellipsis  of 
small  eccentricity,  that  if  we  let  a  drop  fall  into  the  cup  near  its  centre,  the 
little  wave  which  is  excited  will  be  made  to  converge  to  a  point  at  an  equal 
distance  on  the  other  side  of  the  centre.  (Plate  XXV.  Fig.  340,  341.) 

If  an  ellipsis  be  prolonged  without  limit,  it  will  become  a  parabola  :  hence 
a  parabola  is  the  proper  form  of  the  section  of  a  tube  calculated  for  collect- 
ing a  sound  which  proceeds  from  a  great  distance  into  a  single  point,  or 
for  carrying  a  sound  nearly  in  parallel  directions  to  a  very  distant  place. 
It  appears,  therefore,  that  a  parabolic  conoid  is  the  best  form  for  a  hearing 
trumpet,  and  for  a  speaking  trumpet ;  but  for  both  purposes  the  parabola 
ought  to  be  much  elongated,  and  to  consist  of  a  portion  of  the  conoid  re- 
mote from  the  vertex  ;  for  it  is  requisite,  in  order  to  avoid  confusion,  that 
the  sound  should  enter  the  ear  in  directions  confined  within  certain  limits : 
the  voice  proceeds  also  from  the  mouth  without  any  very  considerable  di- 
vergence, so  that  the  parts  of  the  curve  behind  the  focus  would  in  both  cases 
be  wholly  useless.  A  trumpet  of  such  a  shape  does  not  very  materially 
differ  from  a  part  of  a  cone ;  and  conical  instruments  are  found  to  answer 
sufficiently  well  for  practice  ;  it  appears,  however,  unnecessary  to  suppose, 
as  Mr.  Lambert  has  done,  that  they  differ  essentially  in  principle  from 
parabolic  trumpets.*  It  is  not  yet  perfectly  decided  whether  or  no  a  speak- 
*  On  Acoustic  Instruments,  Hist,  et  Mem.  de  Berlin,  1763,  p.  87. 


294  LECTURE  XXXI. 

ing  trumpet  has  any  immediate  effect  in  strengthening  the  voice,  inde- 
pendently of  the  reflection  of  sound.  (Plate  XXV.  Fig.  342.) 

An  umbrella,  held  in  a  proper  position  over  the  head,  may  serve  to  collect 
the  force  of  a  distant  sound  by  reflection,  in  the  manner  of  a  .hearing 
trumpet ;  but  its  substance  is  too  slight  to  reflect  any  sound  very  perfectly, 
unless  the  sound  fall  on  it  in  a  very  oblique  direction.  The  whispering 
gallery  at  St.  Paul's  produces  an  effect  nearly  similar,  by  a  continued  repe- 
tition of  reflections.  Mr.  Charles's  paradoxical  exhibition  of  the  Invisible 
Girl  *  has  also  been  said  to  depend  on  the  reflection  of  sound  ;  but  the  de- 
ception is  really  performed  by  conveying  the  sound  through  pipes,  artVully 
concealed,  and  opening  opposite  to  the  mouth  of  the  trumpet,  from  which 
it  seems  to  proceed. 

When  a  portion  of  a  pulse  of  sound  is  separated  by  any  means  from  the 
rest  of  the  spherical  or  hemispherical  surface  to  which  it  belongs,  and  pro- 
ceeds through  a  wide  space,  without  being  supported  on  either  side,  there  is 
a  certain  degree  of  divergence,  by  means  of  which  it  sometimes  becomes 
audible  in  every  part  of  the  medium  transmitting  it :  but  the  sound  thus 
diverging  is  comparatively  very  faint ;  and  more  so  indeed  than  the  effect 
of  a  wave  of  water,  admitted  under  similar  circumstances,  into  a  wide  re- 
servoir, which  we  have  already  examined.  Hence,  in  order  that  a  speaking 
trumpet  may  produce  its  full  effect,  it  must  be  directed  in  a  right  line  to- 
wards the  hearer :  and  the  sound  collected  into  the  focus  of  a  concave 
mirror  is  far  more  powerful  than  at  a  little  distance  from  it,  which  could 
not  happen  if,  as  some  have  erroneously  supposed,  sound  in  all  cases  tended 
to  spread  equally  in  all  directions.  The  sounds  that  enter  a  room,  in  which 
there  is  an  open  window,  are  generally  heard  by  a  mixture  of  this  faint 
divergence  with  the  reflection  from  various  parts  of  the  window  and  of  the 
room,  and  with  the  effect  of  the  impulse  transmitted  through  the  walls. 
This  diverging  portion,  however  faint,  probably  assists  in  preserving  the 
rectilinear  motion  of  the  principal  sound,  and  gradually  gains  a  little  ad- 
ditional strength  at  the  expense  of  this  portion. 

The  decay  of  sound  is  the  natural  consequence  of  its  distribution  through- 
out a  larger  and  larger  quantity  of  matter,  as  it  proceeds  to  diverge  every 
way  from  its  centre.  The  actual  velocity  of  the  particles  of  the  medium 
transmitting  it,  appears  to  diminish  simply  in  the  same  proportion  as  the 
distance  from  the  centre  increases  ;  consequently  their  energy,  which  is  to 
be  considered  as  the  measure  of  the  strength  of  sound,  must  vary  as  the 
square  of  the  distance  ;  so  that,  at  the  distance  of  ten  feet  from  the  sounding 
body,  the  velocity  of  the  particles  of  the  medium  becomes  one  tenth  as 
great  as  at  the  distance  of  one  foot,  and  their  energy,  or  the  strength  of  the 
sound,  only  one  hundredth  as  great. 


LECT.  XXXI.— ADDITIONAL  AUTHORITIES. 

Sound  in  general. — Mersenne,  Harmonie  Universelle,  fol.  Paris,  1636.  Lahire, 
Hist,  et  Mem.  de  Paris,  1716,  p.  262,  H.  66.  Hales,  Doctrina  Sonorum,  4to,  Lorfd. 
1778.  Dr.  T.  Young  on  Sound  and  Light,  Ph.  Tr.  1800,  p.  106.  Huddlestone's 

*  See  Nich.  Jour.  1802,  p.  56  ;  1807,  p.  69. 


ON  THE  SOUECES  AND  EFFECTS  OF  SOUND.          295 

Observations  on  Sound,  Nich.  Jour.  8vo,  i.  329.  Armi,  Ristretto  di  Fatti  Acustici, 
4to,  Rom.  1821,  Append.  1822. 

Propagation  of  Sound.— Walker  on  the  Velocity  of  Sound,  Ph.  Tr.  1698,  xx. 
433.  Mairan,  Hist,  et  Mem.  de  Paris,  1737,  H.  1.  Cassini,  ibid.  1738,  p.  128, 
H.  1,  1739.  La  Condamine,  ibid.  1745,  p.  448,  and  Introd.  Hist.  &c.  1751,  p.  98. 
Euler,  Hist,  et  Mem.  de  Berlin,  1765,  p.  335.  Winckler,  Tentamina  circa  Soni 
Celeritatem,  4to,  Leipz.  1763.  Blagden,  Ph.  Tr.  1784,  p,  201.  Miiller,  Gotting. 
Gelehrte  Anzeigen,  1791.  Espinosa  and  Bauza,  Annales  de  Chimie,  vii.  93.  Ben- 
zenburg,  Gilbert's  Annalen,  new  series,  v.  383.  Arago,  &c.  Connoissance  des 
Temps,  1825,  p.  361.  Goldingham,  Ph.  Tr.  1823,  p.  96.  Moll,  &c.  ibid.  1824, 
p.  424.  Gregory,  Trans.  Camb.  Ph.  Soc.  1824,  ii.  120.  Myrbach  and  Stampfer, 
Jahrbuch  des  Instit.  zu  Wien,  vol.  vii. 

Propagation  in  Gases.— Perolle,  Melanges  de  Turin,  1786,  iii.  Corr.  1  ;  1790, 
v.  Corr.  195.  Dulong,  Annales  de  Chimie,  vol.  xli. 


LECTURE    XXXII. 


ON  THE  SOURCES  AND  EFFECTS  OF  SOUND. 

THE  examination  of  the  origin  of  sound  might  naturally  be  deemed  an- 
terior to  the  inquiry  respecting  its  propagation  ;  but  it  will  appear,  that  the 
properties  of  many  of  the  most  usual  sources  of  sound  depend  immediately 
on  the  velocity  with  which  an  impulse  of  any  kind  is  transmitted  through  an 
elastic  medium  ;  it  was  therefore  necessary  to  consider  this  velocity,  before 
the  production  of  sound  in  general  could  be  discussed. 

The  origin  of  a  simple  sound,  without  any  alternation,  requires  very 
little  investigation  :  it  appears  that  the  only  condition  necessary  for  its 
production  is  a  sufficient  degree  of  velocity  in  the  motion  or  impulse  which 
occasions  it.  A  very  moderate  velocity  must  be  sufficient  for  producing  an 
impression  on  the  ear ;  there  is  reason  to  believe  that,  when  the  sound  is 
continued,  it  may  remain  audible  with  a  velocity  of  no  more  than  one  hun- 
dredth of  an  inch  in  a  second,  and  perhaps  even  with  a  velocity  much 
smaller  than  this  ;  but  at  its  origin,  it  is  probable  that  the  velocity  of  the 
motion,  constituting  a  sound,  must  always  be  considerably  greater. 

A  continued  sound  may  be  produced  by  a  repetition  of  separate  im- 
pulses independent  of  each  other,  as  when  a  wheel  strikes  in  rapid  succes- 
sion the  teeth  of  a  pinion,  so  as  to  force  out  a  portion  of  air  from  between 
them  ;  when  a  pipe,  through  which  air  is  passing,  is  alternately  opened 
and  shut,  either  wholly  or  partially,  by  the  revolution  of  a  stopcock  or 
valve  ;  or  when  a  number  of  parallel  surfaces  are  placed  at  equal  distances 
in  a  line  nearly  perpendicular  to  them,  and  a  noise  of  any  kind  is  reflected 
from  each  of  them  in  succession  ;  a  circumstance  which  may  often  be  ob- 
served when  we  are  walking  near  an  iron  railing,  an  acute  sound  being 
heard,  which  is  composed  of  such  reflections  from  the  surfaces  of  the 
palisades. 

Musical  sounds  are,  however,  most  frequently  produced  by  the  alternate 
motions  of  substances  naturally  capable  of  isochronous  vibrations,  and  these 


296  LECTURE  XXXII. 

substances  may  be  either  fluids  or  solids,  or  instruments  composed  of  a  com- 
bination of  fluids  with  solids.  The  resonance  of  a  room  or  passage  is  on?  of 
the  simplest  sources  of  a  musical  sound  ;  the  walls  being  parallel,  the  impulse 
is  reflected  backwards  and  forwards  continually  at  equal  intervals  of  time, 
so  as  to  agree  with  the  definition,  and  to  produce  the  effect,  of  a  musical 
sound.  When  we  blow  obliquely  and  uniformly  into  a  cylindrical  pipe 
closed  at  one  end,  it  is  probable  that  the  impulse  or  condensation  must 
travel  to  the  bottom  and  back  before  the  resistance  is  increased  ;  the  cur- 
rent of  our  breath  will  then  be  diverted  from  the  mouth  of  the  pipe  for  an 
equal  time,  which  will  be  required  for  the  diminution  of  the  resistance  by 
the  discharge  of  the  condensed  air,  so  that  the  whole  time  of  a  vibration 
will  be  equal  to  the  time  occupied  by  an  impulse  of  any  kind  in  passing 
through  four  times  the  length  of  the  pipe.  An  open  pipe  may  be  considered 
nearly  as  if  it  consisted  of  two  such  pipes,  united  at  their  closed  ends,  the 
portions  of  air  contained  by  them  being  agitated  by  contrary  motions,  so  as 
always  to  afford  each  other  a  resistance  similar  to  that  which  the  bottom  of 
the  stopped  pipe  would  have  furnished.  It  is  probable  that  when  an 
open  pipe  is  once  filled  with  air  a  little  condensed,  the  oblique  current 
is  diverted,  until  the  effect  of  the  discharge,  beginning  at  the  remoter  end, 
has  returned  to  the  inflated  orifice,  and  allowed  the  current  to  re-enter  the 
pipe.  Where  the  diameter  of  the  pipe  is  different  at  different  parts  of  its 
length,  the  investigation  of  the  sound  becomes  much  more  intricate  ;  but  it 
has  been  pursued  by  Daniel  Bernoulli*  with  considerable  success,  although 
upon  suppositions  not  strictly  consistent  with  the  actual  state  of  the  motions 
concerned. 

In  the  same  manner  as  an  open  pipe  is  divided  by  an  imaginary  basis, 
so  as  to  produce  the  same  sound  with  a  stopped  pipe  of  half  the  length,  a 
pipe  of  any  kind  is  capable  of  being  subdivided  into  any  number  of  such 
pipes,  supposed  to  meet  each  other's  corresponding  ends  only  ;  and,  in 
general,  the  more  violently  the  pipe  is  inflated,  the  greater  is  the  number 
of  parts  into  which  it  subdivides  itself,  the  frequency  of  the  vibrations  being 
always  proportional  to  that  number.  Thus,  an  open  pipe  may  be  divided 
not  only  into  two,  but  also  into  four,  six,  eight,  or  more  portions,  producing 
the  same  sounds  as  a  pipe  of  one  half,  one  third,  one  fourth,  or  any  other 
aliquot  part  of  the  length  ;  but  a  stopped  pipe  cannot  be  divided  into  any 
even  number  of  similar  parts,  its  secondary  sounds  being  only  those  of  a 
pipe  of  which  the  proportion  is  determined  by  the  odd  numbers,  its  length 
being,  for  example,  one  third,  one  fi/th,  or  one  seventh  of  the  original 
length.  These  secondary  notes  are  sometimes  called  harmonics  ;  they  are 
not  only  produced  in  succession  from  the  same  pipe,  but  they  are  also  often 
faintly  heard  together,  while  the  fundamental  note  of  the  pipe  continues  to 
sound.  When  the  pipe  has  a  large  cavity  connected  with  it,  or  consists 
principally  of  such  a  cavity,  with  a  small  opening,  its  vibrations  are  usually 
much  less  frequent,  and  it  is  generally  incapable  of  producing  a  regular 
series  of  harmonics. 

It  is  obvious  from  this  statement  of  the  analogy  between  the  velocity  of 

*  Hist,  et  Mem.  de  1'Acad.  1762,  p.  431,  H.  170.  See  Euler,  Nov.  Com.  Petr. 
xvi.  281.  Hauy,  Traite  de  Physique,  i.  316.  Biot,  do.  ii.  111. 


ON  THE  SOURCES  AND  EFFECTS  OF  SOUND.          297 

sound  and  the  vibrations  of  the  air  in  pipes,  that  they  must  he  affected  in 
•  a  swiilar  manner  by  all  alterations  of  temperature.  Thus  the  frequency  of 
the  vibrations  of  a  pipe  must  be  increased  nearly  in  the  ratio  of  33  to  34  by 
an  elevation  of  30  degrees  of  Fahrenheit's  thermometer  ;  and  if  this  change 
be  accompanied  by  a  transition  from  dampness  to  simple  moisture,  the  sound 
will  be  still  more  altered. 

Dr.  Chladni  has  discovered  that  solids  of  all  kinds,  when  of  a  proper  form, 
are  capable  of  longitudinal  vibrations,  exactly  resembling  in  their  nature 
those  of  the  air  in  an  organ  pipe,  having  also  their  secondary  or  harmonic 
noter*  related  to  them  in  a  similar  manner.  These  vibrations  are  always  far 
more  frequent  than  those  of  a  column  of  air  of  equal  length,  the  velocity 
with  which  an  impulse  is  transmitted  by  a  solid  of  any  kind  being  usually 
from  5  to  16  times  as  great  as  the  velocity  of  sound  in  air,  so  that  the 
longitudinal  sounds  are  always  extremely  acute  when  they  are  produced  by 
substances  of  moderate  length.  These  sounds  afford,  perhaps,  the  most  ac- 
curate mode  of  determining  the  velocity  of  the  transmission  of  an  impulse 
through  any  elastic  substance,  and  of  obtaining  from  that  velocity  the  exact 
measure  of  its  elasticity  ;  they  may  be  easily  exhibited  by  holding  a  long 
bar  or  wire  of  iron  or  brass  in  the  middle,  and  striking  it  at  one  end  with  a 
small  hammer  in  the  direction  of  its  length. 

The  vibrations  by  which  solid  bodies  most  usually  produce  sound  are, 
however,  not  longitudinal,  but  lateral,  and  they  are  governed  either  by  a 
tension  derived  from  the  operation  of  a  weight,  or  of  some  other  external 
force,  or  by  the  natural  elasticity  of  the  substance.  The  vibrations  of  ex- 
tended substances  resemble  most  in  their  properties  those  of  elastic  fluids, 
and  they  occur  the  most  frequently  in  practice,  although  the  vibrations 
produced  by  the  elasticity  of  the  substance  may  be  considered  as  the  most 
natural. 

Vibrations  derived  from  tension  are  either  those  of  cords  or  musical 
strings,  or  those  of  membranes  :  but  the  vibrations  of  membranes  afford 
little  variety,  and  have  not  hitherto  been  very  accurately  investigated,  the 
drum  being  almost  the  only  instrument  in  which  they  are  concerned  ;  they 
do  not  however  appear  to  differ  materially  in  their  properties  from  the 
vibrations  of  strings.  A  musical  string  or  cord  is  supposed  to  be  perfectly 
flexible,  and  of  uniform  thickness,  to  be  stretched  between  two  fixed  points 
by  a  force  incomparably  greater  than  its  own  weight,  and  to  vibrate  in  a 
single  plane  through  a  minute  space  on  each  side  of  its  natural  position. 
Its  motions  may  then  be  traced  through  all  their  stages,  by  comparing  the 
cord  to  a  portion  of  an  elastic  medium  of  the  same  length,  contained 
between  two  bodies  capable  of  reflecting  any  impulse  at  each  end  ;  for 
example,  to  a  portion  of  air  situated  between  two  walls,  or  inclosed  in  a 
pipe  stopped  at  both  ends  ;  for  the  vibration  of  such  a  medium  will  be 
performed  in  the  time  occupied  by  any  impulse  in  travelling  through  twice 
its  length ;  and  the  vibration  of  the  cord  will  be  performed  in  the  same 
time,  supposing  the  height  or  depth  of  the  medium  equal  to  the  length  of 
a,  portion  of  the  cord,  of  which  the  weight  is  equivalent  to  the  force 
applied  to  stretch  it,  and  which  may  be  called  with  propriety  the  modulus 


298  LECTURE  XXXII. 

of  the  tension.  If  the  cord  be  at  first  bent  into  a  figure  of  any  kind,  and 
then  set  at  liberty,  the  place  of  any  part  of  it  at  every  subsequent  time  will 
be  such,  that  it  will  always  be  in  a  right  line  between  two  points  moving 
along  the  figure  each  way  with  the  appropriate  velocity  ;  but  in  order  to 
pursue  this  determination,  we  must  repeat  the  figure  of  the  cord  on  each 
side  of  the  fixed  points  in  an  inverted  position,  changing  the  ends  as  well 
as  the  sides.  Hence  it  appears  that,  at  the  end  of  a  single  vibration,  the 
whole  cord  will  assume  a  similar  figure  on  the  opposite  side  of  its  natural 
place,  but  in  an  inverted  position,  and  after  a  complete  or  double  vibration, 
it  will  return  precisely  to  the  form  which  it  had  in  the  beginning. »  The 
truth  of  this  result  is  easily  shown  by  inflecting  any  long  cord  near  one  of 
its  ends,  having  first  drawn  a  line  under  its  natural  position,  and  it  will 
then  be  evident  that  the  cord  returns  in  each  vibration  nearly  to  the  point 
of  inflection,  and  passes  at  that  end,  but  to  a  much  shorter  distance  on  the 
opposite  side  of  the  line,  while  at  the  other  end  its  excursions  are  greatest 
on  the  opposite  side  of  the  line.  The  result  of  the  calculation  of  the  fre- 
quency of  vibration  agrees  also  perfectly  with  experiment,  nor  is  the 
coincidence  materially  affected  by  the  inflexibility  or  elasticity  of  the 
string,  by  the  resistance  of  the  air,  nor  by  the  slight  increase  of  the 
tension  occasioned  by  the  elongation  of  the  string  when  it  is  inflected  : 
thus,  if  the  weight  or  force  causing  the  tension  of  a  string  were  equal 
or  equivalent  to  the  weight  of  200  feet  of  the  same  string,  that  is,  if  the 
modulus  of  tension  were  200  feet  long,  the  velocity  corresponding  to  half 
this  height  would  be  80  feet  in  a  second  ;  and  every  impulse  would  be  con- 
veyed with  this  velocity  from  one  end  of  the  string  to  the  other,  so  that  if 
the  string  were  1  foot  long,  if  would  vibrate  40  times  in  a  second,  if  6 
inches,  80  times,  and  if  it  were  40  feet  long,  only  once  in  a  second.  Hence, 
it  is  obvious  that  the  time  of  vibration  of  any  cord  is  simply  proportional 
to  the  length  ;  and  this  may  be  shown  either  by  means  of  such  vibrations 
as  are  slow  enough  to  be  reckoned,  or  by  a  comparison  with  the  sounds  of 
pipes,  or  with  other  musical  sounds.  But  if  the  tension  of  a  cord  of 
given  length  were  changed,  it  would  require  to  be  quadrupled  in  order  to 
double  the  frequency  of  vibration  ;  and  if  the  tension  and  length  remained 
unaltered,  and  the  weight  of  the  cord  were  caused  to  vary,  it  would  also 
be  necessary  to  make  the  weight  four  times  as  great  in  order  to  reduce  the 
frequency  of  vibration  to  one  half. 

It  appears  from  the  mode  of  tracing  the  progress  of  a  vibration,  which 
has  already  been  laid  down,  that  every  cord  vibrates  in  the  same  manner 
as  if  it  were  a  part  of  a  longer  cord,  composed  of  any  number  of  such 
cords,  continually  repeated  in  positions  alternately  inverted  ;  consequently 
if  a  long  cord  be  initially  divided  into  any  number  of  such  equal  portions, 
its  parts  will  continue  to  vibrate  in  the  same  manner  as  if  they  were  sepa- 
rate cords  ;  the  points  of  division  only  remaining  always  at  rest.  Such 
subordinate  sounds  are  called  harmonics  :  they  are  often  produced  in  violins 
by  lightly  touching  one  of  the  points  of  division  with  the  finger,  when  the 
bow  is  applied,  and  in  all  such  cases  it  may  be  shown,  by  putting  sma.ll 
feathers  or  pieces  of  paper  on  the  string,  that  the  remaining  points  of 


ON  THE  SOURCES  ANI>  EFFECTS  OF  SOUND.  299 

division  are  also  quiescent,  while  the  intervening  portions  are  in  motion.* 
1  (Pfete-XXV.  Fig.  343.) 

These  harmonic  sounds  are  also  generally  heard  together  with  the  funda- 
mental sound  of  the  cord,  and  it  is,  therefore,  necessary,  in  such  cases,  to 
consider  the  subordinate  vibrations  as  combined  with  a  general  one.  It  is 
not,  however,  universally  true  that  the  fundamental  sound  must  always  be 
accompanied  by  all  the  harmonics  of  which  the  cord  is  susceptible  ;  for  I 
have  found  that  by  inflecting  the  cord  exactly  at  any  point  in  which  the 
cord  might  be  divided  into  a  number  of  equal  parts,  and  then  suffering  it 
to  Vibrate,  we  lose  the  effect  of  the  corresponding  harmonic.  There  is 
some  difficulty  in  explaining  the  reason  of  the  distinct  production  of  these 
sounds,  in  cases  where  the  theory  appears  to  indicate  a  single  and  simple 
vibration  only ;  but  it  appears  to  be  most  probable  that  they  usually 
become  audible  in  consequence  of  some  imperceptible  irregularity  in  the 
form  or  weight  of  the  cord,  which  is  just  sufficient  to  derange  the  perfect 
coincidence  of  the  actual  motions  with  those  which  the  theory  indicates? 
without  producing  a  discordance  capable  of  offending  the  ear.  That  a 
cord  irregularly  loaded  may  have  the  relations  of  its  harmonics  disturbed, 
may  easily  be  understood  by  considering  the  effect  of  a  small  weight  placed 
at  one  of  the  points  of  division,  which  will  obviously  retard  the  principal 
vibration,  without  materially  affecting  that  of  the  portions  terminated  by 
it.  An  abrupt  and  irregular  agitation  appears  also  in  many  cases  to  make 
the  secondary  notes  more  audible,  while  a  gradual  and  delicate  impulse, 
like  that  of  the  wind  on  the  strings  of  an  Aeolian  harp,  produces  a  sound 
almost  entirely  free  from  subordinate  harmonics. 

It  usually  happens  that  the  vibration  of  a  cord  deviates  from  the  plane 
of  its  first  direction,  and  becomes  a  rotation  or  revolution,  which  may  be 
considered  as  composed  of  various  vibrations  in  different  planes,  and  which 
is  often  exceedingly  complicated.  These  vibrations  may  be  combined  in 
the  first  instance  in  a  manner  similar  to  that  which  has  been  already  ex- 
plained respecting  the  vibrations  of  pendulums  ;  and  if  the  motion  of  the 
cord  be  supposed  to  follow  the  same  law  as  that  of  a  pendulum,  the  result 
of  two  entire  vibrations  thus  united,  may  be  either  a  vibration  in  an  inter- 
mediate direction,  or  a  revolution  in  a  circle  or  in  an  ellipsis.  But  besides 
these  compound  vibrations  of  the  whole  cord,  it  is  also  frequently  agitated 
by  subordinate  vibrations,  which  constitute  harmonic  notes  of  different 
kinds,  so  that  the  whole  effect  becomes  very  intricate  ;  as  we  may  observe 
by  a  microscopic  inspection  of  any  luminous  point  on  the  surface  of  the 
cord,  for  instance  the  reflection  of  a  candle  in  the  coil  of  a  fine  wire  wound 
round  it.  The  velocity  of  the  motion  is  such  that  the  path  of  the  luminous 
point  is  marked  by  a  line  of  light,  in  the  same  manner  as  when  a  burning 
coal  is  whirled  round  ;  and  the  figures,  thus  described,  are  not  only  different 
at  different  parts  of  the  same  chord,  but  they  often  pass  through  an  amusing 
variety  of  forms  during  the  progress  of  the  vibration  ;  they  also  vary  con- 
siderably according  to  the  mode  in  which  that  vibration  is  excited.  (Plate 
XXV.  Fig.  344,  345.) 

The  vibrations  immediately  dependent  on  elasticity  are  those  of  rods, 
*  Wallis,  Op.  II.  466.     Sauveur,  Hist,  et  Mem.  de  1'Acad.  1701. 


300  LECTURE  XXXII. 

plates,  rings,  and  vessels.  These  admit  of  much  greater  variety,  and  are 
of  more  difficult  investigation  than  the  vibrations  of  cords.  A  rfc4  nifty 
be  either  wholly  loose,  or  fixed  at  one  end  only,  or  at  both  ;  and  it  may 
either  be  loosely  fixed,  in  situation  only,  or  firmly  fixed,  in  direction  as 
well  as  in  situation  ;  and  these  conditions  may  be  variously  combined  with 
each  other  ;  the  rod  may  also  have  a  variety  of  secondary  vibrations  besides 
the  principal  or  fundamental  sound.  All  these  cases  have  been  examined 
by  various  mathematicians  :  the  subject  was  begun  by  Daniel  Bernoulli,* 
and  much  extended  by  Euler,t  some  of  whose  conclusions  have  been  cor- 
rected by  Riccati ;  J  and  Chladni  §  has  compared  them  all  with  experinent. 
The  sounds  produced  by  the  same  rod,  either  under  different  circum- 
stances, or  as  harmonics  which  may  be  heard  at  the  same  time,  are  scarcely 
ever  related  to  each  other  in  any  simple  proportion,  except  that  when  a  rod 
is  loosely  fixed  at  both  ends,  the  frequency  of  the  vibrations  of  the 
subordinate  notes  is  expressed  by  the  series  of  the  squares  of  the 
natural  numbers,  as  1,  4,  9,  and  1G.  But  the  times  occupied  by  any 
similar  vibrations  of  rods,  similarly  circumstanced,  are  always  directly  as 
the  squares  of  their  lengths,  and  inversely  as  their  depths.  When  the  rod 
is  wholly  at  liberty,  two  at  least  of  its  points  must  be  at  rest,  and  these  are 
at  the  distance  of  about  one  fifth  of  its  length  from  either  end  :  in  the  next 
sound  of  the  same  rod,  the  middle  point  is  at  rest,  with  two  others  near  the 
ends.  There  is  by  no  means  the  same  regularity  in  the  progress  of  the 
vibrations  of  rods  of  different  kinds  as  in  those  of  cords ;  it  can  only 
happen  in  particular  cases  that  the  rod  will  return  after  a  complete 
vibration  to  its  original  state,  and  these  cases  are  probably  such  as  seldom 
occur  in  nature. 

The  vibrations  of  plates  differ  from  those  of  rods  in  the  same  manner  as 
the  vibrations  of  membranes  differ  from  those  of  cords,  the  vibrations 
which  cause  the  plate  to  bend  in  different  directions  being  combined  with 
each  other,  and  sometimes  occasioning  singular  modifications.  These  vi- 
brations may  be  traced  through  wonderful  varieties  by  Professor  Chladni' s 
method  of  strewing  dry  sand  on  the  plates,  which,  when  they  are  caused  to 
vibrate  by  the  operation  of  a  bow,  is  collected  into  such  lines  as  indicate 
those  parts,  which  remain  either  perfectly  or  very  nearly  at  rest  during  the 
vibrations.  Dr.  Hooke||  had  employed  a  similar  method,  for  showing  the 
nature  of  the  vibrations  of  a  bell,  and  it  has  sometimes  been  usual,  in  mili- 
tary mining,  to  strew  sand  on  a  drum,  and  to  judge,  by  the  form  in  which 
it  arranges  itself,  of  the  quarter  from  which  the  tremors  produced  by 
countermining  proceed.  (Plate  XXV.  Fig.  346... 348.) 

The  vibrations  of  rings  and  of  vessels  are  nearly  connected  with  those  of 
plates,  but  they  are  modified  in  a  manner  which  has  not  yet  been  suf- 

*  Comm.  Petr.  iii.  62.     Nov.  Comm.  Petr.  xv.  xvi.  257. 

t  Comm.  Petr.  vii.  99.  Nov.  Comm.  Petr.  x.  243  ;  xvii.  381 ;  1780,  iv.  11.99. 
Acta  Petr.  iii.  I.  103. 

J  Mem.  della  Soc.  Jtal.  i.  444. 

§  Entdeckungen  iiber  die  Theorie  des  Klanges,  Leipz.  1787.  Acta  Ac.  Electr 
Mogunt.  Erford,  1796.  Neue  Schriften  der  Berl.  Gesell.  1799.  Traite  d'Acous- 
tique,  1809,  PI.  3.. .7.  Neue  Beytrage  zur  Akustik,  1817. 

1|  Birch's  Hist,  of  the  Roy.  Soc.  ii.  475. 


ON  TH     SOURCES  AND  EFFECTS  OF  SOUND.          301 

ficiently  in\ssatigated.  A  glass,  or  a  bell,  divides  in  general  into  four 
porlioTS?  vibrating  separately,  and  sometimes  into  six  or  eight ;  they  may 
readily  be  distinguished  by  means  of  the  agitations  excited  by  them  in  a 
fluid  contained  in  the  glass.  It  is  almost  unnecessary  to  observe,  that  the 
fluid  thus  applied,  by  adding  to  the  mass  of  matter  to  be  moved,  makes  the 
vibration  slower,  and  the  sound  more  grave. 

In  some  cases  the  vibrations  of  fluids  and  solids  are  jointly  concerned  in 
the  production  of  sound  :  thus,  in  most  of  the  pipes  of  an  organ  denomi- 
nated reed  pipes,  the  length  of  a  tongue  of  metal  is  so  adjusted  as  to  be 
capable  of  vibrating  in  the  same  time  with  the  air  contained  in  the  pipe. 
Sometimes,  however,  the  air  only  serves  to  excite  the  motion  of  the  solid, 
as  in  some  other  organ  pipes,  which  are  usually  much  shorter  than  would 
be  required  for  producing  the  proper  note  alone,  and  probably  in  the 
glottis,  or  organ  of  the  voice  of  animals.  On  the  other  hand,  the  alternate 
opening  and  shutting  of  the  lips,  in  blowing  the  trumpet  or  French  horn, 
can  scarcely  be  called  a  vibration,  and  the  pitch  of  the  sound  is  here  de- 
termined by  the  properties  of  the  air  in  the  pipe  only.  The  vibrations  of  a 
solid  may  be  excited  by  an  undulation  propagated  through  a  fluid ;  thus, 
when  a  loud  sound  strikes  against  a  cord,  capable  of  vibrating,  either  ac- 
curately, or  very  nearly,  with  the  same  frequency,  it  causes  a  sympathetic 
tone,  resembling  that  from  which  it  originated ;  and  the  cord  may  pro- 
duce such  a  sound  either  by  vibrating  as  a  whole,  or  by  dividing  itself  into 
any  number  of  equal  parts.  Thus,  if  the  damper  be  raised  from  any  of  the 
strings  of  a  harpsichord,  it  may  be  made  to  vibrate,  by  striking  or  singing 
•  any  note,  of  which  the  sound  corresponds  either  to  that  of  the  whole  string, 
or  to  that  of  any  of  its  aliquot-  parts.  Sometimes  also  two  cords  that  are 
very  nearly  alike,  appear,  when  sounding  together,  to  produce  precisely 
the  same  note,  which  differs  a  little  from  each  of  those  which  the  cords 
would  produce  separately ;  and  a  similar  circumstance  has  been  observed 
with  respect  to  two  organ  pipes  placed  near  each  other.  In  these  cases  the 
vibrating  substances  must  affect  each  other  through  the  medium  of  the  air ; 
nearly  in  the  same  manner  as  two  clocks,  which  rest  on  the  same  support, 
have  been  found  to  modify  each  other's  motions,  so  as  to  exhibit  a  perfect 
coincidence  in  all  of  them. 

It  is  uncertain  whether  any  fibres  in  the  ear  are  thus  sympathetically  agi- 
tated in  the  process  of  hearing,  but  if  there  are  any  such  vibrating  fibres, 
their  motions  must  necessarily  be  of  short  duration,  otherwise  there  would 
be  a  perpetual  ringing  in  our  ears,  and  we  should  never  be  able  to  judge 
accurately  of  the  termination  of  a  sound.  Besides,  a  sympathetic  vibration 
may  be  excited  not  only  by  a  sound  producing  vibrations  of  equal  fre- 
quency, but  also  by  a  sound,  of  which  every  alternate,  or  every  third  or 
fourth  vibration,  coincides  with  its  motions :  it  would,  therefore,  be 
difficult  to  distinguish  such  sounds  from  each  other,  if  hearing  depended 
simply  on  the  excitation  of  sympathetic  vibrations.  It  is  true  that  we 
generally  distinguish,  in  listening  to  a  loud  and  deep  sound,  precisely  such 
notes  as  would  be  thus  produced  ;  but  it  is  only  when  the  sounding  body 
is  capable  of  affording  them  from  the  nature  of  its  vibrations  ;  for  we  may 
listen  for  them  in  vain  in  the  sound  of  a  bell  or  of  a  humming  top.  There 


302  LECTURE  XXXII. 

is,  however,  no  doubt  that  the  muscles,  with  which  the  difi^ent  parts  of 
the  ear  are  furnished,  are  concerned  in  accommodating  the  tensionN/f  soihe ' 
of  them  to  the  better  transmission  of  sound  ;  and  it  is  equally  certain  that 
their  operation  is  not  absolutely  necessary  in  the  process. 

The  external  ear  serves  in  some  measure  for  collecting  the  undulations 
of  sounds  transmitted  through  the  air,  and  reflecting  them  into  the  auditory 
passage,  at  the  bottom  of  which  they  strike  against  the  membrane  of  the 
tympanum  or  drum,  which,  being  larger  and  more  moveable  than  some  of 
the  subsequent  parts,  is  capable  of  transmitting  a  stronger  impulse  than 
they  would  immediately  receive.  In  the  same  manner  we  may  oftew  feel 
the  tremors  produced  in  a  sheet  of  thick  paper,  held  in  the  hand,  by  the 
agitation  of  the  air,  derived  from  a  loud  sound,  which  would  not  otherwise 
have  affected  the  organ  of  touch.  The  impulse  received  by  the  membrane 
of  the  tympanum  is  conveyed  by  the  hammer  and  anvil,  two  small  bones, 
which  together  constitute  a  kind  of  bent  lever,  through  a  third  minute  flat- 
tened bone,  to  a  fourth  called  the  stirrup,  which  serves  merely  as  a  handle 
to  its  basis,  a  plate  covering  the  orifice  of  a  cavity  called  the  vestibule,  and 
communicating  the  impulse  to  the  mucous  fluid  which  fills  this  cavity. 
The  fluid  of  the  vestibule,  thus  agitated,  acts  immediately  on  the  termi- 
nations of  the  nerves,  which  form  a  loose  membranous  tissue,  almost  float- 
ing in  it,  while  another  portion  of  them  is  distributed  on  the  surface  of 
three  semicircular  tubes  or  canals,  opening  at  both  ends  into  the  cavity, 
and  a  third  portion  supplies  the  cochlea,  a  detached  channel,  which  appears 
to  be  arranged  with  singular  art  as  a  micrometer  of  sound.  It  resembles 
the  spiral  convolutions  of  a  snail  shell,  and  if  uncoiled,  would  constitute 
two  long  conical  tubes  connected  at  their  summits,  the  base  of  one  opening 
into  the  vestibule,  that  of  the  other  being  covered  by  a  membrane  only, 
which  separates  the  fluid  from  the  air  contained  in  the  general  cavity  of 
the  ear,  or  the  tympanum.  It  is  evident  from  the  properties  of  fluids 
moving  in  conical  pipes,  that  the  velocity  of  any  impulse  affecting  the  fluid 
at  the  base  of  the  cone  must  be  extremely  increased  at  its  vertex,  while 
the  flexibility  of  the  membrane  at  the  base  of  the  second  channel  allows 
this  motion  to  be  effected  without  difficulty.  It  has  also  been  supposed 
that  a  series  of  fibres  are  arranged  along  the  cochlea,  which  are  susceptible 
of  sympathetic  vibrations  of  different  frequency  according  to  the  nature  of 
the  sound  which  acts  on  them  ;  and,  with  some  limitations,  the  opinion 
does  not  appear  to  be  wholly  improbable.  We  must,  however,  reason  with 
great  caution  respecting  the  functions  of  every  part  of  the  ear,  since  its 
structure  varies  so  much  in  different  animals,  that  we  cannot  pronounce 
with  certainty  respecting  the  indispensable  necessity  of  any  one  arrange- 
ment for  the  perfection  of  the  sense.  And  even  in  the  case  of  the  human 
ear,  many  of  these  parts  may  be  spared  without  great  inconvenience  ;  thus, 
we  hear  very  perfectly,  by  means  of  impressions  communicated  to  the 
teeth,  and  through  them  to  the  large  bones  of  tjie  head  ;  and  even  when  the 
membrane  of  the  tympanum,  and  all  the  small  bones  of  the  ear  have  been 
destroyed  by  disease,  the  undulations  of  the  air  still  continue  to  affect  tho 
organ  in  the  usual  manner.*  (Plate  XXV.  Fig.  349... 351.) 
*  Douglas,  De  Aure  Humana,  4to,  Bonon.  1704. 


ON  THll  SOURCES  AND  EFFECTS  OF  SOUND.  303 

~*  ^Such  is  tjj^d^licacy  of  the  organs  of  hearing  in  their  perfect  state,  that 
we  reaHtfy  distinguish  not  only  the  frequency  of  the  vibrations  of  a  sound, 
whether  constant  or  variable,  and  its  loudness  or  softness,  but  also  the 
quality  of  tone,  depending  on  the  law  which  governs  each  separate  vibra- 
tion, and  which  constitutes  the  difference  between  instruments  of  different 
kinds,  or  different  instruments  of  the  same  kind,  or  even  the  same  instru- 
ment differently  employed.  Thus,  we  can  distinguish  very  accurately  the 
voices  of  our  friends,  even  when  they  whisper,  and  those  modifications  of 
the  same  voice  which  constitute  the  various  vowels  and  semivowels,  and 
whicil  with  the  initial  and  final  noises  denominated  consonants,  compose 
the  words  of  a  language.  We  judge  also,  without  an  error  of  many  degrees, 
of  the  exact  direction  in  which  the  sound  approaches  us  ;  but  respecting 
the  manner  in  which  the  ear  is  enabled  to  make  this  discrimination,  we 
cannot  reason  upon  any  satisfactory  grounds. 


LECT.  XXXII.— ADDITIONAL  AUTHORITIES. 

Vibrations  of— 1.  Fluids. — Euler  on  the  Motion  of  Air  in  Pipes,  Nov.  Com. 
Petr.  xvi.  281.  Chladni,  Ph.  Mag.  iv.  275.  Delarive  on  the  Sounds  from  Hydrogen 
Gas,  Jour,  de  Physique,  Iv.  165  ;  Nich.  Jour.  8vo,  iv.  23.  Higgins  on  do.  Nich. 
Jour.  8vo,  i.  129.  Biot,  Mem.  d'Arcueil,  ii.  99.  Leslie,  Trans.  Camb.  Ph.  Soc. 
i.  267. 

2.  Cords. — Sauveur  on  the  Sounds  of  Cords,  Hist,  et  Mem.  de  Paris,  1713, 
p.  324,  H.  68.     Jo.  Bernoulli,  Com.  Petr.  iii.  13.     D.  Bernoulli,  Com.  Petr.  iii. 
62;  Hist,  et  Mem.  de  Berlin,  1753,  pp.  147,  173.     Bernoulli  on  the  Vibrations  of 
Unequal  and  Compound  Cords,  Hist,  et  Mem.  de  Berlin,  1765,  p.  281  ;  Nov.  Com. 
Petr.  xvi.  257.     Euler  on  the  Vibrations  of  Cords,  Hist,  et  Mem.  de  Berlin,  1748, 
p.  69,  &c.  &c.    D'Alembert,  ibid.  1747,  pp.  214,  220  ;  1750,  p.  355  ;  1763,  p.  235. 
Voigton  the  Nodes  of  Cords,  Ph.  Mag.  iv.  347.     Pellisov,  Poggendorf's  Annalen, 
xix.  237. 

3.  Surfaces. — Biot,  Mem.  de  1'Institut,  iv.  21.     Jo.  Bernoulli  on  the  Vibrations 
of  Rectangular  Plates,  Nov.  Act.  Petr.  1787,  v.  197.     Voigt,  Ph.  Mag.  iii.  389. 
Comparisons  with  Chladni's  Experiments.     Savart,   Annales  de  Chimie,  vol.  xii. 
&c.  &c.      Kastner's  Archiv,  B.  8.     Faraday,  Ph.  Tr.  1831,  p.  237.     Wheatstone, 
ibid.  1833,  p.  593.     Tomlinson,  Records  of  General  Science,  vol.  ii. 

Vibrations  in  general. — On  Numbering  the  Vibrations  of  Sound,  Com.  Bon.  i. 
180.  Poisson  sur  la  Theorie  du  Son,  Journal  de  1'Ecole  Poly  technique,  torn.  xiv.  ; 
sur  le  Mouvement  dans  les  Tuyaux  Cylindriques,  Mem.  de  1'Acad.  1818-19,  Me- 
canique,  ii.  693.  Savart,  Annales  de  Chimie,  xliv.  337,  xlvii.  69.  Cagniard  Latour, 
Annales  de  Chimie,  Ivi.  280.  Blein  sur  la  Theorie  des  Vibrations,  4to,  1827,  8vo, 
1831.  Trevelyan  on  the  Vibrations  of  Heated  Metals,  Ph.  Mag.  1832,  vi.  141, 
1833.  Faraday,  Jour,  of  the  Royal  Inst.  vol.  iv.  Forbes,  Ph.  Mag.  vol.  iv.  Trans- 
actions  of  the  Royal  Soc.  of  Edin.  vol.  xii.  Eisenlohr  Lehrbuch  der  Physik,  Mann- 
heim, 1836.  Dove's  Repertorium  der  Physik,  Band.  vi.  1842.  On  Reflection  of 
Waves,  Annales  de  Chimie,  Ixxi.  20.  Fechner,  Repertorium  der  Physik,  Band  i. 

Interference  of  Vibrations. — Dr.  Young  pointed  out  the  fact,  that  a  tuning  fork 
held  vertically  at  a  short  distance  from  the  ear,  and  turned  on  its  axis,  emits  a  louder 
or  softer  sound,  according  to  its  position — the  vibrations  of  the  two  prongs  tending 
alternately  to  strengthen  and  to  diminish  each  other's  effect.  Mr.  Hopkins  (Trans. 
Camb.  Ph.  Soc.  v.  231)  exhibited  a  similar  interference  to  the  eye. 

Ear  and  Hearing. — Perrault  on  the  Organ  of  Hearing,  Hist,  et  Mem.  de  Paris,  i. 
158.  Duverney,  ibid.  i.  256.  Treatise  on  do.  Lond.  1737.  Valsalvade  Aure,  4to, 
Bologna,  1704.  Mairan  on  the  Effect  of  Sound  on  the  Ear,  Hist,  et  Mem.  de  Paris, 
1?37,  p.  49,  H.  97.  Nollet  on  the  Hearing  of  Fishes,  Hist,  et  Mem.  de  Paris,  1743. 
Klein  on  do.  Ph.  Tr.  1748,  p.  233.  Arderon  on  do.  ibid.  1748,  p.  149.  Camper 
on  do.  Mem.  des  Savans  Etrangers,  vi.  177.  Hunter  on  do.  Ph.  Tr.  1782,  p.  379. 
Geoffroy  on  the  Hearing  of  Reptiles,  Mem.  des  Savans  Etrangers,  ii.  164.  Haller, 


304  LECTURE  XXXIII. 

Physiol.  Elliott  on  Vision  and  Hearing,  1780.  Vicq  d'Azyr  ofc^e  Hearing  of 
Birds,  Hist,  et  Mem.  de  Paris,  1778,  p.  381,  H.  5.  Galvani  on  do.  Corn^Dn.  vi. 
O.  420.  Scarpa  de  Auditu  et  Olfactu,  fol.  Patav.  1789.  Comparetti  de  Aure 
Interna,  4to,  Paris,  1789.  Home  on  the  Membrana  Tympani,  Ph.  Tr.  1800,  p.  1. 
Cooper  on  do.  ibid.  1800,  p.  151  ;  1801,  p.  435.  Gough  on  the  Method  of  judging 
of  the  Position  of  Sonorous  Bodies,  Manch.  Mem.  v.  622.  Darwin's  Zoonomia,  ii. 
487.  Saunders's  Anatomy  of  the  Ear,  1806.  Ramdohr,  Magazin  der  Gess.  Nat. 
Freunde,  Berlin,  1811,  p.  389.  Cuvier's  Report  on  a  Paper  of  Flourens,  Annales 
de  Chimie,  xxxix.  104.  Muncke,  Kastner's  Archiv,  vii.  1.  Wollaston  on  Sounds 
inaudible  to  certain  Ears,  Ph.  Tr.  1820.  Weber  de  Aure,  Lips.  1820.  Wheat- 
stone,  Journal  of  Science,  1827,  vol.  ii.  Breschet,  Recherches  sur  1'Organe  de 
1'Ouie,  1836.  Cyclopaedia  of  Anat.  and  Phys.  art.  Organ  of  Hearing,  by  Jones. 
Lincke,  Handbuch  der  Ohren  heilkunde,  Leipz.  1837.  * 


LECTURE    XXXIII. 


ON  HARMONICS. 

THE  philosophical  theory  of  harmonics,  or  of  the  combinations  of 
sounds,  was  considered  by  the  ancients  as  affording  one  of  the  most  refined 
employments  of  mathematical  speculation ;  nor  has  it  been  neglected  in 
modern  times,  but  it  has  been  in  general  either  treated  in  a  very  abstruse 
and  confused  manner,  or  connected  entirety  with  the  practice  of  music,  and 
habitually  associated  with  ideas  of  mere  amusement.  We  shall,  however, 
find  the  difficulties  by  no  means  insuperable,  and  the  subject  will  appear  to 
be  worthy  of  attention,  not  only  on  its  own  account,  but  also  for  the  sake 
of  its  analogy  with  many  other  departments  of  science. 

It  appears  both  from  theory  and  from  experience,  that  the  transmission 
of  one  sound  does  not  at  all  impede  the  passage  of  another  through  the 
same  medium.  The  ear  too  is  capable  of  distinguishing,  without  difficulty, 
not  only  two  sounds  at  once,  but  also  a  much  greater  number.  The  mo- 
tions produced  by  one  series  of  undulations  being  wholly  indifferent  with 
respect  to  the  effect  of  another  series,  and  each  particle  of  the  medium  being 
necessarily  agitated  by  both  sounds,  its  ultimate  motion  must  always  be 
the  result  of  the  motions  which  would  have  been  produced  in  it  by  the 
separate  sounds,  combined  according  to  the  general  laws  of  the  composition 
of  motion,  which  are  the  foundation  of  the  principal  doctrines  of  mechanics. 
When  the  two  sounds,  thus  propagated  together,  coincide  very  nearly  in 
direction,  the  motions  belonging  to  each  sound  may  be  resolved  into  two 
parts,  the  one  in  the  common  or  intermediate  direction,  and  the  other 
transverse  to  it ;  the  latter  portions  will  obviously  be  very  small ;  they  will 
sometimes  destroy  each  other,  and  may  always  be  neglected  in  determining 
the  effect  of  the  combination,  since  the  ear  is  incapable  of  distinguishing  a 
difference  in  the  directions  of  sounds  which  amounts  to  a  very  few  degrees 
only.  Thus,  when  two  equal  undulations,  of  equal  frequency,  coincide  in 
this  manner,  and  when  the  particular  motions  are  directed  the  same  way 
at  the  same  time,  the  velocities  in  each  direction  are  added  together,  and 


ON  HARMONICS.  805 

jthe  joint  effecj><£  doubled,  or  perhaps  quadrupled,  since  it  appears  that  the 
'sfeno^r-dfsound  ought  to  be  estimated  from  the  squares  of  the  velocities 
of  the  particles  :  but  when  the  particular  motions  of  the  two  sounds  coun- 
teract each  other,  both  their  effects  are  wholly  destroyed.  These  combina- 
tions resemble  the  effects  of  the  waves  of  water  in  similar  circumstances, 
which  we  have  already  examined,  and  they  may  be  illustrated  by  drawing 
two  curved  lines  representing  the  motions  which  constitute  the  sounds,  in 
the  same  manner  as  we  have  already  supposed  them  to  be  described,  by  a 
vibrating  particle,  on  a  surface  moving  uniformly  in  a  transverse  direction  ; 
these  figures  being  placed  side  by  side,  the  joint  effect  may  be  represented 
by  a  third  curve  drawn  in  such  a  direction  as  to  be  always  in  the  middle 
between  the  corresponding  points  of  the  first  two.  A  similar  result,  but 
still  more  strongly  marked,  may  be  obtained  mechanically,  by  cutting  two 
boards  or  plates  of  any  kind  into  the  form  of  the  curves,  and  then  dividing 
one  of  them  into  a  number  of  thin  pieces  or  sliders  by  lines  perpendicular 
to  the  general  direction  of  the  curve,  or  to  the  termination  of  the  plate 
which  is  parallel  to  it :  the  bottom  of  these  sliders  being  then  placed  on  the 
other  curve,  their  general  outline  will  represent  the  effect  of  the  combina- 
tion. We  may  assume  for  this  purpose  the  form  of  the  harmonic  curve, 
which  represents  the  motions  of  a  body  vibrating  like  a  pendulum,  and 
which  probably  agrees  very  nearly  with  the  purest  and  simplest  sounds. 
(Plate  XXV.  Fig.  352.) 

If  the  two  undulations  differ  a  little  from  each  other  in  frequency,  they 
alternately  tend  to  destroy  each  other,  and  to  acquire  a  double,  or  perhaps 
a  quadruple  force,  and  the  sound  gradually  increases  and  diminishes  in 
continued  succession  at  equal  .-intervals.  This  intension  and  remission  is 
called  a  beat,  and  furnishes  us  with  a  very  accurate  mode  of  determining 
the  proportional  frequency  of  the  vibrations,  when  the  absolute  frequency 
of  one  of  them  is  known,  or  the  absolute  frequency  of  both  when  their  pro- 
portion is  known  ;  since  the  beats  are  usually  slow  enough  to  lqe  reckoned, 
although  the  vibrations  themselves  can  never  be  distinguished.  Thus,  if  one 
sound  consisted  of  100  vibrations  in  a  second,  and  produced  with  another 
acuter  sound  a  single  beat  ^n?"  every  second,  it  is  obvious  that  the  second 
sound  must  consist  of  101  vibrations  in  a  second.  Again,  if  we  have  two 
portions  of  a  similar  cord  equally  stretched,  or  two  simple  pipes,  of  which 
the  lengths  are  in  the  proportion  of  15  to  16,  they  will  produce  a  beat  in  15 
vibrations  of  the  longer  ;*  and  if  we  count  the  number  of  beats  in  15  seconds, 
we  shall  find  the  number  of  vibrations  in  a  single  second.  The  easiest  way 
of  procuring  two  such  strings  or  pipes,  in  practice,  is  to  tune  them  by  a 
third,  so  that  they  may  be  respectively  -t  and  -|  Of  its  length ;  the  vibrations 
of  the  third  pipe  in  a  second  will  also  be  equal  to  the  number  of  beats  of  the 
first  two  in  12  seconds.  (Plate  XXV.  Fig.  353.) 

When  the  beats  of  two  sounds  are  too  frequent  to  be  heard  as  distinct 

*  For  the  times  of  performing  a  vibration  are  as  the  lengths  of  the  cords  or  pipes, 
and  therefore  15  of  the  latter  correspond  to  16  of  the  former.  Now  an  interval 
between  two  beats  is  that  interval  which  occurs  between  one  relative  state  of  the  two 
cords  or  pipes  and  the  return  to  the  same  state.  Hence  this  interval  is  that  due  to 
16  vibrations  of  the  shorter,  or  15  of  the  longer. 


300  LECTURE  XXXIII. 

augmentations  of  their  force,  they  have  the  same  effect  as  another  impulse? 
which  recur  in  regular  succession,  and  produce  a  musical  note^-w^zh  has 


been  denominated  a  grave  harmonic.  Thus,  two  sounds  in  the  proportion 
of  4  to  5,  produce,  when  they  are  both  very  low  or  grave,  an  audible  suc- 
cession of  beats  ;  but  when  they  are  higher  or  more  acute,  a  grave  harmonic, 
which  may  be  separately  distinguished  as  a  third  sound  by  an  attentive  ear. 
Those  combinations  of  sounds  which  produce  beats  distinctly  audible,  have 
in  general  a  harsh  and  coarse  effect,  and  are  called  discords  ;  but  those  of 
which  the  vibrations  are  so  related,  as  to  have  a  common  period  after  a  few 
alternations,  and  which  may  be  observed  to  produce  a  third  sound,  consti- 
tute concords,  which  are  in  themselves  the  more  perfect  as  the  common 
periods  are  shorter.  (Plate  XXV.  Fig.  353.) 

The  natural  association  of  the  secondary  sounds,  which  generally  ac- 
company almost  all  musical  notes,  serves,  in  some  measure,  as  a  foundation 
for  the  science  of  harmonics,  the  same  sounds  as  are  thus  frequently  con- 
nected in  nature,  being  found  to  be  agreeable  when  united  by  art.  But  it 
appears  to  depend  still  more  immediately  on  a  love  of  order,  and  a  predi- 
lection for  a  regular  recurrence  of  sensations,  primitively  implanted  in  the 
human  mind.  Hence,  when  two  sounds  are  heard  together,  those  propor- 
tions are  the  most  satisfactory  to  the  ear  which  exhibit  a  recurrence  of  a 
more  or  less  perfect  coincidence  at  the  shortest  intervals,  expressed  by  the 
smallest  numbers  of  the  separate  vibrations  ;  for  though  we  cannot  im- 
mediately estimate  the  magnitude  of  the  vibrations,  yet  the  general  effect  of 
a  regular  or  irregular  succession  necessarily  produces  the  impression  of 
sweetness  or  harshness.  The  same  sounds  as  form  the  best  accompaniment 
for  each  other,  are  also  in  general  the  most  agreeable  for  melodies,  consist- 
ing of  a  succession  of  single  notes  ;  their  intervals  are,  however,  too  large 
to  be  sufficient  for  the  purposes  of  music,  and  they  require  to  be  mixed  with 
other  sounds  which  are  related  to  them  in  a  manner  nearly  similar. 

The  same  constitution  of  the  human  mind  which  fits  it  for  the  perception 
of  harmony,  appears  also  to  be  the  cause  of  the  love  of  rhythm,  or  of  a  re- 
gular succession  of  any  impressions  whatever,  at  equal  intervals  of  time. 
Even  the  attachment  to  the  persons  and  places  to  which  we  are  accustomed, 
and  to  habits  of  every  kind,  bears  a  considerable  resemblance  to  the  same 
principle.  The  most  barbarous  nations  have  a  pleasure  in  dancing  ;  and 
in  this  case,  a  great  part  of  the  amusement,  as  far  as  sentiment  and  grace 
are  not  concerned,  is  derived  from  the  recurrence  of  sensations  and  actions 
at  regular  periods  of  time.  Hence  not  only  the  elementary  parts  of  music, 
or  the  single  notes,  are  more  pleasing  than  any  irregular  noise,  but  the 
whole  of  a  composition  is  governed  by  a  rhythm,  or  a  recurrence  of  periods 
of  greater  or  less  extent,  generally  distinguished  by  bars,  which  are  also  the 
constituent  parts  of  larger  periods,  and  are  themselves  subdivided  into 
smaller.  An  interruption  of  the  rhythm  is  indeed  occasionally  introduced, 
but  merely  for  the  sake  of  contrast  ;  nearly  in  the  same  manner  as,  in  all 
modern  pieces  of  music,  discords  are  occasionally  mixed  with  concords,  in 
order  to  obtain  an  agreeable  variety  of  expression. 

In  a  simple  composition,  all  the  intervals  are  referred  to  a  single  funda- 
mental or  key  note.  Thus,  any  air  which  can  be  played  on  a  trumpet  or 


J  ON  HARMONICS.  307 

dti  a  bud£*5irtJrn,  must  consist  of  the  harmonics  of  a  single  sound  only  :  and 
when  teiaccompaniment  is  performed  by  a  French  horn,  the  length  of  the 
instrument  is  first  adjusted  to  the  principal  note,  and  all  the  sounds  which 
it  is  to  produce  are  selected  from  this  natural  series.  But  the  notes  consti- 
tuting the  most  natural  scale  are  not,  without  exception,  comprehended 
among  the  harmonics  ;  they  are,  however,  all  immediately  dependent  on  a 
similar  relation.  A  sound  of  which  the  vibrations  are  of  equal  frequency 
with  those  of  another,  is  called  a  unison  ;  if  two  vibrations  occur  for  every 
one  of  the  fundamental  note,  the  sound  is  called  its  superior  octave,  being 
the  eighth  of  those  which  are  commonly  considered  as  filling  up  the  scale  ; 
and  on  account  of  its  great  resemblance  to  the  fundamental  note,  it  is  de- 
scribed by  the  same  letter  of  the  alphabet,  or  by  the  same  syllable  ;  so  that 
all  audible  sounds  are  considered  as  repetitions  of  a  series  contained  within 
the  interval  of  an  octave.  One  third  part  of  the  string  or  pipe  gives  the 
fifth  above  the  octave  ;  one  fourth  the  double  octave,  and  one  fifth  of  the 
string  its  third.  Thus  we  obtain  the  common  accord  or  chord,  or  the  har- 
monic triad,  consisting  of  the  fundamental  note,  with  its  third  and  fifth, 
which  produces  the  most  perfect  harmony,  and  which  also  contains  the 
constituent  parts  of  the  most  simple  and  natural  melodies.  But  we  are 
still  in  want  of  intermediate  steps  for  the  scale ;  these  are  supplied  by 
completing  first,  the  triad  of  the  fifth,  which  gives  us  the  second,  and  the 
seventh,  of  which  9  and  15  vibrations  correspond  respectively  to  8  of  the 
fundamental,  and  which  may  also  be  found  in  the  ascending  series  of 
natural  harmonics;  and  in  the  second  place,  by  adding  the  fourth  and 
sixth  in  such  proportions  as  with  the  octave  to  make  up  another  perfect 
triad  ;  the  respective  notes  consisting  of  4  and  5  vibrations,  while  the  fun- 
damental note  makes  3,  and  being  no  where  found  among  the  natural  har- 
monics. The  complete  scale  is,  therefore,  formed  by  these  harmonic  triads 
contiguous  to  and  connected  with  each  other ;  the  middle  one  being  the 
triad  of  the  key  note,  the  superior  one  that  of  its  fifth,  which  is  sometimes 
called  the  dominant  or  governing  note,  and  the  inferior  one  that  of  the 
fourth,  or  subdominant.  This  scale  is  derived  from  principles  so  simple, 
that  it  may  properly  be  considered  as  a  natural  arrangement,  and  it 
appears  to  be  found  with  little  variation  in  barbarous  as  well  as  in  civil- 
ized countries.  (Plate  XXV.  Fig.  354.) 

A  long  piece  would,  however,  be  too  monotonous,  unless  the  funda- 
mental note  were  sometimes  changed ;  we  may,  therefore,  take  at  pleasure 
one  of  the  auxiliary  triads  for  the  principal  harmony,  and  we  may  continue 
the  modulation  or  progression,  until  every  note  of  the  scale  becomes  in  suc- 
cession a  key  note.  But,  in  order  to  fill  up  the  intervals  of  these  several 
scales  in  just  proportion,  it  becomes  necessary  to  add  several  new  notes  to 
the  first  series  ;  for  instance,  if  we  take  the  seventh  for  a  key  note,  we  shall 
want  five  new  sounds  within  the  octave,  making  twelve  in  the  whole, 
which  is  the  number  usually  employed  in  music.  The  interval  between 
any  two  adjoining  sounds  of  the  twelve  is  called  a  semitone  or  half  note, 
two  semitones  making  a  tone  or  note ;  these  terms  are,  however,  sometimes 
employed  with  various  subordinate  distinctions  and  limitations.  The  five 
additional  sounds  have  no  separate  names,  but  they  are  denominated  from 

x2 


V 

308  LECTURE  XXXIII. 

the  neighbouring  notes  on  either  side,  with  the  addition  of  fiTe<^tni  js 

or  flat,  accordingly  as  they  are  a  semitone  higher  or  lower  than  the  notes 

of  which  they  bear  the  names. 

For  still  further  variety,  we  sometimes  change  the  place  of  the  middle 
note  of  each  triad,  placing  the  minor  third,  or  the  interval  expressed  by  the 
ratio  of  5  to  6,  below  the  major,  which  is  in  the  ratio  of  4  to  5 ;  and  the 
scale  thus  formed  is  called  the  scale  of  the  minor  mode,  in  contradistinction 
to  the  major,  the  three  principal  thirds  being  depressed  a  semitone.  Some- 
times, however,  the  alteration  is  made  in  the  third  of  the  key  note  only, 
especially  in  ascending,  in  order  to  retain  the  seventh  of  the  major  scale, 
which  leads  so  naturally  into  the  -octave,  as  to  be  sometimes  called  the 
characteristic  semitone  of  the  key ;  and  it  is  for  this  reason,  that  the  triad, 
in  which  it  is  found,  is  called  the  accord  of  the  dominant,  which,  in  all 
regular  compositions,  immediately  precedes  the  termination  in  the  key 
note. 

The  major  and  minor  triads,  with  the  discord  of  the  flat  seventh,  may  be 
considered  as  constituting  the  foundation  of  all  essential  harmonies.  The 
flat  seventh  is  principally  used  with  the  major  triad,  in  transitions  from 
the  fundamental  key  into  its  fourth,  to  which  that  seventh  naturally 
belongs  as  a  concord ;  so  that  it  serves  to  introduce  the  new  key,  by 
strongly  marking  the  particular  note  in  which  it  differs  from  the  old  one  ; 
and  in  such  cases  the  flat  seventh  always  descends  into,  or  is  followed  by, 
the  third  of  the  new  key,  and  the  third  of  the  first  triad  ascends  into  the 
new  key  note.  Other  discords  are  also  sometimes  introduced,  but  they  are 
in  general  either  partial  continuations  of  a  preceding,  or  anticipations  of  a 
following  accord.  Two  different  parts  of  a  harmony  are  never  allowed,  in 
regular  and  serious  compositions,  to  accompany  each  other  in  successive 
octaves  or  fifths,  since  such  a  succession  is  found  to  produce  a  disagreeable 
monotony  of  effect,  except  when  a  series  of  octaves  is  continued  for  some 
time,  so  as  to  be  considered  as  a  repetition  of  the  same  part. 

These  are  almost  the  only  principles  upon  which  the  art  of  accompani- 
ment, as  well  as  the  general  theory  of  practical  music,  is  founded.  Many 
prolix  treatises  have  been  written  on  the  subject,  but  they  only  contain 
particular  illustrations  of  the  application  of  these  principles,  together  with 
a  few  refinements  upon  them.  The  art  of  composition,  however,  depends 
much  more  on  a  good  taste,  formed  by  habitual  attention  to  the  best 
models,  and  aided,  perhaps,  by  some  little  natural  predisposition,  than 
upon  all  the  precepts  of  science,  which  teach  us  only  how  to  avoid  what  is 
faulty,  without  instructing  us  in  the  mode  of  attaining  what  is  beautiful  or 
sublime. 

It  is  impossible  to  assign  any  such  proportions  for  the  twelve  sounds 
thus  employed,  that  they  may  be  perfectly  appropriate  to  all  the  capacities 
in  which  they  are  used  ;  their  number  is,  therefore,  sometimes  considerably 
increased  ;  and  in  some  instruments  they  may  be  varied  without  limit,  at 
the  performer's  pleasure,  as  in  the  voice,  in  instruments  with  finger  boards, 
and  in  some  wind  instruments  ;  but  in  many  cases  this  is  impracticable, 
nor  could  any  imaginable  alteration  make  all  the  intervals  perfect,  unless 
every  note  were  varied,  whenever  we  returned  to  it  by  steps  different  from 


/  ON  HARMONICS.  309 

,U*ose  by  whi^inve  had  left  it.  The  simplest  mode  of  arranging  the  twelve 
'  s0un<|^j*s*'to  divide  the  octave  into  twelve  equal  intervals,  all  the  notes 
being  in  the  same  proportion  to  those  which  immediately  follow  them  : 
this  is  called  the  equal  temperament,  because  the  imperfection  is  equal  in 
all  keys.  In  this  system  of  temperament,  the  fifths,  which  consist  of 
seven  semitones,  are  a  little  too  flat,  that  is,  the  interval  is  a  little  too 
small ;  the  minor  thirds,  consisting  of  three  semitones,  are  also  too  flat, 
and  the  major  thirds  too  sharp.  But  it  has  generally  been  esteemed  best 
to  preserve  some  keys  more  free  from  error  ;  partly  for  variety,  and  partly 
because  some  are  more  frequently  used  than  others  :  this  cannot,  however, 
be  done  without  making  some  of  the  scales  more  imperfect  than  in  the  equal 
temperament.  A  good  practical  mode  of  performing  it,  is  to  make  six 
perfect  fifths,  in  descending  from  the  key  note  of  the  natural  scale,  and 
six  ascending  fifths  equally  imperfect  among  themselves.  We  thus  retain 
a  slight  imperfection  in  the  scales  most  commonly  used,  and  make  the  keys 
which  are  most  remote  from  them  considerably  less  perfect.  Another 
method,  which  is  perhaps  somewhat  more  easily  executed,  is  to  make  the 
fifth  and  third  of  the  natural  scale  perfectly  correct,  to  interpose  between 
their  octaves,  the  second  and  sixth,  so  as  to  make  three  fifths  equally  tem- 
pered, and  to  descend  from  the  key  note  by  seven  perfect  fifths,  which  will 
complete  the  scale.  Any  of  these  modes  of  temperament  may  be  actually 
executed,  either  by  the  estimation  of  a  good  ear,  or,  still  more  accurately, 
by  counting  the  frequency  of  the  beats  which  the  notes  make  with  each 
other.* 

For  denoting  precisely  the  absolute  as  well  as  the  relative  frequency  of 
the  sounds  of  the  different  octaves,  we  employ  the  first  seven  letters  of  the 
alphabet ;  A  being  the  key  note  of  the  minor  mode,  in  the  scale  of  natural 
notes,  and  C  of  the  major.  The  peculiar  characters  used  in  music  are 
generally  disposed  on  five  or  more  lines,  with  their  intervening  spaces, 
each  implying  a  separate  step  in  the  scale,  setting  out  from  any  line  at 
pleasure,  which  is  marked  with  an  ill  formed  G,  a  C,  or  an  F  :  a  sharp  or 
a  flat  implying  that  all  the  notes  written  on  the  line,  or  in  the  space, 
to  which  it  belongs,  are  to  be  raised  or  depressed  a  semitone,  and  a  natural 
restoring  the  note  to  its  original  value.  The  actual  frequency  of  the  vibra- 
tion of  any  note,  according  to  the  pitch  most  usually  employed,  may  be 
found,  if  we  recollect  to  call  a  noise,  recurring  every  second,  the  first  C, 
then  the  C  denoted  by  the  mark  of  the  tenor  cliff  will  be  the  ninth,  con- 
sisting of  256  vibrations  in  a  second.  The  fifth,  consisting  of  sixteen 
vibrations,  will  be  nearly  the  lowest  audible  note,  and  the  fourteenth  the 
highest  note  used  in  music,  but  the  sixteenth,  consisting  of  above  30,000 
vibrations  in  a  second,  may  perhaps  be  an  audible  sound.  The  frequency 
of  the  vibrations  of  the  other  notes  may  easily  be  calculated  from  the 
known  relations  which  they  bear  to  the  note  thus  determined.  (Plate 
XXV.  Fig.  355.) 

*  Consult  Marpurg's  Anfangsgriinde  der  Theoretischen  Musik,  4to,  Leipz.  1757. 
Versuch  iiber  die  Temperatur,  Bresl.  1776.  Cavallo,  Ph.  Tr.  1788,  p.  238.  Robi- 
son's  Mech.  Phil. 


3JO  LECTURE  XXXIV. 


LECT.  XXXIII.— ADDITIONAL  AUTHORITIES. 


Zarlino,  Institution!  Harmoniche,  fol.  Venice,  1558.  Salinas,  do.  fol.  Salamanca, 
1577.  Tigrini,  II  Compendio  della  Musica,  4to,  Venice,  1588.  Cartesii  Musicse 
Compendium,  Utr.  1650.  Menzoli,  Musica  Speculativa,  4to,  Bologna,  1670. 
Salmon  on  Music,  Lond.  1672.  Dechales,  Cursus  Mathematicus,  3  vols.  fol.  Lyons, 
1674.  Holder  on  the  Natural  Grounds  and  Principles  of  Harmony,  Lond.  1694. 
Wallis,  Ph.  Tr.  1698,  pp.  80,  249.  Henfling's  Musical  System,  Miscel.  Berol.  i.  265. 
Malcolm  on  Music,  Edin.  1721.  Rameau,  Traite  de  1' Harmonic,  4  to,  Paris,  1722. 
Systeme  de  Musique,  4to,  1726.  Euler,  Tentamen  Novae  Theorise  Musicse,  4to, 
Petrop.  1729  ;  also  Hist,  et  Mem.  de  Berlin,  1764,  pp.  165,  175  ;  Novi  Com.  Petr. 
xviii.  330.  Montvallon,  Hist,  et  Mem.  de  Paris,  1742,  H.  117.  Smith's  Harmonies, 
Camb.  1749.  Serre,  Principes  d'Harmonie.  Esteves  on  Temperament,  Mem.  des 
Savans  Etrangers,  ii.  113.  Romieu  on  do.  Hist,  et  Mem.  1758,  p.  483.  Avison  on 
Musical  Expression,  12mo,  1752.  Antoniotto  on  Music,  2  vols.  fol.  1760.  Doni, 
Opere,  3  vols.  fol.  1763.  BaiUiere  de  Laisement,  Theorie  de  la  Musique, 4to,  Paris, 
1764.  Jamard,  do.  1768.  Holden,  4to,  Lond.  1770.  Kirnberger,  Kunst  der 
Reinen  Satzes,  4to,  Berlin,  1771.  Sulzer's  Theorie  der  Schonen  Kiinste,  4  vols. 
Leipz.  1772.  Lambert  on  Temperament,  Hist,  et  Mem.  de  Berlin,  1774,  p.  55. 
Bemetzreider,  Traite  de  Musique,  Paris,  1776  ;  Essai  sur  1'Harmonie,  1781.  Van- 
dermonde,  Systeme  d'Harmonie,  1778.  Choron,  Abrege  des  Principes  de  Composi- 
tion, 2  vols.  fol.  Paris.  Steele's  Prosodia'.Rationalis,  4to,  Lond.  1779.  Pizzali,  La 
Scienza  de'  Suoni  e  dell'  Armonia,  4to,  Venice,  1782.  Young  on  Compound  Sounds, 
Nich.  Jour.  8vo,  ii.  264  ;  iii.  145  ;  iv.  72,  101.  Weber,  Theorie  der  Tonsetzkunst, 
4  vols.  Mainz.  Shield's  Introduction  to  Harmony,  4to,  1800.  Kollman's  New 
Theory  of  Harmony,  4to,  1806.  Busby's  Treatises,  v.  y.  Catel,  Traite  d'Har- 
monie, 1808.  Raymond,  Bases  Physico-math.  de  1'Art  Musical,  Paris,  1813. 
Morel,  La  Musique  expliquee,  1816.  Macdonald's  Treatise  on  the  Harmonic 
System,  fol.  Lond.  1822.  Nathan's  Essay,  1823.  Baldwin's  Science  of  Music, 
12mo,  1829.  Blein,  Principes  de  Melodic,  1832.  Prony,  Introduction  Elementaire 
aux  Intervalles  Musicaux,  4to,  1832.  Beethoven,  Etudes  d'Harmonie,  2  vols.  Paris, 

1833.  Albrechtsberger,  Methode  Elementaire  d'Harmonie,  translated  into  English, 

1834.  Woolhouse's  Essay  on  Musical  Intervals,  12mo,  1835.    Busset,  La  Musique 
expliquee,  1836.     Fetis,   La  Musique  mise  a  la  Portee  de  tout  le  Monde,  1836. 
Graham's  Essay  on  Musical  Composition,  Edin.  1838. 


LECTURE   XXXIV. 


ON  MUSICAL  INSTRUMENTS. 

THE  application  of  the  theory  of  harmonics  to  practice  depends  on  the 
construction  of  musical  instruments  of  different  kinds  :  of  these  we  shall 
only  be  able  to  take  a  cursory  view,  and  we  shall  afterwards  attend  to  the 
historical  order  of  the  most  remarkable  steps,  by  which  both  the  theory  and 
practice  of  music  have  been  advanced  to  a  high  degree  of  refinement. 

Musical  instruments  may  be  most  conveniently  arranged,  accordingly  as 
they  are  principally  calculated  for  exciting  sound  by  the  vibrations  of 
cords,  of  membranes,  of  elastic  plates,  or  of  the  air  ;  or  by  the  joint  effects 
of  the  air  and  a  solid  body  vibrating  together.  The  essential  varieties  o,f 
stringed  instruments  are  found  in  the  harp,  the  harpsichord,  the  pianoforte, 
the  clavichord,  the  guitar,  the  violin,  the  vielle  or  monochord,  and  the 


ON  MUSICAL  INSTRUMENTS.  311 

n  all  these,  the  immediate  force  of  the  sound  of  the  strings 
is  increased  by  means  of  a  sounding  board,  which  appears  to  be  agitated  by 
their  motion,  and  to  act  more  powerfully  on  the  air  than  the  strings  could 
do  alone. 

In  the  harp,  the  sound  is  produced  by  inflecting  the  string  with  the  finger, 
and  suffering  it  to  return  to  its  place.  The  lyre  of  the  ancients  differed 
from  the  harp  only  in  its  form  and  compass,  except  that  the  performer 
sometimes  used  a  plectrum,  which  was  a  small  instrument,  made  of  ivory, 
or  some  other  substance,  for  striking  the  strings.  Each  note  in  the  harp 
has  £  separate  string ;  and  in  the  Welsh  harp  there  are  two  strings  to  each 
note  of  the  principal  scale,  with  an  intermediate  row  for  the  semitones  ;  but 
in  the  pedal  harp,  the  half  notes  are  formed  by  pressing  pins  against  the 
strings,  so  as  to  shorten  their  effective  length.  Instead  of  this  method,  an 
attempt  has  lately  been  made  to  produce  the  semitones  by  changing  the 
tension  of  the  strings,  which  is  said  to  have  succeeded  tolerably  well,  al- 
though it  appears  at  first  sight  somewhat  unpromising. 

In  the  harpsichord,  and  in  the  spinet,  which  is  a  small  harpsichord,  the 
quill  acts  like  the  finger  in  the  harp,  or  the  plectrum  in  the  lyre,  and  it  is 
fixed  to  the  jack  by  a  joint  with  a  spring,  allowing  it  without  difficulty  to 
repass  the  string,  which  is  here  of  metal.  Sometimes  leather  is  used  instead 
of  quills  ;  and  this  serves  to  make  the  tone  more  mellow,  but  less  powerful. 
Besides  two  strings  in  unison,  for  each  note,  the  harpsichord  has  generally 
a  third  which  is  an  octave  above  them.  Different  modifications  of  the  tone 
are  sometimes  produced  by  striking  the  wire  in  different  parts,  by  bringing 
soft  leather  loosely  into  contact  with  its  fixed  extremity,  and  by  some  other 
means.  When  the  finger  is  removed  from  the  key,  a  damper  of  cloth  falls 
on  the  string,  and  destroys  its  motion.  In  all  instruments  of  this  kind,  the 
perfection  of  the  tone  depends  much  on  the  construction  and  situation  of 
the  sounding  board  :  it  is  usually  made  of  thin  deal  wood,  strengthened  at 
different  parts  by  thicker  pieces  fixed  below  it. 

In  the  pianoforte,  the  sound  is  produced  by  a  blow  of  a  hammer,  raised 
by  a  lever,  which  is  as  much  detached  from  it  as  possible.  The  dulcimer, 
or  hackbrett  of  the  Germans,  is  also  made  to  sound  by  the  percussion  of 
hammers,  but  they  are  simply  held  in  the  hand  of  the  performer. 

The  clavichord,  the  clavier  of  the  Germans,  differs  from  other  keyed 
instruments  in  the  manner  in  which  the  length  of  the  string  is  determined ; 
it  is  attached  at  one  end  to  a  bridge,  and  at  the  other  to  a  pin  or  screw  as 
usual ;  but  the  effective  length  is  terminated  on  one  side  by  the  bridge,  and 
on  the  other  by  a  flat  wire  projecting  from  the  end  of  the  key,  which  strikes 
the  string,  and  at  the  same  time  serves  as  a  temporary  bridge  as  long  as  the 
sound  continues  :  the  remaining  portion  of  the  string  is  prevented  from 
sounding  by  being  in  contact  with  a  strip  of  cloth,  which  also  stops  the 
whole  vibration  as  soon  as  the  hammer  falls.  The  instrument  is  capable  of 
great  delicacy  and  neatness  of  expression,  but  it  is  deficient  in  force.  The 
guitar  is  generally  played  with  the  fingers,  like  a  harp  ;  but  each  string  is 
made  to  serve  for  several  notes,  by  means  of  frets,  or  cross  wires,  fixed  to 
the  finger  board,  on  which  it  is  pressed  down  by  the  other  hand.  But  in 
the  pianoforte  guitar,  hammers  are  interposed  between  the  fingers  and  the 


312  LECTURE  XXXIV. 

strings,  acting  like  those  of  the  pianoforte.     The  mandolinfess^d  lute 
species  of  the  guitar  :  and  the  arch  lute  was  a  very  powerful  instrument  of 
the  same  kind,  formerly  much  used  in  full  pieces. 

In  the  violin,  and  in  other  instruments  resembling  it,  all  the  strings  are 
capable  of  having  their  length  altered  at  pleasure,  by  being  pressed  down 
on  the  finger  board.  The  sound  is  produced  by  the  friction  of  the  bow, 
rubbed  with  resin  :  the  string  is  carried  forwards  by  its  adhesion  to  the 
bow,  and  when  its  resistance  has  overcome  this  adhesion,  it  begins  to  return 
in  opposition  to  the  friction  ;  for  the  friction  of  bodies  in  motion  is  gene- 
rally less  than  their  adhesion  when  they  are  at  rest  with  respect  to  £ach 
other,  besides  that  the  contact  of  the  string  with  the  bow  is  usually  in  great 
measure  interrupted  by  subordinate  vibrations,  which  may  be  distinguished, 
by  the  assistance  of  a  microscope,  in  the  manner  already  described ;  but 
when  the  string  changes  once  more  the  direction  of  its  motion,  it  adheres 
again  to  the  bow,  and  is  accelerated  by  it  as  before.  The  original  instru- 
ment appears  to  have  been  the  viola  or  tenor,  its  diminutive  the  violino,  its 
intensitive,  expressing  a  greater  bulk,  the  violone  or  double  bass,  and  the 
diminutive  of  this,  the  violoncello,  or  common  bass.  The  viola  di  gamba 
had  one  or  more  long  strings  separate  from  the  finger  board,  serving  as  an 
occasional  accompaniment. 

The  vielle,  or  monochord,  commonly  called  the  hurdy  gurdy,  has  frets 
which  are  raised  by  the  action  of  the  fingers  on  a  row  of  keys ;  and  instead 
of  a  bow,  the  string  is  made  to  vibrate  by  the  motion  of  a  wooden  wheel : 
there  is  a  second  string  serving  as  a  drone,  producing  always  the  same 
sound  ;  this  is  furnished  with  a  bridge  loosely  fixed,  which  strikes  continu- 
ally against  the  sounding  board,  and  produces  a  peculiar  nasal  effect.  The 
trumpet  marine,  or  trumpet  Marigni,  was  a  string  of  the  same  kind,  which 
was  lightly  touched  at  proper  points,  so  as  to  produce  harmonic  notes  only; 
it  was  impelled  by  a  bow.  The  aeolian  harp,  when  agitated  by  the  wind, 
affords  a  very  smooth  and  delicate  tone,  frequently  changing  from  one  to 
another  of  the  harmonics  of  the  string,  accordingly  as  the  force  of  the  wind 
varies,  and  as  it  acts  more  or  less  unequally  on  different  parts  of  the  string. 
(Plate  XXV.  Fig.  356.) 

The  human  voice  depends  principally  on  the  vibrations  of  the  mem- 
branes of  the  glottis,  excited  by  a  current  of  air,  which  they  alternately 
intercept  and  suffer  to  pass  ;  the  sounds  being  also  modified  in  their  sub- 
sequent progress  through  the  mouth.  Perhaps  the  interception  of  the  air 
by  these  membranes  is  only  partial ;  or  it  may  be  more  or  less  completely 
intercepted  in  sounds  of  different  kinds :  the  operation  of  the  organs  con- 
cerned is  not  indeed  perfectly  understood,  but  from  a  knowledge  of  their 
structure,  we  may  judge  in  some  measure  of  the  manner  in  which  they  are 
employed. 

The  trachea,  or  windpipe,  conveys  the  air  from  the  chest,  which  serves 
for  bellows  :  hence,  it  enters  the  larynx,  which  is  principally  composed  of 
five  elastic  cartilages.  The  lowest  of  these  is  the  cricoid  cartilage,  a  strong 
ring,  which  forms  the  basis  of  the  rest :  to  this  are  fixed,  before,  the  thy< 
reoid  cartilage,  and  behind,  the  two  arytaenoid  cartilages,  composing 
together  the  cavity  of  the  glottis,  over  which  the  epiglottis  inclines  back- 


/ON  MUSICAL  INSTRUMENTS.  313 


as  if^g^ends  from  its  origin  at  the  upper  part  of  the  thyreoid  cartilage, 
fne  glottis  are  extended  its  ligaments,  contiguous  to  each  other 
before,  where  they  are  inserted  into  the  thyreoid  cartilage,  but  capable  of 
diverging  considerably  behind  whenever  the  arytaenoid  cartilages  separate. 
These  ligaments,  as  they  vary  their  tension,  in  consequence  of  the  motions 
of  the  arytaenoid  cartilages,  are  susceptible  of  vibrations  of  various  fre- 
quency, and  as  they  vibrate,  produce  a  continuous  sound.  Properly  speak- 
ing, there  are  two  ligaments  on  each  side ;  but  it  is  not  fully  understood 
how  they  operate  ;  probably  one  pair  only  performs  the  vibrations,  and  the 
other*  assists,  by  means  of  the  little  cavity  interposed,  in  enabling  the  air  to 
act  readily  on  them,  and  in  communicating  the  vibrations  again  to  the  air. 
(Plate  XXVI.  Fig.  357,  358.) 

The  vowels  and  semivowels  are  continuous  sounds,  chiefly  formed  by 
this  apparatus  in  the  glottis,  and  modified  either  in  their  origin  or  in  their 
progress  by  the  various  arrangements  of  the  different  parts  of  the  mouth. 
Of  simple  vowels  sixteen  or  eighteen  may  be  enumerated  in  different  lan- 
guages :  in  the  French  nasal  vowels  the  sound  is  in  part  transmitted 
through  the  nostrils,  by  means  of  the  depression  of  the  soft  palate  :  the 
perfect  semivowels  differ  from  the  vowels  only  in  the  greater  resistance 
which  the  air  undergoes  in  its  passage  through  the  mouth ;  there  are  also 
nasal  and  seminasal  semivowels.  The  perfect  consonants  may  be  either 
explosive,  susurrant,  or  mute;  the  explosive  consonants  begin  or  end 
with  a  sound  formed  in  the  larynx,  the  others  are  either  whispers,  or  mere 
noises,  without  any  vocal  sound.  By  attending  to  the  various  positions 
of  the  organ,  and  by  making  experiments  on  the  effects  of  pipes  of  dif- 
ferent forms,  it  is  possible  to  construct  a  machine  which  shall  imitate  very 
accurately  many  of  the  sounds  of  the  human  voice  ;  and  this  has  indeed 
been  actually  performed  by  Kratzenstein  *  and  by  Kempelen.t  (Plate 
XXVI.  Fig.  359.) 

Although  the  vibrating  ligaments  of  the  glottis  may  be  anatomically 
denominated  membranes,  yet  their  tension  is  probably  confined  to  the 
direction  of  their  length,  and  their  action  is,  therefore,  the  same  with  that 
of  a  simple  string  or  cord.  But  in  the  case  of  a  tambourine  and  a  drum, 
the  membrane  is  stretched  in  every  direction,  and  the  force  of  tension  con- 
sequently acts  in  a  different  manner.  The  principal  character  of  such  in- 
struments is  their  loudness,  derived  from  the  magnitude  of  the  surface  which 
strikes  the  air,  and  the  short  duration  of  the  sound,  on  account  of  the  great 
resistance  necessarily  produced  by  the  air's  reaction. 

Musical  instruments  which  produce  sounds,  by  means  of  vibrations  de- 
pending on  the  elasticity  of  solid  bodies,  are  less  frequently  employed  than 
others ;  they  have  a  peculiar  character  of  tone,  which  is  by  no  means  un- 
pleasant, but  which  renders  them  less  fit  to  be  mixed  with  other  instru- 
ments, since  their  secondary  harmonics  are  in  different  proportions.  Such 
is  the  stacada,  a  series  of  cylinders  of  glass,  or  of  metal,  struck  either  im- 

t   *  Journal  de  Physique,  xxi.  358.     Acta  Petr.  1780,  iv.  II.  H.  16. 

f  Ueber  den  Mechanismus  der  Menschlichen  Sprache,  Vienna,  1791.  On  this 
subject  consult  Willis,  Trans.  Camb.  Phil.  Soc.  iii.  231.  Purkinje  on  the  Physio- 
logy  of  Speech,  Cracow,  1836. 


314  LECTURE  XXXIV.  \  ^ 


mediately  with  hammers,  or  by  means  of  keys  ;  the  tuning>«^the 
the  cymbal,  and  the  bell.  Bells  and  other  similar  instruments  are  usually 
made  of  a  mixture  of  copper  and  tin,  with  a  little  brass  or  zinc,  which  is 
more  highly  elastic  than  either  of  the  component  parts  taken  separately. 
The  harmonica  consists  of  a  series  of  vessels  of  glass,  either  placed  side  by 
side,  or  fixed  on  a  common  axis,  and  made  to  sound  by  the  friction  of  the 
fingers,  and  sometimes  by  that  of  rubbers  of  cork.  The  vibrations  of  an 
elastic  plate,  agitated  by  a  current  of  air,  which  it  continually  admits  and 
excludes,  constitute  the  sound  of  the  vox  humana  and  regal  organ  pipes, 
resembling  the  human  voice  as  much  in  their  effects  as  in  the  mechanism 
on  which  they  depend.  (Plate  XXVI.  Fig.  360... 362.) 

Of  simple  wind  instruments,  in  which  the  quality  of  the  sound  is  deter- 
mined by  the  vibrations  of  the  air,  the  principal  are  the  syrinx,  the  flute, 
the  flageolet,  the  diapason  organ  pipe,  whether  open,  stopped,  or  with  a 
chimney,  the  humming  top,  and  the  cavity  of  the  mouth  in  whistling,  or 
in  playing  on  the  Jew's  harp.  The  pipes  of  the  syrinx  are  adjusted  to  their 
respective  notes  by  cutting  them,  or  filling  them  up,  until  they  are  reduced 
to  a  proper  length ;  and  the  effective  length  of  the  flute  and  flageolet  is 
altered  at  pleasure  by  opening  or  shutting  the  holes  made  at  proper  dis- 
tances in  them ;  the  opening  a  hole  at  any  part  having  the  same  effect  as 
if  the  pipe  were  cut  off  a  little  beyond  it,  and  the  elevation  of  the  tone  being 
somewhat  greater  as  the  hole  is  larger.  The  instruments  differ  little  except 
in  the  mechanism  by  which  the  breath  is  directed  in  such  a  manner  as  to 
excite  a  sound  ;  and  the  flageolet,  when  furnished  with  bellows,  becomes  a 
bagpipe.  The  tongue  of  the  Jew's  harp  is  an  elastic  plate,  but  the  sound, 
which  it  immediately  produces,  serves  only  as  a  drone  ;  its  vibration,  how- 
ever, appears  to  act  like  the  motion  of  the  bow  of  a  violin  in  exciting 
another  sound  :  this  sound,  although  faint,  is  still  sufficiently  musical,  and 
appears  to  be  determined  by  the  magnitude  of  the  cavity  of  the  mouth, 
nearly  in  the  same  manner  as  that  of  the  humming  top,  or  as  the  sound  of 
the  same  cavity  produced  in  whistling,  by  a  current  of  air  which  is  forced 
through  it.  (Plate  XXVI.  Fig.  363... 367.) 

In  mixed  wind  instruments,  the  vibrations  or  alternations  of  solid  bodies 
are  made  to  cooperate  with  the  vibrations  of  a  given  portion  of  air.  Thus, 
in  the  trumpet,  and  in  horns  of  various  kinds,  the  force  of  inflation,  and 
perhaps  the  degree  of  tension  of  the  lips,  determines  the  number  of  parts 
into  which  the  tube  is  divided,  and  the  harmonic  which  is  produced.  In 
the  serpent,  the  lips  cooperate  with  a  tube,  of  which  the  effective  length  may 
be  varied  by  opening  or  shutting  holes,  and  the  instrument  which  has  been 
called  an  organized  trumpet  appears  to  act  in  a  similar  manner  ;  the  trom- 
bone has  a  tube  which  slides  in  and  out  at  pleasure,  and  changes  the  actual 
length  of  the  whole  instrument.  The  hautboy  and  clarinet  have  mouth- 
pieces of  different  forms,  made  of  reeds  or  canes  ;  and  the  reed  pipes  of  an 
organ,  of  various  constructions,  are  furnished  with  an  elastic  plate  of  metal, 
which  vibrates  in  unison  with  the  column  of  air  that  they  contain.  An 
organ  generally  consists  of  a  number  of  different  series  of  such  pipes,  se, 
arranged,  that  by  means  of  registers  the  air  proceeding  from  the  bellows 
may  be  admitted  to  supply  each  series,  or  excluded  from  it,  at  pleasure,  and 


1 


/  ON  MUSICAL  INSTRUMENTS.  315 


is  ope£*!a,  when  the  proper  key  is  touched,  which  causes  all  the  pipes 
*  belon^in^to  the  note,  in  those  series  of  which  the  registers  are  open,  to 
sound  at  once.  These  pipes  are  not  only  such  as  are  in  unison,  but  fre- 
quently also  one  or  more  octaves  above  and  below  the  principal  note,  and 
sometimes  also  twelfths  and  seventeenths,  imitating  the  series  of  natural 
harmonics.  But  these  subordinate  sounds  ought  to  be  comparatively  faint, 
otherwise  their  irregular  interference  would  often  occasion  an  intolerable 
discord,  instead  of  the  grand  and  sublime  effect  which  this  instrument  is 
capable  of  producing,  when  it  is  judiciously  constructed  and  skilfully 
employed.  (Plate  XXVI.  Fig.  368.) 

The  practice  of  music  appears  to  be  of  earlier  origin  than  either  its 
theory,  or  any  attention  to  the  nature  and  general  phenomena  of  sound. 
The  first  lyre,  with  three  strings,  is  said  to  have  been  invented  in  Egypt 
by  Hermes,  under  Osiris,  between  the  years  1800  and  1500  before  Christ  ;* 
but  a  tradition  so  remote,  concerning  a  personage  so  enveloped  in  fable, 
can  scarcely  be  considered  as  constituting  historical  evidence  :  we  cannot, 
therefore,  expect  to  ascertain  with  any  certainty  the  proportions  of  these 
strings  to  each  other ;  some  suppose  that  they  were  successive  notes  of  the 
natural  scale,  others  that  they  contained  the  most  perfect  concords  ; 
perhaps  in  reality  each  performer  adjusted  them  in  the  manner  which  best 
suited  his  own  fancy.  The  trumpet  is  said  to  have  been  employed  about  the 
same  time  ;  its  natural  harmonics  might  easily  have  furnished  notes  for  the 
extension  of  the  scale  of  the  lyre,  but  it  does  not  appear  that  the  ancients 
ever  adopted  this  method  of  regulating  the  scale.  The  lyre  with  seven 
strings  is  attributed  to  Terpander,t  about  700  years  before  our  era,  and 
two  centuries  afterwards,  either  Pythagoras,  or  Simonides,  completed  the 
octave,  which  consisted  of  intervals  differing  very  little  from  the  modern 
scale,  the  key  note  being  nearly  in  the  middle  of  the  series.  {  In  subse- 
quent times  the  number  of  the  strings  was  much  increased  ;§  the  modula- 
tions, and  the  relations  of  the  intervals,  became  very  intricate,  and  were 
greatly  diversified  in  a  variety  of  modes  or  scales,  which  must  have  afforded 
an  inexhaustible  supply  of  original  and  striking  melodies,  but  which  could 
scarcely  admit  so  many  pleasing  combinations  as  our  more  modern 
systems.  Although  it  is  certain  that  the  ancients  had  frequent  accom- 
paniments in  perfect  harmony  with  the  principal  part,  yet  they  had  no 
regular  art  of  counterpoint,  or  of  performing  different  melodies  together ; 
nor  does  it  appear  that  they  ever  employed  discords.  The  tibia  of  the 
ancients  resembled  a  hautboy  or  clarinet,  for  it  had  a  reed  mouth  piece, 
about  three  inches  long  ;  the  same  performer  generally  played  on  two  of 
these  instruments  at  once.  There  were,  however,  several  varieties  of  the 
tibia  ;  and  it  is  not  improbable  that  some  of  them  may  have  had  the  simple 
mouth  piece  of  the  flageolet. 

The  first  philosophical  observer  of  the  phenomena  of  sound,  after  Pytha- 
goras, appears  to  have  been  Aristotle  ;  he  notices  a  great  variety  of  curious 
facts  in  harmonics  among  his  mechanical  problems ;  and  he  entertained  a 

'  *  Rollin's  History  of  the  Arts  and  Sciences  (trans.),  4  vols.  8vo,  Lond.  1737. 
f  Ibid.  i.  156.  J  Jamblichus,  Vita  Pythag. 

§  See  Aristophanes,  Nubes. 


316  .       LECTURE  XXXIV. 

very  correct  idea  of  the  true  nature  of  the  motions  of  the\^r  constituti^ 
sound.  He  knew  that  a  pipe  or  a  cord  of  a  double  length  p"r^duT;ed  >  a 
sound  of  which  the  vibrations  occupied  a  double  time  ;  and  that  the  pro- 
perties of  concords  depended  on  the  proportions  of  the  times  occupied  by 
the  vibrations  of  the  separate  sounds.  It  is  not  indeed  improbable  that  at 
least  as  much  as  this  was  known  to  Pythagoras,  since  he  established  cor- 
rectly the  numerical  ratios  between  various  sounds ;  but  so  little  justice  has 
been  done  to  his  discoveries  by  the  imperfect  accounts  of  them  which  have 
been  preserved,  that  we  cannot  expect  to  be  able  to  ascertain  his  opinions 
on  any  subject  with  accuracy.  t 

The  invention  of  the  organ,  by  Ctesibius  of  Alexandria,  about  2000 
years  ago,  forms  a  remarkable  epoch  in  harmonics.  The  larger  instruments 
of  this  kind  were  furnished  with  hydraulic  bellows,  the  smaller  with 
bellows  of  leather  only  ;  and  they  had  keys  which  were  depressed,  like 
those  of  the  modern  organs,  by  the  fingers  of  the  performer,  and  which 
opened  valves  communicating  with  the  pipes. 

The  modern  system  of  music  is  one  of  the  few  sciences,  if  such  it  can 
be  called,  which  owe  their  improvement  to  the  middle  ages.  The  old 
ecclesiastical  music  was  probably  founded  in  great  measure  on  that  of  the 
Greeks  ;  its  peculiar  character  consisted  in  the  adoption  of  any  note  of  the 
scale  at  pleasure  for  a  key  note,  without  altering  materially  the  other 
intervals  ;  and  in  this  manner  they  obtained  a  variety  much  resembling 
that  of  the  modes  or  kinds  of  music  in  use  among  the  ancients.  Pope 
Gregory,  about  the  year  600,  distinguished  the  notes  by  literal  characters  ; 
the  rules  of  counterpoint  were  formed  by  degrees  from  the  experience 
of  the  ecclesiastical  musicians ;  and  early  in  the  eleventh  century,  Guido 
of  Arezzo,  otherwise  called  Aretin  the  monk,  introduced,  together  with 
some  improvements  in  the  theory  and  practice  of  music,  a  new  method  of 
naming  the  notes  by  syllables. 

Some  curious  experiments  on  sound  may  be  found  in  the  works  of 
Bacon,  but  they  added  very  little  to  the  true  theory  of  acustics,  and  some 
of  them  are  not  perfectly  accurate.  Galileo*  rediscovered  what  was  well 
known  to  Aristotle,  respecting  the  nature  of  sound  ;  for  the  words  of  Ari- 
stotle had  been  so  much  misunderstood  and  misinterpreted,  that  he  could 
have  profited  but  little  by  them.  His  cotemporaries  Mersennet  and 
Kircher^  made  a  variety  of  very  ingenious  experiments  and  observations, 
on  sound  and  on  sounding  bodies,  many  of  them  unknown  to  authors  of 
later  date.  The  theory  of  the  ancient  music  was  very  accurately  investi- 
gated, in  the  middle  of  the  17th  century,  by  Meibomius  :  §  our  countryman 
Wallis,  also,  besides  employing  much  learning  and  penetration  in  the  illus- 
tration of  the  ancient  music,  observed  some  insulated  facts  in  harmonics 
which  were  new  and  interesting.  || 

Sir  Isaac  Newton's  propositions^  respecting  the  velocity  of  the  pro- 
pagation of  sound  were  the  beginning  of  all  the  more  accurate  inves- 

*  Op.  iii.  58.  t  Harmonicorum  Liber,  Par.  1635. 

+  Musurgia,  2vols.  fol.  Rom.  1650.     Phonurgia,  fol.  1673.  , 

§  Musicse  Antiq.  Scrip.  Meibomii,  2  vols.  4to,  Amst.  1652. 

II   Opera,  vol.  iii.  and  Cl.  Ptolemsei  Op.  a  Wallis,  4  to,  Oxf.  1682. 

11  Principia,  lib.  ii.  Prop.  46,  &c. 


J 


ON  MUSICAL  INSTRUMENTS.  317 


tiga\ions  j<^atingto  acustics.  It  must  not  be  denied  that  these  propositions 
contain  some  very  inconclusive  reasoning  respecting  the  nature  of  the 
motions  constituting  sound,  hy  which  the  determination  of  a  particular 
case  is  erroneously  extended  into  a  general  solution  of  the  problem.  The 
velocity  is,  however,  truly  calculated,  because  it  is  in  fact  independent  of 
the  particular  nature  of  the  vibration,  and  all  that  is  wanting  to  generalise 
the  proposition  is  the  remark,  that  if  the  velocity  of  sound  is  the  same  in 
all  cases,  it  must  be  such  as  the  calculation  indicates.  An  error  nearly 
similar  was  committed  by  Brook  Taylor,*  who  in  the  year  1714  investi- 
gated the  time  occupied  by  the  vibration  of  a  string  or  cord  upon  a 
particular  supposition,  which  he  considered  as  a  necessary  condition,  but 
which  in  fact  confined  the  inquiry  to  a  limited  case.  It  happens,  however, 
that  the  same  determination  of  the  frequency  of  vibration  is  equally  true 
in  all  possible  cases.  Sauveur  obtained,  about  the  same  time,  a  similar  con- 
clusion from  reasoning  still  less  accurate :  his  merits  with  respect  to  the 
theory  of  acustics  in  general  are,  however,  by  no  means  contemptible. 
Lagranget  and  Euler^  have  corrected  and  much  extended  the  investi- 
gations of  Newton,  and  of  Taylor,  and  Bernoulli§  and  Dalembert||  have 
also  materially  contributed  to  the  complete  examination  and  discussion  of 
the  subject. 

About  the  year  1750,  Daniel  Bernoulli  succeeded  in  obtaining  a  solution 
of  a  problem  still  more  difficult  than  those  which  relate  to  the  motions  of 
cords :  he  determined  the  frequency  of  the  vibrations  of  an  elastic  rod 
fixed  at  one  end,  as  well  as  the  relations  of  its  subordinate  sounds.  The 
solution  is  not  indeed  absolutely  general,  but  it  may  perhaps  be  adapted  to 
all  possible  cases,  by  considering  the  effect  of  a  combination  of  various 
sounds  produced  at  the  same  time.  Euler  has  also  great  merit  in  extend- 
ing and  facilitating  the  mathematical  part  of  this  investigation,  although  he 
has  committed  several  mistakes  respecting  the  mechanical  application  of  it, 
some  of  which  he  has  himself  corrected,  and  others  have  been  noticed  by 
Riccati  and  Chladni. 

The  grave  harmonics  produced  by  the  combination  of  two  acute  sounds 
were  noticed  about  the  same  time  by  Romieu  and  by  Tartini,  but  first  by 
Romieu  :  ^[  their  existence  is  not  only  remarkable  in  itself,  but  particularly 
as  it  leads  to  some  interesting  consequences  respecting  the  nature  of  sound 
and  hearing  in  general. 

Bernoulli  has  also  investigated,  in  a  very  ingenious  manner,  the  sounds 
produced  by  the  air  in  pipes  of  various  forms,  although  confessedly  on 
suppositions  deviating  in  some  measure  from  the  truth :  the  results  of  his 

•  *  De  Motu  Nervi  Tensi,  Ph.  Tr.  1713,  xxviii.  26.  Methodus  Incrementorum, 
Lond.  1715.  t  Mel.  de  Turin,  i.  ii.  &  UL 

J  Hist,  et  Mem.  de  Berlin,  1748,  1753,  1759,  p.  185,  &c. ;  1765,  p.  355.  Nov. 
Com.  Petr.  ix.  xvii.  xix.  ActaPetr.  1779,  p.  2;  1780,  p.  2;  1781,  p.  1.  Mel.  de 
Turin,  vol.  iii.  §  See  Lect.  XXXI. 

||  Hist,  et  Mem.  de  Berlin,  1747,  1750, 1753,  1763.     Opuscula,  i.  &  iv. 

IT  Mem.  de  1'Acad.  de  Montpellier,  1751.  See  Tartini,  Trattato  diMusica,  Pad. 
1754;  and  Mercadier  de  Belesta,  Systeme  de  Musique,  Paris,  1776;  or  Matthew 
Young's  Enquiry  into  the  principal  Phenomena  of  Musical  Strings,  Dublin,  1784, 
p.  2,  sect.  vi.  The  existence  of  the  grave  harmonic  was  first  noticed  by  Sorge, 
Anweisung  zur  Stimmung  der  Orgelwerke,  &c.  Hamburg,  1744. 


318  LECTURE  XXXIV.  V 

computations  have,  however,  been  amply  confirmed  by  the  expt^Jmen^pl  4 
Lambert*  on  the  sounds  of  flutes.  '" 

Dr.  Chladni's  method  of  examining  the  sounds  of  plates  has  afforded  a 
very  interesting  addition  to  our  knowledge  of  the  nature  of  vibrations  ;  his 
discovery  of  the  longitudinal  sounds  of  solids  is  of  considerable  importance, 
and  he  is  said  to  be  engaged  in  an  extensive  work  on  the  subject  of  acustics 
in  general.t  Some  remarks  which  I  have  made  in  the  Philosophical  Trans- 
actions may  perhaps  also  be  considered  as  tending  to  illustrate  the  vi- 
brations of  cords.  The  latest  improvement  which  deserves  to  be  mentioned, 
with  respect  to  the  theory  of  sound,  is  Laplace's  explanation  of  the  increase 
of  its  velocity  on  account  of  the  effect  of  heat,  which  appears  to  afford  a 
satisfactory  explanation  of  a  difficulty  so  much  the  more  important,  as  it 
tended  to  lessen  our  confidence  in  every  part  of  a  theory,  which  differed  so 
widely  from  the  most  accurate  and  best  established  observations. 


1. 


LECT.  XXXIV.— ADDITIONAL  AUTHORITIES. 

Musical  Instruments. — Sauveur  on  the  Composition  of  Organ  Pipes,  Hist,  et 
Me*m.  de  Paris,  1702,  p.  308,  H.  90.  Carre,  ibid.  1702,  H.  136.  Weber,  Poggen- 
dorf's  Annalen,  xvi.  xvii.  193.  Savart,  Mem.  surla  Construction  des  Instrumens  a 
Cordes,  &c.  Paris,  1819. 

Human  Voice.— Dodart,  Hist,  et  Mem.  1700,  p.  244,  H.  17  ;  1706,  pp.  136,  388  ; 
1707,  p.  66,  H.  18.  Ferrein,  ibid.  1741,  p.  409,  H.51.  Vicq  d'Azyr,  ibid.  1779, 
p.  178,  H.  5.  Liscovius,  Theorie  der  Stimme,  Leipz.  1814.  Savart,  Annales  de 
Chimie,  xxx.  64,  &c.  Biot,  Precis  Elementaire  de  Physique,  1824.  Fechner's 
German  Trans,  of  do.  Chladni,  Gilbert's  Ann.  Ixxvi.  187.  Mayer,  Meckel's 
Archiv,  1826.  Willis  on  the  Mechanism  of  the  Human  Larynx,  Tr.  Camb.  Ph.  Soc. 
iv.  323.  Bennati,  Recherches  sur  la  Mechanisme  de  la  Voix  Humaine,  Paris,  1832. 
Sir  C.  Bell,  Ph.  Tr.  1832.  Muncke  in  Gehler's  Physik  Worterbuch,  viii.  373. 
Rush,  The  Philosophy  of  the  Human  Voice,  Philadelphia,  1833.  Malgaigne,  Archiv. 
Gen.  de  Med.  25.  Lauth,  Mem.  de  1'Acad.  Royale  de  Me"d.  1835.  Lehfeldt,  Dis. 
de  Vocis  Formatione,  Berol.  1835.  Bishop,  Ph.  Mag.  1836.  Mayer,  Outlines  of 
Physiology,  1837.  Miiller's  Handbuch  der  Physiol.  ii.  179,  English  translation, 
1838,  p.  1002. 

Voice  of  Birds. — Duvernay,  Hist,  et  Mem.  ii.  4.  Herissant,  ibid.  1753,  p.  279, 
H.  107.  Parsons,  Ph.  Tr.  1766,  p.  204.  Barrington,  ibid.  1773,  p.  249.  Dau- 
benton,  Hist,  et  Mem.  1781,  p.  369,  H.  12.  Cuvier,  Bulletin  de  la  Societe  Philo- 
mat.  No.  15.  Le9ons  d'Anatomie  Comparee,  torn.  iv.  lee.  28.  Latham,  Trans,  of 
the  Linnaean  Soc.  Savart,  Annales  de  Chimie,  xxx.  64,  and  Froriep's  Not.  331. 

History. — Dodart  on  Ancient  and  Modern  Music,  Hist,  et  Mem.  1706,  p.  388. 
Pepusch  on  the  Genera  and  Species  of  Music  among  the  Ancients,  Ph.  Tr.  1746, 
p.  266.  Styles  on  do.  ibid.  1760,  p.  695.  Hawkins's  History  of  Music,  5  vols.  4to, 
1776.  Burney's  Hist,  of  Music,  4  vols.  4to,  1789.  Forkel,  Allgemeine  Litteratur 
der  Musik,  Leipz.  1792.  Jones,  Asiatic  Researches,  iii.  55.  Busby's  Hist,  of 
Music,  2  vols.  1819. 

*  Observations  sur  les  Flutes,  Mem.  de  Berlin,  1775. 
f  The  work  is  Traite  d'Acoustique,  Paris,  1809. 


ON  MUSICAL  INSTRUMENTS. 


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LECTURE    XXXV. 


ON  THE  THEORY  OF  OPTICS. 

THE  science  of  optics  is  one  of  the  most  elegant,  and  the  most  important 
branches  of  natural  and  mechanical  philosophy.  It  presents  us  with 
experiments  attractive  by  their  beauty  and  variety,  with  investigations 
affording  an  ample  scope  for  mathematical  refinements,  and  with  instru- 
ments of  extensive  utility  both  in  the  pursuit  of  other  sciences,  and  in 
the  common  employments  of  life  ;  nor  is  there  any  department  of  the 
study  of  nature  in  which  an  unprejudiced  observer  is  more  convincingly 
impressed  with  the  characteristic  marks  of  the  perfect  works  of  a  supremely 
intelligent  Artist. 

We  shall  first  consider  the  essential  properties  which  we  discover  in 
light,  and  which  are  the  basis  of  our  calculations,  together  with  the  con- 
clusions immediately  deducible  from  those-  properties  ;  and  next,  the  ap- 
plication of  these  laws  to  practical  purposes,  in  the  construction  of  optical 
instruments.  We  shall  afterwards  proceed  to  examine  the  more  compli- 
cated phenomena,  which  are  derived  from  the  same  laws,  and  which  are 
observed  as  well  in  natural  as  in  artificial  circumstances,  constituting  the 
subdivision  of  physical  optics.  The  description  of  the  eye,  and  the  ex- 
planation of  the  sense  of  vision,  by  means  of  which  all  these  effects  are 
connected  with  the  human  mind,  is  properly  a  continuation  of  the  subject 
of  physical  optics  :  the  intimate  nature  of  light  will  be  the  next  subject 
of  investigation,  and  a  historical  sketch  of  the  progress  of  the  science  of 
optics  will  conclude  the  second  part  of  this  course  of  lectures. 

In  order  to  avoid  all  hypothesis  in  the  beginning,  it  will  be  necessary  to 
define  light  from  its  sensible  qualities.  The  sensation  of  light  is  sometimes 
produced  by  external  pressure  on  the  eye  ;  we  must  exclude  this  sensation 
from  the  definition  of  light,  and  must  therefore  call  light  an  influence 
capable  of  entering  the  eye,  and  of  affecting  it  with  a  sense  of  vision.  A 
body,  from  which  this  influence  appears  to  originate,  is  called  a  luminous 
body.  We  do  not  include  in  this  definition  of  the  term  light  the  invisible 
influences  which  occasion  heat  only,  or  blacken  the  salts  of  silver,  although 
they  both  appear  to  differ  from  light  in  no  other  respects  than  as  one  kind 
of  light  differs  from  another ;  and  they  might  probably  have  served  the 
purpose  of  light,  if  our  organs  had  been  differently  constituted. 

A  ray  of  light  is  considered  as  an  infinitely  narrow  portion  of  a  stream 
of  light,  and  a  pencil  as  a  small  detached  stream,  composed  of  a  collection 
of  such  rays  accompanying  each  other.  As  a  mathematical  line  is  some- 
times conceived  to  be  described  by  the  motion  of  a  mathematical  point,  so 
a  ray  of  light  may  be  imagined  to  be  described  by  the  motion  of  a  point 
of  light.  We  cannot  exhibit  to  the  senses  a  single  mathematical  lino, 
except  as  the  boundary  of  two  surfaces  ;  in  the  same  manner,  we  cannot 


ON  THE  THEORY  OF  OPTICS.  321 

?-vliibit  a  single-  ray  of  light,  except  as  the  confine  between  light  and  dark- 
nesspor  as  the  lateral  limit  of  a  pencil  of  light. 

When  light  passes  through  a  space  free  from  all  material  substances,  it 
moves,  with  great  velocity,  in  a  direction  perfectly  rectilinear  ;  when  also 
it  passes  through  a  material  substance  perfectly  uniform  in  its  structure, 
it  probably  always  moves  in  a  similar  manner.  But  in  many  cases  its 
motions  are  much  interrupted.  Those  substances  through  which  light 
passes  the  most  freely,  and  in  straight  lines,  are  called  homogeneous  trans- 
parent mediums.  Perhaps  no  medium  is,  strictly  speaking,  absolutely 
transparent ;  for  even  in  the  air,  a  considerable  portion  of  light  is  inter- 
cepted.* It  has  been  estimated  that  of  the  horizontal  sunbeams,  passing 
through  about  200  miles  of  air,  one  two  thousandth  part  only  reaches  us  ; 
and  that  no  sensible  light  can  penetrate  more  than  700  feet  deep  into  the 
sea  ;  a  length  of  seven  feet  of  water  having  been  found  to  intercept  one 
half  of  the  light  which  enters  it. 

It  is  possible  that  mediums,  not  in  other  respects  identical,  may  be 
homogeneous  with  respect  to  the  transmission  of  light ;  for  example,  a 
glass  may  be  filled  with  a  fluid  of  such  a  density,  that  the  light  may  pass 
uninterruptedly  through  their  common  surface  ;  but  it  generally  happens, 
that  whenever  the  nature  of  the  medium  is  changed,  the  path  of  light 
deviates  from  a  straight  line  ;  thus,  the  apparent  places  of  the  sun  and 
stars  are  changed  by  the  effect  of  the  atmosphere,  because  the  light,  by 
which  we  judge  of  their  situations,  is  deflected,  in  its  passage  out  of  the 
empty  space  beyond  the  atmosphere,  first  into  the  rarer  and  then  into  the 
denser  air.  In  the  same  manner,  when  we  view  a  distant  object  over  a 
fire  or  a  chimney,  it  appears  to  dance  and  quiver,  because  the  rays  of  light, 
by  which  it  is  seen,  are  perpetually  thrown  into  new  situations,  by  the 
different  changes  of  the  density  of  the  air  in  consequence  of  the  action 
of  heat. 

When  rays  of  light  arrive  at  a  surface  which  is  the  boundary  of  two 
mediums  not  homogeneous,  they  continue  their  progress  without  deviating 
from  those  planes  in  which  their  former  paths  lay,  and  which  are  perpen- 
dicular to  the  surface  of  the  mediums  ;  but  they  no  longer  retain  the  same 
direction,  a  part  of  them,  and  sometimes  nearly  the  whole,  is  reflected  back 
from  the  surface,  while  the  remaining  part  is  transmitted  and  refracted, 
or  bent.  The  name  refraction  is  derived  from  the  distortion  which  it 
occasions  in  the  appearance  of  an  object  viewed  in  part  only  by  refracted 
light :  thus  an  oar,  partially  immersed  in  water,  appears  to  be  bent,  on 
account  of  the  refraction  of  the  light  by  which  its  lower  part  is  seen,  in  its 
passage  out  of  the  water  into  the  air. 

There  is  no  instance  of  an  abrupt  change  of  the  density  of  a  medium, 
without  a  partial  reflection  of  the  light,  passing  either  into  the  denser  or 
into  the  rarer  medium ;  and  the  more  obliquely  the  light  falls  on  the 
surface,  the  greater,  in  general,  is  the  reflected  portion.  No  body  is  so 

*  Consult  Bouguer,  Traite  d'Optique  sur  la  Gradation  de  la  Lumiere,  4to,  Par. 
17£0.  Herschel's  Description  of  an  Actinometer,  Ed.  Jour,  of  Sci.  iii.  107. 
Pouillet,  Mem.  sur  la  Chaleur  Solaire,  Comptes  Rendus,  July  9,  1838.  Forbes  on 
the  Extinction  of  the  Solar  Rays  in  passing  through  the  Atmosphere,  Ph.  Tr.  1842, 
p.  225. 

y 


322  LECTURE  XXXV. 

black  as  to  reflect  no  light  at  all,  and  to  be  perfectly  invisible  in  a  strou^, 
light ;  although  at  the  surface  separating  two  very  rare  bodies,  ffs  two 
kinds  of  gas,  the  reflection  is  too  faint  to  be  perceptible ;  but  in  this  case 
the  separation  is  seldom  perfectly  abrupt. 

The  angles  of  incidence  and  reflection  are  the  angles  made  by  a  ray  of 
light,  before  and  after  its  reflection,  with  a  line  perpendicular  to  the  re- 
flecting surface ;  and  these  angles  are  always  equal  to  each  other ;  conse- 
quently the  inclination  of  the  rays  to  the  surface  remains  also  the  same. 
The  quantity  of  light  reflected,  when  other  circumstances  are  equal, 
appears  to  be  always  greatest  when  the  difference  of  the  optical  or  refrac- 
tive density  of  the  two  substances  is  greatest.  Thus  the  reflection  from 
the  common  surface  of  glass  and  water  is  much  weaker  than  from  a  surface 
of  glass  exposed  to  the  air.  Metals  in  general  reflect  a  great  proportion 
of  the  light  falling  on  them,  and  even  the  reflection  from  the  common 
surface  of  glass  and  mercury  appears  to  be  but  little  weaker  than  the 
reflection  from  the  surface  of  mercury  immediately  exposed  to  the  air,  so 
that  the  optical  density  of  the  metals  must  be  exceedingly  great. 

It  appears  also  that  a  portion  of  the  light  falling  on  a  reflecting  surface 
is  always  transmitted,  at  least  to  a  certain  depth,  notwithstanding  the 
apparent  opacity  of  any  large  masses  of  the  substance.  Thus,  if  we  cover 
a  small  hole  of  a  window  shutter  with  the  thinnest  leaf  gold,  we  shall  find 
that  it  transmits  a  greenish  light,  which  must  have  passed  the  reflecting 
surface,  but  which,  if  the  gold  had  been  but  one  ten  thousandth  of  an  inch 
in  thickness,  would  have  been  wholly  intercepted,  and  probably  almost  in 
the  same  manner  as  by  passing  through  700  feet  of  water.  In  transparent 
substances,  however,  the  greater  part  of  the  light  penetrates  to  all  distances 
with  little  interruption,  and  all  rays  of  the  same  kind,  thus  transmitted  by 
the  same  surface,  form  with  the  perpendicular  an  angle  of  refraction  which 
is  ultimately  in  a  certain  constant  proportion  to  the  angle  of  incidence  ; 
that  is,  for  instance,  one  half,  three  fourths,  or  two  thirds,  according  to  the 
nature  of  the  surface.  Thus,  if  the  refractive  properties  of  the  substance 
were  such,  that  an  incident  ray,  making  an  angle  of  one  degree  with  the 
perpendicular,  would  be  so  refracted  as  to  make  an  angle  of  only  half  a 
degree  with  the  same  line,  another  ray,  incident  at  an  angle  of  two  degrees, 
would  be  refracted,  without  sensible  error,  into  an  angle  of  one  degree.  But 
when  the  angles  are  larger,  they  vary  from  this  ratio,  their  sines  only  pre- 
serving the  proportion  with  accuracy :  for  example,  if  the  angle  of  inci- 
dence at  the  supposed  surface  were  increased  to  90°,  the  angle  of  refraction 
would  be  30°  only,  instead  of  45°.  Rays  of  the  same  kind  are  in  general 
distinguished  by  the  same  colour,  although  some  rays  which  differ  from 
each  other  in  refrangibility,  have  scarcely  a  discernible  difference  of  colour  ; 
and  it  is  possible,  on  the  other  hand,  to  find  a  surface  at  which  the  ratio  of 
the  angles  is  the  same  for  rays  of  all  kinds.  (Plate  XXVI.  Fig.  369,  370.) 
In  order  to  obtain  the  effects  of  regular  reflection  and  transmission,  we 
must  have  perfectly  smooth  and  polished  substances ;  for  all  rough  bodies, 
and  sometimes  even  such  as  to  the  touch  seem  tolerably  smooth,  have  their 
surfaces  divided  into  innumerable  eminences  and  depressions,  constituting, 
in  reality,  as  many  separate  surfaces,  disposed  in  all  imaginable  directions, 


,     ON  THE  THEORY  OF  OPTICS.  323 

co  that  from  the  equality  of  the  angles  of  incidence  and  reflection  with 
resp'&At  to  each  of  these  surfaces,  the  light  must  be  scattered  every  way, 
and  no  regularity  can  be  observed  in  its  direction.  It  is  true  that  by  con- 
tinuing the  mechanical  operation  of  polishing,  we  only  render  these  sur- 
faces more  minute  and  more  numerous  ;  but  when  they  are  so  much 
reduced  in  magnitude  as  not  to  be  elevated  or  depressed  more  than  about 
the  millionth  part  of  an  inch,  they  appear  to  become,  for  some  physical 
reason,  incapable  of  acting  separately,  and  only  to  conspire  in  the  general 
effect. 

In*  all  cases  of  refraction,  as  well  as  of  reflection,  if  the  ray  of  light 
return  directly  backwards  in  the  same  line  to  the  surface,  it  would  proceed, 
after  a  second  refraction  or  reflection,  in  the  direction  precisely  opposite 
to  that  in  which  it  first  was  incident,  so  that  the  same  lines  would  mark  its 
path  in  both  cases.  Thus,  if  we  stand  before  a  looking  glass,  with  one  eye 
shut,  and  cover  its  place  on  the  glass  with  a  finger,  the  same  finger  will 
hide  the  other  eye  as  soon  as  it  is  shut  and  the  first  is  opened  in  its  place ; 
and  a  similar  effect  might  be  observed  if  the  glass  were  under  water,  or 
behind  any  other  refracting  substance.  (Plate  XXVI.  Fig.  371.) 

The  medium,  in  which  the  rays  of  light  are  caused  to  approach  nearest 
to  the  line  perpendicular  to  its  surface,  is  said  to  have  the  greatest  refrac- 
tive density.  In  general  there  is  a  considerable  analogy  between  this 
refractive  density  and  the  specific  gravity  of  the  substance :  thus  water  is 
more  refractive  than  air,  and  glass  than  water.  But  inflammable  bodies 
are  usually  more  refractive  than  bodies  of  the  same  specific  gravity,  which 
are  not  inflammable ;  and  it  is  well  known  that  from  the  high  refractive 
power  of  the  diamond,  in  proportion  to  its  actual  density,  Sir  Isaac  New- 
ton most  ingeniously  conjectured  that  it  was  combustible,  as  more  modern 
experiments  have  actually  shown  it  to  be.  It  is  still  more  singular  that 
he  also  imagined,  from  the  same  analogy,  that  water  consists  of  a  combi- 
nation of  oily  or  inflammable  particles,  with  others  earthy  or  not  inflam- 
mable. In  the  order  of  refractive  density,  beginning  from  the  lowest,  or  a 
vacuum,  we  have  airs  and  gases  of  different  rarities,  water,  which  is  the 
least  refractive  of  all  liquids,  and  which  is  still  less  refractive  when  frozen 
into  ice  :  alcohol,  oils,  glass,  and  lastly  the  diamond  ;  but  probably  some 
metallic  substances  are  much  more  refractive  than  even  the  diamond. 

The  refractive  powers  of  different  substances,  are  usually  estimated  by  a 
comparison  of  the  refractions  produced  at  their  surfaces  in  contact  with 
the  air,  which,  in  all  common  experiments,  has  the  same  sensible  effect  as 
a  vacuum  or  an  empty  space  ;  the  ratio  of  the  angles  of  refraction  and  inci- 
dence, when  small,  and  that  of  their  sines,  in  all  cases,  being  expressed  by 
the  ratio  of  1  to  a  certain  number,  which  is  called  the  index  of  the  refrac- 
tive density  of  the  medium.  Thus,  when  a  ray  of  light  passes  out  of  air 
into  water,  the  sines  of  the  angles  are  in  the  ratio  of  3  to  4,  or  of  1  to  £, 
which  is,  therefore,  the  index  of  the  refractive  density  of  water.  In  the 
same  manner,  for  crown  glass,  the  ratio  is  that  of  2  to  3,  and  the  index 
l^  ;  but  for  flint  glass  it  is  somewhat  greater,  the  ratio  being  nearly  that 
of  5  to  8. 

It  may  easily  be  shown  that  a  refractive  substance,  limited  by  parallel 

Y2 


324  LECTURE  XXXV. 

surfaces,  must  transmit  a  ray  of  light,  after  a  second  refraction  at  its  pos-. 
terior  surface,  in  a  direction  parallel  to  that  in  which  it  first  passed  through 
the  air.  It  is  also  found  by  experiment  that  such  a  substance,  interposed: 
between  any  two  mediums  of  different  kinds,  produces  no  alteration  in  the 
whole  angular  deviation  of  a  ray  passing  from  one  of  them  into  the  'other. 
Hence  it  may  be  inferred,  that  the  index  of  refraction  at  the  common  sur- 
face of  any  two  mediums  is  the  quotient  of  their  respective  indices.  For 
instance,  a  plate  of  crown  glass  being  interposed  between  water  on  one  side 
and  air  on  the  other,  it  produces  no  change  in  the  direction  of  a  ray  of  light 
entering  the  water  ;  and  the  index  of  refraction  at  the  common  surfe^e  of 
glass  and  water  is  -£.  (Plate  XXVI.  Fig.  372,  373.) 

There  is  one  remarkable  consequence  of  the  general  law  by  which  the 
angles  of  incidence  and  refraction  are  related,  that  when  the  angle  of  inci- 
dence exceeds  a  certain  magnitude,  the  refraction  may  become  impossible  ; 
and  in  this  case  the  ray  of  light  is  wholly  reflected,  in  an  angle  equal  to 
the  angle  of  incidence.  Thus,  if  the  law  of  refraction  required  the  sine  of 
the  angle  of  refraction  to  be  twice  as  great  as  that  of  incidence,  this  con- 
dition could  not  take  place  if  the  angle  of  incidence  were  greater  than  30°, 
so  that  when  a  ray  passing  within  a  dense  medium  falls  very  obliquely  on 
its  surface,  it  must  be  wholly  reflected  ;  and  the  greater  the  density  of  the 
medium,  the  more  frequently  will  the  light  be  totally  reflected.  This  re- 
flection is  more  perfect  than  any  other  ;  the  diamond  owes  much  of  its 
brilliancy  to  it :  the  great  refractive  density  of  this  substance  not  only 
giving  a  lustre  to  its  anterior  surface,  but  also  facilitating  the  total  reflec- 
tion of  such  rays  as  fall  obliquely  on  its  posterior  surface.  If  we  hold  a 
prism  near  a  window,  in  a  proper  position,  we  may  observe  that  its  lower 
surface  appears  to  be  divided  into  two  parts,  the  one  much  brighter  than 
the  other  ;  the  common  partial  reflection  taking  place  in  one,  and  the  total 
reflection  in  the  other.  The  two  surfaces  are  separated  by  a  coloured  arch : 
it  is  coloured,  because  the  total  reflection  commences  at  different  angles  for 
the  rays  of  different  colours  ;  and  it  is  curved,  because  the  points,  at  which 
the  light  passing  to  the  eye  forms  a  given  angle  with  the  surface,  do  not  lie 
in  a  straight  line  ;  and  if  we  throw  a  light  on  a  wall  by  a  reflection  of  this 
kind,  we  may  easily  observe,  as  we  turn  the  prism,  the  point  at  which  the 
brightness  of  the  image  is  very  conspicuously  increased.  (Plate  XXVI. 
Fig.  374.) 

Such  are  the  principal  properties  which  we  discover  in  light.  Before  we 
consider  their  immediate  application  to  optical  instruments,  we  must  ex- 
amine the  general  theory  of  refraction  and  reflection  at  surfaces  of  dif- 
ferent kinds,  or  the  doctrines  of  dioptrics  and  catoptrics. 

The  rays,,  which  constitute  a  pencil  of  light,  are  sometimes  parallel  to 
each  other,  sometimes  divergent  from  a  point,  and  sometimes  convergent  to 
a  point.  The  intersection  of  the  directions  of  any  two  or  more  rays  of  light 
is  called  their  focus  ;  and  the  focus  is  either  actual  or  virtual,  accordingly 
as  they  either  meet  in  it,  or  only  tend  to  or  from  it.  Thus,  a  small  luminous 
object  may  represent  an  actual  focus  of  diverging  rays,  since  the  light 
spreads  from  it  in  all  directions;  and  the  small  surface  into  which  the 
image  of  such  an  object,  or  of  the  sun,  is  collected  by  a  lens  or  mirror, 


ON  THE  THEORY  OF  OPTICS.  325 

lua'j  ^represent  the  actual  focus  of  converging  rays.  It  was  to  such  an 
image  of  the  sun  that  the  term  focus,  meaning  a  fire  place,  was  first  applied. 
But  if  the  rays  tending  to  this  focus  be  intercepted  and  made  to  diverge,  the 
point  will  then  be  their  virtual  focus,  since  they  will  never  actually  arrive 
at  it,  being  made  to  diverge  as  if  they  proceeded  from  a  new  point,  which 
will  also  be  a  virtual  focus.  When  the  divergence  or  convergence  of  rays 
of  light  is  altered  by  refraction  or  reflection  at  any  surface,  the  foci  of  the 
incident  and  refracted  or  reflected  rays  are  called  conjugate  to  each  other : 
the  ^ew  focus  is  also  called  the  image  of  the  former  focus.  Thus,  in  the 
case  already  mentioned,  where  the  convergence  of  the  rays  to  one  focus  is 
converted  into  divergence  from  another,  the  two  virtual  foci  are  conjugate 
to  each  other ;  and  the  original  focus  of  the  lens  or  mirror  is  conjugate  to 
the  place  of  the  sun,  or  of  the  luminous  object.  If  the  object  had  been  put 
in  the  place  of  its  image,  the  image  would  then  have  occupied  that  of  the 
ohject ;  a  property  which  follows  from  the  direct  return  of  every  ray  of 
light  through  the  path  by  which  it  has  arrived,  and  which  may  easily  be 
illustrated  by  experimental  confirmation.  (Plate  XXVII.  Fig.  375.) 

Whenever  light  is  reflected  by  a  plane  surface,  the  conjugate  foci  are  at 
equal  distances  from  it,  and  in  the  same  perpendicular.  Thus,  every  point 
of  an  image  in  a  looking  glass  is  perpendicularly  opposite  to  the  correspond- 
ing point  of  the  object,  and  is  at  the  same  distance  behind  the  looking  glass 
as  the  point  of  the  object  is  before  it.  (Plate  XXVII.  Fig.  376.) 

The  focus  into  which  parallel  rays  are  collected,  or  from  which  they  are 
made  to  diverge,  is  called  the  principal  focus  of  a  surface  or  substance. 
The  sun  is  so  distant,  that  the  rays  proceeding  from  any  point  of  his  sur- 
face, affect  our  senses  as  if  they  were  perfectly  parallel,  and  the  principal 
focal  distance  of  a  surface  or  substance  may  often  be  practically  determined 
by  measuring  the  distance  of  the  image  of  the  sun  or  of  any  other  remote 
object,  which  is  formed  by  it. 

In  order  that  the  rays  of  light,  proceeding  from  or  towards  any  one 
point,  may  be  made  to  converge  by  reflection  towards  another,  the  form 
of  the  surface  must  be  elliptical,  parabolic,  or  hyperbolic  ;  there  are  also 
curves  of  still  more  intricate  forms,  which  possess  the  same  property  with 
respect  to  refraction.  A  small  portion,  however,  of  any  of  these  curves, 
differs  very  little  from  a  circle  ;  and  a  spherical  surface  is  almost  universally 
substituted  in  practice  for  all  of  them,  except  that  the  mirrors  of  large 
reflecting  telescopes  are  sometimes  made  parabolical. 

The  principal  focus  of  a  spherical  reflecting  surface,  whether  convex  or 
concave,  is  half  way  between  the  surface  and  its  centre.  If  a  luminous 
point  be  placed  in  the  centre  of  a  concave  mirror,  the  rays  will  all  return 
to  the  same  point ;  if  the  point  be  beyond  the  centre,  the  image  will  be 
between  the  centre  and  the  principal  focus,  its  distance  from  that  focus 
being  always  inversely  as  that  of  the  radiant  point.  Such  a  focus  is  never 
absolutely  perfect,  for  the  rays  are  never  collected  from,  the  whole  surface 
of  the  mirror  into  the  same  point,  except  when  both  the  point  and  its  image 
are  in  the  centre :  but,  provided  that  the  surface  be  only  a  small  portion 
of  that  of  the  whole  sphere,  the  aberration  will  be  too  small  to  be  easily 


32G  LECTURE  XXXV. 

observed  :  and  the  same  is  true  of  the  foci  produced  by  refracting  sur£*ces. 
(Plate  XXVII.  Fig.  377,  378.) 

When  a  ray  of  light  passes  through  two  surfaces  forming  an  angle  with 
each  other,  including  a  denser  medium,  as  in  the  case  of  a  prism  of  'glass, 
it  is  always  deflected  from  the  angle  in  which  the  two  surfaces  meet.  A 
greater  number  of  surfaces,  placed  in  different  directions,  constitute  what 
is  sometimes  called  a  multiplying  glass,  each  of  them  bending  the  rays  of 
light  into  a  different  direction.  (Plate  XXVII.  Fig.  379,  380.) 

A  lens  is  a  detached  portion  of  a  transparent  substance,  of  whic^  the 
opposite  sides  are  regular  polished  surfaces,  of  such  forms  as  may  be 
described  by  lines  revolving  round  a  common  axis.  These  lines  may  be 
portions  of  circles,  of  ellipses,  hyperbolas,  or  of  any  other  curves,  or  they 
may  be  right  lines.  But  in  general,  one  of  the  sides  is  a  portion  of  a 
spherical  surface,  and  the  other  either  a  portion  of  a  spherical  surface  or 
a  plane ;  whence  we  have  double  convex,  double  concave,  planoconvex, 
planoconcave,  and  meniscus  lenses.  The  figures  of  all  these  are  suffi- 
ciently described  by  their  names,  except  that  the  term  meniscus,  which 
properly  implies  a  little  moon  or  crescent,  is  applied  in  general  to  all  lenses 
which  are  convex  on  the  one  side  and  concave  on  the  other,  although  they 
may  be  thicker  at  the  edges  than  in  the  middle.  Sometimes,  however,  a 
lens  of  this  kind  is  distinguished  by  the  term  concavoconvex.  A  lens  is 
generally  supposed,  in  simple  calculations,  to  be  infinitely  thin,  and  to  be 
denser  than  the  surrounding  medium.  (Plate  XXVII.  Fig.  381.) 

The  general  effect  of  a  lens  may  be  understood,  from  conceiving  its  sur- 
face to  coincide  at  any  given  point  with  that  of  a  prism ;  for  if  the  angle 
of  the  prism  be  external,  as  it  must  be  when  the  lens  is  convex,  the  rays 
will  be  inflected  towards  the  axis  ;  but  if  the  base  of  the  prism  be  external, 
and  the  lens  concave,  the  rays  will  be  deflected  from  the  axis :  so  that  a 
convex  lens  either  causes  all  rays  to  converge,  or  lessens  their  divergence, 
and  a  concave  lens  either  causes  them  to  diverge,  or  lessens  their  conver- 
gence. (Plate  XXVII.  Fig.  382.) 

The  principal  focus  of  a  double  convex  or  double  concave  lens,  of  crown 
glass,  is  at  the  distance  of  the  common  radius  of  its  surfaces  ;  and  the  focal 
length  of  a  planoconvex  lens  is  equal  to  the  diameter  of  the  convex  surface. 
If  the  radii  of  the  surfaces  are  unequal,  their  effect  will  be  the  same  as  if 
they  were  each  equal  to  the  harmonic  mean  between  them,  which  is  found 
by  dividing  the  product  by  half  the  sum  ;  or,  in  the  meniscus,  by  half  the 
difference.  Thus,  if  one  of  the  radii  were  two  inches,  and  the  other  six,  the 
effect  would  be  the  same  as  that  of  a  lens  of  three  inches  radius  ;  and  if  it 
were  a  meniscus,  the  same  as  that  of  a  lens  of  six  inches.  (Plate  XXVII. 
Fig.  383,  384.) 

The  focal  length  of  a  lens  of  flint  glass,  of  water,  or  of  any  other  sub- 
stance, may  be  found,  by  dividing  that  of  an  equal  lens  of  crown  glass  by 
twice  the  excess  of  the  index  of  refraction  above  unity.  Thus,  the  index 
for  water  being  1£,  we  must  divide  the  radius  by  f,  or  increase  it  one  half, 
for  the  principal  focal  distance  of  a  double  convex  or  double  concave  lens 
of  water. 


I 

ON  THE  THEORY  OF  OPTICS.  327 

\yiien  a  radiant  point  is  at  twice  the  distance  of  the  principal  focus 
'  from  fc  convex  lens,  the  image  is  at  an  equal  distance  on  the  other  side  ; 
when  the  radiant  point  is  nearer  than  this,  the  image  is  more  remote,  the 
distance  of  the  image  from  the  principal  focus  nearest  to  it  being  always 
inversely  as  the  distance  of  the  object  from  the  principal  focus  on  the 
opposite  side.  (Plate  XXVII.  Fig.  385.) 

The  joint  focus  of  two  lenses,  in  contact  with  each  other,  is  also  found  by 
multiplying  together  their  separate  focal  lengths,  and  dividing  the  product 
by  their  sum  or  difference,  accordingly  as  they  agree  or  differ  with  respect 
to  convexity  and  concavity. 

We  have  hitherto  considered  the  place  of  the  focus  only  in  relation  to  a 
single  point,  placed  in  the  axis  of  the  lens  or  mirror ;  but  it  is  equally 
necessary  to  attend  to  other  points,  out  of  the  principal  axis  ;  for  in  order 
to  form  a  picture,  the  rays  from  a  great  number  of  such  points  must  be 
collected  into  as  many  distinct  points  of  the  image.  Some  of  the  rays 
proceeding  from  every  radiant  point  must  be  considerably  bent,  in  order  to 
be  collected  into  a  common  focus ;  others  remain  nearly  straight ;  and  if 
we  can  discover  which  of  the  rays  are  ultimately  either  in  the  same  line 
with  their  original  direction,  or  in  a  direction  parallel  to  it,  we  may 
determine  the  line  in  which  the  image  of  the  point  in  question  is  to  be 
found.  For  this  purpose  we  employ  the  property  of  the  optical  centre, 
which  is  a  point  so  situated,  that  all  rays  which  pass  through  it,  or  tend 
towards  it,  while  they  are  within  the  lens,  must  ultimately  acquire  a  direc- 
tion parallel  to  their  original  direction.  In  some  cases,  the  optical  centre 
may  be  without  the  lens,  but  no  practical  inconvenience  results  from 
supposing  it  to  be  always  situated  within  the  lens,  especially  when  its 
thickness  is  inconsiderable  ;  so  that  all  rays  which  pass  through  the  middle 
point  of  the  lens  must  proceed,  without  sensible  error,  in  the  same  straight 
line,  and  the  image  of  any  radiant  point  must  consequently  be  found  some- 
where in  this  line  :  but  in  the  case  of  a  mirror,  the  centre  of  its  figure  is 
also  the  optical  centre.  Now  when  any  radiant  point  is  removed  a  little 
from  the  axis  of  a  lens  or  mirror,  the  distance  of  its  image  is  in  general  a 
little  diminished,  but  the  difference  is  too  small  to  be  observable  in  common 
cases.  We  may,  therefore,  suppose  it  to  be  at  the  same  distance  as  if  the 
point  remained  in  the  axis,  or  even  to  be  in  a  plane  crossing  the  axis 
perpendicularly  at  that  distance,  so  as  to  form  part  of  a  flat  image,  of 
which  the  magnitude  is  determined  by  straight  lines  drawn  from  the  ex- 
tremities of  the  object  through  the  centre  of  the  lens.  This  is,  however,  an 
approximation  which  is  only  admitted  for  the  greater  convenience  of  com- 
putation and  representation,  the  image  being  almost  always  in  reality 
considerably  curved.  (Plate  XXVII.  Fig.  386.) 


LECT.  XXXV.— ADDITIONAL  AUTHORITIES. 

,  Optics  in  general. — Euclidis  Optica,  4to,  Paris,  1557.  Faulhaber,  Descriptio 
Inst.  Geom.  et  Opt.  4to,  Frankf.  1610.  Kepler,  Dioptrice,  4to,  Augsb.  1611. 
Aquilo,  Op.  Autw,  1613.  Schneider  de  Luce,  1616.  Mathise  Buchholdii  Lucis 
Contemp.  4 to,  1630.  Descartes,  Dioptrique,  1637.  Bwllialdus  de  Natura  Lucis, 


328  LECTURE  XXXVI. 

fcl.  Par.  1638.  Zucchius,  2  vols.  4to,  Lugd.  1652-6.  Thomasius,  4to,  l/)53. 
Lichtner,  4to,  1653,  and  4to,  1654.  Balthasar,  4to,  1656.  Mancini,  Bolog.*1660. 
De  la  Chambre,  La  Lumiere,  Paris,  1662.  Vossius  de  Nat.  Lucis,  4to,  Amst.  1662. 
Kohlhausen,  Lips.  1663.  Grandorgeeus,  4to,  Cad.  1664.  Fabri,  Synopsis  Optica, 
Lyon,  1667.  Saggi  del  Acad.  di  Cimento,  1667.  Cherubin,  Dioptrique,  fol.  Paris, 
1671.  Kirchmaier  de  Luce,  Misc.  Acad.  Nat.  Cur.  1677,  App.  p.  219.  '  Moly- 
neux,  Dioptrica  Nova,  4to,  Lond.  1694.  Hartsoeker,  Essai  de  Diop.  4to,  Par. 
1694.  Gregorii  (D.)  Catop.  et  Diop.  Oxf.  1695.  Huygens,  Op.  Post.  Lugd.  1704. 
Craig<  Optica  Analytica,  1708.  Rizetti  de  Luminis  Affectionibus,  Ven.  1727. 
Smith's  Optics,  4to,  Camb.  1738.  (German  by  Kastner,  Altenb.  1775.)  Euler, 
Dioptrica,  3  vols.  4to,  Petrop.  Martin's  Optics,  1750.  Courtivron,  Traite,  Paris, 
1752.  LacaiUe,  1756.  Deincken,  Alt.  1757.  Bischoff,  Ulm,  1760  &  1772.  Al- 
garotti  (trans.},  The  Philosophy  of  Sir  I.  Newton  explained  in  Six  Dial,  on  Light, 
12mo,  Glasg.  1765.  Thomin's  Traite  d'  Op.  Paris,  1769.  Harris's  Optics,  4to, 
1775.  Scherfer,  4  vols.  4to,  Vindob.  1775.  Biirja,  Berlin,  1793.  Karstens, 
Lehr.  derMathem.  Theil  viii.  Rampinellius,  Optique,  Brix.  1760.  Emerson's  Op- 
tics, 1768.  Ferguson's,  1770.  Stack's,  Dub.  1811.  Settele,  Elem.  di  Ottica,  2  vols. 
Rom.  1818-19.  Nobili,  Milan,  1820.  Maseres,  Scriptores  Optici,  4to,  Lond. 
1823.  Bourgeois,  Manuel  d'Optique  Experimental,  2  vols.  12mo.  1823.  Brew- 
ster's  Optics,  Edin.  Encyc.,  Cab.  Cyc.,  and  Encyc.  Brit.  Herschel's,  Encyc.  Me- 
tropolit.  (complete  and  good),  Transl.  in  French  by  Verhulst,  with  Supplement  by 
Quetelet,  3  vols.  1826.  Amondieu,  Lehr.  der  Optik,  Leipz.  1827.  Rottger,  Halle, 
1828.  Prechtl.  Wien,  1829.  Higgins,  Lond.  1829.  Coddington  on  Reflection 
and  Refraction,  Camb.  1829.  Littrow,  Dioptrik,  Wien,  1830.  Wood's  Optics,  Camb. 
v.  y.  Lloyd  on  Light,  1831.  Powell's  Optics,  Oxf.  1833.  Schmidt,  Gott.  1834. 
Johnson's  Optical  Investigations,  Oxf.  1835.  Phelps's  Optics,  Camb.  1835.  Grif- 
fin's, Camb.  1840.  Bartlett's,  New  York,  1841. 


LECTURE   XXXVI. 


ON  OPTICAL  INSTRUMENTS. 

AMONG  the  great  variety  of  instruments  depending  on  optical  principles, 
it  is  most  consistent  with  our  plan  to  attend  first  to  those  which  may  be 
denominated  optical  measures,  which  are  calculated  either  for  the  determi- 
nation of  the  quantity  or  intensity  of  light  itself,  or  for  the  examination  of 
the  properties  of  various  material  substances  with  respect  to  light.  Reflect- 
ing quadrants  and  circles,  which  are  often  used  in  astronomical  and 
nautical  observations,  although  they  derive  their  utility  in  some  measure 
from  optical  laws,  may  most  properly  be  considered  as  belonging  to  the 
subject  of  practical  astronomy. 

It  is  a  problem  of  frequent  occurrence  in  economical  investigations,  to 
compare  the  intensity  of  the  light  afforded  by  any  two  luminous  objects. 
For  this  purpose  it  is  necessary  to  assume  as  a  principle,  that  the  same 
quantity  of  light,  diverging  in  all  directions  from  a  luminous  body,  remains 
undiminished  at  all  distances  from  the  centre  of  divergence.  Thus,  we 
must  suppose  that  the  quantity  of  light  falling  on  every  body  is  the  same 
as  would  have  fallen  on  the  place  occupied  by  its  shadow  :  and  if  there 
were  any  doubt  of  the  truth  of  the  supposition,  it  might  be  confirmed  by 
some  simple  experiments.  It  follows  that  since  the  shadow  of  a  square 


ON  OPTICAL  INSTRUMENTS.  329 

inch  of  any  surface,  occupies,  at  twice  the  distance  of  the  surface  from  the 
luminous  point,  the  space  of  four  square  inches,  the  intensity  of  the  light 
diminishes  as  the  square  of  the  distance  increases.  We  can  judge  with 
tolerable  accuracy  of  the  equality  of  two  lights  by  the  estimation  of  the 
eye,  but  we  cannot  form  any  idea  of  the  proportions  of  lights  of  different 
intensities  :  if,  however,  we  remove  two  sources  of  light  to  such  distances 
from  an  object,  that  they  may  illuminate  it  in  equal  degrees,  we  may  con- 
clude that  their  original  intensities  are  inversely  as  the  squares  of  their 
distances.  Count  Rumford's  *  photometer  performs  this  very  conveniently, 
by  casting  two  shadows  of  a  given  object  near  each  other,  on  the  same 
surface,  the  lights  being  removed  to  such  distances  that  the  shadows 
appear  equally  dark.  (Plate  XXVII.  Fig.  387,  388.) 

For  determining  the  refractive  density  of  solids,  it  has  been  usual  to  form 
them  into  a  prism,  and  to  measure  the  angular  deviations  which  they 
produce  ;  and  for  fluids,  to  inclose  them  either  in  a  hollow  prism,  or  between 
two  meniscus  lenses,  and  to  measure  the  angular  deviations  produced  by 
the  prisms,  and  the  focal  distances  of  the  lenses.  But  in  most  cases,  Drv 
Wollaston's  apparatus t  is  far  preferable  to  both  these  methods:  it  is 
arranged  for  ascertaining  the  angle  at  which  light,  moving  within  a  certain 
dense  transparent  substance,  begins  to  be  totally  reflected  from  the  common 
surface  of  that  substance  and  the  solid  or  fluid  which  is  to  be  examined.  Thus, 
if  we  first  measure  the  angle  at  which  light  begins  to  be  totally  reflected 
from  the  posterior  surface  of  a  prism  of  glass,  in  contact  with  air,  we  may 
readily  determine  its  refractive  power ;  and  then,  having  caused  a  drop  of 
a  fluid  to  adhere  to  that  surface,  or  fixed  a  solid  to  it  by  a  small  portion  of 
some  fluid  denser  than  itself,  we  may  observe,  as  we  turn  the  prism  round 
its  axis,  at  what  angle  the  drop  or  spot  begins  to  disappear,  and  may  thence 
calculate  the  refractive  density  of  the  substance  ;  and  even  without  actual 
measurement  of  the  angle,  we  may  readily  compare  the  disappearance  of 
the  drop  or  spot  with  that  of  others  placed  near  it,  of  which  the  properties 
are  known.  Dr.  Wollaston  has,  however,  rendered  the  process  still  easier 
and  more  simple,  by  employing  a  rectangular  prism  of  glass,  with  sights 
fixed  to  a  jointed  frame,  of  such  a  construction  as  to  enable  him  to  read  off, 
by  a  vernier,  without  any  calculation,  the  index  of  the  refractive  power  of 
any  substance  less  dense  than  glass.  (Plate  XXVII.  Fig.  389.) 

All  instruments  strictly  optical  are  employed  for  forming  an  image  of  an 
external  object :  the  simplest  are  mirrors  and  lenses,  which  form  a  single 
image  only,  either  actual  or  virtual,  and  sometimes  depict  it  on  a  surface 
calculated  for  receiving  and  exhibiting  it.  Other  instruments  repeat  the 
image  once  or  more  under  several  forms,  in  general  enlarging  it  con- 
tinually ;  and  these  are  either  microscopes  or  telescopes,  which  present  us 
with  great  diversity  in  their  arrangements,  and  in  the  appurtenances  sub- 
servient to  their  uses. 

It  is  a  general  rule,  that  when  an  image  of  an  actual  object  is  formed  by 

any  lens  or  speculum,  if  the  rays  converge  to  an  actual  focus,  the  image  is 

inverted  ;  but  erect,  if  they  diverge  from  a  virtual  focus,  and  the  object 

and  image  subtend  equal  angles  at  the  centre  of  the  lens  or  speculum. 

*  Ph.  Tr.  1794,  Ixxxiv.  67,  f  Ibid.  1802,  p.  365. 


330  LECTURE  XXXVI. 

Hence,  a  convex  lens  and  a  concave  mirror  form  an  inverted  image, 
smaller  than  the  object,  whenever  the  object  is  at  a  greater  distance  than, 
twice  the  principal  focal  length ;  but  larger,  when  the  object  is  within  this 
distance  ;  and  when  it  is  within  the  principal  focal  distance,  the  magnified 
image  is  virtual  and  erect,  and  may  be  seen  by  looking  into  the  concave 
mirror,  or  by  looking  through  the  lens  towards  the  object.  But  a  concave 
lens  and  a  convex  mirror  always  form  a  virtual  image  of  a  real  object, 
which  is  erect  and  smaller  than  the  object.  (Plate  XXVII.  Fig.  390... 
394.) 

When  the  object  is  precisely  in  the  principal  focus  of  a  convex  lens'br  a 
concave  mirror,  the  virtual  image  becomes  infinitely  distant ;  so  that  from 
whatever  point  in  the  neighbourhood  of  the  lens  it  may  be  viewed,  it  must 
subtend  the  same  angle,  which  is  always  equal  to  that  which  the  object 
subtends  at  the  centre  of  the  lens  :  and  since  this  angle  may  easily  be 
much  greater  than  that  under  which  the  object  can  be  conveniently  viewed 
by  the  naked  eye,  such  a  lens  or  mirror  is  often  used  as  a  simple  micro- 
scope ;  and  its  magnifying  power  may  be  ascertained  from  a  comparison 
of  the  angles  which  the  object  and  image  subtend.  Thus,  if  a  person 
cannot  see  a  minute  object  with  the  naked  eye  at  a  distance  less  than  eight 
inches,  a  lens  of  half  an  inch  focal  length  will  represent  it  to  him  in  an 
angle  16  times  as  great :  but  if  he  can  see  it  without  the  lens  at  the  dis- 
tance of  four  inches,  the  lens  will  magnify  it  to  his  eye  but  eight  times. 
Supposing,  however,  the  eye  to  be  applied  close  to  the  lens,  the  object  may 
be  viewed  a  little  within  the  focal  distance,  and  its  apparent  angular  mag- 
nitude may  be  increased  17  times  instead  of  16,  and  9  times  instead  of  8. 
(Plate  XXVII.  Fig.  395,  396.) 

Since  the  magnifying  power  of  a  lens  is  the  greater,  the  smaller  its 
focus,  it  is  usual  to  employ  the  minutest  lenses  that  can  be  ground,  and 
sometimes  a  small  globule  is  formed  by  fusion  in  a  lamp.  Even  a  drop  of 
water,  placed  in  the  perforation  of  a  plate,  makes  a  tolerable  magnifier ; 
and  it  has  been  proposed  to  substitute  for  water  a  transparent  varnish, 
which  is  less  liable  to  evaporate. 

Supposing  the  whole  light  that  proceeds  from  a  distant  object,  and  falls 
on  a  lens  or  speculum,  to  be  collected  in  the  image,  its  intensity  must  be 
increased  in  the  ratio  of  the  surface  of  the  lens  or  speculum  to  that  of  the 
image.  The  image  is  greater  in  proportion  as  the  object  is  greater  ;  conse- 
quently the  degree  of  condensation  produced  by  any  lens  is  the  greater  as 
the  object  is  smaller,  thus  if  the  diameter  of  a  lens  were  an  inch,  and  the 
image  of  the  sun  formed  by  it  were  also  an  inch  in  diameter,  the  density  of 
the  light  would  be  unaltered  ;  but  the  image  of  a  star  would  be  infinitely 
brighter  than  the  direct  light  of  the  star  falling  on  the  lens.  The  illumina- 
tion of  any  image  formed  by  a  lens  or  mirror,  supposing  no  light  to  be 
lost,  is  always  the  same  as  would  be  produced  by  the  direct  light  of  the 
surface  of  the  lens  or  mirror,  if  it  were  equally  luminous  with  the  surface 
of  the  object  which  emits  the  light.  It  may  also  be  shown,  that  when  two 
lenses  are  of  similar  forms,  their  focal  lengths  being  proportional  to  their 
diameters,  they  must  produce  the  same  degree  of  illumination  in  the  image : 
but  as  far  as  the  heat  excited  may  be  supposed  to  be  a  measure  of  the 


ON  OPTICAL  INSTRUMENTS.  331 

quantity  of  light,  this  conclusion  is  not  confirmed  by  experiment :  it  is 
probable,  however,  that  the  greater  heat,  produced  by  a  larger  lens,  is  only 
derived  from  the  greater  extent  of  surface  exposed  at  once  to  the  solar 
rays. 

Lenses  are  most  commonly  made  of  glass,  but  sometimes  of  rock  crystal, 
or  of  other  transparent  substances.  It  is  difficult  to  find  glass,  especially 
flint  glass,  for  large  lenses,  sufficiently  free  from  veins :  it  has  been  pro- 
posed to  suffer  the  melted  glass  to  cool  without  agitation,  and  to  cut  the 
lens  out  of  any  of  its  strata  taken  in  a  horizontal  direction  ;  but  this  method 
appears  to  be  liable  to  several  practical  objections.  Mirrors  are  made  either 
of  glass,  coated  with  an  amalgam  of  mercury  and  tin,  or  of  metal,  as  of 
platina,  of  silver,  or  of  an  alloy  of  copper  and  tin,  to  which  a  little  arsenic 
and  silver  are  sometimes  added.  Mirrors  of  metal  are  more  perfect  than 
those  of  glass,  because  they  are  free  from  the  inconvenience  of  a  double  re- 
flection ;  but  they  are  more  expensive,  and  are  liable  to  tarnish.  Where  a 
large  mirror  is  required,  with  a  wreak  reflection  only,  we  may  employ  a 
single  surface  of  glass,  the  back  of  the  piece  being  covered  with  a  black 
coating  of  some  substance  differing  little  from  glass  in  its  refractive  density, 
by  means  of  -which  the  second  reflection  is  avoided.  Dr.  Wollaston  has 
very  ingeniously  applied  the  effect  of  the  reflection  of  two  plane  surfaces, 
inclined  to  each  other,  to  the  construction  of  an  instrument  for  drawing, 
which  he  calls  a  camera  lucida.*  He  usually  employs  the  internal  re- 
flection of  a  prism  of  glass,  of  which  the  four  surfaces  are  ground  so  as  to 
form  proper  angles  with  each  other.  The  image  formed  by  the  first  sur- 
face is  inverted,  and  the  second  reflection  restores  it  to  its  original  posi- 
tion, but  places  it  in  a  direction  which  is  at  right  angles  with  the  direction 
of  the  object ;  so  that  when  we  look  down  through  the  prism  on  a  sheet  of 
paper,  we  see  a  perfect  picture  of  the  objects  immediately  before  us,  while 
at  the  same  time,  the  aperture  through  which  we  look,  is  only  partly  occu- 
pied by  the  edge  of  the  prism,  the  remaining  part  being  left  open,  or  simply 
covered  with  a  lens,  for  the  admission  of  the  direct  rays  of  light  by  which 
we  may  see,  at  the  same  time,  the  paper  and  the  pencil  to  be  employed  for 
making  a  drawing  or  a  copy  of  any  object  placed  before  us. 

When  the  image  formed  by  a  lens  or  mirror  is  received  on  a  smooth  but 
unpolished  surface,  which  is  capable  of  irregular  reflection,  it  is  visible  in 
every  direction.  Such  an  image  is  exhibited  in  the  camera  obscura,  the 
solar  microscope,  and  the  magic  lantern,  or  lucernal  microscope. 

The  general  effect  of  the  camera  obscura  f  is  the  same  as  may  often  be 
observed  in  a  dark  room,  where  there  is  a  small  hole  in  the  window  shutter : 
the  great  masses  of  light  and  shade,  before  the  windows,  being  represented 
in  an  inverted  position,  in  the  parts  of  the  room  diametrically  opposite  to 
them,  which  are  illuminated  in  different  degrees,  according  to  the  quantity 

*  Nich.  Jour.  8vo,  xvii.  1.  Compare  Wren,  Ph.  Tr.  1669,  iv.  898.  Peacock, 
ibid.  Ixxv.  366.  Ramsden  and  Jones,  Phil.  Jour,  xxviii.  Brewster's  Account  of 
New  Phil.  Insts.  An  account  of  the  modifications  which  Prof.  Amici  has  effected  in 
\his  instrument  is  given  in  the  Edin.  Jour,  of  Sci.  v.  157.  Chevalier,  Notice  sur 
1'Usage  des  Chambres  Obscures  et  des  Chambres  Claires,  Par.  1829.  Ludicke, 
Gilb.  Ann.  xlii.  338. 

f  Invented  by  Baptista  Porta,  Magia  Naturalis,  p.  12,  Lug.  Bat.  1650. 


332  LECTURE  XXXVI. 

of  light  which  can  reach  them  in  straight  lines  from  the  external  objects. 
A  lens,  of  a  focal  length  somewhat  smaller  than  the  distance  of  the  surface 
on  which  the  picture  is  projected,  renders  the  images  much  more  distinct ; 
but  some  of  them  are  unavoidably  imperfect  and  ill  denned,  unless  the  ob- 
jects happen  to  be  situated  at  the  same  distance  from  the  aperture  ;  for  the 
focus  of  the  lens  can  never  be  adjusted  at  once  to  nearer  and  more  remote 
objects ;  nor  would  the  picture  be  rendered  more  natural  by  such  an 
adjustment,  for  it  would  present  to  the  eye  at  one  view,  with  equal  distinct- 
ness, objects  which  never  can  be  seen  at  once  without  some  degree  of  con- 
fusion. Sometimes  the  picture  is  intercepted,  by  a  speculum  placed  ob- 
liquely, and  is  thrown  upwards  on  the  surface  of  a  plate  of  ground  glass, 
upon  which  its  outline  may  be  traced  with  a  black  lead  pencil,  and  an  im- 
pression may  be  taken  from  it  on  moist  paper,  which  will  represent  the 
natural  situation  of  the  objects  without  inversion.  Another  arrangement 
is,  to  place  the  lens  horizontally,  with  a  speculum  above  it,  which  throws 
the  image  through  the  lens,  upon  a  flat  surface  placed  below,  on  which  the 
objects  may  be  delineated  in  their  natural  position,  but  not  without  some 
impediment  from  the  interception  of  the  light  by  the  hand  and  the  instru- 
ment employed.  Such  a  surface,  however,  ought  not  to  be  perfectly  flat, 
in  order  to  afford  the  most  distinct  image,  although  by  means  of  a  meniscus 
lens,  with  a  cover  admitting  the  light  only  through  a  small  aperture  near 
its  centre,  on  the  principle  of  Dr.  Wollaston's  periscopic  spectacles,*  an 
image  nearly  flat  might  be  obtained  ;  but  in  this  case  too  much  of  the  light 
would  be  excluded.  It  has  been  usual  to  consider  the  image  of  a  very  dis- 
tant object,  formed  by  a  convex  lens,  as  a  portion  of  a  spherical  surface  of 
which  every  part  is  equally  distant  from  the  centre  of  the  lens ;  but  this 
estimate  is  extremely  erroneous,  for  the  effect  of  the  obliquity  of  the 
different  pencils  of  rays  materially  increases  the  curvature  of  the  image. 
In  fact  no  pencil  of  rays,  falling  obliquely  on  a  spherical  surface,  can  be 
collected  any  where  to  a  perfect  focus  :  the  image  of  a  circle  would  become 
most  distinct  at  one  distance,  and  that  of  its  diameter  at  another ;  but  for 
both  these  images,  the  surface  ought  to  be  much  more  curved  than  that 
which  has  been  usually  considered,  and  the  mean  of  the  curvatures  re- 
quired for  them,  which  must  be  the  best  form  for  the  ground  or  bottom  of 
a  camera  obscura,  is  equal  to  that  of  a  sphere  of  which  the  radius  is  three 
eighths  of  the  focal  distance,  when  a  double  convex  lens  of  crown  glass  is 
employed.  (Plate  XXVIII.  Fig.  397. .  .399.) 

In  the  solar  microscope,  an  image  is  formed  on  a  wall  or  screen,  by 
means  of  a  lens  of  small  focal  length,  near  to  which  the  object  is  placed,  so 
that  the  image  is  very  much  magnified.  For  this  purpose  the  room  must 
be  darkened,  and  the  object  strongly  illuminated  by  the  sun's  light,  which 
is  condensed  by  means  of  a  large  lens,  and  sometimes  by  two  or  more  lenses 
placed  at  a  distance  from  each  other ;  but  care  must  be  taken  to  avoid 
burning  the  object  by  bringing  it  exactly  into  the  focus  ;  and,  on  the  other 
hand,  if  it  be  much  beyond  the  focus,  the  light  will  be  thrown  upon  a  small 
part  of  the  image  only ;  the  best  arrangement  appears  to  be,  to  bring  the* 
focus  of  the  condensing  lenses  very  near  to  the  small  lens  ;  and  in  order  to 
*  Nicli.  Jour.  vii.  143,  241. 


ON  OPTICAL  INSTRUMENTS.  333 

adjust  the  instrument  in  the  most  convenient  manner,  the  distances  of  all 
the  lenses  ought  to  he  moveahle  at  pleasure  :  the  want  of  this  precaution  is 
a  material  defect  in  the  usual  construction  of  the  instrument.  The  specu- 
lum which  first  receives  the  light  must  be  capable  of  motion  in  all  angular 
directions,  in  order  to  allow  us  to  accommodate  its  position  to  the  change- 
able place  of  the  sun  ;  and  the  adjustment  has  sometimes  been  performed 
by  means  of  a  heliostate,  an  instrument  calculated  for  turning  the  speculum 
by  clockwork,  into  such  a  position  as  always  to  reflect  the  sun's  light  in 
the  required  direction.  An  easier  method  would  be  to  employ  two  specu- 
lum^ the  one  moveable  round  an  axis  parallel  to  that  of  the  earth,  and  re- 
flecting the  sun's  light  into  the  direction  of  its  axis,  the  other  fixed,  and 
changing  this  direction  into  any  other  that  might  be  required.  When  an 
opaque  object  is  to  be  examined,  the  light  may  be  thrown  on  it  either  by  a 
plane  mirror  placed  obliquely,  or  by  a  perforated  concave  mirror ;  and  if 
the  object  is  small,  the  concave  mirror  appears  to  be  the  more  eligible. 
(Plate  XXVIII.  Fig.  400.) 

By  night,  a  lamp  with  a  large  lens  before  it,  may  supply  the  place  of 
the  sun's  light,  and  the  instrument  will  become  a  lucernal  microscope, 
which,  when  painted  glass  sliders  are  employed  as  objects  for  the  amuse- 
ment of  children,  is  called  a  magic  lantern  :  and  this,  exhibited  on  a 
larger  scale,  and  projecting  an  image  on  a  semitransparent  screen  of  taffetas, 
instead  of  a  wall,  has  of  late  been  the  source  of  much  entertainment  under 
the  name  of  the  phantasmagoria,  a  term  which  implies  the  raising  of 
spectres.  In  order  to  favour  the  deception,  the  sliders  are  made  perfectly 
opaque,  except  where  the  figures  are  introduced,  the  glass  being  covered, 
in  the  light  parts,  with  a  more  or  less  transparent  tint,  according  to  the 
effect  required.  Several  pieces  of  glass  may  also  be  occasionally  placed 
behind  each  other,  and  may  be  made  capable  of  such  motions  as  will  nearly 
imitate  the  natural  motions  of  the  objects  which  they  represent.  The 
figures  may  also  be  drawn  with  water  colours  on  thin  paper,  and  after- 
wards varnished.  By  removing  the  lantern  to  different  distances,  and 
altering  at  the  same  time  more  or  less  the  position  of  the  lens,  the  image 
may  be  made  to  increase  or  diminish,  and  to  become  more  or  less  distinct 
at  pleasure,  so  that  to  a  person  unaccustomed  to  the  effects  of  optical  in- 
struments, the  figures  may  appear  actually  to  advance  and  retire.  In 
reality,  however,  these  figures  become  much  brighter  as  they  are  rendered 
smaller,  while  in  nature  the  imperfect  transparency  of  the  air  causes  them 
to  appear  fainter  when  they  are  remote  than  when  they  are  near :  this 
imperfection  might  be  easily  remedied  by  the  interposition  of  some  semi- 
opaque  substance,  which  might  gradually  be  caused  to  admit  more  light  as 
the  figure  became  larger,  or  by  uncovering  a  larger  or  a  smaller  portion  of 
the  lamp,  or  of  its  lens.  Sometimes,  by  throwing  a  strong  light  upon  an 
actual  opaque  object,  or  on  a  living  person,  its  image  is  formed  on  the 
curtain,  retaining  its  natural  motions  :  but  in  this  case  the  object  must  be 
considerably  distant,  otherwise  the  images  of  its  nearer  and  remoter  parts 
will  never  be  sufficiently  distinct  at  once,  the  refraction  being  either  too 
great  for  the  remoter,  or  too  small  for  the  nearer  parts  :  and  there  must 
also  be  a  second  lens,  placed  at  a  sufficient  distance  from  the  first  to  allow 


834  LECTURE  XXXVI. 

an  inverted  image  to  be  formed  between  them,  and  to  throw  a  second 
picture  of  this  image  on  the  screen,  in  its  natural  erect  position,  unless  the 
object  be  of  such  a  nature  that  it  can  be  inverted  without  inconvenience. 
This  effect  was  very  well  exhibited  at  Paris  by  Robertson  ;  he  also  com- 
bined with  his  pictures  the  shadows  of  living  objects,  which  imitate  toler- 
ably well  the  appearance  of  such  objects  in  a  dark  night,  or  by  moonshine  : 
and  while  the  room  was  in  complete  darkness,  concealed  screens  were  pro- 
bably let  down  in  various  parts  of  it,  on  which  some  of  the  images  were 
projected  ;  for  they  were  sometimes  actually  situated  over  the  heads  of  the 
audience.  (Plate  XXVIII.  Fig.  401.)  r- 

In  almost  all  telescopes  and  compound  microscopes,  the  image  formed 
by  one  lens  or  mirror  stands  in  the  place  of  a  new  object  for  another. 
The  operation  of  such  instruments  may  be  illustrated  by  placing  a  screen 
of  fine  gauze  at  the  place  of  the  image,  which  receives  enough  light  to 
make  the  image  visible  in  all  directions,  and  yet  transmits  enough  to  form 
the  subsequent  image.  The  simplest  of  such  instruments  is  the  astrono- 
mical telescope.  Here  the  object  glass  first  forms  an  actual  inverted  image, 
nearly  in  the  principal  focus  of  the  eye  glass,  through  which  this  image  is 
viewed  as  by  a  simple  microscope,  and  therefore  still  remains  apparently 
inverted.  In  order  to  find  the  angular  magnifying  power,  we  must  divide 
the  focal  length  of  the  object  glass  by  that  of  the  eye  glass  :  this  quotient 
is  consequently  the  greater  as  the  focal  length  of  the  object  glass  is  greater, 
and  as  that  of  the  eye  glass  is  smaller :  but  the  power  of  the  instrument 
cannot  be  increased  at  pleasure  by  lessening  the  focal  length  of  the  eye 
glass,  because  the  object  glass  would  not  furnish  light  enough  to  render  the 
view  distinct,  if  the  magnifying  power  were  too  great.  (Plate  XXVIII. 
Fig.  402.) 

The  double  or  compound  microscope  resembles  in  its  construction  the 
astronomical  telescope,  except  that  the  distance  of  the  lenses  much  exceeds 
their  joint  focal  length;  and  the  angular  magnitude  is  greater  than  when 
the  same  object  is  viewed  through  the  eye  glass  alone,  in  proportion  as  the 
first  image  is  further  from  the  object  glass  than  the  object  itself.  (Plate 
XXVIII.  Fig.  403.) 

In  the  Galilean  telescope  or  opera  glass,  a  concave  eye  glass  is  placed  so 
near  the  object  glass  that  the  first  image  would  be  formed  beyond  it,  and 
near  its  principal  focus ;  and  the  second  image,  formed  by  the  eye  glass, 
which  is  the  virtual  image  viewed  by  the  eye,  being  on  the  opposite  side  of 
the  centre,  is  inverted  with  respect  to  the  first  image,  and  erect  with  respect 
to  the  object.  In  this  case  also  the  magnifying  power  is  indicated  by  the 
quotient  of  the  numbers  expressing  the  focal  lengths  of  the  glasses.  (Plate 
XXVIII.  Fig.  404.) 

The  inverted  image  of  the  astronomical  telescope  may  be  made  erect  by 
means  of  an  additional  eye  glass.  In  the  common  day  telescope  of  Rheita, 
two  such  eye  glasses  are  employed,  of  nearly  equal  focus,  which  have  the 
advantage  of  procuring  a  greater  extent  in  the  field  of  view  ;  they  are 
usually  so  placed  as  to  have  little  or  no  effect  on  the  magnifying  power. 
(Plate  XXVIII.  Fig.  405.) 

Dr.  Herschel's  reflecting  telescopes  resemble,  in  their  effects,  the  simple 


ON  OPTICAL  INSTRUMENTS.  335 

astronomical  telescope  ;  a  concave  speculum  or  mirror  being  substituted 
for  the  object  glass,  and  the  eye  glass  being  so  placed  as  to  magnify  the 
image  formed  by  the  speculum.  But  since  the  speculum,  if  it  received  the 
principal  rays  perpendicularly,  would  send  them  back  in  the  same  direc- 
tion, it  is  necessary,  in  this  construction,  to  have  them  reflected  somewhat 
obliquely,  the  speculum  being  a  little  inclined  to  the  axis  of  the  telescope, 
in  order  that  the  light  may  have  free  access  to  it.  An  arrangement  of  this 
kind  was  proposed  long  ago  by  Maire,*  but  it  has  been  very  little  employed 
before  Dr.  Herschel's  time.  This  excellent  philosopher  and  mechanic  has 
carried  the  perfection  of  his  telescopes  to  a  degree  far  exceeding  all  that 
could  have  been  expected  from  the  labours  of  former  opticians.  His  in- 
struments allow  him  to  extend  the  linear  dimensions  of  his  objects  several 
thousand  times  :  but  he  commonly  finds  it  more  eligible  to  employ  only 
powers  of  5  or  600,  which  afford  a  much  stronger  illumination.  (Plate 
XXVIII.  Fig.  406.) 

The  Newtonian  reflector  has  a  plane  speculum  placed  in  its  axis,  at  the 
inclination  of  half  a  right  angle,  which  intercepts  the  rays  about  to  form 
the  image,  and  throws  them  into  the  focus  of  an  eye  glass  fixed  in  the  side 
of  the  tube.  The  plane  speculum  which  he  employed  was  the  posterior 
surface  of  a  rectangular  prism  of  glass,  which  produces  a  total  reflection  : 
but  Dr.  Herschel  has  found  that  the  sources  of  error  are  diminished  by 
wholly  omitting  this  speculum.  (Plate  XXVIII.  Fig.  407.) 

In  the  Gregorian  telescope,  the  object  speculum  is  perforated,  and  the 
image  formed  by  it  is  received  into  the  focus  of  a  smaller  concave  speculum, 
which  returns  it  to  be  viewed  through  the  aperture  by  the  eye  glasses.  It 
has  been  objected  to  this  form  of  the  reflecting  telescope,  which  is  the  first 
that  was  invented,  that  the  best  part  of  the  speculum  is  sacrificed  by  the 
perforation.  But  Dr.  Herschel  has  found  that  the  image  formed  by  the 
external  part  of  a  speculum  is  in  general  more  perfect  than  that  which  is 
formed  by  the  central  part.  (Plate  XXVIII.  Fig.  408.) 

For  the  smaller  concave  speculum  of  Gregory,  Mr.  Cassegraint  substi- 
tuted a  convex  one,  placing  it  within  the  focal  distance  of  the  large  specu- 
lum, so  as  to  form  the  first  actual  image  nearly  in  the  same  place  as  the 
second  image  of  the  Gregorian  telescope  ;  but  this  image  is  inverted.  The 
instrument  has  some  advantage  in  theory,  with  respect  to  the  perfection  of 
the  focus  ;  but  it  is  little  used.  (Plate  XXVIII.  Fig.  409.) 

Dr.  Smith's  reflecting  microscope  resembles  Cassegrain's  telescope,  but 
the  rays  of  light  are  first  admitted  through  a  perforation  in  the  small 
speculum,  that  part  of  them  which  tends  to  fall  immediately  on  the  eye 
being  intercepted  by  a  screen.  The  convexity  of  the  one  mirror  is  nearly 
equal  to  the  concavity  of  the  other  ;  and  the  instrument,  although  seldom 
employed,  is  said  to  succeed  extremely  well.  (Plate  XXVIII.  Fig.  410.) 

The  image  of  a  very  distant  object,  formed  by  a  speculum  of  any  kind, 
is  considerably  less  curved  than  that  which  is  depicted  by  a  lens  of  equal 

*  Mach.  Approuv.  vi.  61.  Herschel  on  his  Forty-foot  Telescope,  Ph.  Tr.  1795, 
p.  347.  See  also  Herschel,  ibid.  1782,  p.  173;  1786,  p.  499;  1800,  p.  49;  1803, 
p. 214. 

t  Journal  des  Savans,  1672.     See  Newton,  Ph.  Tr.  1672,  p.  4056. 


336  LECTURE   XXXVI. 

focal  length.  There  is  a  similar  imperfection  in  the  nature  of  the  focus  of 
oblique  pencils,  but  it  is  confined  within  narrower  limits,  the  remotest  part 
of  the  image  in  which  any  radiating  lines  would  be  most  distinctly  repre- 
sented, being  a  flat  surface,  and  the  nearest,  in  which  circles  would  become 
most  distinct,  being  a  part  of  a  sphere  touching  the  speculum  :  so  that  the 
radius  of  the  mean  curvature  is  equal  to  the  focal  distance.  (Plate 
XXVIII.  Fig.  411.) 

The  magnifying  power  of  a  refracting  telescope  may  often  be  measured 
by  comparing  the  diameter  of  the  object  glass  with  that  of  the  narrowest 
space  into  which  the  beam  of  light  is  contracted  beyond  the  eye  glass,  pro- 
vided that  none  of  the  light  has  been  intercepted  in  its  passage  through  the 
telescope  :  for  the  object  will  be  viewed  through  the  telescope  in  an  angle 
as  much  greater  than  that  which  it  naturally  subtends,  as  the  diameter  of 
the  object  glass  is  greater  than  that  of  this  contracted  pencil,  which  may  be 
considered  as  an  image  of  the  object  glass.  But  in  the  Galilean  telescope 
this  method  cannot  be  employed,  since  no  such  image  is  formed.  The  field 
of  view  in  a  simple  telescope,  or  the  angular  magnitude  of  that  part  of  an 
object  which  can  be  seen  through  it  at  once,  is  nearly  equal  to  the  magni- 
tude of  the  eye  glass  as  seen  from  the  object  glass. 

If  a  lens  be  added  to  any  refracting  telescope  at  the  place  of  the  first 
image,  it  will  have  no  effect  either  on  the  place  or  on  the  magnitude  of  any 
subsequent  image,  but  it  will  enlarge  the  field  of  view,  by  throwing  more 
pencils  of  light  on  the  original  eye  glass.  If,  however,  the  image  fell 
exactly  on  such  a  lens,  it  would  be  liable  to  be  impaired  by  any  accidental 
impurities  of  its  substance  or  on  its  surface,  every  opaque  particle  inter- 
cepting the  whole  of  the  light  belonging  to  one  of  its  points,  which  would 
not  happen  if  the  image  were  at  a  small  distance  from  the  lens.  A  field 
glass  is,  therefore,  usually  placed,  both  in  telescopes,  and  in  the  common 
compound  microscope,  a  little  nearer  to  the  object  glass  than  the  place  of 
the  first  image.  The  best  places  for  the  various  lenses,  in  an  eye  piece, 
are  partly  determined  from  similar  considerations,  but  they  require  also  in 
general  to  be  adjusted  by  experiment,  for  several  circumstances  are  con- 
cerned in  the  performance  of  a  telescope,  which  are  almost  too  intricate  for 
practical  calculation,  although  some  assistance  may  certainly  be  obtained 
from  theory  with  regard  to  the  most  important  of  them.  The  curvature  of 
the  image  produced  by  any  lens  has  already  been  mentioned  :  it  may  be 
in  some  measure  remedied  by  Mr.  Ramsden's  method  of  placing  a  plano- 
convex lens  a  little  beyond  the  image,  with  its  flat  side  turned  towards  it. 
Mr.  Ramsden*  also  employs  an -eye  piece  constructed  on  this  principle  in- 
stead of  a  simple  microscope,  under  the  name  of  a  double  magnifier.  The 
aberration  of  the  different  parts  of  any  single  pencil  of  rays,  from  the  cor- 
responding point  of  the  image,  requires  also  to  be  considered  in  the  con- 
struction of  telescopes  :  its  magnitude  is  such,  in  the  case  of  a  double  convex 
lens  of  crown  glass,  that  those  parts  of  a  pencil  of  parallel  rays  which  fall 
on  it  near  the  circumference  meet  each  other  in  a  point,  which  is  within 
the  true  focus,  by  a  distance  a  little  more  than  half  as  great  again  as  the 
thickness  of  the  lens.  In  an  image  formed  by  a  concave  speculum  of  equal 
*  Ph.  Tr.  1783,  Ixxiii.  94. 


ON  OPTICAL  INSTRUMENTS.  337 

focal  length,  this  aberration  would  be  only  -^  as  great ;  it  may,  however, 
1  be  almost  entirely  corrected,  in  refracting  telescopes,  by  employing  proper 
proportions  in  the  dimensions  of  the  various  lenses.     (Plate  XXVIII.  Fig. 
412,  413.) 

A  still  more  important  aberration,  from  which  reflecting  telescopes  are 
also  wholly  free,  is  that  which  arises  from  the  different  refrangibilities  of 
the  rays  of  light  of  different  colours,  which  form  an  infinite  number  of 
images,  neither  agreeing  perfectly  in  situation  nor  in  magnitude,  so  that 
the  objects  are  rendered  indistinct  by  an  appearance  of  colours  at  their 
edgesrf  this  imperfection,  however,  Mr.  Dollond  has  in  great  measure 
obviated,  by  his  achromatic  object  glasses  :  *  the  construction  of  which  de- 
pends on  the  important  discovery,  that  some  kinds  of  glass  separate  the 
rays  of  different  colours  from  each  other  much  more  than  others,  while  the 
whole  deviation  produced  in  the  pencil  of  light  is  the  same.  Mr.  Dollond 
combined,  therefore,  a  concave  lens  of  flint  glass  with  a  convex  lens  of 
crown  glass,  and  sometimes  with  two  such  lenses  ;  the  concave  lens  of  flint 
glass  being  sufficiently  powerful  to  correct  the  whole  dispersion  of  coloured 
light  produced  by  the  crown  glass,  but  not  enough  to  destroy  the  effect  of 
its  refraction,  which  was  still  sufficient  to  collect  the  rays  of  light  into  a 
distant  focus.  For  this  purpose,  it  is  necessary  that  the  focal  lengths  of  the 
two  lenses  should  be  in  the  same  proportion  as  the  dispersive  powers  of  the 
respective  substances,  when  the  mean  deviations  of  the  pencils  are  equal ; 
that  is,  in  the  case  of  the  kinds  of  glass  commonly  used,  nearly  in  the  ratio 
of  7  to  10.  Sometimes  also  the  chromatic  aberration,  that  is,  the  error 
arising  from  the  different  refrangibilities  of  the  different  rays,  is  partially 
corrected  in  an  eye  piece,  by  placing  a  field  glass  in  such  a  manner  as  con- 
siderably to  contract  the  dimensions  of  the  image  formed  by  the  least 
refrangible  rays,  which  is  nearest  to  the  eye  glass,  and  to  cause  it  to  subtend 
an  equal  angle  with  the  image  formed  by  the  most  refrangible  rays, 
this  image  being  little  affected  by  the  glass.  (Plate  XXVIII.  Fig.  414, 
415.) 

The  apparent  magnitude  of  an  object  viewed  through  a  telescope,  may 
be  measured,  with  great  accuracy,  by  a  scale  or  by  wires,  introduced  at  the 
place  of  the  last  image,  reducing  afterwards  the  angle  thus  ascertained 
according  to  the  magnifying  power.  Care  must,  however,  be  taken  to 
avoid  as  much  as  possible  the  distortion  which  usually  accompanies  any 
curvature  of  the  image ;  and  the  wires,  one  of  which  is  sometimes  made 
moveable  by  means  of  a  micrometer  screw,  must  be  sufficiently  illuminated 
to  be  distinctly  visible.  Sometimes  a  scale  is  introduced,  which,  from  the 
apparent  magnitude  of  a  known  object,  such  as  that  of  a  man  of  ordinary 
height,  or  of  a  portion  of  a  wall  built  with  bricks  of  the  usual  size,  enables 
us  at  once  to  read  off  its  actual  distance,  which  is  expressed  on  the  scale  in 
hundreds  of  yards.  The  angular  magnitude  of  an  object  seen  through  a 
telescope  may  also  be  found,  by  viewing  at  the  same  time,  with  the  other 
eye,  either  a  scale,  or  any  other  object  of  known  dimensions,  placed  at  a 
given  distance :  the  lucid  disc  micrometer  of  Dr.  Herschel  t  is  employed 

*  Ph.  Tr.  1758,  1.  733,  and  1765,  Iv.  54. 
f  Ibid.  1782,  Ixxii.  163;  1785,  p.  46. 


338  LECTURE  XXXVI. 

in  this  manner  for  judging  of  the  magnitude  of  the  celestial  bodies.  The 
divided  object  glass  micrometer  affords  another  mode  of  measurement.:* 
the  object  glass  being  divided  into  two  semicircular  portions,  one  of  which 
slides  on  the  other ;  each  portion  acts  as  a  separate  lens,  and  two  images 
of  every  part  of  the  object  being  formed,  the  angular  distance  of  any  two 
points  is  determined  by  bringing  their  images  together,  and  measuring  the 
displacement  of  the  moveable  portion  of  the  object  glass  which  is  required 
for  procuring  the  coincidence.  Sometimes  also  a  similar  purpose  is 
answered  by  inserting  a  divided  glass  in  the  eye  piece,  which  acts  nearly 
on  the  same  principle,  and  which  seems  to  be  somewhat  less  liable  to  flrror. 
In  a  reflecting  telescope  of  Cassegrain's  construction,  Mr.  Ramsden  t  has 
also  produced  the  same  effect  by  dividing  the  convex  speculum,  and 
causing  a  part  of  it  to  turn  round  an  axis.  All  these  arrangements  parti- 
cularly deserve  the  attention  of  those  who  are  employed  in  practical  astro- 
nomy and  in  geography,  since  the  advancement  of  these  sciences  much 
depends  on  the  accuracy  of  the  telescopic  and  microscopic  measures,  which 
are  performed  by  means  of  optical  instruments.  (Plate  XXVIII.  Fig. 
416,  417.) 


LECT.  XXXVI.— ADDITIONAL  AUTHORITIES. 

Photometry. — Marie,  Nouvelle  Decouverte  en  Lumiere,  1701.  Mairan,  Hist, 
et  Mem.  1721.  Celsius,  Nouvelle  Idee  sur  la  Mesure  de  la  Lumiere,  ibid.  1735, 
H.  5.  Euler,  Hist,  et  Mem.  de  Berlin,  1750,  p.  280.  Karsten,  Photometric, 
Greifswald,  1777.  Fontana,  Mem.  della  Soc.  Ital.  i.  111.  Fossombroni,  Sull' 
Intensita  del  Lume,  fol.  Arezzo,  1781.  Langsdorf,  Grundlehren  der  Photometric, 
2  vols.  Erlangen,  1803-5.  Leslie's  Photometer,  Nich.  Jour.  iii.  461.  Ritchie's, 
Ph.  Mag.  v.  139.  Potter's,  ibid,  new  series,  iii.  284.  Xavierde  Maistre's,  Bibliot. 
Univ.  1832,  p.  323.  Osann's,  Pogg.  Ann.  xxxiii.  405.  Steinheil's,  ibid,  xxxiv.  644. 

Measurement  of  Refractive  Powers. — J.  A.  Porta,  De  Refractione,  4to,  Neap. 
1583.  Lahire  on  the  Refraction  of  Ice,  Hist,  et  Mem.  ix.  328,  x.  172  ;  of  Oil  and 
Water,  ix.  382,  577.  Lowthorp  on  the  Refraction  of  Air,  Ph.  Tr.  1699,  p.  339. 
Cassini  on  do.  Hist,  et  Mem.  1700,  p.  78,  H.  112.  Hauksbee  on  the  Refraction  of 
Fluids,  Ph.  Tr.  1710,  p.  204.  Euler  on  do.  Hist,  et  Mem.  de  Berlin,  1756,  p. 
235;  of  Glass,  1766,  p.  202.  J.  A.  Euler,  ibid.  1762,  pp.  279,  302,  318,  328. 
Cadet  and  Brisson,  Hist,  et  Mem.  1777,  p.  541.  Biot  and  Arago,  Memoire  sur 
les  Affinites  des  Corps  pour  la  Lumiere,  Mem.  de  1'Institut,  1806,  ii.  301.  Frau- 
enhofer,  Bestimmung  des  Brechungs  und  Farbenszerstreuungs-vermbgens  Ver- 
schiedener  Glasarten  Schum.  Astron.  Abhandl.  1815.  Hartmann,  in  Schum.  Astr. 
Nachr.  vii.  265.  Malus,  in  Gilb.  Ann.  xxxi.  225.  Marx,  in  Schweigger's  Jour.  v. 
385,  Ixi.  46.  Arago,  Annales  de  Chimie,  vol.  i.  &c.  Dulong,  Mem.  sur  les  Pouvoirs 
Refringens  des  Fluides  Elastiques,  Mem.  de  1'  Acad.  1825. 

Construction  of  Mirrors.— Mudge  on  the  Best  Composition  of  Metals,  Ph.  Tr. 
1777,  p.  296.  Potter  on  Improvements  in  Casting  and  Working,  Ph.  Mag.  1831, 
iv.  13,  vi.  228.  Lord  Oxmantown,  ibid.  ix.  213. 

Theory  of  Lenses. — Kastner,  Com.  Gott.  i.  185,  ii.  183.  Lagrange  surlaTheorie 
des  Lunettes,  Hist,  et  Mem.  de  Berlin,  1778,  p.  162.  Bohnenberger,  Zeitschrift  fur 
Astron.  i.  277,  385.  Von  Munchow,  ibid.  ii.  448.  Gauss,  ibid.  iv.  345.  Mobius, 
inCrelle's  Jour.  v.  113  ;  Schleiermacher,  in  Poggendorf's,  xiv.  1.  Schulten,  Supp. 
a  la  Theorie  des  Verres  Simples,  Vedensk  Aph.  1821,  p.  265.  Herschel,  Ph.  Tr. 
1821,  p.  222.  Hamilton  on  a  System  of  Rays,  Tr.  Roy.  Ir.  Ac.  1824,  &c.  Barlow, 
Ph.  Tr.  1827,  p.  231.  Santini,  Teoria  degli  Stromenti  Ottici,  Padua,  1828.  Lub- 
bock,  Ph.  Mag.  vii.  161. 

Reflecting  Goniometer.— Wollaston,  Ph.  Tr.  1809,  p.  253.     Malus,  Mem.  d'Ar- 

*  Savery  and  Dollond,  Ph.  Tr.  xlviii.  165,  178,  551. 

t  Ramsden,  Description  of  two  new  Micrometers,  Ph.  Tr.  1779,  Ixix.  419. 


ON  OPTICAL  INSTRUMENTS.  339 

cueil,  iii.  122.  Studer,  Gilb.  Ann.  Ixvi.  8.     Von  Reise,  Vorschlage  zu  einem  Neuen 
Goniometer,  Bonn,  1829. 
'Kaleidoscope. — Art.  in  Ed.  Encyc.  by  the  inventor,  Brewster. 

Sextant. — Hooke,  Animadversions  on  Hevelius,  4to,  1674,  Birch,  ii.  394.  Had- 
ley's  Inst.  Ph.  Tr.  1731,  p.  147;  1732,  p.  32.  Dollond's  Alterations  on  do.  ibid. 
1772,  p.  99.  Atwood's  Theory  of  do.  ibid.  1781,  p.  395.  Encke  on  do.  Astron. 
Jahrbuch,  1830,  p.  285.  Adie  on  Metallic  Reflectors  for  do.  Proceedings  of  Roy. 
Soc.  Ed.  1845. 

Microscope.  Treatises. — Hooke's  Micrographia,  fol.  1665.  Grindelius,  Micros. 
Nov.  Norimb.  1687.  Joblot,  Description  des  Plusieurs  Micros.  Paris,  1708. 
Observations  Micros.  1754.  Wideburg,  De  Micros.  Solari,  Erlang.  1755.  Due  de 
Chaulnes,  Descrip.  d'un  Micros,  fol.  Paris,  1768.  Brander,  Beschreibung  zweier 
Mic.,Augsb.  1769.  Baker  on  the  Mic.  1769.  Martin's  Optical  Essays,  1770. 
Descrip.  of  a  Graphical  Perspective  and  Micrometer,  1771.  De  la  Barre,  Mem.  sur 
les  Mic.  1777.  Gleichen,  Vom  Sonnenmicros.  4to,  Nurimb.  1781.  Tiedemann, 
Stuttgart,  1785.  Adam's  Essays  on  the  Mic.  4to,  1798.  Villars,  Mem.  sur  le 
Mic.  Paris,  1806.  Amici,  Mem.  di  Micros.  Modena,  1818.  Goring  and  Pritchard's 
Micros.  Illustrations,  1830.  In  Journals.— Fabri's,  Ph.  Tr.  1668,  p.  842.  Leu- 
wenhoek's,  ibid.  1673,  p.  6037.  Huygens's,  Hist,  et  Mem.  x.  427.  Wilson's,  Ph. 
Tr.  1702,  p.  1241.  Adams's,  ibid.  1710,  p.  24.  Baker's,  ibid.  1736,  p.  442. 
Lieberkuhn's  Solar  do.  ibid.  1740,  p.  516,  and  Hist,  et  Mem.  de  Berlin,  1745,  p.  14. 
Euler's,  Nov.  Com.  Petr.  iii.  363.  Aepinus's,  ibid.  ix.  316.  Zeiher's,  ibid.  x.  299. 
Selva's,  Hist,  et  Mem.  de  Paris,  1769,  H.  129.  Brewster's,  Ph.  Mag. iii.  74,  viii.  316, 
and  New  Philosophical  Insts.  Rossi's,  Baumgartners  Zeitsch.  v.  95.  Ehrenberg's, 
Pogg.  Ann.  xxiv.  188.  Wollaston's  Mic.  Doublet,  Ph.  Tr.  1829,  p.  9.  Codding- 
ton's,  Tr.  Camb.  Ph.  Soc.  iii.  421.  Lister  on  the  Mic.,  Ph.  Mag.  1831,  v.  169. 
Chevalier  and  Goring,  ibid.  p.  224,  &c. 

Telescope. — Mersenne,  Universse  Geometrise  Synopsis,  4to,  Paris,  1644.  Hooke, 
Auzout,  and  Campani,  Ph.  Tr.  1665-6,  i.  Huygens,  ibid.  1684,  p.  668.  Hist,  et 
Mem.  x.  351,  &c.  Hadley's  Telescope  (has  a  rectangular  prism  instead  of  the  plane 
mirror  of  Newton's),  Ph.  Tr.  1723,  p.  382.  Euler,  Hist,  et  Mem.  de  Berlin,  1747 
— 1767  (various  memoirs).  Kratzenstein  and  Euler  on  the  Iconantidiptic  Teles. 
Acta  Petr.  iii.  I.  192,  201.  Hertel,  Anweisung  Teles,  zu  Verfertigen,  Halle,  1747. 
Clairaut  on  the  Improvement  of  Teles.  Hist,  et  Mem.  1756,  p.  380,  H.  112  ;  1757, 
p.  524,  H.  153  ;  1762,  p.  578,  H.  160.  Scherfer  on  Dioptrical  Tel.  by  Hardy, 
1768.  Rochon's  Achromatic  Tel.  Hist,  et  Mem.  1773,  p.  299  ;  Reflecting  do.  Ph. 
Mag.  ii.  19,  170.  Lagrange  on  the  Theory  of  do.  Mis.  Taur.  iii.  II.  152  ;  Hist. 
et  Mem.  de  Berlin,  1778,  p.  162.  Navarre's  Tel.  Hist,  et  Mem.  1778,  H.56. 
Fuss  on  Tel.  4to,  Leipz.  1778.  Oriani,  Mem.  de  la  Soc.  Ital.  iii.  664.  Biirja,  Hist, 
et  Mem.  de  Berlin,  1797,  ii.  8, 1798,  p.  3.  Blair  (Fluid  Lenses)  Tr.  Roy.  Soc.  Ed. 
iii.  3.  Repertory  of  Arts,  vii.  15.  Kater,  Comparison  of  Cassegrain's  with  Gre- 
gory's, Ph.  Tr.  1813,  p.  206.  Kitchiner,  Practical  Observations  on  Telescopes.  &c. 
1818.  Guilio,  Mem.  di  Torino,  xvi.  128.  Brewster's,  Phil.  Mag.  vii.  323.  Lord 
Oxmantown,  ibid.  ix.  25,  new  series,  ii.  136. 

Micrometers. — Huygens,  Systema  Saturnium,  Hag.  Com.  1659.  Auzout  and 
Hooke,  Ph.  Tr.  1665-6,  i.  123.  Hooke  on  Gascoigne's  Screw  Mic.  ibid.  ii.  541. 
Lefevre's  Mic.,  Mach.  Appr.  ii.  103.  Kirckius's,  Mis.  Berl.  i.  202.  Cassini's,  Hist, 
et  Mem.  1724,  p.  347.  Fouchy's,  Mach.  Appr.  vi.  45.  Aepinus's,  Hist,  et  Mem. 
de  Berlin,  1756,  p.  365.  Wilcke's,  Schwed.  Abhand.  1772,  p.  56.  Boscovich's, 
Ph.  Tr.  1777,  p.  789.  Kohler's,  Bode's  Jahrbuch,  1785,  p.  155.  Smeaton's,  Ph.  Tr. 
1787,  p.  318.  Rochon's  (Rock  Crystal),  Nov.  Act.  Petr.  1788,  H.  37.  Jour,  de 
Phy.  liii.  169.  Cavallo's,  Ph.  Tr.  1791,  p.  283.  Wollaston's,  ibid.  1813,  p.  119  ; 
also  1820,  p.  126.  Dollond's,  ibid.  1821,  p.  101.  Brewster's,  Ph.  Mag.  i.  104;  iv. 
164.  Treatise  on  New  Philosophical  Instruments,  ed.  1813,  pp.  48, 173.  Amici's, 
Mem.  della  Soc.  Ital.  xvii.  II.  344.  Frauenhofer's,  Schumacher's  Astr.  Nach.  ii.  361, 
364.  Hansen  on  do.  Gotha,  1827.  Bessel  on  do.  Schumacher,  viii.  397.  Stein- 
heil's,  ibid.  v.  359. 


z2 


840 


LECTURE   XXXVIL 


ON  PHYSICAL  OPTICS. 

HAVING  examined  the  general  theory  of  optics,  and  the  construction  of 
optical  instruments,  we  are  now  to  consider  those  properties  and  affections 
of  light,  which  rather  belong  to  its  natural  history  than  to  its  mechanical 
effects  ;  to  trace  its  relations  to  the  particular  phenomena  of  nature ;  to 
investigate  the  manner  in  which  it  is  connected  with  our  sensations,  and 
to  inquire  on  what  intimate  mode  of  action  the  various  effects  of  light 
depend.  All  these  subjects  may  be  properly  comprehended  under  the 
denomination  of  physical  optics,  but  we  shall  find  it  convenient  to  reserve 
each  of  the  two  last  for  a  separate  examination.  The  sources  of  light,  the 
velocity  of  its  motion,  its  interception  and  extinction,  its  dispersion  into 
different  colours  ;  the  manner  in  which  it  is  affected  by  the  variable  den- 
sity of  the  atmosphere,  the  meteorological  appearances  in  which  it  is 
concerned,  and  the  singular  properties  of  particular  substances  with  regard 
to  it,  will  be  the  first  subjects  of  our  investigation. 

The  sources  from  which  light  is  commonly  derived,  are  either  the  sun  or 
stars,  or  such  terrestrial  bodies  as  are  undergoing  those  changes  which 
con^itute  combustion.  The  process  of  combustion  implies  a  change  in 
which  a  considerable  emission  of  light  and  heat  is  produced  ;  but  it  is  not 
capable  of  a  very  correct  definition  :  in  general  it  requires  an  absorption, 
or  at  least  a  transfer,  of  a  portion  of  oxygen :  but  there  appear  to  be  some 
exceptions  to  the  universality  of  this  distinction  ;  and  it  has  been  observed 
that  both  heat  and  light  are  often  produced  where  no  transfer  of  oxygen 
takes  place,  and  sometimes  by  the  effect  of  a  mixture  which  cannot  be 
called  combustion. 

Light  is  also  afforded,  without  any  sensible  heat,  by  a  number  of  vege- 
table and  animal  substances,  which  appear  to  be  undergoing  a  slow  decom- 
position not  wholly  unlike  combustion.  Thus  decayed  wood,  and  animal 
substances  slightly  salted,  often  afford  spontaneously  a  faint  light,  without 
any  elevation  of  temperature  ;  and  it  is  not  improbable  that  the  light  of  the 
ignis  fatuus  may  proceed  from  a  vapour  of  a  similar  nature. 

The  effects,  which  are  commonly  attributed  to  the  motions  of  the  elec- 
trical fluid,  are  often  attended  by  the  production  of  light ;  and  violent  or 
rapid  friction  frequently  seems  to  be  the  immediate  cause  of  its  appearance. 
But  it  is  difficult  to  ascertain  whether  friction  may  not  be  partly  concerned 
in  the  luminous  phenomena  attributed  to  electricity,  or  electricity  in  the 
apparent  effects  of  friction.  Light  is  sometimes  produced  by  friction  with  a 
much  lower  degree  of  heat  than  is  required  for  combustion,  and  even  when 
it  is  accompanied  by  combustion,  the  heat  produced  by  the  union  of  these 
causes  may  be  very  moderate :  thus  it  is  usual  in  some  coal  mines,  ,to 
obtain  a  train  of  light  by  the  continual  collision  of  flint  and  steel,  effected 
by  the  machine  called  a  fire  wheel,  in  order  to  avoid  setting  fire  to  the 


ON  PHYSICAL  OPTICS.  341 

inflammable  gas  emitted  by  the  coal,  which  would  be  made  to  explode  if 
it  came  near  the  flame  of  a  candle. 

There  is  a  remarkable  property,  which  some  substances  possess  in  an 
eminent  degree,  and  of  which  few,  except  metals  and  water,  are  entirely 
destitute.*  These  substances  are  denominated  solar  phosphori;  besides 
the  light  which  they  reflect  and  refract,  they  appear  to  retain  a  certain 
portion,  and  to  emit  it  again  by  degrees  till  it  is  exhausted,  or  till  its  emis- 
sion is  interrupted  by  cold.  The  Bolognan  phosphorus  was  one  of  the  first 
of  these  substances  that  attracted  notice  ;  it  is  a  sulfate  of  barytes,  found 
in  the  state  of  a  stone ;  it  is  prepared  by  exposure  to  heat,  and  is  after- 
wards made  up  into  cakes  :  these,  when  first  placed  in  a  beam  of  the  sun's 
light,  and  viewed  afterwards  in  a  dark  room,  have  nearly  the  appearance 
of  a  burning  coal,  or  a  red  hot  iron.  Burnt  oyster  shells,  t  and  muriate 
of  lime  have  also  the  same  property,  and  some  specimens  of  the  diamond 
possess  it  in  a  considerable  degree.  From  the  different  results  of  experi- 
ments apparently  accurate,  made  by  different  persons,  there  is  reason  to 
conclude  that  some  of  these  phosphori  emit  only  the  same  kind  of  light  as 
they  have  received,  while  others  exhibit  the  same  appearances,  to  whatever 
kind  of  light  they  may  have  been  exposed.  Sometimes  it  has  even  been 
found  that  light  of  a  particular  colour  has  been  most  efficacious  in  exciting 
in  a  diamond  the  appearance  of  another  kind  of  light,  which  it  was  natu- 
rally most  disposed  to  exhibit.  The  application  of  heat  to  solar  phosphori 
in  general  expedites  the  extrication  of  the  light  which  they  have  borrowed, 
and  hastens  its  exhaustion ;  it  also  produces,  in  many  substances,  which 
are  not  remarkable  for  their  power  of  imbibing  light,  a  temporary  scintil- 
lation or  flashing,  at  a  heat  much  below  ignition :  the  most  remarkable 
of  these  are  fluor  spar  in  powder,  and  some  other  crystallized  substances. 
It  appears  that  luminous  bodies  in  general  emit  light  equally  in  every 
direction,  not  from  each  point  of  any  of  their  surfaces,  as  some  have 
supposed,  but  from  the  whole  surface  taken  together,  so  that  the  surface, 
when  viewed  obliquely,  appears  neither  more  nor  less  bright  than  when 
viewed  directly.^ 

However  light  of  any  kind  may  have  at  first  originated,  there  is  reason 
to  believe  that  the  velocity  with  which  it  passes  through  a  given  medium 
is  always  the  same.  It  has  been  ascertained  by  the  astronomical  observa- 
tions of  Roemer  and  of  Bradley,  that  each  ray  of  light,  emitted  by  the 
sun,  arrives  at  the  earth  in  eight  minutes  and  one  eighth,  when  the  earth 
is  at  its  mean  distance  of  about  95  millions  of  miles.  Roemer  §  deduced 
this  velocity  from  observations  on  the  eclipses  of  the  satellites  of  Jupiter, 
and  Bradley  1 1  confirmed  it  by  his  discovery  of  the  cause  of  the  apparent 
aberration  of  the  fixed  stars. 

*  See  Cellio,  La  Pietra  Bolognese  Preparata,  Rom.  1680.  Beccari  de  Phospho- 
ris,  4to,  Bolog.  1744.  T.  Wedgwood,  Ph.  Tr.  1792,  p.  28. 

f  See  Bartholinus  de  Luce  Animalium,  1669.     Boyle  on  the  Light  of  Fish,  &c. 
Ph.  Tr.  ii.  581,  605,  1672  ;  vii.  5107.     Works,  iii.  304.     Canton,  Ph.  Tr.  1768, 
p.  337  ;  1769,  p.  446.     Hulme,  ibid.  1800,  p.  161 ;  1801,  pp.  403,  426. 
•   t  Hauksbee,   on  the  Production  of  Light  from  Phosphorus  in  vacua,  Ph.  Tr. 
xxiv.  p.  1865. 

§  Hist,  et  Mem.  x.  399,  Ph.  Tr.  1677,  xii.  893. 

||  Ph.  Tr.  1728,  xxxv.  637. 


342  LECTURE  XXXVII. 

This  aberration  is  produced  by  the  effect  of  the  revolution  of  the  earth 
in  its  orbit,  combined  with  that  of  the  progressive  motion  of  light.  Since 
light  proceeds  always  in  right  lines,  when  its  motion  is  perfectly  undis- 
turbed, if  a  fine  tube  were  placed  so  as  to  receive  a  ray  of  light,  passing 
exactly  through  its  axis  when  at  rest,  and  then,  remaining  in  the  same 
direction,  were  moved  transversely  with  great  velocity,  it  is  evident  that 
the  side  of  the  tube  would  strike  against  the  ray  of  light  in  its  passage, 
and  that  in  order  to  retain  it  in  the  axis,  the  tube  must  be  inclined,  in  the 
same  manner  as  if  the  light,  instead  of  coming  in  its  actual  direction,  had 
also  a  transverse  motion  in  a  contrary  direction  to  that  of  the  tube.  The 
axis  of  a  telescope,  or  even  of  the  eye,  may  be  considered  as  resembling 
such  a  tube,  the  passage  of  the  light  through  the  refracting  substances  not 
altering  the  necessary  inclination  of  the  axis.  In  various  parts  of  the 
earth's  orbit,  the  aberration  of  any  one  star  must  be  different  in  quan- 
tity and  in  direction ;  it  never  exceeds  20  seconds  each  way,  and  must 
therefore,  in  common  observations,  be  wholly  insensible.  (Plate  XXIX. 
Fig.  418.) 

The  quantity  of  light,  which  is  reflected  by  a  substance  of  any  kind, 
depends  not  only  on  the  nature  of  the  substance,  but  also  on  the  obliquity 
of  its  incidence :  and  it  sometimes  happens,  that  a  surface,  which  reflects 
a  smaller  portion  of  direct  light  than  another,  reflects  a  greater  portion 
when  the  light  falls  very  obliquely  on  its  surface.  Bouguer  found  that 
the  surface  of  water  reflected  only  one  fifty  fifth  part  of  the  light  fall- 
ing perpendicularly  on  it,  that  of  glass  one  fortieth,  and  that  of  quick- 
silver more  than  two  thirds :  but  when  the  obliquity  was  as  great  as  possi- 
ble, the  water  reflected  nearly  three  fourths  of  'the  incident  light,  and  the 
glass  about  two  thirds  only. 

Of  the  light  which  passes  by  a  dense  substance  of  any  kind,  the  greatest 
part  pursues  its  course  undisturbed,  but  there  is  always  a  certain  divergence, 
which  has  been  called  by  Grimaldi  diffraction,  and  by  Newton  inflection. 
This  effect  is  usually  attended  by  the  production  of  colours,  and  will 
therefore  require  to  be  more  particularly  considered  hereafter. 

The  separation  of  colours  by  refraction  is  one  of  the  most  striking  of  all 
optical  phenomena.  It  was  discovered  by  Newton*  that  white  light  is  a 
compound  of  rays  of  different  kinds,  mixed  in  a  certain  proportion,  that 
these  rays  differ  in  colour  and  in  refrangibility,  that  they  constitute  a 
series,  which  proceeds  by  gradual  changes  from  red  to  violet,  and  that 
those  substances  which  appear  coloured  when  placed  in  white  light,  derive 
their  colours  only  from  the  property  of  reflecting  some  kind  of  rays  most 
abundantly,  and  of  transmitting  or  extinguishing  the  rest.  Dr.  Herschelt 
has  added  to  this  series  rays  of  heat  less  refrangible  than  the  red,  and 
Hitter  J  and  Dr.  Wollaston  §  have  discovered,  beyond  the  violet,  other  still 
more  refrangible  rays,  which  blacken  the  salts  of  silver. 

*  Ph.  Tr.  167J,  vi.  3075  ;  vii.  4059,  4087,  5004,  5012,  5084 ;  viii.  6086,  6108, 
&c.  &c.  Opuscula,  ii.  181. 

f  On  Heat  and  Light,  Ph.  Tr.  1800. 

J  Gilbert's  Ann.  vii.  527  ;  xii.  409. 

§  Ph.  Tr.  1802,  p.  365.  See  also  Scheele  on  Air  and  Fire  (trans.},  Loud.  1780, 
§  66. 


ON  PHYSICAL  OPTICS.  343 

,  It  has  generally  been  supposed,  since  the  time  of  Newton,  that  when  the 
rays  of  light  are  separated  as  completely  as  possible  by  means  of  refrac- 
tion, they  exhibit  seven  varieties  of  colour,  related  to  each  other  with 
respect  to  the  extent  that  they  occupy,  in  ratios  nearly  analogous  to  those 
of  the  ascending  scale  of  the  minor  mode  in  music.  The  observations 
were,  however,  imperfect,  and  the  analogy  was  wholly  imaginary.  Dr. 
Wollaston  *  has  determined  the  division  of  the  coloured  image  or  spectrum, 
in  a  much  more  accurate  manner  than  had  been  done  before  :  by  looking 
through  a  prism,  at  a  narrow  line  of  light,  he  produces  a  more  effectual 
separation  of  the  colours,  than  can  be  obtained  by  the  common  method  of 
throwing  the  sun's  image  on  a  wall.  The  spectrum  formed  in  this  manner 
consists  of  fo.ur  colours  only,  red,  green,  blue,  and  violet,  which  occupy 
spaces  in  the  proportion  of  16,  23,  36,  and  25,  respectively,  making  toge- 
ther 100  for  the  whole  length ;  the  red  being  nearly  one  sixth,  the  green 
and  the  violet  each  about  one  fourth,  and  the  blue  more  than  one  third  of 
the  length.  The  colours  differ  scarcely  at  all  in  quality  within  their 
respective  limits,  but  they  vary  in  brightness ;  the  greatest  intensity  of 
light  being  in  that  part  of  the  green  which  is  nearest  to  the  red.  A  narrow 
,line  of  yellow  is  generally  visible  at  the  limit  of  the  red  and  green,  but  its 
I  breadth  scarcely  exceeds  that  of  the  aperture  by  which  the  light  is  ad- 
,  mitted,  and  Dr.  Wollaston  attributes  it  to  the  mixture  of  the  red  with  the 
green  light.  There  are  also  several  dark  lines  t  crossing  the  spectrum 
within  the  blue  portion  and  its  neighbourhood,  in  which  the  continuity  of 
the  light  seems  to  be  interrupted.  This  distribution  of  the  spectrum  Dr. 
Wollaston  has  found  to  be  the  same,  whatever  refracting  substance  may 
have  been  employed  for  its  formation  ;  and  he  attributes  the  difference 
which  has  sometimes  been  observed  in  the  proportions,  to  accidental  varia- 
tions of  the  obliquity  of  the  rays.  The  angular  extent  of  the  spectrum 
formed  by  a  prism  of  crown  glass  is  one  27th  of  the  deviation  of  the  red 
rays  ;  by  a  prism  of  flint  glass,  one  19th.  (Plate  XXIX.  Fig.  419.) 

In  light  produced  by  the  combustion  of  terrestrial  substances,  the  spec- 
trum is  sometimes  still  more  interrupted ;  thus,  the  bluish  light  of  the 

*  Ph.  Tr.  1802,  p.  365. 

f  This  fact  did  not  excite  the  attention  which  it  merited  at  the  time  of  its  dis- 
covery. Several  years  afterwards,  M.  Fraunhofer,  of  Munich,  by  viewing  the 
spectrum  formed  from  a  narrow  line  of  solar  light,  when  in  its  purest  state,  at 
the  angle  of  minimum  deviation,  discovered  that  it  was  crossed  by  a  very  great 
number  of  dark  lines,  not  separating  different  colours,  but  mixed  up  with  them, 
without  any  order.  In  solar  light  they  are  nearly  600  in  number,  and  with 
the  same  kind  of  light  always  retain  the  same  places,  but  are  very  different  for  dif- 
ferent kinds  of  light ;  and  even  that  of  the  sun,  after  it  has  been  transmitted  through 
nitrous  acid  gas,  exhibits  very  different  lines  from  what  it  did  previously.  By  far  the 
readiest  mode  of  viewing  such  lines,  is  to  cause  sun-light  to  pass  through  a  bottle  of 
this  gas  before  it  falls  on  the  prism.  Since  these  lines  always  retain  their  places  in 
the  spectrum,  they  afford  the  most  accurate  method  of  determining  the  refractive 
and  dispersive  powers  of  bodies,  to  which  purpose  Fraunhofer  himself  applied  them. 
See  Fraunhofer,  Bestimmung  des  Brechungs  und  F-arbenszerstreuungs-vermogens 
verschiedener  Glasarten.  Miincher  Akad.  Abhand.  1821,'  xxii.  Brewster's  Obser- 
yations  on  the  Lines  produced  by  the  Earth's  Atmosphere  and  by  the  Action  of 
Nitrous  Acid  Gas,  Tr.  Roy.  Soc.  Ed.  xii.  519.  Ed.  Jour,  of  Sci.  No.  XV.  7.  Mil- 
ler, ibid.  ii.  381.  Rudberg,  Pogg.  Ann.  xxxv.  523.  Wheatstone  (Electrical  Light), 
Ph.  Mag.  vii.  299. 


344  LECTURE  XXXVII. 

lower  part  of  a  flame  of  a  candle  is  separated  by  refraction  into  five  parcels 
cf  various  colours;  the  light  of  burning  spirits,  which  appears  perfectly 
blue,  is  chiefly  composed  of  green  and  violet  rays ;  and  the  light  of  a 
candle  into  which  salt  is  thrown  abounds  with  a  pure  yellow,  inclining  to 
green,  but  not  separable  by  refraction.  The  electrical  spark  furnishes  also 
a  light  which  is  differently  divided  in  different  circumstances.  (Plate 
XXIX.  Fig.  420.) 

If  the  breadth  of  the  aperture  viewed  through  a  prism  is  somewhat 
increased,  the  space  occupied  by  each  variety  of  light  in  the  spectrum  is 
augmented  in  the  same  proportion,  and  each  portion  encroaches  on  the 
neighbouring  colours,  and  is  mixed  with  them  :  so  that  the  red  is  suc- 
ceeded by  orange,  yellow,  and  yellowish  green,  and  the  blue, is  mixed  on 
the  one  side  with  the  green,  and  on  the  other  with  the  violet ;  and  it  is  in 
this  state  that  the  prismatic  spectrum  is  commonly  exhibited.  (Plate 
XXIX.  Fig.  421.) 

When  the  beam  of  light  is  so  much  enlarged  as  to  exceed  the  angular 
magnitude  of  the  spectrum,  it  retains  its  whiteness  in  the  centre,  and  is  ter- 
minated by  two  different  series  of  colours  at  the  different  ends.  These  series 
are  still  divided  by  well  marked  lines  :  on  the  one  hand  the  red  remains 
unmixed  ;  the  space  belonging  to  the  green  and  blue  becomes  a  greenish 
yellow,  nearly  uniform  throughout,  and  here  the  appearance  of  colour  ends, 
the  place  of  the  violet  being  scarcely  distinguishable  from  the  neighbouring 
white  light :  on  the  other  hand,  the  space  belonging  to  the  red,  green,  and 
blue  of  the  simple  spectrum,  appears  of  a  bluish  green,  becoming  more  and 
more  blue  till  it  meets  the  violet,  which  retains  its  place  without  alteration. 
This  second  series  is  also  the  same  that  accompanies  the  limit  of  total 
reflection  at  the  posterior  surface  of  a  prism.  (Plate  XXIX.  Fig.  422.) 

Sir  Isaac  Newton  observed  that  the  effect  of  white  light  on  the  sense  of 
sight  might  be  imitated  by  a  mixture  of  colours  taken  from  different  parts 
of  the  spectrum,  notwithstanding  the  omission  of  some  of  the  rays  naturally 
belonging  to  white  light.  Thus,  if  we  intercept  one  half  of  each  of  the  four 
principal  portions  into  which  the  spectrum  is  divided,  the  remaining  halves 
will  still  preserve,  when  mixed  together,  the  appearance  of  whiteness  ;  so 
that  it  is  probable,  that  the  different  parts  of  those  portions  of  the  spectrum, 
which  appear  of  one  colour,  have  precisely  the  same  effect  on  the  eye.  It 
is  certain  that  the  perfect  sensations  of  yellow  and  of  blue  are  produced 
respectively,  by  mixtures  of  red  and  green  and  of  green  and  violet  light,  and 
there  is  reason  to  suspect  that  those  sensations  are  always  compounded  of 
(  the  separate  sensations  combined ;  at  least,  this  supposition  simplifies  the 
theory  of  colours  :  it  may,  therefore,  be  adopted  with  advantage,  until  it  be 
found  inconsistent  with  any  of  the  phenomena ;  and  we  may  consider  white 
light  as  composed  of  a  mixture  of  red,  green,  and  violet  only,  in  the  pro- 
portion of  about  two  parts  red,  four  green,  and  one  violet,  with  respect  to 
the  quantity  or  intensity  of  the  sensations  produced.* 

*  So  WUnsch,  Versuche  iiber  die  Farben,  Leipz.  1792.  Mayer,  in  an  essay  De 
Affinitate  Colorum,  pub.  1722,  refers  all  colours  to  red,  yellow,  and  blue  :  and  thk 
is  the  more  common  hypothesis.  See  Guyot,  Recreations,  Par.  1769.  Goethe,  Far- 
benlehre,  1810.  Brewster,  Tr.  Roy.  Soc.  Ed.  xii.  123.  Nollet,  Lesons  de  Phy- 
sique, v.  388,  considers  the  three  colours  to  be  orange,  green,  and  indigo. 


.    ON  PHYSICAL  OPTICS,  345 

If  we  mix  together,  in  proper  proportions,  any  substances  exhibiting 
tliese  colours  in  their  greatest  purity,  and  place  the  mixture  in  a  light 
sufficiently  strong,  we  obtain  the  appearance  of  perfect  whiteness ;  but  in 
a  fainter  light  the  mixture  is  grey,  or  of  that  hue  which  arises  from  a  com- 
bination of  white  and  black  ;  black  bodies  being  such  as  reflect  white  light 
but  in  a  very  scanty  proportion.  For  the  same  reason,  green  and  red  sub- 
stances mixed  together  usually  make  rather  a  brown  than  a  yellow  colour, 
and  many  yellow  colours,  when  laid  on  very  thickly,  or  mixed  with  black, 
become  brown.  The  sensations  of  various  kinds  of  light  may  also  be  com- 
bined in  a  still  more  satisfactory  manner,  by  painting  the  surface  of  a  circle 
with  different  colours,  in  any  way  that  may  be  desired,  and  causing  it  to 
revolve  witi^such  rapidity,  that  the  whole  may  assume  the  appearance  of  a 
single  tint,  or  of  a  combination  of  tints,  resulting  from  the  mixture  of  the 
colours.  (Plate  XXIX.  Fig.  423... 426.) 

From  three  simple  sensations,  with  their  combinations,  we  obtain  seven 
primitive  distinctions  of  colours  ;  but  the  different  proportions  in  which 
they  may  be  combined,  afford  a  variety  of  tints  beyond  all  calculation. 
The  three  simple  sensations  being  red,  green,  and  violet,  the  three  binary 
combinations  are  yellow,  consisting  of  red  and  green  ;  crimson,  of  red  and 
violet ;  and  blue,  of  green  and  violet ;  and  the  seventh  in  order  is  white 
light,  composed  by  all  the  three  united.  But  the  blue  thus  produced,  by 
combining  the  whole  of  the  green  and  violet  rays,  is  not  the  blue  of  the 
spectrum,  for  four  parts  of  green  and  one  of  violet  make  a  blue,  differing 
very  little  from  green  ;  while  the  blue  of  the  spectrum  appears  to  contain 
as  much  violet  as  green  :  and  it  is  for  this  reason  that  red  and  blue  usually 
make  a  purple,  deriving  its  hue  from  the  predominance  of  the  violet. 

It  would  be  possible  to  exhibit  at  once  to  the  eye  the  combinations  of  any 
three  colours  in  all  imaginable  varieties.  Two  of  them  might  be  laid  down 
on  a  revolving  surface,  in  the  form  of  triangles,  placed  in  opposite  direc- 
tions, and  the  third  on  projections  perpendicular  to  the  surface,  which, 
while  the  eye  remained  at  rest  in  any  one  point,  obliquely  situated,  would 
exhibit  more  or  less  of  their  painted  sides,  as  they  passed  through  their 
different  angular  positions  ;  and  the  only  further  alteration,  that  could  be 
produced  in  any  of  the  tints,  would  be  derived  from  the  different  degrees  of 
light  only.  The  same  effect  may  also  be  exhibited  by  mixing  the  colours 
in  different  proportions,  by  means  of  the  pencil,  beginning  from  three 
equidistant  points  as  the  centres  of  the  respective  colours.  (Plate  XXIX. 
Fig.  427.) 

The  ordinary  atmospherical  refraction  cannot  be  determined  in  the 
usual  manner  from  the  knowledge  of  its  density,  and  of  the  angular  direc- 
tion of  the  incident  or  refracted  light,  since  the  constitution  of  the  atmo- 
sphere is  such,  that  its  density  varies  every  where  with  its  height,  and  the 
curvature  of  the  earth's  surface  causes  the  inclination  of  the  strata  through 
which  the  ray  passes  to  be  perpetually  changed  ;  the  difference  of  tempera- 
ture at  different  elevations  increases  also  the  difficulty  of  an  exact  calcula- 
tion, and  it  is  only  very  lately  that  Mr.  Laplace,**  by  a  comparison  of 
I  astronomical  with  meteorological  observations,  has  given  a  satisfactory 

*  Mec.  Cel.  iv.  268. 


346  LECTURE  XXXVII. 

solution  of  the  problem  in  all  its  extent.  But  for  practical  uses,  the  refrac- 
tion may  be  determined  with  sufficient  accuracy  by  an  approximation 
which  is  easily  remembered  ;  the  deviation  being  at  all  altitudes  one  sixth 
part  as  great  as  the  refracted  ray  would  undergo  at  the  horizontal  surface 
of  a  medium  six  times  as  dense  as  the  air.  When  a  celestial  object  appears 
exactly  in  the  horizon,  it  is  actually  more  than  half  a  degree  below  it, 
since  the  refraction  amounts  to  33  minutes,  when  the  barometer  stands  at 
29-^V  inches,  and  Fahrenheit's  thermometer  at  50°. 

The  accidental  variations  of  the  temperature  of  the  air  at  different  parts, 
produce,  however,  great  irregularities  in  its  refraction,  especially  near  the 
horizon.  The  most  remarkable  of  these  is  occasioned  by  the  rarefaction  of 
the  air  in  the  neighbourhood  of  the  surface  of  water,  of  a  budding,  or  of 
the  earth  itself,  in  consequence  of  which  a  distant  object  appears  to  be 
depressed  instead  of  being  elevated,  and  is  sometimes  seen  at  once  both 
depressed  and  elevated,  so  as  to  appear  double,  one  of  the  images  being 
generally  in  an  inverted  position,  as  if  the  surface  possessed  a  reflective 
power;  and  there  seems  indeed  to  be  a  considerable  analogy  between  this 
kind  of  refraction  and  the  total  reflection  which  happens  within  a  denser 
medium.  These  effects  are  known  by  the  appellations  looming,  mirage, 
•  and  Fata  Morgana  ;  they  may  be  very  completely  imitated,  as  Dr.  Wollas- 
ton  as  shown,*  by  looking  at  a  distant  object  along  a  red  hot  poker,  or 
through  a  saline  or  saccharine  solution  with  water  and  spirit  of  wine 
floating  on  it.  The  effect  of  refraction  on  the  apparent  places  of  terrestrial 
objects  must  be  frequently  disturbed  by  circumstances  of  this  kind ;  but 
its  magnitude  is  usually  about  one  tenth  of  the  angular  distance  of  the 
object,  considered  as  a  part  of  the  earth's  circumference.  (Plate  XXIX. 
Fig.  428,  429.) 

The  atmospherical  phenomena  of  rainbows  and  halos  present  us  with 
examples  of  the  spontaneous  separation  of  colours  by  refraction.  The 
rainbow  is  universally  attributed  to  the  refraction  and  reflection  of  the 
sun's  rays  in  the  minute  drops  of  falling  rain  or  dew,  and  the  halos, 
usually  appearing  in  frosty  atmospheres,  are  in  all  probability  produced  by 
the  refraction  of  small  triangular  or  hexagonal  crystals  of  snow.  It  is 
only  necessary,  for  the  formation  of  a  rainbow,  that  the  sun  should  shine  on  a 
dense  cloud  or  a  shower  of  rain,  in  a  proper  situation,  or  even  on  a  number 
of  minute  drops  of  water,  scattered  by  a  brush  or  by  a  syringe,  so  that  the 
light  may  reach  the  eye  after  having  undergone  a  certain  angular  deviation, 
by  means  of  various  refractions  and  reflections  ;  and  the  drops  so  situated 
must  necessarily  be  found  somewhere  in  a  conical  surface,  of  which  the 
eye  is  the  vertex,  and  must  present  the  appearance  of  an  arch.  The  light, 
which  is  reflected  by  the  external  surface  of  a  sphere,  is  scattered  almost 
equally  in  all  directions,  setting  aside  the  difference  arising  from  the 
greater  efficacy  of  oblique  reflection  ;  but  when  it  first  enters  the  drop,  and 
is  there  reflected  by  its  posterior  surface,  its  deviation  never  exceeds  a 
certain  angle,  which  depends  on  the  degree  of  refrangibility,  and  is,  there- 
fore, different  for  light  of  different  colours  ;  and  the  density  of  the  light  being 
the  greatest  at  the  angle  of  greatest  deviation,  the  appearance  of  a  lumi- 
*  Ph.  Tr.  1800,  p.  239.  See  also  ibid.  1803,  p.  1. 


ON  PHYSICAL  OPTICS.  347 

nous  arch  is  produced  by  the  rays  of  each  colour  at  its  appropriate  dis- 
tance. The  rays  which  never  enter  the  drops  produce  no  other  effect, 
than  to  cause  a  brightness,  or  haziness  round  the  sun,  where  the  reflection  is 
the  most  oblique  ;  those  which  are  once  reflected  within  the  drop  exhibit 
the  common  internal  or  primary  rainbow,  at  the  distance  of  about  41 
degrees  from  the  point  opposite  to  the  sun  ;  those  which  are  twice  reflected, 
the  external  or  secondary  rainbow,  of  52°  ;  and  if  the  effect  of  the  light, 
three  times  reflected,  were  sufficiently  powerful,  it  would  appear  at  the 
distance  of  about  42  degrees  from  the  sun.  The  colours  of  both  rainbows 
encroach  considerably  on  each  other ;  for  each  point  of  the  sun  may  be 
considered  as  affording  a  distinct  arch  of  each  colour,  and  the  whole  disc 
as  produciflg^an  arch  about  half  a  degree  in  breadth  for  each  kind  of  light ; 
so  that  the  arrangement  nearly  resembles  that  of  the  common  mixed  spec- 
trum. There  is,  however,  another  cause  of  a  further  mixture  of  the 
colours  ;  the  arch  of  any  single  colour,  which  belongs  to  any  point  of  the 
sun,  is  accurately  defined  on  one  side  only,  while  on  the  other  it  becomes 
gradually  fainter,  the  breadth  of  the  first  minute  containing  about  five  times 
as  much  light  as  a  minute  at  the  distance  of  a  quarter  of  a  degree  ;  the 
abrupt  termination  is  on  the  side  of  the  red,  that  is,  without  the  inner  bow, 
and  within  the  outer,  so  that,  for  this  reason,  the  order  of  colours  partakes, 
in  some  degree,  of  the  nature  of  the  red  termination  of  a  broad  beam  of  light 
seen  through  a  prism ;  but  it  is  more  or  less  affected  by  this  cause,  on 
account  of  some  circumstances,  which  will  be  explained  when  we  examine 
the  supernumerary  rainbows,  which  sometimes  accompany  the  bows  more 
commonly  observed.  A  lunar  rainbow  is  much  more  rarely  seen  than  a 
solar  one,  but  its  colours  differ  little,  except  in  intensity,  from  those  of  the 
common  rainbow.  (Plate  XXIX.  Fig.  430.) 

In  the  highest  northern  latitudes,  where  the  air  is  commonly  loaded  with 
frozen  particles,  the  sun  and  moon  usually  appear  surrounded  by  halos  or 
coloured  circles,  at  the  distances  of  about  22  and  46  degrees  from  their 
centres;  this  appearance  is  also  frequently  observed  in  other  climates, 
especially  in  the  colder  months,  and  in  the  light  clouds  which  float  in  the 
highest  regions  of  the  air.  The  halos  are  usually  attended  by  a  horizontal 
white  circle,  with  brighter  spots,  or  parhelia,  near  their  intersections  with 
this  circle,  and  with  portions  of  inverted  arches  of  various  curvatures  ;  the 
horizontal  circle  has  also  sometimes  anthelia,  or  bright  spots  nearly  opposite 
to  the  sun.  These  phenomena  have  usually  been  attributed  to  the  effect 
of  spherical  particles  of  hail,  each  having  a  central  opaque  portion  of  a 
certain  magnitude,  mixed  with  oblong  particles,  of  a  determinate  form, 
and  floating  with  a  certain  constant  obliquity  to  the  horizon.  But  all 
these  arbitrary  suppositions,  which  were  imagined  by  Huygens,*  are  in 
themselves  extremely  complicated  and  improbable,  and  are  wholly  unau- 
thorised by  observation.  A  much  simpler,  and  more  natural,  as  well  as  more 
accurate  explanation,  which  was  suggested  at  an  earlier  period  by  Mariotte,t 
had  long  been  wholly  forgotten,  until  the  same  idea  occurred  to  me,^ 

*  Ph.  Tr.  1670,  v.  1065.     Op.  Rel.  vol.ii. 
f  Trait6  des  Couleurs,  Paris,  1686.     OEuv.  i.  272. 
x  J  Jour,  of  the  Roy.  Inst.  ii.  4. 


348  LECTURE  XXXVII. 

without  any  previous  knowledge  of  what  Mariotte  had  done.  The  natural « 
tendency  of  water  to  crystallize,  in  freezing,  at  an  angle  of  GO  degrees,  is 
sufficiently  established  to  allow  us  to  assume  this  as  the  constant  angle  of 
the  elementary  crystals  of  snow,  which  are  probably  either  triangular  or 
hexagonal  prisms  :  the  deviation  produced  by  such  a  prism  differs  very 
little  from  the  observed  angle  at  which  the  first  circle  is  usually  seen  ;  and 
all  the  principal  phenomena,  which  attend  this  circle,  may  be  explained, 
by  supposing  the  axis  of  the  crystals  to  assume  a  vertical  or  a  horizontal 
position,  in  consequence  of  the  operation  of  gravity :  thus  the  parhelia, 
which  are  sometimes  a  little  more  distant  from  the  sun  than  the  halo,  are 
attributed  by  Mariotte  to  the  refraction  of  the  prisms  which  are  situated 
vertically,  and  produce  a  greater  deviation,  on  account  of  tb?iobliquity  of 
the  rays  of  light  with  respect  to  their  axes.  The  horizontal  circle  may  be 
deduced  from  the  reflection,  or  even  the  repeated  refractions  of  the  vertical 
facets ;  the  anthelia  from  two  refractions  with  an  intermediate  reflection, 
and  the  inverted  arch  from  the  increase  of  the  deviation,  in  the  light 
passing  obliquely,  through  prisms  lying  in  a  horizontal  position.  The 
external  circle  may  be  attributed  either  to  two  successive  refractions 
through  different  prisms,  or  with  greater  probability,  as  Mr.  Cavendish 
has  suggested  to  me,  to  the  effect  of  the  rectangular  terminations  of  the 
single  crystals.  The  appearance  of  colours,  in  halos,  is  nearly  the  same 
as  in  rainbows,  but  less  distinct ;  the  red  being  nearest  to  the  luminary, 
and  the  whole  halo  being  externally  very  ill  defined.  (Plate  XXIX.  Fig. 
431,  432.) 

From  the  observed  magnitude  of  these  halos,  I  had  concluded  that  the 
refractive  power  of  ice  must  be  materially  less  than  that  of  water,  although 
some  authors  had  asserted  that  it  was  greater ;  and  Dr.  Wollaston  after- 
wards fully  confirmed  this  conclusion  by  means  of  the  very  accurate 
instrument  which  has  already  been  described  :  his  measurement  agreeing 
precisely  with  the  mean  of  the  best  observations  on  these  halos ;  so  that 
ice  must  be  considered  as  the  least  refractive  of  any  known  substances  not 
aeriform. 

Sometimes  the  figures  of  halos  and  parhelia  are  so  extremely  compli- 
cated, as  to  defy  all  attempts  to  account  for  the  formation  of  their  different 
parts :  but  if  we  examine  the  representations  which  have  been  given,  by 
various  authors,  of  the  multiplicity  of  capricious  forms  frequently  assumed 
by  the  flakes  of  snow,  we  shall  see  no  reason  to  think  them  inadequate  to 
the  production  of  all  these  appearances.  (Plate  XXIX.  Fig.  433,  434.) 

The  most  singular  of  all  the  phenomena  of  refraction  is  perhaps  the 
property  of  some  natural  substances,  which  have  a  double  effect  on  the 
light  transmitted  through  them,  as  if  two  mediums  of  different  densities 
freely  pervaded  each  other,  the  one  only  acting  on  some  of  the  rays  of 
light,  the  other  on  the  remaining  portion.  These  substances  are  usually 
crystallized  stones,  and  their  refractions  have  sometimes  no  further  pecu- 
liarity ;  but  the  rhomboidal  crystals  of  calcarious  spar,  commonly  called 
Iceland  crystals,  possess  the  remarkable  property  of  separating  such  pencils 
of  light,  as  fall  perpendicularly  on  them,  into  two  parts,  one  of  them  only 
being  transmitted  in  the  usual  manner,  the  other  being  deflected  towards 


ON  PHYSICAL  OPTICS.  349 

the  greater  angle  of  the  crystal.*  It  appears  from  the  experiments  of 
Hi5ygens,t  confirmed  and  extended  by  Dr.  Wollaston,  £  that  the  medium, 
which  causes  the  unusual  refraction,  has  a  different  refractive  power, 
according  to  the  direction  in  which  the  light  passes  through  it,  and  that 
if  an  oblate  or  flattened  spheroid  be  described  within  a  crystal,  its  axis 
being  in  the  middle  of  one  of  the  obtuse  solid  angles,  and  its  principal 
diameters  in  the  proportion  of  9  to  10,  the  refractive  power,  with  respect 
to  light  passing  in  any  direction,  will  always  be  inversely  as  the  diameter 
of  the  spheroid  which  is  parallel  to  it ;  and  where  it  is  greatest,  will  be 
equaLgto  that  of  the  medium  which  produces  the  usual  refraction,  of  which 
the  index  is  -§• .  A  ray  of  light,  falling  perpendicularly  on  any  surface  of 
the  spar,  its  point  of  incidence  being  considered  as  the  centre  of  the  spher- 
oid, will  meef  the  surface  of  the  spheroid  at  the  point  where  it  is  parallel 
to  that  of  the  spar ;  and  a  ray  incident  on  the  same  surface  in  any  other 
direction,  will  preserve  a  relation  to  the  perpendicular  ray,  which  is  nearly 
the  same  as  in  ordinary  refraction.  (Plate  XXIX.  Fig.  435.) 

It  is  also  remarkable,  that  the  two  portions  of  light,  thus  separated,  will 
not  be  further  subdivided  by  a  transmission  through  a  second  piece,  pro- 
vided that  this  piece  be  in  a  position  parallel  to  that  of  the  first ;  but  if  it 
be  placed  in  a  transverse  direction,  each  of  the  two  pencils  will  be  divided 
into  two  others ;  a  circumstance  which  appears  to  be  the  most  unintel- 
ligible of  any  that  has  been  discovered  respecting  the  phenomena  of  double 
refraction. 

The  appearances  of  colours,  which  are  produced  by  transparent  plates 
of  different  thicknesses,  and  of  those  which  are  seen  in  light  variously 
diffracted  or  inflected,  will  be  more  conveniently  examined,  when  we  in- 
vestigate the  intimate  nature  of  light,  since  the  general  explanation  of  these 
colours,  which  will  then  be  given,  will  enable  us  to  follow  them  through 
all  their  varieties,  with  much  more  ease  than  could  be  done  at  present, 
without  the  help  of  some  theory  respecting  their  origin. 


LECT.  XXXVII.— ADDITIONAL  AUTHORITIES. 

Colour  and  dispersion. — Castelli,  Optica  Colorum,  1740.  Euler,  Hist,  et  Mem. 
de  Berlin,  1753,  p.  294.  Acta  Petr.  i.  I.  174.  Nov.  Com.  Petr.  xii.  166.  Dol- 
lond,  Ph.  Tr.  1759,  p.  733.  Beguelin,  Mem.  sur  les  Prismes  Achromatiques,  Hist, 
et  Mem.  de  Berlin,  1762,  p.  66.  Lambert's  Farben-pyramide,  4to,  Berl,  1772. 
Rochon,  Recueil  de  Mecanique,  p.  279.  Comparetti  de  Luce  et  Coloribus,  4to, 
Pad.  1787.  Gruber  iiber  die  Strahlenbrechung,  4to,  Dresd.  1787.  Seebeck, 
Schweig.  Jour.  1810,  p.  1.  Mollweide,  Demonstratio  Prop,  quse  th.  Col.  Hewtoni 
Fundamenti  loco  est,  Lips.  1811.  Hoppe,  Versuch  einer  ganz  neuen  Theorie  der 
Entstehung  Sammtlicher  Farben,  Breslau,  1824.  Deal,  Nouvelle  Essai  sur  la  Lum. 
et  les  Couleurs,  1827.  Talbot,  Ph.  Mag.  iii.  45  ;  iv.  112,  &c.  Brewster,  Ph.  Tr. 
1836,  &c.  Helwag,  Newton's  Farbenlehre,  Liibeck,  1835.  Rudberg,  Pogg.  Ann- 
ix.  483.  An  account  of  Amici's  prismatic  telescope  will  be  found  in  Quetelet's  Sup- 


*  Bartholin  on  Iceland  Crystals  (quibus  mira  et  insolita  refractio  detegitur),  Co- 
penhagen, 1669.     Ph.  Tr.  v.  2039. 
'  t  Traite  de  la  Lumiere  par  C.  H.  D.  Z.  A  Leyde,  1690. 

I  Ph.Tr.  1802,  p.  381.     On  this  subject  see  Beccaria,  Ph.  Tr.  1762,  p.  486  i 
Brewster,  Edin.  Ph.  Jour.  i.  289  ;  ii.  167,  &c.  &c.     See  also  Lect.  XXXIX. 


350  LECTURE  XXXVIII. 

plement  to  Herschel,  p.  432.  Becquerel  on  the  Constitution  of  the  Solar  Spectrum, 
Scientific  Memoirs,  iii.  537. 

Atmospheric  Refraction.  Ordinary. — Cassini,  Novissimae  Motuum  Solis  Epne- 
merides  a  Malvasia  supputatae,  1G61.  Hist,  et  Mem.  i.  103,  1700,  p.  39,  H.  112  ; 
1714,  p.  33,  H.61;  1742,  p.  203,  H.  72;  1743,  p.  249,  H.  140.  Halley,  Ph. 
Tr.  1721,  p.  169,  with  Newton's  table.  Lacaille,  Hist,  et  Mem.  1755,  p.  547.  H. 
111.  Lambert,  Route  de  la  Lumiere  par  les  Airs,  A  la  Haye,  1758.  Lagrange, 
Hist.etMem.de  Berl.  1772,  p.  259.  Maskelyne,  Ph.  Tr.  1777,  p.  722.  Her- 
schel, ibid.  1785,  p.  88.  Oriani,  Ephem.  Mediol.  1788.  Hennert,  Hind.  Arch.ii. 
1,  129.  Kramp,  Analyse  des  Refractions  Astronom.  et  Terr.  4to,  Strasb.  1799. 
Humboldt's  Voy.  i.  134.  Bessel,  Fundamenta  Astronomiae,  fol.  Regiom.  1818, 
pp.28,  43.  Konigsb.  Beobacht.  vii.  38;  viii.  22.  Svanberg,  Nov.  Act.  Upsal, 
ix.  89.  Plana,  Recherches  Analytiques,  4to,  Turin,  1823.  Ivory,  Ph.  Tr.  ,1823, 
p.  409.  T.  Young,  ibid.  1824,  p.  159.  Forster,  Ph.  Mag.  1824,  p.  192. 

Extraordinary. — Mariotte  on  the  Rainbow,  Hist,  et  Mem.  i.  189.  Halley  on 
do.  Ph.  Tr.  1698,  p.  193  ;  1700,  p.  714.  Weidler  de  Parheliis,  4tq,  Wittemb. 
1738.  Biisch,  Tractatus  duo  Optici,  Hamb.  1788.  Huddart  on  Horizontal  Re- 
fractions, Ph.  Tr.  1797,  p.  29.  Latham,  ib.  1798,  p.  357.  Monge  on  the  Mirage 
in  Egypt,  Ann.  de  Ch.  xxix.  207.  Vince  on  Horizontal  Refraction,  Ph.  Tr.  1799, 
p.  13.  Biot,  Mem.  del'Inst.  i.  266.  Brandes,  Beobachtungen  uber  die  Strahlen- 
brechung,  Oldenb.  1807.  Frauenhofer,  Theorie  der  Hofe,  &c.  Schumacher's 
Ast.  Abh.  iii.  33.  Arago,  Bullet.  Univ.  1825. 


LECTURE    XXXVIII. 


ON  VISION. 

THE  medium  of  communication,  by  which  we  become  acquainted  with 
all  the  objects  that  we  have  been  lately  considering,  is  the  eye ;  an  organ 
that  exhibits  to  an  attentive  observer,  an  arrangement  of  various  sub- 
stances, so  correctly  and  delicately  adapted  to  the  purposes  of  the  sense  of 
vision,  that  we  cannot  help  admiring,  at  every  step,  the  wisdom  by  which 
each  part  is  adjusted  to  the  rest,  and  made  to  conspire  in  effects,  so  remote 
from  what  the  mere  external  appearance  promises,  that  we  have  only  been 
able  to  understand,  by  means  of  a  laborious  investigation,  the  nature  and 
operations  of  this  wonderful  structure,  while  its  whole  mechanism  still 
remains  far  beyond  all  rivalship  of  human  art. 

The  eye  is  an  irregular  spheroid,  not  very  widely  differing  from  a 
sphere  ;  it  is  principally  composed  of  transparent  substances,  of  various 
refractive  densities,  calculated  to  collect  the  rays  of  light,  which  diverge 
from  each  point  of  an  object,  to  a  focus  on  its  posterior  surface,  which  is 
capable  of  transmitting  to  the  mind  the  impression  of  the  colour  and 
intensity  of  the  light,  together  with  a  distinction  of  the  situation  of  the 
focal  point,  as  determined  by  the  angular  place  of  the  object.  (Plate 
XXX.  Fig.  436.) 

The  first  refraction  happens  at  the  surface  of  the  cornea,  or  that  trans- 
parent coat  which  projects  forwards  from  the  ball  of  the  eye  :  but  the 
cornea,  being  very  nearly  of  equable  thickness,  has  little  effect  by  its  own 
refractive  power,  and  serves  only  to  give  a  proper  form  to  the  aqueous 


ON  VISION.  351 

humour,  which  fills  its  concavity,  and  distends  it.  This  humour  is  par- 
tially divided  by  the  uvea  or  iris,  which  is  of  different  colours  in  different 
persons,  having  a  perforation  in  its  centre,  called  the  pupil.  Immediately 
behind  the  uvea,  and  closely  connected  to  its  base,  are  the  ciliary  processes, 
the  summits  of  which  hang  like  a  short  fringe,  before  the  crystalline  lens, 
a  substance  much  more  refractive  than  the  aqueous  humour,  and  increas- 
ing in  density  towards  its  centre.  The  remaining  cavity  is  filled  by  an 
aqueous  fluid,  lodged  in  a  cellular  texture  of  extremely  fine  membrane, 
and  called  the  vitreous  humour.  The  retina  lines  the  whole  posterior 
partaof  this  cavity  ;  it  is  semitransparent,  and  is  supported  by  the  choroid 
or  chorioid  coat,  a  very  opaque  black  or  brown  membrane,  continued  from 
the  uvea  and  ciliary  processes  ;  but  immediately  where  the  retina  is  con- 
nected witUPbhe  optic  nerve,  the  choroid  is  necessarily  perforated ;  and  at 
this  part  a  small  portion  of  the  retina  is  nearly  insensible.  The  whole  is 
surrounded  by  an  opaque  continuation  of  the  cornea,  called  the  sclerotica.^ 

The  rays  of  light  which  have  entered  the  cornea  and  passed  through  the 
pupil,  being  rendered  still  more  convergent  by  the  crystalline  lens,  are 
collected  into  foci  on  the  retina,  and  form  there  an  image,  which,  according 
to  the  common  laws  of  refraction,  is  inverted,  since  the  central  rays  of  each 
pencil  cross  each  other  a  little  behind  the  pupil ;  and  the  image  may  easily 
be  seen  in  a  dead  eye,  by  laying  bare  the  posterior  surface  of  the  retina. 
(Plate  XXX.  Fig.  437.) 

By  means  of  this  arrangement  of  the  various  refracting  substances, 
many  peculiar  advantages  are  procured.  The  surface  of  the  cornea  only, 
if  it  had  been  more  convex,  could  not  have  collected  the  lateral  rays  of  a 
direct  pencil  to  a  perfect  focus,  without  a  different  curvature  near  its 
edges ;  and  then  the  oblique  pencils  would  have  been  subjected  to  greater 
aberration,  nor  could  they  have  been  made  to  converge  to  any  focus  on  the 
retina.  A  second  refraction  performs  both  these  offices  much  more  com- 
pletely, and  has  also  the  advantage  of  admitting  a  greater  quantity  of 
light.  If  also  the  surfaces  of  the  crystalline  lens  thus  interposed,  had  been 
abrupt,  there  would  have  been  a  reflection  at  each,  and  an  apparent 
haziness  would  have  interfered  with  the  distinct  view  of  every  luminous 
object;  but  this  inconvenience  is  avoided  by  the  gradual  increase  of 
density  in  approaching  the  centre,  which  also  makes  the  crystalline  equiva- 
lent to  a  much  more  refractive  substance  of  equal  magnitude ;  while,  at 
the  same  time,  the  smaller  density  of  the  lateral  parts  prevents  the  usual 
aberration  of  spherical  surfaces,  occasioned  by  the  too  great  refraction  of 
the  lateral  rays  of  direct  pencils,  and  causes  also  the  focus  of  each  oblique 
pencil  to  fall  either  accurately  or  very  nearly  on  the  concave  surface  of 
the  retina,  throughout  its  extent. 

Opticians  have  often  puzzled  themselves,  without  the  least  necessity,  in 
order  to  account  for  our  seeing  objects  in  their  natural  erect  position,  while 
the  image  on  the  retina  is  in  reality  inverted  :  but  surely  the  situation  of  a 
focal  point  at  the  upper  part  of  the  eye  could  be  no  reason  for  supposing  the 
object  corresponding  to  it  to  be  actually  elevated.  We  call  that  the  lower 
end  of  an  object  which*  is  next  to  the  ground  ;  and  the  image  of  the  trunk 
of  a  tree  ,being  in  contact  with  the  image  of  the  ground  on  the  retina,  we 


352  LECTURE  XXXVIII. 

may  naturally  suppose  the  trunk  itself  to  be  in  contact  with  the  actual 
ground  :  the  image  of  the  branches  being  more  remote  from  that  of  the 
ground,  we  necessarily  infer  that  the  branches  are  higher  and  the  trunk 
lower :  and  it  is  much  simpler  that  we  should  compare  the  image  of  the 
floor  with  the  image  of  our  feet,  with  which  it  is  in  contact,  than  with  the 
actual  situation  of  our  forehead,  to  which  the  image  of  the  floor  on  the 
retina  is  only  accidentally  near,  and  with  which  indeed  it  would  perhaps 
be  impossible  to  compare  it,  as  far  as  we  judge  by  the  immediate  sensa- 
tions only.* 

We  might  indeed  call  in  experience  to  our  assistance,  and  habitually 
correct  the  errors  of  one  sense  by  a  comparison  with  the  perceptions  of 
another.  But  it  appears  that  some  philosophers  have  been  too  hasty  in 
supposing  that  the  use  of  all  our  senses  is  derived  from  experience  alone, 
and  in  disbelieving  the  existence  of  instinct  independent  of  it.  Without 
any  other  authority  than  that  of  their  own  imaginations,  they  have  denied 
the  observation  recorded  by  Galen,  on  the  instincts  of  a  kid,  which  is  suffi- 
ciently credible  to  counterbalance  much  more  than  bare  assertion.  The 
instant  after  its  birth,  accompanied  by  the  loss  of  its  mother,  the  little 
animal  ran  to  some  green  vegetables,  and  having  first  smelt  them,  chewed 
and  swallowed  them.  The  kid  could  have  been  taught  by  no  experience  to 
be  tempted  by  the  sight,  to  act  with  the  proper  muscles  of  locomotion,  to  go 
near  and  smell,  and  to  be  induced  by  the  smell  to  masticate,  and  by  the 
taste  to  swallow  and  digest  its  food,  had  it  not  been  provided  with  some 
fundamental  instinct,  by  the  same  intelligence  which  so  calculated  the 
adjustments  of  the  eye,  that  the  lens  should  be  able  to  produce  a  perfect 
image  of  every  object,  and  that  the  retina  should  be  of  that  precise  form, 
which  is  exactly  suited  to  the  reception  of  the  image  to  be  depicted  on  it. 

The  whole  surface  of  the  retina  appears  to  be  usually  occupied  by  such 
an  image,  but  it  is  not  all  of  equal  sensibility  ;  a  certain  portion  only,  near 
the  axis,  is  capable  of  conveying  distinct  impressions  of  minute  objects. 
But  the  perfection  of  this  limited  distinctness  is  a  far  greater  advantage  to 
us,  than  a  more  extensive  field  of  moderately  accurate  vision  would  have 
been ;  for  by  means  of  the  external  muscles,  we  can  easily  so  change  the 
position  of  the  eye,  that  the  image  of  any  object  before  us  may  be  made 
to  fall  on  the  most  sensible  part  of  the  retina.  We  may  readily  observe 
the  want  of  sensation  at  the  entrance  of  the  optic  nerve,  by  placing  two 
candles  so  that  the  distance  of  each  from  the  eye  may  be  about  four  times 
their  distance  from  each  other:  then  if  we  direct  our  right  eye  to  the 
left  hand  candle,  the  right  hand  candle  will  be  lost  in  a  confused  mass  of 
faint  light,  its  image  on  the  retina  falling  on  the  point  at  which  its  sensi- 
bility is  deficient,  t 

*  Consult  Berkeley  on  Vision,  Dub.  1709.  Lecat,  Traite  des  Sens,  1767.  Wal- 
ter, Berlin  Mem.  1788,  p.  3.  Wells,  Essay  on  Single  Vision,  1791.  Wollaston, 
Ph.  Tr.  1824,  p.  222.  Berthold,  Ueber  das  Aufrecht-erscheinen  der  Gesichtsob- 
jecte,  Gott.  1830.  Bartels,"Beitrage  zur  Phys.  des  Gesichtsinnes,  Berl.  1834. 
Volkmann,  doTLeipz.  1836. 

t  A  better  way  of  doing  this  is  to  make  two  blots  on  a  sheet  of  paper,  about  four 
inches  apart,  and  to  look  attentively  with  the  right  eye  on  that  which  lies  to  the  left 
hand ;  the  eye  being  placed  right  over  it.  When  the  eye  is  raised  to  the  height  of 


ON  VISION.  363. 

When  the  attention  is  not  directed  to  any  particular  object  of  sight,  the 
refractive  powers  of  the  eye  are  adapted  to  the  formation  of  an  image  of 
objects  at  a  certain  distance  only,  which  is  different  in  different  individuals, 
and  also  generally  increases  with  increasing  age.  *  Thus,  if  we  open  our 
eyelids  suddenly,  without  particular  preparation,  we  find  that  distant 
objects  only  appear  as  distinct  as  we  are  able  to  make  them  ;  but  by  an 
exertion  of  the  will,  the  eye  may  be  accommodated  to  the  distinct  percep- 
tion of  nearer  objects,  yet  not  of  objects  within  certain  limits.  Between 
the  ages  of  40  and  50,  the  refractive  powers  of  the  eye  usually  begin  to 
diminish,  but  it  sometimes  happens  that  where  they  are  already  too  great, 
the  defect  continues  unaltered  to  an  advanced  age.  It  appears  also  that 
after  50  or  60,  the  power  of  changing  the  focus  of  the  eye  is  always  much 
impaired,  amjtfstmietimes  wholly  lost. 

The  mode,  in  which  the  accommodation  of  the  eye  to  different  distances 
is  effected,  has  long  been  a  subject  of  investigation  and  dispute  among 
opticians  and  physiologists,  but  I  apprehend  that  at  present  there  is  little 
further  room  for  doubting  that  the  change  is  produced  by  an  increase  of 
the  convexity  of  the  crystalline  lens,  arising  from  an  internal  cause.  The 
arguments  in  favour  of  this  conclusion  are  of  two  kinds ;  some  of  them 
are  negative,  derived  from  the  impossibility  of  imagining  any  other  mode 
of  performing  the  accommodation,  without  exceeding  the  limits  of  the 
actual  dimensions  of  the  eye,  and  from  the  examination  of  the  eye  in  its 
different  states  by  several  tests,  capable  of  detecting  any  other  changes  if 
they  had  existed  :  for  example,  by  the  application  of  water  to  the  cornea, 
which  completely  removes  the  effect  of  its  convexity,  without  impairing 
the  power  of  altering  the  focus,  and  by  holding  the  whole  eye,  when 
turned  inwards,  in  such  a  manner  as  to  render  any  material  alteration  of 
its  length  utterly  impossible.  Other  arguments  are  deduced  from  positive 
evidence  of  the  change  of  form  of  the  crystalline,  furnished  by  the  parti- 
cular effects  of  refraction  and  aberration  which  are  observable  in  the 
different  states  of  the  eye ;  effects  which  furnish  a  direct  proof  that  the 
figure  of  the  lens  must  vary  ;  its  surfaces,  which  are  nearly  spherical  in 
the  quiescent  form  of  the  lens,  assuming  a  different  determinable  curvature 
when  it  is  called  into  exertion.  The  objections  which  have  been  made  to 
this  conclusion  are  founded  only  on  the  appearance  of  a  slight  alteration 
of  focal  length  in  an  eye  from  which  the  crystalline  had  been  extracted  ; 
but  the  fact  is  neither  sufficiently  ascertained,  nor  was  the  apparent  change 
at  all  considerable :  and  even  if  it  were  proved  that  an  eye  without  the 
lens  is  capable  of  a  certain  small  alteration,  it  would  by  no  means  follow 
that  it  could  undergo  a  change  five  times  or  ten  times  as  great,  t 

about  11  inches,  the  second  spot  disappears  as  though  it  had  passed  under  a  curtain  : 
on  continuing  to  lift  the  head,  the  spot  will  reappear  when  the  eye  is  .about  15  inches 
from  the  paper.  This  was  pointed  out  by  Mariotte,  Ph.  Tr.  1G68,  p.  668  ;  1670, 
p.  1023.  On  the  vanishing  of  images  at  points  not  coincident  with  the  entrance  of 
the  optic  nerve,  consult  Brewster's  Jour,  of  Sci.  iii.  289. 

*  On  the  effects  of  attention  in  vision  see  Purkinje,  Beobachtungen  zur  Physio- 
logic der  Sinne,  vol.  i.  Prag.  1823  ;  vol.  ii.  Berlin,  1825.  Heermann,  Ueber  die 
BHdung  der  Gesichtsvorstellungen,  Hanover,  1835. 

t  Consult  Pemberton,  De  Facultate  Oc.  ad  Diversas  Dist.  se  Acoommodandi, 
Lug.  Bat.  1719.  Camper,  De  Oculo  Humane,  Lug.  Bat.  1742.  Albinus,  Lug. 

2  A 


354  LECTURE  XXXVIII. 

The  iris  serves,  by  its  variable  magnitude,  to  exclude  more  or  less  of  the 
light  falling  on  the  cornea,  when  its  intensity  would  otherwise  be  too  great ; 
hence  the  pupil  is  usually  smallest  by  day,  and  its  increased  magnitude  at 
night  sometimes  gives  the  eye  a  greater  apparent  lustre.  The  iris  also  inter- 
cepts such  rays  as  would  fall  on  parts  incapable  of  refracting  them  regu- 
larly ;  and  by  its  contraction  when  a  nearer  object  is  viewed,  it  lessens  the 
confusion  which  would  arise,  in  such  eyes  as  cannot  accommodate  them- 
selves sufficiently,  from  the  magnitude  of  the  imperfect  focal  points  on  the 
retina.  Such  a  contraction  almost  always  accompanies  the  diminution  of 
the  focal  length,  even  in  a  perfect  eye,  and  it  may  easily  be  rendered  visible 
by  walking  gradually  up  to  a  looking  glass,  and  observing  the  magnitude 
of  the  pupil  as  we  approach  nearer  and  nearer  to  our  image.  It  would  be 
difficult  to  assign  a  reason  for  this  change  of  the  state  of  theTpupil  within 
the  limits  of  perfect  vision,  unless  we  allowed  the  irregularity  of  the  form 
assumed  by  the  marginal  parts  of  the  crystalline  lens.  The  iris  is  also 
peculiarly  useful  in  excluding  such  parts  of  lateral  pencils  of  light  as 
fall  very  obliquely  on  the  cornea,  and  are  too  much  refracted,  while  a 
smaller  pencil  only,  which  enters  the  eye  more  directly,  is  admitted  into 
the  pupil. 

The  refractive  powers  and  properties  of  the  eye  may  be  very  conveniently 
ascertained  by  means  of  an  instrument  to  which  I  have  given  the  name 
optometer,  a  term  first  employed  in  a  sense  nearly  similar  by  Dr.  Porter- 
field.*  If  two  or  more  separate  parcels  of  the  rays  of  the  same  pencil  be 
admitted  at  distant  parts  of  the  pupil,  they  will  only  be  reunited  on  the 
retina  when  the  focus  is  perfect,  so  that  if  we  look  through  two  small  per- 
forations, or  slits,  at  a  minute  object,  to  the  distance  of  which  the  eye  is 
not  accommodated,  it  will  appear  as  if  double ;  and  when  the  object  is  a 
line  directed  nearly  towards  the  eye,  each  point  of  it  will  appear  double, 
except  that  which  is  at  the  distance  of  perfect  vision,  and  an  image  of  two 
lines  will  be  seen,  crossing  each  other  in  this  point ;  so  that  the  measure- 
ment of  the  focal  length  of  the  eye  is  immediately  performed  by  inspection 
of  the  optometer  only.  The  scale  may  be  extended  by  the  addition  of  a 
lens,  which  enables  us  to  produce  the  effect  of  a  longer  line,  while  the 
instrument  still  remains  portable. 

When  the  eye  is  possessed  of  too  great  a  refractive  power  for  the  distinct 
perception  of  distant  objects,  the  pupil  is  generally  large,  so  that  the  confu- 
sion of  the  image  is  somewhat  lessened  by  partially  closing  the  eyelids ; 
and  from  this  habit  an  eye  so  formed  is  called  myopic.  In  such  cases,  by 
the  help  of  a  concave  lens,  the  divergence  of  the  rays  of  light  may  be 
increased,  and  a  virtual  image  may  be  formed,  at  a  distance  so  much 
smaller  than  that  of  the  object  as  to  afford  perfect  vision.  For  a  long 

Bat.  1746.  Le  Roy,  Mem.  sur  la  M6e.  par  lequel  1'CEil  s'Accommode,  Hist,  et 
Mem.  1755,  p.  594.  Gibers,  De  Oculi  Mutationibus  Intends,  4to,  Gott.  1780. 
Young,  Ph.  Tr.  1793,  p.  169  ;  1801,  p.  23.  De  Corp.  Hum.  Viribus  Conserva- 
tricibus,  Gott.  1780.  Hunter,  Ph.  Tr.  1794,  p.  21.  Home,  ibid.  1800,  p.  146. 
Brewster  in  Ed.  Jour,  of  Science,  i.  77.  Treviranus,  zur  Anat.  der  Sinneswerk- 
zeuge,  1828.  Kolrausch  on  Treviranus'  Hypoth.  1837.  Luchtman,  De  Mutatione 
Oculi,  Tr.  ad  Rhenum,  1832.  Simonoff,  Jour,  de  Physiol.  iv.  260. 
*  Edinb.  Med.  Essays,  iv.  185. 


ON  VISION.  355 

sighted  or  presbyopic  eye,  on  the  contrary,  a  convex  lens  is  required,  in 
order  to  obtain  a  virtual  image  at  a  greater  distance  than  the  olyect ;  and 
it  often  happens  that  the  rays  must  be  made  not  only  to  diverge  less  than 
before,  but  even  to  converge  towards  a  focus  behind  such  an  eye,  in  order 
to  make  its  vision  distinct.  Presbyopic  persons  have  in  general  a  small 
pupil,  and,  therefore,  seldom  acquire  the  habit  of  covering  any  part  of  it 
with  their  eyelids. 

When  the  images  of  the  same  object  fall  on  certain  corresponding  points 
of  the  retina  in  each  eye,*  they  appear  to  the  sense  only  as  one ;  but  if 
they  fall  on  parts  not  corresponding,  the  object  appears  double  ;f  and  in 
general,  all  objects  at  the  same  distance,  in  any  one  position  of  the  eyes, 
appear  ajlke  either  double  or  single.  The  optical  axes,  or  the  directions 
of  the  rays  falling  on  the  points  of  most  perfect  vision,  naturally  meet  at 
a  great  distance ;  that  is,  they  are  nearly  parallel  to  each  other,  and  in 
looking  at  a  nearer  object  we  make  them  converge  towards  it,  wherever  it 
may  be  situated,  by  means  of  the  external  muscles  of  the  eye ;  while  in 
perfect  eyes  the  refractive  powers  are  altered,  at  the  same  time,  by  an 
involuntary  sympathy,  so  as  to  form  a  distinct  image  of  an  object  at  the 
given  distance.  This  correspondence  of  the  situation  of  the  axes  with  the 
focal  length  is  in  most  cases  unalterable  ;  but  some  have  perhaps  a  power 
of  deranging  it  in  a  slight  degree,  and  in  others  the  adjustment  is  imper- 
fect :  but  the  eyes  seem  to  be  in  most  persons  inseparably  connected  toge- 
ther with  respect  to  the  changes  that  their  refractive  powers  undergo, 
although  it  sometimes  happens  that  those  powers  are  originally  very  dif- 
ferent in  the  opposite  eyes. 

These  motions  enable  us  to  judge  pretty  accurately,  within  certain 
limits,  of  the  distance  of  an  object ;  and  beyond  these  limits,  the  degree 
of  distinctness  or  confusion  of  the  image  still  continues  to  assist  the  judg- 
ment. We  estimate  distances  much  less  accurately  with  one  eye  than 
with  both,  since  we  are  deprived  of  the  assistance  usually  afforded  by  the 
relative  situation  of  the  optical  axes ;  thus  we  seldom  succeed  at  once  in 
attempting  to  pass  a  finger  or  a  hooked  rod  sideways  through  a  ring,  with 
one  eye  shut.  Our  idea  of  distance  is  also  usually  regulated  by  a  know- 
ledge of  the  real  magnitude  of  an  object,  while  we  observe  its  angular 
magnitude  ;  and  on  the  other  hand  a  knowledge  of  the  real  or  imaginary 
distance  of  the  object  often  directs  our  judgment  of  its  actual  magnitude. 
The  quantity  of  light  intercepted  by  the  air  interposed,  and  the  intensity 
of  the  blue  tint  which  it  occasions,  are  also  elements  of  our  involuntary 
calculation  :  hence,  in  a  mist,  the  obscurity  increases  the  apparent  distance, 
and  consequently  the  supposed  magnitude,  of  an  unknown  object.  We 
naturally  observe,  in  estimating  a  distance,  the  number  and  extent  of  the 

*  On  corresponding  points  of  the  two  retinae,  see  Newton,  Op.  Qu.  15.  Wol- 
laston,  Ph.  Tr.  1824.  On  single  vision,  see  Le  Clerc,  Paris,  1679.  Wells,  Lond. 
1791.  Herholt,  Kopenhag.  1814.  Wollaston,  Ph.  Tr.  1824,  p.  222.  Twining, 
Ed.  Jour.  ix.  143. 

f  The  most  simple  mode  of  witnessing  this  is  to  place  a  small  wafer  on  a  pane  of 
a  window,  and  to  look  attentively  through  that  pane  at  a  well-defined  object  without 
so  as  to  fix  the  direction  of  the  axes  of  the  eyes.  The  spot  will  be  distinctly 
doubled. 


356  LECTURE  XXXVIII. 

intervening  objects  ;  so  that  a  distant  church  in  a  woody  and  hilly  country 
appears  more  remote  than  if  it  were  situated  in  a  plain  ;  and  for  a  similarr 
reason,  the  apparent  distance  of  an  object  seen  at  sea,  is  smaller  than  its 
true  distance.  The  city  of  London  is  unquestionably  larger  than  Paris  ; 
but  the  difference  appears  at  first  sight  much  greater  than  it  really  is  ;  and 
the  smoke,  produced  by  the  coal  fires  of  London,  is  probably  the  principal 
cause  of  the  deception. 

The  sun,  moon,  and  stars,  are  much  less  luminous  when  they  are  near 
the  horizon,  than  when  they  are  more  elevated,  on  account  of  the  greater 
quantity  of  their  light  that  is  intercepted,  in  its  longer  passage  through 
the  atmosphere  :  we  also  observe  a  much  greater  variety  of  nearer  objects 
almost  in  the  same  direction :  we  cannot,  therefore,  help  imagining  them 
to  be  more  distant,  when  they  rise  or  set,  than  at  other  times ;  and  since 
they  subtend  the  same  angle,  they  appear  to  be  actually  larger.  For  similar 
reasons  the  apparent  figure  of  the  starry  heavens,  even  when  free  from 
clouds,  is  that  of  a  flattened  vault,  its  summit  appearing  to  be  much  nearer 
to  us  than  its  horizontal  parts,  and  any  of  the  constellations  seems  to  be 
considerably  larger  when  it  is  near  the  horizon  than  when  in  the  zenith.  * 
(Plate  XXX.  Fig.  438.) 

The  faculty  of  judging  of  the  actual  distance  of  objects  is  an  impedi- 
ment to  the  deception,  which  it  is  partly  the  business  of  a  painter  to  pro- 
duce. Some  of  the  effects  of  objects  at  different  distances  may,  however, 
be  imitated  in  painting  on  a  plane  surface.  Thus,  supposing  the  eye  to  be 
accommodated  to  a  given  distance,  objects  at  all  other  distances  may  be 
represented  with  a  certain  indistinctness  of  outline,  which  would  accom- 
pany the  images  of  the  objects  themselves  on  the  retina :  and  this  indis- 
tinctness is  so  generally  necessary,  that  its  absence  has  the  disagreeable 
effect  called  hardness.  The  apparent  magnitude  of  the  subjects  of  our 
design,  and  the  relative  situations  of  the  intervening  objects,  may  be  so 
imitated  by  the  rules  of  geometrical  perspective  as  to  agree  perfectly  with 
nature,  and  we  may  still  further  improve  the  representation  of  distance  by 
attending  to  the  art  of  aerial  perspective,  which  consists  in  a  due  observa- 
tion of  the  loss  of  light,  and  the  bluish  tinge,  occasioned  by  the  interposi- 
tion of  a  greater  or  less  depth  of  air  between  us  and  the  different  parts  of 
the  scenery. 

We  cannot  indeed  so  arrange  the  picture,  that  either  the  focal  length 
of  the  eye,  or  the  position  of  the  optical  axes,  may  be  such  as  would  be 
required  by  the  actual  objects :  but  we  may  place  the  picture  at  such  a 
distance  that  neither  of  these  criterions  can  have  much  power  in  detecting 
the  fallacy  ;  or,  by  the  interposition  of  a  large  lens,  we  may  produce  nearly 
the  same  effects  in  the  rays  of  light,  as  if  they  proceeded  from  a  picture  at 
any  required  distance.  In  the  panorama,  which  has  lately  been  exhibited 
in  many  parts  of  Europe,  the  effects  of  natural  scenery  are  very  closely 
imitated :  the  deception  is  favoured  by  the  absence  of  all  other  visible 
objects,  and  by  the  faintness  of  the  light,  which  assists  in  concealing  the 
defects  of  the  representation,  and  for  which  the  eye  is  usually  prepared,  by 

*  Hooke  on  the  Horizontal  Moon,  Birch,  iii.  503,  507. 


ON  VISION.  357 

being  long  detained  in  the  dark  winding  passages,  which  lead  to  the  place 
<5f  exhibition. 

The  impressions  of  light  on  the  retina  appear  to  be  always  in  a  certain 
degree  permanent,  and  the  more  so  as  the  light  is  stronger  ;  but  it  is  uncer- 
tain whether  the  retina  possesses  this  property  merely  as  a  solar  phosphorus, 
or  in  consequence  of  its  peculiar  organization.  The  duration  of  the  im- 
pression is  generally  from  one  hundredth  of  a  second  to  half  a  second,  or 
more  ;  hence  a  luminous  object  revolving  in  a  circle  makes  a  lucid  ring  ; 
and  a  shooting  star  leaves  a  train  of  light  behind  it,  which  is  not  always 
real.  If  the  object  is  painfully  bright,  it  generally  produces  a  permanent 
spot,  which  continues  to  pass  through  various  changes  of  colour  for  some 
time,  wiiVut  much  regularity,  and  gradually  vanishes :  this  may,  how- 
ever, be  considered  as  a  morbid  effect. 

When  the  eye  has  been  fixed  on  a  small  object  of  a  bright  colour, 
and  is  then  turned  away  to  a  white  surface,  a  faint  spot,  resembling  in 
form  and  magnitude  the  object  first  viewed,  appears  on  the  surface,  of  a 
colour  opposite  to  the  first,  that  is,  of  such  a  colour  as  would  be  produced 
by  withdrawing  it  from  white  light ;  thus  a  red  object  produces  a  bluish 
green  spot ;  and  a  bluish  green  object  a  red  spot.  The  reason  of  this 
appearance  is  probably  that  the  portion  of  the  retina,  or  of  the  sensorium, 
that  is  affected,  has  lost  a  part  of  its  sensibility  to  the  light  of  that  colour, 
with  which  it  has  been  impressed,  and  is  more  strongly  affected  by  the 
other  constituent  parts  of  the  white  light.  A  similar  effect  is  also  often 
produced,  when  a  white,  or  grey  object  is  viewed  on  a  coloured  ground, 
even  without  altering  the  position  of  the  eye  :  the  whole  retina  being 
affected  by  sympathy  nearly  in  the  same  manner  as  a  part  of  it  was 
affected  in  the  former  case.  These  appearances  are  most  conveniently 
exhibited  by  means  of  the  shadows  of  objects  placed  in  coloured  light :  the 
shadow  appearing  of  a  colour  opposite  to  that  of  the  stronger  light,  even 
when  it  is  in  reality  illuminated  by  a  fainter  light  of  the  same  colour.  It 
seems  that  the  eye  cannot  perfectly  distinguish  the  intensity  of  a  colour, 
either  when  the  light  is  extremely  faint,  as  that  of  many  of  the  fixed  stars, 
which  Dr.  Herschel  has  found  to  be  strongly  coloured,  or  when  the  light  ' 
is  excessively  vivid  ;  and  that  when  a  considerable  part  of  the  field  of  vision 
is  occupied  by  coloured  light,  it  appears  to  the  eye  either  white,  or  less 
coloured  than  it  is  in  reality  :  so  that  when  a  room  is  illuminated  either 
by  the  yellow  light  of  a  candle,  or  by  the  red  light  of  a  fire,  a  sheet  of 
writing  paper  still  appears  to  retain  its  whiteness ;  and  if  from  the  light  of 
the  candle  we  take  away  some  of  the  abundant  yellow  light,  and  leave  or 
substitute  a  portion  actually  white,  the  effect  is  nearly  the  same  as  if  we 
took  away  the  yellow  light  from  white,  and  substituted  the  indigo  which 
would  be  left :  and  we  observe  accordingly,  that  in  comparison  with  the 
light  of  a  candle,  the  common  daylight  appears  of  a  purplish  hue.  (Plate 
XXX.  Fig.  439.. .441.) 


LECT.  XXXVIII.-ADDITIONAL  AUTHORITIES. 

Vision.— Fabricius  ab  Aquapendente,  fol.  Yen.  1600.     Scheineri,  Oculus     4to 
Rom.    1652.     Cherubin,  Vision  parfaite,  1678.     Briggs,   Ph.  Tr.  1683,  p.  17l! 


358  LECTURE  XXXVIII. 

Laurentius,  Mis.  Ac.  Nat.  Cur.  1684,  App.  157.  Trabers,  Nervus  Opticus,  fol.  Vien. 
1690.  Bernoulli,  Com.  Petr.  i.  314.  Scarella,  Com.  Bon.  v.  I.  110;  ii.  446  ;  vi. 
O.  344.  Bonati,  Mem.  della  Soc.  Ital.  ii.  676.  Gauteron,  Mem.  de  Montpellier,  i. 
23.  Wiinsch,  Visus  Phoen.  qusedam,  4to,  Lips.  1776.  Adams  on  Vision,  1792. 
DuTour,  Mem.  de  Tlnstitut,  iii.  514;  iv.  499;  v.  677;  vi.  241.  Horn  on  the 
Seat  of  Vision,  1813.  Muhlibach,  Inquisitio  de  Visus  Sensu.  Vindob.  1816.  Sir 

C.  Bell  on  the  Motions  of  the  Eye,  Ed.  Ph.  Jour.  xii.  371 ;  Ph.  Tr.  1823,  pp.  166, 
289.     Brewster  on  do.  Ed.  Jour,  of  Sc.  ii.  1  ;  3rd  Series,  ii.  168  ;  v.  259.     Smith, 
ibid.  v.  52  and  3rd  Series,  i.  249.     Lehot,   Nouvelle  Theorie  de  la  Vision,    1825. 
Miiller,  Vergleichende  Physiologic  des  Gescihtsinnes,  Leipz.  1826.     Plagge,   Hec- 
ker's  Annallen,  1830,  p.  404.     Hanow,  Danz.  Nat.  Ges.  Neue  Sam.  i.  1.     Quete- 
let,   Pog.   Ann.  xxxi.  494.     Mbser  on  Vision,  &c,  Scientific   Memoirs,   iii.  422. 
Mackenzie,  Physiology  of  Vision,  1841. 

Structure  of  the  Eye Vasali,  De  Hum.  Corp.  fabrica,  Bas.  1543.     Leeuwen- 

hoek  on  the  Crystalline  Lens,  Ph.  Tr.  1684,  p.  780.  On  the  Eyes  of  Insects,  ibid. 
1698,  p.  169.  On  the  Eyes  of  Whales,  &c.  ibid.  1704,  1723.  B.rigg'4  Ophthal- 
mographia,  1686.  Zahn,  Oculus  artificialis,  fol.  Nuremb.  1702.  Petit  on  the 
Chambers  of  the  Eye.  Hist,  et  Mem.  de  Paris,  1723,  p.  38,  H.  19  ;  1728,  pp. 
206,  289,  H.  17.  On  the  Capsule  of  the  Crystalline,  ibid.  1730,  p.  435,  H.  33 ;  viii. 
612.  On  the  Crystalline  in  different  Animals,  ibid.  1730,  p.  4,  H.  33.  Eye  of  the 
Turkey,  ibid.  1735,  p.  123.  Of  the  Owl,  ibid.  1736,  p.  121.  Of  the  Frog  and 
the  Tortoise,  ibid.  1737,  p.  142.  Appel,  De  Oculi  Humani  Fabrica,  Lug.  Bat. 
1740.  Haller,  Disquisitiones  Anatom.  6  vols.  4to,  Gott.  1746.  Zinn,  Descriptio 
Oculi  Humani,  4to,  Gott.  1753.  Von  Grimm,  De  Visu,  Gott.  1758.  Albinus, 
Mussch.  Introd.  ii.  744.  Haseler,  Ueber  das  Menschliche  auge.  Hamb.  1771. 
Horrebow,  De  Oculo  Humano,  Hafn.  1792.  Monro,  Treatises  on  the  Brain,  the 
Eye,  and  the  Ear,  4to,  Edin.  1797.  Rudolph,  De  Oculi  Partibus,  4to,  Greifsw.  1801. 
S.  T.  Sommering  Abbildungen  des  Menschlichen  Auges,  fol.  Frank.  1801.  Che- 
nevix,  Ph.  Tr.  1803,  p.  195.  Schreger,  Anatomie  des  Auges.  Leipz.  1810.  Blu- 
menthal,  De  Externis  Oculi  Integumentis,  4to,  Berol.  1812.  Bock,  Beschreibung 
des  f  iinfter  Nervenpaares  Meissen,  1817.  Hegar,  De  Oculi  Partibus,  Gott.  1818. 

D.  W.  Sommering  Com.  Gott.   1818.     Home,    Ph.  Tr.  1822,  p.  76.     Brewster, 
Ed.  Ph.  Jour.  i.  42  ;  Ph.  Tr.  1833,  p.  323.     Knox,  ibid.  ix.  358 ;  x.  323,  338. 

Achromatism  of  the  Eye. — D'Alembert,  Opusc.  de  Math.  viii.  324.  Maskelyne, 
Ph.  Tr.  Ixxix.  256.  Tortual,  Meckel's  Archiv.  1830,  p.  129.  Powell,  Report  of 
Br.  Ass.  1833,  p.  374.  Frauenhofer,  Gilb.  Ann.  Ivi.  304.  Brewster,  Phil.  Mag. 
ix.  358.  Powell  in  Reply,  ibid.  vi.  247. 

Duration  of  Impressions. — Segner,  De  Raritate  Luminis.  Gott.  1740.  D'Arcy, 
Hist,  et  Mem.  ix.  614.  Roget,  Ph.  Tr.  1825,  p.  131.  ^Plateau,  Dissertation  sur 
quelques  Proprietes  des  Impressions  produites  par  la  Lumiere  sur  1'Organe  de  la  Vue, 
Liege,  1829.  Annales  de  Chimie,  liii.  304.  Stamfer,  Die  Stroboskopischen 
Scheiben.  Wien,  1833.  Homer  on  the  Daedalium,  Ph.  Mag.  iv.  36.  Wheatstone 
on  the  Velocity  of  Electrical  Light,  Ph.  Tr.  1835,  p.  583.  Description  of  the 
Kaleidophon,  Quart.  Jour,  of  Science,  xi.  344.  See  also  Faraday,  Jour,  of  Roy. 
Inst.  i.  205.  Dandelin,  Mem.  de  Bruxelles,  ii.  169.  Talbot,  Ph.  Mag.  iv.  113. 
Addams,  ibid.  v.  373.  Dove,  Pogg.  Ann.  xxxv.  379. 

Miscellaneous. — Buffon  on  Accidental  Colours,  Hist,  et  Mem.  1743,  p.  147. 
Darwin  on  Ocular  Spectra,  Ph.Tr.  1786,  p.  313.  Brewster  on  the  Optical  Illusion 
of  the  Conversion  of  Cameos  into  Intaglios,  Ed.  Jour,  of  Sci.  iv.  99.  Ph.  Mag. 
Wollaston  on  the  Direction  of  the  Eyes  in  a  Portrait,  Ph.  Tr.  1824,  p.  247.  New- 
ton (Sir  I.)  on  Ocular  Spectra,  Ed.  Jour,  of  Sc.  iv.  75.  Brewster  on  do.  Ph.  Mag. 
iv.  353.  On  the  Influence  of  successive  Impulses  on  the  Retina,  ibid.  iv.  241. 
Plateau  Sur  le  Phenomene  des  Couleurs  accidentelles,  Ann.  de  Ch.  liii.  386.  Essai 
d'une  Theorie  generate  comprenant  les  Couleurs  accidentalles,  &c.  ibid.  Iviii.  337. 
Chevreuil  sur  1'Influence  que  deux  Couleurs  peuvent  avoir  1'une  sur  1'autre,  Mem. 
de  I'lnstit.  xi.  448.  Dalton  on  some  Facts  relating  to  the  Vision  of  Colours, 
Manch.  Mem.  v.  28 ;  Dalton  could  not  distinguish  blue  from  pink  by  daylight, 
but  by  candlelight  the  pink  appeared  red.  Tortual,  Ueber  die  Escheinung  des 
Schattens,  Berl.  1830. 


359 


XECTURE    XXXIX, 


ON  THE  NATURE  OF  LIGHT  AND  COLOURS. 

THE  nature  of  light  is  a  subject  of  no  material  importance  to  the  con- 
cerns of  life  or  to  the  practice  of  the  arts,  but  it  is  in  many  other  respects 
extremely  interesting,  especially  as  it  tends  to  assist  our  views  both  of  the 
natflre  of  our  sensations,  and  of  the  constitution  of  the  universe  at  large. 
The  examination  of  the  production  of  colours,  in  a  variety  of  circum- 
stances, it  f:?timately  connected  with  the  theory  of  their  essential  properties, 
and  their  causes  ;  and  we  shall  find  that  many  of  these  phenomena  will 
afford  us  considerable  assistance  in  forming  our  opinon  respecting  the 
nature  and  origin  of  light  in  general. 

It  is  allowed  on  all  sides,  that  light  either  consists  in  the  emission  of  very 
minute  particles  from  luminous  substances,  which  are  actually  projected, 
and  continue  to  move  with  the  velocity  commonly  attributed  to  light,  or 
in  the  excitation  of  an  undulatory  motion,  analogous  to  that  which  con- 
stitutes sound,  in  a  highly  light  and  elastic  medium  pervading  the  universe  ; 
but  the  judgments  of  philosophers  of  all  ages  have  been  much  divided  with 
respect  to  the  preference  of  one  or  the  other  of  these  opinions.  There  are 
also  some  circumstances  which  induce  those,  who  entertain  the  first  hypo- 
thesis, either  to  believe,  with  Newton,*  that  the  emanation  of  the  par- 
ticles of  light  is  always  attended  by  the  undulations  of  an  etherial  medium, 
accompanying  it  in  its  passage,  or  to  suppose,  with  Boscovich,t  that  the 
minute  particles  of  light  themselves  receive,  at  the  time  of  their  emission, 
certain  rotatory  and  vibratory  motions,  which  they  retain  as  long  as  their 
projectile  motion  continues.  These  additional  suppositions,  however  neces- 
sary they  may  have  been  thought  for  explaining  some  particular  pheno- 
mena, have  never  been  very  generally  understood  or  admitted,  although  no 
attempt  has  been  made  to  accommodate  the  theory  in  any  other  manner  to 
those  phenomena. 

We  shall  proceed  to  examine  in  detail  the  manner  in  which  the  two 
principal  hypotheses  respecting  light  may  be  applied  to  its  various  proper- 
ties and  affections  ;  and  in  the  first  place  to  the  simple  propagation  of  light 
in  right  lines  through  a  vacuum,  or  a  very  rare  homogeneous  medium.  In 
this  circumstance  there  is  nothing  inconsistent  with  either  hypothesis  ;  but 
it  undergoes  some  modifications,  which  require  to  be  noticed,  when  a  por- 
tion of  light  is  admitted  through  an  aperture,  and  spreads  itself  in  a  slight 
degree  in  every  direction.  In  this  case  it  is  maintained  by  Newton  that 
the  margin  of  the  aperture  possesses  an  attractive  force,  which  is  jcapable 
of  inflecting  the  rays  :  but  there  is  some  improbability  in  supposing  that 
bodies  of  different  forms  and  of  various  refractive  powers  should  possess 
an  equal  force  of  inflection,  as  they  appear  to  do  in  the  production  of  these 

*     *  Ph.  Tr.  vii.  5087. 

f  Dissertatio  de  Lumine,  Part  II.  1748  ;  and  Theoria  Philosopbia  Naturalis,  4to», 
'Venice,  1763,  p.  230. 


SCO  LECTURE  XXXIX. 

effects  ;  and  there  is  reason  to  conclude  from  experiments,  that  such  a  » 
force,  if  it  existed,  must  extend  to  a  very  considerable  distance  from  tfie 
surfaces  concerned,  at  least  a  quarter  of  an  inch,  and  perhaps  much  more, 
which  is  a  condition  not  easily  reconciled  with  other  phenomena.  In  the 
Huygehian  system  of  undulation,  this  divergence  or  diffraction  is  illus- 
trated by  a  comparison  with  the  motions  of  waves  of  water  and  of  sound, 
both  of  which  diverge  when  they  are  admitted  into  a  wide  space  through 
an  aperture,  so  much  indeed  that  it  has  usually  been  considered  as  an  ob- 
jection to  this  opinion,  that  the  rays  of  light  do  not  diverge  in  the  degree 
that  would  be  expected  if  they  were  analogous  to  the  waves  of  water.  'But 
as  it  has  been  remarked  by  Newton,*  that  the  pulses  of  sound  diverge  less 
than  the  waves  of  water,  so  it  may  fairly  be  inferred,  that  '^ae-  ^till  more 
highly  elastic  medium,  the  undulations,  constituting  light,  must  diverge 
much  less  considerably  than  either.  (Plate  XX.  Fig.  26G.) 

With  respect,  however,  to  the  transmission  of  light  through  perfectly 
transparent  mediums  of  considerable  density,  the  system  of  emanation 
labours  under  some  difficulties.  It  is  not  to  be  supposed  that  the  particles 
of  light  can  perforate  with  freedom  the  ultimate  atoms  of  matter,  which 
compose  a  substance  of  any  kind  ;  they  must,  therefore,  be  admitted  in  all 
directions  through  the  pores  or  interstices  of  those  atoms  ;  for  if  we  allow 
such  suppositions  as  Boscovich's,  that  matter  itself  is  penetrable,  that  is, 
immaterial,  it  is  almost  useless  to  argue  the  question  further.  It  is  cer- 
tain that  some  substances  retain  all  their  properties  when  they  are  reduced 
to  the  thickness  of  the  ten  millionth  of  an  inch  at  most,  and  we  cannot  there- 
fore suppose  the  distances  of  the  atoms  of  matter  in  general  to  be  so  great 
as  the  hundred  millionth  of  an  inch.  Now  if  ten  feet  t)f  the  most  trans- 
parent water  transmits,  without  interruption,  one  half  of  the  light  that  enters 
it,  each  section  or  stratum  of  the  thickness  of  one  of  these  pores  of  matter 
must  intercept  only  about  one  twenty  thousand  millionth,  and  so  much  must 
the  space  or  area  occupied  by  the  particles  be  smaller  than  the  interstices 
between  them,  and  the  diameter  of  each  atom  must  be  less  than  the  hun- 
dred and  forty  thousandth  part  of  its  distance  from  the  neighbouring  par- 
ticles ;  so  that  the  whole  space  occupied  by  the  substance  must  be  as  little 
filled  as  the  whole  of  England  would  be  filled  by  a  hundred  men,  placed  at 
the  distance  of  about  thirty  miles  from  each  other.  This  astonishing 
degree  of  porosity  is  not  indeed  absolutely  inadmissible,  and  there  are 
many  reasons  for  believing  the  statement  to  agree  in  some  measure  with 
the  actual  constitution  of  material  substances ;  but  the  Huygenian  hypo- 
thesis does  not  require  the  disproportion  to  be  by  any  means  so  great,  since 
the  general  direction  and  even  the  intensity  of  an  undulation  would  be 
very  little  affected  by  the  interposition  of  the  atoms  of  matter,  while  these 
atoms  may  at  the  same  time  be  supposed  to  assist  in  the  transmission  of 
the  impulse,  by  propagating  it  through  their  own  substance.  Euler  indeed 
imagined  that  the  undulations  of  light  might  be  transmitted  through  the 
gross  substance  of  material  bodies  alone,  precisely  in  the  same  manner  as 
sound  is  propagated  ;  but  this  supposition  is  for  many  reasons  inadmis-' 
sible. 

*  Op.  Qu.  28. 


ON  THE  NATURE  OF  LIGHT  AfrD  COLOURS.  3G1 

A  very  striking  circumstance,  respecting  the  propagation  of  light,  is  the 
uniformity  of  its  velocity  in  the  same  medium.  According  to  the  projec- 
tile hypothesis,  the  force  employed  in  the  free  emission  of  light  must  be 
about  a  million  million  times  as  great  as  the  force  of  gravity  at  the  earth's 
surface  ;  and  it  must  either  act  with  equal  intensity  on  all  the  particles  of 
light,  or  must  impel  some  of  them  through  a  greater  space  than  others, 
if  its  action  be  less  powerful,  since  the  velocity  is  the  same  in  all  cases  ; 
for  example,  if  the  projectile  force  is  weaker  with  respect  to  red  light  than 
with  respect  to  violet  light,  it  must  continue  its  action  on  the  red  rays  to  a 
greater  distance  than  on  the  violet  rays.  There  is  no  instance  in  nature 
besides  of  a  simple  projectile  moving  with  a  velocity  uniform  in  all  cases, 
whateve^iiir1  ^be  its  cause,  and  it  is  extremely  difficult  to  imagine  that  so 
immense  a  force  of  repulsion  can  reside  in  all  substances  capable  of 
becoming  luminous,  so  that  the  light  of  decaying  wood,  or  of  two  pebbles 
rubbed  together,  may  be  projected  precisely  with  the  same  velocity  as  the 
light  emitted  by  iron  burning  in  oxygen  gas,  or  by  the  reservoir  of  liquid 
fire  on  the  surface  of  the  sun.  Another  cause  would  also  naturally  inter- 
fere with  the  uniformity  of  the  velocity  of  light,  if  it  consisted  merely  in 
the  motion  of  projected  corpuscles  of  matter  ;  Mr.  Laplace  has  calculated,* 
that  if  any  of  the  stars  were  250  times  as  great  in  diameter  as  the  sun, 
its  attraction  would  be  so  strong  as  to  destroy  the  whole  momentum  of  the 
corpuscles  of  light  proceeding  from  it,  and  to  render  the  star  invisible  at  a 
great  distance  ;  and  although  there  is  no  reason  to  imagine  that  any  of  the 
stars  are  actually  of  this  magnitude,  yet  some  of  them  are  probably  many 
times  greater  than  our  sun,  and  therefore  large  enough  to  produce  such  a 
retardation  in  the  motion  of  their  light  as  would  materially  alter  its  effects. 
It  is  almost  unnecessary  to  observe  that  the  uniformity  of  the  velocity  of 
light,  in  those  spaces  which  are  free  from  all  material  substances,  is  a 
necessary  consequence  of  the  Huygenian  hypothesis,  since  the  undulations 
of  every  homogeneous  elastic  medium  are  always  propagated,  like  those 
of  sound,  with  the  same  velocity,  as  long  as  the  medium  remains  un- 
altered. 

On  either  supposition,  there  is  no  difficulty  in  explaining  the  equality  of 
the  angles  of  incidence  and  reflection ;  for  these  angles  are  equal  as  well 
in  the  collision  of  common  elastic  bodies  with  others  incomparably  larger, 
as  in  the  reflections  of  the  waves  of  water  and  of  the  undulations  of  sound. 
And  it  is  equally  easy  to  demonstrate,  that  the  sines  of  the  angles  of  inci- 
dence and  refraction  must  be  always  in  the  same  proportion  at  the  same 
surface,  whether  it  be  supposed  to  possess  an  attractive  force,  capable  of 
acting  on  the  particles  of  light,  or  to  be  the  limit  of  a  medium  through 
which  the  undulations  are  propagated  with  a  diminished  velocity.  There 
are,  however,  some  casfe  of  the  production  of  colours,  which  lead  iis  to 
suppose  that  the  velocity  of  light  must  be  smaller  in  a  denser  than  in  a 
rarer  medium  ;  and  supposing  this  fact  to  be  fully  established,  the  exist- 
ence of  such  an  attractive  force  could  no  longer  be  allowed,  nor  could  the 
System  of  emanation  be  maintained  by  any  one.f 

*  Zachs  Geographische  Ephemeriden,  iv.  1. 

f  Arago  put  this  remark  to  the  test,  Annales  de  Chimie,  Ixxi.  49. 


362  LECTURE  XXXIX. 

The  partial  reflection  from  all  refracting  surfaces  is  supposed  by  Newton 
to  arise  from  certain  periodical  retardations  of  the  particles  of  light, 
caused  by  undulations,  propagated  in  all  cases  through  an  ethereal  me- 
dium. The  mechanism  of  these  supposed  undulations  is  so  complicated, 
and  attended  by  so  many  difficulties,  that  the  few  who  have  examined 
them  have  been  in  general  entirely  dissatisfied  with  them  ;  and  the  internal 
vibrations  of  the  particles  of  light  themselves,  which  Boscovich  has 
imagined,  appear  scarcely  to  require  a  serious  discussion.  It  may,  there- 
fore, safely  be  asserted,  that  in  the  projectile  hypothesis  this  separation  of 
the  rays  of  light  of  the  same  kind  by  a  partial  reflection  at  every  refract- 
ing surface,  remains  wholly  unexplained.  In  the  undulatory  system,  on 
the  contrary,  this  separation  follows  as  a  necessary  consequence.  It  is 
simplest  to  consider  the  ethereal  medium  which  pervades  any  transparent 
substance,  together  with  the  material  atoms  of  the  substance,  as  constituting 
together  a  compound  medium  denser  than  the  pure  ether,  but  not  more 
elastic  ;*  and  by  comparing  the  contiguous  particles  of  the  rarer  and  the 
denser  medium  with  common  elastic  bodies  of  different  dimensions,  we 
may  easily  determine  not  only  in  what  manner,  but  almost  in  what  degree, 
this  reflection  must  take  place  in  different  circumstances.  Thus,  if  one  of 
two  equal  bodies  strikes  the  other,  it  communicates  to  it  its  whole  motion 
without  any  reflection ;  but  a  smaller  body  striking  a  larger  one  is  re- 
flected, with  the  more  force  as  the  difference  of  their  magnitude  is  greater  ; 
and  a  larger  body,  striking  a  smaller  one,  still  proceeds  with  a  diminished 
velocity  ;  the  remaining  motion  constituting,  in  the  case  of  an  undulation 
falling  on  a  rarer  medium,  a  part  of  a  new  series  of  motions  which  neces- 
sarily returns  backwards  with  the  appropriate  velocity  ;  and  we  may 
observe  a  circumstance  nearly  similar  to  this  last  in  a  portion  of  mercury 
spread  out  on  a  horizontal  table  ;  if  a  wave  be  excited  at  any  part,  it  will 
be  reflected  from  the  termination  of  the  mercury  almost  in  the  same 
manner  as  from  a  solid  obstacle. 

The  total  reflection  of  light,  falling,  with  a  certain  obliquity,  on  the 
surface  of  a  rarer  medium,  becomes,  on  both  suppositions,  a  particular  case 
of  refraction.  In  the  undulatory  system,  it  is  convenient  to  suppose  the 
two  mediums  to  be  separated  by  a  short  space  in  which  their  densities 
approach  by  degrees  to  each  other,  in  order  that  the  undulation  may  be 
turned  gradually  round,  so  as  to  be  reflected  in  an  equal  angle  ;  but  this 
supposition  is  not  absolutely  necessary,  and  the  same  effects  may  be  ex- 
pected at  the  surface  of  two  mediums  separated  by  an  abrupt  termination. 

The  chemical  process  of  combustion  may  easily  be  imagined  either  to 
disengage  the  particles  of  light  from  their  various  combinations,  or  to  agi- 
tate the  elastic  medium  by  the  intestine  motions  attending  it :  but  the 
operation  of  friction  upon  substances  incapable  jof  undergoing  chemical 
changes,  as  well  as  the  motions  of  the  electric  fluid  through  imperfect 
conductors,  afford  instances  of  the  production  of  light  in  which  there 

*  Some  modern  writers  have  adopted  the  contrary  hypothesis,  that  the  ethereal 
medium  which  pervades  a  substance  is  of  the  same  density  as  it  is  in  void  space, 
but  that  its  elasticity  is  different.  See  Neumann,  Memoirs  of  the  Academy  of 
Berlin,  vol.  xxii.  for  1835,  and  Annalen  der  Physik,  xxv.  418. 


ON  THE  NATURE  OF  LIGHT  AND  COLOURS.  363 

seems  to  be  no  easy  way  of  supposing  a  decomposition  of  any  kind.  The 
phenomena  of  solar  phosphor!  appear  to  resemble  greatly  the  sympathetic 
sounds  of  musical  instruments,  which  are  agitated  by  other  sounds  con- 
veyed to  them  through  the  air  :  it  is  difficult  to  understand  in  what  state 
the  corpuscles  of  light  could  be  retained  by  these  substances  so  as  to  be 
reemitted  after  a  short  space  of  time  ;  and  if  it  is  true  that  diamonds  are 
often  found,  which  exhibit  a  red  light  after  having  received  a  violet  light 
only,  it  seems  impossible  to  explain  this  property,  on  the  supposition  of  the 
retention  and  subsequent  emission  of  the  same  corpuscles. 

Tbe  phenomena  of  the  aberration  of  light  agree  perfectly  well  with  the 
system  of  emanation ;  and  if  the  ethereal  medium,  supposed  to  pervade 
the  earth  ^nd  its  atmosphere,  were  carried  along  before  it,  and  partook 
materially  in  its  motions,  these  phenomena  could  not  easily  be  reconciled 
with  the  theory  of  undulation.  But  there  is  no  kind  of  necessity  for  such 
a  supposition :  it  will  not  be  denied  by  the  advocates  of  the  Newtonian 
opinion  that  all  material  bodies  are  sufficiently  porous  to  leave  a  medium 
pervading  them  almost  absolutely  at  rest ;  and  if  this  be  granted,  the 
effects  of  aberration  will  appear  to  be  precisely  the  same  in  either  hypo- 
thesis. 

The  unusual  refraction  of  the  Iceland  spar  has  been  most  accurately 
and  satisfactorily  explained  by  Huygens,  on  the  simple  supposition  that 
this  crystal  possesses  the  property  of  transmitting  an  impulse  more  rapidly 
in  one  direction  than  in  another ;  whence  he  infers  that  the  undulations 
constituting  light  must  assume  a  spheroidical  instead  of  a  spherical  form, 
and  lays  down  such  laws  for  the  direction  of  its  motion,  as  are  incompar- 
ably more  consistent  with  experiment  than  any  attempts  which  have  been 
made  to  accommodate  the  phenomena  to  other  principles.  It  is  true  that 
nothing  has  yet  been  done  to  assist  us  in  understanding  the  effects  of  a 
subsequent  refraction  by  a  second  crystal,*  unless  any  person  can  be  satis- 
fied with  the  name  of  polarity  assigned  by  Newton  to  a  property  which  he 
attributes  to  the  particles  of  light,  and  which  he  supposes  to  direct  them  in 
the  species  of  refraction  which  they  are  to  undergo  :  but  on  any  hypothesis, 
until  we  discover  the  reason  why  a  part  of  the  light  is  at  first  refracted  in 
the  usual  manner,  and  another  part  in  the  unusual  manner,  we  have  no 
right  to  expect  that  we  should  understand  how  these  dispositions  are  con- 
tinued or  modified,  when  the  process  is  repeated. 

In  order  to  explain,  in  the  system  of  emanation,  the  dispersion  of  the 
rays  of  different  colours  by  means  of  refraction,  it  is  necessary  to  suppose 
that  all  refractive  mediums  have  an  elective  attraction,  acting  more 
powerfully  on  the  violet  rays,  in  proportion  to  their  mass,  than  on  the  red. 
But  an  elective  attraction  of  this  kind  is  a  property  foreign  to  mechanical 
philosophy,  and  when  we  use  the  term  in  chemistry,  we  only  confess  our 
incapacity  to  assign  a  mechanical  cause  for  the  effect,  and  refer  to  an  ana- 
logy with  other  facts,  of  which  the  intimate  nature  is  perfectly  unknown 
to  us.  It  is  not  indeed  very  easy  to  give  a  demonstrative  theory  of  the 
dispersion  of  coloured  light  upon  the  supposition  of  undulatory  motion  ; 
but  we  may  derive  a  very  satisfactory  illustration  from  the  well  known 
*  See  additional  remarks  at  the  end  of  this  Lecture. 


364  LECTURE  XXXIX. 

effects  of  waves  of  different  breadths.  The  simple  calculation  of  the  velo-  • 
city  of  waves,  propagated  in  a  liquid  perfectly  elastic,  or  incompressible, 
and  free  from  friction,  assigns  to  them  all  precisely  the  same  velocity,  what- 
ever their  breadth  may  be  :  the  compressibility  of  the  fluids  actually  exist- 
ing introduces,  however,  a  necessity  for  a  correction  according  to  the 
breadth  of  the  wave,  and  it  is  very  easy  to  observe,  in  a  river  or  a  pond  of 
considerable  depth,  that  the  wider  waves  proceed  much  more  rapidly  than 
the  narrower.  We  may,  therefore,  consider  the  pure  ethereal  medium  as 
analogous  to  an  infinitely  elastic  fluid,  in  which  undulations  of  all  kinds 
move  with  equal  velocity,  and  material  transparent  substances,  o\\  the 
contrary,  as  resembling  those  fluids,  in  which  we  see  the  large  waves  ad- 
vance beyond  the  smaller ;  and  by  supposing  the  red  li^t  t&»  consist  of 
larger  or  wider  undulations  and  the  violet  of  smaller,  we  may  sufficiently 
elucidate  the  greater  refrangibility  of  the  red  than  of  the  violet  light.* 

It  is  not,  however,  merely  on  the  ground  of  this  analogy  that  we  may  be 
induced  to  suppose  the  undulations  constituting  red  light  to  be  larger  than 
those  of  violet  light :  a  very  extensive  class  of  phenomena  leads  us  still  more 
directly  to  the  same  conclusion  ;  they  consist  chiefly  of  the  production  of 
colours  by  means  of  transparent  plates,  and  by  diffraction  or  inflection, 
none  of  which  have  been  explained  upon  the  supposition  of  emanation,  in  a 
manner  sufficiently  minute  or  comprehensive  to  satisfy  the  most  candid 
even  of  the  advocates  for  the  projectile  system  ;  while  on  the  other  hand 
all  of  them  may  be  at  once  understood,  from  the  effect  of  the  interference 
of  double  lights,  in  a  manner  nearly  similar  to  that  which  constitutes  in 
sound  the  sensation  of  a  beat,  when  two  strings  forming  an  imperfect 
unison,  are  heard  to  vibrate  together. 

Supposing  the  light  of  any  given  colour  to  consist  of  undulations  of  a 
given  breadth,  or  of  a  given  frequency,  it  follows  that  these  undulations 
must  be  liable  to  those  effects  which  we  have  already  examined  in  the  case 
of  the  waves  of  water  and  the  pulses  of  sound.  It  has  been  shown  that 
two  equal  series  of  waves,  proceeding  from  centres  near  each  other,  may  be 
seen  to  destroy  each  other's  effects  at  certain  points,  and  at  other  points  to 
redouble  them  ;  and  the  beating  of  two  sounds  has  been  explained  from  a 
similar  interference.  We  are  now  to  apply  the  same  principles  to  the 
alternate  union  and  extinction  of  colours.  (Plate  XX.  Fig.  267.) 

In  order  that  the  effects  of  two  portions  of  light  may  be  thus  combined, 
it  is  necessary  that  they  be  derived  from  the  same  origin,  and  that  they 
arrive  at  the  same  point  by  different  paths,  in  directions  not  much  devi- 
ating from  each  other.  This  deviation  may  be  produced  in  one  or  both  of 
the  portions  by  diffraction,  by  reflection,  by  refraction,  or  by  any  of  these 
effects  combined  ;  but  the  simplest  case  appears  to  be,  when  a  beam  of 
homogeneous  light  falls  on  a  screen  in  which  there  are  two  very  small  holes 
or  slits,  which  may  be  considered  as  centres  of  divergence,  from  whence  the 

*  See  Cauchy,  Memoire  sur  la  Dispersion  de  la  Lumiere,  Prague,  1835.  Powell, 
Ph.  Mag.  vi.  16,  107,  189,  262.  Ph.  TV.  1835,  p.  249,  &c. ;  and  Essay  on  the  Un- 
dulatory  Theory,  as  applied  to  the  Dispersion  of  Light.  Challis,  Ph.  Mag.  viii. 
Kelland,  Trans.  Camb.  Ph.  Soc.  vi.  153.  Difference  of  colour  was  referred  to  dif- 
ference of  velocity  by  Melvil,  Ph.  Tr.  1753,  p.  262,  and  Essays,  ii.  12. 


ON  THE  NATURE  OF  LIGHT  AND  COLOURS.  365 

light  is  diffracted  in  every  direction.  In  this  case,  when  the  two  newly 
formed  beams  are  received  on  a  surface  placed  so  as  to  intercept  them,  their 
light  is  divided  by  dark  stripes  into  portions  nearly  equal,  but  becoming- 
wider  as  the  surface  is  more  remote  from  the  apertures,  so  as  to  subtend 
very  nearly  equal  angles  from  the  apertures  at  all  distances,  and  wider  also 
in  the  same  proportion  as  the  apertures  are  closer  to  each  other.  The 
middle  of  the  two  portions  is  always  light,  and  the  bright  stripes  on  each 
side  are  at  such  distances,  that  the  light  coming  to  them  from  one  of  the 
apertures,  must  have  passed  through  a  longer  space  than  that  which  comes 
from^the  other,  by  an  interval  which  is  equal  to  the  breadth  of  one,  two, 
three,  or  more  of  the  supposed  undulations,  while  the  intervening  dark 
spaces  correspond  to  a  difference  of  half  a  supposed  undulation,  of  one  and 
a  half,  of  two  ctnd  a  half,  or  more. 

From  a  comparison  of  various  experiments,  it  appears  that  the  breadth 
of  the  undulations  constituting  the  extreme  red  light  must  be  supposed  to 
be,  in  air,  about  one  36  thousandth  of  an  inch,  and  those  of  the  extreme 
violet  about  one  60  thousandth  ;  the  mean  of  the  whole  spectrum,  with 
respect  to  the  intensity  of  light,  being  about  one  45  thousandth.  From 
these  dimensions  it  follows,  calculating  upon  the  known  velocity  of  light, 
that  almost  500  millions  of  millions  of  the  slowest  of  such  undulations  must 
enter  the  eye  in  a  single  second.  The  combination  of  two  portions  of  white 
or  mixed  light,  when  viewed  at  a  great  distance,  exhibits  a  few  white  and 
black  stripes,  corresponding  to  this  interval :  although,  upon  closer  inspec- 
tion, the  distinct  effects  of  an  infinite  number  of  stripes  of  different 
breadths  appear  to  be  compounded  together,  so  as  to  produce  a  beautiful 
diversity  of  tints,  passing  by  degrees  into  each  other.  The  central  white- 
ness is  first  changed  to  a  yellowish,  and  then  to  a  tawny  colour,  succeeded 
by  crimson,  and  by  violet  and  blue,  which  together  appear,  when  seen  at  a 
distance,  as  a  dark  stripe ;  after  this  a  green  light  appears,  and  the  dark 
space  beyond  it  has  a  crimson  hue  ;  the  subsequent  lights  are  all  more  or 
less  green,  the  dark  spaces  purple  and  reddish  ;  and  the  red  light  appears 
so  far  to  predominate  in  all  these  effects,  that  the  red  or  purple  stripes 
occupy  nearly  the  same  place  in  the  mixed  fringes  as  if  their  light  were 
received  separately. 

The  comparison  of  the  results  of  this  theory  with  experiments  fully  esta- 
blishes their  general  coincidence  ;  it  indicates,  however,  a  slight  correction 
in  some  of  the  measures,  on  account  of  some  unknown  cause,  perhaps  con- 
nected with  the  intimate  nature  of  diffraction,  which  uniformly  occasions 
the  portions  of  light  proceeding  in  a  direction  very  nearly  rectilinear,  to  be 
divided  into  stripes  or  fringes  a  little  wider  than  the  external  stripes,  formed 
by  the  light  which  is  more  bent.  (Plate  XXX.  Fig.  442,  443.) 

When  the  parallel  slits  are  enlarged,  and  leave  only  the  intervening 
substance  to  cast  its  shadow,  the  divergence  from  its  opposite  margins  still 
continues  to  produce  the  same  fringes  as  before,  but  they  are  not  easily 
visible,  except  within  the  extent  of  its  shadow,  being  overpowered  in  other 
parts  by  a  stronger  light ;  but  if  the  light  thus  diffracted  be  allowed  to  fall 
on  the  eye,  either  within  the  shadow  or  in  ite  neighbourhood,  the  stripes 


366  LECTURE  XXXIX. 

will  still  appear ;  and  in  this  manner  the  colours  of  small  fibres  are  pro- 
bably formed.  Hence  if  a  collection  of  equal  fibres,  for  example  a  lock-  of 
wool,  be  held  before  the  eye  when  we  look  at  a  luminous  object,  the  series 
of  stripes  belonging  to  each  fibre  combine  their  effects,  in  such  a  manner, 
as  to  be  converted  into  circular  fringes  or  coronae.  This  is  probably  the 
origin  of  the  coloured  circles  or  coronae  sometimes  seen  round  the  sun 
and  moon,  two  or  three  of  them  appearing  together,  nearly  at  equal  dis- 
tances from  each  other  and  from  the  luminary,  the  internal  ones  being, 
however,  like  the  stripes,  a  little  dilated.  It  is  only  necessary  that  the  air 
should  be  loaded  with  globules  of  moisture,  nearly  of  equal  size  among 
themselves,  not  much  exceeding  one  two  thousandth  of  an  inch  in  diameter, 
in  order  that  a  series  of  such  coronae,  at  the  distance  of  two  or  three  degrees 
from  each  other,  may  be  exhibited.  (Plate  XXX.  Fig.  44-fT) 

If,  on  the  other  hand,  we  remove  the  portion  of  the  screen  which  sepa- 
rates the  parallel  slits  from  each  other,  their  external  margins  will  still 
continue  to  exhibit  Jhe  effects  of  diffracted  light  in  the  shadow  on  each 
side  ;  and  the  experiment  will  assume  the  form  of  those  which  were  made 
by  Newton  on  the  light  passing  between  the  edges  of  two  knives,  brought 
very  nearly  into  contact ;  although  some  of  these  experiments  appear  to 
show  the  influence  of  a  portion  of  light  reflected  by  a  remoter  part  of  the 
polished  edge  of  the  knives,  which  indeed  must  unavoidably  constitute  a 
part  of  the  light  concerned  in  the  appearance  of  fringes,  wherever  their 
whole  breadth  exceeds  that  of  the  aperture,  or  of  the  shadow  of  the  fibre. 

The  edges  of  two  knives,  placed  very  near  each  other,  may  represent  the 
opposite  margins  of  a  minute  furrow,  cut  in  the  surface  of  a  polished  sub- 
stance of  any  kind,  which,  when  viewed  with  different  degrees  of  obliquity, 
present  a  series  of  colours  nearly  resembling  those  which  are  exhibited 
within  the  shadows  of  the  knives  :  in  this  case,  however,  the  paths  of  the 
two  portions  of  light  before  their  incidence  are  also  to  be  considered,  and 
the  whole  difference  of  these  paths  will  be  found  to  determine  the  appear- 
ance of  colour  in  the  usual  manner  :  thus  when  the  surface  is  so  situated, 
that  the  image  of  the  luminous  point  would  be  seen  in  it  by  regular  reflec- 
tion, the  difference  will  vanish,  and  the  light  will  remain  perfectly  white, 
but  in  other  cases  various  colours  will  appear,  according  to  the  degree  of 
obliquity.  These  colours  may  easily  be  seen,  in  an  irregular  form,  by 
looking  at  any  metal,  coarsely  polished,  in  the  sunshine ;  but  they  be- 
come more  distinct  and  conspicuous,  when  a  number  of  fine  lines  of 
equal  strength  are  drawn  parallel  to  each  other,  so  as  to  conspire  in  their 
effects.* 

It  sometimes  happens  that  an  object,  of  which  a  shadow  is  formed  in  a 
beam  of  light,  admitted  through  a  small  aperture,  is  not  terminated  by 
parallel  sides ;  thus  the  two  portions  of  light,  which  are  diffracted  from 
two  sides  of  an  object,  at  right  angles  with  each  other,  frequently  form 
a  short  series  of  curved  fringes  within  the  shadow,  situated  on  each  side 
of  the  diagonal,  which  were  first  observed  by  Grimaldi,t  and  which  are 

*  Young's  Introduction  to  Medical  Literature,  1813,  p.  559. 

•f*  Physico-Mathesis  de  I^imine,  Coloribus  et  Iride,   Bonon.  1665. 


ON  THE  NATURE  OF  LIGHT  AND  COLOURS.  367 

completely  explicable  from  the  general  principle,  of  the  interference  of  the 
two  portions  encroaching  perpendicularly  on  the  shadow.  (Plate  XXX. 
Fig.  445.) 

But  the  most  obvious  of  all  the  appearances  of  this  kind  is  that  of  the 
fringes  which  are  usually  seen  beyond  the  termination  of  any  shadow, 
formed  in  a  beam  of  light,  admitted  through  a  small  aperture :  in  white 
light  three  of  these  fringes  are  usually  visible,  and  sometimes  four ;  but 
in  light  of  one  colour  only,  their  number  is  greater ;  and  they  are  always 
much  narrower  as  they  are  remoter  from  the  shadow.  Their  origin  is 
easity  deduced  from  the  interference  of  the  direct  light  with  a  portion  of 
light  reflected  from  the  margin  of  the  object  which  produces  them,  the 
obliquity  of  its  incidence  causing  a  reflection  so  copious  as  to  exhibit  a 
visible  effect,  however  narrow  that  margin  may  be  ;  the  fringes  are,  how- 
ever, rendered  more  obvious  as  the  quantity  of  this  reflected  light  is 
greater.  Upon  this  theory  it  follows  that  the  distance  of  the  first  dark 
fringe  from  the  shadow  should  be  half  as  great  as  that  of  the  fourth,  the 
difference  of  the  lengths  of  the  different  paths  of  the  light  being  as  the 
squares  of  those  distances ;  and  the  experiment  precisely  confirms  this  calcu- 
lation, with  the  same  slight  correction  only  as  is  required  in  all  other  cases ; 
the  distances  of  the  first  fringes  being  always  a  little  increased.  It  may 
also  be  observed,  that  the  extent  of  the  shadow  itself  is  always  augmented, 
and  nearly  in  an  equal  degree  with  that  of  the  fringes  :  the  reason  of  this 
circumstance  appears  to  be  the  gradual  loss  of  light  at  the  edges  of  every 
separate  beam,  which  is  so  strongly  analogous  to  the  phenomena  visible  in 
waves  of  water.  The  same  cause  may  also  perhaps  have  some  effect  in 
producing  the  general  modification  or  correction  of  the  place  of  the  first 
fringes,  although  it  appears  to  be  scarcely  sufficient  for  explaining  the 
whole  of 'it.  (Plate  XXX.  Fig.  446.) 

A  still  more  common  and  convenient  method  of  exhibiting  the  effects  of 
the  mutual  interference  of  light,  is  afforded  us  by  the  colours  of  the  thin 
plates  of  transparent  substances.  The  lights  are  here  derived  from  the 
successive  partial  reflections  produced  by  the  upper  and  under  surface  of 
the  plate,  or  when  the  plate  is  viewed  by  transmitted  light,  from  the  direct 
beam  which  is  simply  refracted,  and  that  portion  of  it  which  is  twice  [or 
more  times]  reflected  within  the  plate.  The  appearance  in  the  latter  case 
is  much  less  striking  than  in  the  former,  because  the  light  thus  affected  is 
only  a  small  portion  of  the  whole  beam,  with  which  it  is  mixed ;  while  in 
the  former  the  two  reflected  portions  are  nearly  of  equal  intensity,  and  may 
be  separated  from  all  other  light  tending  to  overpower  them.  In  both 
cases,  when  the  plate  is  gradually  reduced  in  thickness  to  an  extremely 
thin  edge,  the  order  of  colours  may  be  precisely  the  same  as  in  the  stripes 
and  coronae  already  described  ;  their  distance  only  varying  when  the 
surfaces  of  the  plate,  instead  of  being  plane,  are  concave,  as  it  frequently 
happens  in  such  experiments.  The  scale  of  an  oxid,  which  is  often 
formed  by  the  effect  of  heat  on  the  surface  of  a  metal,  in  particular  of 
h'on,  affords  us  an  example  of  such  a  series  formed  in  reflected  light :  this 
scale  is  at  first  inconceivably  thin,  and  destroys  none  of  the  light  reflected, 
it  soon,  however,  begins  to  be  of  a  dull  yellow,  which  changes  to  red,  and 


368  LECTURE  XXXIX. 

then  to  crimson  and  blue,  after  which  the  effect  is  destroyed  by  the  opacity 
which  the  oxid  acquires.  Usually,  however,  the  series  of  colours  produce0d 
in  reflected  light  follows  an  order  somewhat  different :  the  scale  of  oxid 
is  denser  than  the  air,  and  the  iron  below  than  the  oxid ;  but  where  the 
mediums  above  and  below  the  plate  are  either  both  rarer  or  both  denser 
than  itself,  the  different  natures  of  the  reflections  at  its  different  surfaces 
appear  to  produce  a  modification  in  the  state  of  the  undulations,  and  the 
infinitely  thin  edge  of  the  plate  becomes  black  instead  of  white,  one  of  the 
portions  of  light  at  once  destroying  the  other,  instead  of  cooperating  with 
it.  Thus  when  a  film  of  soapy  water  is  stretched  over  a  wine  glass,  and 
placed  in  a  vertical  position,  its  upper  edge  becomes  extremely  thin,  and 
appears  nearly  black,  while  the  parts  below  are  divided  by  horizontal  lines 
into  a  series  of  coloured  bands ;  and  when  two  glasses,  one  of  which  is 
slightly  convex,  are  pressed  together  with  some  force,  the  plate  of  air 
between  them  exhibits  the  appearance  of  coloured  rings,  beginning  from 
a  black  spot  at  the  centre,  and  becoming  narrower  and  narrower,  as  the 
curved  figure  of  the  glass  causes  the  thickness  of  the  plate  of  air  to  increase 
more  and  more  rapidly.  The  black  is  succeeded  by  a  violet,  so  faint  as  to 
be  scarcely  perceptible ;  next  to  this  is  an  orange  yellow,  and  then  crim- 
son and  blue.  When  water  or  any  other  fluid,  is  substituted  for  the  air 
between  the  glasses,  the  rings  appear  where  the  thickness  is  as  much  less 
than  that  of  the  plate  of  air,  as  the  refractive  density  of  the  fluid  is 
greater ;  a  circumstance  which  necessarily  follows  from  the  proportion  of 
the  velocities  with  which  light  must,  upon  the  Huygenian  hypothesis,  be 
supposed  to  move  in  different  mediums.  It  is  also  a  consequence  equally 
necessary  in  this  theory,  and  equally  inconsistent  with  all  others,  that 
when  the  direction  of  the  light  is  oblique,  the  effect  of  a  thicker  plate  must 
be  the  same  as  that  of  a  thinner  plate,  when  the  light  falls  perpendicularly 
upon  it ;  the  difference  of  the  paths  described  by  the  different  portions  of 
light  precisely  corresponding  with  the  observed  phenomena.  (Plate  XXX. 
Fig.  447... 449.) 

Sir  Isaac  Newton  supposes  the  colours  of  natural  bodies  in  general  to  be 
similar  to  these  colours  of  thin  plates,  and  to  be  governed  by  the  magni- 
tude of  their  particles.  If  this  opinion  were  universally  true,  we  might 
always  separate  the  colours  of  natural  bodies  by  refraction  into  a  number  of 
different  portions,  with  dark  spaces  intervening  ;  for  every  part  of  a  thin 
plate  which  exhibits  the  appearance  of  colour,  affords  such  a  divided 
spectrum,  when  viewed  through  a  prism.  There  are  accordingly  many 
natural  colours  in  which  such  a  separation  may  be  observed ;  one  of  the 
most  remarkable  of  them  is  that  of  blue  glass,  probably  coloured  with 
cobalt,  which  becomes  divided  into  seven  distinct  portions.  It  seems, 
however,  impossible  to  suppose  the  production  of  natural  colours  perfectly 
identical  with  those  of  thin  plates,  on  account  of  the  known  minuteness  of 
the  particles  of  colouring  bodies,  unless  the  refractive  density  of  these  par- 
ticles be  at  least  20  or  30  times  as  great  as  that  of  glass  or  water ;  which  is 
indeed  not  at  all  improbable  with  respect  to  the  ultimate  atoms  of  bodies, 
but  difficult  to  believe  with  respect  to  any  of  their  arrangements  consti- 
tuting the  diversities  of  material  substances. 


ON  THE  NATURE  OF  LIGHT  AND  COLOURS.  369 

•%  The  colours  of  mixed  plates  constitute  a  distinct  variety  of  the  colours  of 
thin  plates,  which  has  not  been  commonly  observed.  They  appear  when 
the  interstice  between  two  glasses  nearly  in  contact,  is  filled  with  a  great 
number  of  minute  portions  of  two  different  substances,  as  water  and  air, 
oil  and  air,  or  oil  and  water  ;  the  light  which  passes  through  one  of  the 
mediums,  moving  with  a  greater  velocity,  anticipates  the  light  passing 
through  the  other;  and  their  effects  on  the  eye  being  confounded  and 
combined,  their  interference  produces  an  appearance  of  colours  nearly 
similar  to  those  of  the  colours  of  simple  thin  plates,  seen  by  transmission  ; 
but  a£  much  greater  thicknesses,  depending  on  the  difference  of  the  refrac- 
tive densities  of  the  substances  employed.  The  effect  is  observed  by  hold- 
ing the  glasses  between  the  eye  and  the  termination  of  a  bright  object,  and 
it  is  most  conspicuous  in  the  portion  which  is  seen  on  the  dark  part  beyond 
the  object,  being  produced  by  the  light  scattered  irregularly  from  the  sur- 
faces of  the  fluid.  Here,  however,  the  effects  are  inverted,  the  colours 
resembling  those  of  the  common  thin  plates  seen  by  reflection ;  and  the 
same  considerations  on  the  nature  of  the  reflections  are  applicable  to  both 
cases.  (Plate  XXX.  Fig.  450.) 

The  production  of  the  supernumerary  rainbows,  which  are  sometimes 
seen  within  the  primary  and  without  the  secondary  bow,  appears  to  be 
intimately  connected  with  that  of  the  colours  of  thin  plates.  We  have 
already  seen  that  the  light  producing  the  ordinary  rainbow  is  double,  its 
intensity  being  only  greatest  at  its  termination,  where  the  common  bow 
appears,  while  the  whole  light  is  extended  much  more  widely.  The  two 
portions  concerned  in  its  production  must  divide  this  light  into  fringes ; 
but  unless  almost  all  the  drops  of  a  shower  happen  to  be  of  the  same  mag- 
nitude, the  effects  of  these  fringes  must  be  confounded  and  destroyed  ;  in 
general,  however,  they  must  at  least  cooperate  more  or  less  in  producing 
one  dark  fringe,  which  must  cut  off  the  common  rainbow  much  more 
abruptly  than  it  would  otherwise  have  been  terminated,  and  consequently 
assist  the  distinctness  of  its  colours.  The  magnitude  of  the  drops  of  rain, 
required  for  producing  such  of  these  rainbows  as  are  usually  observed,  is 
between  the  50th  and  the  100th  of  an  inch  ;  they  become  gradually  nar- 
rower as  they  are  more  remote  from  the  common  rainbows,  nearly  in  the 
same  proportions  as  the  external  fringes  of  a  shadow,  or  the  rings  seen  in 
a  concave  plate.*  (Plate  XXX.  Fig.  451.) 

The  last  species  of  the  colours  of  double  lights,  which  it  will  be  neces- 
sary to  notice,  constitutes  those  which  have  been  denominated,  from 
Newton's  experiments,  the  colours  of  thick  plates,  but  which  may  be 
called,  with  more  propriety,  the  colours  of  concave  mirrors.  The  anterior 
surface  of  a  mirror  of  glass,  or  any  other  transparent  surface  placed  before 
a  speculum  of  metal,  dissipates  irregularly  in  every  direction  two  portions 
of  light,  one  before  and  the  other  after  its  reflection.  When  the  light  falls 
obliquely  on  the  mirror,  being  admitted  through  an  aperture  near  the 
centre  of  its  curvature,  it  is  easy  to  show,  from  the  laws  of  reflection,  that 
the  two  portions,  thus  dissipated,  will  conspire  in  their  effects,  throughout 

*  Young's  Exp.  and  Obs.  relative  to  Physical  Optics,  Ph.  Tr.  1804,  p.  1.  Potter, 
Math.  Considerations  on  the  Rainbow,  Tr.  Camb.  Ph.  Soc.  vi.  141. 

2  B 


370  LECTURE  XXXIX. 

the  circumference  of  a  circle,  passing  through  the  aperture  ;  this  circle  will 
consequently  be  white,  and  it  will  be  surrounded  with  circles  of  colours 
very  nearly  at  equal  distances,  resembling  the  stripes  produced  by  diffrac- 
tion. The  analogy  between  these  colours  and  those  of  thin  plates  is  by  no 
means  so  close  as  Newton  supposed  it ;  since  the  effect  of  a  plate  of  any  con- 
siderable thickness  must  be  absolutely  lost  in  white  light,  after  ten  or 
twelve  alternations  of  colours  at  most,  while  these  effects  would  require 
the  whole  process  to  remain  unaltered,  or  rather  to  be  renewed,  after 
many  thousands  or  millions  of  changes.  (Plate  XXX.  Fig.  452.) 

It  is  presumed,  that  the  accuracy,  with  which  the  general  law  of  the 
interference  of  light  has  been  shown  to  be  applicable  to  so  great  a  variety 
of  facts,  in  circumstances  the  most  dissimilar,  will  be  allowed  to  establish 
its  validity  in  the  most  satisfactory  manner.  The  full  confirmation  or 
decided  rejection  of  the  theory,  by  which  this  law  was  first  suggested,  can 
be  expected  from  time  and  experience  alone ;  if  it  be  confuted,  our 
prospects  will  again  be  confined  within  their  ancient  limits,  but  if  it  be 
fully  established,  we  may  expect  an  ample  extension  of  our  views  of  the 
operations  of  nature,  by  means  of  our  acquaintance  with  a  medium,  so 
powerful  and  so  universal,  as  that  to  which  the  propagation  of  light  must 
be  attributed. 

[The  principle  of  interference  which  Dr.  Young  advanced  in  this  lecture 
and  elsewhere,  has  done  much  towards  establishing  the  undulatory  theory 
as  a  true  physical  theory.  This  principle  explains  in  the  most  satisfac- 
tory way,  not  only  the  colours  of  thin  plates,  the  fringes  which  accompany 
shadows,  and  the  like,  but  more  refined  and  complicated  phenomena,  such 
as  those  produced  by  placing  gratings  of  different  forms  before  the  object 
glass  of  a  telescope.  The  simplest  form  in  which  the  operation  of  inter- 
fering light  is  witnessed,  and  consequently  the  most  direct  mode  of  com- 
paring theory  witlpi  experiment,  is  to  suffer  a  small  pencil  of  light  to  fall 
on  a  prism  of  a  very  large  angle  (say  179°).  The  two  sides  of  this  prism 
constitute  two  prisms  of  an  angle  of  \°  each,  and  serve  to  bend  the  same 
pencil  so  as  to  render  it  virtually  two.  By  receiving  the  light  from  these 
two  pencils  on  any  eye  piece,  it  is  evident  that,  in  different  parts  of  the 
field  of  view,  the  one  will  mix  with  the  other  in  different  states  of  distance 
from  the  original  focus.  In  the  centre  both  will  have  travelled  the  same 
distance,  and  there  will  be  a  white  bar  formed  by  their  mixture.  On  each 
side  of  this,  at  a  certain  distance,  the  one  will  have  travelled  further  than 
the  other  by  half  the  length  of  a  wave.  Here  the  motions  of  the  one  will 
be  the  reverse  of  those  of  the  other — the  one,  for  instance,  tending  to  raise 
a  particle  of  the  undulating  medium,  whilst  the  other  tends  to  depress  it, 
and  by  the  same  amount.  The  result  is,  that  no  motion  at  all  ensues,  and 
we  are  presented  with  a  dark  bar :  and  so  on.  Moreover,  as  the  lengths 
of  the  waves  are  different  for  different  colours,  the  next  bright  bar  will  not 
be  quite  white,  the  space  requisite  to  allow  the  one  pencil  to  be  in  advance 
of  the  other  l?y  a  whole  undulation  (which  is  equivalent  to  not  being  in 
advance  of  it  at  all),  being  less  for  the  violet  rays  than  for  the  red.  We 
find,  consequently,  a  coloured  fringe ;  and  as  we  recede  from  the  centre, 
the  bars  become  more  and  more  coloured,  until  the  dark  of  the  one  alto-] 


ON  THE  NATURE  OF  LIGHT  AND  COLOURS.  371 

[gether  obliterates  the  light  of  the  other  colour.  Nothing  can  be  more 
satisfactory  than  the  explanation  which  the  theory  affords  of  such  pheno- 
mena, and,  whilst  we  do  not  assert  that  it  has  as  yet  brought  every 
observed  fact  within  its  pale,  yet  it  does  not  appear  that  the  arguments 
which  were  raised  against  it  have  any  power  to  shake  it.  Regarding  it 
as  true,  we  shall  adopt  its  language  in  giving  a  very  brief  sketch  of  the 
phenomena  of  polarized  light. 

It  has  been  stated  that  when  a  pencil  of  light  falls  on  a  surface  of  Ice- 
land spar,  it  is  divided  into  two.     Huygens,  by  the  hypothesis  that  one 
series  of  waves  diverges  into  a  spheroid,  whilst  the  other  diverges  into  a 
sphere,  gave  a  most  satisfactory  explanation  of  the  course  of  the  two  rays  ; 
and  his  conclusions  were  confirmed  by  the  accurate  measurements  of  Wol- 
laston.*     Dr.  Young  t  perceived  that  this  difference  of  divergence  must 
arise  from  a  difference  of  elasticity  within  the  crystal.      Combining  this 
with  the  idea  of  Newton,  that  a  ray  of  light  possesses  sides,  the  hypothesis 
of  a  transverse  vibration  is  a  natural  result.     Dr.  Young  advanced  this 
hypothesis  about  1817,  and  from  that  period  the  progress  of  the  theory 
has  been  rapid  and  satisfactory.     The  hypothesis  consists  in  supposing 
that  the  particles  of  light  do  not,  like  those  whose  motions  constitute  sound, 
oscillate  in  the  direction  of  the  wave,  but  transversely  to  it,  so  as  more  to 
resemble  those  of  the  particles  of  water  which  move  up  and  down  whilst 
the  wave  advances  horizontally.     The  explanation  of  double  refraction  is 
now  quite  simple.     A  ray  of  light  falls  on  the  surface  of  a  crystal,  the 
elasticity  of  which  is  different  in  different  directions.     The  motions,  con- 
sequently, are  not  all  transmitted  with  the  same  velocity,  and  as  the  index 
of  refraction  depends  on  the  velocity,  one  set  of  vibrations  will,  on  emer- 
gence, be  totally  separated  from  another.     Moreover,  the  light  on  emerging 
is  quite  different  from  common  light.    In  each  ray  it  consists  only  of  vibra- 
tions in  one  direction.     Suppose,  therefore,  one  of  these  rays  to  fall  on  a 
second  crystal  placed  in  a  similar  position  with  the  first,  it  will  not  now  be 
divided  into  two,  but  will  emerge  just  as  it  entered.    Light  which  consists  of 
vibrations  in  one  direction  only  is  termed  polarized  light.    It  was  discovered 
by  Malus  that  light  reflected  from  the  same  face  of  unsilvered  glass  is  more 
or  less  polarized  ;  and  Brewster  ascertained  that  it  is  perfectly  so,  when  the 
tangent  of  the  angle  of  incidence  is  equal  to  the  refractive  index,  and  also 
that  the  transmitted  ray  is  partially  polarized.    Moreover,  Seebeck  and  Biot 
discovered  a  property  of  the  tourmaline,  that  when  it  is  cut  into  slices, 
whose  surfaces  are  parallel  to  the  axis  of  the  crystal,  it  absorbs  one  of  the 
two  rays,  and  consequently  transmits  a  polarized  ray  only.    Thus  we  are 
presented  with  various  ways  of  effecting  the  polarization  of  light.     The 
simplest  to  understand  is  that  by  the  tourmaline,  and  to  it  we  shall  conse- 
quently refer.     On  looking  through  a  plate  of  tourmaline,  the  effect  to  the 
eye  is  similar  to  that  produced  by  a  bit  of  coloured  glass.     If  a  second 
plate  of  tourmaline  be  placed  on  the  first,  so  that  their  axes  are  parallel  to 
each  other,  the  same  is  true.    But  if  the  axis  of  the  one  be  perpendicular 
to  that  of  the  other,  the  one  horizontal,  the  other  vertical,  the  compound 
plate  becomes  opaque.     The  first  suffering  only  horizontal  vibrations  to] 
*  Ph.  Tr.  1802,  p.  381.  f  Quarterly  Review,  1809,  ii.344. 

2B2 


372  LECTURE  XXXIX. 

[pass  through  it,  the  second  only  vertical  ones.  Another  remarkable  pro-  t 
perty  of  crystals  was  discovered  by  M.  Arago,  that  of  depolarizing  light. 
A  plate  of  Iceland  spar  cut  perpendicular  to  the  axes,  and  placed  between 
two  tourmalines,  exhibits  a  beautiful  series  of  concentric  rings  broken 
by  a  dark  or  bright  rectangular  cross.  This  complex  phenomenon  admits 
of  the  readiest  explanation.  Suppose  the  axes  of  the  tourmalines  at  right 
angles  to  each  other.  The  light  which  has  passed  through  the  first  con- 
sists of  horizontal  vibrations  only.  These  fall  on  the  plate  of  Iceland 
spar,  which  being  symmetrical  relative  to  its  axis,  those  vibrations  which 
fall  perpendicularly  on  it  pass  through  without  suffering  any  modification. 
They  are  subsequently  stopped  by  the  second  tourmaline,  and  hence  a 
dark  horizontal  band.  For  a  nearly  similar  reason  there  is  a  dark  vertical 
band.  The  direction  of  motion  of  the  particles  in  these  cases  is  either 
coincident  with  or  at  right  angles  to  a  plane  which  passes  through  the  ray 
and  the  axis  of  the  crystal.  But  in  other  places,  the  direction  of  motion 
is  oblique  to  such  a  plane,  and  the  ray  is  doubly  refracted,  so  that  on 
emergence  it  consists  of  two,  which  on  being  united  no  longer  form  a 
polarized  ray  as  before.  The  second  tourmaline,  consequently,  is  incapa- 
ble of  wholly  absorbing  this  ray,  and  thus  we  are  presented  with  brightness. 
Moreover,  the  distance  from  the  centre  at  which  the  maxima  of  brightness 
occur  depends  on  the  length  of  the  wave  ;  these  maxima  are  therefore 
recurring,  and  form  rings,  which,  since  the  waves  of  different  colours  are 
different  in  length,  must  be  coloured. 

Such  is  an  outline  of  the  explanation  afforded  by  the  principles  of  this 
lecture  to  the  phenomena  of  double  refraction  and  polarization.  To  enter 
into  detail  exceeds  our  limits.  We  must  refer  the  reader  to  Airy's 
Mathematical  Tracts,  or  Lloyd's  Lectures  on  Light,  the  latter  being  a 
popular  treatise.  In  Gehler's  Physikalisches  Worterbuch,  art.  Undula- 
tions (1842),  is  a  tolerably  complete  analytical  investigation  of  the  subject.] 


LECT.  XXXIX.— ADDITIONAL  AUTHORITIES. 

Diffraction. — Hooke,  Ph.  Tr.  1672.  Newton's  Op.  lib.  3.  Maraldi,  Hist,  et 
M6m.  1723,  p.  111.  Dutour,  Mein.  des  Sav.  Etr.  v.  636.  Stratico,  Saggi  di  Pa- 
dova,  ii.  185.  Jordan  on  the  Inflections  of  Light,  Lond.  1799.  Arago,  Ann.  de 
Chimie,  i.  199,  332;  Sur  la  Scintillation  des  Etoiles,  xxvi.  431.  Rapport  sur 
quelques  Mem.  xi.  5.  Fresnel,  Mem.  de  1'Acad.  v.  Annales  de  Ch.  xi.  246,  337. 
Frauenhofer,  Neue  Modification  des  Lichtes,  Miinchen,  1818.  Gilbert's  Ann.  Ixxiv. 
337.  Mayer,  Phaenom.  ab  Inflexione  Luminis  pendent.  Com.  Gott.  1820,  p.  49. 
T.  Young  on  Frauenhofer's  Experiments,  Ed.  Jour,  of  Sc.  New  Series,  i.  112. 
Airy,  Camb.  Tr.  vol.  v. 

Coloured  Rings.—  Boyle,  Experiments  touching  Colours,  1663.  Hooke,  Microg. 
and  Birch's  Hist.  iii.  29,  53.  Newton,  Op.  lib.  2.  Jordan  on  the  Colours  of  thin 
transparent  Bodies,  1800.  T.  Young  on  the  Colours  of  thin  Plates,  Jour,  of  the 
Roy.  Inst.  i.  241.  Introduction  to  Medical  Literature,  p.  556.  W.  Herschel,  Ph. 
Tr.  1807,  pp.  180,  189,  338;  1810,  p.  365.  Knox,  ibid.  1815,  p.  161.  Arago, 
Mem.  d'Arcueil,  iii.  223.  Brewster,  Ed.  Tr.  1815,  xii.  191.  Airy  on  a  Modifica- 
tion of  Newton's  Rings,  Camb.  Tr.  iv.  219,  409. 

Colours  by  Reflection. — Brewster  on  the  Optical  Phenomena  of  Mother-of- Pearl, 
Ph.  Tr.  1814,  p.  397.  Colours  of  grooved  Surfaces,  ibid.  1829,  p.  301. 

Miscellaneous.— Babinet,  Mem.  d'Op.  Compte  Rendue,  1837,  p.  638. 

ON  POLARIZED  LIGHT. 
Apparatus.— Biot  on  Tourmaline,  Ann.  de  Chimie,  1815.     Seebeck,  in  Biot's 


ON  THE  NATURE  OF  LIGHT  AND  COLOURS.  373 

Traite  de  Ph.  vol.  iv.  Marx  (two  tourmalines)  Schweigger's  Jahrb.  xix.  167. 
A'iry  on  a  new  Analyser,  Camb.  Tr.  Nicol's  Polarizing  Prism,  Edinb.  Ph.  Jour. 
xx.  83.  Hachette,  Descrip.  de  1'App.  de  M.  No'rrenberg.  Bullet,  dela  Soc.  Philom. 
1833.  Dove,  Pogg.  Ann.  xxxv.  596.  Scientific  Memoirs,  i.  86. 

Polarization  by  Reflection. — Malus  sur  une  Propriete  de  la  Lumiere  Reflechie, 
Mem.  d'Arcueil,  ii.  143,  254.  Mayer,  Com.  Gott.  1813,  p.  1.  Brewster  on  the 
Laws  of  Polarization  by  Reflection,  Ph.  Tr.  1815,  p.  125  ;  1830,  pp.  69,  145.  See- 
beck  on  do.  4to,  Berlin,  1830;  and  Pogg.  Ann.  xx.  27;  xxi.  22,  290;  xxii.  126  ; 
and  xxxviii.  276. 

Polarization  by  Refraction.— Brewster,  Ph.Tr.  1816,  p.  46;  1830,  pp.  133,  145. 

Circular  Polarization  by  Rrflection. — Fresnel,  Ann.  de  Chimie,  xxix.  175. 

Elliptic  Polarization. — Fresnel,  Mem.  sur  la  Loi  des  Modifications  que  la  Re- 
flexion imprime  &  la  Lumiere  polarisee,  Ann.  de  Chimie,  xlvi.  225.  Brewster,  El- 
liptic Pol.  exhibited  in  the  Action  of  Metals  upon  Light,  Ph.  Tr.  1830,  p.  28. 
Neumann,  Theorie,  Pogg.  Ann.  xxvi.  89. 

Depolarization. — Arago,  Mem.  sur  une  Modification,  qu'eprouvent  les  Rayons 
Lumineux  dans  leur  Passage  a  travers  certains  Corps  Diaphanes,  Mem.  de  1'Jn- 
stitut,  xii.  93  (1811).  Brewster,  New  Phil.  Inst.  1813.  On  the  Affections  of  Light 
transmitted  through  crystallized  Bodies,  Ph.  Tr.  1814,  p.  187,  Laws  of  Pol.  in 
Crystals,  1818,  p.  199.  Biot,  Mem.  de  1'Institut,  1812,  i.  1,  II.  i. ;  1816,  p.  275  ; 
1818,  p.  135.  Mem.  d'Arcueil,  iii.  132.  Lloyd  on  the  Phenomena  by  Light 
passing  along  the  axes  of  biaxal  Crystals,  Ph.  Mag.  xi.  112,  207.  Potter,  ibid. ; 
together  with  various  memoirs  on  the  action  of  different  crystals,  such  as  Brewster 
on  Agate,  Ph.  Tr.  1813,  p.  101  ;  on  Calcspar,  &c.  1814,  p.  203;  1815,  p.  270. 
Ed.  Tr.  viii.  270.  Apophyllite,  ibid.  ix.  317.  Glauberite,  ibid.  xi.  273.  Analcime, 
1822.  Amethyst,  ix.  139.  Muriate  of  Soda,  &c.  viii.  157.  Topaz,  Camb.  Tr. 
1822,  ii.  1.  Lithion  Mica,  Ed.  Jour.  ii.  205.  Oxhaverite,  No.  13,  p.  115. 
Diamond,  ibid.  iii.  98  ;  Ph.  Mag.  vii.  245.  Haytorit,  Ed.  Jour.  vi.  301.  Fresnel 
on  Rock  Crystal,  Ann.  de  Ch.  xxviii.  147.  Herschel  on  do.  Camb.  Tr.  i.  43. 
Herschel  on  Borax,  Quetel.  Corres.  vii.  77.  Bicarbonate  of  Potash,  art.  Light, 
§  1082,  Apophyllite,  Camb.  Tr.  i.  241.  Airy  on  Quartz,  Camb.  Tr.  iv.  79,  199. 
Miller,  Crystals  of  Oblique  Prismatic  System,  Camb.  Tr.  v.  3. 

Compressed  and  heated  Glass,  8?c.— Brewster,  Ph.  Tr.  1814,  p.  436  ;  1815,  pp. 
1,  60 ;  1816,  pp.  46,  311  ;  Ed.  Tr.  viii.  353.  Effect  of  Comp.  on  Crystals,  ibid, 
viii.  281.  Effect  of  Heat  on  do.  Mitscherlich,  Pogg.  Ann.  viii.  519;  x.  137; 
xli.  213.  Brewster,  Ph.  Mag.  i.  417.  Rudberg,  Pogg.  Ann.  xxvi.  291.  Neumann, 
ibid.  xxxv.  81.  Seebeck,  Schweig.  Jour.  vii.  284.  Effect  of  Vibration  on  Glass, 
Biot,  Ann.  de  Ch.  xiii.  151.  Double  Refraction  of  do.  Fresnel,  Annales  de  Ch. 
xx.  376.  Brewster,  Ph.  Tr.  1830,  p.  87.  Guerard,  Compte  Rendue,  xix.  474. 

Fluids.— Biot,  Traite  de  Phy.  iv.  536 ;  Ann.  de  Chimie,  Iii.  58,  72. 

Undulatory  Theory. — Besides  many  memoirs  already  mentioned,  see  the  follow- 
ing Treatises : — Young,  Supp.  to  Encyc.  Brit.  art.  Chromatics.  Fresnel,  Supp. 
a  la  Traduction  Fransoise  de  la  5me  ed.  du  Traite  de  Chimie  de  Thomson,  par 
Riffault,  Paris,  1822.  Herschel's  art.  Light,  in  the  Encyc.  Metrop.  and  the  French 
Translation  of  it  by  Quetelet  and  Verhulst.  Airy's  Tract  on  the  Undulatory 
Theory,  in  his  Tracts,  2nd  edition,  Camb.  1831.  Schwerd,  Die  Beugungserschei- 
nungen  aus  den  FundamentaJgesetzen  der  Undulations  Theorie  analytisch  ent- 
wickelt,  4to,  Munich,  1835.  Powell,  The  Undulatory  Theory  applied  to  Disper- 
sion, &c.  184.  Lloyd's  Lectures,  Dublin,  1836-41. 

Memoirs. — Laplace  sur  le  Mouvement  de  la  Lumiere  dans  les  Corps  Diaphanes, 
Mem.  de  1'Inst.  1809,  p.  300.  Malus,  Theorie  de  la  Double  Refraction,  4to,  1810. 
Fresnel,  Annales  de  Chimie,  1815.  Expl.  de  Refraction,  ibid.  xv.  379.  Note  sur 
le  Calcul  des  Teintes  que  la  Polarisation  developpe  dans  les  Lames  crystallisees, 
ibid.  xvii.  pp.  102,  167,  312.  Des  Anneaux  colores,  ibid.  xxii.  129.  Arago,  ibid.  i. 
199.  Fresnel  sur  la  Double  Refraction,  Mem.  de  1'Inst.  1827,  vii.  45.  Navier,  sur 
le  Mouvement  des  Corps  elastiques,  ibid.  vii.  375.  Poisson,  do.  viii.  and  x. 
Cauchy  on  do.  ibid.  ix.  114.  Theorie  de  la  Lumiere,  ibid.  x.  293.  Exercises  de 
Math.  v.  19,  &c.  Ampere,  Ann.  de  Ch.  xxxix.  113.  On  the  Laws  of  Refraction, 
Mem.  del'Inst.  xiv.  235.  Neumann,  Theorie  der  Doppleten  Strahlenbrechung,  Pogg. 
Ann.  xxv.  418.  On  Crystalline  Reflection,  4to,  Berl.  1837,  and  Berlin  Mem.  xxii. 
•1.  Challis,  Ph.  Mag.  xi.  161.  Hamilton,  Theory  of  Systems  of  Rays,  Ir.  Tr.  xv. 
69;  xvi.  1,  94.  M'Cullagh  on  Double  Refraction,  ibid.  xvi.  Geometrical  Pro- 
positions applied  to  the  Wave  Theory  of  Light,  ibid,  xviii.  On  Crystalline  Reflec- 


374  LECTURE  XL. 

tion,  ibid,  xviii.  Kelland  on  the  Transmission  of  Light  in  crystallized  Media,  Camb. 
Tr.  vi.  323.  On  Reflection,  Ed.  Tr.  xiv.  393  ;  xv.  37,  511.  On  the  Aggregate 
Effect  of  Interference,  Camb.  Tr.  vii.  Ed.  Tr.  xv.  315.  Green  on  Reflection, 
&c.  Camb.  Tr.  vii. 


LECTURE   XL. 

<i 

ON  THE  HISTORY  OF  OPTICS. 

THE  science  of  optics  is  not  one  of  those  which  had  been  cultivated  with 
the  greatest  diligence  and  success  by  the  philosophers  of  antiquity  ;  almost 
every  refinement  relating  to  it  has  originated  in  the  course  of  about  two 
centuries  ;  and  some  of  its  greatest  improvements  have  been  made  within 
these  fifty  years.  The  reflection  of  the  rays  of  light  is  indeed  an  occur-, 
rence  too  frequent  and  too  obvious  to  have  escaped  the  notice  even  of  the 
earliest  observers :  a  river  or  a  fountain  was  the  first  mirror  ;  its  effect  was 
easily  imitated  by  speculums  of  metal :  and  as  soon  as  any  philosophical 
attention  was  paid  to  the  phenomenon,  it  was  easy  to  collect  the  equality 
of  the  angles  of  incidence  and  reflection ;  but  although  it  was  well  known 
that  an  oar,  partially  immersed  in  water,  no  longer  appeared  straight,  it 
was  long  before  any  attempts  were  made  to  ascertain  the  relation  between 
the  angles  of  incidence  and  refraction.  The  Greeks  were,  however, 
acquainted  with  the  properties  of  the  burning  glass,  which  was  sold  as  a 
curiosity  in  the  toy  shops  ;  for  it  is  well  known,  that  one  of  the  per- 
sonages introduced  by  Aristophanes,*  proposes  to  destroy  the  papers 
[writing  in  wax]  of  his  adversary  by  the  assistance  of  this  instrument. 
The  magnifying  powers  of  lenses  were,  however,  but  little  understood, 
although  it  is  scarcely  credible  that  they  could  have  escaped  the  notice  of 
a  person  in  possession  of  a  burning  glass  ;  it  appears  from  Seneca  that  the 
Romans  at  least  were  informed  of  the  effects  of  spherical  refracting  sub- 
stances, and  it  is  not  improbable  that  some  use  was  occasionally  made  of 
them  in  the  arts. 

Empedocles  is  perhaps  the  first  person  on  record  that  wrote  systemati- 
cally on  light.  He  maintained  that  it  consisted  of  particles  projected  from 
luminous  bodies,  and  that  vision  was  performed  both  by  the  effect  of  these 
particles  on  the  eye,  and  by  means  of  a  visual  influence  emitted  by  the  eye 
itself.  Both  of  these  doctrines  were  combated  by  Aristotle,t  who  thought 
it  absurd  to  suppose  that  a  visual  influence  should  be  emitted  by  the  eye, 
and  that  it  should  not  enable  us  to  see  in  the  dark  ;  and  who  considered  it 
as  more  probable  that  light  consisted  in  an  impulse,  propagated  through  a 
continuous  medium,  than  in  an  emanation  of  distinct  particles.  Light,  he 

•    *  Nubes. 

t  -De  Sensu,  ii.  &c.  But  compare  Meteor,  i.  6  ;  iii.  4,  5  ;  and  see  authorities  in 
Kelland 's  Lectures,  p.  6. 


ON  THE  HISTORY  OF  OPTICS.  375 

says,  is  the  action  of  a  transparent  substance  ;  and  if  there  were  absolutely 
no  medium  between  the  eye  and  any  visible  object,  it  would  be  absolutely 
impossible  that  we  should  see  it. 

It  is  said  that  Archimedes  made  a  compound  burning  mirror,  of  suffi- 
cient power  to  set  on  fire  the  Roman  ships  ;  in  this  form  the  story  is 
scarcely  probable,  although  the  possibility  of  burning  an  object  at  a  great 
distance  by  a  collection  of  plane  mirrors  has  been  sufficiently  shown  by 
the  experiments  of  Buffon.*  It  is,  however,  not  unlikely  that  Archimedes 
was  acquainted  with  the  properties  of  reflecting  surfaces,t  and  that  he 
confirmed  his  theories  by  some  experimental  investigations.  The  work  on 
catoptrics,  attributed  to  Euclid,  contains  the  determination  of  the  effects  of 
reflecting  surfaces  of  different  forms  ;  but  it  is  not  supposed  to  be  genuine. 
The  existence  and  the  magnitude  of  the  atmospheric  refraction  were  well 
known  to  Ptolemy,  and  a  treatise  of  this  astronomer  on  the  subject  is  still 
extant  in  manuscript. 

The  mathematical  theory  of  optics,  or  the  science  of  dioptrics  and 
catoptrics,  made  some  advances  in  the  middle  ages  from  the  labours  of 
Alhazen  and  Vitellio.;j:  Alhazen  was  mistaken  in  some  of  his  proposi- 
tions respecting  refraction  ;  Vitellio,  a  native  of  Poland,  gave  a  more 
correct  theory  of  this  subject,  and  constructed  a  table  of  refractive  densi- 
ties, showing  the  supposed  proportions  of  the  angles  of  incidence  and 
refraction  in  the  respective  mediums.  § 

The  invention  of  the  magic  lantern  is  attributed  to  Roger  Bacon,  and 
the  lens  was  soon  afterwards  commonly  applied  to  the  assistance  of  de- 
fective sight.  It  has  been  much  disputed  whether  or  no  Bacon  was  ac- 
quainted with  telescopes  ;  the  prevalent  opinion  is,  that  the  passages, 
which  have  been  alleged  to  prove  it,  are  insufficient  for  the  purpose ;  but 
there  is  reason  to  suspect,  from  the  testimony  of  Recorde,||  who  wrote  in 
1551,  not  only  that  Bacon  had  actually  invented  a  telescope,  but  that 
Recorde  himself  knew  something  of  its  construction.  Digges  also,  in  a 
work  published  in  1571, IF  has  a  passage  of  a  similar  nature,  and  from 
Bacon's  own  words  it  has  been  conjectured  that  an  instrument  resem- 
bling a  telescope  was  even  of  much  higher  antiquity.  But  the  first  person 
who  is  certainly  known  to  have  made  a  telescope,  is  Janson,  a  Dutchman, 
whose  son,  by  accident  placing  a  concave  and  a  convex  spectacle  glass  at 
a  little  distance  from  each  other,  observed  the  increased  apparent  mag_ 
nitude  of  an  object  seen  through  them  ;  the  father  upon  this  fixed  two 
such  glasses  in  a  tube  a  few  inches  long,  and  sold  the  instrument  in  this 
form.**  He  also  made  some  telescopes  of  greater  powers,  and  one  of  his 

*  Ph.  Tr.  1748,  p.  504. 

f  See  Kircher's  Ars  Magna  Lucis  et  Umbrae,  4to,  1646.  Parsdhs,  Ph.  tr. 
1754,  p.  621. 

+  Opticse  Thesaurus  per  Risnerum,  fol.  Basle,  1572. 

§  Kepler,  in  his  Paralipomena  ad  Vitellionem,  4to,  Frankf.  1604,  laboured  un- 
successfully to  discover  the  true  law  of  refraction. 

||   See  Ph.  Mag.  xviii.  245. 

^f  Pantometria. 

**  Borellus,  De  Vero  Telescopii  Tnventore,  4to,  Hagse,  1655. 


376  LECTURE  XL. 

family  discovered  a  satellite  of  Jupiter  with  them.*  Galileo  t  had  heard 
of  the  instrument,  but  had  not  been  informed  of  the  particulars  of  its  con- 
struction ;  he  reinvented  it  in  1609,  and  the  following  year;};  rediscovered 
also  the  satellite  which  Janson  had  seen  a  little  before. 

It  was,  however,  Kepler  §  that  first  reduced  the  theory  of  the  telescope 
to  its  true  principles  ;  he  laid  down  the  common  rules  for  finding  the  focal 
lengths  of  simple  lenses  of  glass  ;  he  showed  how  to  determine  the  magni- 
fying power  of  the  telescope,  and  pointed  out  the  construction  of  the  simple 
astronomical  telescope,  which  is  more  convenient  for  accurate  observations 
than  the  Galilean  telescope,  since  the  micrometer  may  be  more  easily  applied 
to  it ;  a  third  glass,  for  recovering  the  erect  position  of  the  object,  was  after- 
wards added  by  Scheiner,  and  a  fourth,  for  increasing  the  field  of«view,  by 
Rheita.  Kepler  made  also  some  good  experiments  on  the  nature  of  coloured 
bodies,  and  showed  the  inverted  situation  of  the  image  formed  on  the  retina 
of  the  eye.  Maurolycus  ||  of  Messina  had  demonstrated,  in  1575,  that  the 
pencils  of  light  are  brought  to  focal  points  on  the  retina  ;  Kepler's  obser- 
vations were  thirty  or  forty  years  later. 

The  next  great  step  in  optics  was  made  by  De  Dominis,1F  who  in  1611 
first  explained  the  cause  of  the  interior  or  primary  rainbow,  and  this  was 
soon  followed  by  a  still  more  important  discovery  respecting  the  nature  of 
refraction,  first  made  by  Snellius,  who  ascertained,  about  1621,  that  the 
sines  of  the  angles  of  incidence  and  refraction  are  always  in  the  same  pro- 
portion to  each  other  at  the  same  surface  ;  he  died,  however,  in  1626, 
without  having  made  his  discovery  public.  Descartes  is  generally  supposed 
to  have  seen Snellius's  papers,  although  he  published  the  law  of  refraction** 
without  acknowledging  to  whom  he  was  indebted  for  it.  Descartes  also 
explained  the  formation  of  the  secondary  rainbow,  ft  and  truly  determined 
the  angular  magnitude  of  both  the  bows  from  mathematical  principles  ;  he 
did  not,  however,  give  a  sufficient  reason  for  the  production  of  colours  in 
either  case.  Descartes  imagined  light  to  consist  in  motion,  or  rather  pres- 
sure, transmitted  instantaneously  through  a  medium  infinitely  elastic,  and 
colours  he  attributed  to  a  rotatory  motion  of  the  particles  of  this  medium.^ 
He  supposed  that  light  passed  more  rapidly  through  a  denser  medium  than 
through  a  rarer;  other  philosophers  about  the  same  time  maintained  a 
contrary  opinion,  without  deciding  with  respect  to  any  general  theory  of 
light :  thus  Fermat  and  Leibnitz  deduced,  on  this  supposition,  the  path  of 
refracted  light  from  the  natural  tendency  of  every  body  to  attain  its  end 

*  Borellus,  De  Vero  Telescopii  Inventore,  4to,  Hagse,  1655,  p.  40.  ThatBo- 
rellus  had  no  just  grounds  for  this  statement  is  shown  by  Moll,  Journal  of  the  Roy. 
Inst.  Nos.  2  and  3  ;  and  Drinkwater,  Ph.  Mag.  1832,  i.  14.  The  credit  of  the  dis- 
covery of  Jupiter's  satellites  is  certainly  due  to  Galileo. 

t  Opere,  ii.  4. 

£  Ibid.  p.  17,  and  Nuncius  Sidereus,  Venet.  1610. 

§  Dioptrice,  4to,  Augsb.  1611. 

II  Theoremata  deLumine,  4to,  Lugd.  1613. 

1[  De  Radiis  visis  in  Iride,  4to,  Venet.  1611.  But  see  Descartes,  Meteorum,  cap. 
viii.  p.  196. 

*  Specim.  Dioptrices,  chap.  ii.  §  7.     See  Huygens,  Dioptrica,  p.  2. 

ft  Spec.  Meteorum,  chap.  viii.  ++  De  Lumine,  chap.  i. 


ON  THE  HISTORY  OF  OPTICS.  377 

by  the  shortest  possible  way  ;*  and  Barrowf  derived  the  same  law,  in  a 
more  geometrical  manner,  from  a  similar  hypothesis  respecting  the  velocity 
of  light,  by  considering  a  pencil  of  light  as  a  collection  of  collateral  rays 
influencing  each  other's  motions.  We  are  indebted  to  this  learned  mathe- 
matician for  the  first  accurate  investigation  of  the  properties  of  refracting 
and  reflecting  surfaces,  and  for  the  most  general  determination  of  the  situ- 
ations of  focal  points. 

The  industrious  Mr.  Boyle  J  had  noticed  with  attention  the  phosphores- 
cence of  diamonds,  the  colours  produced  by  the  effect  of  scratches  on  the 
surfaces  of  polished  metals,  and  the  diversified  tints  which  a  bubble  or  a 
film  of  soapy  water  usually  assumes.  His  assistant,  Dr.  Hooke,  investi- 
gated th«se  and  other  similar  appearances  with  still  greater  accuracy,  and 
proposed,  in  his  Micrographia,  which  was  published  in  1665,  a  theory  of 
light  considerably  resembling  that  of  Descartes  :  he  supposes  that  light  is 
an  impulse  propagated  through  a  medium  highly,  but  not  infinitely, 
elastic  ;  §  that  refraction  is  produced  by  the  readier  transmission  of  light 
through  the  denser  medium,  and  that  difference  of  colour  consists  in  the 
different  law  of  the  particular  impulse  constituting  coloured  light,  so  that 
red  and  blue  differ  from  each  other  in  the  same  manner  as  the  sound  of  a 
violin  and  of  a  flute.  He  explained  the  colours  of  thin  plates  from  the 
interference  of  two  such  pulses  partially  reflected  from  the  upper  and  under 
surface;  ||  but  the  hypothesis  which  he  assumed  respecting  the  nature  of 
colours,  renders  this  explanation  wholly  inadequate,  nor  were  the  pheno- 
mena at  that  time  sufficiently  investigated  for  a  complete  solution  of  the 
difficulties  attending  them. 

It  was  still  believed  that  every  refraction  actually  produces  colour,  instead 
of  separating  the  colours  already  existing  in  white  light ;  but  in  the  year 
1666,  Newton  first  made  the  important  discovery  of  the  actual  existence  of 
colours  of  all  kinds  in  white  light,  which  he  showed  to  be  no  other  than  a 
compound  of  all  possible  colours,  mixed  in  certain  proportions  with  each 
other,  and  capable  of  being  separated  by  refraction  of  any  kind. 

About  the  same  time  that  Newton  was  making  his  earliest  experiments 
on  refraction,  Grimaldi's  treatise  on  light  appeared  ;^[  it  contained  many 
interesting  experiments  and  ingenious  remarks  on  the  effects  of  diffraction, 
which  is  the  name  that  he  gave  to  the  spreading  of  light  in  every  direction, 
upon  its  admission  into  a  dark  chamber,  and  on  the  colours  which  usually 
accompany  these  effects.  He  had  even  observed  that  in  some  instances  the 
light  of  one  pencil  tended  to  extinguish  that  of  another,  but  he  had  not 
inquired  in  what  cases  and  according  to  what  laws  such  an  interference 
must  be  expected. 

The  discoveries  of  Newton  were  not  received  without  some  controversy 
either  at  home  or  abroad  ;  the  essential  points  of  his  theory  were,  however, 
soon  established,  but  Dr.  Hooke  very  warmly  opposed  the  hypothesis  which 

*  See  Maupertius,  Hist,  et  Mem.  de  Paris^  1744,  p.  417,  H.  53. 

f  Lectiones  Opticae,  4 to,  Cantab.  1674. 

J  Works,  iii.  304.  §  Microg.  p.  56. 

||  Microg.  p.  65. 

^  Physico-Mathesis  de  Lumine,  Bonon.  1665. 


378  LECTURE   XL. 

Newton  had  suggested  respecting  the  nature  and  propagation  of  light.*  On 
this  subject  Newton  professed  himself  by  no  means  tenacious  ;  he  was  not, 
however,  convinced  by  Dr.  Hooke,  and  disliked  the  dispute  so  much,  that 
he  deferred  the  publication  of  his  treatise  on  optics  till  after  Hooke's  death 
in  1703.  Veiy  soon  after  his  first  communication  to  the  Royal  Society,  in 
1672,  he  had  sent  them  a  description  of  his  reflecting  telescope, t  which  was 
perhaps  the  first  that  had  been  constructed  with  success,  although  Gregory^ 
had  invented  his  instrument  some  years  before,  and  a  plan  of  a  similar 
kind  had  been  suggested  by  Eskinard  §  as  early  as  1615.  The  principal 
parts  of  the  treatise  on  optics  had  been  communicated  at  different  times  to 
the  Royal  Society  ;  besides  the  experiments  on  refraction  and  the  theory  of 
the  rainbow,  they  consist  of  an  elegant  analysis  of  the  colours  of  thin  trans- 
parent substances,  in  which  the  phenomena  are  reduced  to  their  simplest 
forms,  and  of  a  collection  of  miscellaneous  experiments  on  the  colours  pro- 
duced in  cases  of  inflection  or  diffraction. 

With  respect  to  the  nature  of  light,  the  theory  which  Newton  adopted 
was  materially  different  from  the  opinions  of  most  of  his  predecessors.  He 
considered  indeed  the  operation  of  an  ethereal  medium  as  absolutely  neces- 
sary to  the  production  of  the  most  remarkable  effects  of  light,  but  he  denied 
that  the  motions  of  such  a  medium  actually  constituted  light ;  he  asserted, 
on  the  contrary,  that  the  essence  of  light  consisted  in  the  projection  of  mi- 
nute particles  of  matter  from  the  luminous  body,  and  maintained  that  this 
projection  was  only  accompanied  by  the  vibration  of  a  medium  as  an  acci- 
dental circumstance,  which  was  also  renewed  at  the  surface  of  every  re- 
fractive or  reflective  substance. 

In  the  mean  time  Bartholin  had  called  the  attention  of  naturalists  and 
opticians  to  the  singular  properties  of  the  Iceland  crystal,  and  had  hastily 
examined  the  laws  of  its  unusual  refraction.  On  this  subject  Huygens  had 
been  much  more  successful :  his  analysis  of  the  phenomena  of  the  double 
refraction  is  a  happy  combination  of  accurate  experiment  with  elegant 
theory ;  it  was  published  in  1690,  making  a  part  of  his  treatise  on  light, 
the  fundamental  doctrines  of  which  he  had  communicated  to  the  Academy 
of  Paris  in  1678.  They  scarcely  differ  in  their  essential  parts  from  those 
of  our  countryman  Dr.  Hooke,  but  the  subject  of  colours  Huygens  has  left 
wholly  untouched.  Roemer  had  then  lately  made  the  discovery  of  the 
immense  velocity  with  which  light  passes  through  the  celestial  regions,  by 
observing  the  apparent  irregularities  of  the  eclipses  of  Jupiter's  satellites  ; 
and  Huygens  readily  admitted  this  property  into  his  system ;  although 
Hooke,  1 1  by  a  singular  caprice,  professed  himself  more  ready  to  believe 
that  the  propagation  of  light  might  be  absolutely  instantaneous,  than  that 
its  motion  could  be  successive,  and  yet  so  inconceivably  rapid.  The  merits 

*  Birch,  iii.  10,  52.     Ph.  Tr.  viii.  5084,  6086. 

t  Ph.  Tr.  1672,  pp.  4004,  4032;  1673,  p.  6087. 

i  Optica  Promote,  1663. 

§  Eskinard's  Century  of  Optical  Problems. 

||  Lectures  of  Light,  in  Waller's  Life  and  Works  of  Hooke,  p.  77.  From  a 
passage  in  the  Micrographia,  p.  56,  it  is  evident  not  only  that  Hoake  was  ready  to 
admit  the  fact  of  the  finite  velocity  of  light,  when  proved,  but  that  he  anticipated 
both  the  manner  of  proof  and  the  result. 


ON  THE  HISTORY  OF  OPTICS.  379 

of  JHuygens  in  the  mathematical  theory  of  optics  were  no  less  considerable 
than  in  the  investigation  of  the  nature  of  light ;  his  determinations  of  the 
aberrations  of  lenses  were  the  first  refinement  on  the  construction  of  tele- 
scopes, but  with  respect  to  the  theory  of  halos  and  parhelia  he  was  less 
successful  than  Mariotte  had  been  some  years  before. 

In  the  year  1720,  Dr.  Bradley  had  the  good  fortune  to  discover  both  the 
existence  and  the  cause  of  the  aberration  of  the  fixed  stars.  He  had  for 
some  time  observed  an  irregularity  in  the  places  of  the  stars,  which  he  was 
wholly  unable  to  explain,  and  the  idea  of  attributing  it  to  a  combination  of 
the  effect  of  the  earth's  motion  in  its  orbit,  with  the  progressive  motion  of 
light,  occurred  to  him  first  as  he  happened  to  observe  the  apparent  di- 
rection of*  the  wind  on  board  of  a  boat  which  was  moving  in  a  transverse 
direction.  He  also  determined  with  accuracy  the  magnitude  of  the  at- 
mospherical refraction,*  which  had  been  theoretically  investigated  by 
Newton  and  by  Taylor,t  but  never  before  practically  ascertained  with 
sufficient  precision.  The  formula,  which  Bradley  appears  to  have  deduced 
from  observation  only,  agrees  precisely  with  an  approximation  which  was 
obtained  by  Simpson  J  from  calculation ;  but  it  cannot  be  considered  as 
rigidly  accurate. 

The  optics  of  Bouguer  were  first  published  in  1729,  and  an  improved 
edition  appeared  thirty  years  afterwards  ;  the  merits  of  this  author  in  the 
examination  of  the  properties  of  a  variety  of  substances,  with  respect  to 
the  transmission  and  reflection  of  light  in  different  circumstances,  and  in 
the  comparison  of  lights  of  different  kinds,  require  to  be  mentioned  with 
the  highest  commendation. §  Dr.  Porterfield's||  investigations  of  the 
functions  of  the  eye  tended  greatly  to  illustrate  the  economy  of  this  admi- 
rable organ,  and  some  valuable  remarks  of  Dr.  Jurin  on  the  same  subject 
were  soon  after  published  in  Dr.  Smith's  elaborate  treatise  on  optics,  which 
contains  all  that  had  been  done  at  that  time  with  respect  to  the  mathema- 
tical part  of  the  science. 

The  invention  of  achromatic  telescopes  is  with  justice  universally  attri- 
buted to  our  countryman  Mr.  Dollond,^[  but  there  is  reason  to  believe  that 
he  was  not  absolutely  the  first  author  of  the  improvement.  Mr.  Hall,  a 
gentleman  of  Worcestershire,  is  said  to  have  discovered,  about  the  year 
1 729,  Sir  Isaac  Newton's  mistake,  in  supposing  that  the  rays  of  different 
colours  must  of  necessity  be  equally  separated  by  all  surfaces  which  pro- 
duce an  equal  mean  refraction ;  and  by  combining  the  different  dispersive 
properties  of  different  kinds  of  glass,  he  constructed,  in  1733,  several  com- 
pound object  glasses,  which  were  calculated  not  only  for  avoiding  all  ap- 
pearance of  colour,  but  also  for  correcting  the  imperfect  refractions  of  the 
spherical  surfaces  of  the  separate  lenses.  He  did  not,  however,  make  known 
the  particulars  of  his  investigations,  and  his  invention  was  soon  wholly 
forgotten.  It  was  in  consequence  of  a  discussion  **  with  Euler,  Klingen- 

*  See  Ph.Tr.  1787,  p.  156.  f  Methodus  Incrementorum,  p.  108. 

J  Mathematical  Dissertations,  4to,  1743,  p.  46. 

•  §  Hist,  et  Mem.  1726,  H.  11 ;  1757,  p.  1.     Optique,  4to,  Paris,  1760. 
||  On  the  Eye  and  Vision,  2  vols.  Edin.  1759. 

^  Ph.  Tr.  1.  735.     Compare  Newton's  Optics,  book  i.  part  ii.  Prop.  3,  Exp.  8. 
**  Hist,  et  Mem.  1756-7. 


380  LECTURE  XL. 

stierna,  and  some  other  mathematicians,  that  Mr.  Dollond  was  led  to  make 
experiments  on  the  refraction  of  different  kinds  of  glass  ;  these  gentlemen 
had  not  questioned  the  general  truth  of  Newton's  opinion  respecting  the 
dispersion  of  the  different  colours,  but  Euler  had  asserted  that  the  eye  itself 
produced  a  refraction  free  from  the  appearance  of  colour,  and  Klingen- 
stierna*  had  shown  the  possibility  of  producing  a  deviation  by  refraction, 
without  a  separation  of  colour,  according  to  the  laws  of  refraction  laid 
down  by  Newton  himself.  When  Dollond  had  once  discovered  the  mate- 
rial difference  which  exists  between  the  dispersive  properties  of  flint  glass 
and  of  crown  glass,  it  was  easy  to  produce  the  combination  required  ;  but 
this  ingenious  artist  was  not  satisfied  with  the  advantage  of  freedom  from 
colours  only  ;  he  adjusted  the  forms  and  apertures  of  his  lensts  in  the 
most  skilful  manner  to  the  correction  of  aberrations  of  various  kinds,  and 
he  was  also  particularly  fortunate  in  being  able  to  obtain,  about  the  time 
of  his  discovery,  a  glass  of  a  quality  superior  to  any  that  has  been  since 
manufactured. 

This  opinion  of  Euler  respecting  the  eye  was,  however,  by  no  means 
well  founded,  for  the  eye  acts  very  differently  on  rays  of  different  colours, 
as  we  may  easily  observe  by  viewing  a  minute  object  in  different  parts  of 
a  beam  of  light,  transmitted  through  a  prism.  It  must  be  allowed  that 
this  great  mathematician  was  less  fortunate  in  his  optical  theories  than  in 
many  other  departments  of  science  ;  his  mathematical  investigations  of  the 
effects  of  lenses  are  much  more  intricate  and  prolix  than  the  subject 
actually  requires,  and  with  respect  to  the  nature  and  propagation  of  light, 
he  adopted  several  paradoxical  opinions.  Assuming  the  theory  of  Huygens, 
with  the  additional  hypothesis  respecting  the  nature  of  colours,  which  had 
been  suggested  by  Newton,  and  maintained  by  Pardies  and  Malebranche, 
that  is,  that  the  difference  of  colours,  like  that  of  tones  in  music,  depends 
on  the  different  frequency  of  the  vibrations  constituting  light ;  he  imagined 
that  opaque  bodies  are  not  seen  by  reflected  light,  but  that  their  particles 
are  agitated  by  the  impulse  of  the  light  which  falls  on  them,  and  that  the 
vibrations  of  these  particles  render  the  bodies  again  visible  in  every  direc- 
tion ;  he  also  conceived  that  the  undulations  of  light  are  simply  propagated 
through  the  solid  substances  of  transparent  mediums,  in  the  same  manner 
as  sound  travels  through  the  air.  But  on  these  suppositions,  all  bodies 
would  have  the  properties  of  solar  phosphori,  and  the  refraction  of  the 
rarest  of  natural  bodies  would  be  incomparably  greater  than  that  of  the 
densest  is  actually  found  to  be  :  and  on  the  whole,  although  the  character 
of  Euler  has  been  so  highly  and  so  deservedly  respected  as  to  attach  a  cer- 
tain degree  of  authority  to  all  his  opinions,  so  that  in  this  instance  the 
name  of  Huygens  has  been  almost  superseded  by  that  of  Euler,  yet  in  fact 
he  has  added  no  argumentative  evidence  whatever  to  the  theory,  but,  by 
inaccurate  and  injudicious  reasoning,  has  done  a  real  injury  to  the  cause 
which  he  endeavoured  to  support. 

The  researches  of  Lambert  t  may  be  considered  as  a  continuation  of 

*  Schwed.  Abhand.  1754,  xvi.  300;  1760,  xxii.  79.     Ph.  Tr.  1760,  p.  944  ;  and 
Tentameu  de  Corrig.  Aberrat.  Luminis,  4to,  Petrop.  1762. 
f  Photometria,  Augsb.  1760. 


ON  THE  HISTORY  OF  OPTICS.  381 

those  of  Bouguer  ;  they  present  us  with  many  interesting  observations  on 
the  natural  history  of  light,  and  the  properties  of  various  bodies  with  regard 
to  it.  Mr.  Lambert  first  ascertained  that  a  luminous  surface  emits  its  light 
very  nearly  with  equal  intensity  in  all  directions,  so  that  any  part  of  it 
appears  almost  equally  brilliant  to  an  eye  placed  in  any  direction,  while 
the  light  thrown  by  each  square  inch  or  square  foot  of  the  surface  in  any 
direction  differs  according  to  the  obliquity  of  that  direction.  The  mathe- 
matical theory  of  optics  is  considerably  indebted  to  the  labours  of 
Clairaut,*  Dalembert,t  and  Boscovich  ;  ^  Jeaurat,  §  Beguelin,||  Redern,*[ 
anc1,  Kliigel**  have  also  continued  the  investigation  ;  their  calculations 
may  be  of  considerable  utility  to  the  practical  optician,  but  it  requires  the 
ingenuity  of  a  Dollond  or  a  Ramsden  to  apply  the  whole  of  the  results  to 
any  useful  purposes. 

The  experiments  of  Mazeas  ft  on  the  colours  of  thin  plates  are  mere  re- 
petitions of  those  of  Newton  under  disadvantageous  circumstances ;  Mr. 
DutourJ^  has,  however,  considerably  diversified  and  extended  these  expe- 
riments, as  well  as  those  on  the  colours  which  are  produced  in  diffracted 
light,  yet  without  obtaining  any  general  results  of  importance.  Compa- 
retti's§§  experiments  on  inflection  have  every  appearance  of  accuracy,  but 
they  are  much  too  intricate  to  be  easily  compared  with  each  other,  or  with 
those  of  former  observers. 

The  late  Dr.  Priestley  ||||  rendered  an  essential  service  to  the  science  of 
optics,  considered  as  a  subject  for  the  amusement  of  the  general  reader,  by 
an  elegant  and  well  written  account  of  the  principal  experiments  and 
theories,  which  had  been  published  before  the  year  1770.  But  this  work 
is  very  deficient  in  mathematical  accuracy,  and  the  author  was  not  suffi- 
ciently master  of  the  science  to  distinguish  the  good  from  the  indif- 
ferent. 

Mr.  Delaval's^T^T  experiments  on  colours  appear  to  show  very  satisfac- 
torily, that  all  the  colouring  substances,  in  common  use,  owe  their  tints  to 
rays,  which  are  separated  from  white  light,  during  its  passage  through 
them,  and  not,  as  Newton  supposed,  to  the  reflection  of  a  particular  colour 
from  the  first  surface.  It  has  been  observed  that  Kepler  and  Zucchius  *** 
had  long  ago  made  experiments  nearly  similar  to  those  of  Mr.  Delaval. 

*  Hist,  et  Mem.  de  Paris,  1756,  vii.380,  H.  112;  1757,  p.  524,  H.  153;  1762, 
p.  578,  H.  160. 

t  Ibid.  1764,  p.  75,  H.  175;  1765,  p.  53,  H.  119;  1767,  p.  43,  H.  153. 
Opuscules,  vol.  i.  Hist,  et  Mem.  de  Berlin,  1769,  p.  254. 

t  Com.  Bon.  v.  II.  265. 

§  Hist,  et  Mem.  de  Paris,  1770,  p.  461,  H.  103. 

||  On  the  Improvement  of  Telescopes,  Hist,  et  Mem.  de  Berlin,  1762,  pp.  66, 
343 ;  1764,  p.  7 ;  1769,  p.  1  ;  1784,  H.  40. 

H  On  Object-Glasses,  ibid.  1759,  p.  89 ;  1760,  p.  3;  1761,  p.  3. 

**  On  do.  Comm.  Gott.  1795,  xiii.  2,  28.  Gilbert's  Annalen,  xxiv.  265,  276. 
Analytische  Dioptrik,  4to,  Leipz.  1778. 

ft  Hist,  et  M6m.  de  Berl.  1752,  p.  262.     Mem.  des  Savans  Etrangers,  ii.26. 

U  Ibid.  vols.  iv.  and  v.  Rozier's  Journal,  i.  368;  ii.  11,  249;  v.  120,  230; 
vi.  135,  330,  341,412. 

§§  De  Luce  Inflexa  et  Coloribus,  4to,  Pad.  1787. 

HI)  The  History  and  present  State,  &c.  of  Vision,  Light,  and  Colours,  4to,  Lond. 
1772. 

HH  Manch.  Mem.  ii.  131.       ***  Optica  Philosophia,  2  vols.  4to,  Lugd.  1652-6. 


382  LECTURE   XL. 

Dr.  Robert  Darwin's*  investigation  of  the  effects  of  strong  lights  on  the  eye 
appears  to  comprehend  almost  all  possible  varieties  of  these  ocular  spectra, 
but  it  does  not  lead  to  any  fundamental  analogy,  capable  of  explaining  the 
most  intricate  of  them. 

The  phenomena  of  the  unusual  atmospheric  refraction,  which  frequently 
produces  double  or  triple  images  of  objects  seen  near  a  heated  surface,  have 
been  successively  illustrated  by  Mr.  Huddart,t  Mr.  Vinc«,^  and  Dr.  Wol- 
laston,  §  so  that  at  present  there  appears  to  be  little  doubt  remaining  with 
respect  to  their  origin.  Dr.  Wollaston's  instrument  for  the  measurement 
of  refractive  densities,  very  much  facilitates  the  examination  of  the  optical 
properties  of  substances  of  various  kinds  :  he  has  applied  it  very  success- 
fully to  the  confirmation  of  Huygens's  theory  of  double  refraction^;  he  has 
corrected  the  common  opinion  respecting  the  division  of  the  prismatic 
spectrum  ;  he  discovered,  without  being  acquainted  with  the  observations 
of  Ritter,  the  dark  rays  which  blacken  the  salts  of  silver  ;  and  he  has  re- 
marked a  singular  property  in  some  natural  as  well  as  artificial  crystals, 
which  appear  of  one  colour  when  viewed  in  the  direction  of  the  axis,  and 
of  another  when  in  a  transverse  direction. 

To  Dr.  Herschel  the  sciences  of  optics  and  astronomy  are  equally  in- 
debted. He  has  carried  the  construction  of  the  reflecting  telescope  to  a 
degree  of  perfection,  far  exceeding  all  that  had  been  before  attempted,  and 
the  well  known  improvements  which  astronomy  has  derived  from  his  ob- 
servations are  numerous  and  important.  In  the  course  of  his  researches 
for  the  attainment  of  his  more  immediate  objects,  he  has  also  had  the  good 
fortune  to  discover  the  separation  of  the  rays  of  heat  from  those  of  light  by 
means  of  refraction  ;  a  fact  which  has  been  sufficiently  established  by  the 
experiments  of  several  other  persons. 

The  investigations  of  Mr.  Laplace,  relating  to  atmospherical  refraction, 
may  be  considered  as  the  latest  application  of  refined  mathematics  to  the 
purposes  of  optics  and  of  astronomy.  I  have  myself  attempted  to  attain  a 
degree  of  certainty,  in  attributing  the  changes  of  the  refractive  powers  of 
the  eye  to  a  variation  in  the  form  of  the  crystalline  lens  ;  I  have  discovered 
a  general  law  of  the  mutual  action  of  two  portions  of  light  interfering  with 
each  other,  to  which  no  exception  has  yet  been  shown  ;  and  by  reviving  a 
theory  of  light  similar  to  that  of  Hooke  and  Huygens,  with  an  improve- 
ment originally  suggested  by  Newton,  respecting  the  nature  of  colours,  1 
have  endeavoured  to  obtain  a  satisfactory  explanation  of  many  circum- 
stances, which  appear,  upon  a  minute  examination,  to  be  in  every  other 
hypothesis  difficulties  absolutely  insuperable.  It  cannot  be  expected  that 
all  objections  to  such  a  system  will  at  once  be  silenced,  but  if  a  full  and 
candid  discussion  only  of  the  facts  which  I  have  advanced,  should  be  ex- 
cited, I  trust  that  the  science  of  optics  will  be  essentially  benefited,  even 
if  the  theory  should  be  ultimately  confuted. 

*  Ph.  Tr.  1786,  p.  313.        >  Ph.  Tr.  1797,  p.  29. 

t  Ph.  Tr.  1799,  p.  13.         §  Ibid.  1800,  p.  239  ;  1803,  p.  1. 


ON  THE  HISTORY  OF  OPTICS.  383 

For  the  history  of  optics  consult  Priestley's  Hist.  4to,  1772.  Pringle  on  the 
Invention  of  the  Telescope,  4to,  Lond.  1778,  Ph.  Mag.  xviii.  245  ;  xix.  66,  176, 
232,  344  ;  xx.  14.  Venturi,  Comm.  sopra  la  Storia  e  la  Teoria  dell'  Ottica,  Bolog. 
1814.  Meister,  Nov.  Comm.  Gott.  v.  V.  141 ;  VI.  189.  Arago,  Ann.  de  Ch.  xiv. 
434.  Lloyd,  Report  of  Brit.  Assoc.  1835.  Powell,  British  Annual.  1837. 


WORKS  ON  NATURAL  PHILOSOPHY  IN  GENERAL,  NOT  QUOTED  IN  THE  PRECEDING 

LECTURES. 

Sennerti,   Philosophia  Naturalis,  4to,  Wittenb.  1618.     Herigone,  Cursus  Math. 

5  vcis.    Paris,   1634-7,     Etten,    Mathematicall  Recreations,    by  Oughtred,  1652. 
Jungii  Doxoscopise  Physicse    Minores,  4to,  Hamb.   1663.     Power's  Experimental 
Philosophy,  4to,  1664.     Duchess  of  Newcastle's  Do.  fol.  1666.     Senguerdi,  Philo- 
sophia N«eturalis,  4to,  Leyd.  1685.     Paul  Hoste,  Hydrostatique,   &c.,  the  part  on 
Naval  Tactics  translated  by  Capt.  J.  D.  Boswall,  4to,  Ed.  1834.    Hoffmanni  Lexi- 
con Universale,  4  vols.  fol.  Leyd.  1698.  Muys,  Elementa  Physices,  4to,  Amst.  1711. 
Scheuchzer's   Naturwissenchaft,  2  vols.  8vo,  Tur.  1711.     Nieuwentyt's   Religious 
Philosopher,  3  vols.   8vo,   1719.     Verdries  Conspectus  Philos.    Nat.  Giess.  1720. 
Wolff's  Niitzliche  Versuche,  3  vols.  Halle,  1721-43.      Vernunftige  Gedanken,    3 
vols.    Halle,    1723-5.      Keill's    Natural   Philosophy,    1726.      Pemberton's   New- 
tonian  Philosophy,  4to,  1728.      Crivelli  Fisica,  2  vols.  4to,  Ven.  1731-2.     Mo- 
liere's  Lemons  de  Physique.    Teichmeyeri    Philos.    Nat.  4to,    Jena,    1733.     Ham- 
bergi  Elementa  Physices,  Jena,  1735.     Helsham's  Lectures  on  Natural  Philosophy, 
1739.     Bulfingeri    Elementa    Physices,    Leipz.    1742.      Nollet,  Lefons   de    Phy- 
sique, 6  vols.  12mo,  Paris,    1743.      Segner's   Einleitung,    1746,   1770.     Ruther- 
forth's   Natural   Philosophy,    2   vols.    4to,  1748.      Kraftii   Prselectiones,    3  vols. 
Tubing.  1750.     Kriiger's  Naturlehre,    Halle,    1750.     Saverien,    Dictionnaire    de 
Math,  et  de  Physique,  2  vols.  4to,    Paris,  1753.     Winkler's  Natural  Phil,  (trans.), 
1757.     Martin's,  1781.     Jones's,  1762.     Guyton  de  Morveau,  Essais  de  Physique, 
12mo,  Dijon,  1762.     Hennert,  Cursus  Math.  6  vols.  Traj.  ad  Rhen.  1768-75.     Eu- 
ler's  Letters  to  a  German  Princess  (trans.),  2  vols.  1795,   1802.     Karsten's  Lehr- 
begriff,  Greifsw.  1764.     Anfangsgriinde   der  Naturlehre,  Halle,  1790,  &c.     Row- 
ning's  Natural  Philosophy,    2  vols.  1765.      Sigaud  de   la  Fond,    Physique,  Paris, 
1767,   1771.      Silberschlags,    Ausgesuchte   Versuche,    Berl.  1768.      Hamberger's 
Naturlehre,   Jena,  1774.      Bookman's   Naturlehre,  Carlsr.  1775.     Senebier,   Art. 
d'Observer,    2   vols.    Geneve,    1775.      Ferguson's   Lectures,    1776.     Goldsmith's 
Exp.    Ph.   2  vols.  1776.     Sauri,    Cours  de  Phy.  4  vols.  12mo,  1777.     Gabler's 
Naturlehre,  4  vols.  Munich,  1778.     Richter's  Lehrbuch,   1779.     De  Luc,  Lettres 
Physiques,  4  vols.  La  Haye,  1779.     Turner's  Introduction  to  Arts  and  Sciences. 
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6  vols.  12mo,  1783-6.    Bruckhausen's  Physik,  von  Bergmann.  Schurer,  Elemens  de 
Physique,  Strasb.  1786.     Van  Swinden,   Positiones  Physicse,    2  vols.  Harderwick, 
1786.     Nicholson's  Nat.  Phil.  2  vols.  Lond.  1787.      Serrati,  Fisica,  Flor.  1787. 
Kratzenstein's  Physik,  Copenh.  1787.     Gren's  Naturlehre,    Halle,   1788.     Ingen- 
housz,  Nouvelles  Experiences,    Par.  1789.      Hobert's  Naturlehre,    Berlin,    1789. 
Ciscar  Maquinas   y  Maniobras,  fol.  Madrid,  1791.     Kliigel's  Naturlehre,  Berlin, 
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bung  der  Neuesten   Instrumenten,    3   vols.   Zittau,  1792-7.     Hube,    Naturlehre, 

2  vols.  Leipz.  1793.     Erxleben's  Naturlehre  von  Lichtenberg,    Gott.  1794.     An- 
derson's  Institutes   of  Physics,    Glasgow,  1795.      Gregory's  Economy  of  Nature, 

3  vols.  1796.      Barruel,    Physique  en  Tableaux,    4to,  Paris,    An.  7.      Enfield's 
Nat.  Phil.  4to,    1799.     Adams's  Do.  4  vols.  1799.      Walker's  Do.   4to,  1799. 
Brisson,  Dictionnaire  de  Physique,  6  vols.  An.  8.     Traite  de  Phy.  1803.     Biisch, 
Mathematik  zum  Niitzen,  2  vols.   Hamb.  1800.     Berard,  Melanges,  Par.  An.  9. 
Jacotot,  Cours   de  Physique,  2  vols.  Paris,  An.  9.     Libes,  Traite   de   Physique, 
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384  LECTURE   XL. 

vost,  Deux  Traites  de  Phys.  Geneve,  1818.  Mollet,  Cours  de  Phys.  2  vols.  Lyon, 
1822.  Babinet,  Resume  Complet  de  Physique,  2  vols.  32mo,  Paris,  1825.  Des- 
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Grundziige  der  Physik,  2  vols.  Nuremberg,  1832-3.  Quetelet,  Positions  de  Phy- 
sique, 3  vols.  12mo,  Brux.  1834.  Pinault,  Traite  de  Phy.  2  vols.  1836.  Lame, 
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Physics  (trans.),  1845. 


ON  THE  HISTORY  OF  OPTICS. 


385 


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PART     III 


LECTURE   XLI. 


ON  THE  FIXED  STARS. 

THE  departments  of  natural  philosophy,  which  are  to  be  the  subjects  of 
the  third  and  last  division  of  these  lectures,  are  included  in  the  description 
implied  by  the  term  physics,  or  the  history  of  the  particular  phenomena  of 
nature  ;  and  the  account  which  will  be  given  of  these  phenomena,  will  be 
accompanied  by  as  much  of  mechanical  theory  and  analogical  reasoning, 
as  can  be  applied  to  them  with  sufficient  certainty,  and  without  too  great 
intricacy  of  calculation. 

The  science  of  astronomy  might,  without  any  great  impropriety,  have 
been  considered  as  a  part  of  mechanics  ;  but  there  are  circumstances 
intimately  connected  with  it,  for  the  complete  investigation  of  which,  a 
knowledge  of  the  motions  of  fluids  in  general,  and  also  of  optics,  is  abso- 
lutely necessary.  It  could  not,  therefore,  hold  any  other  place  in  a  strict 
order  of  arrangement,  than  that  which  is  here  allotted  to  it ;  and,  since  it 
will  not  be  in  our  power  to  enter  completely  into  a  mathematical  examina- 
tion of  all  the  motions  of  the  heavenly  bodies,  although  we  shall  be  able  to 
pursue  the  detail  of  the  most  remarkable  appearances  which  they  exhibit, 
we  may  for  this  reason  more  properly  consider  such  a  view  of  astronomy 
as  belonging  to  descriptive  than  to  theoretical  philosophy.  This  method  of 
treating  the  subject  is  sometimes  denominated  plain  astronomy,  in  contra- 
distinction to  the  mechanical  theory  of  the  science,  which  is  called  physical 
astronomy ;  but  it  is  obvious  that  in  the  sense  which  we  are  at  present 
annexing  to  the  word  physics,  that  which  is  commonly  called  plain 
astronomy  must  be  termed  physical  or  descriptive,  and  what  is  usually 
called  physical,  must  be  denominated  mathematical  astronomy.  We  shall, 
therefore,  confine  ourselves  in  great  measure  to  descriptive  astronomy, 
and  shall  take  only  a  general  view  of  the  laws  of  gravitation,  as  an  illus- 
tration of  the  phenomena  previously  described.  After  having  considered 
the  magnificent  objects  of  astronomy,  which  are  scattered  throughout  the 
universe,  we  descend  to  geography,  or  the  particular  history  of  the  terra- 
queous globe,  and  to  the  tides,  produced  by  the  influence  of  the  celestial 
bodies  on  the  ocean  ;  and  then,  quitting  the  affections  of  the  larger  features 

2c2 


388  LECTURE  XLI. 

of  the  matter  that  constitutes  the  earth,  we  come  naturally  to  the  properties 
and  powers  of  its  individual  particles,  and  to  the  phenomena  of  heat, 
electricity,  and  magnetism,  which  are  either  qualities  of  matter,  or  depen- 
dent on  substances  differing  in  some  respects  from  common  matter ;  and 
in  the  next  place,  to  the  combination  of  all  these  substances  and  actions  in 
meteorology,  and  in  the  phenomena  of  vegetable  and  animal  life,  a  general 
view  of  which  will  complete  our  discussions  on  the  subject  of  physics. 
The  science  of  chemistry,  or  the  doctrine  of  the  qualities  of  particular 
kinds  of  matter,  might  be  said  to  belong  to  the  investigation  of  the  proper- 
ties of  matter  in  general ;  but  this  science  is  of  too  great  extent1'  and 
importance  to  occupy  a  subordinate  place  in  a  system  of  natural  philoso- 
phy, and  must,  therefore,  be  considered  as  requiring  a  separate  i^urse  of 
study. 

In  our  astronomical  inquiries,  we  shall  first  examine  the  phenomena  of 
the  heavens  and  earth  in  their  simplest  form,  not  as  they  immediately 
appear  to  our  observation,  but  as  they  are  shown  by  unexceptionable 
proofs  to  be  naturally  arranged.  The  stars  and  sun,  the  planets  and  their 
satellites,  and  lastly  the  comets,  will  be  severally  described  ;  the  causes  of 
the  motions  of  these  bodies  will  be  superficially  indicated  ;  their  sensible 
effects  with  respect  to  the  inhabitants  of  the  earth  will  be  shown,  and  the 
practical  modes  of  determining  their  .situations  and  orbits  will  be  ex- 
plained. 

When  we  begin  to  consider,  on  a  large  scale,  the  affections  of  matter 
and  of  space,  we  are  impressed,  at  the  first  sight,  with  the  inconceivable  dis- 
proportion between  the  magnitude  of  space  and  of  sensible  matter  ;  and  we 
are  naturally  led  to  inquire  if  the  apparently  void  expanse  of  the  universe 
is  wholly  without  all  matter  or  all  substance.  The  atmospheres  of  the  planets 
cannot  indeed  be  said  absolutely  to  terminate  at  any  given  point,  but  they 
must  become  rare  beyond  all  imagination  at  a  very  moderate  distance. 
The  substance  which  produces  the  sensation  of  light  must,  however,  be 
every  where  found,  at  least  without  any  sensible  interval ;  for  if  an  eye 
were  placed  in  any  point  of  the  regions  of  unbounded  space,  wherever 
human  investigation  or  fancy  can  penetrate  them,  some  luminous  object 
would  at  each  instant  be  visible  to  it,  and,  in  general,  objects  without 
number  might  be  seen  in  every  direction.  Light,  therefore,  must  be  every 
where  present,  whether  we  suppose  it  to  consist  of  separate  projected  cor- 
puscles, or  to  be  an  affection  of  a  highly  elastic  ether,  pervading  the  uni- 
verse in  a  state  so  rare,  that  although  it  constitutes  a  continuous  medium, 
it  suffers  all  bodies  to  move  through  it  without  sensible  resistance,  and  is 
admitted  even  into  their  pores  with  perfect  freedom ;  and  if  we  follow 
Newton's  opinion  of  the  nature  of  light,  we  must  suppose  both  such  an 
ethereal  medium,  nearly  at  rest,  and  the  particles  of  light  also,  moving 
swiftly  through  it,  to  exist  together  in  all  places ;  to  say  nothing  of  the 
possibility  of  the  coexistence  of  a  thousand  other  unseen  and  unknown 
substances,  essences,  and  influences,  in  the  same  individual  place,  which 
may  for  ever  set  at  defiance  the  pride  of  a  presumptuous  philosophy, 
that  would  aspire  to  comprehend,  within  its  own  contracted  sphere,  the 
whole  extent  of  the  mighty  work  of  the  creation. 


ON  THE  FIXED  STARS.  389 

,  The  expanse  of  the  universe  is  strewed,  at  immense  distances,  with  de- 
tached portions  of  a  substance,  which  we  suppose  to  be  matter,  constituting 
stars,  or  suns,  planets,  and  comets  ;  bodies  which  certainly  agree  with  each 
other  in  the  power  of  emitting  or  reflecting  light,  and  which,  in  all  proba- 
bility, have  many  other  properties  in  common.  Such  of  these  as  emit 
then-  own  light,  are  called  fixed  stars  ;  and  this  appears  to  be  the  only 
criterion  that  we  can  apply  to  a  star  :  for  the  word  fixed  is  only  to  be 
understood  in  a  comparative  sense. 

The  stars  must  necessarily  shine  by  their  own  light ;  for  if  we  grant  that 
they  consist  of  gravitating  matter,  it  must  be  allowed  that  no  star  could  be 
near  enough  to  another  to  be  seen  by  reflected  light,  without  a  very  sensible 
change  of  the  places  of  both  in  consequence  of  their  mutual  gravitation,  nor 
would  Jfbe  possible,  on  account  of  their  immense  distance  from  us,  to  dis- 
tinguish two  such  bodies  from  each  other.  It  follows  also,  on  the  same 
supposition  of  the  universality  of  the  force  of  gravity,  that  the  form  of  the 
stars  must  be  nearly  spherical. 

The  light  of  the  stars  appears  to  the  naked  eye  to  be  generally  white  ; 
being  too  faint  to  excite  the  idea  of  a  particular  colour ;  but  when  it  is 
concentrated  by  Dr.  Herschel's  large  speculums,  it  becomes,  in  various 
stars,  of  various  hues ;  and  indeed  to  the  naked  eye  some  of  the  stars 
appear  a  little  redder  and  others  a  little  bluer.  The  cause  of  the  twinkling 
of  the  stars  is  not  fully  ascertained,  but  it  is  referred,  with  some  proba- 
bility, to  changes  which  are  perpetually  taking  place  in  the  atmosphere, 
and  which  affect  its  refractive  density.  It  is  said  that  in  some  climates, 
where  the  air  is  remarkably  serene,  the  stars  have  scarcely  any  appearance 
of  twinkling.* 

Above  two  thousand  stars  are  visible  to  the  naked  eye ;  and  when  a  tele- 
scope is  employed,  their  number  appears  to  increase  without  any  other 
limit  then  the  imperfection  of  the  instrument.  Dr.  Herschel  has  observed 
in  the  milky  way  above  ten  thousand  stars  in  the  space  of  a  square  degree. 
Lucretius  and  Dr.  Halley  t  have  argued  that  their  number  must  be  abso- 
lutely infinite,  in  order  that  all  of  them  may  remain  at  rest  by  the  oppo- 
sition of  attractions  acting  in  every  possible  direction ;  but  we  are  by  no 
means  certain  that  they  do  remain  in  perfect  equilibrium. 

Of  the  actual  magnitude  of  the  stars  we  can  give  no  exact  account ;  but 
they  are  divided  into  seven  or  more  orders,  according  to  the  degrees  of  their 
apparent  brightness.  There  is,  however,  reason  to  suppose,  from  the  quan- 
tity of  light  emitted  by  the  brightest  stars,  that  some  of  them  are  much 
larger  than  the  sun.  Those  stars  which  are  below  the  sixth  magnitude  are 
scarcely  visible  without  the  help  of  telescopes.  The  distances  of  all  the  stars 
from  us  and  from  one  another  are  so  great,  as  not  to  be  capable  of  being 
immediately  compared  with  their  diameters ;  for  no  star  subtends  an  angle 
large  enough  to  be  ascertained  by  direct  observation.  The  more  perfect  the 
instruments  that  we  employ,  the  smaller  are  the  apparent  diameters  of  the 
fixed  stars.  Dr.  Herschel  found  that  one  of  the  stars  of  the  first  magnitude, 
when  viewed  in  his  best  telescopes,  appeared  to  be  about  one  third  of  a 

*  See  Garcia,  Hist,  et  Mem.  1743,  H.  28  ;  and  Michell,  Ph.  Tr.  1767,  p.  234. 
f  Ph.  Tr.  1720,  xxxi.  22. 


390  LECTURE  XLI. 

second  in  diameter.  But  there  is  always  a  limit  to  the  perfection  of  the 
focus  of  the  telescope  and  of  the  eye,  and,  however  accurate  both  may  be, 
the  image  of  every  radiant  point  will  occupy  on  the  retina  a  space  of  a 
certain  magnitude,  not  depending  on  that  of  the  object :  so  that  it  will  per- 
haps be  for  ever  impossible  to  measure  any  angle,  which  is  only  a  very 
small  fraction  of  a  second.  (Plate  XXXI.  Fig.  453,  454.) 

There  is,  however,  reason  to  suppose,  that  the  angle  subtended  by  the 
nearest  stars  is  in  reality  more  than  a  hundred  times  less  than  the  angle 
measured  by  Dr.  Herschel,  for  it  may  be  conjectured  that  our  distance 
from  the  nearest  stars  is  about  a  hundred  million  million  miles  ;  taking 
about  one  third  of  a  second  for  the  annual  parallax  of  the  earth,  that  is, 
for  the  change  of  the  apparent  places  of  some  of  the  fixed  stars  in  conse- 
quence of  the  earth's  annual  motion.*  This  seems  to  be  nearly  the' utmost 
amount  of  an  annual  parallax  that  could  wholly  have  escaped  observation ; 
for  Dr.  Herschelf  supposes  that,  by  means  of  double  stars,  a  parallax  of 
one  tenth  of  a  second  only  might  become  sensible,  and  even  this  has  never 
yet  been  discovered  ;  on  the  other  hand,  if  the  parallax  were  really  much 
smaller  than  this,  it  would  be  necessary  to  suppose  the  actual  magnitude  or 
splendour  of  the  brightest  stars  to  be  incomparably  greater  than  that  of  the 
sun  ;  for  at  the  distance  of  a  hundred  million  million  miles,  our  sun  would 
appear,  according  to  Lambert's  calculations,  but  about  one  fourth  as  bright 
as  Saturn,  or  like  a  star  of  the  second  or  third  magnitude  only.  Perhaps, 
indeed,  the  stars  may  differ  as  much  from  each  other  in  magnitude  as  the 
planetary  bodies,  but  it  is  somewhat  more  natural  to  imagine  them  more 
nearly  equal,  until  we  have  some  reason  for  supposing  any  material  inequal- 
ity in  their  dimensions.  At  any  rate  there  is  little  doubt,  that  the  diversity 
of  their  apparent  magnitudes  is  principally  owing  to  their  different  dis- 
tances ;  perhaps  none  of  them  are  much  nearer  to  each  other  than  the 
nearest  to  us  ;  and  there  may  still  be  a  very  great  variety  in  their  actual 
dimensions.  There  can  be  only  twelve  points  on  the  surface  of  a  sphere  as 
far  from  each  other  as  from  the  centre  J  ;  in  a  sphere  of  twice  the  radius, 
there  may  be  about  50  points  at  the  same  distance  ;  in  a  sphere  of  three 
times  the  radius,  more  than  100 :  and  it  has  been  observed  that  these 
numbers  do  not  greatly  differ  from  the  actual  numbers  of  the  stars  of  the 

*  The  accuracy  of  modern  instruments  establishes  the  existence  of  a  sensible  paral- 
lax to  one  star  at  the  least.  By  means  of  an  excellent  heliometer,  Bessel  has  obtained 
a  series  of  distances  of  the  two  stars  which  constitute  the  double  star  61  Cygni, 
from  which  he  concludes  that  this  star  has  a  sensible  parallax  of  about  one-third  of  a 
second.  Other  astronomers  have  attacked  the  subject  with  vigour,  and  amongst  the 
rest,  Mr.  Henderson  has  made  out  a  highly  probable  parallax  to  a  Centauri.  A  dis- 
cussion of  this  subject  will  be  found  in  Fockens's  Commentatio  Ast.  de  annua  stel. 
paral.  Lugd.  1835 ;  and  in  Mr.  Main's  Report  on  the  present  State  of  our  Know- 
ledge of  the  Parallax  of  the  fixed  Stars,  Trans,  of  the  Astron.  Soc.  vol.  xii. 

See  also  Clairaut,  Hist,  et  Mem.  1739,  p.  358.  Schubert,  Bode's  Jahrbuch,  1796. 
Piazzi,  Mem.  della  Soc.  Ital.  1805,  xii.  1809.  Calendrelli,  Opusc.  Astr.  1806. 
Brinkley,  Ir.  Tr.  1815,  p.  25.  Ph.  Tr.  1821.  Ast.  Soc.  vol.  i.  Pond.  ibid.  1817. 
J.  Herschel,  Ph.  Tr.  1826,  p.  266  ;  1827.  Struve,  Introd.  to  Duplicium  Mensura, 
&c.  fol.  Dorpat,  1827.  Bessel,  Astronomische  Nachrichten,  vol.  xvi.  Taylor, 
Madras  Obs.  vol.  ii.  Airy,  Ast.  Soc.  vol.  x.  Henderson,  ibid.  vol.  xi. 

t  Ph.  Tr.  1782,  Ixxii.  82. 

I  Halley,  Ph.  Tr.  1720,  p.  22.     Kastner,  Dissert.  Math. 


ON  THE  FIXED  STARS.  391 

first,  second,  and  third  magnitudes  ;  although  it  is  true  that  they  are  not 
by,  any  means  placed  at  equal  angular  distances  from  each  other.  But 
from  a  comparison  of  the  light  of  different  stars,  we  may  infer,  that  if  their 
real  magnitudes  are  nearly  equal,  their  distances  must  increase  much 
faster  than  in  this  arithmetical  progression  ;  that  is,  that  the  stars  of  the 
second  magnitude  are  more  than  twice  as  remote  as  those  of  the  first,  and 
those  of  the  third  more  than  three  times  as  remote.  Mr.  Michell  found 
the  light  of  Sirius  between  400  and  1000  times  as  great  as  that  of  a  star  of 
the  sixth  magnitude  ;*  consequently,  supposing  these  stars  actually  equal, 
their  distances  must  differ  in  the  ratio  of  1  to  20  or  30 ;  since  light  always 
diminishes  in  proportion  to  the  square  of  the  distance  of  the  luminous  ob- 
ject. The  light  of  stars  of  different  magnitudes,  situated  near  each  other, 
may  ^Blf  compared  by  viewing  them  through  two  apertures  of  different 
sizes,  cut  in  cards,  one  held  before  each  eye,  the  apertures  being  reduced  to 
such  magnitudes,  that  the  stars  may  appear  equally  bright ;  and  the  com- 
parison may  be  extended  to  the  light  of  the  sun,  by  finding  a  star  and  a 
planet  of  equal  brightness,  and  calculating  what  proportion  of  the  sun's 
light  must  be  reflected  by  the  planet,  upon  the  most  probable  supposition 
respecting  the  disposition  of  its  surface  to  reflect  more  or  less  of  the  light 
which  falls  on  it. 

The  stars  are  in  general  dispersed  without  any  regular  order,  but  we  may 
observe  in  many  parts  of  the  heavens  that  a  number  of  them  are  so  much 
nearer  together  than  to  the  rest,  as  to  form  a  cluster  or  nebula.  The  an- 
cients had  noticed  some  of  the  most  conspicuous  nebulae,  but  Huygens  t 
first  directed  the  attention  of  modern  astronomers  to  the  large  one  situated 
in  the  constellation  Orion.  Herschel^  has  now  given  us  catalogues  of  2500 
nebulae  :  many  of  them  can  be  resolved  by  very  high  magnifying  powers 
into  separate  stars  ;  but  others  appear  to  consist  of  a  luminous  matter, 
spread  uniformly  in  the  neighbourhood  of  the  several  stars  to  which  they 
seem  to  belong.  (Plate  XXXI.  Fig.  455... 463.) 

It  has  been  conjectured  that  all  stars  are  disposed  in  nebulae,  and  that 
those  which  appear  to  us  to  be  more  widely  separated,  are  individual  stars 
of  that  particular  nebula  in  which  we  are  placed,  and  of  which  the  mar- 
ginal parts  may  be  observed,  in  the  form  of  a  lucid  zone,  which  is  called 
the  milky  way,  being  too  distant  to  allow  the  single  stars  to  be  perceived 
by  the  naked  eye.  This  opinion  was  first  suggested  by  Professor  Kant, 
the  author  of  the  system  of  metaphysics  called  the  critical  philosophy. 
The  idea  was  adopted  by  Lambert,§  who  considers  the  largest  stars  as  con- 
stituting a  distinct  nebula  placed  among  a  multitude  of  others,  which  toge- 
ther produce  the  appearance  of  a  continued  zone ;  and  Dr.  Herschel  has 
investigated  very  particularly  the  figure  of  a  single  nebula,  which  would  be 
capable  of  being  projected  into  the  form  of  the  milky  way.||  We  must  not, 

*  An  Enquiry  into  the  probable  Parallax  of  the  fixed  Stars,  Ph.  Tr.  1767,  Ivii. 
234. 

f  Systema  Saturnium,  p.  8.     Ph.  Tr.  1716,  p.  390. 

J  Ph.  Tr.  1786,  Ixxvi.  457  ;  Ixxix.  212  ;  1802,  p.  477.  Catalogue  of  Nebulae  in 
Connaissance  de  Tems  for  1783  and  1784.  See  also  J.  Herschel,  Ph.  Tr.  1833,  &c. 

§  Photometria,  §  1139,  1140.  ||   Ph.  Tr.  1784,  Ixxiv.  437. 


392  LECTURE  XLI. 

however,  suppose  that  each  of  Dr.  HerschePs  2500  nebulae  can  be  at  all 
comparable  in  magnitude  to  this  supposed  nebula,  since  many  of  them  are 
almost  as  much  resolved  by  the  telescope  into  single  stars  as  the  milky  way 
itself ;  which  would  be  utterly  impossible,  if  the  stars  which  they  con- 
tain were  equally  numerous  with  those  of  the  nebula  to  which  the  milky 
way  belongs.  Supposing  all  the  stars  of  this  nebula  to  be  as  remote  £rom 
each  other  as  the  nearest  of  them  are  from  the  sun,  it  may  be  calculated 
that  the  most  distant  are  about  500  times  as  far  from  us  as  the  nearest,  and 
that  light,  which  is  probably  15  or  20  years  in  travelling  to  us  from  Sirius, 
would  be  nearly  twenty  thousand  in  passing  through  the  whole  diameter  of 
the  milky  way.  A  nebula  of  the  same  size  as  this,  appearing  like  a  diffused 
light  of  a  degree  in  diameter,  must  be  at  such  a  distance,  that  its  light  would 
require  a  million  years  to  reach  us.  (Plate  XXXI.  Fig.  464.) 

The  stars  are  not,  properly  speaking,  absolutely  fixed  with  respect  to 
each  other,  for  several  of  them  have  particular  motions,  which  have  been 
discovered  by  a  comparison  of  accurate  observations,  made  at  very  distant 
times.  Arcturus,  for  instance,  has  a  progressive  motion,  amounting  to 
more  than  two  seconds  annually.  *  Dr.  Maskelyne  found,  that  out  of  36 
stars,  of  which  he  ascertained  the  places  with  great  precision,  35  had  a 
proper  motion.  Mr.  Michellt  and  Dr.  Herschel  :£  have  conjectured,  that 
some  of  the  stars  revolve  round  others  which  are  apparently  situated  very 
near  them  ;  and  perhaps  even  all  the  stars  may  in  reality  change  their 
places  more  or  less,  although  their  relative  situations,  and  the  directions  of 
their  paths  may  often  render  their  motions  imperceptible  to  us. 

Respecting  all  these  arrangements  of  stars  into  different  systems,  Dr. 
Herschel  §  has  lately  entered  into  a  very  extensive  field  of  observation  and 
speculation,  and  has  divided  them  into  a  number  of  classes,  to  each  of 
which  he  has  assigned  a  distinct  character.  Some  he  supposes,  like  our 
sun,  to  be  insulated  stars,  beyond  the  reach  of  any  sensible  action  of  the 
gravitation  of  others ;  and  around  these  alone  he  conceives  that  planets 
and  comets  revolve.  Double  stars,  in  general,  he  imagines  to  be  much 
nearer  to  each  other,  so  as  to  be  materially  affected  by  their  mutual  gravi- 
tation, and  only  to  preserve  their  distance  by  means  of  the  centrifugal 
force  derived  from  a  revolution  round  their  common  centre  of  inertia  ;  an 
opinion  which,  he  thinks,  is  strongly  supported  by  his  own  observations  of 
some  changes  in  the  positions  of  double  stars.  Others  again  he  supposes 
to  be  united  in  triple,  quadruple,  and  still  more  compound  systems.  A 
fourth  class  consists  of  nebulae  like  the  milky  way,  the  clusters  of  stars 
being  rounded,  and  appearing  brightest  in  the  middle.  Groups  of  stars 
Dr.  Herschel  distinguishes  from  these  by  a  want  of  apparent  condensation 

*  Halley,  Ph.  Tr.  No.  355.  Cassini,  Mem.  de  1'Acad.  1738,  p.  231.  Monnier, 
ibid.  1767,  p.  417,  proves  that  the  latitude  of  Arc.  varies  at  the  rate  of  two  seconds 
annually;  and  that  the  longitude  decreases  at  the  rate  of  60  seconds  in  100  years. 
See  also  Mem.  de  1'Acad.  1769,  p.  21.  La  Caille,  Fundamenta  Astron.  pp.169, 
187.  Hornsby,  Ph.  Tr.  1773,  Ixiii.  93,  is  of  opinion  that  his  deductions  prove  that 
the  obliquity  of  the  ecliptic  has  become  less. 

t  Ph.  Tr.  1767,  Ivii.  234  ;  1784,  p.  35. 

I  Ibid.  1783,  Ixxiii.  247. 

§  On  the  Construction  of  the  Heavens,  Ph.  Tr.  1785,  Lxxv.  213. 


ON  THE  FIXED  STARS.  393 

about  a  centre  of  attraction  ;  and  clusters  by  a  still  greater  central  com- 
pression. A  seventh  class  includes  such  nebulae  as  have  not  yet  been 
resolved  into  stars,  some  of  which  Dr.  Herschel  supposes  to  be  so  remote, 
that  the  light  emitted  by  them  must  actually  have  been  two  millions  of 
years  in  travelling  to  our  system.  The  nebulae  of  another  description 
resemble  stars  surrounded  by  a  bur,  or  a  faint  disc  of  light ;  a  diffused 
milky  nebulosity,  apparently  produced  by  some  cause  distinct  from  the 
immediate  light  of  any  stars,  is  the  next  in  order  :  and  Dr.  Herschel  has 
distinguished  other  more  contracted  nebulous  appearances,  in  different 
states  of  condensation,  into  the  classes  of  nebulous  stars  and  planetary 
neDulae,  with  and  without  bright  central  points.  Many  of  these  distinc- 
tions are  perhaps  too  refined  to  be  verified  by  common  observers  ;  but  the 
discovery  of  the  existence  of  double  and  triple  stars,  revolving  round  a 
common  centre,  will,  if  it  be  confirmed,  add  one  more  to  the  catalogue  of 
Dr.  Herschel's  important  improvements.* 

It  is,  however,  fully  ascertained,  that  some  of  the  stars  have  periodical 
changes  of  brightness,  which  are  supposed  to  arise  either  from  the  tem- 
porary interposition  of  opaque  bodies  revolving  round  them,  or  still  more 
probably,  from  a  rotatory  motion  of  their  own,  which  brings  at  certain 
periodical  times  a  less  luminous  part  of  the  surface  into  our  view.  Thus, 
the  star  Algol,  which  is  usually  of  the  second  magnitude,  becomes,  at 
intervals  of  2  days  and  21  hours  each,  of  the  fourth  only,  and  occupies  7 
hours  in  the  gradual  diminution  and  recovery  of  its  light,  f  A  less  pro- 
bable conjecture  respecting  this  change  of  brightness  was  advanced  by 
Maupertuis,^  who  imagined  that  the  disc  of  the  star  might  be  greatly 
flattened  by  a  rapid  rotation,  and  its  edge  occasionally  presented  to  us,  in 
consequence  of  the  disturbances  produced  by  the  attraction  of  planets  re- 
volving round  the  luminary.  Other  irregular  variations  may  possibly  be 
occasioned  by  the  appearance  and  disappearance  of  spots,  occurring,  like 
the  spots  of  the  sun,  without  any  determinate  order  or  assignable  cause ; 
and  many  stars  have  in  the  course  of  ages  wholly  disappeared,  and  some- 
times have  been  again  recovered  ;  others  have  made  their  appearance  for  a 
short  time,  where  no  star  had  before  been  seen.  Such  a  temporary  star  was 
observed  by  Hipparchus,  120  years  before  our  era,  and  the  circumstance 
suggested  to  him  the  propriety  of  making  an  accurate  catalogue  of  all  the 
stars,  with  their  respective  situations,  which  is  still  extant,  having  been 
preserved  by  Ptolemy,  who  added  4  stars  to  the  1022  that  it  contained.  In 
1572,  Cornelius  Gemma  discovered  a  new  star  in  Cassiopeia, §  which  was 
so  bright  as  to  be  seen  in  the  day  time,  and  gradually  disappeared  in  six- 
teen months.  Kepler,  in  1604,  observed  a  new  star  in  Serpentarius,  more 

*  Catalogue  of  Double  Stars,  Ph.  Tr.  1782,  p.  112  ;  1785,  p.  40;  1811,  1814, 
1817.  On  their  changes,  ibid.  1803,  p.  339  ;  1804,  p.  353.  Also  Mem.  of 
the  Astronomical  Society,  1822.  Bessel,  Konigsberg  Obs.  Pat.  10.  Astronomische 
Nachrichten,  No.  88.  Struve,  Catalogus  Novus  Stellarum  Duplicium,  &c.  fol. 
Dorpat,  1827.  J.  Herschel,  Ph.  Tr.  1824,  1830.  Ast.  Soc.  1821,  &c.  &c.  South, 
Ph.  Tr.  1824-6. 

t  Goodricke,  Ph.  Tr.  1783,  Ixxiii.  474,  and  Ixxiv.  287.  See  also  Ixxvi.  48;  and 
,Lalande,  Hist,  et  Mem.  1788,  p.  240. 

J  Ph.  Tr.  1732,  p.  240. 

§  See  Ph.  Tr.  1715,  xxix.  354. 


394  LECTURE  XLI. 

brilliant  than  any  other  star  or  planet,  and  changing  perpetually  into  all 
the  colours  of  the  rainbow,  except  when  it  was  near  the  horizon ;  it  re- 
mained visible  for  about  a  year.  Many  other  new  stars  have  also  been 
observed  at  different  times.* 

For  describing  the  particular  fixed  stars  according  to  their  relative  situ- 
ations, it  is  necessary  to  consider  them  as  they  are  visible  to  the  inhabitants 
of  the  earth.  They  have  been  divided,  for  the  sake  of  convenience,  into 
parcels,  making  up  imaginary  forms,  denominated  constellations.  This 
division  is  of  very  remote  antiquity,  and  though  it  may  be  useless,  and  some- 
times even  inconvenient,  for  the  purposes  of  minute  observation,  yet(  for 
a  general  recollection  of  the  great  features  of  the  heavens,  these  arbitrary 
names  and  associations  cannot  but  greatly  assist  the  memory.  It  is  also 
usual  to  describe  particular  stars  by  their  situation  with  respec^'to  the 
imaginary  figure  to  which  they  belong,  or,  more  commonly,  at  present,  by 
the  letters  of  the  Greek  alphabet,  which  were  first  applied  by  Bayert  in 
1603,  and  in  addition  to  these,  by  the  Roman  letters,  and  by  the  numbers 
of  particular  catalogues. 

There  are  two  principal  modes  of  representing  the  stars  ;  the  one  by 
delineating  them  on  a  globe,  where  each  star  occupies  the  spot  in  which 
it  would  appear  to  an  eye  placed  in  the  centre  of  the  globe,  and  where  the 
situations  are  consequently  reversed,  when  we  look  on  them  from  without, 
in  the  same  manner  as  a  word  appears  reversed  when  seen  from  the  back 
of  the  paper  ;  the  other  mode  is  by  charts,  which  are  generally  so  arranged 
as  to  represent  the  stars  in  positions  similar  to  their  natural  ones,  or  as 
they  would  appear  on  the  internal  concave  surface  of  the  globe.  Some- 
times also  the  stars  have  been  delineated  as  they  would  be  projected  on 
imaginary  surfaces,  without  any  reference  to  a  globe  ;  for  instance,  on  the 
surfaces  of  transparent  cones  or  cylinders.  The  art  of  constructing  all 
such  projections  belongs  to  the  subject  of  perspective. 

In  describing  the  particular  stars,  it  will  be  most  convenient  to  begin 
with  such  as  never  set  in  our  climates,  and  we  may  then  refer  the  situa- 
tions of  others  to  their  positions  with  respect  to  these. 

The  great  bear  is  the  most  conspicuous  of  the  constellations  which  never 
set ;  it  consists  of  seven  stars,  placed  like  the  four  wheels  of  a  waggon,  and 
its  three  horses,  except  that  the  horses  are  fixed  to  one  of  the  wheels.  The 
two  hind  wheels  are  the  pointers,  which  direct  us  to  the  pole  star,  in  the 
extremity  of  the  tail  of  the  little  bear  ;  and  further  on,  to  the  constellation 
Cassiopeia,  which  is  situated  in  the  milky  way,  where  it  is  nearest  to  the 
pole,  and  which  consists  of  several  stars,  nearly  in  the  form  of  the  letter 
W.  The  two  northernmost  wheels  of  the  great  bear,  or  wain,  point  at  the 
bright  star  Capella,  the  goat,  in  Auriga.  Descending  along  the  milky 
way  from  Cassiopeia,  if  we  go  towards  Capella,  we  come  to  Algenib,  in 
Perseus ;  and  a  little  further  from  the  pole  we  find  Algol,  or  Medusa's 
head  ;  but  if  we  take  the  opposite  direction,  we  arrive  at  Cygnus,  the 
swan  ;  and  beyond  it,  a  little  out  of  the  milky  way,  is  the  bright  star 

*  See  Ph.  Tr.  1715,  p.  354  ;  1780,  p.  338 ;  1786,  p.  189 ;  1792,  p.  24  ;  1795,, 
p.  166;  1796,  p.  452. 

f  Baieri  Uranometria,  Augsb.  1603. 


ON  THE  FIXED  STARS.  395 

Lyra.  The  dragon  consists  of  a  chain  of  stars  partly  surrounding  the 
liitle  bear  ;  and  between  Cassiopeia  and  the  swan  is  the  constellation 
Cepheus. 

Near  Algenib,  and  pointing  directly  towards  it,  are  two  stars  of  Andro- 
-*«feda,  and  a  third  is  a  little  beyond  them.  A  line  drawn  through  the 
great  bear  and  Capella  passes  to  the  Pleiades,  and  then,  turning  at  a  right 
angle  towards  the  milky  way,  reaches  Aldebaran,  or  the  bull's  eye,  and  the 
shoulders  of  Orion,  who  is  known  by  his  belt,  consisting  of  three  stars, 
placed  in  the  middle  of  a  quadrangle.  Aldebaran,  the  Pleiades,  and  Algol, 
make  the  upper,  and  Menkar,  or  the  whale's  jaw,  with  Aries,  the  lower 
poiits  of  a  W.  In  Aries  we  observe  two  principal  stars,  one  of  them  with 
a  smaller  attendant. 

A  Utfe  drawn  from  the  pole,  midway  between  the  great  bear  and  Capella, 
passes  to  the  twins  and  to  Procyon  ;  and  then,  in  order  to  reach  Sirius,  it 
must  bend  across  the  milky  way.  Algol  and  the  twins  point  at  Regulus, 
the  lion's  heart,  which  is  situated  at  one  end  of  an  arch,  with  Denebola  at 
the  other  end. 

The  pole  star  and  the  middle  horse  of  the  wain  direct  us  to  Spica  Vir- 
ginis,  considerably  distant ;  the  pole  and  the  first  horse  nearly  to  Arcturus, 
in  the  waggoner,  or  Bootes.  Much  further  southwards,  and  near  the  milky 
way,  is  Antares,  in  the  scorpion,  forming,  with  Arcturus  and  Spica,  a 
triangle,  within  which  are  the  two  stars  of  Libra.  The  Northern  crown 
is  nearly  in  a  line  between  Lyra  and  Arcturus,  and  the  heads  of  Hercules 
and  Serpentarius  are  between  Lyra  and  Scorpio. 

In  the  milky  way,  below  the  part  nearest  to  Lyra,  and  on  a  line  drawn 
from  Arcturus  through  the  head  of  Hercules,  is  Aquila,  making  with  Lyra 
and  Cygnus  a  conspicuous  triangle.  The  last  of  the  three  principal  stars 
in  Andromeda  makes,  with  three  of  Pegasus,  a  square,  of  which  one  of  the 
sides  points  to  Fomalhaut,  situated  at  a  considerable  distance  in  the  south- 
ern fish,  and  in  the  neighbourhood  of  the  whale,  which  has  already  been 
mentioned. 

By  means  of  these  allineations,  all  the  principal  stars  that  are  ever 
visible  in  Britain  may  be  easily  recognized.  Of  those  which  never  rise 
above  our  horizon,  there  are  several  of  the  first  magnitude  ;  Canopus,  in 
the  ship  Argo,  and  Achernar,  in  the  river  Eridanus,  are  the  most  brilliant 
of  them  ;  the  feet  of  the  centaur,  and  the  crosier  are  the  next ;  and  ac- 
cording to  Humboldt's  observations,  perhaps  some  others  may  require  to 
be  admitted  into  the  same  class.  (Plate  XXXVI.  XXXVII.) 


LECT.  XLI.— ADDITIONAL  AUTHORITIES. 

Treatises  on  Astronomy. — Albumasar,  Introd.  ad  Ast.  4to,  Aug.  1489.  Coper- 
nici  Astr.  reformata,  4to,  Amst.  1617.  Tychonis  de  Brahe,  Ast.  Progymnasmatum, 
4to,  Prag.  1603.  De  Mundi  Phaenomenis,  1610.  Epistolse,  1610.  Lansbergius, 
4to,  Middleb.  1619.  Galilaei  Dialogus  de  Systemate  Mundi,  4to,  1635.  Kepleri 
Epitome  Ast.  Copernicanse,  Franco?.  1635.  Riccioli,  Almagestum  Novum,  2  vols. 
fol.  Bonon.  1657.  Wardi  Ast.  Geomet.  Lond.  1656.  Duhamel,  Ast.  Phys.  4to, 
.  Paris,  1660.  Mercator,  Institutionum  Ast.  Lib.  II.  Lond.  1676.  Petit,  Traite"  de 
PUnivers  Materiel,  3  vols.  12mo,  1729-30.  Simpson's  Essays,  4to,  1740.  Cassini, 
Elemens  d'Ast.  4  vols.  4to,  Paris,  1742.  Wright's  Theory  of  the  Universe,  4to, 


396  LECTURE  XLI. 

1742.  Long's  Ast.  2  vols.  4to,  Camb.  1742-64.  Lemonnier,  Institutions  Astr. 
4to,  Paris,  1746.  Lacaille's  Elements  (trans.),  Lond.  1750.  Werdler's  Instit. 
Astr.  4to,  Witt.  1754.  Hill's  Dictionary,  4to,  1754.  D'Alembert,  Sur  le  Systeme 
du  Monde,  3  vols.  4to,  Paris,  1754-6.  Stewart's  (M.)  Tracts,  Ed.  1761.  Harris's 
Ast.  Dial.  12mo,  1766.  Condorcet,  Systeme  du  Monde,  4to,  Par.  1768.  Hennert, 
Elem.  Ast.  Traj.  ad  Rhenum,  1768.  Kohl's  Einleitung,  8vo,  Greifsw.  1768.  -  Keil's 
Introd.  to  Ast.  1769.  Lambert,  Systeme  du  Monde,  Bouillon,  1770.  DicquenW  ve, 
Ast.  Paris,  1771.  Segner,  Astron.  Vorlesungen,  4to,  Halle,  1775-6.  Hellmuth, 
Sternwissenschaft,  Brunsw.  1776.  Lalande's  Astr.  3  vols.  4to,  Par.  1792.  Bode, 
Anleitung  zur  Kentniss  des  Gestirnten  Himmels,  Berl.  1792.  Biirja,  Lehrbuch  der 
Ast.  5  vols.  Berl.  1794—1806.  Vince's  Complete  System  of  Ast.  3  vols.  4to,  Camb. 
1797;  Elements,  Camb.  1816.  Ewing's  Ast.  Ed.  1797.  Riidiger,  Handbuch  der 
Rechnenden  Ast.  4  vols.  Leipz.  1802-4.  Cagnoli,  Notizie  Ast.  2  vols.  12mo,  Mod. 
1802.  Gregory's  (O.)  Ast.  Lond.  1803.  Hassenfratz,  Cours  de  Physique  Celyte, 
Paris,  1803.  Mollet,  Etude  du  Ciel,  Lyon,  1803.  Oriani,  Opusc.  Ast.  Milan, 
1806.  Monteiro,  Mem.  sur  1'Ast.  Pratique,  4to,  Paris,  1808.  Marechal  s'*-  le 
Systeme  de  I'Univers,  Paris,  1810.  Biot,  Traite  d'Ast.  Physique,  3  vols.  fc>jO-ll. 
Bohnenberger,  Ast.  Tubing.  1811.  Schon,  Grundriss  der  Gesammten  Theoretischen 
Ast.  Niirnb.  1811.  Brandes,  Die  Vornehmsten  Lehren  der  Ast.  Leipz.  1813. 
Woodhouse,^  Treatise  on  Ast.  2  vols.  Camb.  1821.  Elements,  Camb.  1812.  De- 
lambre,  Abrege  d'Ast.  Paris,  1813.  Astronomic  Theorique  et  Pratique,  3  vols.  4to, 
Paris,  1814.  Brinkley's  Astronomy,  Dublin,  1819.  Littrow,  Theoretische  und 
Practische  Astronomic,  3  vols,  Wien,  1821-7.  Ferguson's  Astronomy,  by  Brewster, 
2  vols.  Edin.  1821.  Schubert,  Traite  d' Astronomic,  3  vols.  4to,  St.  Petersb.  1822. 
Pearson's  Astronomy,  2  vols.  4to.  Lond.  1824-9.  Baily's  Tables  and  Formulae,  1827. 
Farrar's  Astronomy,  Camb.  N.  E.  1827.  Hassler's  System  of  the  Universe,  New 
York,  1828.  Jambon's  Astronomic,  1828.  Santini,  Elementi  di  Ast.  2  vols.  Pad. 
1830.  Francoeur,  Astr.  Pratique,  1830.  Malkin's  Astron.  (Lib.  of  Useful  Know- 
ledge), 1830.  Quetelet,  Astr.  Populaire,  Brux.  1832.  Marcoz,  Astr.  Solaire,  Paris, 
1832.  Veley,  Astr.  Elementaire,  Lausanne,  1833.  Herschel's  Astr.  12mo,  1833. 
Whewell's  Bridgwater  Treatise,  1833.  Bailly's  Resume,  32mo,  1835.  Moseley's 
Lectures  on  Astr.  1839.  Maddy's  Astr.  by  Hymers,  Camb.  1840.  Nichol's  Archi- 
tecture of  the  Heavens.  Solar  System. 

Collections.— Transactions  of  the  Royal,  Astronomical  and  other  Societies.  Bode's 
Astron.  Jahrbuch,  Berlin,  1788  ....  Sammlung  Astr.  Abhandlungen,  1793  .... 
Effemeridi  Astr.  di  Milano,  1774  ....  by  Cesaris  and  others  ;  Zach's  Monatliche 

Correspondenz,  Gotha,    1800 Lindenau  und  Bohnenberger,   Zeitschrift   fiir 

Astr.  Tubingen,  1816....  Connaissance  des  Temps,  Paris,  1679.  Schumacher's 
Astr.  Nachrichten,  4to,  Altona,  1823 Annuaire  de  1'Acad.  de  Bruxelles,  18mo. 

Catalogues  of  Stars,  fyc. — Alfonsus,  Tabulae  Astr.  4to,  Venice,  1492, 1503.  Kep- 
leri  Tabulae  Rudolphinae,  fol.  Ulm,  1627.  Lansbergius  Uranometria,  4to,  Mid- 
dleb.  1631  ;  Tabulae,  fol.  1632.  Riccioli,  Almagestum  Novum,  2  vols.  fol.  Bon. 

1651.    Wing's  Ephemeris,  1669 Halley,  Catal.  Stel.  Austral.  4to,  Lond.  1679 ; 

Astr.  Tables,  4to,  1752.  Lahire,  Ephemerides  ad  Ann.  1701,  4to,  1700.  Tab. 
Astr.  4to,  1727.  FlamsteediiHistoriaCselestis,  3  vols.  fol.  Lond.  1725.  Winston's 
Lect.  with  Tables,  1728.  Manfred!  Ephem.  4to,  Bon.  1739.  Lemonnier,  Histoire 
Celeste,  4to,  Paris,  1741  ;  Observations,  4  vols.  fol.  1757-73.  Dopplemaieri  Atlas 

C&elestis,  Nuremb.   1742.     Zanotta's  Ephemeris,  4to,  Bonon.  1750 Hell's 

Ephem.  Vienna,  1757.  Lacaille,  Coelum  Australe,  4to,  Paris,  1763.  Obs.  faites 
au  Cap  de  Bonne  Esperance.  Hallenstein,  Obs.  Pekini  factse,  2  vols.  4to, 
Vindob,  1768.  Ludlam's  Cambridge  Observations,  4to,  Camb.  1769.  Darguier, 
Obs.  faites  a  Toulouse,  2  vols.  4to,  Avignon,  1777.  Bugge,  Obs.  Havni,  4to, 
Havnise,  1784.  Wollaston,  Astron.  Catal.  fol.  1789.  Fasciculus  Astr.  4to,  1800. 
Herschel's  (Caroline)  Catalogue,  fol.  Lond.  1798.  Bode,  Uranographia,  fol.  1801  ; 
also  Trois  Cat.  de  1'Ascension  droite  et  de  la  Declinaison  de  17240,  5505,  et  de  5877 
Etoiles,  4to,  Berlin,  1801-5.  Histoire  Celeste,  Paris,  1801.  Piazzi's  Cat.  fol. 
Palermo,  1803-14.  Cagnoli,  Cat.  de  501  Etoiles,  4to,  Modene,  1807.  Mayer's, 
1826.  Baily's  Catalogue  of  2881  Stars,  4to,  1827.  Plana,  Obs.  a  Turin,  4to,  Turin, 
1817,  &c.  Harding,  Atlas  Cselestis,  fol.  Gott.  1822.  Caturegli,  Ephem.  4to,  Bon. 
1823.  David,  Astr.  Beobach.  Prag.  1823.  Brioschi,  Comentari  Astr.  4to,  Napoli, 

1824-6.     Robinson,   Obs.  at  Armagh,  4to,  Lond.  1829 Argelander,  Obs. 

Astr.  2  vols.  fol.  Helsingf.  1830-1.    Positiones  560  Stel.  4to.  1835.   Johnson,  Obs.  • 
at  Helena,  4to,  St.  Helen.  1832.     Cat.  of  606  Stars  of  Southern  Hemisphere,  4to, 
Lond.  1835.     Rumker,  Catal.  from  Obs.  at  Paramatta,  4to,  Hamb.  1832.    Taylor, 


ON  THE  SOLAR  SYSTEM.  397 

Obs.  at  Madras,  1832.  Bianchi,  Atti  del  Osserv.  di  Modena,  fol.  1834.  Richard- 
sdn,  Obs.  at  Paramatta,  4to,  Lond.  1835.  Cerquero,  Obs.  en  San  Fernando,  fol. 
S.  F.  1835,  Henderson,  Decl.  of  172  Fixed  Stars  observed  at  the  Cape  of  Good 
Hope,  4to,  Edin.  1835. 

•-To  these  we  must  add  the  volumes  which  are  issued  from  the  observatories  of 

'trafnwich  (Airy),  Cambridge  (Challis),  Edinburgh  (Henderson),  Dorpat  (Struve), 

Oxford   (Johnson),    Berlin  (Encke),    Konigsberg  (Bessel),  Altona  (Schumacher), 

Paris  (Arago),  Vienna  (Littrow),  Palermo  (Cacciatore) ;  the    Nautical  Almanac, 

&c.  &c. 


LECTURE    XLII. 


ON  THE  SOLAR  SYSTEM. 

THE  most  conspicuous  of  all  the  celestial  bodies,  which  we  have  been 
examining,  is  the  sun,  that  magnificent  luminary  which  occupies  the  centre 
of  the  system  that  comprehends  our  earth,  together  with  a  variety  of  other 
primary  and  secondary  planets,  and  a  still  greater  number  of  comets. 

The  sun  agrees  with  the  fixed  stars  in  the  property  of  emitting  light  con- 
tinually, and  in  retaining  constantly  its  relative  situation  with  very  little 
variation  ;  it  is  probable  also  that  these  bodies  have  many  other  properties 
in  common.  The  sun  is,  therefore,  considered  as  a  fixed  star  compara- 
tively near  us ;  and  the  stars  as  suns  at  immense  distances  from  us :  and 
we  infer  from  the  same  analogy,  that  the  stars  are  possessed  of  gravitation, 
and  of  the  other  general  properties  of  matter ;  they  are  supposed  to  emit 
heat  as  well  as  light ;  and  it  has  with  reason  been  conjectured  that  they 
serve  to  cherish  the  inhabitants  of  a  multitude  of  planetary  bodies  revolving 
round  them. 

The  sun,  like  many  other  stars,  has  probably  a  progressive  motion, 
which  is  supposed,*  from  a  comparison  of  the  apparent  motions  of  a  great 
number  of  the  stars,  to  be  directed  towards  the  constellation  Hercules. 
It  is  beyond  all  question  that  many  of  the  stars  have  motions  peculiar  to 
themselves,  and  it  is  not  certain  that  any  of  them  are  without  such  motions : 
it  is,  therefore,  in  itself  highly  probable  that  the  sun  may  have  such  a 
motion.  But  Dr.  Herschelt  has  confirmed  this  conjecture  by  arguments 
almost  demonstrative.  He  observes  that  the  apparent  proper  motions  of  44 
stars  out  of  56  are  very  nearly  in  the  direction  which  would  be  the  result 
of  such  a  real  motion  of  the  solar  system :  and  that  the  bright  stars 
Arcturus  and  Sirius,  which  are  probably  the  nearest  to  us,  have,  as  they 
ought  to  have,  the  greatest  apparent  motions.  Besides,  the  star  Castor 
appears,  when  viewed  with  a  telescope,  to  consist  of  two  stars,  of  nearly 
equal  magnitude;  and  though  they  have  both  a  considerable  apparent 
motion,  they  have  never  been  found  to  change  their  distance  a  single 

*  Mayer,  De  Motu  Fixarum,  Getting.  1760.  Wilson,  Thoughts  on  general  Gra- 
vitation, and  Views  thence  arising  as  to  the  state  of  the  Universe,  1777.  Lalande, 
Mem.  del'Acad.  1776. 

f  Herschel,  Ph.  Tr.  1783,  Ixxiii.  247. 


398  LECTURE  XLII. 

second  ;  a  circumstance  which  is  easily  understood  if  both  their  apparent 
motions  are  supposed  to  arise  from  a  real  motion  of  the  sun,  but  which 
is  much  less  probable  on  the  supposition  of  two  separate  and  independent 
motions. 

Besides  this  progressive  motion,  the  sun  is  subjected  to  some  small  ch&iige 
of  place,  dependent  on  the  situations  of  the  planetary  bodies,  which  was 
long  inferred  from  theory  only,  but  which  has  been  actually  demonstrated 
by  modern  observations.  Supposing  all  the  planets  to  be  in  conjunction, 
or  nearly  in  the  same  direction  from  the  sun,  the  common  centre  of  inertia 
of  the  system  is  at  the  distance  of  about  a  diameter  of  the  sun  fron}3  his 
centre  :  and  since  the  centre  of  inertia  of  the  whole  system  must  be  undis- 
turbed by  any  reciprocal  actions  or  revolutions  of  the  bodies  comper:  Jg  it, 
the  sun  must  describe  an  irregular  orbit  round  this  centre,  his  greatest 
distance  from  it  being  equal  to  his  own  diameter.  We  may  form  an  idea 
of  the  magnitude  of  this  orbit  by  a  comparison  with  the  orbit  of  the 
moon :  a  body  revolving  round  the  sun,  in  contact  with  his  surface,  must 
be  nearly  twice  as  remote  from  his  centre  as  the  moon  is  from  the  earth, 
and  the  sun's  revolution  round  the  common  centre  of  gravity  of  the  system 
must  therefore  be,  where  it  is  most  remote,  at  four  times  the  distance  of 
the  moon  from  the  earth. 

The  sun  revolves  on  his  axis  in  25  days  10  hours,  with  respect  to  the 
fixed  stars  :  this  axis  is  directed  towards  a  point  about  half  way  between 
the  pole  star  and  Lyra,  the  plane  of  the  rotation  being  inclined  a  little 
more  than  7°  to  that  in  which  the  earth  revolves.  The  direction  of  this 
motion  is  from  west  to  east,  terms  which  we  can  only  define  from  our  pre- 
supposed knowledge  of  the  stars,  by  saying  that  the  motion  is  such,  that  a 
point  of  the  sun's  surface  at  first  opposite  Aries,  moves  towards  Taurus. 
Nor  have  we  any  better  mode  of  describing  north  and  south,  or  right  and 
left :  we  can  only  say  comparatively,  that  if  we  are  placed  with  our  heads 
northwards,  and  looking  towards  the  centre,  our  right  hands  will  be  east- 
wards, and  our  left  westwards.  All  the  rotations  of  the  different  bodies 
which  compose  the  solar  system,  as  far  as  they  have  been  ascertained,  are 
in  the  same  direction,  and  all  their  revolutions,  excepting  those  of  some  of 
the  comets,  of  which  the  motions  are  retrograde,  and  those  of  some  of  the 
satellites  of  the  Georgian  planet,  which  revolve  in  planes  so  distant  from 
those  of  the  other  planetary  motions,  that  the  directions  of  their  revolutions 
can  scarcely  be  called  either  direct  or  retrograde. 

The  time  and  direction  of  the  sun's  rotation  is  ascertained  by  the  change 
of  the  situation  of  the  spots,*  which  are  usually  visible  on  his  disc,  and 
which  some  astronomers  suppose  to  be  elevations,  but  others,  apparently 
on  better  foundations,  to  be  excavations  or  deficiencies  in  the  luminous 
matter  covering  the  sun's  surface.  These  spots  are  frequently  observed  to 
appear  and  disappear,  and  they  are  in  the  mean  time  liable  to  great  varia- 
tions, but  they  are  generally  found  about  the  same  points  of  the  sun's 
surface.  Lalande  t  imagines  that  they  are  parts  of  the  solid  body  of  the 

*  Discovered  by  Fabricius.  See  his  treatise  De  Maculis  in  Sole  observatis,  Wit- 
tenb.  1611. 

f  Hist,  et  Mem.  1776.     Brugnatelli,  Bibliot.  Fisic.  i.  55. 


ON  THE  SOLAR  SYSTEM.  399 

sun,  which,  by  some  agitations  of  the  luminous  ocean,  with  which  he 
conceives  the  sun  to  be  surrounded,  are  left  nearly  or  entirely  bare.  Dr. 
Wilson*  and  Dr.  Herschel  are  disposed  to  consider  this  ocean  as  consisting 
jjiher  of  a  flame  than  of  a  liquid  substance,  and  Dr.  Herschel  attributes 
''iybr-Fspots  to  the  emission  of  an  aeriform  fluid,  not  yet  in  combustion,  which 
displaces  the  general  luminous  atmosphere,  and  which  is  afterwards  to 
serve  as  fuel  for  supporting  the  process ;  hence  he  supposes  the  appear- 
ance of  copious  spots  to  be  indicative  of  the  approach  of  warm  seasons 
on  the  surface  of  the  earth,  and  he  has  attempted  to  maintain  this  opinion 
by  (historical  evidence.  The  exterior  luminous  atmosphere  has  an  appear- 
aacfc  somewhat  mottled  ;  some  parts  of  it,  appearing  brighter  than  others, 
hav;r  ^nerally  ^een  called  faculae ;  but  Dr.  Herschel  distinguishes  them 
by  the  names  of  ridges  and  nodules.  The  spots  are  usually  surrounded 
by  margins  less  dark  than  themselves,  which  Dr.  Herschel  calls  shallows, 
and  which  he  considers  as  parts  of  an  inferior  stratum  consisting  of 
opaque  clouds,  capable  of  protecting  the  immediate  surface  of  the  sun 
from  the  excessive  heat  produced  by  combustion  in  the  superior  stratum, 
and  perhaps  of  rendering  it  habitable  to  animated  beings.  (Plate  XXXI. 
Fig.  465. ..469.) 

But  if  we  inquire  into  the  intensity  of  the  heat  which  must  necessarily 
exist  wherever  this  combustion  is  performed,  we  shall  soon  be  convinced 
that  no  clouds,  however  dense,  could  impede  its  rapid  transmission  to  the 
parts  below.  Besides,  the  diameter  of  the  sun  is  111  times  as  great  as  that 
of  the  earth  ;  and  at  its  surface,  a  heavy  body  would  fall  through  no  less 
than  450  feet  in  a  single  second  ;  so  that  if  every  other  circumstance  per- 
mitted human  beings  to  reside  on  it,  their  own  weight  would  present  an 
insuperable  difficulty,  since  it  would  become  nearly  thirty  times  as  great  as 
upon  the  surface  of  the  earth,  and  a  man  of  moderate  size  would  weigh 
above  two  tons.  Some  of  the  most  celebrated  astronomers  have  imagined, 
from  the  comparative  light  of  different  parts  of  the  sun's  disc,  or  apparent 
surface,  that  he  is  surrounded  by  a  considerably  dense  and  extensive  atmo- 
sphere, imperfectly  transparent ;  conceiving  that,  without  such  an  atmo- 
sphere, the  marginal  parts,  which  are  seen  most  obliquely,  must  appear 
considerably  the  brightest ;  but  this  opinion  is  wholly  erroneous,  and  the 
inferences  which  have  been  drawn  from  it,  respecting  the  sun's  atmosphere, 
are  consequently  without  foundation. 

We  are,  however,  assured,  by  direct  observation,  of  the  existence  of  some 
aerial  substance  in  the  neighbourhood  of  the  sun,  producing  the  appearance 
called  the  zodiacal  light,  which  is  sometimes  seen,  nearly  in  the  plane 
of  the  sun's  rotation  on  its  axis,  extending  beyond  the  orbit  of  Mercury. 
It  is  said  to  have  been  first  distinctly  described  in  Childrey's  Britannia 
Baconica,  a  work  published  in  1661 ;  and  it  was  afterwards  more  par- 
ticularly observed  by  Cassini,t  Mairan,*  and  others.  In  the  torrid  zone  it 

*  Ph.  Tr.  1774,  p.  1 ;  1783,  p.  144.  See  also  ibid.  vi.  2216,  2295,  and  3020 
Cassini,  Mem.  de  1'Acad.  x.  581.  Herschel,  Ph.  Tr.  1795,  p.  46  ;  1801,  pp.  265, 
354.  Mossotti,  Cesaris  Effemeridi,  1820-1.  Nicollet,  Connoissance  des  Temps 

t  Hist,  et  Mem.  vii.  119 ;  viii.  193. 

£  Mairan,  Traite  de  1' Aurore  Boreale,  Suite  des  Mem.  de  1'Acad.  Par.  1731  and 
1751,  4to,  Paris,  1733. 


400  LECTURE  XLII. 

is  almost  constantly  visible ;  and  in  these  climates  it  may  often  be  distin- 
guished in  the  beginning  of  March,  after  the  termination  of  twilight, 
exhibiting  the  appearance  of  a  narrow  triangle,  somewhat  rounded  off,  of  a 
whiteness  resembling  the  milky  way,  ascending  from  the  sun  as  a  base,  like 
the  projection  or  section  of  a  very  flat  spheroid,  and  extending  to  a  disWi^e 
of  more  than  50°  from  the  sun.  The  whole  orbit  of  Venus  never  subtends 
so  great  an  angle  from  the  earth  as  96°,  consequently  this  substance  must 
occasionally  involve  both  Mercury  and  Venus  ;  and  if  it  were  not  extremely 
rare,  it  would  produce  some  disturbance  in  their  motions  ;  while  in  fact  it 
does  not  appear  to  impede  the  progress  even  of  the  tails  of  the  comets,  which 
are  probably  themselves  of  very  inconsiderable  density.  It  cannot  ££•„  a 
continuous  fluid  atmosphere,  revolving  with  the  same  velocity  as  the;ran  ; 
for  the  gravitation  of  such  an  atmosphere  would  cause  it  to  assume  a  form 
more  nearly  spherical ;  and  the  only  probable  manner  in  which  it  can  be 
supposed  to  retain  its  figure,  is  by  means  of  a  revolution  much  more  rapid 
than  the  sun's  rotation.  Some  persons  have  attributed  the  appearance  to 
the  refraction  of  the  earth's  atmosphere  only  ;  but  if  it  arose  from  any  such 
cause  as  this,  its  direction  could  scarcely  be  oblique  with  respect  to  the 
horizon,  and  it  is  highly  improbable  that  it  should  always  happen  to  coin- 
cide with  the  plane  of  the  sun's  rotation.  (Plate  XXXI.  Fig.  470.) 

The  sun  is  accompanied  in  his  progressive  motion  among  the  fixed  stars 
by  ten  [eleven]  planetary  bodies,  of  different  magnitudes,  revolving  round 
him,  from  west  to  east,  in  orbits  approaching  to  circles,  and  visible  to  us  by 
means  of  the  light  which  they  receive  from  him.  These  are  Mercury,  Venus, 
the  Earth,  Mars,  Juno,  Pallas,  Ceres  [Vesta],  Jupiter,  Saturn,  and  the 
Georgian  planet.  It  is  unnecessary  to  adduce  at  present  any  arguments  to 
prove  the  actual  existence  or  direction  of  any  of  these  motions  ;  their  com- 
plete agreement  with  the  visible  phenomena  of  the  heavens,  and  with  the 
laws  of  gravitation,  will  hereafter  appear  to  afford  sufficient  evidence  of  the 
accuracy  of  the  received  theory  of  the  arrangement  of  the  solar  system.  The 
motion  of  the  earth  is  the  most  unanswerably  proved  by  the  apparent  aber- 
ration of  the  fixed  stars,  derived  from  the  different  directions  of  this  motion 
at  different  times,  and  corresponding  precisely  with  the  known  velocity  of 
light,  deduced  from  observations  of  a  very  different  kind.  That  the  planets 
receive  their  light  from  the  sun,  is  undeniably  shown  by  the  appearance  of 
the  discs  of  many  of  them,  when  viewed  through  a  telescope,  those  parts  of 
their  surfaces  only  being  luminous,  on  which  the  sun  shines  at  the  time  of 
observation. 

These  planets  are  neither  all  in  one  plane,  nor  does  any  one  of  them 
remain  precisely  in  the  same  plane  at  all  times  ;  but  their  deviations  from 
their  respective  planes  are  inconsiderable,  and  they  are  commonly  repre- 
sented by  supposing  each  planet  to  revolve  in  a  plane  passing  through  the 
sun,  and  the  situation  of  this  plane  to  be  liable  to  slight  variations.  There 
is,  however,  a  certain  imaginary  plane,  determinable  from  the  situations, 
the  velocities,  and  the  masses  of  the  planets,  which,  like  the  centre  of  inertia, 
never  changes  its  position  on  account  of  any  mutual  actions  of  the  bodies  of 
the  system,  and  this  plane  of  inertia  is  called  the  fixed  ecliptic.  Its 
situation  is  nearly  half  way  between  the  orbits  of  Jupiter  and  of  Saturn  ; 


ON  THE  SOLAR  SYSTEM.  401 

'    and  it  is  inclined  in  a  small  angle  only  to  the  plane  of  the  earth's  orbit, 
which  is  called  the  earth's  ecliptic,  or  simply  the  ecliptic. 

The  ecliptic  passes  through  the  constellations  denominated  the  signs  of 

the  zodiac,  between  Aries,  the  Pleiades,  the  twins,  and  Regulus,  to  the  north, 

yuft^Aldebaran,  Spica,  and  Antares,  to  the  south.     Its  position  has  varied 

^   Mowly  in  the  course  of  many  ages,  so  that  its  northmost  point  is  now  more 

^  than  one  third  of  a  degree  more  remote  from  the  pole  star  than  it  was  in 

the  time  of  Eratosthenes,  who  observed  its  place  230  years  before  the  birth 

ot  Christ.     It  appears  from  Lagrange's  calculations,  that  the  limit  of  its 

greatest  possible  variation  is  about  10  or  11  degrees.     The  ecliptic  is  sup- 

po&ji  to  be  divided  into  twelve  angular  parts,  or  signs,  each  containing 

thh JW  degrees  :  they  are  named  Aries,  Taurus,  Gemini,  Cancer,  Leo,  Virgo, 

Libra,  Scorpio,  Sagittarius,  Capricornus,  Aquarius,   Pisces.     Those  who 

prefer  the  cadence  of  a  Latin  distich,  in  order  to  assist  the  memory,  may 

repeat  them  thus, — 

Sunt  Aries,  Taurus,  Gemini,  Cancer,  Leo,  Virgo, 
Libraque,  Scorpius,  Arcitenens,  Caper,  Amphora,  Pisces. 

The  planes  of  the  orbits  of  the  other  primary  planets,  excepting  the  three 
[four]  minute  planets  lately  discovered,  intersect  the  ecliptic  in  small 
angles,  and  the  lines  of  intersection  are  called  lines  of  the  nodes.  The  nodes 
of  all  the  planets  move  very  slowly,  but  not  quite  uniformly,  from  east  to 
west,  that  is,  with  respect  to  the  fixed  stars.  At  present  the  inclinations  of 
all  the  orbits  appear  to  be  somewhat  diminishing :  that  of  the  orbit  of 
Jupiter  is  less  by  6  minutes  than  it  was  in  the  time  of  Ptolemy. 

The  orbit  of  each  planet  is  very  nearly  an  ellipsis,  one  of  the  foci  of  which 
coincides  with  the  sun,  or  rather  with  the  common  centre  of  inertia  of  the 
sun  and  planet.  The  extremities  of  the  greater  axis,  where  the  orbit  is 
furthest  from  the  sun  and  nearest  to  it,  are  called  the  upper  and  the  lower 
apsis,  or  the  aphelion  and  perihelion ;  the  mean  distance  being  at  either 
end  of  the  lesser  axis  ;  and  the  distance  of  the  centre  of  the  ellipsis  from  the 
sun  is  called  the  eccentricity.  The  slight  deviations  of  the  planets  from 
these  elliptic  paths  are  expressed  by  considering  the  apsides  as  moveable, 
and  this  motion  is  direct,  that  is,  from  west  towards  east,  in  the  case  of 
all  the  planets  except  Venus,  of  which  the  aphelion  has  a  retrograde  motion, 
with  respect  to  the  fixed  stars. 

The  elliptic  motion  of  the  planets  was  first  discovered  by  Kepler ;  and 
he  found  that  a  right  line,  joining  the  sun  and  any  planet,  describes  always 
equal  areas  in  equal  times.  The  observations,  on  which  Kepler*  founded 
these  important  laws,  were  made  principally  on  the  planet  Mars.  He 
determined  by  calculation,  upon  the  supposition  which  was  then  generally 
adopted,  of  a  motion  in  an  eccentric  circle,  what  must  be  nearly  the  situ- 
ation of  the  planet,  with  respect  to  the  sun,  that  is,  its  heliocentric  place,  and 
observing  its  geocentric  place,  with  respect  to  the  earth,  he  was  thus  able  to 
construct  a  triangle  representing  the  situation  of  the  three  bodies  ;  repeating 
this  operation  in  various  parts  of  the  orbit,  he  discovered  its  form  ;  and 
Raving  done  this,  the  velocity  of  the  motion  in  different  parts  of  the  orbit 

*  See  Lect.  IV.  and  Kepler,  Astronomia  Nova,  fol.  Pragse.  1609. 

2D 


402  LECTURE   XLII. 

was  easily  determined  from  the  apparent  change  of  place  in  a  given  time. 
(Plate  XXXII.  Fig.  471.) 

The  same  astronomer  also  ascertained,  that  the  squares  of  the  times  of 
revolution  of  the  different  planets  are  in  proportion  to  the  cuhes  of  thejr 
mean  distances  from  the  sun.  For  example,  if  one  planet  were  four  ti^iev 
as  distant  as  another,  it  would  revolve  in  a  period  eight  times  as  long, 
since  the  cube  of  4  is  equal  to  the  square  of  8 ;  thus  Mars  is  nearly 
four  times  as  remote  from  the  sun  as  Mercury,  and  the  Georgian  planet, 
four  times  as  remote  as  Jupiter,  and  their  periods  are  nearly  eight  times  a"s 
long  respectively.  i 

It  is  probable  that  all  the  planets  have  a  rotatory  motion  from  w 
east,  either  perfectly  or  very  nearly  equable.*  This  motion  has 
observed  in  Venus,  the  Earth,  Mars,  Jupiter,  and  Saturn  :  and  from  some 
phenomena  of  the  satellites  of  the  Georgian  planet,  Mr.  Laplace  thinks  that 
it  may  also  be  assumed  as  nearly  certain  that  this  planet  has  also  a  rota- 
tory motion.  The  figure  of  the  planets  is  spheroidical ;  they  are  more  or 
less  flattened  at  the  poles,  as  they  revolve  more  or  less  rapidly  on  their 
axes.  These  axes  retain,  with  a  very  slight  deviation,  a  situation  always 
parallel,  in  every  part  of  the  orbits. 

But,  in  the  course  of  time,  the  gradual  change  of  the  position  of  the  axis 
produces  a  sensible  effect.  In  the  case  of  the  earth,  this  effect  is  denomi- 
nated the  precession  of  the  equinoxes.  The  equinoctial  points  are  the 
intersections  of  the  apparent  ecliptic,  or  the  path  of  the  sun  in  the  heavens, 
with  the  plane  of  the  equinoctial,  which  is  perpendicular  to  the  earth's 
axis  and  which  passes  through  the  equator  on  the  earth's  surface  ;  these 
points  of  intersection  have  a  retrograde  motion,  from  east  to  west,  on  the 
ecliptic.  This  motion  was  discovered  by  Hipparchus,  in  the  year  128 
before  Christ,  from  a  comparison  of  his  own  observations  with  those  of 
Timocharis,  made  155  years  before ;  and  since  the  time  of  Hipparchus, 
the  equinoctial  points  have  receded  about  26^°.  Hence  it  happens  that 
the  constellations  called  the  signs  of  the  zodiac,  are  now  at  a  considerable 
distance  from  those  divisions  of  the  ecliptic  which  bear  the  same  names. 

The  earth's  axis  has  also  a  small  periodical  change  of  inclination,  or  a 
nutation,  performed  in  about  19  years,  and  amounting  in  the  whole  to  18 
seconds  only.  Its  existence  was  determined  by  Newton  from  theory, 
although  he  failed  in  the  attempt  to  ascertain  its  quantity  with  accuracy  ; 
it  was  first  actually  observed  by  Dr.  Bradley,t  about  the  year  1747.  The 
absolute  direction  of  the  axis  in  the  heavens  is  also  liable  to  some  variation, 
in  the  course  of  many  ages,  but  this  change  has  not  always  been  sufficiently 
distinguished  from  the  change  of  the  position  of  the  ecliptic.  The  inclina- 
tion of  the  equator  to  the  ecliptic  is  now  very  nearly  23°  28*. 

In  order  to  retain  in  memory  a  general  idea  of  the  proportional  distances 
of  the  primary  planets  from  the  sun,  we  may  call  that  of  the  earth  10  and 
that  of  Saturn  100  ;  the  distance  of  Mercury  will  then  be  4,  to  which  we 
must  add  3  for  Venus,  making  7  ;  twice  3  or  6  for  the  earth,  making  10  ; 
twice  6  or  12  for  Mars,  making  16  ;  twice  12  or  24,  making  28,  for  the  three 

*  Herschelon  the  Rotation  of  the  Planets,  Ph.  Tr.  1781,  p.  115. 
f  Ph.  Tr.  1748,  p.  1. 


ON  THE  SOLAR  SYSTEM.  403 

[four]  small  planets,  Juno,  Pallas,  and  Ceres  [Vesta],  twice  24  or  48,  making 
5$,  for  Jupiter ;  twice  48  or  96  for  Saturn,  making  100 ;  and  twice  9G  or  192, 
making  1Q6,  for  the  Georgian  planet ;  and  these  sums  will  represent  the 
d;  £°nces,  without  any  material  exception,  in  the  nearest  integer  numbers. 

,/yTne  planet  Mercury  is  little  more  than  one  third  as  large  as  the  earth  in 
Diameter.     He  performs  his  revolution  in  somewhat  less  than  three  months, 

v  at  about  two  fifths  of  the  distance  of  the  earth.  His  orbit  is  more  eccentric, 
t>^d  more  inclined  to  the  ecliptic,  than  those  of  any  of  the  planets  except 
the  three  [four]  small  ones  lately  discovered  ;  the  eccentricity  being  one 
fift^of  the  mean  distance,  and  the  inclination  7°.  Of  his  density  and  his 
rocl&on  we  know  nothing  but  from  conjecture.* 

"Ve1'.7.s  is  very  nearly  as  large  as  the  earth;  Dr. Herschel  thinks  her 
even  a  little  larger.  Her  revolution  occupies  about  7  months,  her  distance 
from  the  sun  being  about  seven  tenths  of  that  of  the  earth,  and  her  orbit 
nearly  circular,  inclined  in  an  angle  of  3°  24'  to  the  ecliptic.  Mr.  Schroeterf 
attributes  to  her  mountains  much  higher  than  those  of  the  earth,  he  has 
observed  strong  indications  of  an  atmosphere  surrounding  her,  and  he 
assigns  for  her  rotation  on  her  axis  the  period  of  23  hours  21  minutes. 
Her  density  has  been  estimated  from  the  perturbations,  occasioned  by  her 
attraction,  in  the  motions  of  the  other  planets,  and  it  has  been  supposed 
to  be  a  little  less  than  that  of  the  earth. 

The  distance  of  the  earth  from  the  sun  is  about  95  million  English  miles  ; 
and  this  determination  is  generally  supposed  to  be  so  far  accurate,  that 
there  is  no  probability  of  an  error  of  more  than  a  million  or  two,  at  most, 
although  some  authors  are  still  disposed  to  believe  that  the  distance  may  be 
even  greater  than  a  hundred  millions.  The  period  of  its  revolution,  with 
respect  to  the  equinoctial  points,  which  are  the  usual  standard  of  compari- 
son, since  their  situation  determines  the  annual  return  of  the  seasons,  is 
365  days,  5  hours,  48  minutes,  and  48  seconds;  and  this  is  called  its 
tropical  revolution  ;  that  of  its  absolute  or  sidereal  revolution  is  365  days, 
6  hours,  9  minutes,  and  8  seconds  ;  the  difference,  which  is  20  minutes  and 
20  seconds,  being  the  time  occupied  in  passing  over  the  space,  through 
which  the  equinoctial  points  have  retreated  in  the  course  of  the  tropical 
year.  By  a  day,  we  always  understand  the  time  which  elapses  during  the 
rotation  of  the  earth  with  respect  to  the  sun  ;  a  sidereal  day  is  about  four 
minutes  shorter. 

At  a  distance  from  the  sun  exceeding  that  of  the  earth  by  one  half,  the 
planet  Mars  revolves,  in  about  a  year  and  seven  eighths.  He  is  of  half 
the  earth's  linear  dimensions  :  he  has  spots  which  change  their  form,  and, 
therefore,  probably,  an  atmosphere.  Dr.  Herschel  J  found  his  rotation  per- 
formed in  39  minutes  more  than  a  day ;  his  equator  inclined  28°  42'  to 
the  plane  of  his  orbit,  and  his  figure  so  much  flattened  at  the  poles,  that 
his  axis  is  -^th  shorter  than  his  equatorial  diameter.  From  this  form, 

*  Consult  Lalande,  Mem.  de  1'Inst.  v.  442. 

,f  Beobachtungen,  4to,  Erfurth,  1793.  Aphroditographische  Fragmenten,  4  to, 
Helm.  1796.  Journal  de  Physique,  xlviii.  459.  Beytrage,  8vo,  Berlin,  1788.  Ph. 
Tr.  1792,  Ixxxii.  309  ;  1795,  Ixxxv.  117. 

J  Herschel,  On  the  Planet  Mars,  Ph.  Tr.  1781,  p.  115  ;  1784,  p.  223. 

2  D  2 


404  LECTURE  XLII. 

compared  with  the  time  of  his  rotation,  it  may  be  inferred  that  his 
density  must  be  very  unequal  in  different  pails :  Laplace  supposes  it 
from  calculation  to  be  on  the  whole  about  three  fourths  as  great  as  that  of 
the  earth. 

In  the  interval  between  Mars  and  Jupiter,  and  nearly  at  the 
where,  from  a  dependance  on  the  regularity  of  the  progression  already  men- 
tioned, a  number  of  astronomers  had  for  some  years  been  seeking  for  a 
primary  planet,  the  observations  of  Mr.  Piazzi,*  Dr.  Olbers,t  and  M* . 
Harding  ;£  have  placed  three  very  small  bodies,  differing  but  little  in  their 
mean  distance  and  their  periodical  time.  They  have  named  them  Cf-res, 
Pallas,  and  Juno  :§  none  of  them  subtends  an  angle  large  enough  ttV'je 
measured  by  our  best  instruments ;  and  all  the  circumstances  af-'their 
motions  are  yet  but  imperfectly  established.  Juno,  however,  appears  to  be 
somewhat  less  remote  than  the  other  two  :  all  their  orbits  are  considerably 
inclined  to  the  ecliptic,  especially  that  of  Pallas,  which  is  also  extremely 
eccentric.  Dr.  Herschel  does  not  admit,  that  they  deserve  the  name  of 
planets,  and  chooses  to  call  them  asteroids. 

Jupiter  is  the  largest  of  all  the  planets,  his  diameter  being  11  times  as 
great  as  that  of  the  earth,  and  the  force  of  gravitation  at  his  surface  being 
triple  the  terrestrial  gravitation.  He  revolves  in  about  12  years,  at  a  little 
more  than  five  times  the  earth's  distance  from  the  sun.  His  rotation  is 
performed  in  less  than  ten  hours,  his  equator  being  inclined  about  three 
degrees  to  his  ecliptic,  which  makes  an  angle  of  1°  19'  with  ours.  His  belts 
are  supposed  by  many  to  be  clouds  in  his  asmosphere  ;  they  seem  to  have 
a  rotation  somewhat  slower  than  that  of  the  planet. 

The  diameter  of  Saturn  is  ten  times  as  great  as  that  of  the  earth,  but,  on 
account  of  the  smaller  density  of  his  substance,  the  force  of  gravity  at  his 
surface  scarcely  exceeds  its  force  at  the  surface  of  the  earth.  He  revolves 
in  29  years  and  a  half,  in  an  orbit  inclined  2^°  to  the  ecliptic,  at  the  dis- 
tance of  9 1  semidiameters  of  the  earth's  orbit :  his  rotation  occupies  only 
10^  hours,  and  his  equator  is  inclined  about  30°  to  our  ecliptic.  The  most 
remarkable  circumstance  attending  him  is  the  appearance  of  a  double  ring,|| 
which  is  suspended  over  his  equator,  and  revolves  with  a  rapidity  almost 
as  great  as  that  of  the  planet.  His  figure  appears  also,  according  to  Dr. 
Herschel's  observations,  to  be  extremely  singular ;  deviating  very  consi- 
derably from  that  of  an  elliptical  spheroid,  which  is  the  form  assumed  by 
all  the  other  planets  that  appear  flattened,  and  approaching  in  some  degree 
to  a  cylinder  with  its  angles  rounded  off.  Such  a  form  can  only  be  derived 
from  some  very  great  irregularities  in  the  density  of  the  internal  parts  of 
his  substance. 

*  Discovered  Ceres,  1st  Jan.  1801.     Zach's  Mon.  Corresp.  iv.  53. 

t  Disc.  Pallas,  28th  March,  1802. 

I  Disc.  Juno,  1st  Sept.  1804. 

§  A  fourth,  named  Vesta,  was  discovered  by  Olbers,  on  19th  March,  1807. 

||  Pound.  Ph.  Tr.  1732,  p.  240.  Laplace,  Memoire  sur  la  Theorie  de  1'An- 
neau  de  Saturne.  Herschel,  Ph.  Tr.  1790,  pp.  4,  427  ;  1792,  p.  1  ;  1794,  p.  48  ; 
1805-6-8.  Bessel  makes  the  inclination  of  the  ring  to  our  ecliptic  to  be  28°  22', 
Berlin,  Ephem.  1814,  1822.  He  estimates  the  mass  of  the  ring  at  T}g  of  that  of 
Saturn,  Ast.  Nach.  Nos.  193-4-5. 


ON  THE  SOLAR  SYSTEM.  405 

•          The  Georgian  planet,  discovered  by  Dr.  Herschel  *  in  1780,  sometimes 

also  called  Herschel,  and  sometimes  Uranus,  revolves  in  83|  years,  at  a 

distance  from  the  sun  equal  to  19  times  that  of  the  earth.     Its  diameter  is 

at  little  more  than  4  times  that  of  the  earth,  and  the  weight  of  bodies  at  its 

aw  face  a  little  less  than  here.     Notwithstanding  its  dimensions  are  by  no 

/means  comparatively  small,  it  appears  to  us  as  a  star  of  the  sixth  or  seventh 

„  /  magnitude,  and  is  seldom  seen  by  the  naked  eye.     Its  orbit  approaches 

.very  near  to  the  ecliptic  ;  its  disc  is  said  to  be  somewhat  flattened,  and  it  is 

supposed  to  revolve  with  considerable  rapidity. 

These  ten  [eleven]  planetary  bodies  are  the  only  ones  hitherto  discovered 
^'i  \ch  have  any  title  to  be  considered  as  primary  planets,  that  is,  as  bodies 
reviving  round  the  sun,  in  orbits  so  nearly  circular,  as  to  remain  always 
within  the  reach  of  our  observation.  It  has  been  conjectured  that  the 
number  of  planets  may  in  reality  be  much  greater,  that  not  only  many 
small  and  perhaps  invisible  bodies  may  be  revolving  in  the  intervals  of  the 
planets  with  which  we  are  acquainted,  but  that  larger  bodies  also  may 
belong  to  our  system,  which  never  approach  within  such  a  distance  as  to  be 
seen  by  us.  Some  have  even  bestowed  names,  borrowed  from  the  ancient 
mythology,  on  these  imaginary  planets  ;  but  the  idea  of  such  an  appropria- 
tion of  terms  is  rather  to  be  regarded  as  belonging  to  the  regions  of  poetical 
fiction  than  to  those  of  solid  philosophy. 

The  largest  and  the  most  remote  of  the  primary  planets  have  their 
attendant  satellites,  or  secondary  planets,  accompanying  them  in  their 
respective  revolutions  round  the  sun,  and  moving,  at  the  same  time,  in 
subordinate  orbits,  round  the  primary  planets.  The  earth  is  attended  by 
the  moon,  Jupiter  by  four  moons  or  satellites,  Saturn  by  seven,  besides  his 
ring,  and  the  Georgian  planet  by  six  moons.  All  these  satellites  move  in 
the  direct  order  of  the  signs,  and  in  planes  not  very  remote  from  the  eclip- 
tic, excepting  those  of  the  Georgian  planet,  which  revolve  in  planes  nearly 
perpendicular  to  the  ecliptic.  Each  of  these  planets  thus  becomes  the  cen- 
tral luminary  of  a  little  system  of  its  own,  in  which  the  motions  and  the 
periods  observe  the  same  general  laws  as  prevail  in  the  solar  system  at  large. 
Of  the  28  primary  and  secondary  planets,  we  are  indebted  to  Dr.  Herschel 
for  the  knowledge  of  9  ;  the  Georgian  planet,  with  its  six  satellites,t  and 
the  two  innermost  moons  of  Saturn. 

The  motions  of  some  of  these  satellites,  in  particular  of  those  of  Jupiter 
and  of  the  moon,  are  of  considerable  importance  for  the  assistance  they 
afford  us  in  determinations  of  time,  and  of  the  relative  situations  of  places. 
They  are  subjected  to  considerable  irregularities,  but  the  united  labours  ol 
various  astronomers  have  enabled  us  to  calculate  all  their  motions  with  the 
greatest  accuracy. 

The  moon  performs  a  complete  sidereal  revolution  in  27  days  7|  hours, 

*  Account  of  a  Comet,  Ph.  Tr.  1781,  Ixxi.  492.  Herschel,  Ph.  Tr.  1783,  p.  1. 
Bode,  Von  dem  neu  Entdeckten  Plan.  Berl.  1784.  Lexell,  do.  4to,  Petersb.  Wurm, 
Gotha,  1791.  Robison,  Ed.  Tr.  i.  305. 

•  f  An  Account  of  the  Discovery  of  the  Satellites  of  the  Georgian  Planet,  Ph.  Tr. 
1787,  p.  125  ;  1788,  p.  364  ;  1798,  p.  47.  Account  of  the  Discovery  of  a  Sixth  and 
Seventh  Satellite  of  the  Planet  Saturn,  Ph.  Tr.  1790,  p.  1 ,  427. 


406  LECTURE  XLII. 

and  a  synodical  revolution,  during  which  she  returns  to  the  same  position 
with  respect  to  the  earth  and  sun,  in  29  days  12f  hours  ;  a  period  which 
constitutes  a  lunation,  or  a  lunar  month.  Her  orbit  is  inclined  to  the 
ecliptic  in  an  angle  of  a  little  more  than  five  degrees,  hut  this  inclination  is 


liable  to  great  variations  :  the  place  of  its  nodes  is  also  continually  caji  \ 
ing,  their  motion  being  sometimes  retrograde,  and  sometimes  direct,  but  on^  ^» 
the  whole  the  retrograde  motion  prevails.  The  form  of  the  moon's  orbit  is 
irregularly  elliptic,  and  the  velocity  of  its  motion  deviates  considerably 
from  the  Keplerian  law  of  the  description  of  equal  areas  in  equal  timer;  ; 
the  apsides,  or  the  extremities  of  the  greater  axis  of  the  ellipsis,  which  ,>re 
called  the  apogee  and  perigee,  have  on  the  whole  a  direct  motion.  Frory  a 
comparison  of  modern  observations  with  the  most  ancient,  the  mean  motion 
of  the  moon  is  found  to  be  somewhat  accelerated. 

The  moon  revolves  on  her  own  axis  with  a  very  equable  motion,  and 
the  period  of  her  rotation  is  precisely  equal  to  the  mean  period  of  her 
revolution  round  the  earth  ;  so  that  she  always  presents  to  us  the  same 
portion  of  her  surface,  excepting  the  apparent  librations  produced  by  her 
unequal  velocities  in  her  orbit,  and  by  the  position  of  her  axis,  which  is 
inclined  1°  43'  to  the  ecliptic,  and  sometimes  as  much  as  7°  to  her  own 
orbit.  Her  distance  from  the  earth  is  about  240,000  miles  ;  her  diameter 
-^r  of  that  of  the  earth,  or  21GO  miles  ;  and  the  weight  of  bodies  at  her 
surface  is  supposed  to  be  about  one  fifth  of  their  weight  at  the  surface  of 
the  earth, 

The  surface  of  the  moon  presents  to  us,  when  viewed  with  a  telescope, 
a  great  diversity  of  light  and  shade,  the  principal  features  of  which  are 
visible  even  to  the  naked  eye.  Many  of  these  inequalities  resemble  very 
strongly  the  effects  of  volcanos  ;  several  astronomers  have  imagined  that 
they  have  seen  volcanos  actually  burning  in  the  unenlightened  part  of  the 
planet  ;  and  Dr.  Herschel's  instruments  have  enabled  him  to  obtain  satis- 
factory evidence  of  the  truth  of  the  conjecture.*  The  appearance  of  a 
perforation,  which  Ulloa  supposed  that  he  observed  near  the  margin  of 
the  Moon's  disc,  in  a  solar  eclipse,  has  been  attributed  by  some  to  a  volcano 
actually  burning.  Dr.  Halley  and  Mr.  Weidlerf  have  also  observed 
flashes  of  light  on  the  dark  part  of  the  moon,  considerably  resembling  the 
effect  of  lightning.  The  height  of  the  lunar  mountains  has  been  com- 
monly supposed  to  exceed  very  considerably  that  of  the  mountains  of  the 
earth  ;  but  Dr.  Herschel  J  is  of  opinion  that  none  of  them  are  so  much  as 
two  miles  high.  The  names,  which  have  been  given  by  astronomers  to 
various  parts  of  the  moon's  surface,  are  of  some  utility  in  the  observation 
of  the  progress  of  an  eclipse. 

Of  the  satellites  of  Jupiter,  §  some  are  a  little  larger,  and  others  smaller 
than  the  moon  :  they  all  revolve  in  planes  inclined  between  2£°  and  3£°  to 
the  orbit  of  the  planet,  and  they  are  therefore  always  seen  nearly  in  the 
same  line.  It  is  inferred,  from  some  periodical  changes  of  light  which  they 

*  An  Account  of  the  Volcanos  in  the  Moon,  Ph.  Tr.  1787,  Ixxvii.  229.  See  also 
Ph.  Tr.  1794,  pp.  84,  429,  435. 

t  Ibid.  1739,  p.  228.  J  Ibid.  1780,  p.  507. 

§  Marii  Mundus  Jovialis,  ito,  Nuremb.  1611.     Herschel,  l'h.  Tr.  1797,  p.  332. 


ON  THE  SOLAR  SYSTEM.  407 

undergo,  that,  like  our  moon,  they  always  present  the  same  face  to  their 
primary  planet. 

The  ring  of  Saturn  is  inclined  31  degrees  to  our  ecliptic  ;  of  his  seven 

satellites,  six  are  nearly  in  the  same  plane  with  the  ring ;  hut  the  plane 

•  of  Jhe  seventh  or  outermost  satellite  is  hut  half  as  much  inclined  to  the 

i^    ^'j/ecliptic.     The  ring  has  heen  observed  by  Dr.  Herschel  to  revolve  in  10 1 

hours,  which  is  considerably  less  than  the  time  that  would  be  occupied  by 

.the  revolution  of  a  satellite  at  the  same  distance.     The  planes  of  the  six 

s^ellites  of  the  Georgian  planet  are  nearly  perpendicular  to  the  ecliptic  ; 

anil  some  of  their  revolutions  are  supposed  to  be  rather  retrograde  than 

**iet.* 

\  -sides  the  bodies  which  revolve  completely  round  the  sun,  within  the 
limits  of  our  observation,  there  are  others,  of  which  we  only  conclude  from 
analogy,  that  they  perform  such  revolutions.  These  are  the  comets  ;  they 
generally  appear  attended  by  a  nebulous  light,  either  surrounding  them  as 
a  coma,  or  stretched  out  to  a  considerable  length  as  a  tail ;  and  they  some- 
times seem  to  consist  of  such  light  only.  Their  orbits  are  so  eccentric, 
that  in  their  remoter  situations  the  comets  are  no  longer  visible  to  us, 
although  at  other  times  they  approach  much  nearer  to  the  sun  than  any 
of  the  planets  :  for  the  comet  of  1680,  when  in  its  perihelion,  was  at  the 
distance  of  only  one  sixth  of  the  sun's  diameter  from  his  surface.  Their 
tails  are  often  of  great  extent,  appearing  as  a  faint  light,  directed  always 
towards  a  point  nearly  opposite  to  the  sun  :  it  is  quite  uncertain  of  what 
substance  they  consist ;  and  it  is  difficult  to  determine  which  of  the  con- 
jectures respecting  them  can  be  considered  as  the  least  improbable ;  it  is 
possible  that,  on  account  of  the  intense  cold,  to  which  the  comets  are  sub- 
jected in  the  greatest  part  of  their  revolutions,  some  substances,  more  light 
than  any  thing  we  can  imagine  on  the  earth,  may  be  retained  by  them  in 
a  liquid,  or  even  in  a  solid  form,  until  they  are  disengaged  by  the  effect 
of  the  sun's  heat :  but  we  are  still  equally  at  a  loss  to  explain  the  rapidity 
of  their  ascent :  for  the  buoyancy  of  the  sun's  atmosphere  cannot  possibly 
be  supposed  to  be  adequate  to  the  effect ;  and  on  the  whole  there  is,  per- 
haps, reason  to  believe  that  the  appearances  are  derived  from  some  cause, 
bearing  a  considerable  analogy  to  the  fluid,  supposed  to  be  concerned  in 
the  effects  of  electricity.  It  is  probable  that  the  density  of  the  nucleus, 
or  the  body  of  the  comet  itself,  is  comparatively  small,  and  its  attraction 
for  the  tail  consequently  weak,  so  that  it  has  little  tendency  to  reduce 
the  tail,  even  if  it  consists  of  a  material  substance,  to  a  spherical  form : 
for  since  some  comets  have  no  visible  nucleus  at  all,  there  is  no  difficulty 
in  supposing  the  nucleus,  when  present,  to  be  of  very  moderate  density, 
and  perhaps  to  consist  of  the  same  kind  of  substance  as  constitutes  the  tail 
or  coma,  in  a  state  of  somewhat  greater  condensation.  If,  therefore,  it 
should  ever  happen  to  a  planet  to  fall  exactly  in  the  way  of  a  comet,  of 
which  there  is  but  very  little  probability,  it  is  to  be  supposed  that  the 
inconvenience  suffered  by  the  inhabitants  of  the  planet  might  be  merely 
.temporary  and  local :  the  chances  are,  however,  much  greater,  that  a  comet 

*  J.  Herschel  on  the  Satellites  of  Uranus,  Mem.  of  the  Ast.  Soc.  vol.  viii. 


408  LECTURE  XLII. 

might  interfere  in  such  a  manner  with  a  planet,  as  to  deflect  it  a  little  from     i 
its  course,  and  retire  again  without  coming  actually  into  contact  with  it. 

Nearly  500  comets  are  recorded  to  have  been  seen  at  different  times,  and 
the  orbits  of  about  a  hundred  have  been  correctly  ascertained :  but  we 
have  no  opportunity  of  observing  a  sufficient  portion  of  the  orbit  of  Sny  v 
comet,  to  determine  with  accuracy  the  whole  of  its  form  as  an  ellipsis^    7 
since  the  part  which  is  within  the  limits  of  our  observation  does  not  sensibly  N 
differ  from  the  parabola,  which  would  be  the  result  of  an  ellipsis  prolonged 
without  end. 

Two  comets  at  least,  or  perhaps  three,  have  been  recognized  in  t^ir 
return.  A  comet  appeared  in  1770,  which  Prosperin*  suspected  to  iipvT? 
in  an  orbit  materially  different  from  a  parabola  :  Mr.  Lexellf  determjUed 
its  period  to  be  5  years  and  7  months,  and  its  extreme  distances  i/o  be 
between  the  orbits  of  Jupiter  and  of  Mercury  ;  but  it  does  not  appear  that 
any  subsequent  observations  have  confirmed  his  theory.  It  has,  however, 
been  calculated,  that  supposing  the  theory  correct,  it  must  afterwards  have 
approached  so  near  to  Jupiter  as  to  have  the  form  of  its  orbit  entirely 
changed. 

Dr.  Halley  J  foretold  the  return  of  a  comet  about  1758,  which  had 
appeared  in  1531,  in  1607,  and  in  1682,  at  intervals  of  about  75  years ; 
and  with  Clairaut's§  further  correction  for  the  perturbations  of  Jupiter 
and  Saturn,  the  time  agreed  within  about  a  month.  The  mean  distance 
of  this  comet  from  the  sun  must  be  less  than  that  of  the  Georgian  planet ; 
so  that  by  improving  our  telescopes  still  more  highly,  we  may,  perhaps, 
hereafter  be  able  to  convert  some  of  the  comets  into  planets,  so  far  as 
their  remaining  always  visible  would  entitle  them  to  the  appellation. 
Dr.  Halley  also  supposed  the  comet  of  1680  to  have  been  seen  in  1106,  in 
531,  and  in  the  year  44  before  Christ,  having  a  period  of  575  years  ;  and 
it  has  been  suspected  that  the  comets  of  1556  and  1264  were  the  same,  the 
interval  being  292  years ;  a  conjecture  which  will  either  be  confirmed  or 
confuted  in  the  year  1848.  Some  persons  have  even  doubted  of  the  perfect 
coincidence  of  the  orbits  of  any  comets,  seen  at  different  times,  with  each 
other,  and  have  been  disposed  to  consider  them  as  messengers  forming  a 
communication  between  the  neighbouring  systems  of  the  sidereal  world, 
and  visiting  a  variety  of  stars  in  succession,  so  as  to  have  their  courses 
altered  continually,  by  the  attraction  towards  many  different  centres  ;  but 
considering  the  coincidence  of  the  calculation  of  Halley  and  Clairaut  with 
the  subsequent  appearance  of  the  comet  of  1759,  this  opinion  can  scarcely 
be  admitted  to  be  in  any  degree  probable  with  respect  to  the  comets  in 
general,  however  possible  the  supposition  may  be  in  some  particular  cases. 
(Plate  XXXII.  Fig.  472... 475.  Plate  XXXIII.  Fig.  476... 485.) 

*  On  Com.  1770,  4to,  Upsal.  1776. 

t  Lexell,  Mem.  de  1'Acad.  Par.  1776,  p.  638 ;  and  Disquisitio  de  Temp.  per.  Co- 
metse  An.  1770,  Ph.  Tr.  1779,  p.  68. 

t  Ph.  Tr.  1705,  p.  1882  ;  and  Gregory's  Elements  of  Ast.  1726.  See  History  of 
Halley's  Comet,  with  an  Account  of  its  Return  in  1835,  as  predicted  by  MM.  Damoi- 
seau  and  De  Pontecoulant,  translated  from  the  French  of  M.  De  Pontecoulant,  by 
Gold,  1835.  Moseley's  Lect.  on  Ast.  1839. 

§  Journal  des  Savans,  1759.     See  his  Theoriedu  Mouvement  des  Cornetes,  Paris, 


ON  THE  LAWS  OF  GRAVITATION.  409 

i 

LECT.  XLIL— ADDITIONAL  AUTHORITIES. 

Descriptions.  Sun. — Hausen,  4to,  Leipz.  1726.  Schroter,  4to,  Erfurt.  1789. 
Woodward,  Washington,  1801. 

JL*"°,o». — Hevelii  Selenographia,  fol.   Dantz.  1667.     Cassini,  Carte  de  la  Lune. 

Mylivis,  Uber  die  Atmosphare  des  Mondes,  4to,  1746.     Mayer's   Cosmographische 

%          J/achrichten.  1748,  p.  379.    Von  dem  Mondkiigeln,  4to,  Numb.  1750.     Schroter's 

rSelenotopographische   Fragmenten,  2   vols.  4to,  Gott.   1791.     Beer's  Map  of  the 

Moon. 

V  Orbits. — See  Lect.  43  ;  also  Primary  Planets. — Halley's  Mode  of  determining  the 
Orwts,  Ph.  Tr.  1676,  p.  683.  Huygenii  Cosmotheros,  4to,  Hag.  1698.  Varignon, 
HisA  et  Mem.  1 700,  p.  224,  H.  78.  Cacciatore,  Sull'  Origine  della  Sistema  Solare, 
Palermo,  1826. 

'/'•  Kepler's  Prob.— Keill,  Ph.  Tr.  1713,  p.  1  ;  Machin,  ibid.  1783,  p.  205. 
Stewart,  Ed.  Ess.  ii.  105.  Lagrange,  Hist,  et  Mem.  de  Berlin,  1764,  p.  204. 
Sejour,  Hist,  et  Mem.  1790,  p.  401.  Ivory,  Ed.  Tr.  v.  203.  Brinkley,  Ir.  Tr.  vi. 
349  ;  ix.  83. 

Secondary  Planets. — Clairaut  on  the  Moon's  Orbit,  Hist,  et  Mem.  1743,  p.  17, 
H.  123  ;  1748,  p.  421.  Theorie  de  laLune,  4to,Petersb.  1752.  Stewart,  The  Dis- 
tance of  the  Sun  deduced  by  Theory,  Ed.  1763.  Mayer,  Theoria  Lunse,  4to,  Lond. 
1767.  Euler,  do.  Laplace,  Hist,  et  Mem.  1784,  p.  1  ;  1785,  Errata;  1786, 
p.  235  ;  1788,  p.  249  ;  1789,  p.  1,  237. 

Comets. — Bartholinus  de  Cometis,  4to,  Copen.  1665.  Lubinietz,  Theatrum 
Cometicum,fol.  Amst.  1668.  Hevelius,  Cometographia,  fol.  Gedani,  1668.  Cassini, 
Sur  la  Comete  de  1680,  4to,  Paris,  1681.  Bernoulli,  Conamen  Novi  Systematis 
Cometarum,  12mo,  Amst.  1682.  Whiston's  Praelectiones,  1710.  Lemonnier,  La 
Theorie  des  Cometes,  Paris,  1743.  Heinsius,  Ueber  den  Comet,  von  1743,  4to, 
Petersb.  1744.  Loys  des  Cheseaux,  do.  Lausanne,  1744.  Martin's  Theory  of  Comets, 
4to,  1757.  Lambert,  Insigniores  Orbitae  Cometarum  Proprietates,  Augsb.  1761. 
Wideburg,  Ueber  den  Com.  Jena,  1769.  Lambert  on  the  Apparent  Orbit  of 
Comets,  Hist,  et  Mem.  de  Berlin,  1771,  p.  352.  Oliver  on  Comets,  Salem,  1772. 
Laplace,  Mem.  des  Sav.  Etr.  1773,  p.  503.  Dionis  de  Sejour,  Hist,  et  Mem.  1774, 
H.  78;  Essai,  Paris,  1775.  Condorcet,  Dissertation,  4to,  Utr.  1780.  Pingre", 
Cometographie,  2  vols.  Paris,  1783.  Piazzi,  Della  Cometa  del  1811,  4to,  Palermo, 
1812.  Englefield  on  Comets,  4to,  1793.  Legendre,  Sur  les  Orbites  des  Cometes, 
4to,  Paris,  1806  ;  Supplement,  4to,  1820.  Schroter,  Ueber  den  Grossen  Com.  von 
1811,  Gott.  1815.  Cacciatore,  Delia  Com.  di  1819,  Palermo,  1819.  Lubbock,  On 
the  Orbit  of  a  Comet,  Mem.  of  the  Ast.  Soc.  1829.  Encke,  Ueber  die  Nachste 
Wiederker  des  Cometen  von  Ponsin  Jahr.  1832,  Altona,  1831.  Airy  on  Encke's 
Comet,  Camb.  1832.  Littrow  on  do.  Wien,  1832.  Stratford,  Ephemeris  of  Halley's 
Comet,  1835.  Arago,  Des  Cometes,  18mo,  Par.  1834.  Virlet,  do.  18mo,  Avesnes, 
1835.  Mime  on  Comets,  Ed. 


LECTURE    XLIII. 


ON  THE  LAWS  OF  GRAVITATION. 

IT  was  first  systematically  demonstrated  by  Sir  Isaac  Newton,  that  all 
the  motions  of  the  heavenly  bodies,  which  have  been  described,  may  be 
deduced  from  the  effects  of  the  same  force  of  gravitation  which  causes  a 
heavy  body  to  fall  to  the  earth  ;  he  has  shewn  that  in  consequence  of  this 
universal  property  of  matter,  all  bodies  attract  each  other  with  forces  de- 
creasing as  the  squares  of  the  distances  increase  ;  and  of  later  years  the 
same  theory  has  been  still  more  accurately  applied  to  the  most  complicated 


410  LECTURE  XLIII. 

phenomena.  We  are  at  present  to  take  a  general  view  of  the  operation  of 
this  law,  in  the  same  order  in  which  the  affections  of  the  celestial  bodies 
have  been  enumerated.  It  will  not  be  possible  to  investigate  mathemati- 
cally the  effects  of  gravity  in  each 'particular  motion,  but  we  may  in  some 
measure  illustrate  the  subject,  by  considering  in  what  manner  astronoTners. 
have  proceeded  in  their  explanations  and  calculations,  and  we  may  entV  , 
sufficiently  into  the  principles  of  the  theory,  to  understand  the  possibility 
of  its  applications. 

The  bodies  which  exist  in  nature  are  never  single  gravitating  points  ;  <Cnd 
in  order  to  determine  the  effects  of  their  attraction,  we  must  suppos^  the 
actions  of  an  infinite  number  of  such  points  to  be  combined.  It  was  sltajvn 
by  Newton,  that  all  the  matter  of  a  spherical  body,  or  of  a  spherical  sur- 
face, may  be  considered,  in  estimating  its  attractive  force  on  other  matter, 
as  collected  in  the  centre  of  the  sphere.  The  steps  of  the  demonstration 
are  these :  a  particle  of  matter,  placed  at  the  summit  of  a  given  cone  or 
pyramid,  is  attracted  by  a  thin  surface,  composed  also  of  attractive  matter, 
occupying  the  base  of  the  cone,  with  equal  force,  whatever  may  be  the 
length  of  the  cone,  provided  that  its  angular  position  remain  unaltered ; 
hence  it  is  easily  inferred  that  if  a  gravitating  point  be  placed  any  where 
within  a  hollow  sphere,  it  will  remain  in  equilibrium,  in  consequence  of 
the  opposite  and  equal  actions  of  the  infinite  number  of  minute  surfaces, 
terminating  the  opposite  pyramids  into  which  the  sphere  may  be  divided  ; 
it  is  also  demonstrable,  by  the  assistance  of  a  fluxional  calculation,  that  a 
point,  placed  without  the  surface,  is  attracted  by  it,  precisely  in  the  same 
manner,  as  if  the  whole  matter  which  it  contains  were  collected  in  the 
centre ;  consequently  the  same  is  true  of  a  solid  sphere,  which  may  be 
supposed  to  consist  of  an  infinite  number  of  such  hollow  spheres.  If, 
however,  the  point  were  placed  within  a  solid  sphere  it  would  be  urged 
towards  the  centre,  by  a  force  which  is  simply  proportional  to  its  distance 
from  that  centre.  This  proposition  tends  very  much  to  facilitate  all  calcu- 
lations of  the  attractions  of  the  celestial  bodies,  since  all  of  them  are  so 
nearly  spherical,  that  their  action  on  any  distant  bodies  is  the  same  as  if 
the  whole  of  the  matter  of  which  they  consist  were  condensed  into  their 
respective  centres;  but  if  the  force  of  gravity  varied  according  to  any 
other  law  than  that  which  is  found  to  prevail,  this  simplification  would  no 
longer  be  admissible,  even  with  respect  to  a  sphere. 

It  can  scarcely  be  doubted  that  the  power  of  gravitation  extends  from 
one  fixed  star  to  another,  although  its  effects  may  in  this  case  be  much  too 
inconsiderable  to  be  perceived  by  us.  It  may  possibly  influence  the  pro- 
gressive motions  of  some  of  the  stars ;  and  if,  as  Dr.  Herschel  supposes, 
there  are  double  and  triple  stars  revolving  round  a  common  centre,  they 
must  be  retained  in  their  orbits  by  the  force  of  gravity.  Dr.  Herschel 
also  imagines  that  the  motion  of  our  sun  is  in  some  measure  derived  from 
the  same  cause,  being  directed  nearly  towards  a  point  in  which  two  strata 
of  the  milky  way  meet ;  the  attraction  of  the  stars,  other  things  being 
equal,  must,  however,  be  proportional  to  their  brightness,  and  that  part  of 
the  heavens,  to  which  the  sun  is  probably  moving  appears  to  afford  less 
light  than  almost  any  other  part,  nor  does  the  hemisphere,  of  which  it  is 


ON  THE  LAWS  OF  GRAVITATION.  411 

the  centre,  abound  so  much  in  bright  stars  as  the  opposite  hemisphere.  If 
Sirius  is  a  million  times  as  far  from  the  sun  as  the  earth,  and  if  he  should 
descend  towards  the  sun  by  means  of  their  mutual  gravitation  only,  he 
would  move,  on  a  rough  estimate,  but  about  40  feet  in  the  first  year,  and 
in  1000  years  only  8000  miles.  It  has  been  conjectured  that  the  mutual 
?.  -ravitatioii  of  the  stars  of  a  nebula  is  sometimes  the  cause  of  the  peculiar 
form  of  the  aggregate,  which  somewhat  resembles  that  of  a  drop  of  a  liquid 
,ield  together  by  its  cohesion ;  but  unless  the  form  of  the  nebula  was  ori- 
gii.ftlly  spherical,  it  could  scarcely  have  acquired  that  form  from  the  opera- 
tioiitof  gravity,  since  the  spherical  form  of  a  drop  is  owing  as  much  to  the 
elasticity  as  to  the  attractive  force  of  the  particles  of  water,  and  it  would 
be  necessary,  in  order  to  preserve  the  analogy,  that  the  stars  should  also 
be  floating  in  an  incompressible  fluid. 

The  sun's  change  of  place,  dependent  on  the  relative  situation  of  the 
planets,  is  so  inconsiderable,  that  it  escaped  observation  until  its  existence 
had  been  deduced  from  theory.  Not  but  that  this  change  would  be  suffi- 
ciently conspicuous  if  we  had  any  means  of  detecting  it,  since  it  may 
amount  in  the  whole  to  a  distance  equal  to  twice  the  sun's  diameter,  or 
seven  times  the  distance  of  the  moon  from  the  earth  ;  and  this  change  is 
readily  deducible  from  the  general  and  unquestionable  law  of  mechanics, 
that  the  place  of  the  centre  of  inertia  of  a  system  cannot  be  changed  by  any 
reciprocal  or  mutual  action  of  the  bodies  composing  it,  the  action  of  gra- 
vity being  found  to  be  perfectly  reciprocal.  But  the  earth  accompanies  the 
sun  in  great  measure  in  this  aberration,  and  the  other  planets  are  also  more 
or  less  affected  by  similar  motions  ;  so  that  the  relative  situations  are  much 
less  disturbed  than  if  the  sun  described  this  irregular  orbit  by  the  ope- 
ration of  a  cause  foreign  to  the  rest  of  the  system. 

The  simple  revolution  of  a  body,  in  a  given  plane,  indicates,  at  first 
sight,  the  existence  of  an  attractive  force  directed  to  some  point  within  the 
orbit ;  and  the  Keplerian  law  of  the  equality  of  the  areas  described  in  equal 
times,  by  a  line  drawn  from  each  planet  to  the  sun,  agrees  precisely  with 
what  is  demonstrable  of  the  effects  of  central  forces,  and  points  at  once 
to  the  sun  as  the  centre  of  attraction  of  the  system.  And  since  the  orbits 
of  the  planets  are  elliptical,  and  the  sun  is  placed  in  one  of  the  foci  of 
each,  it  may  be  mathematically  proved  that  the  force  directed  to  the  sun 
must  increase  in  proportion  as  the  square  of  the  distance  decreases. 

The  times  of  the  revolutions  of  the  planets  are  also  in  perfect  con- 
formity with  the  laws  of  gravitation,  that  is,  the  squares  of  the  times  are 
proportional  to  the  cubes  of  the  distances  from  the  sun.  It  was  easy  to 
infer,  from  what  Huygens  had  already  demonstrated  of  centrifugal  forces, 
that  this  Keplerian  law  must  be  true  of  bodies  revolving  in  circles  by  the 
force  of  gravitation  ;  but  Newton  first  demonstrated  the  same  proportion 
with  respect  to  elliptic  orbits,  and  shewed  that  the  time  of  revolution  in  an 
ellipsis  is  equal  to  the  time  of  revolution  in  a  circle,  of  which  the  diameter 
is  equal  to  the  greater  axis  of  the  ellipsis,  or  the  semidiameter  to  the  mean 
distance  of  the  planet. 

The  universality  of  the  laws  of  gravitation,  as  applied  to  the  different 
planets,  shews  also  that  the  matter,  of  which  they  are  composed,  is  equally 


412  LECTURE   XLIII. 

subjected  to  its  power  ;  for  if  any  of  the  planets  contained  a  portion  of  an 
inert  substance,  requiring  a  force  to  put  it  in  motion,  and  yet  not  liable  to 
the  force  of  gravitation,  the  motion  of  the  planet  would  be  materially  dif- 
ferent from  that  of  any  other  planet  similarly  situated. 

The  deviations  of  each  planet  from  the  plane  of  its  orbit,  and  the  motions 
of  its  nodes,  or  the  points  in  which  the  orbit  intersects  the  plane  of  th 
ecliptic,  as  well  as  the  motions  of  the  aphelion,  or  the  point  where  the  orbit* 
is  remotest  from  the  sun,  have  also  been  deduced  from  the  attractions  of  tb  j 
other  planetary  bodies ;  but  the  calculations  of  the  exact  quantities  of  tfefese 
perturbations  are  extremely  intricate.  In  general,  each  of  the  disturbing 
forces  causes  the  nodes  to  have  a  slight  degree  of  retrograde  motion  ;  but/m 
account  of  the  peculiar  situation  of  the  orbits  of  Jupiter  and  Saturn,  it 
happens  that  the  retrograde  motion  of  Jupiter's  node,  on  the  plane  of  the 
orbit  of  Saturn,  produces  a  direct  motion  on  the  ecliptic,  so  that  the  action 
of  Saturn  tends  to  lessen  the  effect  of  the  other  planets  in  causing  a  retro- 
grade motion  of  Jupiter's  nodes  on  the  ecliptic. 

The  secular  diminution  of  the  obliquity  of  the  ecliptic,  or  that  slow 
variation  of  its  position,  which  is  only  discovered  by  a  comparison  of  very 
distant  observations,  is  occasioned  by  the  change  of  position  of  the  earth's 
orbit,  in  consequence  of  the  attractions  of  the  other  planets,  especially  of 
Jupiter.  It  has  been  calculated  that  this  change  may  amount,  in  the 
course  of  many  ages,  to  10°  or  11°,  with  respect  to  the  fixed  stars  ;  but  the 
obliquity  of  the  ecliptic  to  the  equator  can  never  vary  more  than  two  or 
three  degrees,  since  the  equator  will  follow,  in  some  measure,  the  motion 
of  the  ecliptic. 

The  mutual  attraction  of  the  particles  of  matter,  composing  the  bulk  of 
each  planet,  would  naturally  dispose  them,  if  they  were  either  wholly  or 
partially  fluid,  to  assume  a  spherical  form  :  but  their  rotatory  motion  would 
require,  for  the  preservation  of  this  form,  an  excess  of  attraction  in  the 
equatorial  parts,  in  order  to  balance  the  greater  centrifugal  force  arising 
from  the  greater  velocity  of  their  motion  :  but  since  the  attractive  force  of 
the  sphere  on  the  particles  at  an  equal  distance  from  its  centre  is  every 
where  equal,  the  equatorial  parts  would  necessarily  recede  from  the  axis, 
until  the  greater  number  of  particles,  acting  in  the  same  column,  compen- 
sated for  the  greater  effect  of  the  centrifugal  force.  The  form  would  thus 
be  changed  from  a  sphere  to  an  oblate  or  flattened  spheroid ;  and  the  sur- 
face of  a  fluid,  either  wholly  or  partially  covering  a  solid  body,  must  as- 
sume the  same  figure,  in  order  that  it  may  remain  at  rest.  The  surface  of 
the  sea  is  therefore  spheroidical,  and  that  of  the  earth  deviates  so  far  only 
from  a  spheroidical  figure,  as  it  is  above  or  below  the  general  level  of  the 
sea.  (Plate  XXXIV.  Fig.  486.) 

The  actions  of  the  sun  and  moon,  on  the  prominent  parts  about  the 
earth's  equator,  produce  a  slight  change  of  the  situation  of  its  axis,  in  the 
same  manner  as  the  attractions  of  the  other  planets  occasion  a  deviation 
from  the  plane  of  its  orbit.  Hence  arises  the  precession  of  the  equinoxes, 
or  the  retrograde  motion  of  the  equinoctial  points,  amounting  annually  to 
about  50  seconds.  The  nutation  of  the  earth's  orbit  is  a  small  periodical 
change  of  the  same  kind,  depending  on  the  position  of  the  moon's  nodes  ;  in 


ON  THE  LAWS  OF  GRAVITATION.  413 

consequence  of  which,  according  to  Dr.  Bradley's  original  observations, 
the  pole  of  the  equator  describes  in  the  heavens  a  little  ellipsis,  of  which  the 
diameters  are  16  and  20  seconds.  The  same  cause  is  also  concerned  in 
modifying  the  secular  variation  of  the  obliquity  of  the  ecliptic  :  and  on  the 
other  hand,  this  variation  has  a  considerable  effect  on  the  apparent  preces- 
'ion  of  the  equinoxes.  On  account  of  the  different  quantity  of  the  preces- 
sion at  different  times,  the  actual  length  of  the  tropical  year  is  subjected  to 
*»  slight  variation  :  it  is  now  4  or  5  seconds  shorter  than  it  was  in  the  time 
of  *  fttpparchus.  The  utmost  change,  that  can  happen  from  this  cause, 
amounts  to  43  seconds. 

The  exact  computation  of  the  moon's  motion  is  one  of  the  most  difficult, 
as  well  as  the  most  important  problems  in  astronomy  ;  but  it  is  easy  to 
understand,  in  general,  how  the  difference  in  the  quantity  and  direction  of 
the  sun's  actions  on  the  moon  and  earth,  may  cause  such  a  derangement  of 
the  moon's  gravitation  towards  the  earth,  that  the  inclination  of  the  orbit 
must  be  variable,  that  the  nodes  must  have  a  retrograde,  and  the  apsides  a 
direct  motion  ;  and  that  the  velocity  of  the  moon  must  often  be  different 
from  that  which  she  would  have,  according  to  the  Keplerian  law,  in  a  Sim- 
ple elliptic  orbit. 

For,  the  sun's  attraction  as  far  as  it  acts  equally  on  the  earth  and  the 
moon,  can  have  no  effect  in  disturbing  their  relative  position,  being  always 
employed  in  modifying  their  common  annual  revolution  ;  but  the  difference 
of  the  forces,  occasioned  by  the  difference  of  distances,  always  tends  to 
diminish  the  effect  of  their  mutual  attraction  ;  since  the  sun  acts  more 
powerfully  on  the  nearer  than  on  the  remoter  of  the  two  bodies.  The  dif- 
ference of  the  directions,  in  which  the  sun  acts  on  the  earth  and  the  moon, 
produces  also  a  force,  which  tends,  in  some  degree,  to  bring  them  nearer  to- 
gether ;  but  this  force  is,  on  the  whole,  much  smaller  than  the  former  ;  and 
the  result  of  both  these  disturbing  forces  is  always  directed  to  some  'point 
in  the  line  which  joins  the  earth  and  the  sun,  on  the  same  side  of  the  earth 
with  the  moon.  It  is  obvious  that  when  the  nodes  are  also  in  this  line,  the 
disturbing  force  can  have  no  effect,  either  on  their  position,  or  on  the  in- 
clination of  the  orbit,  since  it  acts  wholly  in  the  plane  of  that  orbit ;  but 
when  they  are  in  any  other  situation,  the  disturbing  force  must  cause  a 
deviation  from  the  plane,  towards  the  side  on  which  the  sun  is  situated,  so 
that  the  inclination  of  the  orbit  increases  and  decreases  continually  and 
equally  ;  but  whatever  may  be  the  position  of  the  nodes,  it  will  appear 
that  they  must  recede  during  the  greater  part  of  the  moon's  revolution,  and 
advance  during  the  smaller.  (Plate  XXXIV.  Fig.  487.) 

When  the  disturbing  force  tends  to  separate  the  earth  and  moon,  it  de- 
ducts from  the  gravitation  of  the  moon  towards  the  earth  a  portion  which 
increases  with  the  distance,  and  therefore  causes  the  remaining  force  to 
decrease  more  rapidly  than  the  square  of  the  distance  increases ;  and  the 
reverse  happens  when  the  disturbing  force  tends  to  bring  the  earth  and 
moon  nearer  together ;  but  the  former  effect  is  considerably  greater  than 
Jbhe  latter.  Now  in  the  simple  ellipsis,  when  the  body  descends  from  the 
mean  distance,  the  velocity  continually  prevails  over  the  attractive  force, 
so  as  to  turn  away  the  direction  of  the  orbit  more  and  more  from  the 


414  LECTURE   XLIII. 

revolving  radius,  until,  at  a  certain  point,  which  is  called  the  lower  apsis, 
it  becomes  perpendicular  to  it :  but  if  the  central  force  increase  in  a  greater 
proportion  than  is  necessary  for  the  description  of  the  ellipsis,  the  point 
where  the  velocity  prevails  over  it  will  be  more  remote  than  in  the  ellipsis ; 
and  this  is  expressed  by  saying  that  the  apsis  moves  forwards.  When,  on  v 
the  contrary,  the  force  varies  more  slowly,  the  apsis  has  a  retrograded 
motion.  Since,  therefore,  the  force  attracting  the  moon  towards  the  earth, , 
increases,  on  the  whole,  a  little  more  rapidly  than  the  square  of  the  distance' 
decreases,  the  apsides  must  have,  on  the  whole,  a  direct  motion.  An4  a 
similar  theory  is  applicable  to  the  mutual  perturbations  of  the  prinfary 
planets.  (Plate  XXXIV.  Fig.  488.) 

The  secular  acceleration  of  the  moon's  mean  motion,  which  had  long 
presented  a  difficulty  amounting  almost  to  an  exception,  against  the  suffi- 
ciency of  the  theory  of  gravitation,  has  at  last  been  satisfactorily  deduced 
by  Mr.  Laplace  from  the  effect  of  the  gradual  change  of  the  eccentricity  of 
the  earth's  orbit,  which  is  subject  to  a  very  slow  periodical  variation,  and 
which  causes  a  difference  in  the  magnitude  of  the  sun's  action  on  the  lunar 
revolution. 

The  perfect  coincidence  of  the  period  of  the  moon's  rotation,  with  that 
of  a  mean  revolution,  has  been  supposed  to  be  in  some  degree  an  effect  of 
the  attraction  exerted  by  the  earth  on  a  prominent  part,  of  her  surface ; 
there  are,  however,  many  reasons  to  doubt  of  the  sufficiency  of  the  expla- 
nation. If  the  periods  had  originally  been  very  nearly  equal,  we  might 
imagine  that  the  motion  of  the  earth  would  have  produced  a  libration  or 
oscillation  in  the  position  of  the  moon,  retaining  it  always  within  certain 
limits  with  respect  to  the  earth  ;  no  libration  is,  however,  observed,  that 
can  be  derived  from  any  inequality  in  the  moon's  rotation  ;  and  it  has 
very  properly  been  suggested  that  the  same  attraction  towards  the  earth 
ought  to  have  made  the  moon's  axis  precisely  perpendicular  to  the  plane  of 
her  orbit,  instead  of  being  a  little  inclined  to  it.  At  the  same  time  the 
appearance  of  a  similar  coincidence,  in  the  periods  of  the  rotation  and  re- 
volution of  many  other  satellites,  makes  it  probable  that  some  general 
cause  must  have  existed,  which  has  produced  the  same  effect  in  so  many 
different  cases. 

The  orbits  of  the  comets  afford  no  very  remarkable  singularity  in  the 
application  of  the  laws  of  gravity,  excepting  the  modifications  which  depend 
on  their  near  approach  to  the  parabolic  form,  and  the  great  disturbance 
which  their  motions  occasionally  suffer,  when  they  happen  to  pass  through 
the  neighbourhood  of  any  of  the  larger  planets.  The  velocity  of  a  comet 
in  its  perihelion  is  such,  that  its  square  is  twice  as  great  as  the  square  of 
the  velocity  of  a  body  revolving  in  a  circle  at  the  same  distance.  It  was 
determined  by  Halley  and  Clairaut,  that  the  attractions  of  Jupiter  and 
Saturn  would  delay  the  return  of  the  comet  of  1759  about  618  days  ;  and 
the  prediction  was  accomplished  within  the  probable  limits  that  they  had 
assigned  for  the  error  of  the  calculation.  The  labours  of  Clairaut  have 
indeed  in  many  respects  improved  the  science  of  mathematical  astronomy  ;> 
he  was  the  first  that  obtained  a  complete  determination  of  the  effects  of  the 
mutual  actions  of  three  gravitating  bodies,  disturbing  each  other's  motions  ; 


APPEARANCES  OF  THE  CELESTIAL  BODIES.  415 

and  his  investigations,  which  were  founded  on  those  of  Newton,  led  the 
way  to  still  further  improvements  and  refinements,  which  have  been  since 
made  in  succession  by  Euler,  Lagrange,  and  Laplace. 


LECT.  XLIIL— ADDITIONAL  AUTHORITIES. 

Analytical  Investigations  on  the  Theory  of  Gravitation. — Euler,  Theoria  Motuum 
ilanet.  4to,  Berl.  1744.  D'Alembert,  Hist,  et  Mem.  1745,  p.  365:  Recherches 
sur  vla  Precession  des  Equinoxes,  &c.  4to,  Paris,  1749  :  Recherches  sur  le  Systeme 
du  ^onde,  3  vols.  4to,  Paris,  1754-6.  Bailly,  Essai  sur  la  Theorie  des  Sat.  de  Jup. 
4to,  f766.  Silvabelle,  Ph.  Tr.  1754,  p.  385.  Walmsley  on  Perturbations,  ibid. 
1756,  p.  700;  1761,  p.  275.  Laplace  on  the  Secular  Variations  of  the  Planets, 
Hist,  et  Mem.  1772,  i.  343,  H.  67  ;  1784,  p.  1 ;  1787,  p.  267 :  on  the  Theory  of 
Jupiter  and  Saturn,  ibid.  1785,  p.  33;  1786,  p.  201.  Lagrange  on  the  Secular 
Variations  of  the  Nodes  and  Inclinations,  ibid.  1774,  p.  97,  H.  39  ;  1780,  p.  285, 
H.  38.  Dionis  de  Sejour,  Traite  Analyt.  des  Mouvemens  Apparens  des  Corps 
Celestes,  2  vols.  4to,  Paris,  1786-9.  Fuss  on  the  True  Anomaly  N.  A.  Petr.  1785, 
iii.  302.  Cousin,  Ast.  Physique,  4to,  1787.  Schubert  on  the  Obliquity  of  the 
Ecliptic,  ibid.  1792,  x.  433.  Gauss,  Theoria  Motus  Corporum  Cselestum,  4to, 
Hamb.  1809.  Plana,  Memoirs  on  the  Coeff.  of  the  great  Inequality  of  Jupiter  and 
Saturn,  4to,  Turin,  1826-28-29-32.  Theorie  de  la  Mouvement  de  la  Lune,  3  vols. 
4to,  Turin,  1832.  Airy's  Tracts,  Camb.  1831.  Cauchy,  Sur  la  Mec.  Cel.  4to, 
Lilhog.  Lubbock  on  the  Theory  of  the  Moon  and  Perturbations  of  the  Planets, 
1833-6.  Hansen,  Theoria  Motus  Lunse,  4to,  Gotha. 

The  number  of  essays  on  this  subject  is  so  very  great,  and  they  are  scattered  so 
widely  over  the  surface  of  all  the  transactions  of  the  learned  societies  of  Europe,  that 
we  can  do  no  more  than  direct  the  reader  to  consult  their  pages.  He  will  find  many 
valuable  memoirs  in  the  introduction  to  the  different  observations  :  in  the  Effemerides 
of  Cesaris,  Hell,  &c. ;  in  Schumacher's  Astronomic  Nachrichten  ;  in  Crelle's  and 
other  Journals.  The  standard  works  are  Newton's  Principia,  and  the  treatises  given 
under  Lect.  II.  at  the  foot  of  p.  20.  The  subject  is  treated  popularly  in  Airy's  Gra- 
vitation, 12mo,  1834. 


LECTURE   XLIV. 


ON  THE  APPEARANCES  OF  THE  CELESTIAL  BODIES. 

WE  are  next  to  proceed  to  examine  the  sensible  effects  produced  by  those 
motions  which  we  have  first  considered  in  their  simplest  state,  and  after- 
wards with  regard  to  their  causes  and  their  laws.  Many  authors  have 
chosen  rather  to  pursue  a  contrary  method,  and  have  attempted  to  imitate 
the  original  and  gradual  development  of  the  primitive  motions  from  their 
apparent  effects.  But  no  conception  is  sufficiently  clear,  and  no  memory 
sufficiently  strong,  to  comprehend  and  retain  all  these  diversified  appear- 
ances with  accuracy  and  facility,  unless  assisted  by  some  previous  idea  of 
the  real  changes  which  produce  them,  or  by  some  temporary  hypothesis 
respecting  them,  which  may  have  been  of  use  in  its  day  for  the  better 
connection  of  the  phenomena,  although  it  does  not  at  present  deserve  to 
be  employed  for  a  similar  purpose,  in  preference  to  simpler  and  better 
theories,  which  happen  to  be  historically  of  a  later  date. 


416  LECTURE  XLIV. 

The  proper  motions  of  the  fixed  stars,  as  they  are  subjected  to  our 
observation,  undergo  two  modifications ;  the  one  from  the  relative  direc- 
tion of  the  motion,  by  which  it  may  be  more  or  less  concealed  from  our 
view  ;  the  other  from  the  proper  motion  of  the  sun,  and  the  planets  attend- 
ing him.  This  motion  has  indeed  only  been  inferred  from  the  apparent 
motions  of  a  great  number  of  stars,  which  are  either  partly  or  totally 
referrible  to  it,  and  which  could  scarcely  have  agreed  so  correctly  as  they 
do,  if  they  had  arisen  from  the  real  and  separate  motion  of  each  star. 

Among  the  motions  of  the  primary  planets,  that  of  the  earth  itself 
requires  a  principal  share  of  our  attention.  The  apparent  places  or  the 
fixed  stars  are  not  sensibly  affected  by  the  earth's  annual  revolution :  if 
any  of  them  had  been  considerably  less  remote  than  they  are,  it  is  probable 
that  this  motion  would  have  occasioned  a  sensible  annual  parallax,  or  a 
change  of  their  relative  situation,  according  to  the  earth's  place  in  its  orbit 
round  the  sun  ;  for  if  this  orbit,  viewed  from  any  of  the  stars,  subtended  an 
angle  even  of  a  single  second,  the  place  of  that  star  might  be  observed  to 
vary  a  second  at  different  times  of  the  year.  Dr.  Hooke  supposed  at  one 
time  that  he  had  discovered  such  a  parallax,  but  later  observations  have 
not  confirmed  those  of  Dr.  Hooke.  The  stars  have,  however,  a  small  aberra- 
tion, in  consequence  of  the  progressive  motion  of  the  earth  in  its  orbit, 
combined  with  the  limited  velocity  of  light ;  and  the  standard  of  com- 
parison being  the  earth's  axis,  its  nutation  must  also  in  some  degree  affect 
the  apparent  places  of  the  stars.  It  was  in  endeavouring  to  ascertain  the 
annual  parallax,  that  Dr.  Bradley  discovered  both  the  aberration  of  light 
and  the  nutation  of  the  earth's  axis. 

The  revolution  of  the  earth,  in  its  orbit  round  the  sun,  produces  the 
apparent  motion  of  the  sun  among  the  stars,  by  which  he  describes  his 
annual  path  in  the  ecliptic,  with  an  apparent  angular  velocity  equal  to  the 
angular  velocity  of  the  earth,  which  varies  considerably  at  various  times. 
It  required  some  investigation  of  the  magnitudes  and  distances  of  the  hea- 
venly bodies,  to  be  convinced  that  the  sun  and  stars  had  not  in  reality  the 
motion  which  a  superficial  inspection  of  the  heavens  would  naturally  lead 
a  spectator  to  attribute  to  them  ;  but  it  is  at  present  perfectly  unnecessary 
to  enter  into  arguments  to  prove  that  the  true  cause  of  these  apparent 
motions  is  the  real  motion  of  the  earth.  The  effect  of  the  earth's  annual 
revolution  is  the  change  of  place  of  the  sun  among  the  fixed  stars :  it  is 
obvious  that  the  sun  will  always  appear,  when  viewed  from  the  earth,  in 
a  place  diametrically  opposite  to  that  in  which  the  earth  would  appear,  if 
seen  from  the  sun  :  consequently,  since  the  earth  and  sun  remain  in  the 
same  plane,  the  apparent  path  of  the  sun  will  mark  the  same  circle  among 
the  stars  as  the  earth  would  appear  to  describe,  if  viewed  from  the  sun, 
that  is,  the  ecliptic.  If  the  light  of  the  stars  were  much  stronger,  or  that 
of  the  sun  much  weaker,  we  might  see  him  pass  by  the  stars  in  each  part 
of  the  ecliptic,  as  we  do  the  moon  ;  but  we  are  now  obliged  to  observe 
what  stars  are  in  turn  diametrically  opposite  to  the  sun,  or  at  certain  dis- 
tances from  him,  and  thus  we  obtain  a  correct  knowledge  of  his  path. 

The  sun's  apparent  diameter  is  larger  by  one  thirtieth  in  January  than 
in  June ;  of  course  the  earth  is  so  much  nearer  to  the  sun  in  winter  than 


APPEARANCES  OF  THE  CELESTIAL  BODIES.  417 

in  summer  ;  and  since  the  revolving  radius  of  the  earth's  orbit  describes 
equal  areas  in  equal  times,  the  angular  motion  must  increase  as  the  square 
of  the  distance  diminishes,  or  about  twice  as  fast  as  the  distance  itself 
diminishes  ;  so  that  the  whole  variation  of  the  apparent  diurnal  motion  of 
the  sun  is  one  fifteenth  of  his  mean  motion  :  hence,  the  sun  passes  through 
the  winter  half  of  the  ecliptic  in  a  time  7  or  8  days  shorter  than  the  summer 
half.  According  to  the  different  situations  of  the  earth,  with  respect  to  the 
plane  of  the  sun's  equator,  his  rotation  on  his  axis  causes  the  paths  of  his 
spots  to  assume  different  forms  ;  when  the  earth  is  in  that  plane,  the  paths 
appear  straight,  but  in  all  other  situations,  elliptical. 

The  rotation  of  the  earth  on  its  axis  produces  the  still  more  obvious 
vicissitudes  of  day  and  night ;  and,  in  combination  with  its  annual  motion, 
occasions  the  change  of  seasons.  Since  the  axis  remains  always  parallel 
to  itself,  and  is  inclined  to  the  plane  of  the  ecliptic  in  an  angle  of  about 
66f  °,  the  plane  of  the  equator,  which  is  perpendicular  to  the  axis,  must 
pass  twice  in  the  year  through  the  sun.  .  When  this  happens,  the  limit  of 
illumination,  or  the  circle  which  separates  the  dark  portion  of  the  earth 
from  the  enlightened  part,  will  then  pass  through  the  poles  ;  and  as  the 
earth  turns  on  its  axis,  each  point  of  its  surface  must  remain  for  an  equal 
length  of  time  in  light  and  in  darkness.  Hence  the  points  of  the  ecliptic, 
in  which  the  sun  is  situated  at  such  times,  are  called  the  equinoctial  points. 
At  all  other  times,  one  pole  of  the  earth  is  in  the  light,  and  the  other  in  the 
shadow  ;  and  all  the  points  of  the  earth  nearest  to  the  illuminated  pole  have 
their  day  longer  than  their  night,  while  the  parts  on  the  opposite  side  of 
the  equator,  which  are  consequently  nearer  to  the  unenlightened  pole,  have 
their  day  shorter.  The  parts  nearest  to  the  poles  have  also  one  of  their 
days  and  one  of  their  nights  protracted  to  a  period  of  several  common 
days,  or  even  months,  whenever  they  revolve  entirely  within  the  limit  of 
illumination.  (Plate  XXXIV.  Fig.  489.) 

The  sun  appears  to  describe  every  day  a  circle  in  the  heavens,  more  or 
less  distant  from  the  plane  of  the  equator,  according  to  the  actual  situation 
of  the  earth's  axis ;  this  distance  being  always  the  same  as  that  of  the 
poles  from  the  limit  of  illumination,  and  never  exceeding  23£°  ;  so  that 
by  determining  the  sun's  path  at  the  time  of  the  equinoxes,  or  the  apparent 
place  of  the  equinoctial  in  the  heavens,  for  any  given  point  on  the  earth's 
surface,  we  may  represent  the  sun's  path  at  any  other  time  by  a  smaller 
circle  parallel  to  it.  Speaking  however,  more  correctly,  the  sun's  apparent 
path  is  a  spiral,  formed  by  the  continuation  of  these  supposed  circles  into 
each  other. 

The  effect  of  the  centrifugal  force,  derived  from  the  earth's  rotation,  is 
perceptible  at  the  equator,  in  the  retardation  of  the  vibrations  of  pendu- 
lums. The  whole  centrifugal  force  at  the  equator  is  found  by  computation, 
to  be  -g-i-g.  of  the  force  of  gravity  ;  but  the  diminution  of  the  force  of  gravi- 
tation appears,  by  experiments  on  pendulums,  to  be  -^  ;  this  diminution 
being  the  sum  of  the  centrifugal  force,  and  of  the  decrease  of  gravity  on 
account  of  the  oblate  figure  of  the  earth,  the  equatorial  parts  being  further 
removed  from  its  centre,  and  the  force  of  gravity  being  less  powerful  there. 
The  changes  of  inclination  in  the  earth's  axis  are  observable  in  the  places 

2  E 


418  LECTURE  XLIV. 

of  the  equinoctial  points,  and  in  the  situation  of  the  plane  of  the  earth's    ' 
equator  with  respect  to  the  fixed  stars  ;  and  the  secular  diminution  of  the 
obliquity  of  the  ecliptic  is  discoverable  by  a  comparison  of  distant  obser- 
vations on  the  sun's  apparent  motion,  and  on  the  places  of  the  fixed  stars 
with  respect  to  the  ecliptic. 

For  the  phenomena  of  twilight,  we  are  principally  indebted  to  the  light 
reflected  by  the  atmosphere  ;  when  the  sun  is  at  a  certain  distance  only 
below  the  horizon,  he  shines  on  some  part  of  the  air  immediately  visible 
to  us,  which  affords  us  a  portion  of  reflected  light.  The  distance  at  wlych 
this  may  happen,  has  been  variously  estimated,  and  it  is  perhaps  actually 
different  in  different  climates,  being  a  little  greater  in  countries  near  tlio 
poles  than  in  those  which  are  nearer  the  equator  ;  there  is  also  sometimes 
a  secondary  twilight,  when  the  parts  of  the  atmosphere,  which  reflect  a 
faint  light  on  the  earth,  are  themselves  indebted  for  this  light  to  an  earlier 
reflection.  Some  have  assigned  18°  as  the  limit  of  twilight,  and  on  this 
supposition,  allowing  for  refraction,  the  atmosphere  must  be  capable  of 
reflecting  sensible  light  at  the  height  of  about  40  miles.  Mr.  Lambert,*  on 
the  contrary,  makes  the  limit  only  about  6£°.  The  duration  of  twilight 
is  greater  or  less  as  the  sun  moves  more  or  less  obliquely  with  respect  to 
the  horizon  ;  it  is,  therefore,  shortest  near  the  time  of  the  equinoxes,  since 
the  equinoctial  intersects  the  horizon  less  obliquely  than  any  lesser  circle 
parallel  to  it.  (Plate  XXXIV.  Fig.  490,  491.) 

The  revolutions  of  the  primary  planets,  combined  with  that  of  the 
earth,  necessarily  produce  the  various  relations,  in  which  they  are  either 
in  opposition  or  conjunction,  with  respect  to  each  other  or  to  the  sun,  and 
in  which  the  apparent  motion  is  direct  or  retrograde,  or  the  planet  is  sta- 
tionary, according  to  the  directions  and  the  comparative  velocities  of  the 
real  motions.  If  the  earth  were  at  rest,  the  inferior  planets  would  appear 
to  be  stationary  when  they  are  at  the  greatest  elongation  or  angular  dis- 
tance from  the  sun  ;  but,  on  account  of  the  effect  of  the  earth's  motion, 
Venus  is  stationary  at  an  elongation  of  about  29°,  while  her  greatest 
elongation  is  between  45°  and  48°.  The  greatest  elongation  of  Mercury,  in 
each  revolution,  is  from  28|°  to  IT^0,  according  to  the  position  of  his  orbit, 
which  is  very  eccentric.  All  these  appearances  are  precisely  the  same  as 
if  the  sun  actually  revolved  round  the  earth,  and  the  planets  accompanied 
him  in  his  orbit,  performing  at  the  same  time  their  several  revolutions 
round  him  ;  and  the  path  which  would  thus  be  described  in  the  heavens, 
and  which  is  of  a  cycloidal  nature,  represents  correctly  the  true  positions 
of  the  planets  with  respect  to  the  earth.  The  apparent  angular  deviation 
from  the  ecliptic,  or  the  latitude  of  the  planet,  is  also  greater  or  less, 
accordingly  as  the  earth  is  nearer  or  remoter  to  the  planet,  as  well  as 
according  to  the  inclination  of  its  orbit  and  its  distance  from  the  node. 
(Plate  XXXIV.  Fig.  492... 494.) 

The  various  appearances  of  the  illuminated  discs,  especially  of  the  in- 
ferior planets,  and  the  transits  of  these  planets  over  the  sunj  depend  on 

*  Photometria,  §  987.  See  Lacaille  on  the  Length  of  Twilight  at  the  Cape,  Hi?t. 
et  Mem.  1751,  p.  544,  H.  158.  Bergmann,  Schwed.  Abhand.  1760,  p.  237.  Opusc. 
v.  331;  vi.l. 


APPEARANCES  OF  THE  CELESTIAL  BODIES.  41!) 

their  positions  in  their  orhits,  and  on  the  places  of  the  nodes,  with  respect 
to  the  earth.  Jupiter,  Saturn,  and  the  Georgian  planet,  are  so  remote  in 
comparison  of  the  earth's  distance  from  the  sun,  that  they  appear  always 
fully  illuminated.  Venus  is  brightest  at  an  elongation  of  ahout  40°  from 
the  sun,*  in  that  part  of  her  orhit  which  is  nearest  to  the  earth  ;  she  then 
appears  like  the  moon  when  5  days  old,  one  fourth  of  her  disc  being  illu- 
minated ;  she  casts  a  shadow,  and  may  even  be  seen  in  the  day  time  in  our 
climates,  if  she  happens  to  be  far  enough  north  ;  a  circumstance  which 
occurs  once  in  about  8  years.  In  order  that  there  may  be  a  transit  of 
Venus  over  the  sun,  she  must  be  within  the  distance  of  l.J°  of  her  node  at 
the  time  of  conjunction,  otherwise  she  will  pass  either  to  the  north  or  to 
the  south  of  the  sun,  instead  of  being  immediately  interposed  between 
him  and  the  earth. 

The  phases  and  eclipses  of  the  moon  are  very  obviously  owing  to  the 
same  causes  ;t  that  part  of  the  moon  only,  on  which  the  sun  shines,  being 
strongly  illuminated,  although  the  remaining  part  is  faintly  visible,  by 
means  of  the  light  reflected  on  it  from  the  earth  ;  it  is,  therefore,  most 
easily  seen  near  the  time  of  the  new  moon,  when  the  greatest  part  of  the 
earth's  surface  turned  towards  the  moon  is  illuminated.  The  parts  of  the 
moon  which  are  immediately  opposed  to  the  earth,  appear  to  undergo  a 
libration,  or  change  of  situation,  of  two  kinds,  each  amounting  to  about 
7  degrees  ;  the  one  arising  from  the  inequality  of  the  moon's  velocity  in 
her  orbit  at  different  times,  the  other  from  the  inclination  of  the  axis  of 
her  rotation  to  her  orbit ;  besides  these  changes,  the  diurnal  rotation  of  the 
earth  may  produce,  to  a  spectator  situated  on  some  parts  of  it,  a  third 
kind  of  libration,  or  a  change  of  almost  two  degrees  in  the  appearance  of 
the  moon  at  her  rising  and  setting.  (Plate  XXXIV.  Fig.  495.) 

When  the  moon  passes  the  conjunction,  or  becomes  new,  near  to  the 
node,  she  eclipses  the  sun,  and  when  she  is  full,  or  in  opposition  in  similar 
circumstances,  she  herself  enters  the  earth's  shadow.  The  earth's  shadow 
consists  of  two  parts,  the  true  shadow,  within  which  none  of  the  sun's 
surface  is  visible,  and  the  penumbra,  which  is  deprived  of  a  part  only  of 
the  sun's  light ;  the  true  shadow  forms  a  cone  terminating  in  a  point  at  a 
little  more  than  3£  times  the  mean  distance  of  the  moon  ;  the  penumbra, 
on  the  contrary,  constitutes,  together  with  the  shadow,  a  portion  of  a  cone 
diverging  from  the  earth  without  limit ;  but  the  only  effect  of  this  imper- 
fect shadow  is,  that  it  causes  the  beginning  of  a  lunar  eclipse  to  be  incapa- 
ble of  very  precise  determination  ;  for  the  limit  of  the  darkened  part  of 
the  moon,  as  it  appears  in  the  progress  of  the  eclipse,  is  that  of  the  true 
shadow,  very  little  enlarged  by  the  penumbra.  The  true  shadow,  where 
the  moon  crosses  it,  is  about  80  minutes  in  diameter,  as  seen  from  the 
earth,  while  the  moon  herself  is  only  30.  This  shadow  is  not,  however, 
wholly  deprived  of  the  sun's  light ;  for  the  atmospheric  refraction  inflects 
the  light  parsing  nearest  to  the  earth,  in  an  angle  of  66  minutes,  and  causes 
a  great  part  of  the  shadow  to  be  filled  with  light  of  a  ruddy  hue,  by  means 

*  Halley,  Ph.  Tr.  1716,  p.  466.     Kies,  Hist,  et  Mem.  de  Berlin,  1750,  218. 
t  Kastner  on  the  Phases  of  the  Moon,  Com.  Gott.  1780,  Hi.  M.  1. 

2  E2 


420  LECTURE  XLIV. 

of  which  the  moon  remains  still  visible  to  us,  the  cone  of  total  darkness 
extending  to  somewhat  less  than  two  thirds  of  the  moon's  distance.  But 
it  has  sometimes  happened,  probably  from  the  effect  of  clouds  occupying 
the  greatest  part  of  our  atmosphere,  that  the  moon  has  totally  disappeared. 
(Plate  XXXIV.  Fig.  496.) 

When  the  sun  is  eclipsed,  it  depends  on  the  situations  of  the  earth  and 
moon  in  their  orbits,  whether  the  sun  or  moon  subtends  the  greatest  angle 
as  seen  from  the  earth ;  since  at  their  mean  distances  their  apparent  dia- 
meters are  each  about  half  a  degree.  If  the  sun's  apparent  diameter  is  the 
greater,  the  eclipse,  when  the  centres  coincide,  must  be  annular,  the  margin 
of  the  sun's  disc  being  still  visible  in  the  form  of  a  ring  :  when  the  moon's 
apparent  diameter  is  greater  than  the  sun's,  the  eclipse,  if  central,  becomes 
total ;  but  still  a  ring  of  pale  light  is  seen  round  the  disc,*  which  has  been 
attributed  to  the  effect  of  the  sun's  atmosphere,  since  that  of  the  moon  is 
probably  too  inconsiderable  to  produce  the  appearance  ;  a  red  streak  t  is 
also  sometimes  observed  at  the  margin,  before  the  actual  emersion  of  the 
sun.  The  degree  of  darkness  depends  on  the  situation  of  the  place  of  obser- 
vation within  the  shadow,  on  account  of  the  greater  or  less  illumination  of 
the  atmosphere  within  view  :  sometimes  a  considerable  number  of  stars 
may  be  seen  during  a  total  eclipse  of  the  sun. 

It  is  obvious  that,  since  the  earth  is  much  larger  than  the  moon,  the 
whole  shadow  of  the  moon  will  only  pass  over  a  part  of  the  earth's  surface : 
and  that  no  solar  eclipse  can  be  visible  in  the  whole  of  the  hemisphere 
turned  to  the  sun  :  while  lunar  eclipses,  on  the  contrary,  present  the  same 
appearance  wherever  the  moon  is  visible.  In  the  same  manner,  to  a  spec- 
tator on  the  moon,  an  eclipse  of  the  earth,  or  a  transit  of  the  moon's  shadow 
over  the  earth's  disc,  would  have  nearly  the  same  appearance  wherever  he 
might  be  stationed  ;  but  an  eclipse  of  the  sun  by  the  earth  would  be  total 
to  that  part  of  the  moon's  surface  only,  which  to  us  appears  dark  at  the 
same  time.  (Plate  XXXIV.  Fig.  497. .  .499.) 

The  moon's  nodes  arrive  very  nearly  at  the  same  situation  with  respect 
to  the  earth  after  223  lunations,  or  revolutions  of  the  moon,  which  are  per- 
formed in  18  years  of  365  days  each,  15  days,  7  hours,  and  43f  minutes  ; 
so  that  after  a  period  of  about  18  years,  the  series  of  eclipses  recommences 
nearly  in  the  same  order.  This  circumstance  was  observed  by  the  ancients, 
and  is  mentioned  by  Ptolemy  and  by  Pliny.  When  the  full  moon  happens 
within  74°  of  the  node,  there  must  be  a  lunar  eclipse  and  there  may  be  an 
eclipse  at  the  distance  of  13°  from  the  node.  An  eclipse  of  the  sun  may 
happen  when  the  moon  changes,  or  comes  into  conjunction  with  the  sun, 
at  any  distance  within  17l°  of  the  node.  The  mean  number  of  eclipses 
which  occur  in  a  year  is  about  4  ;  and  there  are  sometimes  as  many  as  7  : 
there  must  necessarily  be  two  solar  eclipses,  but  it  is  possible  that  there  may 
not  be  even  one  lunar.  In  speaking  of  the  magnitude  of  the  part  of  the 
sun  or  moon  eclipsed,  it  is  usual  to  consider  the  whole  diameter  as  divided 

*  Duillier,  Ph.  Tr.  1706,  p.  2241.     Halley,  ibid.  1715,  p.  245.     Lahire,  Hist,  et 
M6m.  1715,  p.  161,  H.  47.     Ulloa,  ibid.  1779,  p.  105. 
t  Ph.  Tr.  1706,  p.  2240  ;  1748,  p.  490. 


APPEARANCES  OF  THE  CELESTIAL  BODIES.  421 

into  12  parts,  called  digits,  each  of  which  contains  30  minutes :  thus  if  one 
fifth  part  of  the  diameter  were  dark,  the  extent  of  the  eclipse  would  be 
called  2  digits  12  minutes. 

The  moon  travels  through  the  heavens  with  a  motion  contrary  to  their 
apparent  diurnal  revolution.  Hence  she  rises  and  sets,  on  an  average,  about 
three  quarters  of  an  hour  later  every  day.  The  least  possible  difference 
between  the  times  of  the  moon's  rising  on  two  successive  days,  is,  in  Lon- 
don, 17  minutes ;  and  this  circumstance  occurs  once  in  about  19  years, 
which  is  nearly  the  period  of  the  moon's  nodes  with  respect  to  the  heavens  : 
the  greatest  possible  difference  is  1  hour  17  minutes.  But  it  happens  every 
month  that  the  difference  becomes  greater  and  less  by  turns,  and  when  the 
least  difference  is  at  the  time  of  the  full  moon,  it  is  usually  called  the  har- 
vest moon.  In  parts  nearer  to  the  poles,  the  moon  often  rises  at  the  same 
hour  on  two  succeeding  days. 

The  eclipses  of  the  satellites  of  Jupiter  exhibit  appearances  extremely  in- 
teresting for  their  utility  in  identifying  the  same  instant  of  time  in  different 
places.*  On  account  of  the  small  inclination  of  their  orbits  to  the  plane  of 
Jupiter's  orbit,  the  first  three  never  pass  the  shadow  without  being  plunged 
into  it,  and  the  fourth  but  seldom  ;  while  those  of  Saturn  are  much  less 
frequently  liable  to  be  eclipsed,  on  account  of  their  greater  deviation  from 
the  plane  of  his  ecliptic.  These  satellites  are  also  frequently  hidden  be- 
hind the  body  of  the  planet,  and  this  circumstance  constitutes  an  occul- 
tation  :  hence  it  happens  that  we  can  never  see  both  the  immersion  of  the 
first  satellite  into  the  shadow  of  Jupiter,  and  its  emersion  from  it ;  but 
both  the  immersion  and  emersion  of  the  three  outer  satellites  are  sometimes 
observable.  The  ring  of  Saturn  exhibits  a  variety  of  forms  according  to 
its  angular  position  :  it  disappears  to  common  observation  when  either  its 
edge  or  its  dark  side  is  presented  to  us  :  but  to  Dr.  Herschel's  telescopes  it 
never  becomes  invisible  ;  the  light  reflected  from  the  planet  being  probably 
sufficient  for  illuminating  in  some  measure  the  side  not  exposed  to  the  sun's 
direct  rays. 

The  comets  are  seen  for  a  short  time,  and  are  again  lost  to  our  view  ; 
their  tails  are  in  general  situated  in  the  planes  of  their  orbits,  following 
them  in  their  descent  towards  the  sun,  and  preceding  them  in  their  ascent, 
with  a  slight  degree  of  curvature  in  their  forms ;  they  must  also  appear  to 
us  more  or  less  arched,  and  of  different  extent,  according  to  their  distances, 
and  to  the  angular  position  of  the  orbits  with  respect  to  the  ecliptic. 

The  proportion  of  the  light  afforded  by  the  different  heavenly  bodies  has 
been  variously  estimated  by  various  authors  ;  but  there  is  little  reason  to 
call  in  question  the  accuracy  of  the  experiments  and  calculations  of  Mr. 
Bouguer.  He  states  the  intensity  of  the  moon's  light  as  only  one  three 
hundred  thousandth  of  that  of  the  sun.  These  calculations  have  been  ex- 
tended by  Euler  and  by  Lambert ;  Eulert  considers  the  direct  light  of  the 
sun  as  equal  to  that  of  6560  candles  of  a  moderate  size,  supposed  to  be 
placed  at  the  distance  of  1  foot  from  the  object :  that  of  the  moon  to  the 

•    *  Wargentin,  A  New  Method  of  determining  the  Longitude  from  the  Eel.  of  Jup. 
Sat.  Ph.  Tr.  1766,  p.  278. 
t  Hist,  et  M&n.  de  Berlin,  1750,  p.  280. 


422  LECTURE  XLIV. 

effect  of  1  candle,  at  the  distance  of  7  2  feet ;  the  light  of  Venus  to  a  candle 
at  421  feet,  and  of  Jupiter  to  a  candle  at  1620  feet ;  so  that  the  sun  would 
appear  as  bright  only  as  Jupiter  if  he  were  removed  to  a  distance  131  thou- 
sand times  as  great  as  his  present  distance.  (Plate  XXXIV.  Fig.  500.) 

When  we  reflect  on  the  magnificence  of  the  great  picture  of  the  universe, 
the  outlines  of  which  we  have  been  considering,  we  are  lost  in  the  contem- 
plation of  the  immensity  of  the  prospect,  and  returning  to  the  comparatively 
diminutive  proportions  of  our  individual  persons,  and  of  all  the  objects  with 
which  we  are  most  immediately  connected,  we  cannot  help  feeling  our  own 
insignificance  in  the  material  world.  The  mind,  notwithstanding,  endea- 
vours to  raise  itself  above  the  restraints  which  nature  has  imposed  on  the 
body,  and  to  penetrate  the  abyss  of  space  in  search  of  congenial  existences. 
But  in  speculations  of  this  kind,  reason  and  argument  must  give  way  to 
conjecture  and  imagination  ;  and  thus,  from  natural  philosophy,  our  ima- 
ginations wander  into  the  regions  of  poetry  ;  and  it  must  be  confessed  that 
the  union  of  poetical  embellishment  with  natural  philosophy  is  seldom  very 
happy.  A  poet  has  few  facts  to  communicate,  and  these  he  wishes  to 
expand  and  diversify ;  he  dwells  on  a  favourite  idea,  and  repeats  it  in  a 
thousand  emblematical  forms  ;  his  object  is  to  say  a  little,  very  elegantly, 
in  very  circuitous,  and  somewhat  obscure  terms.  But  the  information, 
which  the  natural  philosopher  has  to  impart,  is  too  copious  to  allow  of  pro- 
lixity in  its  detail ;  his  subjects  are  too  intricate  to  be  compatible  with 
digressions  after  amusement,  which,  besides  interrupting,  are  too  likely  to 
enervate  the  mind  ;  and  if  he  is  ever  fortunate  enough  to  entertain,  it 
must  be  by  gratifying  the  love  of  truth,  and  satisfying  the  thirst  after 
knowledge.  We  have,  however,  a  favourable  specimen  of  highly  orna- 
mented philosophy  in  Fontenelle's  Plurality  of  Worlds  ;*  a  work  which 
must  be  allowed  to  convey  much  information  in  a  very  interesting  form, 
although  somewhat  tinctured  with  a  certain  frivolity  which  is  not  always 
agreeable,  We  need  not  attempt  to  accompany  all  the  flights  of  Fonte- 
nelle's imagination  ;  it  will  be  sufficient  for  our  purpose  to  pursue  his 
ideas  in  a  simple  enumeration  of  the  most  remarkable  phenomena,  that 
would  occur  to  a  spectator  placed  on  each  of  the  planets. 

Of  Mercury  we  know  little  except  the  length  of  his  year,  which  is 
shorter  than  three  of  our  months.  Supposing  all  our  heat  to  come  from 
the  sun,  it  is  probable  that  the  mean  heat  on  Mercury  is  above  that  of 
boiling  quicksilver ;  and  it  is  scarcely  possible  that  there  should  be  any 
point  about  his  poles  where  water  would  not  boil.  The  sun's  diameter 
would  appear,  if  viewed  from  Mercury,  more  than  twice  as  great  as  to  us 
on  the  earth. 

Venus  must  have  a  climate  far  more  temperate  than  Mercury,  yet  much 
too  torrid  for  the  existence  of  animals  or  vegetables,  except  in  some  cir- 
cumpolar  parts  ;  her  magnitude  and  diurnal  rotation  differ  but  little  from 
those  of  the  earth,  and  her  year  is  only  one  third  shorter  :  so  that  her  sea- 
sons, and  her  day  and  night,  must  greatly  resemble  ours.  The  earth,  when 
in  opposition  to  the  sun,  must  be  about  four  times  as  bright  as  Venus  ever 
appears  to  us,  and  must,  therefore,  always  cast  a  shadow  ;  it  must  be  fre- 
*  12mo,  1686 ;  par  Lalande,  1800. 


APPEARANCES  OF  THE  CELESTIAL  BODIES.  423 

quently,  and  perhaps  generally,  visible  in  the  day  ;  and  together  with  the 
moon,  must  exhibit  a  very  interesting  object.  The  atmosphere  of  Venus  is 
supposed  to  be  nearly  like  our  own,  or  somewhat  more  rare. 

The  inhabitants  of  the  moon,  if  the  moon  is  inhabited,  must  be  capable 
of  living  with  very  little  air,  and  less  water  :  there  is  reason  to  think  their 
atmosphere  less  than  a  mile  high,  and  it  is  never  clouded  :  so  that  the  sun 
must  shine  without  intermission  for  a  whole  fortnight  on  the  same  spot, 
without  having  his  heat  moderated  by  the  interposition  of  air,  or  by  the 
evaporation  of  moisture.  The  want  of  water  in  the  moon  is  not,  as  some 
have  supposed,  the  necessary  consequence  of  the  want  of  an  atmosphere  ; 
but  it  is  inferred  partly  from  the  total  absence  of  clouds,  and  partly  from  the 
irregular  appearance  of  the  margin  of  the  moon,  as  seen  in  a  solar  eclipse : 
no  part  of  it  being  terminated  by  a  line  sufficiently  regular  to  allow  us  to 
suppose  it  the  surface  of  a  fluid.  The  earth  must  always  appear  to  occupy 
nearly  the  same  part  of  the  sky,  or  rather  to  describe  a  small  oval  orbit  round 
a  particular  point,  exposing  a  surface  13  times  as  great  as  that  of  the  moon 
appears  to  us.  This  large  surface,  suspended,  with  phases  continually 
changing,  like  those  of  the  moon,  must  afford,  especially  when  viewed  with 
a  telescope,  an  excellent  timepiece  ;  the  continents  and  seas  coming  gradu- 
ally and  regularly  into  view,  and  affording  a  variety  equally  pleasing  and 
useful.  To  us  such  a  timepiece  would  be  of  inestimable  value,  as  it  would 
afford  us  an  easy  method  of  discovering  the  longitude  of  a  place,  by  com- 
paring its  motion  with  the  solar  time:  but  in  the  moon,  the  relative 
position  of  the  earth  and  sun,  or  of  the  earth  and  stars  only,  would  be 
sufficient  for  determining  the  situation  of  any  place  in  sight  of  the  earth  ; 
if,  however,  there  are  no  seas  and  no  navigation,  astronomical  observations 
of  this  kind  would  be  of  very  little  utility.  The  assistance  of  the  earth's 
phases  in  the  measurement  of  time  might,  however,  still  be  very  useful  for 
many  purposes,  to  the  inhabitants  of  the  nearer  half  of  the  moon ;  and 
probably  the  remoter  part  is  much  deserted,  for  in  their  long  night  of  half 
a  month,  they  must  be  extremely  in  want  of  the  light  reflected  from  the 
earth,  unless  the  inhabitants  have  the  faculty  of  sleeping  through  the  whole 
of  their  dark  fortnight.  The  surface  of  the  moon  appears  to  be  very  rocky 
and  barren,  and  liable  to  frequent  disturbances  from  volcanos.  These 
have  been  supposed  to  project  some  of  their  contents  within  the  reach  of  the 
earth's  attraction,  which  they  might  easily  do,  if  they  could  throw  them  out 
with  a  velocity  of  about  eight  thousand  feet  in  a  second,  which  is  only  four 
times  as  great  as  that  of  a  cannon  ball :  and  these  stones,  falling  through 
the  atmosphere,  might  very  possibly  generate  so  much  heat,  by  compressing 
the  air,  as  to  cause  the  appearance  of  fiery  meteors,  and  to  fall  in  a  state  of 
ignition.  The  appearance  of  the  moon,  as  viewed  through  a  good  telescope, 
is  extremely  well  imitated  by  Mr.  Russel's  lunar  globe,  which  is  also  capa- 
ble of  exhibiting,  with  great  accuracy,  the  changes  produced  by  its  libra- 
tions. 

The  climate  of  Mars  is  as  much  colder  than  ours,  as  that  of  Venus  is 
.warmer ;  in  other  respects  there  is  no  very  striking  difference  :  the  incli- 
nation of  his  axis  to  his  ecliptic  being  nearly  the  same  as  that  of  the  earth's 
axis,  the  changes  of  seasons  must  be  nearly  like  our  own.  Dr.  Herschel 


424  LECTURE  XLIV. 

has  observed  a  constant  appearance  of  two  bright  spots  or  circles  near  the 
poles  of  Mars,  which  he  attributes  to  the  ice  and  snow  perpetually  sur- 
rounding them.  It  is  not,  however,  probable  that  water  could  remain  fluid 
in  any  part  of  Mars,  and  even  quicksilver  and  alcohol  would,  perhaps,  be 
frozen  in  his  temperate  climates.  It  is  pretty  certain  that  Mars  has  an 
atmosphere,  and  his  dark  spots  seem  to  be  occasioned  by  clouds :  this 
atmosphere  may,  perhaps,  also  be  the  cause  of  the  ruddy  hue  of  his 
light. 

It  appears  to  be  doubtful,  whether  either  of  the  three  little  planets  newly 
discovered  can  be  sufficiently  solid,  to  give  a  firm  footing  to  any  material 
beings  :  we  should  probably  weigh  only  a  few  pounds  each  if  transported 
there.  According  to  Dr.  Herschel's  opinion,  neither  Ceres  nor  Pallas  is 
much  larger  than  a  good  Scotch  estate,  although  they  must,  sometimes, 
appear  to  each  other  as  planets  of  a  most  respectable  size.  The  light 
reflected  from  Ceres  is  of  a  more  ruddy  hue  than  that  of  Pallas  :  both  of 
these  planets  are  attended  by  more  or  less  of  a  nebulosity,  proceeding,  per- 
haps, from  copious  atmospheres ;  and  in  this  respect,  as  well  as  in  the  great 
inclination  of  their  orbits,  they  appear  to  have  some  affinity  to  comets. 
It  is  tolerably  certain  that  neither  of  them  is  200  miles  in  diameter  ;  and 
Juno  is  also  probably  about  the  same  size. 

It  is  obvious  that  the  most  striking  features  of  the  heavens,  when  con- 
templated from  Jupiter,  would  be  the  diversified  positions  and  combina- 
tions of  his  satellites  :  their  light  must  be  faint,  but  yet  of  service  ;  and  to 
a  traveller  on  the  surface  of  this  vast  globe  they  must  afford  useful  infor- 
mation, as  well  with  respect  to  time  as  to  place.  Our  little  earth  must 
probably  be  always  invisible  to  a  spectator  situated  on  Jupiter,  on  account 
of  its  apparent  proximity  to  the  sun,  in  the  same  manner  as  a  planet  at 
half  the  distance  of  Mercury  would  be  invisible  to  us.  The  year  of  Jupiter 
must  contain  nearly  ten  thousand  of  his  days,  and  that  of  Saturn  almost 
thirty  thousand  Saturnian  days.  Besides  the  vicissitudes  of  the  seven 
satellites  revolving  round  Saturn,  his  ring  must  afford,  in  different  parts  of 
his  surface,  very  diversified  appearances  of  magnificent  luminous  archer, 
stretched  across  the  heavens,  especially  in  that  hemisphere  which  is  on  the 
same  side  of  the  ring  with  the  sun. 

From  the  Georgian  planet  the  sun  must  be  seen  but  as  a  little  star,  not 
one  hundred  and  fiftieth  part  as  bright  as  he  appears  to  us.  The  axis  of 
this  planet  being  probably  near  to  the  plane  of  its  ecliptic,  it  must  be 
directed  twice  in  the  year  towards  the  sun,  and  the  limit  of  illumination 
must  approach  to  the  equator,  so  that  almost  every  place  on  his  surface 
must  sometimes  remain,  for  a  great  number  of  diurnal  revolutions,  in  light 
and  in  darkness  ;  the  most  moderate  climates  having  one  night,  in  their 
long  year,  equal  in  duration  at  least  to  several  of  our  years  :  and  it  must  be 
confessed  that  this  planet  would  afford  but  a  comfortless  habitation  to  those 
accustomed  to  our  summer  sunshine,  even  if  it  were  possible  to  colonise  it. 
(Plate  XXXIV.  Fig.  501.) 

On  the  whole,  we  are  tempted,  from  an  almost  irresistible  analogy,  to  con-, 
elude  that  the  planets  are  all  in  some  manner  or  other  inhabited  ;  but  at  the 
same  time  we  can  scarcely  suppose  that  a  single  species  of  terrestrial  animals 


ON  PRACTICAL  ASTRONOMY.  425 

or  even  vegetables  could  exist  in  any  of  them  ;  their  minerals  may,  per- 
haps, resemble  ours,  and  if  the  stones  which  Mr.  Howard  has  analyzed  are 
really  lunar  productions,  we  have  proofs  that  the  moon  at  least  contains 
some  substances  resembling  those  which  compose  the  earth  ;  but  the  seas 
and  rivers  of  the  other  planets  must  consist  of  some  fluid  unknown  to  us, 
since  almost  all  our  liquids  would  either  be  frozen,  or  converted  into 
vapour,  in  any  of  them. 


LECT.  XLIV.— ADDITIONAL  AUTHORITIES. 

Librations  of  the  Moon. — Cassini,  Hist,  et  Mem.  1721,  p.  168,  H.  53.  Lalande, 
ibid.  1764,  p.  555,  H.  112.  Sejour,  ibid.  1776. 

Eclipses. — Hevelius,  Ph.  Tr.  i.  369 ;  v.  2023.  Louville's  Geometrical  Mode  of 
calculating  Eclipses,  Hist,  et  Mem.  1724,  p.  63,  H.  74.  Gersten's  Meth.  Ph.  Tr. 
1744,  p.  22.  Lalande  on  the  Effect  of  Ellipticity,  Hist,  et  Mem.  1756,  p.  364, 
H.  96  ;  1763,  p.  413.  Lambert,  Table  Ecliptique,  12mo,  Berlin,  1765.  Boscovich 
de  Solis  et  Lunae  Defectibus,  4to,  Lond.  1760.  Jeaurat  on  the  Projection  of  Eclipses, 
Mem.  des  Sav.  Etr.  iv.  p.  818.  Goudin,  Mem.  sur  les  Eclipses  du  Soleil,  4to, 
1803.  Lubbock,  Elementary  Treatise  on  the  Computation  of  Eclipses,  1835. 


LECTURE    XLV. 


ON  PRACTICAL  ASTRONOMY. 

IT  is  generally  most  convenient  in  practical  astronomy  to  neglect  the  real, 
and  to  consider  only  the  apparent  motions  of  the  sun,  the  stars,  and  planets, 
for  the  visible  effects  must  be  precisely  the  same,  whether  the  sun  or  the 
earth  perform  a  revolution  in  the  plane  of  the  ecliptic,  and  whether  the 
earth  actually  move  on  its  axis,  or  the  whole  of  the  celestial  bodies  move 
round  it  in  a  day.  We  may,  therefore,  suppose  the  sun  to  move,  as  he 
appears  to  do,  from  west  to  east  in  the  ecliptic,  so  as  to  advance  almost  a 
degree  in  24  hours,  and  from  east  to  west,  together  with  all  the  stars  and 
planets,  so  as  to  perform  a  whole  revolution  in  a  day.  Speaking  more 
correctly,  the  sun  appears  to  describe,  in  every  sidereal  day,  a  spiral,  which 
differs  a  little  from  a  circle,  and  is  also  about  a  degree  shorter,  so  that  about 
four  minutes  more  are  required  for  the  return  of  the  sun  to  the  same  part 
of  the  heavens,  and  the  completion  of  a  solar  day. 

In  order  to  determine  the  place  of  any  point  in  the  heavens,  it  is  usual  to 
compare  its  situation  either  with  the  plane  of  the  earth's  equator,  or  with  the 
ecliptic  ;  its  angular  distance  from  the  equator  being  called  its  declination, 
and  from  the  ecliptic,  its  latitude  ;  these  distances  must  be  measured  in 
planes  perpendicular  to  those  of  the  equator  or  ecliptic,  and  the  distances  of 
.these  planes  from  their  intersection,  or  from  the  equinoctial  point  in  Aries, 
are  called  respectively  the  right  ascension  and  the  longitude  of  the  point  to 
be  described.  For  the  stars,  the  decimation  and  right  ascension  are  most 


426  LECTURE  XLV. 

usually  laid  down  ;  but  with  respect  to  the  sun  and  the  planets,  performing 
their  revolutions  in  or  near  the  ecliptic,  it  is  most  convenient  to  calculate 
their  latitude  and  longitude. 

The  plane  passing  through  the  earth's  axis  and  the  place  of  a  spectator  is 
the  plane  of  the  meridian  of  that  place ;  and  a  plane  touching  the  earth 
in  any  point  is  its  horizon.  With  respect  to  the  appearances  of  the  fixed 
stars,  this  plane  may  he  considered  as  passing  through  the  earth's  centre 
in  the  same  direction  :  and  the  difference  is  scarcely  sensible  with  respect 
to  the  sun  and  the  primary  planets ;  but  in  observations  of  the  moon's 
place,  these  planes  must  be  carefully  distinguished.  (Plate  XXXV.  Fig. 
502.) 

The  instruments  requisite  for  astronomical  observations  are  principally 
referrible  to  geometrical  or  to  optical  apparatus,  or  to  the  measurement  of 
time.  Particular  constructions  and  combinations  are,  however,  necessary 
for  the  accommodation  of  quadrants,  graduated  circles,  telescopes,  and 
transit  instruments,  to  the  uses  of  observatories  ;  and  astronomical  observa- 
tions are  as  necessary  to  the  correct  determination  of  time,  as  artificial 
timekeepers  are  useful  for  other  astronomical  purposes. 

The  most  accurate  standard  of  time  is  the  diurnal  rotation  of  the  earth 
on  its  axis,  as  ascertained  by  its  situation  with  respect  to  the  fixed  stars. 
The  time  elapsing  between  two  successive  passages  of  any  star  over  the 
same  meridian,  which  constitutes  a  sidereal  day,  may  be  measured  with 
great  precision  ;  and  the  star  may  for  this  purpose  be  observed,  with  almost 
equal  accuracy,  in  any  other  situation,  and  sometimes  with  greater  con- 
venience. The  length  of  the  sidereal  day  may  be  considered  as  perfectly 
constant,  the  inequalities  arising  from  the  aberration  of  light,  and  from 
the  nutation  of  the  earth's  axis,  being  too  small  to  be  easily  discovered  ; 
but  the  correction  for  the  aberration  may  be  applied  when  it  is  neces- 
sary. For  observations  of  this  kind,  it  is  usual  to  have  a  clock  adjusted 
to  sidereal  time,  which  not  only  admits  of  a  more  ready  comparison  with 
the  transits  or  passages  of  any  one  star  over  the  meridian,  but,  by  the 
difference  of  the  times  of  any  two  transits,  shows  at  once  the  difference 
of  right  ascension  of  the  stars  or  planets,  expressed  in  time  instead  of 
degrees. 

The  solar  days  are  not  only  about  four  minutes  longer  than  the  sidereal 
days,  but  they  are  also  unequal  among  themselves ;  and  this  inequality 
arises  from  two  causes ;  the  one,  that  even  if  the  sun's  motion  in  the 
ecliptic  were  uniform,  his  diurnal  changes  of  right  ascension  would  be 
different  at  different  times,  and  the  difference  between  his  path  in  every 
sidereal  day,  and  a  whole  circle,  depending  on  this  change,  would  also 
vary ;  the  other  that  the  sun's  motion  in  the  ecliptic  is  actually  variable, 
consequently  the  diurnal  change  of  right  ascension  is  liable  to  a  double 
inequality.  Hence  it  happens  that  the  solar  time  agrees  at  four  instants 
in  the  year  only  with  the  mean  time,  derived  from  supposing  the  whole 
365  days  to  be  divided  into  as  many  equal  parts ;  the  difference  is  called 
the  equation  of  time,  and  amounts  sometimes  to  as  much  as  16  minutes. 
The  term  equation  is  commonly  applied  in  astronomy  to  any  small  quan- 
tity, which  is  to  be  added  to,  or  subtracted  from,  another  quantity ;  thus 


ON  PRACTICAL  ASTRONOMY.  427 

it  is  usual,  in  calculating  the  place  of  a  planet,  to  find  from  the  tables  of 
its  motion,  the  mean  place,  in  which  it  would  be  found  if  its  orbit  were 
circular,  and  thence  to  derive  the  true  place,  by  means  of  various  correc- 
tions called  equations.  In  France  the  solar  time  is  considered  as  the  true 
time,  and  is  used  for  all  civil  purposes,  so  that  the  clocks  are  some- 
times embarrassed  with  a  complicated  apparatus,  calculated  for  imitating 
the  inequalities  of  the  actual  apparent  motion  of  the  sun.  (Plate  XXXV. 
Fig.  503.) 

The  art  of  dialling  consists  principally  in  projecting,  on  a  given  surface, 
such  lines  as  will  coincide  with  the  shadow  of  an  index  or  gnomon  parallel 
to  the  earth's  axis,  at  intervals  corresponding  to  the  different  hours  of  the 
day  :  so  that  nothing  more  is  necessary  for  the  construction  of  a  dial,  than 
to  determine  the  intersections  of  the  surface  on  which  the  dial  is  to  be 
constructed,  writh  planes  passing  through  the  edge  of  the  gnomon,  and 
situated  at  equal  angular  distances  from  each  other :  thus,  supposing  the 
plane  of  the  dial  perpendicular  to  the  gnomon,  and  parallel  to  the  equinoc- 
tial, the  hour  lines  of  the  dial  will  be  at  equal  distances  from  each  other  ; 
but  in  other  cases  their  distances  will  be  unequal,  and  must  be  determined 
either  by  calculation  or  by  construction.  A  point  may  also  be  used  as  a 
gnomon,  as  well  as  a  line ;  but  in  this  case  the  hour  lines  must  cover  a 
larger  portion  of  the  surface,  in  order  that  the  shadow  of  the  point  may 
always  fall  among  them.  (Plate  XXXV.  Fig.  504... 506.) 

The  changes  of  the  seasons  depend  on  the  return  of  the  sun  to  the  same 
position  with  respect  to  the  equator,  or  on  the  length  of  the  tropical  year, 
so  called  from  the  tropics,  which  are  circles  supposed  to  be  parallel  to  the 
equator,  and  between  which  the  sun  travels  continually  backwards  and 
forwards,  appearing  to  remain  for  some  time,  when  he  is  near  them,  with 
very  little  change  of  declination ;  whence  the  time  when  the  sun  touches 
either  tropic  is  called  the  solstice.  The  vicissitudes  of  light  and  darkness 
depending  also  on  the  solar  day,  it  is  necessary,  for  the  regulation  of  the 
civil  calendar,  to  establish  the  proportion  between  the  periods  of  the  solar 
day  and  the  tropical  year  ;  and  since  the  tropical  year  exceeds  the  time  of 
365  days,  by  5  hours,  48  minutes,  and  48  seconds,  it  is  usual  to  add  to  the 
common  year  an  intercalary  day  once  in  about  four  years.  The  ancient 
Egyptians  reckoned  only  365  days  in  a  year,  and  their  nominal  new  year 
arrived  continually  earlier  and  earlier,  so  that  after  1507  of  their  years,  it 
would  have  happened  successively  on  each  of  the  365  days,  and  returned 
to  the  original  place  :  the  same  mode  of  computation  was  also  adopted  by 
the  Greek  astronomers.  The  Romans  inserted  intercalary  days,  at  first 
without  much  regularity,  according  to  the  direction  of  their  augurs,  until 
the  time  of  Julius  Caesar ;  who,  observing  that  the  year  was  almost  6  hours 
longer  than  365  days,  added  a  day  every  fourth  year  to  the  calendar,  by 
reckoning  twice  the  day  in  February  called  sexto  calendas  Martias,  whence 
this  year  of  366  days  was  denominated  a  bissextile  year.  The  new  moon 
immediately  following  the  winter  solstice,  in  the  707th  year  of  Rome,  was 
.made  the  first  of  January  of  the  first  year  of  Caesar ;  the  25th  of  December 
in  his  45th  year  is  considered  as  the  date  of  the  Nativity  of  Christ,  and 
Caesar's  46th  year  is  reckoned  the  first  of  our  era.  The  preceding  year  is 


428  LECTURE  XLV. 

commonly  called  by  astronomers  the  year  0,  but  by  chronologists  the  year 
1  before  Christ.  The  correction  introduced  by  Caesar  was,  however,  too 
great,  the  error  being  exactly  7  days  in  900  years  ;  so  that  in  1582  it 
amounted  to  about  12  days.  This  error  was  not  wholly  removed  by  Pope 
Gregory,  who  reformed  the  calendar  ;  he  omitted  10  days  only  of  the  usual 
reckoning,  in  order  to  bring  back  the  course  of  the  moveable  feasts  to  the 
same  state,  in  which  they  had  been  established  by  the  Nicene  council,  in 
the  fourth  century.  He  determined  at  the  same  time  that  the  last  year 
of  every  century  should  be  passed  without  an  intercalary  day,  excepting 
that  of  every  fourth  century,  which  was  still  to  be  bissextile.  Thus  every 
year  divisible  by  four,  without  a  remainder,  is  in  general  a  bissextile  or 
leap  year,  but  the  last  year  of  every  century  must  be  a  common  year, 
unless  the  number  of  the  century  be  divisible  by  4 ;  the  year  1800  being 
a  common  year,  and  2000  a  bissextile.  In  this  manner  27  Julian  bissex- 
tiles are  omitted  in  3600  years,  while  the  true  length  of  the  year  would 
require  the  omission  of  28 ;  but  so  small  a  difference  can  be  of  no  material 
consequence.  The  Persians  had  introduced  into  their  calendar,  in  the 
llth  century,  an  intercalation  still  more  accurate ;  they  make  8  bissex- 
tiles only  every  33  years,  reckoning  four  common  years  together  instead 
of  three,  at  the  end  of  this  period,  so  that  in  132  years  they  have  32  leap 
years  instead  of  33 ;  and  the  error  is  only  a  day  in  about  five  thousand 
years.  If  any  change  in  the  Gregorian  calendar  were  thought  necessary, 
it  would  be  easy  to  make  the  last  year  of  every  fourth  and  fifth  century 
alternately  a  bissextile,  and  this  correction  would  be  quite  as  accurate  as 
it  is  possible  for  our  calculations  to  render  it.  The  adoption  of  the 
Gregorian  calendar  in  this  country  was  for  some  time  delayed  by  religious 
prejudices ;  one  of  the  best-founded  objections  to  it  was,  that  2  days  of 
the  real  error  was  still  unconnected ;  but  better  arguments  at  last  over- 
came these  difficulties,  and  the  new  style  was  introduced  on  the  14  Sep- 
tember 1754,  which  would  have  been  called,  according  to  the  old  style,  the 
third. 

Any  tolerable  approximation  of  this  kind,  when  once  generally  estab- 
lished, appears  to  be  more  eligible  than  the  mode  which  was  lately  adopted 
in  France,  where  the  republican  year  began  at  the  instant  of  the  midnight 
preceding  the  sun's  arrival  at  the  autumnal  equinox.  Mr.  Lalande  very  judi- 
ciously observes,  that  there  are  several  years,  in  which  the  sun  will  pass  the 
equinox  so  near  to  midnight,  that  it  is  not  at  present  in  the  power  of  calcu- 
lation to  determine  on  what  day  the  republican  year  ought  to  begin  ;  and 
perhaps  these  arguments  have  co-operated  with  others  in  facilitating  the 
restoration  of  the  ancient  calendar. 

The  revolutions  of  the  sun  and  moon  are  not  very  obviously  commen- 
surable, the  solar  year  containing  12  lunations  and  almost  11  days ;  but 
Meto  discovered,  more  than  2000  years  ago,  that  19  solar  years  contain 
exactly  235  lunations  ;  and  this  determination  is  so  accurate,  that  it  makes 
the  lunar  month  only  about  half  a  minute  too  long.  Hence  it  happens, 
that  in  every  period  of  19  years,  the  moon's  age  is  the  same  on  the  same 
day  of  the  year.  The  number  of  the  year,  in  the  Metonic  cycle,  is  called 
the  golden  number,  the  calendar  of  Meto  having  been  ordered,  at  the  cele- 


ON  PRACTICAL  ASTRONOMY.  429 

bration  of  the  Olympic  games,  to  be  engraved  in  letters  of  gold  on  a  pillar 
of  marble.  At  present,  if  we  add  1  to  the  number  of  the  year,  and  divide 
it  by  19,  the  remainder  will  be  the  golden  number ;  thus,  for  1806,  the 
golden  number  is  2.  If  we  subtract  1  from  the  golden  number,  then  mul- 
tiply by  11,  and  divide  by  30,  the  remainder  will  be  the  epact,  which  is  the 
moon's  age  on  the  first  of  January,  without  any  material  error ;  thus,  for 
1806,  the  epact  is  11,  and  the  moon  is  actually  11  days  old  on  the  first  of 
January. 

From  a  combination  of  chronological  periods  of  various  kinds,  Scaliger 
imagined  the  Julian  period,  as  an  epoch  to  which  all  past  events  might 
with  convenience  be  referred,  beginning  4713  years  before  the  birth  of 
Christ.  Laplace  proposes,  as  a  universal  epoch,  the  time  when  the  earth's 
apogee  was  at  right  angles  with  its  nodes,  in  the  year  1250,  calling  the 
vernal  equinox  of  that  year  the  first  day  of  the  first  year.  But  the  fewer 
changes  of  this  kind  that  we  make,  the  less  confusion  we  introduce  into  our 
chronology.  The  astronomical  year  begins  at  noon  on  the  31st  of  Decem- 
ber, and  the  date  of  an  observation  expresses  the  days  and  hours  actually 
elapsed  from  that  time.  Thus,  the  first  of  January,  1806,  at  10  in  the 
morning,  would  be  called,  in  astronomical  language,  1805  December  31 
days  22  hours,  or  more  properly  1806  January  0  day  22  hours.* 

For  ascertaining,  by  immediate  measurement,  the  position  of  any  of  the 
heavenly  bodies,  it  is  usual  to  determine  its  meridian  altitude  by  quadrants, 
and  the  time  of  its  passing  the  meridian  by  transit  instruments.  The  large 
quadrants,  generally  used  for  this  purpose  in  observatories,  are  fixed  to 
vertical  walls,  in  order  to  give  them  greater  stability,  and  are  thence 
called  mural  quadrants ;  sometimes  a  smaller  portion  of  an  arc  only  is 
adapted  for  observations  near  the  zenith,  under  the  name  of  a  zenith  sector. 
A  transit  instrument  is  a  telescope  so  fixed  on  an  axis  as  to  remain  always 
in  the  plane  of  the  meridian  :  the  axis  being  perpendicular  to  this  plane, 
and  consequently  in  a  horizontal  position,  and  directed  east  and  west. 
Those  who  are  in  the  constant  habit  of  observing  with  attention,  can  esti- 
mate, in  this  manner,  the  precise  time  of  the  passage  of  a  celestial  object 
over  the  meridian ;  without  an  error  of  the  tenth  of  a  second,  so  that  its 
angular  right  ascension  may  be  thus  determined  within  about  a  second  of 
the  truth.  A  very  convenient  mode  of  adjusting  a  transit  instrument  is  to 
direct  it  to  the  north  polar  star,  at  the  same  time  that  the  last  of  the  three 
horses  in  the  wain  is  perpendicularly  above  or  below  it :  this  process,  in 
1751,  gave  precisely  the  true  meridian  ;  but  since  that  time,  the  pre- 
cession of  the  equinoxes,  which  produces  a  slight  change  in  the  places 
of  the  stars,  has  made  it  necessary  to  wait  1  minute  13£  seconds  for 
every  ten  years  that  have  elapsed.  Thus,  in  1806,  if  we  wait  6£ 
minutes,  the  pole  star  will  then  be  precisely  in  the  meridian,  and  will 
serve  for  the  correct  adjustment  of  the  instrument.  (Plate  XXXV.  Fig. 
507-..  510.) 

*  On  the  Calendar,  consult  Sauveur,  Hist,  et  Mem.  1732,  H.  94.     Lord  Mac- 
'  clesfield,  Ph.  Tr.  1750,  p.  417.     Lalande,  Hist,  et  Mem.  1789,  p.  95.     Halma,  Sur 
la  Reduction  des  Annees  des  Anciens  a  la  Forme  des  Notres,  4to,  1819.     Sur  les 
Mois  Macedoniens,  4to,  1820.     Encyc.  Brit.  art.  Calendar. 


430  LECTURE  XLV. 

The  quadrant  in  most  common  use,  especially  for  nautical  observations, 
was  first  proposed  by  Newton,*  but  improved,  or  perhaps  reinvented,  by 
Hadley.t  Its  operation  depends  on  the  effect  of  two  mirrors  which  bring 
both  the  objects,  of  which  the  angular  distance  is  to  be  measured,  at  once 
into  the  field  of  view  ;  and  the  inclination  of  the  speculums  by  which  this 
is  performed  serves  to  determine  the  angle.  The  ray  proceeding  from  one 
of  the  objects  is  made  to  coincide,  after  two  reflections,  with  the  ray  coming 
immediately  from  the  other,  and  since  the  inclination  of  the  reflecting  sur- 
faces is  then  half  the  angular  distance  of  the  objects,  this  inclination  is  read 
off  on  a  scale  in  which  every  actual  degree  represents  two  degrees  of 
angular  distance,  and  is  marked  accordingly.  There  is  also  a  second  fixed 
speculum,  placed  at  right  angles  to  the  moveable  one,  when  in  its  remotest 
situation,  which  then  produces  a  deviation  of  two  right  angles  in  the  ap- 
parent place  of  one  of  the  objects,  and  which  enables  us,  by  moving  the 
index,  to  measure  any  angle  between  180°  and  90°.  This  operation  is 
called  the  back  observation ;  it  is  however  seldom  employed,  on  account  of 
the  difficulty  of  adjusting  the  speculum  for  it  with  accuracy.  The  reflect- 
ing instrument  originally  invented  by  Hooke  was  arranged  in  a  manner 
somewhat  different.  (Plate  XXXV.  Fig.  511.) 

From  the  meridian  altitude  of  any  point,  it  is  easy,  when  the  elevation  of 
the  pole  is  known,  to  deduce  its  declination  ;  and  its  right  ascension  may 
be  found  from  the  time  of  its  passage  over  the  meridian  after  that  of  the 
equinoctial  point,  allowing  15  degrees  for  each  sidereal  hour.  (Plate 
XXXV.  Fig.  512.) 

In  all  astronomical  observations  it  is  necessary  to  make  proper  cor- 
rections, according  to  the  rules  of  optics,  for  the  effects  of  atmospherical 
refraction  ;  and  also,  in  observations  on  the  moon  more  especially,  for  those 
of  parallax,  or  the  difference  of  the  apparent  place  of  the  luminary  with 
respect  to  the  earth's  centre,  and  to  the  place  of  the  spectator,  which  is 
equal  to  the  angle  subtended  at  the  centre  of  the  luminary  by  the  semidia- 
meter  of  the  earth  passing  through  the  place  of  observation  ;  since  all  cal- 
culations of  the  geocentric  places  of  the  heavenly  bodies  are  referred  to  the 
earth's  centre.  This  angle,  which  is  to  be  added  to  the  apparent  altitude, 
amounts  sometimes,  in  the  case  of  the  moon,  when  near  the  horizon,  to 
more  than  a  degree ;  the  refraction,  which  is  in  a  contrary  direction,  and  is 
to  be  subtracted  from  the  altitude,  being  at  the  horizon  about  33  minutes. 
(Plate  XXXV.  Fig.  513.) 

The  most  important  applications  of  practical  astronomy  are  in  the  de- 
termination of  the  latitudes  and  longitudes  of  places  on  the  earth's  surface. 
The  latitude,  which  is  the  angular  distance  of  the  place  from  the  equator, 
or  the  angle  formed  by  the  plane  of  its  horizon  with  the  earth's  axis,  is 
easily  ascertained  by  finding  the  meridian  altitude  of  a  body,  of  which  the 
declination  is  known ;  since,  by  deducting  or  adding  the  declination,  we 
have  at  once  the  elevation  of  the  equinoctial,  or  of  the  plane  of  the  equator 
above  the  horizon,  and  subtracting  this  from  a  right  angle,  we  find  the 
elevation  of  the  pole,  or  the  latitude.  (Plate  XXXV.  Fig.  512.) 

It  is  also  common  to  determine  the  latitude  of  a  place  by  means  of  two 
*  Ph.  Tr.  1742,  p.  155.  f  See  Lect.  XXXVI. 


ON  PRACTICAL  ASTRONOMY.  431 

altitudes  observed  at  different  times  in  the  same  day,  noticing  accurately 
the  interval  of  time  that  elapses  between  the  observations.  This  method 
has  a  great  advantage  in  cloudy  weather,  when  it  is  not  possible  to  ensure 
an  observation  of  a  meridian  altitude. 

The  longitude  of  a  place,  or  the  relative  position  of  its  meridian,  is  by  no 
means  so  readily  determined.  For  this  purpose  it  becomes  necessary  to 
ascertain  the  time  that  elapses  between  the  passages  of  a  given  point  in  the 
heavens  over  its  meridian  and  some  other  meridian  which  serves  as  a 
standard  of  comparison.  Thus,  if  the  sun  arrives  three  hours  later  at  the 
meridian  of  any  place  than  at  the  meridian  of  London,  that  place  must 
necessarily  be  45  degrees  west  of  London,  or  in  45°  west  longitude  :  and  if 
we  know,  when  it  is  noon  at  the  given  place,  that  it  is  three  o'clock  in  the 
afternoon  at  Greenwich,  we  may  be  certain  that  we  are  in  some  part  of  a 
meridian  45°  west  of  that  of  Greenwich.  Had  we  perfect  timekeepers,  we 
might  easily  adjust  them  to  the  time  of  our  first  meridian,  and  then,  by 
comparison  with  the  usual  determinations  of  time  in  any  other  place,  to 
which  they  might  be  carried,  the  longitude  of  this  place  might  be  found 
with  perfect  accuracy.  Such  timekeepers  as  we  have  are  indeed  suffi- 
ciently correct,  to  be  of  considerable  utility,  but  it  is  necessary  to  compare 
them  frequently  with  astronomical  observations  of  phenomena,  which  occur 
at  times  capable  of  a  correct  calculation.  Sometimes  the  transits  of  Mer- 
cury and  Venus,  or  the  eclipses  of  the  moon,  are  employed  for  this  purpose, 
but  more  usually  the  eclipses  of  the  satellites  of  Jupiter  ;  these,  however, 
cannot  be  well  observed  without  a  more  powerful  telescope  than  can  be 
employed  at  sea ;  and  the  theory  of  the  moon's  motion,  has  of  late  years 
been  so  much  improved,  that  her  distance  from  the  sun  or  from  a  fixed 
star  can  be  calculated,  with  sufficient  accuracy,  for  determining  the  time  in 
London  or  at  Paris  without  an  error  of  one  third  of  a  minute ;  so  that 
supposing  the  observation  could  be  rendered  perfectly  correct,  the  longitude 
might  be  thus  ascertained  within  about  one  twelfth  of  a  degree,  or  at  most 
five  nautical  miles. 

The  observed  parallax  of  the  sun  and  moon  may  be  employed  for  the 
determination  of  their  distances  from  the  earth  ;  but  in  the  case  of  the  sun, 
the  simple  comparison  of  his  calculated  with  his  apparent  altitude  is  in- 
sufficient for  ascertaining  the  magnitude  of  the  parallax  with  accuracy. 
Sometimes  the  parallax  of  Mars,  which  is  considerably  greater  than  the 
sun's,  has  been  directly  measured ;  but  the  most  correct  mode  of  ascer- 
taining the  actual  dimensions  of  the  solar  system  is,  to  observe  a  transit 
of  Venus  over  the  sun's  disc,  at  two  places  situated  in  opposite  parts  of 
the  earth's  surface.  For,  since  the  diurnal  motion  of  some  parts  of  the 
earth  is  directed  the  same  way  with  the  motion  of  Venus  in  her  orbit, 
and  that  of  others  the  contrary  way,  the  different  effects  of  these  motions 
must  furnish  a  mode  of  comparing  the  rotatory  velocity  of  the  earth, 
with  the  progressive  velocity  of  Venus,  and  consequently  of  inferring, 
from  the  known  velocity  with  which  the  earth's  surface  revolves,  the 
actual  velocity  of  Venus,  and  her  distance  from  the  sun ;  whence  the 
distances  of  all  the  other  planets  may  be  readily  deduced.  (Plate  XXXV. 
Fig.  514.) 


432  LECTURE   XLV. 

Our  countryman  Horrox*  was  the  first  that  particular!}'  attended  to  the 
phenomena  of  a  transit  of  Venus  over  the  sun's  disc  :  Dr.  Halley,t  when 
he  observed  a  transit  of  Mercury  at  St.  Helena,  thought  that  he  could 
ascertain  the  times  of  immersion  and  emersion  without  an  error  of  a  single 
second  ;  and  hence  he  concluded,  that  by  means  of  a  transit  of  Venus,  the 
sun's  distance  might  be  determined  within  a  five  hundredth  part.  The 
most  advantageous  places  for  the  experiment  being  such  as  differ  most  in 
longitude,  and  are  most  remote  from  each  other,  Captain  Cook  was  sent 
by  the  British  government  to  the  South  Seas,  in  the  years  1761  and  1769, 
in  order  to  observe  the  transits  of  Venus  in  the  island  of  Otaheite. 
These  observations  were  compared  with  those  which  were  made  at  Ward- 
huys,  in  Danish  Lapland  ;  the  difference  of  the  times  occupied  by  the 
transit  at  these  places  was  found  to  be  23  minutes  10  seconds,  and  from 
this  comparison,  corrected  by  a  number  of  collateral  observations,  the  sun's 
mean  parallax  was  found  to  be  8  seconds  and  two  thirds,  or  perhaps  8f  ; 
for  it  does  not  appear  that  we  are  sure  of  having  avoided  even  an  error  of 
one  fortieth  part  of  the  whole  ;  although  Mr.  Laplace's  determination  of 
the  sun's  distance,  from  the  lunar  motions,  agrees  very  well  with  that 
which  is  usually  considered  as  the  result  of  the  observations  of  the  transit 
of  Venus.  J 

The  comparative  densities  of  the  sun,  and  of  such  planets  as  have  satel- 
lites, may  be  calculated  from  the  periods  and  distances  of  the  bodies  revolv- 
ing round  them  ;  the  densities  of  the  other  planets  have  sometimes  been 
assigned  from  conjecture  only,  but  of  late  years  the  mathematical  theory 
of  the  planetary  perturbations  has  been  rendered  so  perfect,  that  some 
dependence  may  perhaps  be  placed  on  the  density  assigned  to  them  from 
calculations  of  this  kind.  It  was  formerly  supposed  that  the  densities  of 
the  planets  were  regularly  greater  as  they  were  nearer  to  the  sun  ;  but  it 
is  now  certain  that  the  Georgian  planet  is  more  dense  than  Saturn,  and  it 
is  probable  that  Venus  is  somewhat  less  dense  than  the  earth.  The  mass 
of  the  moon  is  deduced  from  a  comparison  of  the  effects  of  her  attraction  on 
the  earth  and  sea  with  those  of  the  sun's  attraction. 

The  artificial  globe  serves  as  a  useful  instrument  for  determining,  in  a 
rough  manner,  without  calculation,  the  affections  of  the  heavenly  bodies  at 
particular  times  ;  their  places  being  first  ascertained  from  tables,  or,  in  the 
case  of  the  sun,  merely  from  a  scale  on  the  globe's  horizon,  or  on  its  surface. 
We  have  only  to  adjust  the  elevation  of  the  pole  of  the  globe  in  such  a 
manner,  that  its  axis  may  form  the  same  angle  with  its  horizon  as  the  axis 
of  the  earth  does  with  the  real  horizon  of  the  place ;  then  finding  a  point 
on  its  surface  corresponding  to  the  place  of  the  sun  or  planet,  we  may 
represent  its  apparent  motion  by  the  motion  of  this  point,  and  the  time 
occupied  by  that  motion  will  be  shewn  by  the  index  of  the  globe  ;  thus  we 
may  find  the  length  of  the  day  and  night,  and  the  time  and  place  of  rising 

*  See  Hevelius,  Mercurius  in  Sole  visus  Gedani  An.  1661,  cuiannexa  est  Venus 
in  Sole  visa  An.  1639,  Liverpolise,  a  J.  Horroxio,  fol.  Ged.  1662. 

t  De  Parallax!  ope  Veneris  Determinanda,  Ph.  Tr.  1716,  p.  454. 

I  Euler  on  the  Sun's  Parallax,  computed  by  Lexell,  Ph.  Tr.  1772,  p.  69,  makes 
it  8"-55  ;  Laplace,  from  the  moon's  motion,  makes  it  8"-6. 


ON  PRACTICAL  ASTRONOMY.  433 

and  setting  ;  and  by  means  of  a  graduated  circle,  perpendicular  to  the  hori- 
zon, we  may  measure  the  altitude  of  the  sun  or  planet  at  any  other  time, 
and  also  its  azimuth,  or  the  distance  of  this  circle  from  the  north  or  south 
point  of  the  horizon.  If  we  have  a  ring  of  any  kind  parallel  to  the  horizon, 
and  33  minutes  below  it,  we  may  consider  this  ring  as  the  apparent  hori- 
zon, allowing  for  the  effects  of  refraction ;  if  it  be  still  15  or  16  minutes 
lower,  it  will  represent  the  rising  or  setting  of  the  extreme  margin  of  the 
sun  or  moon  :  we  might  also  have  a  circle  about  a  degree  above  either  of 
these,  which  might  represent  the  sensible  or  apparent  horizon,  with  regard 
to  the  moon,  including  the  correction  for  her  parallax  ;  and  a  similar  ring, 
placed  still  lower,  would  show  the  duratkm  of  twilight,  on  any  supposition 
that  might  be  formed  respecting  the  depression  of  the  sun  required  for  pro- 
ducing total  darkness.  By  means  of  the  celestial  globe,  the  apparent 
motions  of  the  fixed  stars  may  be  represented  in  a  manner  nearly  similar, 
proper  attention  being  paid  to  the  situation  of  the  sun  in  the  ecliptic,  as 
determining  the  time  corresponding. 

Many  of  these  operations  may  also  be  performed  with  equal  convenience 
with  a  planisphere,  which  is  a  stereographical  projection  of  the  globe  on  a 
plane  surface.  Professor  Bode's  planisphere  comprehends  in  one  view  all 
the  stars  that  are  ever  visible  at  Berlin :  he  has  added  to  it  a  moveable  cir- 
cle, representing  the  horizon  of  that  place,  carrying  with  it  the  circles  of 
altitude  and  azimuth,  delineated  on  a  transparent  paper,  which  is  adjusted, 
by  graduations  at  the  margin  of  the  chart,  to  the  day  and  hour  for  which 
we  wish  to  ascertain  the  apparent  places  of  the  heavenly  bodies.  Any 
other  chart  of  the  stars,  having  the  pole  in  its  centre,  may  be  applied  to  a 
similar  use,  by  cutting  out  a  circle,  or  a  part  of  a  circle,  to  represent  the 
horizon  of  a  place  of  which  the  latitude  is  given  ;  and  if  the  stars  are  pro- 
jected, as  is  usual,  on  two  equal  charts,  they  must  have  two  equal  arcs  to 
represent  the  respective  parts  of  the  horizon  belonging  to  them.  A  simple 
construction  may  also  often  be  made  to  serve  for  solving  many  problems  of 
a  similar  nature.  (Plate  XXXV.  Fig.  515,  516.  Plate  XXXVI.  Fig.  517. 
Plate  XXXVII.  Fig.  518.) 

For  representing  the  real  as  well  as  the  apparent  motions  of  the  different 
parts  of  the  solar  system,  planetariums  or  orreries  have  sometimes  been 
employed,  in  which  the  comparative  periods  of  the  revolutions  have  been 
expressed  by  various  combinations  of  wheelwork.  Of  these  instruments 
Archimedes  was  the  original  inventor,  and  Huygens  revived  them,  with 
many  improvements,  in  modern  times.  The  construction  of  the  large  pla- 
netarium, which  has  been  made  in  the  house  of  the  Royal  Institution,  was 
principally  directed  by  Mr.  Pearson.  I  suggested  to  him,  that  the  instru- 
ment might  be  placed  in  a  vertical  position,  and  that  the  eccentricities  of 
the  planetary  orbits  might  be  shown  by  the  revolution  of  short  arms,  retained 
in  their  situation  by  weights,  and  their  deviation  from  the  plane  of  the 
ecliptic  by  inclining  the  axes  of  these  arms,  in  a  proper  angle,  to  the  plane 
of  the  instrument.  The  other  parts  of  the  arrangement,  which  have  any 
claim  to  novelty,  were  entirely  of  Mr.  Pearson's  invention,  and  he  appears 
to  have  rendered  the  instrument  in  many  respects  more  accurate  than  any 
other  planetarium  that  has  ever  been  constructed.* 

*  On  this  subject  see  the  article  Planetarium,  by  Pearson,  in  Rees's  Cyclopaedia. 

2  F 


434  LECTURE  XLV. 


LECT.  XLV.— ADDITIONAL  AUTHORITIES. 

Apparatus  in  general. — Hevelii  Organographia  Astr.  fol.  Ghent,  1673.  Hooke's 
Animadversions  on  Hevelius's  Machina  Cselestis,  4to,  1674.  Maskelyne's  Remarks, 
Ph.  Tr.  1764,  p.  348.  Due  de  Chaulnes,  Hist,  et  Mem.  1765,  p.  411,  H.  65.  Bird, 
The  Method  of  Dividing  Astr.  Insts.  4to,  1767.  Magellan,  Collection  deTraites  sur 
des  Instr.  d'Astr.  2  vols.  4to,  1775,  1780.  Descrip.  des  Nouveaux  Instr.  a  Re- 
flexion, 4to,  London,  1779.  Descrip.  des  Octants  et  Sextants  Anglois,  4to,  Paris, 
1775.  Ludlam  on  Bird's  Method  of  Dividing,  4to,  1786.  Piazzi,  della  Specola  Ast.  di 
Palermo,  fol.  Pal.  1792.  Troughton,  Zach's  Mon.  Corres.  ii.  207.  Kluber,  Die 
Sternwarte  zu  Mannheim  beschreiben,  4to,  Mann.  1811.  Quetelet,  Sur  1'Obs.  de 
Bruxelles,  Corresp.  Mathem.  vol.  vii.  Simms,  A  Description  of  Mathematical  In- 
struments, 1834. 

Telescope  Wires,  Sfc. — See  Lect.  XXXVI.  Herschel's  Micrometers,  Ph.  Tr. 
1782,  p.  163;  1783,  p.  4.  Wollaston  on  a  System  of  Wires,  ibid.  1785,  p.  346. 
Rittenhouse  on  Spiders'  Webs,  Am.  Tr.  ii.  181.  Ussher  on  Illuminating  the  Wires 
of  a  Transit,  Ir.  Tr.  1788,  p.  13. 

Transit.— Derham's,  Ph.  Tr.  1704,1578.  Roemer's,  Mis.  Berl.  1727,  p.  276. 
Gensanne's,  Hist,  et  Mem.  1736,  H.  120.  Mach.  App.  vii.  55.  Wollaston,  Ph.  Tr. 
1793,  p.  133.  Ramsden's,  ibid.  1795,  p.  419. 

Equatorial  Instruments.— Short,  Ph.  Tr.  1749,  p.  241.     Nairne's,  ibid.  1771, 

?.  107.  Haupoin's,  Jour,  de  Physique,  xlii.  286.  Shuckburgh  on  the  Equatorial 
nst.  Ph.  Tr.  1793,  p.  67.  Struve,  Beschreibung  des  zu  Dorpat  Refractors  von 
Frauenhofer,  fol.  Dorpat,  1825. 

Mural  Circle. — Bird,  The  Method  of  constructing  Mural  Quadrants,  4to,  Lond. 
1768.  Cesaris,  De  Quadrante  Murale,  quern  Spec.  Med.  construx.  J.  Ramsden, 
4to,  Mediol.  1794.  Ramsden  and  Berge's  Zenith  Sector,  Ph.  Tr.  1803,  p.  383. 

Observations,  with  their  corrections. — Refraction — See  Lect.  XXXVII. 

Aberration,  ^c.— Zach's  Tables,  2  vols.  4to,  Gotha,  1806-7,  Marseille,  1812-13. 
Baily,  Tables  for  Precession,  Aberration,  and  Nutation,  4to,  Lond.  1827.  Bessel, 
Tabulae  Regiomontanse,  1830. 

Parallax. — Halley,  De  Parallaxi  Solis  ope  Veneris  determinanda,  Ph.  Tr.  1716, 
p.  454.  Boscovich,  ibid.  1760,  p.  865.  On  the  Transit  of  6th  June,  1761,  Ph.  Tr. 
1761,  lii.  173,  582,  611....  ;  1763,  pp.  300,  467 ;  1764,  p.  152  ;  1765,  p.  326; 
1766,  p.  244;  1771,  p.  574  ;  1768,  pp.107,  154,  355.  Chappe  d'Auterouche, 
Mem.  4to,  St.  Petersb.  1762.  Rb'hl,  Von  den  Durchgangen  der  Venus,  Greifsw. 
1768.  Lalande  on  the  Solar  ParaUax,  Hist,  et  Mem.  1771,  p.  776,  H.  83.  Cook, 
Ph.  Tr.  1771,  p.  433.  Euler,  ibid.  1772,  p.  69. 

Solar  Tables.— Cassini's,  4to,  Paris,  1740.  Lacaille's,  Vienn.  1763.  Delambre's, 
Bureau  des  Longitudes,  4to,  1806.  Zach's,  4to,  Gotha,  1809.  Carlini's  (Milan  Ef .), 
1810-11.  Burckhardt's,  Conn,  des  Temps,  1816.  South  and  Airy's,  Ph.  Tr. 
1826-7.  Bessel's,  Astr.  Nachr.  1828. 

Lunar  Tables. — Hell's,  Vienn.  1763,  Mayer's,  4to,  Lond.  1787.  Mendoza's, 
4to,  Lond.  1801.  Burg's,  Bureau  des  Long.  4to,  Paris,  1806.  Zach's  Tables 
abrege"s  pour  Paris,  Florence,  1809.  Burckhardt's,  4to,  Paris,  1826.  Damoiseau's, 
fol.  Paris,  1828. 

Tables  of  Mercury. — Lindenau's,  4to,  Gotha,  1813. 

Venus.— Lindenau's,  4to,  Gotha,  1810.  Reboul's,  4to,  Marseille, 

1811. 

Mars. — Lindenau's,  4to,  Eisenb.  1811. 

New  Planets.—  Zach's  of  Ceres,  Ph.  Mag.  xii.  360  ;  xv.  190.  Carlini's, 

Milan,  1818. 

Jupiter. — Delambre's  of  Jup.  and  Sat.  4to,  1789.  Delambre's  New 

Tables  of  his  Satellites,  4to,  1817. 

Saturn. — Bouvard's  of  Jup.  and  Sat.  4to,  Paris,  1808. 

Uranus. — Bouvard's,  1821.     Herschel  on  his  Satellites,  Ph.  Tr.  1815. 

Weisse,  Coordinate  Mercurii,  Veneris,  Martis,  Jovis,  Saturni,  et  Urani  calculate, 
4to,  Cracow,  1826. 


435 


LECTURE    XLVI. 


ON  GEOGRAPHY. 

FROM  the  consideration  of  the  stars,  the  sun,  and  the  planets  in  general, 
we  are  now  to  descend  to  that  of  the  earth,  the  particular  planet  which  we 
inhabit,  and  which  we  can  examine  more  minutely  than  the  other  parts  of 
the  solar  system.  Its  external  form,  its  divisions,  whether  astronomical  or 
natural,  its  most  remarkable  features,  and  its  internal  structure,  will  require 
to  be  separately  investigated. 

The  general  curvature  of  the  earth's  surface  is  easily  observable  in  the 
disappearance  of  distant  objects,  and  in  particular,  when  the  view  is  limited 
by  the  sea,  the  surface  of  which,  from  the  common  property  of  a  fluid, 
becomes  naturally  smooth  and  horizontal :  for  it  is  well  known  that  the 
sails  and  rigging  of  a  ship  come  into  view  long  before  her  hull,  and  that 
each  part  is  the  sooner  seen  as  the  eye  is  more  elevated.  On  shore,  the  fre- 
quent inequalities  of  the  solid  parts  of  the  earth  usually  cause  the  prospect 
to  be  bounded  by  some  irregular  prominence,  as  a  hill,  a  tree,  or  a  build- 
ing, so  that  the  general  curvature  is  the  less  observable. 

The  surface  of  a  lake  or  sea  must  be  always  perpendicular  to  the  direc- 
tion of  a  plumb  line,  which  may  be  considered  as  the  direction  of  the  force 
of  gravity  ;  and  by  means  either  of  a  plumb  line  or  of  a  spirit  level,  we  may 
ascertain  the  angular  situation  of  any  part  of  the  earth's  surface  with 
respect  to  a  fixed  star  passing  the  meridian ;  by  going  a  little  further  north 
or  south,  and  repeating  the  observation  on  the  star,  we  may  find  the  differ- 
ence of  the  inclination  of  the  surfaces  at  both  points  ;  of  course,  supposing 
the  earth  a  sphere,  this  difference  in  latitude  will  be  the  angle  subtended  at 
its  centre  by  the  given  portion  of  the  surface,  whence  the  whole  circum- 
ference may  be  determined  ;  and  on  these  principles  the  earliest  measure- 
ments of  the  earth  were  conducted.  The  first  of  these,  which  can  be  con- 
sidered as  accurate,  was  executed  by  Picart*  in  France,  towards  the  end  of 
the  seventeenth  century. 

But  the  spherical  form  is  only  an  approximation  to  the  truth  ;  it  was 
calculated  by  Newton,  and  ascertained  experimentally  by  the  French  Aca- 
demicians, sent  to  the  equator  and  to  the  polar  circle,  that,  in  order  to 
represent  the  earth,  the  sphere  must  be  flattened  at  the  poles,  and  promi<r 
nent  at  the  equator.  We  may  therefore  consider  the  earth  as  an  oblate 
elliptic  spheroid  ;  the  curvature  being  greater,  and  consequently  every 
degree  shorter,  at  the  equator,  than  nearer  the  poles.  If  the  density  of  the 
earth  were  uniform  throughout,  its  ellipticity,  or  the  difference  of  the 
length  of  its  diameters,  would  be  -3-^5-  of  the  whole  ;  on  the  other  hand,  if 
it  consisted  of  matter  of  inconsiderable  density,  attracted  by  an  infinite  force 
in  the  centre,  the  ellipticity  would  be  only  ^-y ;  and  whatever  may  be 
the  internal  structure  of  the  earth,  its  form  must  be  between  these  limits, 
*  Hist,  et  Mem.  vii.  I.  46. 
2  F2 


43(5  LECTURE  XLVI. 

since  its  internal  parts  must  necessarily  be  denser  than  those  parts  which 
are  nearer  the  surface.  If  indeed  the  earth  consisted  of  water  or  ice, 
equally  compressible  with  common  water  or  ice,  and  following  the  same 
laws  of  compression  with  elastic  fluids,  its  density  would  be  several  thou- 
sand times  greater  at  the  centre  than  at  the  surface  ;  and  even  steel  would 
be  compressed  into  one  fourth  of  its  bulk,  and  stone  into  one  eighth,  if  it 
were  continued  to  the  earth's  centre ;  so  that  there  can  be  no  doubt  but 
that  the  central  parts  of  the  earth  must  be  much  more  dense  than  the  super- 
ficial. Whatever  this  difference  may  be,  it  has  been  demonstrated  by 
Clairaut,*  that  the  fractions  expressing  the  ellipticity  and  the  apparent 
diminution  of  gravity  at  the  equator  must  always  make  together  -^fj.-,  and 
it  has  been  found,  by  the  most  accurate  observations  on  the  lengths  of 
pendulums  in  different  latitudes,  that  the  force  of  gravity  is  less  powerful 
by  -,-^ff  at  the  equator  than  at  the  pole,  whence  the  ellipticity  is  found 
to  be  -g-J-3-  of  the  equatorial  diameter,  the  form  being  the  same  as  would 
be  produced,  if  about  three  eighths  of  the  whole  force  of  gravity  were 
directed  towards  a  central  particle,  the  density  of  the  rest  of  the  earth  being 
uniform. 

This  method  of  determining  the  general  form  of  the  earth  is  much  less 
liable  to  error  and  irregularity,  than  the  measurement  of  the  lengths  of 
degrees  in  various  parts,  since  the  accidental  variations  of  curvature  pro- 
duced by  local  differences  of  density,  and  even  by  superficial  elevations, 
may  often  produce  considerable  errors  in  the  inferences  which  might  be 
deduced  from  these  measurements.  For  example,  a  degree  measured  at 
the  Cape  of  Good  Hope,  in  latitude  33°  south,  was  found  to  be  longer  than 
a  degree  in  France,  in  latitude  46°  north,  and  the  measurements  in  Austria, 
in  North  America,  and  in  England,  have  all  exhibited  signs  of  similar 
irregularities.  There  appears  also  to  be  some  difference  in  the  length  of 
degrees  under  the  same  latitude,  and  in  different  longitudes.  "We  may, 
however,  imagine  a  regular  elliptic  spheroid  to  coincide  very  nearly  with 
any  small  portion  of  the  earth's  surface,  although  its  form  must  be  some- 
what different  for  different  parts  :  thus,  for  the  greater  part  of  Europe,  that 
is,  for  England,  France,  Italy,  and  Austria,  if  the  measurements  have  been 
correct,  this  osculating  spheroid  must  have  an  ellipticity  of  Tf^. 

The  earth  is  astronomically  divided  into  zones,  and  into  climates.  The 
torrid  zone  is  limited  by  the  tropics,  at  the  distance  of  23°  28'  on  each  side 
of  the  equator,  containing  all  such  places  as  have  the  sun  sometimes 
vertical,  or  immediately  over  them  ;  the  frigid  zones  are  within  the  polar 
circles,  at  the  same  distance  from  the  poles,  including  all  places  which 
remain  annually  within  the  limit  of  light  and  darkness,  for  a  whole  diurnal 
rotation  of  the  earth,  or  longer  ;  the  temperate  zones,  between  these,  have 
an  uninterrupted  alternation  of  day  and  night,  but  are  never  subjected  to 
the  sun's  vertical  rays.  At  the  equator,  therefore,  the  sun  is  vertical  at  the 
equinoxes,  his  least  meridian  altitude  is  at  the  solstices,  when  it  is  66°  32', 
that  is,  more  than  with  us  at  midsummer,  and  this  happens  once  on  the 
north  and  once  on  the  south  side  of  the  hemisphere.  Between  the  equator 

*  Sur  la  Figure  de  la  Terre,  Paris,  1743.  Airy's  Tracts,  Figure  of  the  Earth, 
art.  62  ;  or  his  article,  Figure  of  the  Earth,  in  the  Encyclopedia  Metropolitana. 


ON  GEOGRAPHY.  437 

'""and  the  tropics,  he  is  vertical  twice  in  the  year,  when  his  declination  is  equal 
to  the  latitude  of  the  place,  and  his  least  meridian  altitudes,  which  are 
unequal  between  themselves,  are  at  the  solstices.  At  the  tropics,  the 
meridian  sun  is  vertical  once  only  in  the  year,  and  at  the  opposite  solstice, 
or  the  time  of  midwinter,  his  meridian  altitude  is  43°  4',  as  with  us  in 
April,  and  the  beginning  of  September.  At  the  polar  circles,  the  sun 
describes  on  midsummer  day  a  complete  circle,  touching  the  north  or  south 
point  of  the  horizon  ;  and  in  midwinter  he  shows  only  half  his  disc  above 
it  for  a  few  minutes  in  the  opposite  point ;  that  is,  neglecting  the  elevation 
produced  by  refraction,  which,  in  these  climates  especially,  is  by  no  means 
inconsiderable.  At  either  pole,  the  corresponding  pole  of  the  heaven  being 
vertical,  the  sun  must  annually  describe  a  spiral,  of  which  each  coil  is 
nearly  horizontal,  half  of  the  spiral  being  above  the  horizon,  and  half 
below  ;  the  coils  being  much  opener  in  the  middle  than  near  either  end. 

The  climates,  in  the  astronomical  sense  of  the  word,  are  determined  by 
the  duration  of  the  longest  day  in  different  parts  of  the  earth's  surface  ; 
but  this  division  is  of  no  practical  utility,  nor  does  it  furnish  any  criterion 
for  judging  of  the  climate  in  a  meteorological  sense. 

The  natural  division  of  the  surface  of  the  globe  is  into  sea  and  land : 
about  three  fourths  of  the  whole  being  occupied  by  water,  although  pro- 
bably no  where  to  a  depth  comparatively  very  considerable,  at  most  of  a 
few  miles  on  an  average.  The  remaining  fourth  consists  of  land,  elevated 
more  or  less  above  the  level  of  the  sea,  interspersed  in  some  parts,  with 
smaller  collections  of  water,  at  various  heights,  and,  in  a  few  instances, 
somewhat  lower  than  the  general  surface  of  the  main  ocean.  Thus  tho 
Caspian  sea  is  said  to  be  about  300  feet  lower  than  the  ocean,  and  in  the 
interior  part  of  Africa  there  is  probably  a  lake  equally  depressed. 

We  cannot  observe  any  general  symmetry  in  this  distribution^  of  the 
earth's  surface,  excepting  that  the  two  large  continents,  of  Africa  and  South 
America,  have  some  slight  resemblance  in  their  forms,  and  that  each  of 
them  is  terminated  to  the  eastward  by  a  collection  of  numerous  islands. 
The  large  capes  projecting  to  the  southward  have  also  a  similarity  with 
respect  to  their  form  and  the  islands  near  them  :  to  the  west  the  continents 
are  excavated  into  large  bays,  and  the  islands  are  to  the  east  :  thus  Cape 
Horn  has  the  Falkland  Islands,  the  Cape  of  Good  Hope  Madagascar,  and 
Cape  Comorin  Ceylon,  to  the  east.  (Plate  XLII.,  XLIII.) 

The  great  continent,  composed  of  Europe,  Asia,  and  Africa,  constitutes 
about  a  seventh  of  the  whole  surface  of  the  earth,  America  about  a  six- 
teenth, and  Australasia  or  New  South  Wales  about  a  fiftieth ;  or,  in 
hundredth  parts  of  the  whole,  Europe  contains  2,  Asia  7,  Africa  6,  America 
6,  and  Australasia  2,  the  remaining  77  being  sea  ;  although  some  authors 
assign  72  parts  only  out  of  100  to  the  sea,  and  28  to  the  land.  These  pro- 
portions may  be  ascertained  with  tolerable  accuracy  by  weighing  the  paper 
made  for  covering  a  globe,  first  entire,  and  then  cut  out  according  to  the 
terminations  of  the  different  countries  :  or,  if  still  greater  precision  were 
required,  the  greater  part  of  the  continents  might  be  divided  into  known 
portions  of  the  whole  spherical  surface,  and  the  remaining  irregular  por- 
tions only  weighed. 


438  LECTURE  XL VI. 

The  general  inclinations  and  levels  of  the  continents  are  discovered  by 
the  course  of  their  rivers.  Of  these  the  principal  are,  the  River  of  Amazons, 
the  Senegal,  the  Nile,  the  River  St.  Laurence,  the  Hoangho,  the  River  La- 
plata,  the  Jenisei,  the  Mississippi,  the  Volga,  the  Oby,  the  Amur,  the 
Oronooko,  the  Ganges,  the  Euphrates,  the  Danube,  the  Don,  the  Indus,  the 
Dnieper,  and  the  Dwina  ;  and  this  is  said  to  be  nearly  the  order  of  their 
magnitudes.  But  if  we  class  them  according  to  the  length  of  country 
through  which  they  run,  the  order  will,  according  to  Major  Rennel's  calcu- 
lation, be  somewhat  different :  taking  the  length  of  the  Thames  for  unity, 
he  estimates  that  of  the  River  of  Amazons  at  15|,  the  Kiang  Kew,  in  China, 
15$,  the  Hoangho  13$,  the  Nile  12$,  the  Lena  11$,  the  Amur  11,  the  Oby 
10$,  the  Jenisei,  10,  the  Ganges,  its  companion  the  Burrampooter,  the  river 
of  Ava,  and  the  Volga,  each  9$,  the  Euphrates  8$,  the  Mississippi  8,  the 
Danube  7,  the  Indus  5$,  and  the  Rhine  5£. 

We  may  form  a  tolerably  accurate  idea  of  the  levels  of  the  ancient  con- 
tinent, by  tracing  a  line  across  it  in  such  a  direction  as  to  pass  no  river, 
which  will  obviously  indicate  a  tract  of  country  higher  than  most  of  the 
neighbouring  parts.  Beginning  at  Cape  Finisterre,  we  soon  arrive  at  the 
Pyrenees,  keeping  to  the  south  of  the  Garonne  and  the  Loire.  After  taking 
a  long  turn  northwards  to  avoid  the  Rhine,  we  come  to  Swisserland,  and 
we  may  approach  very  near  to  the  Mediterranean  in  the  state  of  Genoa, 
taking  care  not  to  cross  the  branches  of  the  Po.  We  make  a  circuit 
in  Swisserland,  and  pass  between  the  sources  of  the  Danube  and  of  the 
branches  of  the  Rhine  in  Swabia.  Crossing  Franconia,  we  leave  Bohemia 
to  the  north,  in  order  to  avoid  the  Elbe,  and  coming  near  to  the  borders  of 
Austria,  follow  those  of  Hungary,  to  the  south  of  the  Vistla.  The  Dnieper 
then  obliges  us  to  go  northwards  through  Lithuania,  leaving  the  Don 
wholly  to  the  right ;  and  the  Volga,  to  pass  still  further  north,  between 
Petersburg  and  Moscow,  a  little  above  Bjelesero.  We  may  then  go  east- 
wards to  the  boundary  of  Asia,  and  thence  northwards  to  Nova  Zembla. 
Hence  we  descend  to  the  west  of  the  Oby,  and  then  to  the  east  of  the 
branches  of  the  Volga,  and  the  other  inland  rivers  flowing  into  the  lake 
Aral  and  the  Caspian  sea.  Here  we  are  situated  on  the  widely  extended 
elevation  of  India,  in  the  neighbourhood  of  the  sources  of  the  Indus  :  and, 
lastly,  in  our  way  from  hence  towards  Kamschatka,  we  leave  the  Jenisei 
and  Lena  on  the  left,  and  the  Ganges,  the  Kiang  Kew,  the  Hoangho,  and 
the  Amur  to  the  right. 

The  direction  of  the  most  conspicuous  mountains  is,  however,  a  little 
different  from  this,  the  principal  chain  first  constitutes  the  Pyrenees,  and 
divides  Spain  from  France,  then  passes  through  Vivarais  and  Auvergne,  to 
join  the  Alps,  and  through  the  south  of  Germany  to  Dalmatia,  Albania, 
and  Macedonia  ;  it  is  found  again  beyond  the  Euxine,  under  the  names  of 
Taurus,  Caucasus,  and  Imaus,  and  goes  on  to  Tartary  and  to  Kamschatka. 
The  peninsula  of  India  is  divided  from  north  to  south  by  the  mountains 
of  Gate,  extending  from  the  extremity  of  Caucasus  to  Cape  Comorin.  In 
Africa,  Mount  Atlas  stretches  from  Fez  to  Egypt,  and  the  mountains  of 
the  moon  run  nearly  in  the  same  direction ;  there  is  also  a  considerable 
elevation  between  the  Nile  and  the  Red  Sea.  In  the  new  world,  the  neigh- 


ON  GEOGRAPHY.  439 

"  bourhood  of  the  western  coast  is  in  general  the  most  elevated  ;  in  North 
America  the  Blue  mountains,  or  Stony  mountains,  are  the  most  consi- 
derable ;  and  the  mountains  of  Mexico  join  the  Andes  or  Cordeliers,  which 
are  continued  along  the  whole  of  the  west  coast  of  South  America. 

There  are  several  points  in  both  hemispheres  from  which  we  may 
observe  rivers  separating  to  run  to  different  seas ;  such  are  Swisserland, 
Bjelosero,  Tartary,  Little  Tibet,  Nigritia  or  Guinea,  and  Quito.  The 
highest  mountains  are  Chimboracao  and  some  others  of  the  Cordeliers  in 
Peru,  or  perhaps  Descabesado  in  Chili,  Mont  Blanc,  and  the  Peak  of  Tene- 
riffe.  Chimbora9ao  is  about  7000  yards,  or  nearly  4  miles,  above  the  level 
of  the  sea ;  Mont  Blanc  5000,  or  nearly  3  miles ;  the  Peak  of  Teneriffe 
about  4000,  or  2  miles  and  a  quarter ;  Ophir,  in  Sumatra,  is  said  to  be 
5  or  6  hundred  feet  higher.  It  has,  however,  been  asserted  that  some  of 
the  snowy  mountains,  to  the  north  of  Bengal,  are  higher  than  any  of  those 
of  South  America.  The  plains  of  Quito,  in  Peru,  are  so  much  elevated, 
that  the  barometer  stands  at  the  height  of  15  inches  only,  and  the  air  is 
reduced  to  half  its  usual  density.  But  none  of  these  heights  is  equal  to 
a  thousandth  part  of  the  earth's  semidiameter,  and  the  greatest  of  them 
might  be  represented  on  a  six  inch  globe  by  a  single  additional  thickness 
of  the  paper  with  which  it  is  covered.  Mount  Sinai  in  Japan,  Mount 
Caucasus,  Etna,  the  Southern  Pyrenees,  St.  George  among  the  Azores, 
Mount  Adam  in  Ceylon,  Atlas,  Olympus,  and  Taurus  are  also  high 
mountains  :  and  there  are  some  very  considerable  elevations  in  the  island 
Owhyhee.  Ben  Nevis,  in  Scotland,  is  the  loftiest  of  the  British  hills,  but 
its  height  is  considerably  less  than  a  mile.  (Plate  XXXVIII.  Fig.  519.) 

The  most  elevated  mountains,  excepting  the  summits  of  volcanos,  con- 
sist of  rocks,  more  or  less  mixed,  without  regular  order,  and  commonly  of 
granite  or  porphyry.  These  are  called  primary  mountains;  they  run 
generally  from  east  to  west  in  the  old  world,  and  from  north  to  south  in 
the  new  ;  and  many  of  them  are  observed  to  be  of  easier  ascent  on  the  east 
than  on  the  west  side.  The  secondary  mountains  accompany  them  in  the 
same  direction,  they  consist  of  strata,  mostly  calcarious  and  argillaceous, 
that  is,  of  the  nature  of  limestone  and  clay,  with  a  few  animal  and  vege- 
table remains,  in  an  obscure  form,  together  with  salt,  coals,  and  sulphur. 
The  tertiary  mountains  are  still  smaller  ;  and  in  these,  animal  and  vegetable 
remains  are  very  abundant;  they  consist  chiefly  of  limestone,  marble, 
alabaster,  building  stone,  mill  stone,  and  chalk,  with  beds  of  flint.  Where 
the  secondary  and  tertiary  mountains  are  intersected  by  vallies,  the  oppo- 
site strata  often  correspond  at  equal  heights,  as  if  the  vallies  had  been  cut 
or  washed  from  between  them,  but  sometimes  the  mountains  have  their 
strata  disposed  as  if  they  had  been  elevated  by  an  internal  force,  and  their 
summits  had  afterwards  crumbled  away,  the  strata  which  are  lowest  in  the 
plains  being  highest  in  the  mountains.  The  strata  of  these  mountains  are 
often  intermixed  with  veins  of  metal,  running  in  all  possible  directions, 
and  occupying  vacuities  which  appear  to  be  of  somewhat  later  date  than 
the  original  formation  of  the  mountains.  The  volcanic  mountains  inter- 
rupt those  of  every  other  description  without  any  regularity,  as  if  their 
origin  were  totally  independent  of  that  of  all  the  rest. 


440  LECTURE   XLVI. 

The  internal  constitution  of  the  earth  is  little  known  from  actual 
observation,  for  the  depths  to  which  we  have  penetrated  are  comparatively 
very  inconsiderable,  the  deepest  mine  scarcely  descending  half  a  mile  per- 
pendicularly. It  appears  that  the  strata  are  more  commonly  in  a  direction 
nearly  horizontal  than  in  any  other ;  and  their  thickness  is  usually  almost 
equable  for  some  little  distance  ;  but  they  are  not  disposed  in  the  order  of 
their  specific  gravity,  and  the  opinion  of  their  following  each  other  in  a 
similar  series,  throughout  the  greater  part  of  the  globe,  appears  to  rest  on 
very  slight  foundations. 

From  observations  on  the  attraction  of  the  mountain  Shehallion,  Dr. 
Maskelyne*  inferred  the  actual  mean  density  of  the  earth  to  be  to  that  of 
water  as  4^  to  1,  judging  from  the  probable  density  of  the  internal  sub- 
stance of  the  mountain,  which  he  supposed  to  be  a  solid  rock.  Mr. 
Cavendish  f  has  concluded  more  directly,  from  experiments  on  a  mass  of 
lead,  that  the  mean  density  of  the  earth  is  to  that  of  water  as  5^  to  1. 
Mr.  Cavendish's  experiments,  which  were  performed  with  the  apparatus 
invented  and  procured  by  the  late  Mr.  Michell,  appear  to  have  been  con- 
ducted with  all  possible  accuracy,  and  must  undoubtedly  be  preferred  to 
conclusions  drawn  from  the  attraction  of  a  mountain,  of  which  the  internal 
parts  are  perfectly  unknown  to  us,  except  by  conjectures  founded  on  its 
external  appearance.  Supposing  both  series  of  experiments  and  calcula- 
tions free  from  error,  it  will  only  follow  that  the  internal  parts  of  Shehal- 
lion are  denser,  and  perhaps  more  metallic,  than  was  before  imagined. 
The  density  assigned  by  Mr.  Cavendish  is  not  at  all  greater  than  might  be 
conjectured  from  observations  on  the  vibrations  of  pendulums ;  Newton 
had  long  ago  advanced  it  as  a  probable  supposition  that  the  mean  density 
of  the  earth  might  be  about  5  or  6  times  as  great  as  that  of  water,  and  the 
perfect  agreement  of  the  result  of  many  modern  experiments  with  this  con- 
jecture affords  us  a  new  proof,  in  addition  to  many  others,  of  the  accuracy 
and  penetration  of  that  illustrious  philosopher.  $ 


LECT.  XLVI.— ADDITIONAL  AUTHORITIES. 

Figure  of  the  Earth.— Snellius,  Eratosthenes  Batavus  de  Terrse  Ambitus  Quanti- 
tate,  Lugd.  Bat.  1617.  Norwood,  The  Seaman's  Practice,  4to,  Lond.  1637.  Ric- 
cioli,  Geog.  et  Hydrog.  fol.  Bon.  1661.  Cassini,  De  la  Figure  de  laTerre,  12mo, 
Amst.  1723.  Hist,  et  Mem.  1735,  p.  255  ;  1736,  p.  64,  H.  80.  Maupertuis,  Ph. 
Tr.  1733,  1736,  p.  302.  Hist,  et  Mem.  1737,  p.  389,  H.  90.  La  Figure  de  la 
Terre  determinee,  Paris,  1738.  Examen  des  Ouvrages  faits  pour  cet  Objet,  Amst. 
1741.  Clairaut  on  the  Figure  of  Planets  of  unequal  density,  Ph.  Tr.  1738,  p.  277. 
Celsius,  De  Figura  Telluris,  4to,  Upsal,  1738.  Bouguer,  La  Fig.  de  la  Terre,  4to, 
Paris,  1749.  Justification  de  do.  4to,  Paris,  1752.  Lettre  sur  do.  1754.  War- 
gentin,  Schwed.  Abhand.  1749,  p.  243  ;  1750,  pp.  3,  83  ;  Ph.  Tr.  1777,  p.  162.  La 

*  Ph.  Tr.  1775,  p.  501.  Button's  Calculations,  ibid.  1778,  p.  689.  See  also 
Zach,  L' Attraction  des  Montagnes  determinee  par  des  Observations  faites  en  1810, 
pres  de  Marseilles,  2  vols.  Avignon,  1814. 

t  Ph.Tr.  1798,  p.  469. 

I  Cavendish's  Experiment  has  been  repeated  by  Reich,  Versuche  iiber  die  Mitt- 
lere  Dichtigkeit  der  Erde,  Freiburg,  1838,  and  by  Baily,  Memoirs  of  the  Astrono- 
mical  Society,  vol.  xiv.  who  concludes  that  the  mean  density  of  the  earth  is  5-6747 
times  that  of  water. 


ON  THE  TIDES.  441 

Condamine,  Journal  du  Voyage  a  1'Equateur,  4to,  Paris,  1751.  Mesure  des  Trois 
Premiers  Degres,  4to,  Paris,  1751.  Lacaille,  Hist,  et  Mem.  1751,  p.  425,  H.  158  ; 
1755,  p.  53.  Frisii  Disquisitio  de  Fig.  et  Mag.  Tel.  Milan,  1752.  Boscovich,  De 
Expeditione,  &c.  4to,  Romse,  1755.  Laplace,  Mem.  des  Sav.  Etr.  1773,  p.  503  ; 
Hist,  et  Mem.  1783,  p.  17.  Beccaria,  Gradus  Taurinensis,  4to,  Aug.  Taur.  1774. 
Hassencamp,  Geschichte,  Rinteln.  1774.  Gerlach,  Gestalt  der  Erde,  Vienna,  1782. 
Roy,  Meas.  of  a  Base  at  Hounslow  Heath,  Ph.  Tr.  1785,  p.  385  ;  on  the  Relative 
Situations  of  Greenwich  and  Paris,  1787,  p.  188  ;  1790,  p.  11 1.  Cassini,  &c.  on  do. 
4to,  Paris,  1790.  Herschel  on  do.  Ph.  Tr.  1826.  Lorgna,  Geographia,  Verona, 
1789.  Delambre,  see  Lect.  X.  Survey  by  Williams,  Mudge,  and  Dalby,  Ph.  Tr. 
1795,  p.  414;  1797,  p.  432  ;  1800,  p.  539  ;  1803,  p.  383.  Kastner's  Mathema- 
tische  Geographic,  Gott.  1795.  Lambton,  Asiatic  Researches,  vii.  312.  Melander- 
hiem  and  Svanberg,  Zach's  Mon.  Corresp.  i.  372  ;  ii.  250,  257  ;  vii.  561.  Svanberg, 
Exposition  des  Operations  faites  en  Lapponie,  Stockholm,  1805.  Low,  Dissertation, 
Lugd.  1808.  Ivory,  Ph.  Tr.  1809,  1831,  p.  109  ;  1834,  p.  491.  Krayenhoff,  Precis 
des  Operations  faites  en  Hollande,  4to,  La  Haye,  1815.  Cagnoli,  Method  of  ascer- 
taining the  Fig.  of  the  Earth  by  Occupations  (trans.),  Lond.  1819.  Puissant,  Traite 
de  Geodesic,  3  vols.  4to,  1819-27.  Principes  du  Fig.  du  Terrain,  &c.  4to.  Arago, 
Recueil  d' Observations,  4to,  1821.  Carlini,  Relazione  delle  Operation!  intrapese  in 
Italia,  Milan,  1822.  Sabine,  Acct.  of  Experiments  with  Pendulums,  4to,  1825,  and 
Ph.  Tr.  1828-29.  Operations  Geodesiques  executees  en  Piemont  et  en  Savoie, 
2  vols.  4to,  Milan,  1825-7.  Brousseaud,  Mem.  sur  la  Mesure  d'un  Arc  du  Paral- 
lele,  1825.  Goldingham,  Madras  Obs.  Papers,  fol.  1827,  Ph.  Tr.  1822.  Schmidt, 
Lehrbuch  der  Mathematischen  Geographic,  Gott.  1829.  Ivory,  Ph.  Tr.  1809,  1831, 
p.  109;  1834,  p.  491.  Francoeur,  Geodesic,  1835. 

Figures  of  the  Planets. — Maupertuis  sur  la  Figure  des  Astres,  Paris,  1732.  La- 
grange,  Hist,  et  Me"m.  de  Berlin,  1773,  p.  121  ;  1775,  p.  273;  1792,  p.  258. 
Laplace,  Hist,  et  Mem.  de  Paris,  1782,  p.  113,  H.  43.  Legendre,  ibid.  1784, 
p.  370;  1789,  p.  372. 

Navigation.  —  See  Lect.  XXVII.  Duillier,  Navigation  improved,  fol.  Lond. 
1728.  Maupertuis,  Astronomie  Nautique,  Paris,  1743.  Lemonnier,  do.  1771. 
Juan,  Examen  Maritimo,  2  vols.  4to,  Madrid,  1771.  Robertson's  Navigation, 
2  vols.  Lond.  1786.  Moore's,  1796.  Lalande,  Abrege'  de  Nav.  4to,  1793.  Mac- 
kay's  Nav.  2  vols.  1793.  Bowditch's,  Lond.  1809.  Bouguer,  Traite  de  Nav.  4to, 
1814.  Norie's  Nav.  Lond.  1822.  Kelly's  Spherics  and  Naut.  Ast.  1822.  Riddle's 
Nav.  1824.  Inman's,  Portsea,  1826. 


LECTURE   XLVII. 


ON  THE  TIDES. 

THE  form  and  structure  of  the  solid  parts  of  the  globe  have  afforded  but 
few  remarkable  features  capable  of  arresting  our  attention,  except  the 
general  distribution  of  land  and  water,  and  the  permanent  differences  of 
elevation  of  different  parts  of  the  earth.  But  the  sea  exhibits  a  series  of 
phenomena  far  more  interesting  to  the  mathematical  philosopher,  because 
they  admit  of  a  methodical  investigation,  and  of  a  deduction  from  general 
causes,  the  action  of  which  may  be  traced  in  detail.  For  the  height  of  the 
surface  of  the  sea  at  any  given  place  is  observed  to  be  liable  to  periodical 
variations,  which  are  found  to  depend  on  the  relative  position  of  the  moon, 
combined  in  some  measure  with  that  of  the  sun.  These  variations  are 
*  called  tides ;  they  were  too  obvious  to  escape  the  observation  even  of  the 
ancients,  who  inhabited  countries  where  they  are  least  conspicuous :  for 


442  LECTURE  XLVII. 

Aristotle  mentions  the  tides  of  the  northern  seas,  and  remarks  that  they" 
vary  with  the  moon,  and  are  less  conspicuous  in  small  seas  than  in  the 
ocean :  Caesar,  Strabo,  Pliny,  Seneca,  and  Macrobius  give  also  tolerably 
accurate  accounts  of  them. 

There  are  in  the  tides  three  orders  of  phenomena  which  are  separately 
distinguishable  ;  the  first  kind  occurs  twice  a  day,  the  second  twice  a 
month,  and  the  third  twice  a  year.  Every  day,  about  the  time  of  the 
moon's  passing  over  the  meridian,  or  a  certain  number  of  hours  later,  the 
sea  becomes  elevated  above  its  mean  height,  and  at  this  time  it  is  said  to 
be  high  water.  The  elevation  subsides  by  degrees,  and  in  about  six  hours 
it  is  low  water,  the  sea  having  attained  its  greatest  depression  ;  after  this 
it  rises  again  when  the  moon  passes  the  meridian  below  the  horizon,  so 
that  the  ebb  and  flood  occur  twice  a  day,  but  become  daily  later  and  later 
by  about  50 £  minutes,  which  is  the  excess  of  a  lunar  day  above  a  solar  one, 
since  28£  lunar  days  are  nearly  equal  to  29|  solar  ones. 

The  second  phenomenon  is,  that  the  tides  are  sensibly  increased  at  the 
time  of  the  new  and  full  moon ;  this  increase  and  diminution  constitute 
the  spring  and  neap  tides;  the  augmentation  becomes  also  still  more 
observable  when  the  moon  is  in  its  perigee  or  nearest  the  earth.  The 
lowest  as  well  as  the  highest  water  is  at  the  time  of  the  spring  tides  ;  the 
neap  tides  neither  rise  so  high  nor  fall  so  low. 

The  third  phenomenon  of  the  tides  is  the  augmentation  which  occurs  at 
the  time  of  the  equinoxes ;  so  that  the  greatest  tides  are  when  a  new  or 
full  moon  happens  near  the  equinox,  while  the  moon  is  in  its  perigee.  The 
effects  of  these  tides  are  often  still  more  increased  by  the  equinoctial  winds, 
which  are  sometimes  so  powerful  as  to  produce  a  greater  tide  before  or 
after  the  equinox,  than  that  which  happens  in  the  usual  course,  at  the  time 
of  the  equinox  itself. 

These  simple  facts  are  amply  sufficient  to  establish  the  dependence  of  the 
tides  on  the  moon  ;  they  were  first  correctly  explained  by  Newton  as  the 
necessary  consequences  of  the  laws  of  gravitation,  but  the  theory  has  been 
still  further  improved  by  the  labours  of  later  mathematicians.  The 
whole  of  the  investigations  has  been  considered  as  the  most  difficult  of  all 
astronomical  problems ;  some  of  the  circumstances  depend  on  causes 
which  must  probably  remain  for  ever  unknown  to  us;  and  unless  we 
could  every  where  measure  the  depth  of  the  sea,  it  would  be  impossible  to 
apply  a  theory,  even  if  absolutely  perfect,  to  the  solution  of  every  difficulty 
that  might  occur.  A  very  injudicious  attempt  has  been  made  to  refer  the 
phenomena  of  the  tides  to  causes  totally  different  from  these,  and  depending 
on  the  annual  melting  of  the  polar  ice  ;  the  respectability  of  its  author  is 
the  only  claim  which  it  possesses  even  to  be  mentioned ;  and  a  serious 
confutation  of  so  groundless  an  opinion  would  be  perfectly  superfluous. 

A  detached  portion  of  a  fluid  would  naturally  assume,  by  its  mutual 
gravitation,  a  spherical  form,  but  if  it  gravitate  towards  another  body  at 
a  distance,  it  will  become  an  oblong  spheroid  of  which  the  axis  will 
point  to  the  attracting  body  ;  for  the  difference  of  the  attraction  of  this 
body  on  its  different  parts  will  tend  to  separate  them  from  each  other  in 
the  greatest  part  of  the  sphere,  that  is,  at  all  places  within  the  angular 


ON  THE  TIDES.  443 

distance  of  79 £°  from  the  line  passing  through  the  attracting  body,  either 
in  the  nearer  or  in  the  remoter  hemisphere ;  but  to  urge  them  to- 
wards the  centre,  although  with  a  smaller  force,  in  the  remaining  part. 
Hence,  in  order  that  there  may  be  an  equilibrium,  the  depth  of  the  fluid 
must  be  greatest  where  its  gravitation,  thus  composed,  is  least ;  that  is,  in 
the  line  directed  towards  the  attracting  body,  and  it  may  be  shown  that  it 
must  assume  the  form  of  an  oblong  elliptic  spheroid. 

If  the  earth  were  wholly  fluid,  and  the  same  part  of  its  surface  were 
always  turned  towards  the  moon,  the  pole  of  the  spheroid  being  imme- 
diately under  the  moon,  the  lunar  tide  would  remain  stationary,  the 
greatest  elevation  being  at  the  points  nearest  to  the  moon  and  furthest  from 
her,  and  the  greatest  depression  in  the  circle  equally  distant  from  these 
points  ;  the  elevation  being,  however,  on  account  of  the  smaller  surface  to 
which  it  is  confined,  twice  as  great  as  the  depression.  The  actual  height 
of  this  elevation  would  probably  be  about  40  inches,  and  the  depression  20, 
making  together  a  tide  of  5  feet.  If  also  the  waters  were  capable  of 
assuming  instantly  such  a  form  as  the  equilibrium  would  require,  the 
summit  of  a  spheroid  equally  elevated  would  still  be  directed  towards  the 
moon,  notwithstanding  the  earth's  rotation.  This  may  be  called  the 
primitive  tide  of  the  ocean ;  but  on  account  of  the  perpetual  change  of 
place  which  is  required  for  the  accommodation  of  the  surface  to  a  similar 
position  with  respect  to  the  moon,  as  the  earth  revolves,  the  form  must  be 
materially  different  from  that  of  such  a  spheroid  of  equilibrium.  The 
force  employed  in  producing  this  accommodation  may  be  estimated  by 
considering  the  actual  surface  of  the  sea  as  that  of  a  wave  moving  on  the 
spheroid  of  equilibrium,  and  producing  in  the  water  a  sufficient  velocity  to 
preserve  the  actual  form.  We  may  deduce,  from  this  mode  of  considering 
the  subject,  a  theory  of  the  tides  which  appears  to  be  more  simple  and  satis- 
factory than  any  which  has  yet  been  published ;  and  by  comparing  the 
tides  of  narrower  seas  and  lakes  with  the  motions  of  pendulums  suspended 
on  vibrating  centres,  we  may  extend  the  theory  to  all  possible  cases. 

If  the  centre  of  a  pendulum  be  made  to  vibrate,  the  vibrations  of  the 
pendulum  itself,  when  they  have  arrived  at  a  state  of  permanence,  will  be 
performed  in  the  same  time  with  those  of  the  centre  ;  but  the  motion  of  the 
pendulum  will  be  either  in  the  same  direction  with  that  of  the  centre,  or  in 
a  contrary  direction,  accordingly  as  the  time  of  this  forced  vibration  is 
longer  or  shorter  than  that  of  the  natural  vibration  of  the  pendulum  ;  and 
in  the  same  manner  it  may  be  shown  that  the  tides  either  of  an  open  ocean 
or  of  a  confined  lake  may  be  either  direct  or  inverted  with  respect  to  the 
primitive  tide,  which  would  be  produced  if  the  waters  always  assumed  the 
form  of  the  spheroid  of  equilibrium  according  to  the  depth  of  the  ocean, 
and  to  the  breadth  as  well  as  the  depth  of  the  lake.  In  the  case  of  a  direct 
tide  the  time  of  the  passage  of  the  luminary  over  the  meridian  must  coin- 
cide with  that  of  high  water,  and  in  the  case  of  an  inverted  tide  with  that 
of  low  water. 

In  order  that  the  lunar  tides  of  an  open  ocean  may  be  direct,  or  synchro- 

'  nous,  its  depth  must  be  greater  than  13  miles,  and  for  the  solar  tides  than 

14.     The  less  the  depth  exceeded  these  limits,  the  greater  the  tides  would 


444  LECTURE  XLVII. 

be,  and  in  all  cases  they  would  be  greater  than  the  primitive  tides.  But  m 
fact  the  height  of  the  tides  in  the  open  ocean  is  always  far  short  of  that 
which  would  be  produced  in  this  manner ;  it  is  therefore  improbable  that 
the  tides  are  ever  direct  in  the  open  ocean,  and  that  the  depth  of  the  sea 
is  so  great  as  13  miles. 

In  order  that  the  height  of  the  inverted  or  remote  lunar  tides  may  be  five 
feet,  or  equal  to  that  of  the  primitive  tides,  the  depth  of  the  open  sea  must 
be  6 1  miles;  and  if  the  height  is  only  two  feet,  which  is  perhaps  not  far 
from  the  truth,  the  depth  must  be  3  miles  and  five  sevenths. 

The  tides  of  a  lake  or  narrow  sea  differ  materially  from  those  of  the  open 
ocean,  since  the  height  of  the  water  scarcely  undergoes  any  variation  in  the 
middle  of  the  lake  ;  it  must  always  be  high  water  at  the  eastern  extremity 
when  it  is  low  water  at  the  western ;  and  this  must  happen  at  the  time 
when  the  places  of  high  and  low  water,  with  respect  to  the  primitive 
tides,  are  equally  distant  from  the  middle  of  the  lake.  (Plate  XXXVIII. 
Fig.  520.) 

The  tides  may  be  direct  in  a  lake  100  fathoms  deep  and  less  than  8 
degrees  wide  ;  but  if  it  be  much  wider,  they  must  be  inverted.  Supposing 
the  depth  a  mile,  they  will  be  direct  when  the  breadth  is  less  than  25° ;  but 
if  a  sea,  like  the  Atlantic,  were  50  or  60  degrees  wide,  it  must  be  at  least 
four  miles  deep,  in  order  that  the  time  of  high  water  might  coincide  with 
that  of  the  moon's  southing. 

Hitherto  we  have  considered  the  motion  of  the  water  as  free  from  all 
resistance  ;  but  where  the  tides  are  direct,  they  must  be  retarded  by  the 
effect  of  a  resistance  of  any  kind  ;  and  where  they  are  inverted,  they  must 
be  accelerated ;  a  small  resistance  producing,  in  both  cases,  a  considerable 
difference  in  the  time  of  high  water. 

Where  a  considerable  tide  is  observed  in  the  middle  of  a  limited  portion 
of  the  sea,  it  must  be  derived  from  the  effect  of  the  elevation  or  depression 
of  the  ocean  in  its  neighbourhood  ;  and  such  derivative  tides  are  probably 
combined  in  almost  all  cases  with  the  oscillations  belonging  to  each  parti- 
cular branch  of  the  sea.  Mr.  Laplace  supposes  that  the  tides,  which  are 
observed  in  the  most  exposed  European  harbours,  are  produced  almost 
entirely  by  the  transmission  of  the  effect  of  the  main  ocean,  in  about  a  day 
and  a  half ;  but  this  opinion  does  not  appear  to  be  justified  by  observation  ; 
for  the  interval  between  the  times  of  the  high  water  belonging  to  the  same  tide, 
in  any  two  places  between  Brest  and  the  Cape  of  Good  Hope,  has  not  been 
observed  to  exceed  about  twelve  hours  at  most ;  nor  can  we  trace  a  greater 
difference  by  comparing  the  state  of  the  tides  at  the  more  exposed  situations 
of  St.  Helena,  the  Cape  Verd  Islands,  the  Canaries,  the  Madeiras,  and  the 
Azores,  which  constitute  such  a  succession  as  might  be  expected  to  have 
indicated  the  progress  of  the  principal  tide,  if  it  had  been  such  as  Mr. 
Laplace  supposes.  The  only  part  of  the  ocean  which  we  can  consider  as 
completely  open,  lies  to  the  south  of  the  two  great  continents,  chiefly 
between  the  latitudes  30°  and  70°  south,  and  the  original  tide,  which  hap- 
pens in  this  widely  extended  ocean,  where  its  depth  is  sufficiently  uniform, 
must  take  place,  according  to  the  theory  which  has  been  advanced,  at  some  ' 
time  before  the  sixth  lunar  hour.  It  sends  a  wave  into  the  Atlantic,  which 


ON  THE  TIDES.  445 

is  perhaps  12  or  13  hours  in  its  passage  to  the  coast  of  France,  but  cer- 
tainly not  more.  This  tide,  which  would  happen  at  the  sixth  lunar  hour 
after  the  moon's  transit,  if  there  were  no  resistance,  is  probably  so  checked 
by  the  resistance,  that  the  water  begins  to  subside  about  the  fourth,  and  in 
some  seas  even  somewhat  earlier,  although  in  others  it  may  follow  more 
nearly  its  natural  course.  There  is  scarcely  a  single  instance  wrhich 
favours  the  supposition  of  the  time  of  high  water  in  the  open  sea  being 
within  an  hour  of  the  moon's  southing,  as  it  must  be  if  the  depth  were 
very  great ;  so  that  neither  the  height  of  the  tides  nor  the  time  of  high 
water  will  allow  us  to  suppose  the  sea  any  where  quite  so  deep  as  4 
miles. 

The  tide  entering  the  Atlantic  appears  to  advance  northwards  at  the  rate 
of  about  500  miles  an  hour,  corresponding  to  a  depth  of  about  3  miles,  so 
as  to  reach  Sierra  Leone  at  the  8th  hour  after  the  moon's  southing  ;  this 
part  of  Africa  being  not  very  remote  from  the  meridian  of  the  middle  of 
the  south  Atlantic  ocean,  and  having  little  share  in  the  primitive  tides  of 
that  ocean.  The  southern  tide  seems  then  to  pass  by  Cape  Blanco  and 
Cape  Bojador,  to  arrive  at  Gibraltar  at  the  13th  hour,  and  to  unite  its 
effects  with  those  of  other  tides  at  various  parts  of  the  coast  of  Europe. 

We  may  therefore  consider  the  Atlantic  as  a  detached  sea  about  3500 
miles  broad  and  3  miles  deep  ;  and  a  sea  of  these  dimensions  is  susceptible 
of  tides  considerably  larger  than  those  of  the  ocean,  but  how  much  larger 
we  cannot  determine  without  more  accurate  measures.  These  tides  would 
happen  on  the  European  coasts,  if  there  were  no  resistance,  a  little  less 
than  five  hours  after  the  moon's  southing,  and  on  the  coast  of  America,  a 
little  more  that  seven  hours  after  ;  but  the  resistance  opposed  to  the  motion 
of  the  sea  may  easily  accelerate  the  time  of  high  water  in  both  cases  about 
two  hours,  so  that  it  may  be  a  little  before  the  third  hour  on  the  western 
coasts  of  Europe  and  of  Africa,  and  before  the  fifth  on  the  most  exposed 
parts  of  the  eastern  coast  of  America  ;  and  in  the  whole  of  the  Atlantic, 
this  tide  may  be  combined  more  or  less  both  with  the  general  southern 
tide,  and  with  the  partial  effects  of  local  elevations  or  depressions  of  the 
bottom  of  the  sea,  which  may  cause  irregularities  of  various  kinds.  The 
southern  tide  is,  however,  probably  less  considerable  than  has  sometimes 
been  supposed,  for,  in  the  latitudes  in  which  it  must  originate,  the  extent 
of  the  elevation  can  only  be  half  as  great  as  at  the  equator  ;  and  the  Islands 
of  Kergulen's  Land  and  South  Georgia,  in  the  latitudes  of  about  50°  and 
55°,  have  their  tides  delayed  till  the  10th  and  llth  hours,  apparently 
because  they  receive  them  principally  from  distant  parts  of  the  ocean, 
which  are  nearer  to  the  equator. 

On  the  western  coasts  of  Europe,  from  Ireland  to  Cadiz,  on  those  of 
Africa,  from  Cape  Coast  to  the  Cape  of  Good  Hope,  and  on  the  coast 
of  America,  from  California  to  the  streights  of  Magellan,  as  well  as  in  the 
neighbouring  islands,  it  is  usually  high  water  at  some  time  between  two 
and  four  hours  after  the  moon's  southing  ;  on  the  eastern  coast  of  South 
,  America  between  four  and  six,  on  that  of  North  America  between  seven 
and  eleven  ;  and  on  the  eastern  coasts  of  Asia  and  New  Holland  between 
four  and  eight.  The  Society  islands  are  perhaps  too  near  the  middle  of  the 


44G  LECTURE   XLVII. 

Pacific  ocean  to  partake  of  the  effects  of  its  primitive  tide,  and  their  tide, 
being  secondary,  is  probably  for  this  reason  a  few  hours  later.  At  the 
Alniirantes,  near  the  eastern  coast  of  Africa,  the  tide  is  at  the  sixth  hour  ; 
but  there  seem  to  be  some  irregularities  in  the  tides  of  the  neighbouring 
islands. 

The  progress  of  a  tide  may  be  very  distinctly  traced  from  its  source  in 
the  ocean  into  the  narrow  and  shallow  branches  of  the  sea  which  constitute 
our  channels.  Thus  the  tide  is  an  hour  or  two  later  at  the  Scilly  Islands 
than  in  the  Atlantic,  at  Plymouth  three,  at  Cork,  Bristol,  and  Weymouth 
four,  at  Caen  and  Havre  six,  at  Dublin  and  Brighthelmstone  seven,  at 
Boulogne  and  Liverpool  eight,  at  Dover  near  nine,  at  the  Nore  eleven,  and 
at  London  bridge  twelve  and  a  half.  Another  portion  appears  to  proceed 
round  Ireland  and  Scotland  into  the  North  Sea  ;  it  arrives  from  the  Atlantic 
at  Londonderry  in  about  three  hours,  at  the  Orkneys  in  six,  at  Aberdeen 
in  eleven,  at  Leith  in  fourteen,  at  Leostoffe  in  twenty,  and  at  the  Nore  in 
about  twenty-four,  so  as  to  meet  there  the  subsequent  tide  coming  from 
the  south.  From  the  time  occupied  by  the  tide  in  travelling  from  the 
mouth  of  the  English  channel  to  Boulogne,  at  the  rate  of  about  50  miles  an 
hour,  we  may  calculate  that  the  mean  depth  of  the  channel  is  about  28 
fathoms,  independently  of  the  magnitude  of  the  resistances  of  various 
kinds  to  be  overcome,  which  require  us  to  suppose  the  depth  from  30  to  40 
fathoms.  In  the  great  river  of  Amazons,  the  effects  of  the  tides  are  still 
sensible  at  the  streights  of  Pauxis,  500  miles  from  the  sea,  after  an  interval 
of  several  days  spent  in  their  passage  up  ;  for  the  slower  progressive  motion 
of  the  water  no  more  impedes  the  progress  of  a  wave  against  the  stream, 
than  the  velocity  of  the  wind  prevents  the  transmission  of  sound  in  a  con- 
trary direction.  (Plate  XXXVIII.  Fig.  521.) 

Such  are  the  general  outlines  of  the  lunar  tides  ;  they  are,  however,  liable 
to  a  great  variety  of  modifications,  besides  their  combination  with  the  tides 
produced  by  the  sun.  When  the  moon  is  exactly  over  the  equator,  the 
highest  part  of  the  remoter,  or  inferior,  as  well  as  of  the  nearer  or  superior 
tides,  passes  also  over  the  equator,  and  the  effect  of  the  tide  in  various  lati- 
tudes decreases  gradually  from  the  equator  to  the  pole,  where  it  vanishes  ; 
but  when  the  moon  has  north  or  south  declination,  the  two  opposite 
summits  of  the  spheroid  describe  parallels  of  latitude,  remaining  always 
diametrically  opposite  to  each  other.  Hehce  the  two  successive  tides  must 
be  unequal  at  every  place  except  the  equator,  the  greater  tide  happening 
when  the  nearer  elevation  passes  its  meridian  ;  and  the  mean  between  both 
is  somewhat  smaller  than  the  equal  tides  which  happen  when  the  moon 
passes  the  equator.  This  inequality  is,  however,  much  less  considerable 
than  it  would  be  if  the  sea  assumed  at  once  the  form  of  the  spheroid 
of  equilibrium  ;  and  the  most  probable  reasons  for  this  circumstance,  are, 
first,  that  our  tides  are  partly  derived  from  the  equatorial  seas  ;  secondly, 
that  the  effects  of  a  preceding  tide  are  in  some  measure  continued  so 
as  to  influence  the  height  of  a  succeeding  one;  and,  thirdly,  that  the 
tides  of  a  narrow  sea  are  less  affected  by  its  latitude  than  those  of  a  wide 
ocean.  The  height  of  the  sea  at  low  water  is  the  same  whatever  the 
moon's  declination  may  be.  There  is  also  a  slight  difference  in  the  tides, 


ON  THE  TIDES.  447 

according  to  the  place  of  the  moon's  nodes,  which  allows  her  declination  to 
be  greater  or  less,  and  this  difference  is  most  observable  in  high  latitudes, 
for  instance,  in  Iceland  ;  since,  in  the  neighbourhood  of  the  poles,  the  tides 
depend  almost  entirely  on  the  declination. 

In  all  these  cases,  the  law  of  the  elevation  and  depression  of  each  tide  may 
be  derived,  like  that  of  the  vibrations  of  a  pendulum  and  of  a  balance,  from 
the  uniform  motion  of  a  point  in  a  circle.  Thus,  if  we  conceive  a  circle  to 
be  placed  in  a  vertical  plane,  having  its  diameter  equal  to  the  whole  mag- 
nitude of  the  tide,  and  touching  the  surface  of  the  sea  at  low  water,  the 
point,  in  which  the  surface  meets  the  circumference  of  the  circle,  will 
advance  with  a  uniform  motion,  so  that  if  the  circle  be  divided  into  12 
parts,  the  point  will  pass  over  each  of  these  parts  in  a  lunar  hour.  It 
sometimes  happens,  however,  in  confined  situations,  that  the  rise  and  fall 
of  the  water  deviates  considerably  from  this  law,  and  the  tide  rises  some- 
what more  rapidly  than  it  falls  ;  and  in  rivers,  for  example  in  the  Severn, 
the  tide  frequently  advances  suddenly  with  a  head  of  several  feet  in  height. 
These  deviations  probably  depend  on  the  magnitude  of  the  actual  displace- 
ment of  the  water,  which  in  such  cases  bears  a  considerable  proportion  to 
the  velocity  of  the  tide,  while  in  the  open  ocean  a  very  minute  progressive 
motion  is  sufficient  to  produce  the  whole  elevation.  The  actual  progress  of 
the  tides  may  be  most  conveniently  observed,  by  means  of  a  pipe  descending 
to  some  distance  below  the  surface,  so  as  to  be  beyond  the  reach  of  super- 
ficial agitations,  and  having  within  it  a  float,  carrying  a  wire,  and  indicating 
the  height  of  the  water  on  a  scale  properly  divided. 

We  have  hitherto  considered  the  tides  so  far  only  as  they  are  occasioned 
by  the  moon  ;  but  in  fact  the  tides,  as  they  actually  exist,  depend  also  on 
the  action  of  the  sun,  which  produces  a  series  of  effects  precisely  similar  to 
those  of  the  moon,  although  much  less  conspicuous,  on  account  of  the 
greater  distance  of  the  sun,  the  solar  tide  being  only  about  two  fifths  of  the 
lunar.  These  tides  take  place  independently  of  each  other,  nearly  in  the 
same  degree  as  if  both  were  single  ;  and  the  combination  resulting  from 
them  is  alternately  increased  and  diminished,  accordingly  as  they  agree,  or 
disagree,  with  respect  to  the  time  of  high  water  at  a  given  place  ;  in  the 
same  manner  as  if  two  series  of  waves,  equal  among  themselves,  of  which 
the  breadths  are  as  29  to  30,  be  supposed  to  pass  in  the  same  direction  over 
the  surface  of  a  fluid,  or  if  two  sounds  similarly  related  be  heard  at  the  same 
time,  a  periodical  increase  and  diminution  of  the  joint  effect  will  in  either 
case  be  produced.  Hence  are  derived  the  spring  and  neap  tides,  the  effects 
of  the  sun  and  moon  being  united  at  the  times  of  conjunction  and  oppo- 
sition, or  of  the  new  and  full  moon,  and  opposed  at  the  quadratures,  or  first 
and  last  quarters.  The  high  tides  at  the  times  of  the  equinoxes  are  pro- 
duced by  the  joint  operation  of  the  sun  and  moon,  when  both  of  them  are 
so  situated  as  to  act  more  powerfully  than  elsewhere. 

The  lunar  tide  being  much  larger  than  the  solar  tide,  it  must  always 
determine  the  time  of  high  and  low  water,  which,  in  the  spring  and  neap 
tides,  remains  unaltered  by  the  effect  of  the  sun  ;  so  that  in  the  neap  tides, 
the  actual  time  of  low  water  is  that  of  the  solar  high  water ;  but  at  the 
intermediate  times,  the  lunar  high  water  is  more  or  less  accelerated  or 


448  LECTURE  XLVII. 

retarded.  The  progress  of  this  alteration  may  easily  be  traced  by  means  of 
a  simple  construction.  If  we  make  a  triangle  of  which  two  of  the  sides  are 
two  feet  and  five  feet  in  length,  the  external  angle  which  they  form  being 
equal  to  twice  the  distance  of  the  luminaries,  the  third  side  will  show  pre- 
cisely the  magnitude  of  the  compound  tide,  and  the  halves  of  the  two 
angles  opposite  to  the  first  two  sides  the  acceleration,  or  retardation,  of  the 
times  of  high  water  belonging  to  the  separate  tides  respectively.  Hence  it 
appears  that  the  greatest  deviation  of  the  joint  tide  from  the  lunar  tide 
amounts  to  11°  48'  in  longitude,  and  the  time  corresponding,  to  47  minutes, 
supposing  the  proportion  of  the  forces  to  remain  always  the  same  ;  but  in 
fact  the  forces  increase  in  proportion  as  the  cubes  of  the  distances  of  their 
respective  luminaries  diminish,  as  well  as  from  other  causes  ;  and  in  order 
to  determine  their  joint  effects,  the  lengths  of  the  sides  of  the  triangle  must 
be  varied  accordingly.  In  some  ports,  from  a  combination  of  circum- 
stances in  the  channel,  by  which  the  tides  reach  them,  or  in  the  seas,  in 
which  they  originate,  the  influence  of  the  sun  and  moon  may  acquire 
a  proportion  somewhat  different  from  that  which  naturally  belongs  to 
them  :  thus  at  Brest,  the  influence  of  the  moon  appears  to  be  three  times  as 
great  as  that  of  the  sun  ;  when  it  is  usually  only  twice  and  a  half  as  great. 
(Plate  XXXVIII.  Fig.  522.) 

The  greatest  and  least  tides  do  not  happen  immediately  at  the  times  of  the 
new  and  full  moon,  but  at  least  two,  and  commonly  three  tides  after,  even 
at  those  places  which  are  most  immediately  exposed  to  the  effects  of  the 
general  tide  of  the  ocean.  The  theory  which  has  been  advanced  will 
afford  us  a  very  satisfactory  reason  for  this  circumstance ;  the  resistance 
of  fluids  in  general  is  as  the  square  of  the  velocity,  consequently  it  must 
be  much  greater  for  the  lunar  than  for  the  solar  tide,  in  proportion  to  the 
magnitude  of  the  force,  and  the  acceleration  of  the  lunar  tide  produced 
by  this  cause  must  be  greater  than  that  of  the  solar  ;  hence  it  may  happen 
that  when  the  lunar  tide  occurs  two  or  three  hours  after  the  transit  of  the 
moon,  the  solar  tide  may  be  three  or  four  hours  after  that  of  the  sun, 
so  as  to  be  about  an  hour  later,  at  the  times  of  conjunction  and  opposition, 
and  the  tides  will  be  highest  when  the  moon  passes  the  meridian  about  an 
hour  after  the  sun  ;  while  at  the  precise  time  of  the  new  and  full  moon,  the 
lunar  tide  will  be  retarded  about  a  quarter  of  an  hour  by  the  effect  of  the 
solar  tide. 

The  particular  forms  of  the  channels,  through  which  the  tides  arrive  at 
different  places,  produce  in  them  a  great  variety  of  local  modifications ; 
of  which  the  most  usual  is,  that  from  the  convergence  of  the  shores  of  the 
channels,  the  tides  rise  to  a  much  greater  height  than  in  the  open  sea. 
Thus  at  Brest  the  height  of  the  tides  is  about  20  feet,  at  Bristol  30,  at 
Chepstow  40,  at  St.  Maloes  50 ;  and  at  Annapolis  Royal,  in  the  Bay  of 
Fundy,  as  much  sometimes  as  100  feet ;  although  perhaps  in  some  of  these 
cases  a  partial  oscillation  of  a  limited  portion  of  the  sea  may  be  an  imme- 
diate effect  of  the  attraction  of  the  luminary.  In  the  Mediterranean  the 
tides  are  generally  inconsiderable,  but  they  are  still  perceptible  ;  at  Naples 
they  sometimes  amount  to  a  foot,  at  Venice  to  more  than  two  feet,  and  in 
the  Euripus,  for  a  certain  number  of  days  in  each  lunation,  they  are  very 


ON  THE  TIDES.  449 

distinctly  observable,  from  the  currents  which  they  occasion.  In  the  West 
Indies,  also,  and  in  the  gulf  of  Mexico,  the  tides  are  less  marked  than  in 
the  neighbouring  seas,  perhaps  on  account  of  some  combinations  derived 
from  the  variations  of  the  depth  of  the  ocean,  and  from  the  different 
channels  by  which  they  are  propagated. 

In  order  to  understand  the  more  readily  the  effects  of  such  combinations, 
we  may  imagine  a  canal,  as  large  as  the  river  of  Amazons,  to  communi- 
cate at  both  its  extremities  with  the  ocean,  so  as  to  receive  at  each  an  equal 
series  of  tides,  passing  towards  the  opposite  extremity.  If  we  suppose  the 
tides  to  enter  at  the  same  instant  at  both  ends,  they  will  meet  in  the  middle, 
'and  continue  their  progress  without  interruption  :  precisely  in  the  middle 
the  times  of  high  and  low  water  belonging  to  each  series  will  always  coin- 
cide, and  the  effects  will  be  doubled ;  and  the  same  will  happen  at  the 
points  where  a  tide  arrives  from  one  extremity  at  the  same  instant  that  an 
earlier  or  a  later  tide  comes  from  the  other  ;  but  at  the  intermediate  points 
the  effects  will  be  diminished,  and  at  some  of  them  completely  destroyed, 
where  the  high  water  of  one  tide  coincides  with  the  low  water  of  another. 
The  tides  at  the  port  of  Batsha  in  Tonkin  have  been  explained  by  Newton 
from  considerations  of  this  nature.  In  this  port  there  is  only  one  tide  in  a 
day  ;  it  is  high  water  at  the  sixth  lunar  hour,  or  at  the  moon's  setting, 
when  the  moon  has  north  declination,  and  at  her  rising,  when  she  has 
south  declination  ;  and  when  the  moon  has  no  declination  there  is  no  tide. 
In  order  to  explain  this  circumstance,  we  may  represent  the  two  unequal 
tides  which  happen  in  succession  every  day,  by  combining  with  two  equal 
tides  another  tide,  independent  of  them,  and  happening  only  once  a  day  ; 
then,  if  a  point  be  so  situated  in  the  canal  which  we  have  been  considering, 
that  the  effects  of  the  two  equal  semidiurnal  tides  may  be  destroyed,  those 
of  the  daily  tides  only  will  remain  to  be  combined  with  each  other  ;  and 
their  joint  result  will  be  a  tide  as  much  greater  than  either,  as  the  diagonal 
of  a  square  is  greater  than  its  side  ;  the  times  of  high  and  low  water  being- 
intermediate  between  those  which  belong  to  the  diurnal  tides  considered 
separately.  Thus,  in  the  port  of  Batsha,  the  greater  tide  probably  arrives 
at  the  third  lunar  hour  directly  from  the  Pacific  ocean,  and  at  the  ninth 
from  the  gulf  of  Siam,  having  passed  between  Sumatra  and  Borneo  ;  so  that 
the  actual  time  of  high  water  is  at  the  sixth  lunar  hour.  The  magnitude  of 
this  compound  tide  is  by  no  means  inconsiderable  ;  it  sometimes  amounts 
to  as  much  as  13  feet.  (Plate  XXXVIII.  Fig.  523,  524.) 

Besides  the  variations  in  the  height  of  the  sea,  which  constitute  the  tides, 
a  current  is  observed  in  its  most  exposed  parts,  of  which  the  general  direc- 
tion is  from  east  to  west.  This  current  comes  from  the  Pacific  and  Indian 
oceans,  round  the  Cape  of  Good  Hope,  along  the  coast  of  Africa,  then 
crosses  to  America,  and  is  there  divided  and  reflected  southwards  towards 
the  Brazils,  and  northwards  into  the  Gulf  stream  which  travels  round  the 
gulf  of  Mexico,  and  proceeds  north  eastwards  into  the  neighbourhood  of 
Newfoundland,  and  then  probably  eastwards  and  south  eastwards  once 
more  across  the  Atlantic.  It  is  perhaps  on  account  of  these  currents  that 
the  Red  Sea  is  found  to  be  about  25  feet  higher  than  the  Mediterranean  : 
their  direction  may  possibly  have  been  somewhat  changed  in  the  course  of 

2G 


450  LECTURE  XLVII. 

many  ages,  and  with  it  the  level  of  the  Mediterranean  also  ;  since  the  floor 
of  the  cathedral  at  Ravenna  is  now  several  feet  lower  with  respect  to  the  sea 
than  it  is  supposed  to  have  been  formerly,  and  some  steps  have  been  found 
in  the  rock  of  Malta,  apparently  intended  for  ascending  it,  which  are  at 
present  under  water. 

The  atmosphere  is  also  liable  to  elevations  and  depressions  analogous  to 
those  of  the  sea,  and  perhaps  these  changes  may  have  some  little  effect  on 
the  winds  and  on  the  weather ;  but  their  influence  must  be  very  incon- 
siderable, since  the  addition  of  two  or  three  feet  to  the  height  of  the  atmo- 
sphere at  any  part  can  scarcely  be  expected  to  be  perceptible.  The  height  of 
an  aerial  tide  must  be  very  nearly  the  same  with  the  observed  height  of  the 
principal  tides  of  the  sea  ;  and  the  variation  of  atmospherical  pressure,  which 
is  measured  by  the  difference  between  the  actual  form  and  the  spheroid  of 
equilibrium,  must  be  equivalent  to  the  weight  of  a  column  of  about  10  feet 
of  air,  or  only  -^  of  an  inch  of  mercury.  A  periodical  variation  five  times 
as  great  as  this  has  indeed  been  observed  near  the  equator,  where  the  state 
of  'the  atmosphere  is  the  least  liable  to  accidental  disturbances ;  but  this 
change  cannot  in  any  degree  be  referred  to  the  effect  of  the  moon's  action, 
since  it  happens  always  about  the  same  hour  of  the  day  or  night.  The 
atmosphere  is  also  affected  by  a  general  current  from  east  to  west,  like 
that  of  the  sea,  and  there  is  reason,  from  astronomical  observations,  to 
suppose  that  a  similar  circumstance  happens  in  the  atmosphere  of  Jupiter. 
These  currents,  as  well  as  the  general  current  of  the  sea,  have  been  attri- 
buted, by  some  astronomers,  to  the  immediate  attraction  of  the  sun  and 
moon,  and  of  the  satellites  of  Jupiter,  which  they  have  supposed  to  act  in 
the  same  manner  as  the  attraction  of  the  sun  operates  in  retarding  the 
lunar  motions  ;  but  the  fact  is,  that,  according  to  Mr.  Laplace,  the  disturb- 
ing force  of  the  sun  produces  this  effect  on  the  moon  only  in  proportion  as  it 
increases  her  distance  from  the  earth ;  consequently  no  such  retardation 
can  possibly  be  produced  by  the  force  of  gravitation  in  the  rotation  of  the 
sea  or  of  the  atmosphere,  and  the  whole  effect  must  be  attributed  to  the 
operation  of  meteorological  causes,  producing  first  the  trade  winds,  and 
secondly  occasioning,  by  means  of  the  friction  of  these  winds,  a  similar 
motion  in  the  sea.  In  the  case  of  the  atmosphere  of  Jupiter,  the  effects  of 
heat  can  indeed  scarcely  be  supposed  to  be  very  perceptible,  and  the  rota- 
tion of  this  planet  being  extremely  rapid,  it  is  not  at  all  impossible  that  the 
satellites  may  exert  an  action  on  the  atmosphere  somewhat  analogous  to 
the  retardation  of  the  moon's  motion  by  the  disturbing  force  of  the  sun. 


LECT.  XLVII.— ADDITIONAL  AUTHORITIES. 

Borro,  DelFlusso  e  Reflusso  del  Mare,  Fiorenza,  1577.  Moray  on  Observing  the 
Tides,  Ph.  Tr.  1665-6,  i.  298.  Colepresse's  Obs.  at  Plymouth,  ibid.  1668,  iii.  632. 
Davenport  on  the  Tides  at  Tonqueen,  ibid.  1684,  p.  677.  Halley  on  do.  ibid.  1684, 
p.  685.  Newtoni  Principia,  and  Halley's  Remarks,  ibid.  1697,  p.  445.  Prize 
Essays  on  the  Tides,  by  Cavalleri,  Bernoulli,  Maclaurin,  and  Euler,  Hist,  et  Mem. 
Prix  iv.  VI.. .  IX.  Le  Seur's  edition  of  Newton's  Principia.  Jones  and  Saumare* 
on  the  Tides  in  the  Thames,  Ph.  Tr.  1726,  p.  68.  Wright  on  an  irregular  Tide  in  the 
Forth  (the  Leaky),  ibid.  1750,  p.  412.  Toaldo,  Tabula  Barometri  ^Estusque  Maris, 


ON  THE  HISTORY  OF  ASTRONOMY.  451 

4to,  Pavia,  1773.  On  the  Tides  in  the  Adriatic,  Ph.  Tr.  1777,  p.  144.  Lalande, 
Traite  du  Flux  et  du  Reflux  de  la  Mer,  4to,  Paris,  1781.  Laplace,  Mec.  Celeste, 
lib.  v.  Lubbock,  Ph.  Tr.  1831,  p.  379  ;  1832,  pp.  51,  595  ;  1833,  p.  19  ;  1834, 
p.  143;  1835,  p.  275  ;  1836,  pp.  57,  217 ;  1837,  p.  97.  Whewell's  Cotidal  Lines, 
Ph.  Tr.  1833,  p.  147.  Researches  on  the  Tides,  ibid.  1834,  p.  15 ;  1835,  p.  83  ; 
1836,  pp.  1,  131,  289;  1837,  pp.  75,  227;  1838,  p.  231  ;  1839,  pp.  151,  163; 
1840,  pp.  161,255.  Palmer's  Tide  Gauge,  Ph.  Tr.  1831,  p.  209.  Bunt's,  ibid. 
1838,  p.  249.  Daussy,  Connaissance  des  Temps,  1834  (a  low  barometer  is  accom- 
panied with  high  tides).  Bunt,  Eleventh  Report  of  Brit.  Ass. 


LECTURE    XLVIII. 


ON  THE  HISTORY  OF  ASTRONOMY. 

WE  have  now  taken  a  general  view  of  the  most  striking  phenomena  of 
the  universe  at  large,  of  the  great  features  of  the  solar  system,  and  of  the 
peculiarities  of  the  planet  which  we  inhabit,  with  respect  both  to  its  solid 
and  to  its  fluid  parts.  All  these  are  departments  of  astronomy,  and  we  shall 
conclude  our  examination  of  the  subject  with  a  summary  of  the  history  of 
the  science,  principally  extracted  and  abridged  from  Laplace's  Exposition 
du  syst&me  du  monde. 

In  all  probability  the  astronomy  of  the  earliest  ages  was  confined  to 
observations  of  the  obvious  motions  and  eclipses  of  the  sun  and  moon,  the 
rising,  setting,  and  occupations  of  the  principal  stars,  and  the  apparent 
motions  of  the  .planets.  The  progress  of  the  sun  was  followed,  by  remarking 
the  stars  as  they  were  lost  in  the  twilight,  and  perhaps  also  by  the  variation 
of  the  length  of  the  shadow  of  a  detached  object,  observed  at  the  time  of 
the  day  when  it  was  shortest.  In  order  to  recognise  the  fixed  stars,  and 
their  different  motions,  the  heavens  were  divided  into  constellations  ;  and 
twelve  of  these  occupied  the  zone  denominated  the  zodiac,  within  the  limits 
of  which  the  sun  and  planets  were  always  found. 

The  entrance  of  the  sun  into  the  constellation  aries,  or  the  ram,  denoted, 
in  the  time  of  Hipparchus,  the  beginning  of  the  spring ;  and  as  the  season 
advanced,  the  sun  continued  his  progress  through  the  bull,  the  twins,  and 
the  other  signs  in  order ;  some  of  which  appear  to  have  been  denominated 
from  their  relation  to  the  agriculture  and  to  the  climates  of  the  countries 
in  which  they  were  imagined,  and  others  from  the  celestial  phenomena 
attending  the  sun's  passage  through  them  ;  the  crab,  for  example,  denot- 
ing his  retrograde  motion  after  the  time  of  the  solstice,  and  the  balance 
the  equality  of  day  and  night  at  the  autumnal  equinox.  But  the  motion 
of  the  equinoctial  points  having  changed  in  some  degree  the  course  of 
the  seasons  with  regard  to  the  stars,  the  signs  of  the  ecliptic,  by  which 
the  places  of  the  sun  and  planets  are  described,  no  longer  coincide  pre- 
cisely with  the  constellations  of  the  zodiac  from  which  they  derive  their 
names. 

The  most  ancient  observations  of  which  we  are  in  possession,  that  are 

2  G  2 


452  LECTURE  XLVIII. 

sufficiently  accurate  to  be  employed  in  astronomical  calculations,  are  those 
made  at  Babylon  in  the  years  71 9  and  720  before  the  Christian  era,  of  three 
eclipses  of  the  moon.  Ptolemy,*  who  has  transmitted  them  to  us,  employed 
them  for  determining  the  period  of  the  moon's  mean  motion,  and,  therefore, 
had  probably  none  more  ancient  on  which  he  could  depend.  The  Chal- 
deans, t  however,  must  have  made  a  long  series  of  observations  before  they 
could  discover  their  Saros  or  lunar  period  of  6585^  days,  or  about  18  years, 
in  which  (as  they  had  learnt  at  a  very  early  time)  the  place  of  the  moon, 
her  node  and  apogee  return  nearly  to  the  same  situation  with  respect  to 
the  earth  and  sun ;  and  of  course  a  series  of  nearly  similar  eclipses  recurs. 
The  observations  attributed  to  Hermes  indicate  a  date  seven  hundred  years 
earlier  than  those  of  the  Babylonians,  but  their  authenticity  appears  to  be 
extremely  doubtful. 

The  Egyptians  J  were  very  early  acquainted  with  the  length  of  the  year, 
as  consisting  nearly  of  365  days  and  a  quarter,  and  they  derived  from  it 
their  Sothic  period  of  1460  years,  containing  365  days  each.  The  accurate 
correspondence  of  the  faces  of  their  pyramids  with  the  points  of  the  compass 
is  considered  as  a  proof  of  the  precision  of  their  observations  :§  but  their 
greatest  merit  was  the  discovery  that  Mercury  and  Venus  revolve  round 
the  sun,  and  not  round  the  earth,  as  it  had  probably  been  before  believed  :|| 
they  did  not,  however,  suppose  the  same  of  the  superior  planets.  (Plate 
XXXVIII.  Fig.  525,  526.) 

In  Persia  and  in  India,  the  origin  of  astronomy  is  lost  in  the  darkness 
which  envelopes  the  early  history  of  those  countries.  We  find  the  annals 
of  no  country  so  ancient  and  so  well  authenticated  as  those  of  China,  which 
are  confirmed  by  an  incontestable  series  of  historical  monuments.  The 
regulation  of  the  calendar,  and  the  prediction  of  eclipses,  were  regarded  in 
this  country  as  important  objects,  for  which  a  mathematical  tribunal  was 
established  at  a  very  early  period.  But  the  scrupulous  attachment  of  the 
Chinese  to  their  ancient  customs,  extending  itself  even  to  their  astronomy, 
has  impeded  its  progress,  and  retained  it  in  a  state  of  infancy.  The  Indian 
tables  indicate  a  much  higher  degree  of  perfection  in  the  early  state  of  the 
science  than  it  had  attained  in  China  ;  but  we  have  every  reason  to  believe 
that  they  are  not  of  very  remote  antiquity.  "  Here,"  says  Mr.  Laplace, IT 
who  must  be  allowed  to  be  free  from  prejudices  in  favour  of  established 
opinions,  "  I  am  sorry  to  be  obliged  to  differ  from  an  illustrious  philoso- 
pher, Mr.  Bailly,  who,  after  having  distinguished  his  career  by  a  variety  of 
labours  useful  to  the  sciences,  and  to  mankind  at  large,  fell  a  victim  to  the 
most  sanguinary  tyranny  that  ever  disgraced  a  civilised  nation.  The 
Indian  tables  are  referred  to  two  principal  epochs,  which  are  placed  the 
one  3102  years  before  Christ,  the  other  1491.  These  are  connected  by  the 
mean  motions,  and  not  the  true  motions,  of  the  sun,  the  moon,  and  the 
planets ;  so  that  one  of  the  epochs  must  necessarily  be  fabulous.  The  cele- 

.*  Ptol.  Almagest.  1.  4,  c.  6. 

t  Suidas,  Lexicon  (Saros).     Pliny,  Hist.  Nat.  1.  2,  c.  13. 

J  Giraud,  Journal  des  Savans,  1760. 

§  Mem.  del'Acad.  1710.  c 

||  Macrobius,  Comm.  in  Somn.  Scip.  1.1,  c.  9. 

f  Exposition  du  Systeme  du  Monde,  2nd  edit.  p.  239. 


ON  THE  HISTORY  OF  ASTRONOMY.  453 

brated  author,  who  has  been  mentioned,  has  sought  to  establish,  in  his 
treatise  on  Indian  astronomy,  that  the  former  of  these  epochs  is  founded  on 
observation.  But  if  we  calculate  from  our  own  improved  tables,  we  shall 
find  that  the  general  conjunction  of  the  sun,  moon,  and  planets,  which  the 
Indian  tables  suppose,  in  reality  never  happened,  although  it  may  be 
deduced,  according  to  those  tables,  by  ascending  from  the  later  series.  The 
equation  of  the  sun's  centre,  depending  on  the  eccentricity  of  the  earth's 
orbit,  appears  indeed  to  indicate  a  still  higher  antiquity  ;  but  its  magni- 
tude, as  deduced  from  eclipses,  must  have  been  affected  by  a  contrary  error 
with  respect  to  the  moon's  place  :  and  the  determination  of  the  mean  motion 
of  the  moon  seems  to  make  it  probable  that  these  tables  are  even  of  a  later 
date  than  Ptolemy." 

In  astronomy,  as  well  as  in  other  sciences,  the  Greeks  were  the  disciples 
of  the  Egyptians  ;  they  appear  to  have  divided  the  stars  into  constellations 
13  or  1400  years  before  Christ.  Newton  attributes  this  arrangement  to 
Chiron,*  and  he  supposes  that  he  made  the  middle  of  the  constellations  cor- 
respond to  the  beginning  of  the  respective  signs.  But  until  the  time  of  the 
foundation  of  the  school  of  Alexandria,  the  Greeks  treated  astronomy  as  a 
science  purely  speculative,  and  indulged  themselves  in  the  most  frivolous 
conjectures  respecting  it.  It  is  singular  that  amidst  the  confusion  of  sys- 
tems heaped  up  on  each  other,  without  affording  the  least  information  to 
the  mind,  it  should  never  have  occurred  to  men  of  so  great  talents,  that  th 
only  way  to  become  accurately  acquainted  with  nature,  is  to  institute 
experimental  inquiries  throughout  her  works. 

Thales  of  Miletus,  who  was  born  in  the  year  640  before  Christ,  having  tra- 
velled and  studied  in  Egypt,  founded,  on  his  return,  the  Ionian  school  of 
philosophy,  in.  which  he  taught  the  sphericity  of  the  earth,f  and  the  obli- 
quity of  the  ecliptic  with  respect  to  the  equator.^  He  also  explained 
the  true  causes  of  eclipses,§  which  he  was  even  able  to  foretel,||  unques- 
tionably by  means  of  the  information  that  he  had  obtained  from  the  Egyp- 
tian priests. 

Pythagoras  of  Samos  was  born  590  years  before  Christ ;  he  probably 
profited  by  the  information  which  Thales  had  acquired,  and  travelled  also 
into  Egypt  for  his  further  improvement.^  It  is  conjectured  that  he  was 
acquainted  with  the  diurnal  and  annual  motions  of  the  earth,**  but  he  did 
not  publicly  profess  the  true  system  of  the  world.  It  was  taught  after  his 
death,  by  his  disciple  Philolaus,  about  the  year  450,  as  well  as  by  Nicetas,ft 
and  by  others  of  the  school.  They  considered  all  the  planets  as  revolving 
round  the  sun,^  and  as  inhabited  globes  ;  and  they  understood  that  the 

*  Chronology,  p.  25. 

t  Plutarch,  de  Placit.  Philos.  1.  2,  c.  9,  10. 

t  Diogenes  Laertius,  Life  of  Thales.  Plutarch,  Conviv.  Sept.  Sapient.  Proclus, 
Comm.  in  Euc.  1. 1. 

§  Plutarch,  de  Placit.  1.  2,  c.  21,  24,  28. 

||  Herod,  l.-l,  &c.  Pliny,  Nat.  Hist.  1.  2,  c.  12.  Riccioli,  Almagest.  Nov.  i. 
363.  Costard,  Ph.  Tr.  xlviii.  17.  Baily,  ibid.  1811. 

fl  Jamblichus,  Vita  Pythag.  **  Aristotle,  de  Coelo,  1.  2,  c.  13. 

*    ft  Cicero,  Qusest  Acad.  1.  4,  §39. 

Jt  Plin.  Hist.  Nat.  1.  2,  c.  22.  Macrob.  in  Somn.  Scip.  1.  1.  c.  19.  Greeorii 
Prtef.  ad  Ast.  &c. 


454  LECTURE  XLVIII.  / 

comets  were  only  eccentric  planets.*  Some  time  after  this,  the  lunar 
period  of  Meto  was  publicly  made  known  at  the  Olympic  games,  and  was 
universally  adopted  as  the  basis  of  the  calendar.  (Plate  XXXVIII.  Fig. 
527.) 

The  next  occurrence  which  deserves  to  be  noticed,  with  respect  to  astro- 
nomy, is  the  foundation  of  the  school  of  Alexandria,  which  waa  the  first 
source  of  accurate  and  continued  observations.  Upon  the  death  of  Alex- 
ander and  the  subsequent  division  of  his  empire,  the  province  of  Egypt 
fell  to  the  lot  of  Ptolemy  Soter  ;  a  prince  whose  love  of  science,  and  whose 
munificence  towards  its  professors,  attracted  to  his  capital  a  great  number 
of  learned  men  from  various  parts  of  Greece.  His  son,  Ptolemy  Phila- 
delphus,  continued  and  increased  the  benefits  conferred  on  them  by  his 
father,  and  built  the  magnificent  edifice  which  contained,  together  with 
the  celebrated  library,  collected  by  Demetrius  Phalereus,  an  observatory, 
furnished  with  the  necessary  books  and  instruments.t  The  first  astro- 
nomers, who  were  appointed  to  occupy  this  building,  were  Aristyllus  and 
Timocharis ;  they  flourished  about  300  years  before  Christ,  and  observed 
with  accuracy  the  places  of  the  principal  stars  of  the  zodiac. £  Aristarchus 
of  Samos  was  the  next :  he  imagined  a  method  of  finding  the  sun's 
distance,  by  observing  the  portion  of  the  moon's  disc  that  is  enlightened, 
when  she  is  precisely  in  the  quadrature,  or  90°  distant  from  the  sun  ;  and 
although  he  failed  in  his  attempt  to  determine  the  sun's  distance  with 
accuracy,  yet  he  showed  that  it  was  much  greater  than  could  at  that  time 
have  been  otherwise  imagined  ;  and  he  asserted  that  the  earth  was  but  as 
a  point  in  comparison  with  the  magnitude  of  the  universe.  §  His  esti- 
mation of  the  distance  of  the  sun  is  made  by  Archimedes  the  basis  of  a 
calculation  of  the  number  of  grains  of  sand  that  would  be  contained  in  the 
whole  heavenly  sphere,  intended  as  an  illustration  of  the  powers  of 
numerical  reckoning,  and  of  the  utility  of  a  decimal  system  of  notation, 
which  was  the  foundation  of  the  modern  arithmetic.  || 

Eratosthenes,  the  successor  of  Aristarchus,^"  is  known  by  his  observation 
of  the  obliquity  of  the  ecliptic,  and  his  measurement  of  a  certain  portion 
of  the  earth's  circumference  ;  the  whole  of  which  he  determined  to  be 
250,000  stadia  ;  but  the  length  of  his  stadium  is  uncertain.  Ptolemy, 
calculating  perhaps  from  the  same  measures,  or  from  some  others  still 
more  ancient,  calls  it  180,000 ;  which,  if  the  stadium  is  determined  from 
the  Nilometer  at  Cairo,  and  from  the  base  of  the  pyramid,  is  within  one 
thousandth  part  of  the  truth,  the  length  of  the  base  of  the  pyramid  being 
equal  to  400  Egyptian  cubits,  or  to  729  feet  10  inches  English. 

Hipparchus  of  Bithynia  flourished  at  Alexandria  about  the  year  140 
before  Christ.  Employing  the  observations  of  Timocharis,  and  comparing 
them  with  his  own,  he  discovered  the  precession  of  the  equinoxes.  He 
also  observed  that  the  summer  was  9  days  longer  than  the  winter,  and  that 

*  Aristotle,  Meteor.  1.  1,  c.  6.  t  Strabo,  Geog.  1. 13. 

I  Ptolemy,  Almagest.  1. 6,  c.  3. 

§  Arist.  Sam.  de  Magnit.  et  Dist.  Solis  et  Lunse,  4to,  Pis.  1572.  Wallis's  Op. 
vol.  iii. 

||  Archimedes,  Arenarius,  ed.  Paris,  1615,  p.  449. 
^  Cleomedes,  Cyc.  Th.  1. 1,  c.  10,  in  Arati  Op.  Oxf.  1672,  fol. 


ON  THE  HISTORY  OF  ASTRONOMY.  455 

) 

the  solstices  divided  each  of  these  seasons  a  little  unequally.  In  order  to 
explain  this,  Hipparchus  supposed  the  sun  to  move  uniformly  in  an 
eccentric  circle,  the  distance  of  its  centre  from  that  of  the  earth  being  -^  of 
the  radius,  and  placed  the  apogee  in  the  sixth  degree  of  gemini.  Probably 
the  annual  equation  of  the  moon,  which  has  some  influence  on  the  time  of 
eclipses,  was  the  cause  of  his  making  the  eccentricity  too  great ;  had  he 
assumed  it  but  one  fifth  part  less,  the  supposition  would  have  represented 
the  sun's  place  with  tolerable  accuracy.  Hipparchus  appears  to  have  been 
the  first  that  employed  astronomical  observations  for  determining  the  lati- 
tudes and  longitudes  of  places. 

The  interval  of  three  centuries,  which  elapsed  between  Hipparchus  and 
Ptolemy,  offers  us  little  that  is  remarkable  in  the  progress  of  astronomy, 
except  the  reformation  of  the  calendar  by  Julius  Caesar,  who  was  assisted 
in  making  the  arrangement  by  Sosigenes,  an  astronomer  of  the  same 
school  that  gave  birth  to  all  the  preceding  discoveries,  as  well  as  to  the 
improvements  of  Ptolemy.  This  great  astronomer  was  born  at  Ptolemais 
in  Egypt,  and  flourished  about  the  year  140  of  our  era.  He  continued  the 
vast  project,  begun  by  Hipparchus,  of  reforming  the  whole  science  which 
he  studied.  He  discovered  the  evection  of  the  moon,  or  the  change  of  her 
velocity,  occasioned  by  the  position  of  the  apogee  with  respect  to  the  sun  ; 
he  determined  the  quantity  of  this  equation  with  great  precision  ;  and  in 
order  to  represent  it,  he  supposed  the  moon  to  perform  a  subordinate  revo- 
lution in  an  epicycle,  or  a  smaller  circle,  of  which  the  centre  was  carried 
round  in  the  line  of  the  general  orbit,  which  he  considered  as  an  eccentric  cir- 
cle. This  mode  of  approximation  is  exceedingly  ingenious ;  it  is  said  to  have 
been  the  invention  of  Apollonius  of  Perga,  the  mathematician,  and  although 
it  sometimes  becomes  complicated,  yet  it  is  very  convenient  for  calculation ; 
and  it  may  be  employed  with  advantage  in  the  representation  of  the  plane- 
tary motions  by  machinery.  Ptolemy  adopted  the  most  ancient  opinion 
with  respect  to  the  solar  system,  supposing  all  the  heavenly  bodies  to 
revolve  round  the  earth  ;  the  moon  being  nearest,  then  Mercury,  Venus, 
the  Sun,  Mars,  Jupiter,  and  Saturn.  This  opinion  had  long  been  the  most 
general,  although  some  astronomers  had  placed  Mercury  and  Venus  at 
greater  distances  than  the  sun,  and  some  attributed  to  the  earth  a  diurnal 
motion  only  ;  but  the  doctrine  of  the  Pythagoreans  appears  to  have  been 
wholly  exploded  or  forgotten.  Ptolemy  determined  the  quantity  of  the 
precession  of  the  equinoxes  from  a  comparison  of  his  own  observations 
with  those  of  Hipparchus  ;  but  he  made  it  smaller  than  the  truth ;  and  he 
probably  formed  his  table  of  the  places  of  the  stars  by  applying  this 
erroneous  correction  to  the  tables  of  Hipparchus,  in  order  to  accommodate 
them  to  his  own  time.  Both  these  errors  may,  however,  be  otherwise 
explained,  by  supposing  him  to  have  followed  Hipparchus  in  the  length  of 
the  tropical  year,  which  being  somewhat  too  great,  caused  an  error  in  the 
calculation  of  the  sun's  place,  to  which  that  of  the  stars  was  referred  ;  but 
upon  this  supposition,  he  must  also  have  been  mistaken  in  three  obser- 
vations of  the  place  of  the  equinoctial  points.  Ptolemy's  principal  work  is 
nis  mathematical  system  of  astronomy,  which  was  afterwards  called  the 
great  syntax  or  body  of  astronomy,  and  is  at  present  frequently  quoted  by 


456  LECTURE  XLVIII. 

the  Arabic  name  Almagest.  He  also  wrote  a  treatise  on  optics,  in  which 
the  phenomena  of  atmospherical  refraction  are  described,  and  which  is 
extant  is  manuscript  in  the  National  library  at  Paris.*  (Plate  XXXVIII. 
Fig.  528.) 

Ptolemy  was  the  last  as  well  as  the  greatest  of  the  Alexandrian  astrono- 
mers, and  the  science  made  no  further  progress  till  the  time  of  the  Arabians. 
The  first  of  these  was  Almamoun,  the  son  of  the  celebrated  Aaron  Reschid  ; 
he  reigned  at  Bagdad  in  814,  and  having  conquered  the  Greek  emperor, 
Michael  the  Third,  he  made  it  a  condition  of  peace,  that  a  copy  of  the 
works  of  each  of  the  best  Greek  authors  should  be  delivered  to  him  ;  and 
among  them  were  the  works  of  Ptolemy,  of  which  he  procured  an  Arabic 
translation.  Almamoun  also  observed  the  obliquity  of  the  ecliptic,  and 
measured  the  length  of  a  degree  in  the  plains  of  Mesopotamia. 

Among  the  astronomers  protected  by  this  prince  and  his  successors, 
Albategni  was  the  most  eminent/)-  He  ascertained  with  great  accuracy, 
in  880,  the  eccentricity  of  the  solar  motion,  and  discovered  the  change  of 
the  place  of  the  sun's  apogee,  or  of  the  earth's  aphelion. 

Ibn  Junis  made  his  observations  at  Cairo,  about  the  year  1000  ;  he  was 
a  very  assiduous  astronomer,  and  determined  the  length  of  the  year  within 
2  seconds  of  the  truth.  At  this  time  the  Arabians  were  in  the  habit  of 
employing,  in  their  observations,  the  vibrations  of  a  pendulum. 

The  Persians  soon  after  applied  themselves  to  astronomy ;  and  in  the 
eleventh  century  they  invented  the  approximation  of  reckoning  8  bissex- 
tiles in  33  years,  which  was  afterwards  proposed  by  Dominic  Cassini  as  an 
improvement  of  the  Gregorian  calendar.  The  most  illustrious  of  this 
nation  was  Ulugh  Beigh,  who  observed  in  his  capital  Samarcand,  about 
the  year  1437,  with  very  elaborate  instruments.  In  the  mean  time 
Cocheouking  had  made  in  China  some  very  accurate  observations,  which 
are  valuable  for  the  precision  with  which  they  ascertain  the  obliquity  of 
the  ecliptic  :  their  date  is  about  1278. 

It  was  not  long  after  the  time  of  Ulugh  Beigh,  that  Copernicus  laid  the 
foundation  of  the  more  accurate  theories  which  modern  improvements  have 
introduced  into  astronomy.  Dissatisfied  with  the  complicated  hypotheses 
of  the  Ptolemaean  system,  he  examined  the  works  of  the  ancients,  in  quest 
of  more  probable  opinions.  He  found  from  Cicero  that'Nicetas  and  other 
Pythagoreans  had  maintained,  that  the  sun  is  placed  in  the  centre  of  the 
system,  and  that  the  earth  moves  round  him  in  common  with  the  other 
planets.  He  applied  this  idea  to  the  numerous  observations  which  the 
diligence  of  astronomers  had  accumulated,  and  he  had  the  satisfaction  to 
find  them  all  in  perfect  conformity  with  this  theory.  He  quickly  discarded 
the  Ptolemaean  epicycles,  imagined  in  order  to  explain  the  alternations  of 
the  direct  and  retrograde  motions  of  the  planets;  in  these  remarkable 
phenomena,  ^.Copernicus  saw  nothing  but  the  consequences  necessarily 
produced  by  the  combination  of  the  motions  of  the  earth  and  planets  round 

*  Composition  Mathematique,  Gr.  et  Fr.  2  vols.  4to,  Paris,  1813.  See  also 
Table  Chronologique  des  Regnes,  &c.  trad,  de  1'Allemagne  de  M.  Ideler  par  Halma, 
4to,  Paris,  1819.  Hypotheses  et  Epoques  des  Planetes  de  Ptol.  &c.  ibid.  4to,  1820.' 
Tables  Manuelles  Astron.  Gr.  et  Fr.  4to,  1823. 

t  See  Halley's  Dissertation,  in  Ph.  Tr.  xvii.  913. 


ON  THE  HISTORY  OF  ASTRONOMY.  457 

the  sun  ;  and  from  a  minute  examination  of  these  circumstances  he  calcu- 
lated the  relative  distances  of  the  planets  from  the  sun,  which  till  then  had 
remained  unknown.  In  this  system,  every  thing  had  the  marks  of  that 
beautiful  simplicity  which  pervades  all  the  works  of  nature,  and  which, 
when  once  understood,  carries  with  itself  sufficient  evidence  of  its  truth. 
Copernicus  was  born  at  Thorn,  in  Polish  Prussia,  in  the  year  1475 ;  he 
studied  in  Italy  ;  he  taught  mathematics  at  Rome,  and  afterwards  settled 
on  a  canonicate  at  Frauenberg,  where,  in  36  years  of  retirement  and  medi- 
tation, he  completed  his  work  on  the  celestial  revolutions,  which  was 
scarcely  published  when  he  died.* 

About  this  time,  William  the  Fourth,  Landgrave  of  Hesse  Cassel,  not 
only  enriched  astronomy  by  his  own  observations,  but  also  exerted  his 
influence  with  Frederic,  King  of  Denmark,  to  obtain  his  patronage  for  the 
celebrated  Tycho  Brahe.  Frederic  agreed  to  give  him  the  little  island 
Huen,  at  the  entrance  of  the  Baltic,  where  Tycho  built  his  observatory  of 
Uraniburg,  and,  in  a  period  of  21  years,  made  a  prodigious  collection  of 
accurate  observations.  After  the  death  of  his  patron,  his  progress  was 
impeded,  and  he  sought  an  establishment  at  Prague,  under  the  emperor 
Rudolph.  Here  he  died  soon  after,  at  the  age  of  55.  Struck  with  the 
objections  made  to  the  system  of  Copernicus,  principally  such  as  were 
deduced  from  a  misinterpretation  of  the  scriptures,  he  imagined  a  new 
theory,  which,  although  mechanically  absurd,  is  still  astronomically  correct ; 
for  he  supposed  the  earth  to  remain  at  rest  in  the  centre,  the  stars  to  revolve 
round  it,  together  with  the  sun  and  all  the  planets,  in  a  sidereal  day,  and 
the  sun  to  have,  besides,  an  annual  motion,  carrying  with  him  the  planets 
in  their  orbits.  Here  the  apparent  or  relative  motions  are  precisely  the 
same  as  in  the  Copernican  system  ;  the  argument  that  Tycho  Brahe  drew 
from  the  scriptures  in  favour  of  his  theory  was,  therefore,  every  way 
injudicious  ;  for  it  is  not  to  be  imagined  that  any  thing  but  relative  motion 
or  rest  could  be  intended  in  the  scriptures,  when  the  sun  is  said  to  move,  or 
to  stand  still.  But  in  the  Copernican  system,  there  was  an  evident  regu- 
larity in  the  periods  of  all  the  planets,  that  of  the  earth  being  longer  than 
that  of  Venus,  and  shorter  than  that  of  Mars,  which  were  the  neighbouring 
planets  on  each  side ;  and  when  Tycho  imagined  the  sun  to  move  round 
the  earth,  this  analogy  wras  entirely  lost.  Tycho  Brahe  was  the  discoverer 
of  the  variation  and  of  the  annual  equation  of  the  rnoon,  the  one  being  an 
irregularity  in  its  velocity,  dependent  on  its  position  with  respect  to  the 
sun,  the  other  a  change  in  the  magnitude  of  all  the  perturbations  produced 
by  the  sun,  dependent  on  his  distance  from  the  earth.  (Plate  XXXVIII. 
Fig.  529.) 

Kepler  was  the  pupil  and  assistant  of  Tycho,  whose  observations  were 
the  basis  of  his  important  discoveries  :  he  succeeded  him  in  his  appoint- 
ments at  Prague,  and  enjoyed  the  title  of  Imperial  Mathematician.  Adopt- 
ing the  Copernican  system,  which  was  then  becoming  popular,  he  pro- 
ceeded to  examine  the  distances  of  the  celestial  bodies  from  each  other  at 
various  times  ;  and  after  many  fruitless  attempts  to  reconcile  the  places  of 
the  planets  with  the  supposition  of  revolutions  in  eccentric  circles,  at  last 

*  De  Revolutionibus  Orbium  Coelestium,  fol.  1543. 


458  LECTURE  XLVIII. 

\ 

discovered  that  their  orbits  are  ellipses,  and  demonstrated,  chiefly  from  his 
observations  on  the  planet  Mars,  that  the  revolving  radius,  or  the  line 
drawn  from  the  sun  to  the  planet,  always  describes  equal  areas  in  equal 
times.  By  comparing  the  periods  and  the  mean  distances  of  the  different 
planets  with  each  other,  he  found,  after  17  years  calculation,  that  the 
squares  of  the  times  of  revolution  are  always  proportional  to  the  cubes  of 
the  mean  distances  from  the  sun.* 

Kepler  died  in  1630  :  before  his  death  he  had  the  satisfaction  of  applying 
his  theory  to  the  motions  of  the  satellites  of  Jupiter,  which,  as  well  as  the 
phases  of  Venus,  and  the  spots  of  the  sun,  had  lately  been  discovered  in 
Italy  by  the  telescopic  observations  of  Galileo.  This  great  man,  celebrated 
as  well  for  his  theory  of  projectiles,  as  for  his  zealous  defence  of  the 
Copernican  system,  was  born  at  Pisa  in  1564,  and  lived  to  the  age  of  78, 
full  of  that  enthusiasm  which  made  him  despise  the  threats  of  the  Inquisi- 
tion, and  submit  patiently  to  its  persecutions.  He  died  in  1642,  the  year 
in  which  Newton  was  born. 

The  invention  of  logarithms,  by  Baron  Napier,  requires  to  be  noticed 
for  its  importance  to  practical  astronomy,  and  the  laborious  observations  of 
Hevelius  deserve  also  to  be  mentioned  with  commendation.  The  dis- 
coveries of  the  form  of  the  ring  of  Saturn,  and  of  one  of  his  satellites,  by 
Huygens,  and  of  four  more,  together  with  the  belts  and  rotation  of  Jupiter, 
by  Dominic  Cassini,  were  among  the  early  improvements  derived  from 
the  introduction  of  the  telescope.  But,  without  dwelling  on  any  of  these 
subjects,  we  hasten  to  the  establishment  of  the  system  of  gravitation, 
which  has  immortalised  the  name  of  Newton,  and  done  unrivalled  honour 
to  the  country  that  gave  him  birth. 

The  mutual  attraction  of  all  matter  seems  to  have  been  suspected  by  the 
Epicureans,  but  Lucretius  never  speaks  of  it  in  such  terms  as  are  sufficient 
to  convey  by  any  means  a  distinct  idea  of  a  reciprocal  force.  Gregory,  in 
the  preface  of  his  Astronomy,  has  endeavoured  to  prove  that  Pythagoras 
must  have  been  acquainted  even  with  the  law  of  the  decrease  of  gravita- 
tion ;  and  Lalande  appears  to  assent  to  his  arguments ;  but  they  rest  only 
on  the  bare  possibility  that  Pythagoras  might  have  deduced  an  analogy 
from  the  tension  of  cords,  which  we  have  no  reason  to  suppose  that  he 
even  completely  understood :  and  this  merely  because  he  fancifully 
imagined,  that  there  was  a  correspondence  between  the  planets  and  the 
strings  of  a  lyre.  But  the  nature  of  gravitation  had  long  been  in  some 
measure  suspected  ;  Plutarch  had  asserted  that  the  moon  is  retained  by  it 
in  her  orbit,  like  a  stone  in  a  sling;  and  Bacon,  Copernicus,  Kepler, 
Fermat,  and  Roberval  were  aware  of  its  efficacy.  Bacon,  in  his  Novum 
organum,  calls  the  descent  of  heavy  bodies  the  motion  of  "  general  con- 
gregation," and  attributes  the  tides  to  the  attraction  of  the  moon.  Kepler 
mentions  also  the  perfect  reciprocality  of  the  action  of  gravitation,  and 
considers  the  lunar  irregularities  as  produced  by  the  attraction  of  the 
sun.  But  our  most  ingenious  countryman,  Dr.  Hooke,  was  still  more 
decided  in  attributing  the  revolutions  of  the  planets  to  the  combination  of 
a  projectile  motion  with  a  centripetal  force ;  he  expresses  his  sentiments 

*  See  Lect.  IV. 


ON  THE  HISTORY  OF  ASTRONOMY.  459 

on  the  subject  very  clearly  in  his  Attempt  to  prove  the  motion  of  the  earth, 
published  in  1674,  and  had  his  skill  in  mathematics  been  equal  to  his 
practical  sagacity,  he  would  probably  have  completed,  or  at  least  have 
published  the  discovery  before  his  great  cotemporary. 

It  must  be  confessed  that  Newton's  good  fortune  was  equal  to  his  talents 
and  his  application  ;  for  had  he  lived  earlier,  he  might  probably  have  con- 
fined his  genius  to  speculations  purely  mathematical ;  had  he  been  later, 
his  discoveries  in  natural  philosophy  might  have  been  anticipated  by 
others  ;  and  yet  Newton  would  perhaps  have  improved  still  more  on  their 
labours  than  they  have  done  on  his.  It  was  in  1676,  when  he  was  34 
years  old,  that  he  first  demonstrated  the  necessary  connexion  of  the 
planetary  revolutions  in  elliptic  orbits,  with  an  attractive  force  varying 
inversely  as  the  square  of  the  distance.  But  he  had  collected  the  law  of 
the  force,  from  the  discoveries  of  Kepler  respecting  the  periods  of  the  dif- 
ferent planets,  some  time  before  1671,  as  he  asserts  to  Dr.  Halley,  and,  to 
the  best  of  his  recollection,  about  1668,  although  in  his  Principia  he  allows, 
with  the  most  laudable  candour,  to  Wren,  Hooke,  and  Halley,  the  merit 
of  having  made  the  same  discovery,  without  any  connexion  with  each 
other's  investigations,  or  with  his  own.  The  manner,  in  which  Newton 
was  led  to  attend  particularly  to  the  subject,  is  thus  related  by  Pemberton, 
in  the  preface  to  his  View  of  Sir  Isaac  Newton's  philosophy. 

"  The  first  thoughts,"  says  Pemberton,  *  "which  gave  rise  to  his  Prin- 
cipia, he  had,  when  he  retired  from  Cambridge  in  1666,  on  account  of  the 
plague.  As  he  sat  alone  in  a  garden,  he  fell  into  a  speculation  on  the 
power  of  gravity ;  that  as  this  power  is  not  found  sensibly  diminished 
at  the  remotest  distance  from  the  centre  of  the  earth,  to  which  we  can  rise, 
neither  at  the  tops  of  the  loftiest  buildings,  nor  even  on  the  summits  of 
the  highest  mountains ;  it  appeared  to  him  reasonable  to  conclude,  that 
this  power  must  extend  much  further  than  was  usually  thought ;  why  not 
as  high  as  the  moon  ?  said  he  to  himself ;  and  if  so,  her  motion  must  be 
influenced  by  it ;  perhaps  she  is  retained  in  her  orbit  thereby.  However, 
though  the  power  of  gravity  is  not  sensibly  weakened  in  the  little  change 
of  distance,  at  which  we  can  place  ourselves  from  the  centre  of  the  earth  ; 
yet  it  is  very  possible  that  so  high  as  the  moon  this  power  may  differ 
much  in  strength  from  what  it  is  here.  To  make  an  estimate,  what  might 
be  the  degree  of  this  diminution,  he  considered  with  himself,  that  if  the 
moon  be  retained  in  her  orbit  by  the  force  of  gravity,  no  doubt  the  primary 
planets  are  carried  round  the  sun  by  the  like  power.  And  by  comparing 
the  periods  of  the  several  planets  with  their  distances  from  the  sun,  he 
found,  that  if  any  power  like  gravity  held  them  in  their  courses,  its  strength 
must  decrease  in  the  duplicate  proportion  of  the  increase  of  distance.  This 
he  concluded  by  supposing  them  to  move  in  perfect  circles  concentrical  to 
the  sun,  from  which  the  orbits  of  the  greatest  part  of  them  do  not  much 
differ.  Supposing,  therefore,  the  power  of  gravity,  when  extended  to  the 
moon,  to  decrease  in  the  same  manner,  he  computed  whether  that  force 
would  be  sufficient  to  keep  the  moon  in  her  orbit.  In  this  computation 
being  absent  from  books,  he  took  the  common  estimate  in  use  among  geo- 
*  View  of  Newton's  Philosophy,  1728,  Preface. 


460  LECTURE  XLVIII. 

graphers  and  our  seamen,  before  Norwood  had  measured  the  earth,  that  60 
English  miles  were  contained  in  one  degree  of  latitude  on  the  surface  of  the 
earth.  But  as  this  is  a  very  faulty  supposition,  each  degree  containing 
ahout  69^  of  our  miles,  his  computation  did  not  answer  expectation  ;  whence 
he  concluded  that  some  other  cause  must  at  least  join  with  the  action  of 
the  power  of  gravity  on  the  moon.  On  this  account  he  laid  aside  for  that 
time  any  further  thoughts  upon  this  matter.  But  some  years  after,  a  letter 
which  he  received  from  Dr.  Hooke,  put  him  on  inquiring  what  was  the  real 
figure,  in  which  a  body  let  fall  from  any  high  place  descends,  taking  the 
motion  of  the  earth  round  its  axis  into  consideration.  Such  a  body,  having 
the  same  motion,  which  by  the  revolution  of  the  earth  the  place  has  from 
whence  it  falls,  is  to  be  considered  as  projected  forwards,  and  at  the  same 
time  drawn  down  to  the  centre  of  the  earth.  This  gave  occasion  to  his 
resuming  his  former  thoughts  concerning  the  moon  ;  and  Picart,  in  France, 
having  lately  measured  the  earth,  by  using  his  measures,  the  moon  appeared 
to  be  kept  in  her  orbit  purely  by  the  power  of  gravity ;  and  consequently, 
that  this  power  decreases  as  you  recede  from  the  centre  of  the  earth,  in  the 
manner  our  author  had  formerly  conjectured.  Upon  this  principle  he 
found  the  line  described  by  a  falling  body  to  be  an  ellipsis,  the  centre  of 
the  earth  being  one  focus.  And  the  primary  planets  moving  in  such  orbits 
round  the  sun,  he  had  the  satisfaction  to  see,  that  this  inquiry,  which  he 
had  undertaken  merely  out  of  curiosity,  could  be  applied  to  the  greatest 
purposes.  Hereupon  he  composed  near  a  dozen  propositions  relating  to  the 
motion  of  the  primary  planets  about  the  sun.  Several  years  after  this, 
some  discourse  he  had  with  Dr.  Halley,  who  at  Cambridge  made  him  a 
visit,  engaged  Sir  Isaac  Newton  to  resume  again  the  consideration  of  this 
subject ;  and  gave  occasion  to  his  writing  the  treatise  which  he  published 
under  the  title  of  Mathematical  principles  of  natural  philosophy.  This 
treatise,  full  of  such  variety  of  profound  inventions,  was  composed  by  him, 
from  scarce  any  other  materials  than  the  few  propositions  before  men- 
tioned, in  the  space  of  one  year  and  a  half." 

The  astronomers  of  Great  Britain  have  not  been  less  diligent  in  the  prac- 
tical, than  successful  in  the  theoretical  part  of  the  science.  The  foundation 
of  the  observatory  at  Greenwich  was  laid  in  1675,  some  years  before  the 
completion  and  publication  of  the  discoveries  of  Newton.  It  is  with  the 
erection  of  this  edifice  that  the  modern  refinements  in  practical  astronomy 
may  be  said  to  have  commenced ;  its  immediate  object  was  to  assist  in  the 
perfection  of  the  science  of  navigation,  and  the  series  of  observations,  which 
have  been  made  in  it,  has  afforded  an  invaluable  fund  of  materials  to 
astronomers  of  every  country.  A  reward  had  been  proposed,  more  than 
half  a  century  before,  by  Philip  the  Third,  of  Spain,  for  the  discovery  of  a 
mode  of  determining  the  longitude  of  a  ship  at  sea  ;  and  the  states  of  Hol- 
land had  followed  his  example  ;  a  large  reward  was  also  offered  by  the 
French  government  in  the  minority  of  Louis  the  Fifteenth.  In  1674, 
Mr.  St.  Pierre,  a  Frenchman,  had  undertaken  to  determine  the  longitude 
of  a  place  from  observations  of  the  moon's  altitude,  and  King  Charles  the, 
Second  had  been  induced  to  appoint  a  commission  to  examine  his  propo- 
sals. Mr.  Flamsteed  was  consulted  by  the  commissioners,  and  was  added  to 


ON  THE  HISTORY  OF  ASTRONOMY.  461 

their  number :  he  showed  the  disadvantages  of  the  method  proposed  hy 
Mr.  St.  Pierre,  and  the  inaccuracy  of  the  existing  tables  of  the  lunar 
motions,  as  well  as  of  the  catalogues  of  the  places  of  the  stars,  but  expressed 
his  opinion,  that,  if  the  tables  were  improved,  it  would  be  possible  to  deter- 
mine the  longitudes  of  places  with  sufficient  accuracy  by  lunar  observations. 
The  king,  being  informed  of  Flamsteed's  representations,  is  said  to  have 
replied  with  earnestness,  that  he  "  must  have  the  places  of  the  stars  anew 
observed,  examined,  and  corrected,  for  the  use  of  his  seamen ;"  upon  this 
Flamsteed  was  appointed  Astronomer  Royal,  with  a  salary  of  £100  a  year, 
and  it  was  proposed  to  have  an  observatory  built  either  in  Hyde  Park,  or 
at  Chelsea  college  ;  but,  upon  Sir  Christopher  Wren's  recommendation, 
the  situation  of  Greenwich  Park  was  preferred. 

In  the  year  1714,  the  British  Parliament  offered  £20,000  for  a  determi- 
nation of  the  longitude  of  a  ship  at  sea,  without  an  error  of  30  miles,  and 
a  smaller  sum  for  a  less  accurate  method,  appointing  at  the  same  time  a 
Board  of  Longitude  for  the  examination  of  the  methods  which  might  be 
proposed.  Under  this  act  several  rewards  were  assigned,  and  in  1774,  it 
was  superseded  by  another,  which  offers  £5000  for  the  invention  of  any 
timekeeper,  or  other  method,  capable  of  determining  the  longitude  of  a 
place  within  one  degree,  and  £10,000  if  within  30  miles  ;  and  a  reward  of 
£5000  to  the  author  of  any  lunar  tables,  which  should  be  found  within  15 
seconds  of  the  truth  ;  allowing  the  Board  also  the  power  of  granting  smaller 
sums  at  their  discretion.  Timekeepers  are  at  present  very  commonly  em- 
ployed in  the  British  navy,  and  some  of  them  have  been  capable  of  deter- 
mining the  longitude  within  half  a  degree,  after  having  been  two  or  three 
months  at  sea.  The  lunar  tables,  which  have  been  employed  for  the 
Nautical  Almanacs,  are  those  of  Professor  Mayer,  who  adopted  the  methods 
of  calculation  invented  by  Leonard  Euler  ;  but  the  tables  of  Mr.  Burg,  of 
Vienna,  are  still  more  accurate,  and  are  said  to  be  always  within  about  ten 
seconds  of  the  truth. 

The  progress  of  astronomy,  since  the  death  of  Newton,  in  1727,  has  been 
fully  adequate  to  what  its  most  sanguine  votaries  could  have  hoped.  The 
great  discoveries  of  the  aberration  of  the  fixed  stars,  and  of  the  nutation 
of  the  earth's  axis,  were  made  by  our  countryman  Bradley,  with  the 
assistance  of  the  instruments  for  which  he  was  indebted  to  the  delicate 
workmanship  of  our  artists.  Among  these  the  names  of  Bird,  Short, 
Sisson,  Graham,  Dollond,  Harrison,  and  Ramsden  have  long  been  cele- 
brated throughout  Europe.  The  geographical  operations,  which  have  been 
performed  in  every  part  of  the  globe,  have  been  chiefly  conducted  by  the 
liberality  of  the  French  and  English  governments,  although  other  countries 
have  not  been  deficient  in  taking  their  share  of  the  labour.  Observations 
of  the  transit  of  Venus  were  made  with  great  care  in  the  south  seas 
by  British  navigators,  whom  the  munificence  of  our  present  sovereign 
enabled  >to  undertake  so  arduous  a  voyage  for  this  express  purpose  ;  and  we 
are  indebted  to  the  fund  which  was  granted  on  the  occasion,  as  well  as  to 
the  zeal  of  the  Astronomer  Royal,  for  the  experiments  on  the  attraction  of 
mountains,  which  were  instituted  after  their  return.  In  this  country  also, 
Dr.  Herschel,  besides  many  other  important  additions  to  our  astronomical 


462  LECTURE  XLVIII. 

knowledge,  has  discovered  a  primary  planet,  and  eight  secondary  ones, 
unknown  before.  The  astronomers  of  Sicily  and  Germany  have,  however, 
the  honour  of  the  first  discovery  of  the  three  humbler  members  of  the  solar 
system  which  have  been  last  introduced  to  our  acquaintance,  Ceres  by 
Piazzi,  Pallas  by  Olbers,  and  Juno  by  Harding:  and  the  mathemati- 
cians of  France  have  excelled  all  their  predecessors  in  the  elaborate  and 
refined  application  of  the  theory  of  gravitation,  to  the  investigation  of  the 
most  minute  and  intricate  details  of  the  celestial  motions. 

For  the  latest  improvement  that  has  been  made  in  astronomy  we  are 
also  indebted  to  the  zeal  and  ingenuity  of  Dr.  Olbers,  who,  in  pursuit  of 
an  opinion  which  he  had  formed,  respecting  the  origin  of  the  three  small 
planets  from  the  separation  of  a  larger  one  into  fragments,  has  been  in  the 
habit  of  examining  monthly  that  part  of  the  heavens  in  which  he  supposes 
the  event  to  have  taken  place,  and  through  wrhich  each  of  the  bodies  must 
necessarily  pass.  He  has  had  the  good  fortune  to  discover,  in  this  manner, 
a  fourth  planet  [Vesta],  which  nearly  resembles  the  three  others  in  its 
appearance,  except  that  it  seems  to  be  considerably  larger. 


LECT.  XLVIII.— ADDITIONAL  AUTHORITIES. 

Gassendus,  Tychonis  Brahei  Vita,  4to,  Hagse  Comitum,  1655.  Blegny,  Le  Mes- 
sager  Celeste,  12mo,  Paris,  1681.  Champollion,  Resume  de  Chronologie,  32rno, 
Paris,  1730.  De  L'Isle,  Mem.  pour  servir  £  Histoire  de  1'Astr.  &c.  4to,  St.  Petersb. 
1738.  Weidler,  Historia  Astronomise,  4to,  Vitembergse,  1741.  Heilbroner,  Hist. 
Math,  ab  Orbe  Condito  ad  Seculum  XV.  4to,  Lipsise,  1742.  Heathcote,  Historia 
Astronomies,  Cantab.  1747.  Costard  on  the  Chinese  Astr.  Ph.  Tr.  1747,  p.  476. 
Hist,  of  Astr.  4to,  Lond.  1767.  Esteve,  Hist,  de  1'Ast.  3  vols.  12mo,  Paris,  1755. 
Bernoulli,  Lettres  Astronomiques,  Berlin,  1771.  Bailly,  Histoire  de  1' Astronomic 
Anc.  et  Mod.  3  vols.  4to,  Paris,  1775-9.  Do.  Indienne,  4to,  1787  ;  Abrege,  1805. 
Blair's  History  of  Geography,  12mo,  1784.  Schaubach,  Geschichte  der  Greichischen 
Ast.  Gott.  1802.  Lalande,  Bibliographic  Astronomique,  4to,  1803.  Small's 
Account  of  the  Discoveries  of  Kepler,  1803.  Ideler,  Historische  Untersuchungen 
iiberdie  Ast.  Beob.  der  Alten.  Berlin,  1806.  Voiron,  Hist,  de  1'Ast.  depuis  1781 
jusqu'a  1811,  4to,  1810.  Cassini,  Memoires  pour  servir  al'Hist.  des  Sciences,  4to, 
Paris,  1810.  Gautier,  Essai  Historique  sur  le  Probleme  des  trois  Corps,  4to,  Paris, 
1817.  Delambre,  Histoire  de  1' Astronomic  Ancienne,  2  vols.  4to,  Paris,  1817  ;  du 
Moyen  Age,  4to,  1819  ;  Moderne,  2  vols.  4to,  1821 ;  de  18e  Siecle,  publiee  par 
Mathieu,  4to,  1826.  Laplace,  Precis  de  1'Hist.  de  1'Ast.  1821.  Rigaud's  Memoirs 
of  Bradley,  4to,  Oxf.  1832  ;  Suppl.  4to,  Oxf.  1833.  Rothman's  History  of  Astr. 
(Lib.  of  Useful  Knowledge),  1832.  Airy's  Report  on  Astr.  Brit.  Assoc.  1832. 
Baily's  Account  of  Flamsteed,  4to,  Lond.  1835. 


ON  THE  HISTORY  OF  ASTRONOMY. 


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464 


LECTURE    XLIX. 


ON  THE  ESSENTIAL  PROPERTIES  OF  MATTER. 

THE  objects,  which  have  lately  occupied  our  inquiries,  are  the  most 
sublime  and  magnificent  that  nature  any  where  exhibits  to  us,  and  the 
contemplation  of  them  naturally  excites,  even  in  an  uncultivated  mind,  an 
admiration  of  their  dignity  and  grandeur.  But  all  magnitude  is  relative  ; 
and  if  we  examine  with  more  calm  attention,  we  shall  find  still  greater 
scope  for  our  investigation  and  curiosity,  in  the  microscopic,  than  in  the 
telescopic  world.  Pliny  has  very  justly  observed,  that  nature  no  where 
displays  all  her  powers  with  greater  activity,  than  in  the  minutest  objects 
perceptible  to  our  senses  ;  and  we  may  judge  how  wide  a  field  of  research 
the  corpuscular  affections  of  matter  afford,  from  the  comparatively  small 
progress  that  has  hitherto  been  made  in  cultivating  it.  For  while  the 
motions  of  the  vast  bodies,  which  roll  through  the  heavens,  have  been 
completely  subjected  to  the  most  rigorous  calculations,  we  know  nothing, 
but  from  experience  only,  of  the  analogies  by  which  the  minute  actions  of 
the  particles  of  matter  are  regulated.  It  is  probable,  however,  that  they 
all  depend  ultimately  on  the  same  mechanical  principles.  We  have  seen, 
for  example,  that  the  widely  extended  elevations  and  depressions  of  the 
ocean,  which  are  raised  by  the  attractive  powers  of  the  two  great  lumina- 
ries, and  cover  at  once  a  half  of  the  globe,  are  governed  and  combined 
according  to  the  same  laws  which  determine  the  motions  of  the  smaller 
waves  excited  by  different  causes  in  a  canal,  the  rapid  tremors  of  a  medium 
transmitting  sound,  or  the  inconceivably  diminutive  undulations  which 
are  capable  of  accounting  for  the  phenomena  of  light,  and  which  must  be 
exerted  in  spaces  as  much  smaller  than  those  of  sound,  as  a  grain  of  sand 
is  smaller  than  a  mountain.  Thus  the  annihilation  of  the  effects  of  the 
semidiurnal  changes  of  the  tide,  and  the  preservation  of  the  diurnal  change, 
in  the  harbour  of  Batsha,  may  be  explained  precisely  in  the  same  manner 
as  the  reflection  of  red  light  from  a  transparent  substance,  of  such  a  thick- 
ness, as  to  be  capable  of  destroying  a  portion  of  violet  light  under  the  same 
circumstances. 

We  are  at  present  to  descend  from  the  affections  of  the  large  masses  of 
matter,  which  form  the  great  features  of  the  universe,  to  the  particular 
properties  of  the  matter  which  constitutes  them,  as  far  as  they  are  common 
to  all  matter  in  general ;  but  those  properties  which  are  peculiar  to  certain 
kinds  of  matter  only,  being  the  subjects  of  chemical  science,  are  not  to  be 
included  in  the  discussion.  If  we  are  asked  for  a  definition  of  matter,  it 
will  be  somewhat  difficult  to  avoid  all  circuitous  expressions.  We  may 
make  gravitation  a  test  of  matter,  but  then  we  must  say,  that  whatever  is 
attracted  by  other  matter,  is  also  to  be  denominated  matter,  and  this  sup- 
poses the  subject  of  our  definition  already  known  ;  besides  that  the  property* 
of  attraction  may  also  possibly  belong  to  substances  not  simply  material ; 


ON  THE  ESSENTIAL  PROPERTIES  OF  MATTER.      ^465 

for  the  electrical  fluid,  if  such  a  fluid  exists,  is  probably  attracted  by  mat- 
ter, and  yet  it  seems  to  be  different  in  most  respects  from  any  modification 
of  common  matter.  A  similar  difficulty  would  occur  if  we  attempted  to 
define  matter  by  its  impenetrability  or  mutual  repulsion,  or  if  we  consi- 
dered every  thing  as  material  that  is  capable  of  affecting  the  senses.  We 
must,  therefore,  take  it  for  granted  that  matter  is  known  without  a  defi- 
nition, and  we  may  describe  it  as  a  substance  occupying  space,  or  as  a 
gravitating  or  ponderable  substance. 

It  cannot  be  positively  determined  whether  matter  is  originally  of  one 
kind,  owing  its  different  appearances  only  to  the  form  and  arrangement  of 
its  parts  ;  or  whether  there  are  various  kinds  of  simple  matter,  essentially 
distinct  from  each  other ;  but  the  probability  appears  to  be  in  favour  of 
the  former  supposition.  However  this  may  be,  the  properties  of  matter 
are  by  no  means  so  simple  in  their  nature,  nor  so  easily  reducible  to  gene- 
ral laws,  as  the  more  mathematical  doctrines  of  space  and  motion  ;  and 
since  our  knowledge  of  them  depends  more  on  experience  than  on  abstract 
principles,  they  may  properly  be  considered  as  belonging  to  particular 
physics.  We  have  found  no  inconvenience  from  the  omission  of  the  doc- 
trine of  matter  as  a  part  of  the  subject  of  mechanics  ;  although,  in  treating 
of  the  strength  of  materials,  as  subservient  to  practical  mechanics,  it  was 
necessary  to  consider  the  effects  of  some  of  these  properties  as  deduced  from 
experiment ;  but  it  will  appear  that  it  was  impossible  to  examine  their 
origin  and  mutual  connexion,  without  supposing  a  previous  knowledge  of 
many  other  departments  of  natural  philosophy. 

We  may  distinguish  the  general  properties  of  matter  into  two  principal 
classes,  those  which  appear  to  be  inseparable  from  its  constitution,  and  those 
which  are  only  accidental,  or  which  are  not  always  attached  to  matter  of 
all  kinds.  The  essential  properties  are  chiefly  extension  and  divisibility, 
density,  repulsion,  or  impenetrability,  inertia,  and  gravitation  ;  the  acci- 
dental properties  are  in  great  measure  dependent  on  cohesion,  as  liquidity, 
solidity,  symmetry  of  arrangement,  cohesive  elasticity,  stiffness,  toughness, 
strength,  and  resilience. 

The  extension  of  matter  can  scarcely  be  considered  as  a  property  sepa- 
rate from  its  impenetrability,  unless  we  conceive  that  it  can  occupy  space, 
without  excluding  other  bodies  from  it.  This  opinion  has  indeed  been 
maintained  by  some  philosophers,  who  have  imagined  that  the  minute 
particles  which  they  suppose  to  constitute  light,  may  penetrate  the  ulti- 
mate atoms  of  other  matter  without  annihilating  or  displacing  them ; 
and  if  this  hypothesis  were  admitted,  it  would  be  necessary  to  consider 
each  particle  of  matter  as  a  sphere  of  repulsion,  extended  without  being 
impenetrable. 

The  divisibility  of  matter  is  great  beyond  the  power  of  imagination,  but 
we  have  no  reason  for  asserting  that  it  is  infinite  ;  for  the  demonstrations 
which  have  sometimes  been  adduced  in  favour  of  this  opinion,  are  obvi- 
ously applicable  to  space  only.  The  infinite  divisibility  of  space  seems  to 
be  essential  to  the  conception  that  we  have  of  its  nature ;  and  it  may  be 
strictly  demonstrated,  that  it  is  mathematically  possible  to  draw  an  infinite 
number  of  circles  between  any  given  circle  and  its  tangent,  none  of  which 

2H 


460  LECTURE  XLIX. 

shall  touch  either  of  them,  except  at  the  general  point  of  contact ;  and  that 
a  ship,  following  always  the  same  oblique  course  with  respect  to  the  meri- 
dian, for  example,  sailing  north  eastwards,  would  continue  perpetually  to 
approach  the  pole  without  ever  completely  reaching  it.  But  when  we 
inquire  into  the  truth  of  the  old  maxim  of  the  schools,  that  all  matter  is 
infinitely  divisible,  we  are  by  no  means  able  to  decide  so  positively.  New- 
ton observes,  that  it  is  doubtful  whether  any  human  means  may  be  suffi- 
cient to  separate  the  particles  of  matter  beyond  a  certain  limit ;  and  it  is 
not  impossible  that  there  may  be  some  constitution  of  atoms,  or  single 
corpuscles,  on  which  their  properties,  as  matter,  depend,  and  which  would 
be  destroyed  if  the  units  were  further  divided  ;  but  it  appears  to  be  more 
probable  that  there  are  no  such  atoms  ;  and  even  if  there  are,  it  is  almost 
certain  that  matter  is  never  thus  annihilated  in  the  common  course  of 
nature.* 

It  remains  to  be  examined  how  far  we  have  any  experience  of  the  actual 
extent  of  the  divisibility  of  matter  ;  and  we  shall  find  no  appearance  of  any 
thing  like  a  limit  to  this  property.  The  smallest  spherical  object,  visible  to 
a  good  eye,  is  about  -jnjVu-  of  an  inch  in  diameter  ;  by  the  assistance  of  a 
microscope,  we  may  perhaps  distinguish  a  body  one  hundredth  part  as 
large,  or  ir^^rjra.  of  an  inch  in  diameter.  The  thickness  of  gold  leaf  is 
less  than  this,  and  the  gilding  of  lace  is  still  thinner,  probably  in  some 
cases  not  above  one  ten  millionth  of  an  inch  ;  so  that  -jV^  of  a  grain  would 
cover  a  square  inch,  and  a  portion  barely  large  enough  to  be  visible  by  a 
microscope,  might  weigh  only  the  80  million  millionth  part  of  a  grain.t 
A  grain  of  musk  is  said  to  be  divisible  into  320  quadrillions  of  parts,  each 
of  which  is  capable  of  affecting  the  olfactory  nerves.  There  are  even  living 
beings,  visible  to  the  microscope,  of  which  a  million  million  would  not 
make  up  the  bulk  of  a  common  grain  of  sand.  But  it  is  still  more  remark- 
able, that,  as  far  as  we  can  discover,  many  of  these  animalcules  are  as 
complicated  in  their  structure  as  an  elephant  or  a  whale.  It  is  true  that 
the  physiology  of  the  various  classes  of  animals  is  somewhat  more  simple  as 
they  deviate  more  from  the  form  of  quadrupeds,  and  from  that  of  the 
human  species  ;  the  solid  particles  of  the  blood  do  not  by  any  means  vary 
in  their  magnitude  in  the  same  ratio  with  the  bulk  of  the  animal ;  and 
some  of  the  lower  classes  appear  to  approximate  very  much  to  the  nature 
of  the  vegetable  world.  But  there  are  single  instances  that  seem  wholly 
to  destroy  this  gradation  :  Lyonnet  has  discovered  a  far  greater  variety  of 
parts  in  the  caterpillar  of  the  willow  butterfly,  than  we  can  observe  in 
many  animals  of  the  largest  dimensions ;  and  among  the  microscopic 
insects  in  particular,  we  see  a  prodigality  of  machinery,  subservient  to  the 
various  purposes  of  the  contracted  life  of  the  little  animal,  in  the  structure 
of  which  nature  appears  to  be  ostentatious  of  her  power  of  giving  perfection 
to  her  minutest  works. 

If  Newton's  opinion,  respecting  the  origin  of  the  colours  of  natural 
bodies  in  general,  were  sufficiently  established,  it  would  afford  us  a  limit 

*  Consult  Wollaston,  Ph.  Tr.  1822. 

t  SeeHalley,  Ph.  Tr.  1693,  p.  540.  Nicholson,  ibid.  1789,  p.  286.  Button's 
transl.  of  Montucla's  Mathematical  Recreations,  4  vols.  Lond.  1803,  vol.  iv.  p.  80. 


ON  THE  ESSENTIAL  PROPERTIES  OF  MATTER.        467 

to  the  divisibility  of  matter  with  respect  to  coloured  substances  ;  for  the 
colours  of  thin  transparent  substances, which  he  considers  as  resembling  those 
of  most  other  substances,  are  no  longer  observable,  in  any  known  medium, 
when  the  thickness  is  less  than  about  ^mAnnr  of  an  inch.  But  we  have 
positive  evidence  that  coloured  substances  may  be  reduced  to  dimensions 
far  below  this  limit ;  besides  the  instance  of  the  gilt  wire,  which  has  already 
been  mentioned,  a  particle  of  carmine  may  still  retain  its  colour,  when  its 
thickness  is  no  more  than  one  thirty  millionth  of  an  inch,  or  one  sixtieth 
part  of  the  limit  deduced  from  the  supposition  of  Newton ;  and  it  is  there- 
fore scarcely  possible  that  the  colours  of  such  substances  can  precisely 
resemble  those  of  thin  plates,  although  they  may  perhaps  still  be  in  some 
measure  analogousv  to  them. 

Impenetrability  is  usually  attributed  to  matter,  from  the  common  obser- 
vation that  two  bodies  cannot  occupy  the  same  place  at  once.  And  it  is 
thus  that  we  distinguish  matter  from  space ;  for  example,  when  we  dip 
an  inverted  jar  into  mercury,  the  air  contained  in  the  jar  depresses  the 
surface  of  the  mercury,  and  prevents  its  occupying  the  space  within  the 
jar :  but  if  the  jar  had  been  void  of  matter,  like  the  space  above  the  mer- 
cury of  a  barometer,  nothing  would  have  prevented  its  being  filled  by  the 
mercury,  as  soon  as  either  its  weight  or  the  pressure  of  the  atmosphere, 
urged  it  to  enter  the  jar. 

But  it  does  not  appear  that  our  senses  are  fully  competent  to  extend  this 
proposition  to  all  substances,  whether  material  or  not.  We  cannot  prove 
experimentally  that  the  influence  of  gravitation  is  incapable  of  pervading 
even  the  ultimate  particles  of  solid  matter,  for  this  power  appears  to  suffer 
no  diminution  nor  modification,  when  a  third  body  is  interposed  between 
the  two  gravitating  masses.  In  the  same  manner,  a  magnet  operates  as 
rapidly  on  a  needle,  through  a  plate  of  glass  or  of  gold,  whatever  its  thick- 
ness may  be,  as  if  a  vacuum  only  intervened.  It  may,  however,  be 
inquired  if  the  gold  or  the  glass  has  not  certain  passages  or  pores,  through 
which  the  influence  may  be  transmitted  :  and  it  may  be  shown,  in  many 
instances,  that  substances,  apparently  solid,  have  abundant  orifices  into 
which  other  substances  may  enter  ;  thus  mercury  may  easily  be  made  to 
pass  through  leather,  or  through  wood,  by  the  pressure  of  the  atmosphere, 
or  by  any  other  equal  force  :  and,  however  great  we  may  suppose  the  pro- 
portion of  the  pores  to  the  solid  matter,  it  may  be  observed,  that  it  requires 
only  a  more  or  less  minute  division  of  the  matter,  to  reduce  the  magnitude 
of  the  interstices  between  the  neighbouring  particles  within  any  given 
dimensions.  Thus  platina  contains,  in  a  cubic  inch,  above  200  thousand 
times  as  many  gravitating  atoms  as  pure  hydrogen  gas,  yet  both  of  these 
mediums  are  free  from  sensible  interstices,  and  appear  to  be  equally  con- 
tinuous ;  and  there  may  possibly  be  other  substances  in  nature  that  contain 
in  a  given  space  200  thousand  times  as  many  atoms  as  platina  ;  although 
this  supposition  is  not  positively  probable  in  all  its  extent ;  for  the  earth  is 
the  densest  of  any  of  the  celestial  bodies  with  which  we  are  fully  ac- 
quainted, and  the  earth  is  only  one  fourth  as  dense  as  if  it  were  composed 
entirely  of  platina ;  so  that  we  have  no  reason  to  believe  that  there  exists 

2n2 


4G8  LECTURE  XLIX. 

in  the  solar  system  any  considerable  quantity  of  a  substance  even  so  dense 
as  platina. 

Besides  this  porosity,  there  is  still  room  for  the  supposition,  that  even  the 
ultimate  particles  of  matter  may  be  permeable  to  the  causes  of  attractions 
of  various  kinds,  especially  if  those  causes  are  immaterial :  nor  is  there 
anything  in  the  unprejudiced  study  of  physical  philosophy  that  can  induce 
us  to  doubt  the  existence  of  immaterial  substances  ;  on  the  contrary  we  see 
analogies  that  lead  us  almost  directly  to  such  an  opinion.  The  electrical 
fluid  is  supposed  to  be  essentially  different  from  common  matter;  the 
general  medium  of  light  and  heat,  according  to  some,  or  the  principle  of 
caloric,  according  to  others,  is  equally  distinct  from  it.  We  see  forms  of 
matter,  differing  in  subtility  and  mobility,  under  the  names  of  solids, 
liquids,  and  gases ;  above  these  are  the  semimaterial  existences  which 
produce  the  phenomena  of  electricity  and  magnetism,  and  either  caloric  or 
a  universal  ether ;  higher  still  perhaps  are  the  causes  of  gravitation,  and 
the  immediate  agents  in  attractions  of  all  kinds,  which  exhibit  some  phe- 
nomena apparently  still  more  remote  from  all  that  is  compatible  with 
material  bodies ;  and  of  these  different  orders  of  beings,  the  more  refined 
and  immaterial  appear  to  pervade  freely  the  grosser.  It  seems  therefore 
natural  to  believe  that  the  analogy  may  be  continued  still  further,  until  it 
rises  into  existences  absolutely  immaterial  and  spiritual.  We  know  not 
but  that  thousands  of  spiritual  worlds  may  exist  unseen  for  ever  by  human 
eyes ;  nor  have  we  any  reason  to  suppose  that  even  the  presence  of  matter, 
in  a  given  spot,  necessarily  excludes  these  existences  from  it.  Those  who 
maintain  that  nature  always  teems  with  life,  wherever  living  beings  can  be 
placed,  may  therefore  speculate  with  freedom  on  the  possibility  of  indepen- 
dent worlds  ;  some  existing  in  different  parts  of  space,  others  pervading 
each  other,  unseen  and  unknown,  in  the  same  space,  and  others  again  to 
which  space  may  not  be  a  necessary  mode  of  existence. 

Whatever  opinion  we  may  entertain  with  respect  to  the  ultimate  impe- 
netrability of  matter  in  this  sense,  it  is  probable  that  the  particles  of  matter 
are  absolutely  impenetrable  to  each  other.  This  impenetrability  is  not 
however  commonly  called  into  effect  in  cases  of  apparent  contact.  If  the 
particles  of  matter  constituting  water,  and  steam,  or  any  other  gas,  are  of 
the  same  nature,  those  of  the  gas  cannot  be  in  perfect  contact ;  and  when 
water  is  contracted  by  the  effect  of  cold,  or  when  two  fluids  have  their 
joint  bulk  diminished  by  mixture,  as  in  the  case  of  alcohol  or  sulfuric 
acid,  and  water,  the  particles  cannot  have  been  in  absolute  contact  before, 
although  they  would  have  resisted  with  great  force  any  attempt  to  com- 
press them.  Metals  too,  of  all  kinds,  which  have  been  melted,  become 
permanently  more  dense  when  they  are  hammered  and  laminated.  A  still 
more  striking  and  elegant  illustration  of  the  nature  of  repulsive  force  is 
exhibited  in  the  contact  of  two  pieces  of  polished  glass.  The  colours  of 
thin  plates  afford  us,  by  comparison  with  the  observations  of  Newton,  the 
most  delicate  micrometer  that  can  be  desired,  for  measuring  any  distances 
less  than  the  ten  thousandth  of  an  inch  :  it  was  remarked  by  Newton  him- 
self, that  when  two  plates  of  glass  are  within  about  this  distance  of  each 


ON  THE  ESSENTIAL  PROPERTIES  OF  MATTER.        469 

other,  or  somewhat  nearer,  they  support  each  other's  weight  in  the  same 
manner  as  if  they  were  in  actual  contact,  and  that  some  additional  force  is 
required  in  order  to  make  them  approach  still  nearer  ;  nor  does  it  appear 
probable  that  the  contact  is  ever  perfect,  otherwise  they  might  be  expected 
to  cohere  in  such  a  manner  as  to  become  one  mass.  Professor  Robison* 
has  ascertained  by  experiment  the  force  necessary  to  produce  the  greatest 
possible  degree  of  contact,  and  finds  it  equivalent  to  a  pressure  of  about  a 
thousand  pounds  for  every  square  inch  of  glass.  It  is  therefore  obvious 
that  in  all  common  cases  of  the  contact  of  two  distinct  bodies,  it  must  be 
this  repulsive  force  that  retains  them  in  their  situation.  I  have  found  that 
glass,  placed  on  a  surface  of  metal,  exhibits  this  force  nearly  in  the  same 
degree  as  if  placed  on  another  piece  of  glass  ;  it  is  also  independent  of  the 
presence  of  air  ;  but  under  water  it  disappears. 

The  existence  of  a  repulsive  force,  extending  beyond  the  actual  surface 
of  a  material  substance,  being  proved,  it  has  been  conjectured  by  some 
that  such  a  force,  unconnected  with  any  central  atom,  may  be  sufficient  for 
producing  all  the  phenomena  of  matter.  This  representation  may  be 
admitted  without  much  difficulty,  provided  that  it  be  allowed  that  the 
force  becomes  infinite  at  or  near  the  centre ;  but  it  has  been  sometimes 
supposed  that  it  is  every  where  less  than  infinite,  and  consequently  that 
matter  is  not  absolutely  impenetrable  ;  such  a  supposition  appears  however 
to  lead  to  the  necessity  of  believing  that  the  particles  of  matter  must  some- 
times be  annihilated,  which  is  not  a  very  probable  opinion. 

The  magnitude  of  the  repulsive  force  by  which  the  particles  of  any  single 
body  are  enabled  to  resist  compression,  increases  nearly  in  proportion  to 
the  degree  of  compression,  or  to  the  decrease  of  the  distances  between  the 
particles.  This  is  almost  a  necessary  consequence  of  any  primary  law 
that  can  be  imagined,  for  the  immediate  actions  of  the  particles :  for 
instance,  if  the  repulsion  increased  either  as  the  square  or  as  the  cube  of 
the  distance  diminished,  the  effect  of  a  double  change  of  dimensions  would 
always  be  nearly  a  double  change  of  the  repulsive  force  ;  that  is,  if  an 
elastic  substance  were  compressed  one  thousandth  part  of  its  bulk,  it  would 
in  either  case  resist  twice  as  much  as  if  it  were  only  compressed  one  two 
thousandth. 

It  is  obvious  that  if  the  particles  of  matter  are  possessed  of  a  repulsive 
force  decreasing  in  any  regular  proportion  with  the  increase  of  distance, 
they  can  never  remain  at  rest  without  the  operation  of  some  external 
pressure,  but  will  always  retain  a  tendency  to  expand.  This  is  the  case  of 
all  elastic  fluids,  the  density  of  which  is  found  to  vary  exactly  as  the  com- 
pressing force,  whence  it  may  be  demonstrated,  that  the  primary  repulsive 
force  of  the  particles  must  increase  in  the  same  proportion  as  the  distance 
decreases.  It  follows  also  that  this  force  can  only  be  exerted  between  such 
particles  as  are  either  actually  or  very  nearly  in  contact  with  each  other; 
since  it  requires  no  greater  pressure,  acting  on  a  given  surface,  to  retain  a 
gallon  of  air  in  the  space  of  half  a  gallon,  than  to  retain  a  pint  in  the  space 

*  Robison's  Mech.  Phil.  vol.  i.  Corpuscular  Action,  art.  241.  See  also  Huy- 
gens,  Ph.  Tr.  No.  86.  Hauksbce,  ibid.  1709,  p.  306. 


470  LECTURE  XLIX. 

of  half  a  pint ;  which  could  not  be,  if  the  particles  exercised  a  mutual 
repulsion  at  all  possible  distances. 

Mr.  Dalton*  has  proposed  a  singular  theory  respecting  the  constitution 
and  mutual  repulsion  of  elastic  fluids ;  he  imagines  that  when  any  two 
gases  of  different  kinds  are  mixed,  the  particles  of  each  gas  repel  only  the 
similar  particles  of  the  same  gas,  without  exerting  any  action  on  those  of 
the  other  gas,  except  when  the  ultimate  solid  atoms  chance  to  interfere. 
The  idea  is  ingenious  and  original,  and  may  perhaps  be  of  use  in  connect- 
ing some  facts  together,  or  in  leading  to  some  other  less  improbable  suppo- 
sitions ;  but  it  may  easily  be  shown,  that  Mr.  Dalton' s  hypothesis  cannot 
possibly  be  true  in  all  its  extent,  since  it  would  follow  from  it,  that  two 
portions  of  gases  of  different  kinds,  could  not  exist,  for  a  sensible  time,  in 
the  same  vessel,  without  being  uniformly  diffused  throughout  it,  while  the 
fact  is  clearly  otherwise  ;  for  hydrogen  gas  remains,  when  left  completely 
at  rest,  a  very  considerable  time  above,  and  carbonic  acid  gas  below  a 
portion  of  common  air  writh  which  it  is  in  contact ;  nor  is  there  any  cir- 
cumstance attending  the  mixture  of  gases,  which  may  not  be  explained 
without  adopting  so  paradoxical  an  opinion.  Mr.  Dalton  thinks  that, 
from  the  laws  of  hydrostatics,  no  two  gases,  not  chemically  united,  could 
remain  mixed,  if  their  particles  acted  mutually  on  each  other :  but  the 
laws  of  hydrostatics  do  not  apply  to  the  mixture  of  single  particles  of  fluids 
of  different  kinds  ;  since  they  are  only  derived  from  the  supposition  of  a 
collection  of  particles  of  the  same  kind. 

In  liquids  and  in  solids,  this  repulsive  force  appears  at  first  sight  to  be 
wanting  ;  but  when  we  consider  that  the  particles  both  of  liquids  and  of 
solids  are  actuated  by  the  attractive  force  of  cohesion,  we  shall  see  the 
necessity  of  the  presence  of  a  repulsive  force,  in  order  to  balance  it ;  it  is, 
therefore,  probable  .that  the  particles  of  aeriform  fluids  still  retain  their 
original  repulsive  powers,  when  they  are  reduced  to  a  state  of  liquidity  or 
of  solidity,  by  being  subjected  to  the  action  of  a  second  force  which  causes 
them  to  cohere. 

The  mutual  repulsion  of  the  particles  of  matter  is  a  reciprocal  force, 
acting  equally,  in  opposite  directions,  on  each  of  the  bodies  concerned.  It 
scarcely  requires  either  experiment  or  argument  to  show,  that  if  two 
bodies  repel  each  other,  neither  of  them  will  remain  at  rest,  but  both  of 
them  will  move,  with  equal  quantities  of  motion.  Thus,  if  a  portion  of 
condensed  air  be  made  to  act  upon  the  bullet  of  an  air  gun,  it  will  force  the 
gun  backwards  with  as  much  momentum  as  it  impels  the  bullet  forwards. 

Inertia  is  that  property  of  matter,  by  which  it  retains  its  state  of  rest  or 
of  uniform  motion,  with  regard  to  a  quiescent  space,  as  long  as  no  foreign 
cause  occurs  to  change  that  state.  This  property  depends  on  the  intimate 
constitution  of  matter  ;  it  is  generally  exhibited  by  means  of  the  force  of 
repulsion,  which  enables  a  body  in  motion  to  displace  another,  in  order  to 
continue  its  motion,  or  by  means  of  some  attractive  force,  which  causes  two 
bodies  to  approach  their  common  centre  of  inertia  with  equal  momenta. 

*  Manchester  Memoirs,  vol.  v.  See  also  Graham,  Edin.  Tr.  1831 ;  Thomson, 
Phil.  Mag.  3rd  Ser.  vol.  iv.  p.  321,  by  whom  the  hypothesis  of  Dalton  is  established. 


ON  THE  ESSENTIAL  PROPERTIES  OF  MATTER.        471 

Another  universal  property  of  matter  is  reciprocal  gravitation,  of  which 
the  force  is  directly  in  the  joint  proportion  of  the  quantities  of  matter  at- 
tracting each  other,  and  inversely  as  the  square  of  their  distance.  In  order 
to  prove  that  the  gravitation  towards  a  given  substance,  for  instance,  the 
weight  of  a  body,  or  its  gravitation  towards  the  earth,  is  precisely  in  pro- 
portion to  the  mass  or  inertia  of  the  moveable  matter  of  which  it  consists, 
Sir  Isaac  Newton  made  two  equal  pendulums,  with  hollow  balls  of  equal 
size  :  in  order  that  the  resistance  of  the  air  might  be  the  same  with  respect 
to  both,  he  placed  successively  within  the  balls  a  variety  of  different  sub- 
stances, and  found  that  the  time  of  vibration  remained  always  the  same  ; 
whence  he  inferred  that  the  attraction  was  proportional  in  all  cases  to  the 
quantity  of  matter  possessing  inertia.  For  if  any  of  these  substances  had 
contained  particles  capable  of  receiving  and  communicating  motion,  yet 
without  being  liable  to  gravitation,  they  would  have  retarded  the  vibrations 
of  the  pendulum,  by  adding  to  the  quantity  of  matter  to  be  moved,  without 
increasing  the  moving  force.  The  law  of  gravitation,  which  indicates  the 
ratio  of  its  increase  with  the  diminution  of  the  distance,  is  principally 
deduced  from  astronomical  observations  and  computations :  it  is  the 
simplest  that  can  be  conceived  for  any  influence,  that  either  spreads  from  a 
centre,  or  converges  towards  a  centre ;  for  it  supposes  the  force  acting  on 
the  same  substance  to  be  always  proportional  to  the  angular  space  that  it 
occupies. 

Newton  appears  to  have  considered  these  laws  of  gravitation,  which  he 
first  discovered,  rather  as  derivative  than  as  original  properties  of  matter ; 
and  although  it  has  often  been  asserted  that  we  gain  nothing  by  referring 
them  to  pressure  or  to  impulse,  yet  it  is  undoubtedly  advancing  a  step  in  the 
explanation  of  natural  phenomena,  to  lessen  the  number  of  general  prin- 
ciples ;  and  if  it  were  possible  to  refer  either  all  attraction  to  a  modification 
of  repulsion,  or  all  repulsion  to  a  modification  of  attraction,  we  should 
make  an  improvement  of  the  same  kind  as  Newton  made,  when  he  reduced 
all  the  diversified  motions  of  the  heavenly  bodies  to  the  universal  laws  of 
gravitation  only.  We  have,  however,  at  present  little  prospect  of  such  a  sim- 
plification. 

It  has  been  of  late  very  customary  to  consider  all  the  phenomena  of 
nature  as  derived  from  the  motions  of  the  corpuscles  of  matter,  agitated  by 
forces  varying  according  to  certain  intricate  laws,  which  are  supposed  to 
be  primary  qualities,  and  for  which  it  is  a  kind  of  sacrilege  to  attempt  to 
assign  any  ulterior  cause.  This  theory  was  chiefly  introduced  by  Bosco- 
vich,*  and  it  has  prevailed  very  widely  among  algebraical  philosophers,  who 
have  been  in  the  habit  of  deducing  all  their  quantities  from  each  other  by 
mathematical  relations,  making,  for  example,  the  force  a  certain  function 
or  power  of  the  distance,  and  then  imagining  that  its  origin  is  sufficiently 
explained  ;  and  when  a  geometrician  has  translated  this  language  into  his 

*  De  Viribus  Vivis,  4to,  1745;  De  Lumine,  4to,  1748;  De  Lege  Continuitatis, 
4 to,  1754;  De  LegeVirium  in  Natura  existentium,  4to,  1755;  De  Divisibilitate 
Materise  et  Principiis  Corporum,  4to,  1757  ;  Theoria  Philosophise  Naturalis,  4to, 
1763,  p.  4,  Venice.  See  also  Benvenutus,  Physicse  Generalis  Synopsis,  1754. 


472  LECTURE   XLIX. 

own,  and  converted  the  formula  into  a  curve,  with  as  many  flexures  and 
reflections  as  the  labyrinth  of  Daedalus,  he  imagines  that  he  has  depicted 
to  the  senses  the  whole  procedure  of  nature.  Such  methods  may  often  be 
of  temporary  advantage,  as  long  as  we  are  contented  to  consider  them  as 
approximations,  or  as  classifications  of  phenomena  only ;  but  the  grand 
scheme  of  the  universe  must  surely,  amidst  all  the  stupendous  diversity  of 
parts,  preserve  a  more  dignified  simplicity  of  plan  and  of  principles,  than 
is  compatible  with  these  complicated  suppositions. 

"  To  show,"  says  Newton,  in  the  preface  to  the  second  edition  of  his 
Optics,  "  that  I  do  not  take  gravity  for  an  essential  property  of  bodies,  I 
have  added  one  question  concerning  its  cause,  choosing  to  propose  it  by  way 
of  a  question,  because  I  am  not  yet  satisfied  about  it  for  want  of  experi- 
ments." In  the  query  here  mentioned,  he  proceeds  from  the  supposition  of 
an  elastic  medium,  pervading  all  space ;  a  supposition  which  he  advances 
with  considerable  confidence,  and  which  he  supports  by  very  strong  argu- 
ments, deduced  as  well  from  the  phenomena  of  light  and  heat,  as  from  the 
analogy  of  the  electrical  and  magnetic  influences.  This  medium  he  supposes 
to  be  much  rarer  within  the  dense  bodies  of  the  sun,  the  stars,  the  planets, 
and  the  comets,  than  in  the  empty  celestial  spaces  between  them,  and  to 
grow  more  and  more  dense  at  greater  distances  from  them,  so  that  all  these 
bodies  are  naturally  forced  towards  each  other  by  the  excess  of  pressure. 

The  effects  of  gravitation  might  be  produced  by  a  medium  thus  consti- 
tuted, if  its  particles  were  repelled  by  all  material  substances  with  a  force 
decreasing,  like  other  repulsive  forces,  simply  as  the  distances  increase  ;  its 
density  would  then  be  every  where  such  as  to  produce  the  appearance  of  an 
attraction  varying  like  that  of  gravitation.  Such  an  ethereal  medium 
would  therefore  have  the  advantage  of  simplicity,  in  the  original  law  of 
its  action,  since  the  repulsive  force  which  is  known  to  belong  to  all  matter, 
would  be  sufficient,  when  thus  modified,  to  account  for  the  principal  pheno- 
mena of  attraction. 

It  may  be  questioned  whether  a  medium,  capable  of  producing  the  effects 
of  gravitation  in  this  manner,  would  also  be  equally  susceptible  of  those 
modifications  which  we  have  supposed  to  be  necessary  for  the  transmission 
of  light.  In  either  case  it  must  be  supposed  to  pass  through  the  apparent 
substance  of  all  material  bodies  with  the  most  perfect  freedom,  and  there 
would,  therefore,  be  no  occasion  to  apprehend  any  difficulty  from  a  retard- 
ation of  the  celestial  motions  ;  the  ultimate  impenetrable  particles  of  matter 
being  perhaps  scattered  as  thinly  through  its  external  form  as  the  stars 
are  scattered  in  a  nebula,  which  has  still  the  distant  appearance  of  a 
uniform  light  and  of  a  continuous  surface  :  and  there  seems  no  reason 
to  doubt  the  possibility  of  the  propagation  of  an  undulation  through  the 
Newtonian  medium  with  the  actual  velocity  of  light.  It  must  be  remem- 
bered that  the  difference  of  its  pressure  is  not  to  be  estimated  from  the 
actual  bulk  of  the  earth  or  any  other  planet  alone,  but  from  the  effect  of  the 
sphere  of  repulsion  of  which  that  planet  is  the  centre ;  and  we  may  then  de- 
duce the  force  of  gravitation  from  a  medium  of  no  very  enormous  elasticity. 

We  shall  hereafter  find  that  a  similar  combination  of  a  simple  pressure 


ON  COHESION.  473 

•**( 
with  a  variable  repulsion  is  also  observable  in  the  force  of  cohesion  ;  and 

supposing  two  particles  of  matter,  floating  in  such  an  elastic  medium, 
capable  of  producing  gravitation,  to  approach  each  other,  their  mutual 
attraction  would  at  once  be  changed  from  gravitation  to  cohesion,  upon  the 
exclusion  of  the  portion  of  the  medium  intervening  between  them.  This 
supposition  is,  however,  directly  opposite  to  that  which  assigns  to  the  elastic 
medium  the  power  of  passing  freely  through  all  the  interstices  of  the  ulti- 
mate atoms  of  matter,  since  it  could  never  pass  between  two  atoms  cohering 
in  this  manner;  we  cannot  therefore,  at  present,  attempt  to  assert  the 
identity  of  the  forces  of  gravitation  and  cohesion  so  strongly  as  this  theory 
would  allow  us  to  do,  if  it  could  be  established.  In  short,  the  whole  of  our 
inquiries  respecting  the  intimate  nature  of  forces  of  any  kind,  must  be  con- 
sidered merely  as  speculative  amusements,  which  are  of  no  further  utility 
than  as  they  make  our  views  more  general,  and  assist  our  experimental 
investigations. 


LECT.  XLIX.— ADDITIONAL  AUTHORITIES. 

Bernoulli,  De  Gravitate  ^Etheris,  12mo,  Amst.  1683.  Newton's  Optics ;  Queries. 
Huygens,  Op.  Rel.  i.  Hambergerus,  De  Experimento  Huygenii,  4to,  Jena,  1723. 
Hausen,  Programmata  de  Reactione,  Leipz.  1740.  Richmann  on  the  Force  of  Water 
in  Freezing,  Nov.  Com.  Petr.  i.  276.  Keill's  Introd.  Lect.  viii.  Golden  on  the 
Primary  Cause  acting  on  Matter,  1745.  Knight  on  Attraction,  &c.  4to,  Lond.  1748. 
Hollmann,  Commentationum  Sylloge,  4to,  Gott.  1764-1784.  Bossut  sur  la  Resist- 
ance de  1' Ether,  4to,  Charleville,  1766.  Van  Swinden,  De  Attractione,  4to,  Leyd. 
1766.  Kratzenstein,  Amolitio  Vis  Inertise,  Hanov.  1770.  Franklin's  Miscellanies, 
4to,  Lond.  1779.  Zimmermann,  Traitedel'Elasticite  de  1'Eau  et  d'autres  Liquides, 
Leipz.  1779.  Coulomb  on  the  Force  of  Torsion,  Hist,  et  Mem.  1764,  p.  265  ;  1784, 
p.  229.  Delangez  on  the  Mechanics  of  Semi-fluids,  Mem.  della  Soc.  Ital.  iv.  329. 
Mossotti  on  Molecular  Action,  Scientific  Mem.  i.  448.  Kelland  on  do.  Camb.  Tr.  vii. 

Atomic  Theory. — Higgins,  Comparative  View  of  the  Phlogistic  and  Antiphlogistic 
Theories,  1789.  Wenzel,  Lehrevon  der  Verwandschaft  derKbrper,  1777.  Richter, 
Anfangsgriinde  der  Stochyometrie,  1792.  Dalton's  New  System  of  Chemical  Phi- 
losophy, Manch.  1808,  1810.  Avogadro,  Mem.  di  Torino,  xxvi.  440,  xxviii.  xxix. 
30,  xxxi.  xxxiii.  Mem.  della  Soc.  Ital.  1822.  Fisica  dei  Corpi  Ponderabili,  2 
vols.  Torino,  1837-8.  Daubeny's  Introduction  to  the  Atomic  Theory,  Oxf.  1831. 
Thomson's,  Turner's,  and  all  Treatises  on  Chemistry. 


LECTURE   L. 


ON  COHESION. 

THOSE  properties  of  matter,  which  we  have  lately  examined,  if  they  are 
not  absolutely  inseparable  from  its  constitution,  are,  at  least,  always 
found  attached  to  such  matter  as  we  are  able  to  submit  to  our  experi- 
ments. There  are,  however,  many  other  general  affections,  to  which  all 
matter  appears  to  be  liable,  although  none  is  perpetually  subjected  to 
them,  and  these  are  principally,  if  not  entirely,  dependent  on  the  force  of 
cohesion. 


474  LECTURE   L. 

In  order  that  any  two  particles  of  matter  may  cohere,  it  is  necessary 
that  they  be  within  a  very  small  distance  of  each  other,  and  the  density 
of  any  substance,  composed  of  cohesive  particles,  must  probably  always 
be  more  than  half  as  great  as  that  of  water.  There  are  indeed  some  solids 
apparently  a  little  lighter  than  this,  but  they  appear  to  be  extremely 
porous :  and  perhaps  the  solid  substances  of  some  of  the  celestial  bodies 
may  also  be  a  little  more  rare.  It  frequently  happens,  that  the  compres- 
sion of  an  elastic  fluid  alone  is  sufficient  to  cause  the  force  of  cohesion  to 
take  place  between  its  particles  ;  thus,  if  common  steam  be  exposed,  in  a 
close  vessel,  to  a  pressure  greater  than  that  of  the  atmosphere,  it  will  be 
wholly  condensed  into  water,  provided  that  no  elevation  of  temperature  be 
allowed  :  and  the  same  has  been  experimentally  shown  of  many  other 
aeriform  fluids,  which  may  be  reduced  to  liquids  by  pressure  ;  but  others 
of  these  fluids  retain  their  elasticity,  notwithstanding  any  force  which 
human  art  can  apply  to  them. 

It  is  probable  that  as  soon  as  the  particles  of  any  elastic  fluid  are  brought 
within  the  reach  of  the  force  of  cohesion,  it  commences  at  once  in  its  full 
extent,  so  as  to  cause  them  to  rush  together,  until  it  is  balanced  by  that  of 
repulsion,  which  continually  increases  as  the  particles  approach  nearer  to 
each  other ;  they  must  then  remain,  perhaps  after  some  vibrations,  in  a 
state  of  equilibrium  ;  and  if  any  cause  should  tend  to  separate  them,  or  to 
bring  them  nearer  together,  they  would  resist  it,  in  either  case,  with  a  force 
proportional  to  the  degree  of  extension  or  compression.  The  distance  at 
which  the  force  of  cohesion  commences,  is  not  the  same  for  all  kinds  of 
matter,  nor  even  for  the  same  substance  at  different  temperatures ;  it  is 
smaller  for  vapours  of  all  kinds,  in  proportion  as  their  temperature  is 
higher,  the  cohesion  itself  being  also  smaller.  If  the  experiments  on  the 
density  of  steam  have  been  correct,  it  follows  that  the  force  of  repulsion 
must  increase  more  rapidly  than  the  distances  diminish,  for  the  elasticity 
of  water  is  nearly  ten  times  as  great  as  that  which  would  be  inferred  from 
the  compression  of  steam  into  a  substance  of  equal  density :  this  suppo- 
sition agrees  also  with  the  experiments  on  the  mean  density  of  the  earth, 
which  is  probably  not  so  great  as  it  would  be  if  the  force  of  repulsion 
increased  in  the  simple  ratio  of  the  density.  The  law  of  repulsion  appears 
also  to  be  in  some  degree  modified  by  the  effect  of  heat,  which  increases  its 
force  at  greater  distances  more  considerably  than  at  smaller.  It  appears 
indeed,  from  the  diminution  of  the  elasticity  of  a  spring  by  heating  it,  that 
the  repulsive  force  of  the  particles  of  bodies  at  very  small  distances  is  even 
diminished  by  heat,  unless  the  force  be  again  supposed  to  decrease  much 
more  rapidly  than  the  distance  diminishes :  thus  the  diminution  of  the 
elasticity  of  iron  by  heat  is  about  thirty  times  as  great  as  the  increase  of 
the  distance  of  its  particles ;  so  that  the  original  repulsive  force  must  pro- 
bably be  somewhat  diminished,  although  less  than  the  cohesive  force.  At 
greater  distances,  however,  the  force  of  repulsion  is  certainly  increased ; 
for  the  elasticity  of  vapours  and  gases  of  all  kinds  is  evidently  greater  as 
the  temperature  is  higher.  (Plate  XXXIX.  Fig.  530.) 

The  cohesion  of  two  or  more  particles  of  matter  to  each  other  does  not 
interfere  with  their  power  of  repelling  other  particles  situated  in  a  different 


ON  COHESION.  475 

direction :  thus,  two  pieces  of  glass  require  to  be  brought  together  with 
considerable  force,  and  generally  with  some  friction,  before  they  can  begin 
to  cohere ;  and  a  small  drop  of  water,  falling  lightly  on  the  surface  of  a 
pond,  may  remain  for  some  instants  without  coming  into  perfect  contact 
with  it ;  the  same  circumstance  is  also  still  more  observable  in  spirit  of 
wine  a  little  warmed. 

The  first  and  simplest  effect  of  cohesion  is  to  produce  liquidity.  That 
all  liquids  possess  some  cohesion,  is  very  obvious,  from  their  tendency  to 
assume  a  spherical  form  when  they  are  sufficiently  detached  from  other 
substances,  and  from  the  suspension  of  a  drop  from  any  solid,  to  which  its 
upper  surface  adheres  with  sufficient  force.  Without  cohesion,  indeed,  a 
liquid  would  be  only  a  very  fine  powder,  except  that  the  particles  of  powders 
have  not  the  power  of  moving  with  perfect  freedom  on  each  other,  which 
constitutes  fluidity.  The  apparent  weakness  of  the  cohesion  of  liquids  is 
entirely  owing  to  this  mobility,  since  their  form  may  be  changed  in  any 
degree  without  considerably  increasing  the  distances  of  their  particles,  and 
it  is  only  under  particular  circumstances  that  the  effects  of  their  cohesion 
can  become  sensible. 

When  a  liquid  is  considered  as  unlimited  in  its  extent,  the  repulsion  of 
its  particles,  situated  in  all  possible  directions  with  regard  to  each  other, 
may  be  supposed  in  all  cases  precisely  to  balance  the  cohesion,  which  is 
derived  from  the  actions  of  particles  similarly  situated  ;  and  this  must  also 
be  the  state  of  the  internal  parts  of  every  detached  portion  of  a  liquid, 
where  they  are  so  remote  from  the  surface  as  to  be  beyond  the  minute 
distance  which  is  the  limit  of  the  action  of  these  forces.  But  the  external 
parts  of  the  drop  will  not  remain  in  the  same  kind  of  equilibrium  :  they 
may  be  considered  as  a  thin  coating  of  a  liquid  surrounding  a  substance 
which  resists  only  in  a  direction  perpendicular  to  its  surface,  and  does  not 
interfere  with  the  mutual  actions  of  the  particles  of  the  liquid.  Now  since 
the  repulsive  force  increases  as  the  distance  diminishes,  it  must  be  exerted 
more  powerfully  by  the  nearest  particles,  while  the  cohesion  is  directed 
equally  towards  all  the  particles  within  a  certain  distance,  and  wherever 
the  surface  is  curved,  the  joint  cohesive  force  will  be  directed  to  a  remoter 
part  of  the  curve  than  the  repulsive  force  opposed  to  it,  so  that  each 
particle  will  be  urged,  by  the  combination  of  these  forces,  towards  the 
concave  side  of  the  curve,  and  the  more  as  the  curvature  is  greater ; 
hence  the  coating  of  the  liquid,  thus  constituted,  must  exert  a  force  on  the 
parts  in  contact  with  it,  precisely  similar  to  that  of  a  flexible  surface, 
which  is  every  where  stretched  by  an  equal  force ;  and  from  this  simple 
principle  we  may  derive  all  the  effects  produced  by  a  cohesion  of  this  kind, 
which,  from  its  being  most  commonly  observed  in  the  ascent  of  water  in 
capillary  tubes,  has  been  denominated  capillary  attraction.  (Plate  XXXIX. 
Fig.  531.) 

It  is,  therefore,  a  general  law,  that  the  surface  of  every  detached  portion 
of  a  fluid  must  every  where  have  such  a  curvature,  as  to  be  able  to  with- 
stand the  hydrostatical  pressure  which  acts  against  it ;  and  hence  we  may 
calculate  in  many  cases  the  properties  of  the  curve  which  it  must  form  ; 
but  in  other  cases  the  exact  calculation  becomes  extremely  intricate,  and 


476  LECTURE  L. 

perhaps  impracticable.  A  drop  descending  in  a  vacuum  would  be  perfectly 
spherical ;  and  if  its  magnitude  were  inconsiderable,  it  would  be  of  the 
same  form  when  descending  through  the  air  ;  a  small  bubble  rising  in  a 
liquid  must  also  be  spherical ;  but  where  the  drop  or  the  bubble  is  larger, 
its  curvature  will  be  greatest  where  the  internal  pressure  is  greatest,  or 
where  the  external  pressure  is  least,  and  in  different  cases  this  pressure 
may  be  differently  distributed.  Where  a  drop  is  suspended  from  a  solid, 
its  length  may  be  such  that  the  pressure  at  its  upper  part  may  become 
negative,  and  its  surface  will  then  be  concave  instead  of  convex :  and 
when  a  bubble  rises  to  the  surface  of  a  liquid,  it  often  carries  with  it  a  film 
of  the  liquid,  of  which  the  weight  is  probably  smaller  than  the  contractile 
force  with  which  the  surface  resists  the  escape  of  the  air,  so  that,  from  the 
magnitude  of  the  contractile  force,  we  may  determine  the  greatest  possible 
weight  of  a  bubble  of  given  dimensions.  A  slight  imperfection  of  fluidity 
probably  favours  the  formation  of  detached  bubbles,  by  retarding  the  ascent 
of  the  air,  but  it  has  a  still  greater  effect  in  prolonging  their  duration  when 
formed.  (Plate  XXXIX.  Fig.  532.) 

In  order  to  determine  the  forms  of  the  surfaces  of  liquids  in  the  cases 
which  most  commonly  occur,  it  is  necessary  to  examine  how  they  are 
affected  by  the  action  of  other  liquids,  and  of  solids  of  different  descrip- 
tions. We  may  form  some  idea  of  the  effects  of  this  mutual  action,  by 
neglecting  the  force  of  repulsion,  as  Clairaut  has  done,  and  attending  only 
to  that  of  cohesion.  Supposing  the  horizontal  surface  of  a  liquid  to  be  in 
contact  with  a  vertical  plane  surface  of  a  solid  of  half  the  attractive  power, 
it  will  remain  at  rest  in  consequence  of  the  equilibrium  of  attractions  ;  for 
the  particles  situated  exactly  at  the  junction  of  the  surfaces  may  be  con- 
sidered as  actuated  by  three  forces ;  one  deduced  from  the  effect  of  the 
liquid,  the  other  two  from  that  of  the  two  equal  portions  of  the  solid  above 
and  below  the  surface  of  the  fluid  ;  and  it  may  be  shown  that  the  combi- 
nation of  these  three  forces  will  produce  a  joint  result  in  the  direction  of 
gravity ;  consequently  the  direction  of  the  surface  must  remain  the  same 
as  when  it  is  subjected  to  the  force  of  gravity  alone,  since  the  surface  of 
every  fluid  at  rest  must  be  perpendicular  to  the  joint  direction  of  all  the 
forces  acting  on  it.  But  if  the  attractive  power  of  the  solid  be  more  than 
half  as  great  as  that  of  the  liquid,  the  result  of  the  forces  will  be  inclined 
towards  the  solid,  and  the  surface  of  the  liquid,  in  order  to  be  perpendicular 
to  it,  must  be  more  elevated  at  the  side  of  the  vessel  than  elsewhere,  and 
therefore  concave  ;  consequently  the  fluid  must  ascend  until  it  arrives  at  a 
position  capable  of  affording  an  equilibrium  in  this  manner:  if,  on  the 
contrary,  the  attractive  power  of  the  solid  be  weaker,  the  liquid  will 
descend,  and  its  surface  will  be  convex.  (Plate  XXXIX.  Fig.  533.) 

This  mode  of  reasoning  is,  however,  by  no  means  sufficient  to  explain 
all  the  phenomena,  for  it  may  be  inferred  from  it,  that  when  the  attractive 
power  of  the  solid  is  greater  or  less  than  half  that  of  the  liquid,  the  surface 
of  the  liquid  must,  at  its  origin,  be  in  the  same  direction  with  that  of  the 
solid,  instead  of  forming  an  angle  with  it,  as  it  often  does  in  reality.  But 
the  difficulty  may  be  removed  by  reverting  to  the  general  principle  of 
superficial  cohesion,  and  by  comparing  the  common  surface  of  the  liquid 


ON  COHESION.  477 

and  solid  with  the  surface  of  a  single  liquid,  of  which  the  attractive  power 
is  equal  only  to  the  difference  of  the  respective  powers  of  the  substances 
concerned.  In  this  manner  it  may  be  shown,  that  if  the  attractive  power 
of  the  solid  be  equal  to  that  of  the  liquid,  or  still  greater,  it  will  be  wetted 
by  the  liquid,  which  will  rise  until  its  surface  acquires  the  same  direction 
with  that  of  the  solid  ;  and  that,  in  other  cases,  the  angle  of  contact  will  be 
greater,  in  proportion  as  the  solid  is  less  attractive.  A  similar  comparison 
is  also  equally  applicable  to  the  contact  of  two  liquids  of  different  densities. 
The  magnitude  of  the  superficial  cohesion  or  contractility  of  a  liquid  may 
be  expressed,  for  a  certain  extent,  by  a  certain  weight ;  thus  every  inch 
of  the  surface  of  water  is  stretched  each  way  by  a  force  equal  to  the  weight 
of  the  hundredth  part  of  a  cubic  inch  of  water,  or  to  two  grains  and  a  half : 
and  for  each  inch  of  the  surface  of  mercury,  the  force  is  equivalent  to  17 
grains,  which  is  the  weight  of  ^^-y  of  a  cubic  inch  of  mercury.  Thus  if  a 
solid  of  any  form,  of  which  the  surfaces  are  vertical,  and  which  is  capable 
of  being  wetted  by  either  of  these  fluids,  be  immersed  into  a  reservoir  con- 
taining it,  the  fluid  will  be  elevated  around  it  to  such  a  height  that  2^  or 
17  grains  [respectively],  for  each  inch  of  the  circumference  of  the  solid, 
will  remain  above  the  general  level  of  the  reservoir,  the  surface  assuming 
nearly  the  same  form  as  a  very  long  and  slender  elastic  rod,  fixed  horizon- 
tally at  one  end,  and  bearing  a  large  weight  at  the  other.  (Plate  XXXIX. 
Fig.  534.) 

The  elevation  of  the  summit  of  an  extended  surface  of  w^ater,  in  contact 
with  the  flat  and  upright  surface  of  a  solid  which  is  wetted  by  it,  is  one 
seventh  of  an  inch :  but  when  two  such  surfaces,  for  instance,  two  plates  of 
glass,  are  brought  near  to  each  other,  the  elevation  of  the  water  between 
them  must  be  greater  than  this,  in  order  that  each  inch  of  the  line  of  con- 
tact may  support  its  proper  weight :  thus,  if  the  distance  were  one  fiftieth 
of  an  inch,  the  elevation  would  be  a  whole  inch ;  and  if  the  distance  were 
smaller  than  this,  the  elevation  would  be  greater  in  the  same  proportion  ; 
so  that  when  two  plates  are  placed  in  such  a  manner  as  to  touch  each  other 
at  one  of  their  upright  edges,  the  outline  of  the  water  raised  between  them 
assumes  the  form  of  a  hyperbola.  (Plate  XXXIX.  Fig.  535.) 

The  weight  supported  by  the  cohesion  of  the  water  in  a  tube  may  be 
determined,  in  a  similar  manner,  from  the  extent  of  the  circumference  ;  the 
height  being  an  inch  in  a  tube  one  twenty  fifth  of  an  inch  in  diameter,  or 
as  much  greater  as  the  diameter  of  the  tube  is  smaller :  and  in  a  tube 
wetted  with  mercury  the  height  would  be  half  as  great.  It  is  obvious  that 
if  the  lower  part  of  the  tube  be  either  contracted  or  dilated,  the  height  of 
the  fluid  will  remain  unaltered,  while  its  weight  may  be  varied  without 
limit ;  for  the  hydrostatical  pressure  on  the  surface  is  the  same,  in  both 
these  cases,  as  if  the  diameter  of  the  tube  were  equal  throughout  its  length. 
(Plate  XXXIX.  Fig.  536.) 

The  attractive  force  of  glass  to  mercury  is  less  than  half  as  great  as  the 
mutual  attraction  of  the  particles  of  mercury,  and  the  surface  of  mercury 
in  a  dense  glass  vessel  becomes,  therefore,  convex  and  depressed  ;  the  angle 
of  contact  being  about  140°,  and  the  depression  one  17th  of  an  inch. 
Between  two  plates  of  glass,  the  depression  of  mercury  is  an  inch  when 


478  LECTURE  L. 

their  distance  is  -r-f,-,  and  in  a  tube,  when  its  diameter  is  7!T  of  an  inch. 
(Plate  XXXIX.  Fig.  537,  538.) 

A  liquid  may  also  adhere  to  a  horizontal  surface  which  is  gradually 
raised  from  it,  until  the  hydrostatical  pressure  becomes  sufficient  to  over- 
power the  cohesion  of  its  superficial  parts  ;  the  internal  part  of  the  fluid 
being  usually  raised,  not  immediately  by  the  force  of  cohesion,  but  by  the 
pressure  of  the  atmosphere.  The  solid  bears  the  whole  weight  of  the 
liquid,  which  is  elevated  above  the  surface ;  and  when  the  surface  is 
perfectly  wetted,  this  weight  is  equal,  at  the  moment  of  separation,  to  the 
hydrostatical  pressure,  or  rather  suction,  corresponding  to  the  height ;  but 
in  other  cases  the  weight  may  be  somewhat  greater  than  the  hydrostatical 
pressure  on  the  surface  of  the  solid,  on  account  of  the  elevation  which 
surrounds  the  body,  and  which  is  not  compensated  by  the  excavation 
immediately  under  it.  A  surface  thus  raised  from  water  will  elevate  it  to 
the  height  of  one  fifth  of  an  inch,  and  will  require  a  force  of  50|  grains 
for  each  square  inch,  in  order  to  overcome  the  apparent  attraction  of  the 
water  ;  and  for  mercury  the  utmost  height  is  about  one  seventh  of  an  inch. 
(Plate  XXXIX.  Fig.  539,  540.) 

A  -detached  portion  of  a  liquid  may  stand  on  any  surface  which  it  is 
not  capable  of  wetting,  at  a  height  which  is  different  according  to  its 
magnitude  and  to  the  attraction  of  the  surface.  If  the  drop  is  very  small, 
its  form  may  be  nearly  spherical ;  but  when  its  extent  becomes  consider- 
able, its  height  must  always  be  less  than  that  at  which  the  liquid  would 
separate  from  a  horizontal  surface ;  and  it  will  approach  the  nearer  to  this 
limit,  as  its  attraction  to  the  surface  on  which  it  stands  is  weaker.  Thus 
a  wide  portion  of  mercury  stands  on  glass  at  the  height  of  T^  of  an  inch, 
and  on  paper  nearly  at  -f ;  and  a  portion  of  water  will  stand  on  a  cabbage 
leaf,  or  on  a  table  strewed  with  the  seeds  of  lycopodium,  nearly  at  the 
height  of  one  fifth  of  an  inch.  (Plate  XXXIX.  Fig.  541.) 

For  the  operation  of  a  powder  like  lycopodium,  it  appears  to  be  only 
necessary  that  it  should  possess  a  weaker  power  of  attraction  than  water, 
and  should,  therefore,  be  incapable  of  being  readily  wetted  by  it :  each 
particle  of  the  powder  being  then  but  partially  in  contact  with  the  water, 
will  project  beyond  its  surface,  and  prevent  its  coming  into  contact  with 
any  of  the  surrounding  bodies,  while  the  surface  assumes  such  a  curvature 
as  is  sufficient  to  withstand  the  pressure  of  the  internal  parts.  (Plate 
XXXIX.  Fig.  542.) 

When  a  dry  and  light  substance  of  any  kind  is  placed  on  the  surface  of 
water,  its  weight  is  not  sufficient  to  bring  it  within  the  distance  at  which 
cohesion  commences,  and  it  floats  surrounded  by  a  slight  depression.  Any 
substance  of  this  kind,  or  any  other  substance  surrounded  by  a  depression, 
as  a  ball  of  glass  or  iron  floating  on  mercury,  appears  to  be  attracted  by 
another  similar  substance  in  its  neighbourhood  ;  for  the  depression  between 
the  two  substances  is  increased,  and  the  pressure  of  the  fluid  on  that  side 
is  consequently  lessened,  so  that  they  are  urged  together,  by  a  force  which 
varies  inversely  as  the  square  of  the  distance.  And  in  the  same  manner, 
when  two  bodies,  surrounded  by  an  elevation,  approach  each  other,  they 
exhibit  an  attractive  force  of  a  similar  nature,  the  pressure  of  the  atmo- 


ON  COHESION.  479 

sphere  being  diminished  by  the  weight  of  the  water,  which  is  raised  between 
them  to  a  greater  height  than  on  the  opposite  sides.  But  when  a  body, 
surrounded  by  a  depression,  approaches  another,  which  is  surrounded  by 
an  elevation,  they  seem  to  repel  each  other,  the  pressure  of  the  water 
urging  the  one,  and  that  of  the  atmosphere  the  other,  in  opposite  directions. 
(Plate  XXXIX.  Fig.  543.) 

If  two  smooth  plates  of  any  kind  are  perfectly  wetted  by  a  fluid,  and 
brought  into  contact,  they  exhibit  an  appearance  of  cohesion,  which  is  so 
much  the  greater  as  the  quantity  of  fluid  is  smaller  :  if  we  attempt  to 
separate  them,  the  fluid  is  drawn  inwards,  so  as  to  have  its  surface  made 
concave,  and  it  resists  the  separation  of  the  plates  with  a  certain  force, 
which  acts  with  a  hydrostatic  advantage  so  much  the  greater,  as  their 
distance  is  smaller,  and  hence  produces  the  appearance  of  a  cohesion 
varying  in  proportion  to  the  distance.  (Plate  XXXIX.  Fig.  544.) 

Supposing  the  two  plates  to  be  separated  at  one  end,  and  the  fluid 
between  them  to  assume  the  form  of  a  drop,  one  of  the  marginal  surfaces 
of  the  drop,  being  narrower  than  the  other,  will  act.  with  a  greater  advan- 
tage, like  a  tube  of  smaller  diameter,  and  will  tend  to  draw  the  drop 
towards  it ;  and  the  apparent  attraction  towards  the  line  of  contact  of  the 
glasses  will  increase  in  proportion  as  the  square  of  the  distance  decreases. 
This  result  was  experimentally  observed  almost  a  century  ago,  but  it  has 
been  usually  explained  on  mistaken  grounds.  (Plate  XXXIX.  Fig.  545.) 

The  attractive  power  of  water  being  greater  than  that  of  oils,  a  small 
portion  of  oil  thrown  on  water  is  caused  to  spread  on  it  with  great  rapidity 
by  means  of  the  force  of  cohesion ;  for  it  does  not  appear  that  any  want 
of  chemical  affinity  between  the  substances  concerned,  diminishes  their 
cohesive  power ;  water  readily  adheres  to  tallow  when  solid,  and  probably 
essential  oils  would  adhere  still  more  readily  to  ice.  There  is,  however 
some  difficulty  in  understanding  how  these  oils  can  so  suddenly  come 
within  the  limit  of  the  cohesive  force  of  water,  while  the  drops  of  water 
themselves  sometimes  remain  for  a  few  seconds  beyond  it. 

A  sponge  affords  us  a  familiar  instance  of  the  application  of  capillary 
attraction  to  useful  purposes  ;  it  is  well  known  that  in  order  to  its  speedy 
operation,  it  requires  to  be  previously  moistened,  by  the  assistance  of  a 
little  pressure,  otherwise  it  exhibits  the  same  appearance  of  repulsion  that 
is  observable  in  many  other  cases  where  the  contact  is  imperfect.  The 
absorption  of  moisture  by  sugar  depends  on  the  same  principle,  and 
here  the  tubes  are  so  minute,  that  the  height  of  ascent  appears  to  be  almost 
unlimited. 

The  magnitude  of  the  cohesion  between  fluids  and  solids,  as  well  as  of 
the  particles  of  fluids  with  each  other,  is  more  directly  shown  by  an  ex- 
periment on  the  continuance  of  a  column  of  mercury,  in  the  tube  of  a 
barometer,  at  a  height  considerably  greater  than  that  at  which  it  usually 
stands,  on  account  of  the  pressure  of  the  atmosphere.  If  the  mercury  has 
been  well  boiled  in  the  tube,  it  may  be  made  to  remain  in  contact  with  the 
closed  end,  at  the  height  of  70  inches  or  more  ;  and  by  agitation  only  it 
may  be  made  to  cohere  so  strongly  as  to  occupy  the  whole  length  of  the 
tube  of  a  common  barometer,  which  is  several  inches  more  than  the  height 


480  LECTURE  L. 

at  which  the  pressure  of  the  atmosphere  sustains  it.  A  small  siphon  may 
also  convey  mercury  from  one  vessel  into  another  in  the  vacuum  of  an 
air  pump  :  and  in  hoth  these  cases  it  is  ohvious  that  no  other  force  than 
cohesion  can  retain  the  upper  surface  of  the  mercury  in  contact  with  the 
glass,  or  its  internal  parts  in  contact  with  each  other. 

The  force  of  cohesion  may  also  he  exerted  by  solid  substances  on  other 
solids,  either  of  the  same  kind,  or  of  different  kinds.  Thus  two  masses  of 
lead,  when  once  united  by  pressure,  assisted  by  a  little  friction,  require  a 
very  considerable  force  to  separate  them,  and  it  may  be  shown  either  by 
measuring  this  force,  or  by  suspending  the  lead  in  the  vacuum  of  the  air 
pump,  that  the  pressure  of  the  atmosphere  is  not  materially  concerned  in 
producing  this  appearance  of  cohesion,  since  its  magnitude  much  exceeds 
that  of  the  atmospherical  pressure.  A  cohesion  of  this  kind  is  sometimes 
of  practical  utility  in  the  arts ;  little  ornaments  of  laminated  silver  re- 
maining attached  to  iron  or  steel,  with  which  they  have  been  made  to 
cohere  by  the  powerful  pressure  of  a  blow,  so  as  to  form  one  mass 
with  it. 

The  contact  of  two  pieces  of  lead,  although  intimate  enough  to  produce 
a  considerable  cohesion,  is  by  no  means  so  complete  as  to  unite  the  parts 
into  one  mass  ;  the  union,  however,  appears  to  be  nearly  of  the  same  kind  as 
the  common  cohesion  of  aggregation  ;  and  if  the  lead  were  softened  into 
an  amalgam  by  the  addition  of  mercury,  the  cohesion  of  the  two  masses 
would  become  precisely  the  same  as  the  internal  cohesion  of  each  mass. 
Harder  substances,  such  as  marble  or  glass,  cohere  but  weakly,  perhaps 
because  their  surfaces  are  never  so  perfectly  adjusted  to  each  other  as  to 
touch  throughout.  The  interposition  of  a  fluid  usually  increases  the 
apparent  attraction  of  such  substances,  but  this  circumstance  has  already 
been  explained  from  the  effect  of  the  capillary  contraction  of  its  surface  ; 
and  when  the  substances  are  wholly  immersed  in  a  fluid,  the  cohesion  is 
little,  if  at  all,  increased. 

The  immediate  cause  of  solidity,  as  distinguished  from  liquidity,  is  the 
lateral  adhesion  of  the  particles  to  each  other,  to  which  the  degree  of  hard- 
ness or  solidity  is  always  proportional.  This  adhesion  prevents  any  change 
of  the  relative  situation  of  the  particles,  so  that  they  cannot  be  withdrawn 
from  their  places,  without  experiencing  a  considerable  resistance  from  the 
force  of  cohesion,  while  those  of  liquids  may  remain  equally  in  contact 
with  the  neighbouring  particles,  notwithstanding  their  change  of  form. 
When  a  perfect  solid  is  extended  or  compressed,  the  particles,  being  retained 
in  their  situations  by  the  force  of  lateral  adhesion,  can  only  approach 
directly  to  each  other,  or  be  withdrawn  further  from  each  other,  and  the 
resistance  is  nearly  the  same  as  if  the  same  substance,  in  a  fluid  state,  were 
inclosed  in  an  unalterable  vessel,  and  forcibly  compressed  or  dilated.  Thus 
the  resistance  of  ice  to  extension  or  compression  is  found  by  experiment 
to  differ  very  little  from  that  of  water  contained  in  a  vessel ;  and  the  same 
effect  may  be  produced  even  when  the  solidity  is  not  the  most  perfect 
which  the  substance  admits  ;  for  the  immediate  resistance  of  iron  or  steel 
to  flexure  is  the  same  whether  it  may  be  harder  or  softer.  It  often  happens, 
however,  that  the  magnitude  of  the  lateral  adhesion  is  so  much  limited  as 


ON  COHESION.  481 

to  allow  a  greater  facility  of  extension  or  compression,  and  it  may  yet 
retain  a  power  of  restoring  the  bodies  to  their  original  form  by  its  reaction. 
This  force  may  even  be  the  principal  or  perhaps  the  only  source  of  the 
body's  elasticity :  thus  when  a  piece  of  elastic  gum  is  extended,  the  mean 
distance  of  its  particles  is  not  materially  increased,  for  it  is  said  to  become 
rather  more  than  less  dense  during  its  extension  ;  consequently  the  change 
of  form  is  rather  to  be  attributed  to  a  displacement  of  the  particles,  than  to 
their  separation  to  a  greater  distance  from  each  other,  and  the  resistance 
must  be  derived  from  the  lateral  adhesion  only :  some  other  substances 
also,  approaching  more  nearly  to  the  nature  of  liquids,  may  be  extended  to 
many  times  their  original  length,  with  a  resistance  continually  increasing  ; 
and  in  such  cases  there  can  scarcely  be  any  material  change  of  the  specific 
gravity  of  these  substances.  Professor  Robison  has  mentioned  the  juice 
of  bryony  as  affording  a  remarkable  instance  of  such  a  viscidity. 

It  is  probable  that  the  immediate  cause  of  the  lateral  adhesion  of  solids 
is  a  symmetrical  arrangement  of  their  constituent  parts  :  it  is  certain  that 
almost  all  bodies  are  disposed,  in  becoming  solid,  to  assume  the  form  of 
crystals,  which  evidently  indicates  the  existence  of  such  an  arrangement ; 
and  all  the  hardest  bodies  in  nature  are  of  a  crystalline  form.  It  appears, 
therefore,  consistent  both  with  reason  and  with  experience  to  suppose  that 
a  crystallization  more  or  less  perfect  is  the  universal  cause  of  solidity.  We 
may  imagine  that  when  the  particles  of  matter  are  disposed  without  any 
order,  they  can  afford  no  strong  resistance  to  a  motion  in  any  direction, 
but  when  they  are  regularly  placed  in  certain  situations  with  respect  to 
each  other,  any  change  of  form  must  displace  them  in  such  a  manner,  as 
to  increase  the  distance  of  a  whole  rank  at  once  ;  and  hence  they  may  be 
enabled  to  cooperate  in  resisting  such  a  change.  Any  inequality  of  tension 
in  a  particular  part  of  a  solid  is  also  probably  so  far  the  cause  of  hardness, 
as  it  tends  to  increase  the  strength  of  union  of  any  part  of  a  series  of  par- 
ticles which  must  be  displaced  by  a  change  of  form. 

The  immediate  resistance  of  a  solid  to  extension  or  compression  is  most 
properly  called  its  elasticity  ;  although  this  term  has  sometimes  been  used 
to  denote  a  facility  of  extension  or  compression,  arising  from  the  weakness 
of  this  resistance.  A  practical  mode  of  estimating  the  force  of  elasticity 
has  already  been  explained,  and  according  to  the  simplest  statement  of  the 
nature  of  cohesion  and  repulsion,  the  weight  of  the  modulus  of  elasticity 
is  the  measure  of  the  actual  magnitude  of  each  of  these  forces  ;  and  it  fol- 
lows that  an  additional  pressure,  equal  to  that  of  the  modulus,  would 
double  the  force  of  cohesion,  and  require  the  particles  to  be  reduced  to  half 
their  distance  in  order  that  the  repulsion  might  balance  it ;  and  in  the 
same  manner  an  extending  force  equal  to  the  weight  of  half  the  modulus 
would  reduce  the  force  of  cohesion  to  one  half,  and  extend  the  substance  to 
twice  its  dimensions.  But,  if,  as  there  is  some  reason  to  suppose,  the 
mutual  repulsion  of  the  particles  of  solids  varies  a  little  more  rapidly  than 
their  distance,  the  modulus  of  elasticity  will  be  a  little  greater  than  the 
true  measure  of  the  whole.eohesive  and  repulsive  force  :  this  difference  will 
.not,* however,  affect  the  truth  of  our  calculations  respecting  the  properties 

2i 


482  LECTURE  L. 

of  elastic  bodies,  founded  on  the  magnitude  of  the  modulus  as  already- 
determined. 

The  stiffness  of  a  solid  is  measured  by  its  immediate  resistance  to  any 
force  tending  to  change  its  form  ;  in  this  sense,  if  the  force  be  applied  so  as 
to  extend  or  to  compress  it,  or  to  overcome  its  lateral  adhesion  by  the  effect 
which  we  have  formerly  called  detrusion,  the  primitive  elasticity  and 
rigidity  of  the  substance,  together  with  its  magnitude,  will  determine  its 
stiffness  :  but  if  the  force  be  otherwise  applied,  so  as  to  produce  flexure  or 
torsion,  the  form  of  the  body  must  also  be  taken  into  the  calculation,  in  the 
manner  which  has  already  been  explained  in  the  lecture  on  passive  strength. 
The  stiffness  of  a  body  with  respect  to  any  longitudinal  force  is  directly 
as  its  transverse  section,  and  inversely  as  its  length ;  for  the  same  force 
will  compress  or  extend  a  rod  100  yards  long  so  as  to  change  its  length  an 
inch,  that  will  produce  a  change  of  only  half  an  inch  in  a  rod  50  yards 
long.  We  have  seen  that  the  space  through  which  a  body  may  be  extended 
or  compressed,  without  any  permanent  alteration  of  form,  constitutes  its 
toughness :  that  its  strength,  or  the  ultimate  resistance  which  it  affords, 
depends  on  the  joint  magnitude  of  its  toughness  and  elasticity  or  stiff- 
ness, and  that  its  resilience,  or  the  power  of  overcoming  the  energy  or 
impetus  of  a  body  in  motion,  is  proportional  to  the  strength  and  toughness 
conjointly. 

Softness,  or  want  of  solidity,  is  in  general  accompanied  by  a  proportional 
susceptibility  of  permanent  alteration  of  form  without  fracture ;  some- 
times, however,  from  a  want  of  cohesion,  a  soft  body  is  at  the  same  time 
brittle.  Soft  substances,  which  are  capable  of  direct  extension  to  a  consi- 
derable degree  are  called  viscous  or  tenacious  ;  of  these,  birdlime,  sealing 
wax,  and  glass  sufficiently  heated,  are  some  of  the  most  remarkable. 
Harder  substances  which  have  the  same  property  are  called  ductile,  and 
when  the  alteration  is  made  by  percussion  and  compression,  they  are 
termed  malleable.  Of  all  substances  gold  is  perhaps  the  most  ductile :  the 
thinness  of  leaf  gold  and  of  the  gilding  of  silver  wire  has  already  been  men- 
tioned ;  and  it  is  said  that  a  single  grain  of  gold  has  been  drawn  into  a 
wire  500  yards  in  length,  and  consequently  little  more  than  -^Vs-  of  an 
inch  in  diameter.  The  ductility  or  tenacity  of  a  spider's  web  is  of  a  dif- 
ferent kind,  it  is  particularly  shown  by  its  capability  of  being  twisted, 
almost  without  limit,  and  of  accommodating  itself  to  its  new  position  with- 
out any  effort  to  untwist. 

With  respect  to  the  ultimate  agent  by  which  the  effects  of  cohesion  are 
produced,  if  it  is  allowable  to  seek  for  any  other  agent  than  a  fundamental 
property  of  matter,  it  has  already  been  observed,  that  appearances  extremely 
similar  might  be  derived  from  the  pressure  of  a  universal  medium  of  great 
elasticity  ;  and  we  see  some  effects,  so  nearly  resembling  them,  which  are 
unquestionably  produced  by  the  pressure  of  the  atmosphere,  that  we  can 
scarcely  avoid  suspecting  that  there  must  be  some  analogy  in  the  causes. 
Two  plates  of  metal,  which  cohere  enough  to  support  each  other  in  the 
open  air,  will  often  separate  in  a  vacuum  :  when  a  boy  draws  along  a  stone 
by  a  piece  of  wet  leather,  the  pressure  of  the  atmosphere  appears  to  be 


ON  COHESION.  483 

materially  concerned.  The  well  known  experiment,  of  the  two  exhausted 
hemispheres  of  Magdeburg,  affords  a  still  more  striking  instance  of  appa- 
rent cohesion  derived  from  atmospherical  pressure ;  and  if  we  place  between 
them  a  thick  ring  of  elastic  gum,  we  may  represent  the  natural  equilibrium 
between  the  forces  of  cohesion  and  of  repulsion  ;  for  the  ring  would  resist 
any  small  additional  pressure  with  the  same  force  as  would  be  required 
for  separating  the  hemispheres  so  far  as  to  allow  it  to  expand  in  an  equal 
degree :  and  at  a  certain  point  the  ring  would  expand  no  more ;  the  air 
would  be  admitted,  and  the  cohesion  destroyed,  in  the  same  manner  as 
when  a  solid  of  any  kind  is  torn  asunder.  But  all  suppositions  founded  on 
these  analogies  must  be  considered  as  merely  conjectural ;  and  our  know- 
ledge of  every  thing  which  relates  to  the  intimate  constitution  of  matter, 
partly  from  the  intricacy  of  the  subject,  and  partly  for  want  of  sufficient 
experiments,  is  at  present  in  a  state  of  great  uncertainty  and  imperfection. 
One  of  the  most  powerful  agents,  in  changing  and  modifying  the  forms 
of  matter,  is  the  operation  of  heat,  by  which  the  states  of  solidity,  liquidity, 
and  elastic  fluidity  are  often  produced  in  succession  ;  and  the  investigation 
of  the  nature  and  effects  of  heat  will  constitute  the  subject  of  the  two  next 
lectures. 


LECT.  L.— ADDITIONAL  AUTHORITIES. 

Cohesion  in  general. — Desaguliers  on  the  Cohesion  of  Lead,  Ph.  Tr.  1725,  p.  345. 
Hambergus,  De  Cohesione,  4to,  Jena,  1732.  Winckler,  De  Causis  Conjunctionis, 
4to,  Leipz.  1736.  Felice,  do.  4to,  1757. 

Capillary  Action.— Fabri,  Dialogi  Physici,  Lyons,  1669.     Boyle,  Ph.  Tr.  1676, 

?.  775.  Hauksbee  on  the  Effect  of  Capillary  Tubes  remaining  in  a  Vacuum,  ibid. 
706,  p.  2223;  on  Different  Points,  ibid.  1709,  p.  258  ;  1711,  p.  395;  1712,  pp. 413, 
539  ;  1713,  p.  151.  Taylor  on  the  Ascent  of  Water  between  Two  Plates,  ibid.  1712, 
p.  538 ;  on  Attraction  of  Wood  to  Water,  ibid.  1721,  p.  204.  Jurin,  ibid.  1718, 
p.  739;  1719,  p.  1083.  Bulfinger,  Com.  Petr.  ii.  233,  iii.  281.  Musschenbroek, 
Diss.  Phys.  pp.  271, 334.  Clairaut,  Fig.  de  la  Terre,  1743.  GeUert  on  Melted  Lead 
in  Tubes,  Com.  Petr.  xii.  293  ;  on  Prismatic  Tubes,  ibid.  xii.  302.  Segner  on  the 
Surfaces  of  Fluids,  Com.  Gott.  1751,  i.  301.  Tetens,  De  Fluxu  Siphonis  in  Vacuo, 
4to,  Biitzow,  1763.  Lalande,  sur  la  Cause  de  1'Elevation  des  Liqueurs,  12mo,  Par. 
1770.  Morveau  on  the  Attraction  of  Water  and  Oils,  Jour,  de  Phy.  i.  172,  460. 
Lord  C.  Cavendish's  Table  of  the  Depression  of  Mercury,  Ph.  Tr.  1776,  p.  382. 
Achard  on  the  Adherence  of  Solids  to  Fluids,  Hist,  et  Mem.  de  Berlin,  1776,  p.  149. 
Schriften,  i.  355.  Dutour,  Jour,  de  Physique,  xi.  127,  xiii.  Supp.  357,  xiv.  216, 
xv.  46,  234,  xvi.  85,  xix.  137,  287.  Besile,  ibid,  xxviii.  171,  xxix.  287,  339,  xxx. 
125.  Monge  on  Apparent  Attractions  and  Repulsions,  Hist,  et  Mem.  1787,  p.  506, 
Nich.  Jour.  iii.  269.  Bennet,  Manch.  Mem.  iii.  116.  Leslie,  Ph.  Mag.  xiv.  193. 
Young  on  the  Cohesion  of  Fluids,  Ph.  Tr.  1805,  p.  65.  Laplace,  Mec.  Cel.  Sup- 
plem.,  and  Bullet,  de  la  Soc.  Philom.  1819,  p.  122.  Edin.  Encyc.  art.  Capillary 
Attraction.  Gauss,  Principia  Generalia  Theorise  Figurse  Fluid,  in  Statu  ^Equilib. 
Gott.  1830.  Poisson,  Mem.  de  1'Acad.  ix.  Theorie  de  1' Action  CapUlaire,  4to, 
1831.  Link,  Pogg.  Annalen,  1832,  xxv.  270,  xxvii.  193,  xxix.  404. 


2i2 


484 


LECTURE    LI. 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT. 

IT  may  appear  doubtful  to  some  whether  the  subject  of  heat  belongs 
most  properly  to  mechanical  or  to  chemical  philosophy.  Its  influence  in 
chemistry  is  unquestionable  and  indispensable ;  but  its  mechanical  effects 
are  no  less  remarkable :  it  could  not  therefore  with  propriety  be  omitted 
either  in  a  course  of  chemical  or  of  physical  lectures,  especially  by  those 
who  are  persuaded  that  what  we  call  heat  is,  in  its  intimate  nature,  rather 
a  mechanical  affection  of  matter  than  a  peculiar  substance.  We  shall 
first  inquire  into  the  nature  of  the  principal  sources  of  heat,  and  next  into 
the  mode  of  its  communication,  and  its  most  common  effects,  whether 
temporary  or  permanent :  the  measures  of  heat,  and  the  most  probable 
opinions  respecting  its  nature,  will  afterwards  be  separately  considered. 

Heat  is  an  influence  capable  of  affecting  our  nerves  in  general  with  the 
peculiar  sensation  which  bears  its  name,  and  of  which  the  diminution  pro- 
duces the  sensation  denominated  cold.  Any  considerable  increase  of  heat 
gives  us  the  idea  of  positive  warmth  or  hotness,  and  its  diminution  excites 
the  idea  of  positive  cold.  Both  these  ideas  are  simple,  and  each  of  them 
might  be  derived  either  from  an  increase  or  from  a  diminution  of  a  positive 
quality  :  but  there  are  many  reasons  for  supposing  heat  to  be  the  positive 
quality,  and  cold  the  diminution  or  absence  of  that  quality ;  although  we 
have  no  more  experience  of  the  total  absence  of  heat,  than  of  its  greatest 
possible  accumulation,  which  might  be  called  the  total  absence  of  cold. 
Our  organs  furnish  us,  in  some  cases,  with  very  delicate  tests  of  any 
increase  or  diminution  of  heat ;  but  it  is  more  usually  recognised  by  the 
enlargement  of  bulk,  generally  produced  in  those  bodies  to  which  heat  is 
attached  in  an  increased  quantity,  and  the  contraction  of  those  from  which 
it  is  subtracted. 

The  simplest  modes  of  exciting  heat  appear  to  be  the  compression  of 
elastic  fluids,  and  the  collision  or  friction  of  solid  bodies ;  although  a  more 
usual  and  a  more  powerful  source  of  heat  is  found  in  various  chemical 
combinations  and  decompositions,  which  are  produced  by  the  peculiar 
elective  attractions  of  different  substances  for  each  other,  or  from  the  influ- 
ence of  the  solar  rays,  which  are  probably  emitted  in  consequence  of  the 
chemical  processes  that  continually  take  place  at  the  surface  of  the  sun. 

The  effects  of  the  condensation  and  rarefaction  of  elastic  fluids  are 
shewn  by  the  condenser  and  the  air  pump  ;  when  an  exhaustion  is  made 
with  rapidity,  the  thermometer,  placed  in  the  receiver  of  the  air  pump, 
usually  sinks  a  degree  or  two ;  and  when  the  air  is  readmitted  abruptly 
into  a  partial  vacuum,  the  sudden  condensation  of  the  rarefied  air  raises 
the  mercury :  and  a  similar  elevation  of  temperature  is  produced  by  the 
operation  of  the  condenser.  Much  of  this  heat  is  soon  dissipated,  but  by 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT.  485 

observing  the  velocity  with  which  the  thermometer  rises,  Mr.  Dalton  has 
estimated  that  air,  compressed  to  half  its  dimensions,  has  its  temperature 
elevated  about  50  degrees  of  Fahrenheit ;  and  some  of  his  experiments 
indicate,  when  accurately  examined,  a  still  greater  change.*  For  the 
present  we  may  define  the  sense  of  the  term  degree,  in  Fahrenheit's  scale, 
as  corresponding  to  an  expansion  of  a  portion  of  mercury  amounting  to 
one  ten  thousandth  part  of  its  bulk ;  and  a  degree  of  Reaumur  originally 
corresponded  to  an  expansion  of  a  weak  spirit  of  wine,  amounting  to  one 
thousandth  part  of  its  bulk.  It  may  be  inferred  from  the  velocity  of 
sound,  supposing  that  the  excess  of  its  velocity  above  the  common  calcula- 
tion is  wholly  derived  from  the  heat  and  cold  produced  by  condensation 
and  expansion,  that  a  condensation  amounting  to  -r^-  of  the  bulk  of  any 
portion  of  air  will  raise  its  temperature  one  degree  of  Fahrenheit.  When 
air  is  very  rapidly  compressed  in  the  condenser  of  an  air  gun,  it  is  some- 
times so  much  heated  as  actually  to  set  on  fire  a  small  portion  of  tow, 
placed  near  the  end  of  the  barrel,  t 

The  production  of  heat  by  friction  is  too  well  known  to  require  an 
experimental  proof;  but  Count  Rumford  has  taken  particular  pains  to 
ascertain  every  circumstance  which  can  be  supposed  to  be  concerned  in 
the  operation  of  this  cause ;  and  the  results  of  his  experiments  are  so 
striking,  that  they  deserve  to  be  briefly  related.  He  took  a  cannon,  not 
yet  bored,  having  a  projection  of  two  feet  beyond  its  muzzle,  a  part  which 
is  usually  cast  with  the  piece,  in  order  to  insure  the  solidity  of  the  metal 
throughout,  by  the  pressure  which  its  weight  occasions.  This  piece  was 
reduced  to  the  form  of  a  cylinder,  joined  to  the  cannon  by  a  smaller  neck, 
and  a  large  hole  was  bored  in  it :  the  whole  cannon  was  then  made  to 
revolve  on  its  axis  by  means  of  the  force  of  horses,  while  a  blunt  steel 
borer  was  pressed  against  the  bottom  of  the  hollow  cylinder,  by  a  force 
equal  to  about  10,000  pounds  avoirdupois ;  the  surface  of  contact  of  the 
borer  with  the  bottom  of  the  cylinder  being  about  2  square  inches.  This 
apparatus  was  wrapped  up  in  flannel,  when  its  temperature  was  about  60°. 
In  half  an  hour,  when  the  cylinder  had  made  960  turns,  the  horses  being 
stopped,  a  mercurial  thermometer  was  introduced  into  a  perforation  in  the 
bottom  of  the  cylinder,  extending  from  the  side  to  the  axis,  and  it  stood 
at  130°,  which  Count  Rumford  considers  as  expressing  very  nearly  the 
mean  temperature  of  the  cylinder.  The  dust  or  scales,  abraded  by  the 
borer,  weighed  only  837  grains,  or  about  -^  of  the  whole  weight  of  the 
cylinder.  In  another  experiment,  the  cylinder  was  surrounded  by  a  tight 
deal  box,  fitted  writh  collars  of  leather,  so  as  to  allow  it  to  revolve  freely, 
and  the  interval  between  the  cylinder  and  the  box  was  filled  with  19 
pounds  of  cold  water,  which  was  excluded  from  the  bore  of  the  cylinder 
by  oiled  leathers  fixed  on  the  borer ;  and  after  two  hours  and  a  half,  the 
water  was  made  to  boil.  Hence  Count  Rumford  calculates  that  the  heat 

*  Manch.  Mem.  v.  515. 

f  On  the  production  of  heat  by  condensation,  and  cold  by  rarefaction,  see  Dar- 
win, Ph.  Tr.  1788,  p.  43;  Pictet,  Jour,  de  Phy.  xlvii.  186;  Baillet,  ibid,  xlviii. 
166  ;  Ph.  Mag.  xiv.  363. 


486  LECTURE  LI. 

produced  in  this  manner,  by  the  operation  of  friction,  was  equal  to  that  of 
9  wax  candles,  each  three  quarters  of  an  inch  in  diameter,  continuing  to 
burn  for  the  same  time.* 

A  still  more  rapid  increase  of  temperature  may  be  obtained,  where  the 
relative  velocity  of  the  bodies  is  more  considerable,  or  where  they  strike 
each  other  with  violence.  Thus  a  soft  nail  may  be  so  heated,  by  three  or 
four  blows  of  a  hammer,  that  we  may  light  a  match  with  it  ;t  and  by 
continuing  the  operation,  it  may  be  made  red  hot :  two  pieces  of  wood  may 
also  be  set  on  fire  by  means  of  a  lathe.  When  a  waggon  takes  fire,  for 
want  of  having  its  wheels  properly  greased,  the  friction  is  probably 
increased  by  the  tenacity  of  the  hardened  tar,  which  perhaps  becomes  the 
more  combustible  as  it  dries. 

One  of  the  most  remarkable  circumstances,  attending  the  production  of 
heat  by  friction,  is  the  discovery  of  Professor  Pictet,  that  it  is  often  much 
more  powerfully  excited  by  soft  substances  than  by  harder  ones.  In 
making  some  experiments  in  a  vacuum,  in  order  to  examine  how  far  the 
presence  of  air  might  be  concerned  in  the  effects  of  friction,  he  accidentally 
interposed  some  cotton  between  the  bulb  of  his  thermometer  and  the  cup, 
which  was  subjected  to  the  friction  of  various  substances  as  it  revolved  ; 
and  he  found  that  the  soft  filaments  of  the  cotton  excited  much  more  heat, 
than  any  other  of  the  substances  employed.^ 

The  chemical  production  of  heat  is  of  greater  practical  importance  than 
its  mechanical  excitation  ;  but  by  what  means  chemical  changes  operate  in 
exciting  heat,  we  cannot  attempt  to  determine.  There  is  certainly  no 
general  law  of  composition  or  decomposition  that  can  be  applied  to  all  such 
cases :  most  commonly  heat  is  produced  when  oxygen  exchanges  an  aeri- 
form for  a  solid  state,  or  enters  into  a  new  combination,  and  still  remains 
elastic  ;  but  in  the  case  of  gunpowder,  heat  is  disengaged  while  an  elastic 
fluid  is  produced  from  a  solid ;  and  in  some  other  cases  the  oxygenous 
principle  is  wholly  unconcerned.  It  appears  on  the  whole,  that  however 
heat  may  be  excited,  the  corpuscular  powers  of  cohesion  and  repulsion  are 
always  disturbed  and  called  into  action,  their  equilibrium  being  destroyed 
and  again  restored,  whether  by  mechanical  or  by  chemical  means.  A  wax 
candle,  f  of  an  inch  in  diameter,  loses  a  grain  of  its  weight  in  37  seconds, 
and  consumes  about  three  grains,  or  9  cubic  inches,  of  oxygen  gas, 
producing  heat  enough  to  raise  the  temperature  of  about  15,000  grains  of 
water  a  single  degree.  According  to  the  experiments  of  Mr.  Lavoisier  and 
Mr.  Laplace,  the  combustion  of  ten  grains  of  phosphorus  requires  the  con- 
sumption of  15  grains  of  oxygen,  the  combustion  of  ten  grains  of  charcoal 
26,  and  of  hydrogen  gas  56 ;  and  by  the  heat  produced  during  the  combus- 
tion of  a  pound  of  phosphorus,  100  pounds  of  ice  may  be  melted,  during 
that  of  a  pound  of  charcoal  96£,  of  hydrogen  gas  295£,  of  wax  133,  and  of 
olive  oil  149 ;  and  during  the  deflagration  of  a  pound  of  nitre  with  about 

*  Ph.  Tr.  1798,  p.  80.  Essays,  ii.  IX.  Nich.  Jour.  ii.  106.  See  also  Haldot,  ibid, 
xxvi.  30. 

t  Mem.  d'Arcueil,  ii.  441. 

J  Essais  de  Physique,  Geneve,  1790. 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT.  487 

one  sixth  part  of  its  weight  of  charcoal,  twelve  pounds  of  ice  may  be 
melted.* 

The  manner  in  which  heat,  when  excited  or  extricated  by  any  of  these 
means,  passes  from  one  body  to  another,  requires  to  be  very  particularly 
examined.  We  shall  find  that  this  communication  happens  in  one  or  both 
of  two  ways,  by  contact,  or  by  radiation ;  and  that  it  may  also  differ  both 
with  respect  to  the  quantity  of  heat  concerned,  and  to  the  time  occupied 
by  the  process.  Whatever  heat  may  be,  we  may  safely  conclude  that  in 
substances  of  the  same  kind,  at  the  same  temperature  or  apparent  degree 
of  warmth  or  coldness,  its  quantity  must  be  proportional  to  the  mass  or 
weight ;  for  instance,  that  a  quart  of  the  water  of  a  given  cistern  contains 
twice  as  much  heat  as  a  pint ;  and  where  this  is  true  of  the  different  parts 
of  any  substance,  they  must  remain  in  equilibrium  with  respect  to  heat. 
But  if  two  equal  portions  of  the  same  substance,  containing  different 
quantities  of  heat,  be  in  contact,  they  will  affect  each  other  in  such  a 
manner  as  to  have  their  temperatures  equalised,  and  the  more  rapidly  as 
the  contact  is  more  perfect.  Thus,  if  two  portions  of  a  fluid  at  different 
temperatures  be  mixed  together,  they  will  acquire  immediately  an  inter- 
mediate temperature  ;  and  when  two  solids  are  in  contact,  the  quantity  of 
heat,  communicated  by  the  hotter  to  the  colder  in  a  given  time,  is  nearly 
proportional  to  the  difference  of  the  temperatures.  Hence  it  would  follow, 
that  they  could  never  become  precisely  of  the  same  temperature  in  any 
finite  time  ;  but  in  fact  the  difference  of  temperature  is  rendered,  in  a  mode- 
rate time,  too  small  to  be  perceptible.  The  nature  of  the  substances 
concerned  has  also  a  material  effect  on  the  velocity  with  which  heat  is 
communicated  through  their  internal  parts ;  metallic  bodies  in  general 
conduct  it  the  most  readily,  earthy  and  vitreous  bodies  the  least ;  but  the 
various  metals  possess  this  power  in  different  degrees  ;  silver  and  copper 
conduct  heat  more  rapidly  than  iron,  and  platina  transmits  it  but  very 
slowly.  Professor  Pictet  supposes  that  heat  ascends  within  solid  bodies 
more  readily  than  it  descends ;  but  the  effect  of  the  air  remaining  in  the 
imperfect  vacuum  of  the  air  pump  may  be  sufficient  to  explain  his  experi- 
ments ;  the  difference  of  temperature  producing  an  ascending  current 
in  the  neighbourhood  of  the  heated  body,  by  means  of  which  the  cold  ail- 
continually  approaches  its  lower  parts,  and  carries  the  heat  upwards  :  and 
it  has  been  found  that  the  rarefaction  of  air  does  not  by  any  means 
diminish  its  power  of  conducting  heat,  in  proportion  to  the  diminution  of 
its  density. 

Count  Rumford's  experiments  t  have  shown  that  all  fluids  are  very 
imperfect  conductors  of  heat  by  immediate  contact,  although  it  is  scarcely 
credible  that  they  can  be  absolutely  nonconductors ;  but  heat  is  usually 
communicated  between  different  portions  of  the  same  fluid,  almost  entirely 

*  On  combustion,  consult  Hooke,  Micographia,  p.  103.  Lavoisier  and  Laplace,  Hist, 
et  Mem.  1780,  p.  355,  H.  3.  Rumford,  Nich.  Jour,  xxxii.  105  ;  xxxiv.  319  ;  xxxv. 
95.  Davy,  Ph.  Tr.  1817.  Sym,  Annals  of  Ph.  viii.  321.  Davies,  ibid.  (2nd  series), 
x.  447.  Dobereiner,  Schweigger's  Jahrbuch,  iv.  91 ;  viii.  321. 

t  Ph.  Tr.  1786,  p.  273  ;  1792,  p.  48.  Essays,  Lond.  1796.  See  also  Dalton, 
Manch.  Mem.  v.  373.  Thomson,  Nich.  Jour.  iv.  529  ;  8vo,  i.  81.  Murray,  ibid, 
i.  165,  242.  Trail,  ibid.  xii.  133.  Despretz,  Comptes  Rendus,  vii.  933. 


488  LECTURE  LI. 

by  the  mixture  of  their  particles :  hence  a  fluid  heated  on  its  surface 
transmits  the  heat  very  slowly  downwards,  since  the  parts  which  are  first 
heated,  being  rendered  specifically  lighter,  retain  their  situation  above  the 
colder  and  heavier  parts  ;  while,  on  the  contrary,  any  cause  of  heat, 
applied  at  the  bottom  of  a  vessel,  very  soon  reduces  all  its  contents  to  a 
uniform  temperature.  It  appears  also,  from  some  late  experiments,  that 
the  immediate  transmission  of  heat  within  the  internal  parts  of  solids  is 
much  slower  than  has  commonly  been  supposed ;  and  it  has  been  found 
almost  impossible  to  keep  a  thermometer,  at  the  centre  of  a  large  and  solid 
globe  of  metal,  at  the  same  temperature  with  that  of  its  superficial  parts.* 

Besides  the  communication  of  heat  by  contact,  it  is  usually,  if  not 
always,  emitted  from  the  surfaces  of  bodies  in  the  form  of  radiant  heat, 
which  is  thrown  off  in  all  directions,  wherever  it  meets  no  obstacle  from  a 
substance  impervious  to  it,  and  is  propagated  nearly  in  the  same  manner 
as  light,  and  probably  with  the  same  velocity,  without  producing  any 
permanent  effect  on  the  temperature  of  the  medium  transmitting  it.  Thus, 
a  thermometer,  suspended  by  a  fine  thread  under  the  receiver  of  an  air 
pump,  or  in  the  Torricellian  vacuum,  will  continue  to  vary  its  temperature 
with  that  of  the  surrounding  bodies  :  and  in  this  case  the  whole  of  the  heat 
must  be  communicated  by  radiation.  Mr.  Leslie  has  discovered  that  the 
quantity  of  heat  thus  emitted  depends  not  only  on  the  temperature,  but 
also  on  the  nature  of  the  surface  concerned,  a  polished  surface  of  tin 
emitting  only  TW>  or  less  than  one  eighth  part  as  much,  as  the  same  surface 
blackened.  A  surface  of  tin  scraped  with  a  file  in  one  direction  has  its 
powers  of  radiation  more  than  doubled ;  but  by  crossing  the  scratches, 
they  are  reduced  nearly  to  their  original  state  ;  and  a  coating  of  isinglass, 
resin,  or  writing  paper,  or  a  glassy  surface  of  any  kind,  produces  an  effect 
nearly  approaching  to  that  of  black  paint.  This  radiation  from  a  heated 
surface,  like  that  of  light,  takes  place  in  almost  equal  degrees  in  every 
direction ;  and  its  magnitude  is  nearly  independent  of  the  nature  of  the 
fluid  in  contact  with  the  surface,  provided  however  that  it  be  an  elastic 
fluid  ;  for  water  does  not  seem  to  transmit  every  kind  of  radiant  heat  with 
freedom.  It  appears  that  the  radiant  heat  emitted  by  a  surface  of  glass,  or 
of  black  paint,  is  about  one  third  greater  than  that  which  is  at  the  same 
time  carried  off  by  the  atmospheric  air ;  but  that  the  radiation  from  a 
metallic  surface  is  only  one  sixth  of  that  which  the  air  receives.  Mr. 
Leslie  has  also  found  that  the  same  surfaces  which  emit  heat  the  most 
freely,  are  also  the  readiest  to  receive  it  from  the  radiation  of  other  bodies.t 

The  solar  heat  radiates  freely  through  air,  glass,  water,  ice,  and  many 
other  transparent  mediums,  without  producing  any  sensible  effect  on  their 
temperatures,  and  even  when  it  is  concentrated  by  the  effect  of  a  burning 
mirror,  it  scarcely  affects  the  air  through  which  it  passes,  and  other  trans- 
parent mediums  but  little.  But  the  heat  of  a  fire  warms  a  piece  of  common 

*  The  law  of  conduction  is  not  yet  correctly  defined.  See  Kelland,  on  the  pre- 
sent State  of  our  Knowledge  of  the  Laws  of  Conduction  of  Heat,  Rep.  of  Brit. 
Ass.  1841.  The  law  of  radiation  in  vacua  has  been  determined  by  MM.  Dulong  and 
Petit ;  their  experiments  will  be  found  in  the  Annales  de  Chimie,  vii.  225,  &c. 
Thomson's  Annals,  vol.  xiii. ;  or  in  the  art.  Heat,  in  the  Encyclop.  Metr. 

f  Inquiry  into  the  Nature  and  Propagation  of  Heat,  Lond.  1804. 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT.  489 

glass  very  rapidly,  and  its  further  progress  is  almost  entirely  interrupted 
by  the  glass,  although  probably  a  certain  portion  still  continues  to  accom- 
pany the  light  in  all  cases.  Hence  a  screen  of  glass  is  sometimes  practically 
convenient  for  allowing  us  the  sight  of  a  fire,  and  protecting  us  at  the  same 
time  from  its  too  great  heat.  Mr.  Lambert*  showed  that  culinary  heat 
was  much  more  strongly  reflected  by  mirrors  of  metal  than  of  glass,  although 
little  difference  was  observable  in  the  quantity  of  light,  and  he  very  justly 
attributed  this  difference  to  the  interception  of  a  part  of  the  heat  by  the  glass, 
which  operated  with  respect  to  it  like  an  opaque  substance,  although  it  trans- 
mitted the  light  with  freedom.  Opaque  substances  in  general  appear  to  be 
wholly  impervious  to  radiating  heat  of  all  kinds ;  but  Dr.  Herschelt  has  found 
that  dark  red  glass,  which  transmits  a  very  small  portion  of  light  only,  suf- 
fers some  kinds  of  radiant  heat  to  pass  through  it  with  very  little  interruption. 

In  other  respects,  radiating  heat  is  subject,  in  all  cases,  to  the  optical 
laws  which  govern  the  reflection  and  refraction  of  light.  Dr.  Hoffmann 
appears  to  have  been  the  first  that  collected  the  invisible  heat  of  a  stove 
into  a  focus  by  the  reflection  of  one  or  more  concave  mirrors.^  Buffon, 
Saussure,  Pictet,  and  Mr.  King,  made  afterwards  similar  experiments  on 
the  heat  of  a  plate  of  iron  and  of  a  vessel  of  boiling  water.  Mr.  Pictet,  as 
well  as  Hoffmann,  employed  two  mirrors  facing  each  other ;  and  by  means 
of  this  arrangement  the  experiment  may  be  performed  when  the  thermo- 
meter is  placed  at  a  considerable  distance  from  the  heated  body. 

The  temperature  of  the  air,  not  being  affected  by  the  radiation  of  heat, 
is  probably  in  all  respects  indifferent  to  its  emission  in  this  manner  ;  and 
as  the  rays  of  light  cross  each  other  freely  in  all  possible  directions,  so  it 
appears  that  heat  may  flow  in  different  directions  through  the  same  medium 
without  being  interrupted  ;  nor  does  there  seem  to  be  any  more  reason  that 
a  hot  body  should  cease  to  emit  heat  while  it  is  receiving  heat  from  another 
body,  than  that  a  luminous  body  should  cease  to  afford  light  when  another 
body  shines  on  it.  This  continual  interchange  of  heat,  constituting  in 
common  cases  a  kind  of  equilibrium  of  motion,  appears  to  have  been  first 
suggested  by  Mr.  Prevost,§  as  an  explanation  of  an  experiment  on  the 
reflection  of  cold,  revived  by  Mr.  Pictet,  but  originally  made  some  centuries 
before,  by  Plempius,  and  by  the  Academicians  del  Cimento.  A  thermo- 
meter, for  example,  must  be  supposed  to  retain  its  temperature  by  means 
of  the  continual  accession  of  radiant  heat  from  the  surrounding  bodies, 
supplying  the  place  of  that  which  is  continually  thrown  off  in  all  direc- 
tions towards  those  bodies.  Supposing  the  thermometer  to  be  placed  near 
the  focus  of  a  metallic  speculum,  not  much  less  than  a  hemisphere,  about 
one  half  of  the  heat,  which  the  thermometer  would  otherwise  have  received 
from  the  surrounding  bodies,  must  be  intercepted  by  the  mirror,  which, 
being  metallic,  emits  itself  but  little  radiant  heat,  but  reflects,  notwith- 
standing, an  equal  quantity  of  heat,  from  the  objects  on  the  opposite  side, 
so  that  the  temperature  of  the  thermometer  remains  unaltered.  But  all 
the  heat,  which  falls  on  the  thermometer  from  the  mirror,  must  have  passed 

•  *  Pyrometrie,  4to,  Berl.  1779.  See  Mariotte,  Hist,  et  M&n.  i.  223  ;  Traite  de  la 
Nat.  des  Couleurs,  1686. 

f  Ph.  Tr.  1800,  p.  255,  &c.  :  Wolfe,  Ph.  Tr.  1769,  p.  4. 

§  Sur  1'Equilibre  du  Feu,  Geneve,  1792.     Du  Calorique  Rayonnant,  Gen.  1809. 


490  LECTURE  LI. 

through  the  conjugate  or  corresponding  focus  ;  and  if  a  body  at  the  same 
temperature  be  placed  in  that  focus,  the  radiation  will  still  be  the  same  :  but 
if  a  substance  absolutely  cold  were  placed  there,  the  whole  of  the  heat  before 
reflected  by  the  mirror  would  be  intercepted,  that  is,  almost  half  of  that 
which  was  received  by  the  thermometer  from  the  surrounding  bodies ;  and 
if  a  piece  of  ice  be  put  in  the  conjugate  focus,  a  delicate  thermometer  will 
instantly  show  its  effect  in  depressing  the  temperature  ;  as  if  the  cold  were 
absolutely  reflected  in  the  same  manner  as  heat  or  light. 

Dr.  Herschel's  experiments  have  shown  that  radiant  heat  consists  of 
various  parts,  which  are  differently  refrangible,  and  that  in  general,  in- 
visible heat  is  less  refrangible  than  light.  This  discovery  must  be  allowed 
to  be  one  of  the  greatest  that  has  been  made  since  the  days  of  Newton, 
although  the  theories  of  some  speculative  philosophers  might  have  led  to  it 
a  few  years  earlier.  Dr.  Herschel  was  occupied  in  determining  the  pro- 
perties of  various  kinds  of  coloured  glass,  which  rendered  them  more  or  less 
fit  for  enabling  the  eye  to  view  the  sun  through  a  telescope  ;  and  for  this 
purpose  it  was  necessary  to  inquire  which  of  the  rays  would  furnish  the 
greatest  quantity  of  light,  without  subjecting  the  eye  to  the  inconvenience 
of  unnecessary  heat.  He  first  observed  that  the  heat  became  more  and 
more  considerable  as  the  thermometer  approached  the  extreme  red  rays 
in  the  prismatic  spectrum ;  and  pursuing  the  experiment,  he  found  not 
only  that  the  heat  continued  beyond  the  visible  spectrum,  but  that  it  was 
even  more  intense  when  the  thermometer  was  at  a  little  distance  without 
the  limits  of  the  spectrum,  than  in  any  point  within  it.*  (Plate  XXXIX. 
Fig.  546,  547.) 

Sir  Henry  Englefieldt  has  repeated  these  experiments  with  many  ad- 
ditional precautions,  and  Mr.  Davy  was  a  witness  of  their  perfect  accuracy : 
the  excess  of  heat  beyond  the  spectrum  was  even  considerable  enough  to 
be  ascertained  by  the  sense  of  warmth  occasioned  by  throwing  it  on  the 
hand.  The  skin  appears,  when  compared  with  a  thermometer,  to  have  its 
sensibility  more  adapted  to  the  perception  of  radiant  heat  than  to  that  of 
heat  imparted  by  contact,  perhaps  because  a  much  smaller  quantity  of 
heat  is  sufficient  to  raise  the  temperature  of  the  thin  cuticle  very  consider- 
ably, than  would  be  required  in  order  to  affect  any  thermometer  in  the 
same  degree. 

It  was  first  observed  in  Germany  by  Hitter,  and  soon  afterwards  hi 
England  by  Dr.  Wollaston,  that  the  muriate  of  silver  is  blackened  by 
invisible  rays,  which  extend  beyond  the  prismatic  spectrum,  on  the  violet 
side.  It  is  therefore  probable  that  these  black  or  invisible  rays,  the 
violet,  blue,  green,  perhaps  the  yellow,  and  the  red  rays  of  light,  and  the 
rays  of  invisible  heat,  constitute  seven  different  degrees  of  the  same  scale, 
distinguished  from  each  other  into  this  limited  number,  not  by  natural 

*  Herschel,  Ph.  Tr.  1800,  p.  255,  &c.  Leslie,  in  Nich.  Jour.  iv.  244,  called  in 
question  this  experiment.  Landriani  (Volta  Lettere  sull'  Aria  delle  Paludi,  1777, 
p.  136)  andRochon  (Recueil  des  Mem.  1785,  p.  348)  had  placed  the  point  of 
greatest  heat  near  the  yellow.  The  matter  was  completely  investigated  by  Seebeck, 
Abhand.  der  Akad.  Berlin,  1818-19,  p.  305,  and  he  found  that  the  difference  was 
due  to  the  substance  of  the  prism  :  with  water  the  point  of  greatest  heat  is  in  the 
yellow  ray  ;  with  crown  glass  in  the  red ;  and  with  flint-glass,  beyond  the  red. 

f  Jour,  of  the  Royal  Institution,  1802,  p.  202. 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT.  491 

divisions,  but  by  their  effects  on  our  senses  :  and  we  may  also  conclude 
that  there  is  some  similar  relation  between  heated  and  luminous  bodies  of 
different  kinds. 

The  effects  of  heat,  thus  originating,  and  thus  communicated,  may  be 
divided  into  those  which  are  temporary  only,  and  those  which  are  per- 
manent. The  permanent  effects  are  principally  confined  to  solids,  but  the 
temporary  effects  are  different  with  respect  to  substances  in  different  states 
of  aggregation,  and  they  also  frequently  comprehend  a  change  from  one 
of  these  states  to  another.  The  effect  of  heat  on  an  elastic  fluid  is  the 
simplest  of  all  these,  being  merely  an  expansion  of  about  one  five 
hundredth  of  its  bulk  for  each  degree  of  Fahrenheit  that  the  temperature 
is  raised  ;  or  an  equivalent  augmentation  of  the  elasticity  when  the  fluid 
is  confined  to  a  certain  space.  This  expansion  is  very  nearly  the  same  for 
all  gases  and  vapours,  amounting  to  -^  for  each  degree,  at  the  common 
temperature  of  56°  of  Fahrenheit,  but  at  higher  temperatures  it  is  less 
than  3-j-ff  of  the  bulk  of  the  gas,  and  at  lower  temperatures  somewhat 
more,  being  nearly  the  same  in  quantity  for  the  same  portion  of  the  fluid 
at  all  temperatures. 

When  an  elastic  fluid  is  contracted  by  cold  within  certain  limits,  deter- 
mined by  the  degree  of  pressure  to  which  it  is  exposed,  as  well  as  by  the 
nature  of  the  fluid,  its  particles  become  subjected  to  the  force  of  cohesion ; 
they  rush  still  nearer  together,  and  form  a  liquid.  Thus,  when  steam, 
under  the  common  atmospheric  pressure,  is  cooled  below  the  heat  of 
boiling  water,  it  is  instantly  condensed,  and  becomes  water :  but  with  a 
pressure  of  two  atmospheres,  it  wotild  be  condensed  at  a  temperature  36° 
higher,  and  with  the  pressure  of  half  our  atmosphere  only,  it  might 
be  cooled  without  condensation  83°  lower  than  the  common  temperature 
of  boiling  water.  And  similar  effects  take  place  in  vapours  of  other  kinds 
at  higher  or  lower  temperatures,  a  double  pressure  producing  in  all  cases 
an  equal  disposition  to  condensation,  with  a  depression  of  temperature  of 
between  20  and  40  degrees,  and  most  commonly  of  about  35°,  of  Fahren- 
heit. Thus,  the  vapour  of  spirit  of  wine  is  usually  condensed  at  175°  of 
Fahrenheit ;  but  with  a  double  pressure  it  is  condensed  at  a  temperature 
39°  higher  ;  and  with  the  pressure  of  half  an  atmosphere,  at  a  temperature 
35°  lower ;  and  the  vapour  of  ether,  which  is  commonly  condensed  at 
102°,  requires  a  temperature  38°  higher,  with  a  double  pressure,  or  as 
much  lower,  with  half  the  usual  pressure.  If  the  temperature  be  below 
the  freezing  point  of  the  liquid,  the  pressure  being  sufficiently  lessened,  the 
vapour  may  still  retain  its  elasticity,  but  a  further  reduction  of  temperature 
or  increase  of  pressure  will  convert  it  immediately  into  a  solid. 

The  expansion  of  liquids  by  the  effect  of  heat  is  much  less  uniform  and 
regular  than  that  of  elastic  fluids,  since  it  varies  considerably,  not  only  in 
different  liquids,  but  also  in  the  same  liquid  at  different  temperatures, 
being  in  general  greater  as  the  temperature  is  more  elevated,  and  sometimes 
almost  in  proportion  to  the  excess  of  the  temperature  above  a  certain  point, 
at  which  it  begins.  This  variation  appears  to  be  the  least  considerable  in 
mercury,  although  even  this  fluid  expands  a  little  more  rapidly  as  it 
becomes  more  heated  ;  but  the  expansion  is  always  very  nearly  one  ten 


492  LECTURE  LI. 

thousandth  for  each  degree :  that  of  water  is  equal  to  this  at  the  tem- 
perature 64°,  and  is  greater  or  less  nearly  in  proportion,  to  the  distance 
from  39°,  where  it  begins,  but  in  high  temperatures  it  varies  less,  since  it 
is  not  quite  four  times  as  great  at  the  heat  of  boiling  water.  The  expan- 
sion of  spirit  of  wine  at  70°  is  six  times  as  great  as  that  of  mercury  :  its 
utmost  variation  is  much  less  than  that  of  water,  although  it  is  at  least 
twice  as  great  in  some  parts  of  the  scale  as  in  others. 

It  has  already  been  observed  that  an  elevation  of  temperature  consider- 
ably diminishes  the  powers  of  cohesion  and  of  repulsion  in  solid  bodies : 
the  same  is  also  true  of  liquids  ;  for  the  height  to  which  a  liquid  rises  in  a 
capillary  tube  is  diminished  somewhat  less  than  -njV^  for  each  degree  of 
Fahrenheit  that  the  temperature  is  raised,  the  force  of  superficial  cohesion 
being  diminished  both  by  the  diminution  of  the  immediate  actions  of  the 
particles,  and  by  that  of  the  distances  to  which  they  extend. 

When  the  temperature  of  a  liquid  is  so  much  elevated  as  to  become 
equal  to  that  of  its  vapour  in  a  state  capable  of  sustaining  the  atmo- 
spherical pressure,  or  any  other  pressure  which  may  be  substituted  for  it, 
a  certain  portion  of  the  liquid  is  converted  into  vapour,  and  the  heat  being 
generally  applied  at  the  bottom  of  the  vessel,  the  vapour  rises  up  in 
bubbles,  and  the  effect  is  called  boiling.  The  whole  liquid  is  not  converted 
at  once  into  vapour,  because  a  certain  quantity  of  heat  appears  to  be 
consumed  by  the  change,  and  a  constant  supply  of  heat  is  necessary,  in 
order  that  the  operation  may  be  continued. 

It  is  not,  however,  only  at  the  boiling  point  that  a  fluid  begins  to  be 
converted  into  vapour  :  the  pressure  of  the  atmosphere  is  not  sufficient 
wholly  to  prevent  the  detachment  of  a  certain  quantity  of  vapour  from  its 
surface,  at  a  temperature  which  is  incapable  of  supporting  it  separately  in 
the  form  of  steam  in  the  open  air,  and  it  may  be  thus  suspended,  when 
mixed  either  with  common  air,  or  with  any  other  elastic  fluid,  at  the 
ordinary  temperature  of  the  atmosphere.  And  it  appears  that  the 
quantity,  which  is  thus  suspended,  bears  very  nearly  some  constant  pro- 
portion to  the  density  of  which  the  steam  is  capable  at  the  given  tem- 
perature in  a  separate  state,  the  interposition  of  the  air  either  not  affecting 
the  distance  at  which  the  cohesion  would  take  place,  or  altering  it  equally 
in  all  cases.  It  seems  to  be  most  probable  that  the  density  of  vapour, 
suspended  in  this  manner  in  the  atmosphere,  is  always  about  twice  as 
great,  or  at  least  half  as  great  again,  as  that  of  steam  existing  inde- 
pendently at  the  same  temperature.  There  is,  perhaps,  no  liquid  absolutely 
free  from  a  disposition  to  evaporate  :  even  mercury  rises  in  the  vacuum  of 
the  barometer,  and  lines  the  cavity  with  small  globules ;  and  it  is  said  that 
the  effect  of  light  is  favourable  to  this  slow  evaporation.  At  whatever 
temperature  evaporation  takes  place  it  is  always  accompanied  by  the 
production  of  cold ;  hence  it  is  usual  in  warm  climates,  to  employ  various 
methods  of  promoting  evaporation,  in  order  to  lower  the  temperature 
of  the  air,  to  cool  liquids  for  drinking,  or  even  to  procure  ice  for  domestic 
uses. 

It  appears  that  all  aqueous  fluids  are  contracted  by  cold,  until  we  arrive 
at  a  certain  point,  which  is  generally  about  7  or  8  degrees  higher  than  their 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT.  493 

freezing  point  ;*  they  then  expand  again  almost  in  an  equal  degree  as  they 
are  still  more  cooled  ;  and  provided  that  they  be  free  from  agitation,  they 
may  remain  liquid  at  a  temperature  considerably  below  the  point  at  which 
they  usually  freeze,  and  at  which  their  ice  always  melts.  Water  may  be 
cooled  in  this  manner  to  about  10°  of  Fahrenheit,  and  if  it  be  then  agitated, 
or  especially  if  a  small  particle  of  ice  or  snow  be  thrown  into  it,  a  certain 
part  of  it  will  instantly  congeal,  and  its  temperature  will  be  raised  at  once 
to  32°,  in  consequence  of  the  heat  which  is  always  produced  or  extricated 
in  the  act  of  freezing,  f  In  most  cases,  although  not  in  all,  the  solid 
occupies  more  space  than  the  fluid  :  thus,  it  is  probable  that  ice,  when  per- 
fectly free  from  air  bubbles,  is  at  least  one  16th  lighter  than  water  at  the 
same  temperature.  A  saturated  solution  of  Glauber's  salts,  or  sulfate  of 
soda,  in  hot  water,  may  be  cooled  slowly  to  the  temperature  of  the  atmo- 
sphere, when  the  pressure  of  the  air  is  excluded,  and  may  be  made  to  crys- 
tallize by  admitting  it  suddenly,  the  liquor  becoming  at  the  same  time 
warm  in  consequence  of  the  heat  which  is  extricated ;  and  there  is  no 
doubt  but  that  the  congelation  of  water,  and  perhaps  of  all  other  sub- 
stances, is  a  crystallization  of  the  same  kind. 

The  expansions  of  solid  bodies  appear  to  be  more  regular  than  those  of 
liquids  or  even  of  elastic  fluids ;  they  vary  little  at  any  temperature, 
although  it  is  said  that  they  do  not  always  take  place  in  their  full  extent 
at  the  instant  that  the  substance  has  become  heated,  and  that  a  blow,  or 
the  agitation  produced  when  they  are  made  to  sound  by  the  friction  of  the 
bow  of  a  violin,  may  sometimes  be  observed  to  cause  them  to  assume  the 
state  of  equilibrium  with  greater  rapidity.  Brass  expands  about  one  hun- 
dred thousandth  of  its  length  for  each  degree  of  Fahrenheit,  copper  and 
gold  a  little  less  ;  silver  somewhat  more  ;  glass  and  platina  less  than  half 
as  much  ;  iron  and  steel  about  two  thirds  as  much  ;  tin  one  third  more,  and 
lead  and  zinc  about  half  as  much  more.  Wood  and  earthenware  are  the 
least  expansible  of  all  known  solids.  The  diminution  of  the  elasticity  of 
iron  and  steel  by  the  elevation  of  their  temperature  amounts  to  about  5  0'0  0 
of  the  whole  for  each  degree  ;  but  probably  various  substances  are  variously 
affected  in  this  respect. 

The  liquefaction  of  solids,  and  their  conversion  into  fluids  by  the  opera- 
tion of  heat,  is  liable  to  fewer  irregularities  than  any  other  of  its  effects  ; 
the  change  depending  only  on  the  temperature,  and  not  being  accelerated 
or  retarded  by  any  accidental  circumstances.  When  the  temperature  is 
too  low,  or  the  pressure  too  small,  for  the  existence  of  the  substance  in  a 
liquid  form,  it  may  still  be  converted  into  vapour,  either  mixed  with  air, 
or  in  a  separate  state ;  thus  ice  loses  weight  when  it  is  exposed  to  a  dry 
frosty  wind ;  and  camphor,  benzoin,  and  ammonia  are  sublimed  by  heat 
without  being  melted,  although  it  is  probable  that  a  pressure  sufficiently 
strong  might  enable  them  to  exist  as  liquids  in  elevated  temperatures.  In 
all  changes  from  solidity  to  liquidity  or  to  elastic  fluidity,  a  certain  quan- 

*  On  the  point  of  maximum  density  of  water,  see  "Waller's  Trans,  of  the  Floren- 
tine Exp.  p.  77.  Blagden  on  the  Congelation  of  Aqueous  Solutions,  Ph.  Tr.  1788, 
p.  277,  Hope,  Ed.  Tr.  v.  379.  Some  substances  contract  in  freezing  :  see  Despretz, 
in  Pogg.  Ann.  xli.  498. 

f  See  Blagden,  Ph.  Tr.  1788,  p.  125  ;  Walker,  ibid.  1788,  p.  395. 


494  LECTURE  LI. 

tity  of  heat  disappears,  except  some  cases  in  which  a  chemical  decomposi- 
tion has  accompanied  the  change  ;  thus,  in  the  detonation  of  gunpowder,  a 
large  quantity  of  gas  acquires  the  state  of  elasticity,  but  at  the  same  time  a 
great  degree  of  heat  is  produced. 

The  effects  of  the  expansion  of  bodies  by  heat,  and  of  their  contraction 
by  cold,  are  observed  in  the  frequent  accidents  which  happen  to  glass  and 
to  porcelain  from  a  sudden  change  of  temperature.  Glass  conducts  heat  so 
slowly,  that  one  side  of  a  vessel  may  become  much  heated,  and  conse- 
quently expanded,  while  the  other  remains  much  colder,  and  if  the  vessel 
cannot  readily  accommodate  its  form  to  this  change  of  proportions,  it  will 
most  commonly  crack,  the  colder  parts  dividing,  in  consequence  of  their 
being  too  much  stretched  by  the  adjoining  hotter  parts.  Hence  the  thinner 
the  glass  is,  the  less  liable  it  is  to  crack  from  any  sudden  expansion  ;  and 
if  it  be  very  thick,  however  simple  its  form  may  be,  it  will  still  crack  ; 
for  no  flexure,  which  it  can  assume,  can  be  sufficient  for  the  equilibrium 
of  the  external  parts  without  being  too  great  for  that  of  the  parts  near  the 
middle. 

When  glass  in  fusion  is  very  suddenly  cooled,  its  external  parts  become 
solid  first,  and  determine  the  magnitude  of  the  whole  piece  ;  while  it  still 
remains  fluid  within.  The  internal  part,  as  it  cools,  is  disposed  to  contract 
still  further,  but  its  contraction  is  prevented  by  the  resistance  of  the 
external  parts,  which  form  an  arch  or  vault  round  it,  so  that  the  whole  is 
left  in  a  state  of  constraint ;  and  as  soon  as  the  equilibrium  is  disturbed  in 
any  one  part,  the  whole  aggregate  is  destroyed.  Hence  it  becomes  necessary 
to  anneal  all  glass,  by  placing  it  in  an  oven,  where  it  is  left  to  cool  slowly  ; 
for,  without  this  precaution,  a  very  slight  cause  would  destroy  it.  The 
Bologna  jars,  sometimes  called  proofs,  are  small  thick  vessels,  made  for 
the  purpose  of  exhibiting  this  effect ;  they  are  usually  destroyed  by  the 
impulse  of  a  small  and  sharp  body,  for  instance  a  single  grain  of  sand, 
dropped  into  them  ;  and  a  small  body  appears  to  be  often  more  effectual 
than  a  larger  one  ;  perhaps  because  the  larger  one  is  more  liable  to  strike 
the  glass  with  an  obtuse  part  of  its  surface.  In  the  same  manner  the 
glass  drops,  sometimes  called  Prince  Rupert's  drops,  which  are  formed  by 
suffering  a  portion  of  green  glass  in  fusion  to  fall  into  water,  remain  in 
equilibrium  while  they  are  entire  ;  but  when  the  small  projecting  part  is 
broken  off,  the  whole  rushes  together  with  great  force,  and  rebounding  by 
its  elasticity,  exhibits  the  effect  of  an  explosion.  The  ends  of  these  drops 
may,  sometimes,  but  not  always,  be  gradually  ground  off  without  destroy- 
ing them,  so  that  the  concussion  produced  by  breaking  the  drop  seems  to 
be  concerned  in  the  destruction  of  the  equilibrium.* 

The  tempering  of  metals  appears  to  bear  a  considerable  analogy  to  the 
annealing  of  glass  ;  when  they  are  made  red  hot,  and  suddenly  cooled,  they 
acquire  a  great  degree  of  hardness,  which  renders  them  proper  for  some 
purposes,  while  the  brittleness  which  accompanies  it  would  be  inconvenient 
for  others.  By  heating  them  again  to  a  more  moderate  temperature,  and 

*  Hooke's  Microg.  Bruni,  Ph.  Tr.  1745,  p.  272.  Watson,  ibid.  1745,  p.  505. 
Lecat,  ibid.  1749,  p.  175.  Hanow,  Versuche  mit  den  Spring-Kolbchen,  4to,  Danz. 
1751. 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT.  495 

suffering  them  to  cool  more  gradually,  they  are  rendered  softer  and  more 
flexible,  and  the  more  as  the  heat  which  is  thus  applied  is  the  more  consi- 
derable. [The  oxid]  which  forms  itself  on  the  surface  of  polished  iron  or 
steel,  serves  as  a  test  of  the  degree  of  heat  which  is  applied  to  it,  the  yellow- 
ish colour  which  it  assumes  indicating  the  first  stage  of  tempering,  the 
violet  the  second,  and  the  blue  the  last ;  and  if  the  heat  be  raised  till  the 
surface  becomes  grey,  the  steel  will  be  rendered  perfectly  soft.  The  density 
of  metals  is  also  a  little  increased  by  tempering  them,  probably  for  the  same 
reason  as  water  is  more  dense  than  ice.  In  what  manner  the  unequal 
distribution  of  the  mutual  actions  of  the  particles  of  bodies  contributes  to 
increase  their  hardness,  cannot  be  very  positively  ascertained,  although 
some  conjectures  might  be  formed  which  would,  perhaps,  be  in  some  mea- 
sure explanatory  of  the  facts  :  but  it  is  safer,  in  the  present  state  of  our 
knowledge,  to  be  contented  with  tracing  the  analogy  between  these  effects 
in  substances  of  different  kinds,  and  under  different  circumstances,  without 
attempting  to  understand  completely  the  immediate  operation  of  the  forces 
which  are  concerned. 


LECT.  LI.— ADDITIONAL  AUTHORITIES. 

Treatises  on  Heat.—Royle,  De  Frigore,  4to,  Lond.  1683.  Petit  sur  le  Froid  et 
le  Chaud,  1671.  Casatus,  De  Igne,Leipz.  1688.  Muller,  De  Frigore,  4to,  Jena, 
1698.  Winckler,  De  Frigore,  4to,  Leipz.  1737.  Chatelet,  Diss.  sur  le  Feu,  1744. 
Bikker,  De  Igne,  4to,  Utr.  1756.  Hillary  on  Fire,  Lond.  1760.  Belgrado,  Del 
Calore,  Parma,  1764.  Herbert,  De  Igne,  Vienn.  1773.  Marat,  Decouvertes  sur  le 
Feu,  1779.  Recherches  sur  le  Feu,  1780.  Magellan  sur  la  NouveUe  Theorie  du 
Feu,  4to,  Lond.  1780.  Scheele,  Traite  de  1'Air  et  du  Feu  (Jr.),  1781.  Hopson  on 
Fire,  1781.  Baader,  Vom  Warmestoff,  Vienn.  1786.  Carradori,  Teoriadel  Calore, 
2  vols.  Flor.  1787.  Berlinghieri,  4to,  Pisa,  1787.  Marne,  Ueber  Feuer,  1787. 
Weber,  do.  Landshut,  1788.  La  Serre,  Theorie  du  Feu,  Avignon,  1788.  Seguin 
sur  les  Phenomenes  du  Calorique.  De  Luc,  Lettres  Physiques,  5  vols.  Leseme- 
lier  sur  1'Air  et  le  Feu,  2  vols.  Paris,  1788.  Lorenz  Untersuchung  des  Feuers, 
Kopen.  1789.  Mayer,  Ueber  die  Gesetze  des  Warmestoffs,  Erlang,  1791.  Lampa- 
dius,  Ueber  Electr.  und  Warme,  Berl.  1793.  Voigt,  Theorie  des  Feuers,  Jena, 
1793.  Lichtenberg  in  Erxleben's  Naturlehre,  1794  ;  Gottling,  Weimar,  1794. 
Harrington  on  Fire,  1796.  Maugin,  Theorie  du  Feu,  1800.  Berthollet,  Essai  de 
Chimie  Statique,  1803.  Paulet,  Diss.  sur  le  Feu,  Lausanne,  1807.  P.  Prevost, 
Traite  de  Calorique  Rayonnante,  1809.  Oersted,  Ansicht  der  Chemischen  Natur- 
gesetze,  Berl.  1812.  Pasley's  Treatise  on  Heat,  1820.  Paulsen,  De  Caloris 
Theoria,  Gott.  1821.  Fourier,  Theorie  Analytique  de  la  Chaleur,  4to,  1822. 
Nobili,  Nuovi  Trattati  sopra  il  Calorico,  &c.  Modena,  1822.  Bournou,  Obs.  et 
Reflex,  sur  la  Calorique,  Paris,  1824.  Library  of  Useful  Knowledge,  Cab.  Cyc.  &c. 
Peclet,  Traite  de  la  Chaleur  et  de  ses  Applications,  2  vols.  Paris,  1828.  Quetelet, 
Physique  Populaire  de  la  Chaleur,  12mo,  Bruxelles,  1832,  Bischoff,  Warmelehre, 
1837.  Kelland,  Theory  of  Heat,  Camb.  1837.— Thomson  on  Heat,  1840.  Gehler's 
Physikalisches  Worterbuch,  1841  ;  and  Gmelin's  Handbuch,  art.  Warme,  1843,  are 
the  most  complete  treatises  on  the  subject. 

Radiation. — Newton,  Ph.  Tr.  1701,  p.  827;  Opusc.  ii.  422.  Martine's  Essays, 
1740,  p.  236.  Rickmann,  Nov.  Com.  Petr.  i.  174,  195,  U.  172.  Lambert,  Act. 
Helv.  ii.  172.  Erxleben,  Nov.  Com.  Gott.  1777,  p.  74,  and  the  authorities  given  at 
p.  1636.  Rumford,  Ph.  Tr.  1804,  p.  90.  Maycock,  Nich.  Jour.  1810,  vol.  xxvi. 
Delaroche,  Jour,  de  Phy.  Ixxv.  201.  Berard,  Ann.  de  Ch.  Ixxxv.  309.  Powell, 
Ph.  Tr.  1825,  and  Report  of  Br.  Ass.  vols.  i.  and  ix. 

Conducting  Powers. — Ingenhousz,  Nouvelles  Experiences,  Par.  1789.  Humboldt, 
Jour,  de  Phy.  xliii.  304.  Meyer,  Gren's  Jour.  iv.  22.  Biot,  Traite  de  Phy.  vol.  iv. 
Despretz,  Ann.  de  Ch.  xix.  97.  Delarive,  ibid.  xl.  91. 


496 


LECTURE   LII. 


ON  THE  MEASURES  AND  THE  NATURE  OF  HEAT. 

THE  principal  particulars  concerning  the  origin,  the  progress,  and  the 
effects  of  heat,  having  been  noticed  in  the  last  lecture,  we  now  proceed  to 
examine  the  most  usual  modes  of  measuring  its  degrees  and  its  quantity, 
and  to  inquire  into  the  most  probable  opinions  respecting  its  intimate 
nature  and  its  immediate  operation. 

The  expansion  of  solids  is  measured  by  a  pyrometer,  which  is  calculated 
for  rendering  the  smallest  change  of  dimensions  perceptible  either  by 
mechanical  or  by  optical  means.  The  first  of  these  methods  was  adopted 
by  those  who  first  investigated  these  effects  ;  a  bar  of  metal  being  placed 
in  a  vessel  of  water  or  of  oil,  which  was  heated  by  lamps,  while  the  extre- 
mities of  the  bar  were  in  contact  with  a  fixed  point  on  one  side,  and  on  the 
other  with  a  series  of  levers,  which  multiplied  the  expansions  so  as  to 
render  them  easily  observable  by  means  of  the  end  of  the  last  lever,  serving 
as  an  index.  But  it  is  obvious  that  the  expansion  of  the  fixed  part  of  the 
instrument,  and  the  irregular  changes  of  temperature  of  the  levers  them- 
selves, must  very  much  interfere  with  the  accuracy  of  such  an  instrument. 
A  much  more  correct  mode  of  determination  is  to  employ  two  microscopes, 
fixed  to  an  apparatus,  which  is  always  kept,  by  means  of  ice,  at  a  constant 
temperature,  and  to  observe  with  a  micrometer  the  change  of  place  of 
either  end  of  the  heated  bar. 

For  such  purposes,  the  degrees  of  heat  may  be  ascertained  by  the 
natural  measures  of  the  freezing  and  boiling  points  of  certain  liquids,  and 
of  water  in  particular  ;  but  for  subdividing  the  intervals  between  these 
points,  other  means  must  be  employed.  The  most  natural  mode  of  deter- 
mining the  intermediate  degrees  of  heat,  which  must  be  considered  as  the 
standard  for  the  comparison  of  all  others,  is  too  laborious  and  complicated 
for  common  use.  If  we  mix  together  equal  quantities  of  the  same  liquid 
at  two  different  temperatures,  they  will  obviously  acquire  an  intermediate 
temperature,  which  is  the  natural  mean  between  the  separate  temperatures, 
provided  that  no  heat  be  lost  or  gained  during  the  process  ;  and  provided 
that  no  irregularity  be  produced  from  the  approach  of  the  liquid  to  a  state 
of  congelation,  the  existence  of  which  might  be  detected  by  a  comparison  of 
experiments  on  various  liquids  at  the  same  temperatures.  By  repeating 
the  operation,  we  may  subdivide  the  intervals  as  often  as  we  please,  or  we 
may  mix  the  liquids  in  any  other  proportion,  so  as  to  obtain  at  once  any 
other  point  of  the  scale,  which  may  afterwards  be  identified  by  a  thermo- 
meter of  any  description. 

There  is  also  another  method  of  comparing  the  divisions  of  a  thermometer 
with  those  of  the  natural  scale,  but  it  is  not  wholly  free  from  objections  ; 
the  instrument  being  placed  in  a  cone  of  the  sun's  rays,  made  to  converge 
by  means  of  a  lens  or  mirror,  the  quantity  of  heat  falling  on  it  must  be 


THE  MEASURES  AND  THE  NATURE  OF  HEAT.         497 

nearly  in  the  inverse  proportion  of  the  square  of  its  distance  from  the 
focus ;  and  the  elevation  of  a  common  thermometer  appears  to  be  nearly 
proportional  to  the  heat  which  is  thrown  on  it  in  this  manner. 

The  expansion  of  solids  probably  approaches  the  nearest  to  the  steps  of 
the  natural  scale,  although  even  in  this  there  seems  to  be  some  inequality  ; 
but  that  of  mercury  is  scarcely  less  regular,  and  a  portion  of  mercury 
inclosed  in  a  bulb  of  glass,  having  a  fine  tube  connected  with  it,  forms  a 
thermometer  the  most  convenient,  and  most  probably  the  most  accurate,  of 
any,  for  common  use  ;  the  degrees  corresponding  very  nearly  with  those 
of  the  natural  scale,  although,  according  to  the  most  accurate  experiments, 
they  appear  to  indicate,  towards  the  middle  of  the  common  scale  of 
Fahrenheit,  a  temperature  2  or  3  degrees  too  low.  There  is  an  inequality 
of  the  same  kind,  but  still  greater,  in  the  degrees  of  the  spirit  thermometer  ; 
and  this  instrument  has  also  the  disadvantage  of  being  liable  to  burst  in  a 
heat  below  that  of  boiling  water  ;  although  it  is  well -calculated  for  the  mea- 
surement of  very  low  temperatures,  since  pure  alcohol  has  never  yet  been 
frozen,  while  mercury  has  been  reduced  to  a  solid  by  the  cold  of  Siberia 
and  of  Hudson's  Bay  ;  but  both  mercury  and  linseed  oil  support  a  heat  of 
between  5  and  600°  without  ebullition.  For  higher  temperatures  than 
this,  a  thermometer  has  been  made  of  semitransparent  porcelain,  containing 
a  fusible  metal,  which  may  be  compared  with  the  upper  part  of  the  mercu- 
rial scale,  and  then  continued  further ;  and  the  expansion  of  such  of  the 
metals,  as  are  difficult  of  fusion,  affords  another  mode  of  determining  the 
highest  degrees  of  heat.  Mr.  Wedgwood's  thermometer*  derives  its  proper- 
ties from  the  contraction  of  a  small  brick  of  prepared  clay,  which  contracts 
the  more,  as  the  heat  to  which  it  is  exposed  is  higher :  it  may  be  extremely 
useful  for  identifying  the  degree  of  heat  which  is  required  for  a  particular 
purpose  :  but  for  the  comparison  of  temperatures  by  an  extension  of  the 
numerical  scale,  we  have  not  sufficient  evidence  of  its  accuracy  to  allow  us 
to  depend  on  its  indications  ;  and  it  is  scarcely  credible  that  the  operation 
of  furnaces,  of  any  kind,  can  produce  a  heat  of  so  many  thousand  degrees 
of  a  natural  scale,  as  Mr.  Wedgwood's  experiments  have  led  him  to  sup- 
pose ;  nor  is  the  supposition  consistent  with  the  observations  of  other 
philosophers. 

Mercurial  thermometers  are  in  general  hermetically  sealed,  the  tube 
being  perfectly  closed  at  the  end,  in  order  to  exclude  dust,  and  to  prevent 
the  dissipation  of  the  mercury.  When  a  standard  thermometer  is  to  be 
adjusted,  its  freezing  point  is  readily  fixed  by  immersing  it  wholly  in 
melting  snow  or  pounded  ice  ;  but  for  the  boiling  point,  some  further  pre- 
cautions are  required  ;  the  easiest  method  appears  to  be,  to  immerse  its  bulb 
in  an  open  vessel  of  boiling  water,  to  cover  it  with  several  folds  of  cloth, 
and  to  pour  hot  water  continually  over  it ;  for  if  it  were  immersed  to  a 
considerable  depth,  the  pressure  would  raise  the  temperature  of  the  boiling 
point,  and  if  it  were  not  covered,  the  mercury  in  the  tube  would  be  too 
cold.  Attention  must  also  be  paid  to  the  state  of  the  barometer  ;  it  must 
either  stand  at  80  inches,  or  the  place  of  the  boiling  point  must  be  raised, 
when  the  barometer  is  lower  than  30,  and  lowered  when  it  is  higher  ;  the 
*  Ph.  Tr.  1782,  p.  305  ;  1784,  p.  358  ;  1786,  p.  390. 
2  K 


498  LECTURE  LII. 

difference  of  nine  tenths  of  an  inch  either  way  requiring  an  alteration 
amounting  to  T^-  of  the  interval  between  freezing  and  boiling.  This 
interval  is  subdivided,  in  Fahrenheit's  thermometer,  into  180  degrees  ;  in 
Reaumur's,  into  80,  and  in  the  centigrade  thermometer  of  Celsius  and  of  the 
French,  into  100  ;  and  in  making  the  subdivision,  care  must  be  taken  to 
examine  the  equality  of  the  bore  throughout,  by  observing  the  length  occu- 
pied by  a  detached  portion  of  mercury,  and  to  allow  for  any  irregularities 
which  may  have  been  thus  detected.  The  scales  of  Reaumur  and  of  Celsius 
begin  at  the  freezing  point  of  water  ;  but  in  that  of  Fahrenheit  the  freezing 
point  stands  at  32°,  the  scale  beginning  from  the  cold  produced  by  a 
freezing  mixture,  which  was  supposed  by  Fahrenheit  to  be  the  greatest 
that  would  ever  occur  in  nature. 

The  expansion,  which  is  observed  in  a  mercurial  thermometer,  is  in 
reality  only  the  difference  of  the  expansions  of  mercury  and  of  glass  ;  but 
this  circumstance  produces  no  difference  in  the  accuracy  of  the  results.  The 
separate  effects  of  the  expansion  of  glass  are,  however,  sometimes  per- 
ceptible ;  thus,  when  a  thermometer  is  plunged  suddenly  into  hot  water, 
the  glass,  being  first  heated,  expands  more  rapidly  than  the  mercury,  and, 
for  a  moment,  the  thermometer  falls.  This  circumstance  would  perhaps 
be  still  more  observable  in  a  thermometer  of  spirit  or  of  water ;  for  an 
equal  bulk  of  these  liquids  would  be  much  longer  in  acquiring  the  tempe- 
rature of  the  surrounding  medium  than  a  mercurial  thermometer. 

The  expansion  of  elastic  fluids  affords  in  some  cases  a  test  of  heat,  which 
is  very  convenient  from  its  great  delicacy,  and  because  a  very  small  quan- 
tity of  heat  is  sufficient  to  raise  their  temperature  very  considerably.  The 
thermometer  first  invented  by  Drebel  was  an  air  thermometer  ;*  but  instru- 
ments of  this  kind,  when  they  are  subject  to  the  variations  of  the  pressure 
of  the  atmosphere  as  well  as  to  those  of  its  temperature,  are  properly  called 
manometers,  and  require,  for  enabling  us  to  employ  them  as  thermometers, 
a  comparison  with  the  barometer  ;  while  on  the  other  hand,  they  may  be 
used  as  barometers,  if  the  temperature  be  otherwise  ascertained.  They  are 
however,  very  useful  even  without  this  comparison,  in  delicate  experiments 
of  short  duration,  since  the  changes  of  the  barometer  are  seldom  very 
rapid  ;  and  they  may  also  be  wholly  freed  from  the  effects  of  the  pressure 
of  the  atmosphere,  in  various  ways.  Bernoulli's  method  t  consists  in  closing 
the  bulb  of  a  common  barometer,  so  as  to  leave  the  column  of  mercury  in 
equilibrium  with  the  air  contained  in  the  bulb  at  its  actual  temperature, 
and  capable  of  indicating,  by  the  changes  of  its  height  and  of  its  pressure, 
any  subsequent  changes  in  the  temperature  of  the  air,  which  must  affect 
both  its  bulk  and  its  elasticity.  Mr.  Leslie's  photometer,;}:  or  differential 
thermometer,  has  some  advantages  over  this  instrument,  but  it  can  only  be 
employed  where  the  changes  of  temperature  can  be  confined  to  a  part  only 

*  The  invention  is  claimed  for  Drebel,  by  Boerhaave  (Elem.  Chimise,  2  vols.  4to, 
Lugd.  1732,  i.  152),  and  by  Musschenbroek  (Elem.  Phil.  Nat.  §  780)  ;  whereas 
Santorio  claims  it  as  his  own  (Comm.  in  Avicennam,  1626),  and  his  claim  is  sup- 
ported by  others.  See  Martine's  Essays,  Edin.  1787,  and  Dr.  Traill's  Thermome- 
ter and  Pyrometer,  Lib.  of  Useful  Knowledge. 

t  Segner,  De  ^Equandis  Thermometris  Aeris,  4to,  Gott.  1739. 

t  On  Heat ;  and  Nich.  Jour.  iii.  461,  518. 


THE  MEASURES  AND  THE  NATURE  OF  HEAT.  499 

of  the  instrument.  The  elasticity  of  the  air  contained  in  the  bulb  is  here 
counteracted,  not  by  the  pressure  of  a  column  of  mercury,  but  by  the  elas- 
ticity of  another  portion  of  air  in  a  second  bulb,  which  is  not  to  be  exposed 
to  the  heat  or  cold  that  is  to  be  examined  :  and  the  difference  between  the 
temperatures  of  the  two  bulbs  is  indicated  by  the  place  of  a  drop  of  a  liquid, 
moving  freely  in  the  tube  which  joins  them.  (Plate  XXXIX.  Fig.  548... 
550.) 

The  degree  of  heat,  as  ascertained  by  a  thermometer,  is  only  to  be  con- 
sidered as  a  relation  to  the  surrounding  bodies,  in  virtue  of  which  a  body 
supports  the  equilibrium  of  temperature  when  it  is  in  the  neighbourhood  of 
bodies  equally  heated :  thus,  if  a  thermometer  stands  at  60°,  both  in  a 
vessel  of  water,  and  in  another  of  mercury,  we  may  infer  that  the  water 
and  the  mercury  may  be  mixed  without  any  change  of  their  temperature  : 
but  the  absolute  quantity  of  heat,  contained  in  equal  weights,  or  in  equal 
bulks,  of  any  two  bodies  at  the  same  temperature,  is  by  no  means  the  same. 
Thus,  in  order  to  raise  the  temperature  of  a  pound  of  wrater  from  50°  to 
60°,  we  need  only  to  add  to  it  another  pound  of  water  at  70°,  which  while 
it  loses  10°  of  its  own  heat,  will  communicate  10°  to  the  first  pound  ;  but 
the  temperature  of  a  pound  of  mercury  at  50°  may  be  raised  10°,  by  means 
of  the  heat  imparted  to  it,  by  mixing  with  it  one  thirtieth  part  of  a  pound 
of  water,  at  the  same  temperature  of  70°.  Hence  we  derive  the  idea  of  the 
capacities  of  different  bodies  for  heat,  which  was  first  suggested  by  Dr. 
Irvine,*  the  capacity  of  mercury  being  only  about  one  thirtieth  part  as 
great  as  that  of  water.  And  by  similar  experiments  it  has  been  ascer- 
tained, that  the  capacity  of  iron  is  one  eighth  of  that  of  water,  the  capacity 
of  silver  one  twelfth,  and  that  of  lead  one  twenty-fourth.  But  for  equal 
bulks  of  these  different  substances,  the  disproportion  is  not  quite  so  great : 
thus,  copper  contains  nearly  the  same  quantity  of  heat  in  a  given  bulk  as 
water ;  iron,  brass,  and  gold,  a  little  less,  silver  £  as  much,  but  lead  and 
glass  each  about  one  half  only. 

It  is  obvious  that  if  the  capacity  of  a  body  for  heat,  in  this  sense  of  the 
word,  were  suddenly  changed,  it  would  immediately  become  hotter  or 
colder,  according  to  the  nature  of  the  change,  a  diminution  of  the  capacity 
producing  heat,  and  an  augmentation  cold.  Such  a  change  of  capacity  is 
often  a  convenient  mode  of  representation  for  some  of  the  sources  of  heat 
and  cold  :  thus,  when  heat  is  produced  by  the  condensation  of  a  vapour, 
or  by  the  congelation  of  a  liquid,  we  may  imagine  that  the  capacity  of  the 
substance  is  diminished  ;  and  that  it  overflows,  as  a  vessel  would  do  if  its 
dimensions  were  contracted.  It  appears  also  from  direct  experiments,  in 
some  such  cases,  that  the  capacity  of  the  same  substance  is  actually  greater 
in  a  liquid  than  in  a  solid  state,  and  in  a  state  of  vapour,  than  in  either  ; 
and  both  Dr.  Irvine  and  Dr.  Crawford  t  have  attempted  to  deduce,  from  a 
comparison  of  the  proportional  capacities  of  water  and  ice,  with  the  quan- 
tity of  heat  extricated  during  congelation,  a  measure  of  the  whole  heat 
which  is  contained  in  these  substances,  and  an  estimation  of  the  place 
which  the  absolute  privation  of  heat,  or  the  natural  zero,  ought  to  occupy 
"  in  the  scale  of  the  thermometer.  Thus,  when  a  pound  of  ice,  at  32°,  is 
*  Chemical  Essays.  f  On  Animal  Heat,  &c.  2nd  edit.  1788. 

2  K  2 


500  LECTURE  LIT. 

mixed  with  a  pound  of  water  at  172°  of  Fahrenheit,  the  whole  excess  of 
140°  is  absorbed  in  the  conversion  of  the  ice  into  water,  and  the  mixture  is 
reduced  to  the  temperature  of  32°  ;  and,  on  the  other  hand,  when  a  pound 
of  ice  freezes,  a  certain  quantity  of  heat  is  evolved  which  is  probably 
capable  of  raising  the  temperature  of  a  pound  of  water  140°,  or  that  of  140 
pounds  a  single  degree.  Dr.  Crawford  found,  by  means  of  other  experi- 
ments, that  a  quantity  of  heat  capable  of  raising  the  temperature  of  water 
9°  would  raise  that  of  ice  as  much  as  10°  :  hence  he  inferred  that  the  capa- 
city of  ice  was  T9V  as  great  as  that  of  water,  and  that  if  this  capacity, 
instead  of  being  reduced  to  -j-9^,  had  been  wholly  destroyed,  the  quantity  of 
heat  extricated  would  have  been  10  times  as  great,  or  about  1400°,  which 
has,  therefore,  been  considered  as  the  whole  quantity  of  heat  contained  in  a 
pound  of  water  at  32°,  and  the  beginning  of  the  natural  scale  has  been 
placed  about  1368°  below  the  zero  of  Fahrenheit.  Dr.  Irvine  makes  the 
capacity  of  ice  still  less  considerable,  and  places  the  natural  zero  about 
900  degrees  below  that  of  Fahrenheit. 

If  direct  experiments  on  the  quantities  of  heat,  required  for  producing 
certain  elevations  of  temperature,  in  different  states  of  the  same  substance, 
compared  in  this  manner  with  the  emission  or  absorption  of  heat  which 
takes  place  while  those  changes  are  performed,  agreed  with  similar  experi- 
ments made  on  different  substances,  there  could  be  no  objection  to  the 
mode  of  representation.  But  if  it  should  appear  that  such  comparisons 
frequently  present  us  with  contradictory  results,  we  could  no  longer  con- 
sider the  theory  of  capacities  for  heat  as  sufficient  to  explain  the  pheno- 
mena. With  respect  to  the  simple  changes  constituting  congelation  and 
liquefaction,  condensation  and  evaporation,  and  compression  and  rarefaction, 
there  appears  to  be  at  present  no  evidence  of  the  insufficiency  of  this  theory ; 
it  has  not  perhaps  yet  been  shown  that  the  heat  absorbed  in  any  one  change 
is  always  precisely  equal  to  that  which  is  emitted  in  the  return  of  the  sub- 
stance to  its  former  state,  but  nothing  has  yet  been  advanced  which  renders 
this  opinion  improbable  ;  and  the  estimation  of  the  natural  zero,  which  is 
deduced  from  this  doctrine,  may  at  least  be  considered  as  a  tolerable 
approximation. 

If,  however,  we  attempt  to  deduce  the  heat  produced  by  friction  and  by 
combustion,  from  changes  of  the  capacities  of  bodies  thus  estimated,  we  shall 
find  that  the  comparison  of  a  very  few  facts  is  sufficient  to  demonstrate  the 
imperfection  of  such  a  theory.  Count  Rumford*  found  no  sensible  differ- 
ence between  the  capacities  of  solid  iron  and  of  its  chips ;  but  if  we  even 
suppose,  for  the  sake  of  the  argument,  that  the  pressure  and  friction  of  the 
borer  had  lessened  the  capacity  of  the  iron  one  twelfth,  so  as  to  make  it  no 
greater  than  that  of  copper;  we  shall  then  find  that  one  twelfth  of  the 
absolute  heat  of  the  chips,  thus  abraded,  must  have  amounted  to  above 
60,000  degrees  of  Fahrenheit,  and  consequently  that  the  natural  zero  ought 
to  be  placed  above  700,000  degrees  below  the  freezing  point,  instead  of  14  or 
1500  only.  It  is,  therefore,  impossible  to  suppose  that  any  alteration  of 
capacities  can  account  for  the  production  of  heat  by  friction ;  nor  is  it  at 
'  all  easier  to  apply  this  theory  correctly  to  the  phenomena  of  combustion. 
*  Ph.  Tr.  1798,  p.  80. 


THE  MEASURES  AND  THE  NATURE  OF  HEAT.    501 

A  pound  of  nitre  contains  about  half  its  weight  of  dry  acid,  and  the  capa- 
city of  the  acid,  when  diluted,  is  little  more  than  half  as  great  as  that  of 
water ;  the  acid  of  a  pound  of  nitre  must  therefore  contain  less  heat  than 
a  quarter  of  a  pound  of  water  :  hut  Lavoisier  and  Laplace  have  found,*  that 
the  deflagration  of  a  pound  of  nitre  produces  a  quantity  of  heat  sufficient  to 
melt  12  pounds  of  ice,  consequently  the  heat  extricated  by  the  decomposition 
of  a  pound  of  dry  nitrous  acid  must  be  sufficient  to  melt  24  pounds  of  ice ;  and 
even  supposing  the  gases,  extricated  during  the  deflagration,  to  absorb  no 
more  heat  than  the  charcoal  contained,  which  is  for  several  reasons  highly 
improbable,  it  follows  that  a  pound  of  water  ought  to  contain  at  least  as 
much  heat,  as  would  be  sufficient  to  melt  48  pounds  of  ice,  that  is  about 
6720  degrees  of  Farenheit. 

In  short,  the  further  we  pursue  such  calculations,  the  more  we  shall  be 
convinced  of  the  impossibility  of  applying  them  to  the  phenomena.  In 
such  a  case  as  that  of  the  nitrous  acid,  Dr.  Black's  term  of  latent  heat  t 
might  be  thought  applicable,  the  heat  being  supposed  to  be  contained  in  the 
substance,  without  being  comprehended  in  the  quantity  required  for  main- 
taining its  actual  temperature.  But  even  this  hypothesis  is  wholly  inappli- 
cable to  the  extrication  of  heat  by  friction,  where  all  the  qualities  of  the 
substances  concerned  remain  precisely  the  same  after  the  operation  as  before 
it.  If  any  further  argument  were  required  in  confutation  of  the  opinion, 
that  the  heat  excited  by  friction  is  derived  from  a  change  of  capacity,  it 
might  be  obtained  from  Mr.  Davy's  experiment  on  the  mutual  friction  of 
two  pieces  of  ice,  which  converted  them  into  water,  in  a  room  at  the  tem- 
perature of  the  freezing  point :  for  in  this  case  it  is  undeniable  that  the 
capacity  of  the  water  must  have  been  increased  during  the  operation  ;  and 
the  heat  produced  could  not,  therefore,  have  been  occasioned  by  the  dimi- 
nution of  the  capacity  of  the  ice. 

This  discussion  naturally  leads  us  to  an  examination  of  the  various  theories 
which  have  been  formed  respecting  the  intimate  nature  of  heat ;  a  subject 
upon  which  the  popular  opinion  seems  to  have  been  lately  led  away  by  very 
superficial  considerations.  The  facility  with  which  the  mind  conceives  the 
existence  of  an  independent  substance,  liable  to  no  material  variations, 
except  those  of  its  quantity  and  distribution,  especially  when  an  appro- 
priate name,  and  a  place  in  the  order  of  the  simplest  elements  has  been 
bestowed  on  it,  appears  to  have  caused  the  most  eminent  chemical  philoso- 
phers to  overlook  some  insuperable  difficulties  attending  the  hypothesis  of 
caloric.  Caloric  has  been  considered  as  a  peculiar  elastic  or  ethereal  fluid, 
pervading  the  substance  or  the  pores  of  all  bodies,  in  different  quan- 
tities, according  to  their  different  capacities  for  heat,  and  according  to 
their  actual  temperatures  ;  and  being  transferred  from  one  body  to  another 
upon  any  change  of  capacity,  or  upon  any  other  disturbance  of  the  equi- 
librium of  temperature :  it  has  also  been  commonly  supposed  to  be  the 
general  principle  or  cause  of  repulsion  ;  and  in  its  passage  from  one  body 
to  another,  by  radiation,  it  has  been  imagined  by  some  to  flow  in  a  con- 

.    *  Hist,  et  Mem.  1780,  p.  355,  H.  3. 

•f  Black's  Lectures,  2  vols.  4to,  Ed.    See  Lavoisier,  Traite  Elem.  de  Chimie,  1 789. 


502  LECTURE  LII. 

tinued  stream,  and  by  others  in  the  form  of  separate  particles,  moving,  with 
inconceivable  velocity,  at  great  distances  from  each  other. 

The  circumstances  which  have  been  already  stated  respecting  the  produc- 
tion of  heat  by  friction,  appear  to  afford  an  unanswerable  confutation  of 
the  whole  of  this  doctrine.  If  the  heat  is  neither  received  from  the  surround- 
ing bodies,  which  it  cannot  be  without  a  depression  of  their  temperature, 
nor  derived  from  the  quantity  already  accumulated  in  the  bodies  themselves, 
which  it  could  not  be,  even  if  their  capacities  were  diminished  in  any  ima- 
ginable degree,  there  is  no  alternative  but  to  allow  that  heat  must  be  actu- 
ally generated  by  friction ;  and  if  it  is  generated  out  of  nothing,  it  cannot 
be  matter,  nor  even  an  immaterial  or  semimaterial  substance.  The  colla- 
teral parts  of  the  theory  have  also  their  separate  difficulties  :  thus,  if  heat 
were  the  general  principle  of  repulsion,  its  augmentation  could  not  diminish 
the  elasticity  of  solids  and  of  fluids ;  if  it  constituted  a  continued  fluid,  it 
could  not  radiate  freely  through  the  same  space  in  different  directions  ; 
and  if  its  repulsive  particles  followed  each  other  at  a  distance,  they  would 
still  approach  near  enough  to  each  other,  in  the  focus  of  a  burning  glass,  to 
have  their  motions  deflected  from  a  rectilinear  direction. 

If  heat  is  not  a  substance  it  must  be  a  quality ;  and  this  quality  can  only 
be  motion.  It  was  Newton's  opinion,  that  heat  consists  in  a  minute  vibra- 
tory motion  of  the  particles  of  bodies,  and  that  this  motion  is  communicated 
through  an  apparent  vacuum,  by  the  undulations  of  an  elastic  medium, 
which  is  also  concerned  in  the  phenomena  of  light.  If  the  arguments 
which  have  been  lately  advanced,  in  favour  of  the  undulatory  nature  of 
light,  be  deemed  valid,  there  will  be  still  stronger  reasons  for  admitting  this 
doctrine  respecting  heat,  and  it  will  only  be  necessary  to  suppose  the  vibra- 
tions and  undulations,  principally  constituting  it,  to  be  larger  and  stronger 
than  those  of  light,  while  at  the  same  time  the  smaller  vibrations  of  light, 
and  even  the  blackening  rays,  derived  from  still  more  minute  vibrations, 
may,  perhaps,  when  sufficiently  condensed,  concur  in  producing  the  effects 
of  heat.  These  effects,  beginning  from  the  blackening  rays,  which  are  in- 
visible, are  a  little  more  perceptible  in  the  violet,  which  still  possess  but  a 
faint  power  of  illumination ;  the  yellow  green  afford  the  most  light ;  the 
red  give  less  light,  but  much  more  heat,  while  the  still  larger  and  less  fre- 
quent vibrations,  which  have  no  effect  on  the  sense  of  sight,  may  be  sup- 
posed to  give  rise  to  the  least  refrangible  rays,  and  to  constitute  invisible 
heat. 

It  is  easy  to  imagine  that  such  vibrations  may  be  excited  in  the  component 
parts  of  bodies,  by  percussion,  by  friction,  or  by  the  destruction  of  the 
equilibrium  of  cohesion  and  repulsion,  and  by  a  change  of  the  conditions 
on  which  it  may  be  restored,  in  consequence  of  combustion,  or  of  any  other 
chemical  change.  It  is  remarkable  that  the  particles  of  fluids,  which  are 
incapable  of  any  material  change  of  temperature  from  mutual  friction, 
have  also  very  little  power  of  communicating  heat  to  each  other  by  their 
immediate  action,  so  that  there  may  be  some  analogy,  in  this  respect, 
between  the  communication  of  heat  and  its  mechanical  excitation. 

The  effects  of  heat  on  the  cohesive  and  repulsive  powers  of  bodies  have 


THE  MEASURES  AND  THE  NATURE  OF  HEAT.         503 

sometimes  been  referred  to  the  centrifugal  forces  and  mutual  collisions  of 
the  revolving  and  vibrating  particles  :  and  the  increase  of  the  elasticity  of 
aeriform  fluids  has  been  very  minutely  compared  with  the  force  which 
would  be  derived  from  an  acceleration  of  these  internal  motions.  In  solids 
and  in  liquids,  however,  this  increase  of  elasticity  is  not  observable,  and 
the  immediate  effect  of  heat  diminishes  not  only  the  force  of  cohesion,  but 
also  in  some  degree,  that  of  repulsion,  so  that  these  vibrations,  if  they 
exist,  must  derive  their  effect  on  the  corpuscular  forces  from  the  alterations 
which  they  produce  on  the  situation  of  the  particles,  with  respect  to  the 
causes  of  these  forces. 

The  different  chemical  effects  of  heat  and  light  are  far  from  furnishing 
any  objection  to  this  system  ;  it  is  extremely  easy  to  imagine  the  attraction 
between  two  or  three  bodies  to  be  modified  by  the  agitations,  into  which 
their  particles  are  thrown.  If  certain  undulations  be  capable  of  affecting 
one  of  the  three  bodies  only,  its  cohesion  with  both  the  others  may  be 
weakened,  and  hence  their  mutual  attraction  may  be  comparatively 
increased  ;  and  from  various  combinations  of  such  differences,  in  the 
operation  of  different  kinds  of  heat  and  light,  a  great  diversity  of  effects  of 
a  similar  kind  may  be  derived. 

If  heat,  when  attached  to  any  substance,  be  supposed  to  consist  in 
minute  vibrations,  and  when  propagated  from  one  body  to  another,  to 
depend  on  the  undulations  of  a  medium  highly  elastic,  its  effects  must 
strongly  resemble  those  of  sound,  since  every  sounding  body  is  in  a  state 
of  vibration,  and  the  air,  or  any  other  medium,  which  transmits  sound, 
conveys  its  undulation  to  distant  parts  by  means  of  its  elasticity.  And  we 
shall  find  that  the  principal  phenomena  of  heat  may  actually  be  illustrated 
by  a  comparison^with  those  of  sound.  The  excitation  of  heat  and  sound 
are  not  only  similar,  but  often  identical ;  as  in  the  operations  of  friction 
and  percussion :  they  are  both  communicated  sometimes  by  contact  and 
sometimes  by  radiation ;  for  besides  the  common  radiation  of  sound 
through  the  air,  its  effects  are  communicated  by  contact,  when  the  end  of 
a  tuning  fork  is  placed  on  a  table,  or  on  the  sounding  board  of  an  instru- 
ment, which  receives  from  the  fork  an  impression  that  is  afterwards  propa- 
gated as  a  distinct  sound.  And  the  effect  of  radiant  heat,  in  raising  the 
temperature  of  a  body  upon  which  it  falls,  resembles  the  sympathetic 
agitation  of  a  string,  when  the  sound  of  another  string,  which  is  in  unison 
with  it,  is  transmitted  to  it  through  the  air.  The  water,  which  is  dashed 
about  by  the  vibrating  extremities  of  a  tuning  fork  dipped  into  it,  may 
represent  the  manner  in  which  the  particles  at  the  surface  of  a  liquid  are 
thrown  out  of  the  reach  of  the  force  of  cohesion,  and  converted  into 
vapour  ;  and  the  extrication  of  heat,  in  consequence  of  condensation,  may 
be  compared  with  the  increase  of  sound  produced  by  lightly  touching  a 
long  cord  which  is  slowly  vibrating,  or  revolving  in  such  a  manner  as  to 
emit  little  or  no  audible  sound  ;  while  the  diminution  of  heat,  by  expan- 
sion, and  the  increase  of  the  capacity  of  a  substance  for  heat,  may  be 
attributed  to  the  greater  space  afforded  to  each  particle,  allowing  it  to  be 
equally  agitated  with  a  less  perceptible  effect  on  the  neighbouring  particles. 
In  some  cases,  indeed,  heat  and  sound  not  only  resemble  each  other  in 


504  LECTURE  LII. 

their  operations,  but  produce  precisely  the  same  effects  ;  thus,  an  artificial 
magnet,  the  force  of  which  is  quickly  destroyed  by  heat,  is  affected  more 
slowly  in  a  similar  manner,  when  made  to  ring  for  a  considerable  time  ; 
and  an  electrical  jar  may  be  discharged,  either  by  heating  it,  or  by  causing 
it  to  sound  by  the  friction  of  the  finger. 

All  these  analogies  are  certainly  favourable  to  the  opinion  of  the 
vibratory  nature  of  heat,  which  has  been  sufficiently  sanctioned  by  the 
authority  of  the  greatest  philosophers  of  past  times,  and  of  the  most  sober 
reasoners  of  the  present.  Those,  however,  who  look  up  with  unqualified 
reverence  to  the  dogmas  of  the  modern  schools  of  chemistry,  will  probably 
long  retain  a  partiality  for  the  convenient,  but  superficial  and  inaccurate, 
modes  of  reasoning,  which  have  been  founded  on  the  favourite  hypothesis 
of  the  existence  of  caloric  as  a  separate  substance  ;  but  it  may  be  presumed 
that  in  the  end  a  careful  and  repeated  examination  of  the  facts,  which  have 
been  adduced  in  confutation  of  that  system,  will  make  a  sufficient  impres- 
sion on  the  minds  of  the  cultivators  of  chemistry,  to  induce  them  to  listen 
to  a  less  objectionable  theory. 

[Considerable  advances  have  been  made  in  our  knowledge  of  the  pro- 
perties of  heat  since  the  first  publication  of  these  Lectures.  They  have 
owed  their  existence,  for  the  most  part,  to  the  discovery  of  a  very  delicate 
measure  of  variation  of  temperature  by  means  of  its  galvanic  influence. 
It  is  well  known  that  when  a  current  passes  along  a  wire,  a  tangential 
force  is  put  in  play  which  tends  to  cause  the  deflection  of  a  magnetic 
needle  placed  in  the  neighbourhood  of  the  wire.  (See  additions  to  Lect.  LV.) 
Moreover  it  has  been  discovered  that  heat  is  capable  of  producing  a  gal- 
vanic current,  the  intensity  of  which  is  proportional  to  that  of  the  produ- 
cing agent.  This  is  exhibited  in  the  following  manner.  A  number  of  bars 
of  antimony  and  bismuth  are  arranged  so  as  to  lie  compactly,  whilst  they 
alternate  with  each  other.  They  are  then  soldered  together  in  pairs,  so 
that  each  bar  of  the  one  metal  is  connected  at  both  ends  with  a  bar  of  the 
other.  The  extreme  bars  are  united  by  means  of  a  wire,  and  it  is  along 
this  that  a  galvanic  current  travels,  on  the  application  of  heat  to  the  sol- 
dered ends  of  the  bars.  The  instrument  based  on  these  principles,  as  sug- 
gested by  Becquerel  and  improved  by  Nobili,  Melloni,  and  others,  is  called 
a  thermomultiplier.  This  name  arises  from  the  important  fact,  that  by 
crossing  the  wire  so  as  to  cause  it  to  pass  several  times  parallel  to  the  mag- 
netic needle,  the  simple  effect  may  be  increased  to  almost  any  extent,  and 
thus  the  instrument  may  be  made  to  measure  the  minutest  indications  of 
heat.*  Amongst  the  earliest  results  of  the  use  of  this  instrument  was  the 
discovery  of  Melloni,  that  rock  salt  suffers  heat  of  every  kind  to  pass  freely 
through  it,  thus  forming  for  heat  a  substance  analogous  to  that  which 
glass  constitutes  for  light.1*  The  field  of  discovery  of  the  analogous  pro- 
perties of  heat  and  light  was  now  thrown  open.  That  the  former,  as  well 
as  the  latter,  suffers  polarization  under  certain  circumstances  had  been 
conjectured  by  Berard  and  others.  But  the  experiment  on  which  the 

*  For  a  description  of  the  instrument  see  the  Bibliotheque  Universelle  (new  ser.) 
ii.  225.  Ann.  de  Ch.  xlviii.  198.  Ed.  Tr.  vol.  xiii. 

•f  Ann.  de  Ch.  liii.,  or  Taylor's  Scientific  Memoirs,  i.  32. 


THE  MEASURES  AND  THE  NATURE  OF  HEAT.    505 

[belief  was  founded,  failed  on  repetition  by  Powell  and  Nobili.     And  even 
M.  Melloni,  with  his  thermomultiplier,  was  unable  to  detect  the  existence 
of  polarization  in  1833.     In  the  following  year  Prof.  Forbes  took  up  the 
subject,  and  completely  succeeded.     The  characteristic  of  polarization  of 
light  is  the  exhibition  of  a  reference  to  sides  relative  to  its  path.     Thus  light 
which  passes  directly  through  one  slice  of  tourmaline  is  of  the  same  intensity 
in  whatever  way  the  tourmaline  be  presented  to  it.     But  if  a  second  tour- 
maline be  applied,  the  intensity  of  the  ray  which  merges  from  it,  depends 
on  its  situation  relative  to  the  first ;  thus  proving  that  the  light  which  had 
passed  through  the  first  tourmaline  differed  from  common  light  in  having 
acquired  a  property  connected  with  direction  perpendicular  to  its  path. 
Prof.  Forbes  showed  that  the  same  is  equally  true  of  heat.     In  the  first 
place,  he  found  that  two  tourmalines,  with  their  axes  crossed,  stop  more 
heat  than  when  they  are  parallel,  even  if  the  source  of  heat  is  brass  not 
luminous.     In  the  next  place  he  discovered  an  apparatus  which  facilitated 
the  exhibition  of  the  different  facts  connected  with  polarization.     It  con- 
sists of  plates  of  mica  split  very  thin  by  the  application  of  sudden  heat. 
These  placed  at  an  angle  of  about  45°,  formed  an  excellent  polarizer,  and 
enabled  him  to  detect  polarization  with  the  greatest  facility.  By  this  means 
he  established  the  more  delicate  facts  of  depolarization  and  circular  pola- 
rization.    A  plate  of  mica  being  placed  between  the  polarizer  and  ana- 
lyzer, when  in  a  crossed  position,  restored  to  the  heat  its  capacity  of  being 
transmitted  through  the  latter,  so  that  under  certain  circumstances,  the 
interposition  of  the  plate  actually  increased  the  quantity  of  heat  which 
passed  through  the  apparatus.     Prof.  Forbes  discovered  circular  polari- 
zation in  1836,  thus  establishing  the  complete  analogy  between  heat  and 
light.     There  are,  however,  some  points  which  appear  to  present  an  obstacle 
to  basing  our  theory  of  heat  directly  on  the  corresponding  theory  of  light. 
In  the  first  place,  Prof.  Forbes  shows  that  non-luminous  heat  is  less  pola- 
rizable  at  the  same  angle  than  luminous.     In  the  next  place,  most  bodies 
are  found  to  absorb  the  less  refrangible  rays  in  excess,  so  that  the  mean 
refrangibility  is  increased  by  transmission  through  them.     Smoked  rock 
salt,  or  mica,  was  found  by  Melloni*  not  to  possess  this  property,  conse- 
quently it  was  argued  that  the  state  of  the  surface  produces  the  effect ; 
and  accordingly  with  a  roughened  surface  Prof .  Forbes  t  found  the  quantity 
of  dark  heat  transmitted  to  be  in  a  threefold  proportion  to  that  which  was 
transmitted   from  a  glass  lamp.     If,  however,  the  surface  was  regularly 
scratched,  or  if  it  had  a  grating  before  it,  heat  of  every  kind  was  trans- 
mitted in  the  same  proportion.    This  last  fact  may  probably  tend  to  recon- 
cile the  theories  of  heat  and  light,  for  I  have  proved  J  that  interference, 
whether  by  means  of  a  prism  or  by  Franenhofer's  gratings,  when  they 
are  regular,  produces  no  effect  in  adding  to,  or  diminishing  the  quantity  of 
light.     The  total  amount  received  on  a  screen  is  in  exact  proportion  to  the 
amount  of  surface  left  uncovered,  the  effect  of  interference  being  merely  a 
displacement  of  its  position. 

*  Comptes  Rendus,  Sep.  3,  1839. 

f  Proceedings  of  the  Royal  Soc.  of  Edin.  p.  281.  Ed.  Tr.  vol.  xv. 
t  On  the  Aggregate  Effect  of  Interference,  Camb.  Tr.  vol.  vii.  part  ii.     On  the 
Absolute  Intensity  of  Interfering  Light,  Ed.  Tr.  xv.  315. 


506  LECTURE  LII. 

[The  theory  of  heat  may  be  said  to  rest  where  it  did  at  the  time  these 
lectures  were  written.  The  facts  which  have  just  been  mentioned  clearly 
point  out  its  undulatory  character.  But  in  what  way  the  major  part  of 
the  ordinary  phenomena  al-e  to  be  explained  by  this  doctrine  does  not  yet 
appear.  We  have  no  satisfactory  explanation  of  expansion,  of  tardy  con- 
duction, of  the  change  of  form  of  certain  crystals,  of  latent  heat,  and  the 
like.  Neither  will  a  merely  undulatory  hypothesis  relieve  us  from  some  of 
the  difficulty  attendant  on  certain  of  the  very  phenomena  which  appeared 
to  suggest  it ;  such  as  the  difference  between  solar  and  terrestrial  heat, 
which  Melloni  shows  to  depend  on  the  different  mixture  of  the  different 
rays  ;  the  effect  of  different  screens  which  variously  affect  different  kinds 
of  heat,*  the  sifting  of  heat  by  a  screen,  so  as  to  render  it  more  capable  of 
transmission  through  another  similar  screen.  These  facts  appear  to 
demand  a  corpuscular  theory,  wholly  or  partly  accompanied  by  transverse 
vibrations.  The  hypothesis  which  I  have  advancedt  is,  that  heat  is  due  to 
the  existence  of  repulsive  atoms  which  penetrate  all  material  substances ; 
so  that  expansion  arises  from  the  accumulation  of  such  atoms ;  but  that 
the  transmission  of  heat  is  partly  effected  by  transverse  pulses,  very  nearly 
in  the  same  way  as  the  tidal  water  is  conveyed  up  a  channel,  and  accumu- 
lates at  its  upper  extremity.  Solar  heat  is  transmitted  altogether  by  such 
transverse  pulses,  so  that  its  intensity  is  measured  by  the  intensity  of  the 
pulses,  whilst  the  heat  of  a  fire  is  perhaps  due  in  part  to  normal  ones, 
or,  which  is  the  same  thing,  to  a  flow  of  atoms  impelling  by  their  repul- 
sion those  wliich  are  in  advance  of  them. 

The  reader  will  find  Professor  Forbes's  researches  in  the  Edinburgh 
Transactions,  vols.  xiii.,  xiv.,  and  xv.  ;  and  in  the  Philosophical  Maga- 
zine, vol.  vi.,  &c.  Melloni' s,  in  the  Annales  de  Chimie,  vol.  liii.,  &c. ;  or  in 
the  Scientific  Memoirs,  vols.  i.,  ii.,  &c.  He  may  also  consult  Powell's 
Reports  on  Radiant  Heat.  Reports  of  the  British  Association,  1832, 1840.] 


LECT.  LII.— ADDITIONAL  AUTHORITIES. 

Thermometers,  fyc. — Fludd,  De  Philos.  Moysiaca,  1638.  Boyle's  Works.  Hooke's 
Statical  Therm.  Birch,  ii.  1.  Wallis  and  Beale,  Ph.  Tr.  1669,  p.  1113.  Lahire, 
Hist,  et  Mem.  1706,  p.  432  ;  1710,  p.  546,  H.  13  ;  1711,  p.  144,  H.  40.  Amon- 
tons  (air  then),  ibid.  1703,  p.  101,  H.  6.  Taylor  on  the  Expansion  of  Fluids, 
Ph.  Tr.  1723,  p.  291.  Bulfinger,  Comm.  Petr.  iii.  196,  242,  iv.  216.  Reaumur, 
Hist,  et  Mem.  1730,  p.  452  ;  1731,  p.  250,  H.  6.  Delisle,  Ph.  Tr.  1736,  p.  221. 
Ellicott's  Pyrometer,  ibid.  1736,  p.  297.  Weitbrecht,  Comm.  Petr.  viii.  310. 
Krafft,  ibid.  ix.  241.  Ludolff,  Mis.  Berl.  1740,  p.  255.  Grischow,  ibid.  1740, 
p.  267.  Celsius,  Schwed.  Abhand.  1742,  p.  197.  Wargentin,  ibid.  1749,  p.  167. 
Smeaton's  Pyrometer,  Ph.  Tr.  1754,  p.  598.  Lord  Cavendish  on  Max.  and  Min. 
Ther.  ibid.  1757,  p.  300.  Bergen,  DeTher.  4to,  Nuremb.  1757.  Sulzer,  Act.  Helv. 
iii.  259.  Hennert,  Traite  des  Therm.  Hague,  1768.  Haubold,  De  Therm.  Reaum. 
4to,  Leipz.  1771.  Strohmeyer,  Ueber  die  Ther.  Gott.  1775.  Roy  on  Ramsden's 
Pyrometer,  Ph.  Tr.  1785,  p.  461.  Report  on  Ther.  ibid.  1777,  p.  816.  Van 
Swinden,  Comparaison  des  Ther.  Amst.  1778.  Schuckburgh,  Ph.  Tr.  1779.  Luz, 
Ueber  die  Ther.  Nuremb.  1781.  Six's  Register,  Therm.  Ph.  Tr.  Ixxii.  1794, 
Rutherford's  Register,  Ed.  Tr.  iii.  247.  Rumford's  Differential  Ther.  Ph.  Tr.  1804, 
p.  77.  Dalton,  Nich.  Jour.  8vo.  v.  34.  Daniell's  Pyrometer,  Quarterly  Journal  of 

*  Melloni,  Annales  de  Ch.  Iv.  337. 

f  Kelland's  Theory  of  Heat,  art.  155,  169,  194. 


ON  ELECTRICITY  IN  EQUILIBRIUM.  507 

Science,  xi.  309.  Ph.  Tr.  1830,  p.  257.  Guyton  de  Morveau's  Pyrometer,  Ann. 
de  Ch.  xlvi.  276. 

On  the  Expansion  of  Gases. — Priestley,  Experiments  and  Observations  on  Air, 
3  vols.  1774-7.  Gay  Lussac,  Ann.  de  Ch.  cxxviii  (xliii.)  137.  Dalton,  Manch. 
Mem.  v.  595.  Gilbert,  in  Gilb.  Ann.  xiv.  266.  Rudberg,  Pogg.  Ann.  xli.  271 ; 
xliv.  119. 

Expansion  of  Liquids. — Hallstrb'm,  Pogg.  Ann.  i.  129,  xix.  135.  De  Luc, 
Recherches  sur  les  Modifications  de  1'Atmosphere.  Gay  Lussac,  Ann.  de  Ch.  ii. 
130. 

Solids.— Smeaton,  Ph.  Tr.  1754,  p.  598.  Errata.  Roy,  Ph.  Tr.  1777,  p.  653. 
De  Luc  on  Pyrometry  and  Areometry,  ibid.  1778,  p.  419.  Lavoisier  and  Laplace, 
Ann.  de  Ch.  i.  101.  Dulong  and  Petit,  ibid.  ii.  240,  vii.  113,  225.  Daniell,  Ph.  Tr. 
1831,  p.  443. 

Freezing,  Sfc. — Braun,  De  Frigore  Artificial!,  4to,  Petersb.  1760  ;  on  the  Freez- 
ing of  Mercury,  Nov.  Com.  Petr.  ii.  268,  302.  Hutchins  on  do.  Ph.  Tr.  1776, 
p.  174  ;  1783,  p.  303.  Cavendish  on  Hutchins's  Exper.  ibid.  1783,  p.  303  ;  on 
M'Nabs,  ibid.  1786,  p.  241  ;  1788,  p.  166.  Blagden's  Hist,  of  the  Congelation  of 
Mercury,  ibid.  1783,  p.  329.  Guthrie  on  do.  4to,  Petersb.  1785.  Walker  on 
Freezing  Mixtures,  Ph.  Tr.  1788,  p.  395  ;  1795,  p.  270  ;  1801,  p.  120. 

Specific  Heat. — Meyer,  Ann.  de  Ch.  xxx.  46.  De  la  Roche  and  Berard,  ibid. 
Ixxxv.  72.  Dulong  and  Petit,  ibid,  (new  series),  vii.  113,  142,  x.  395.  Ure,  Ph.  Tr. 
1818,  p.  378.  Haycraft,  Ed.  Tr.  x.  195.  Avogadro,  Mem.  di  Torino,  xxviii.  1, 
xxix.  79.  Neumann,  Pogg.  Ann.  xxiii.  1.  Thomson's  Heat  (1840)  is  very  copious. 


LECTURE   LIII. 


ON  ELECTRICITY  IN  EQUILIBRIUM. 

THE  phenomena  of  electricity  are  as  amusing  and  popular  in  their 
external  form  as  they  are  intricate  and  abstruse  in  their  intimate  nature. 
In  examining  these  phenomena  a  philosophical  observer  will  not  he  content 
with  such  exhibitions  as  dazzle  the  eye  for  a  moment,  without  leaving 
any  impression  that  can  be  instructive  to  the  mind,  hut  he  will  be  anxious 
to  trace  the  connexion  of  the  facts  with  their  general  causes,  and  to  com- 
pare them  with  the  theories  which  have  been  proposed  concerning  them  : 
and  although  the  doctrine  of  electricity  is  in  many  respects  yet  in  its 
infancy,  we  shall  find  that  some  hypotheses  may  be  assumed  which  are 
capable  of  explaining  the  principal  circumstances  in  a  simple  and  satisfac- 
tory manner,  and  which  are  extremely  useful  in  connecting  a  multitude  of 
detached  facts  into  an  intelligible  system.  These  hypotheses,  founded  on 
the  discoveries  of  Franklin,  have  been  gradually  formed  into  a  theory,  by 
the  investigations  of  Aepinus  and  Mr.  Cavendish,  combined  with  the 
experiments  and  inferences  of  Lord  Stanhope,  Coulomb,  and  Robison. 

We  shall  first  consider  the  fundamental  hypotheses  on  which  this  system 
depends,  and  secondly  the  conditions  of  equilibrium  of  the  substances 
concerned  in  it ;  determining  the  mode  of  distribution  of  the  electric  fluid, 
and  the  forces  or  pressures  derived  from  its  action  when  at  rest ;  all  which 
will  be  found  to  be  deduced  from  the  theory  precisely  as  they  are  experi- 
mentally observable.  The  motions  of  the  electric  fluid  will  next  be  noticed, 


508  LECTURE  LIII. 

as  far  as  we  can  form  any  general  conclusions  respecting  them ;  and  the 
manner  in  which  the  equilibrium  of  electricity  is  disturbed,  or  the  excita- 
tion of  electricity,  will  also  be  considered  ;  and,  in  the  last  place,  it  will  be 
necessary  to  take  a  view  of  the  mechanism  or  the  practical  part  of  elec- 
tricity, and  to  examine  the  natural  and  artificial  apparatus  concerned  in 
electrical  phenomena,  as  well  as  in  those  effects,  which  have  been  denomi- 
nated galvanic. 

It  is  supposed  that  a  peculiar  ethereal  fluid  pervades  the  pores,  if  not 
the  actual  substance,  of  the  earth  and  of  all  other  material  bodies,  passing 
through  them  with  more  or  less  facility,  according  to  their  different  powers 
of  conducting  it :  that  the  particles  of  this  fluid  repel  each  other,  and  are 
attracted  by  the  particles  of  common  matter  :  that  the  particles  of  common 
matter  also  repel  each  other  :  and  that  these  attractions  and  repulsions  are 
equal  among  themselves,  and  vary  inversely  as  the  squares  of  the  distances 
of  the  particles. 

The  effects  of  this  fluid  are  distinguished  from  those  of  all  other  sub- 
stances by  an  attractive  or  repulsive  quality,  which  it  appears  to  commu- 
nicate to  different  bodies,  and  which  differs  in  general  from  other 
attractions  and  repulsions,  by  its  immediate  diminution  or  cessation,  when 
the  bodies,  acting  on  each  other,  come  into  contact,  or  when  they  are 
touched  by  other  bodies.  The  name  electricity  is  derived  from  electrum, 
amber ;  for  it  was  long  ago  observed  that  amber,  when  rubbed,  continues 
for  some  time  to  attract  small  bodies  ;  but  at  present  electricity  is  usually 
excited  by  other  means.  In  general  a  body  is  said  to  be  electrified,  when 
it  contains,  either  as  a  whole,  or  in  any  of  its  parts,  more  or  less  of  the 
electric  fluid  than  is  natural  to  it ;  and  it  is  supposed  that  what  is  called 
positive  electricity  depends  on  a  redundancy,  and  negative  electricity  on  a 
deficiency  of  the  fluid. 

These  repulsions  and  attractions  are  supposed  to  act,  not  only  between 
two  particles  which  are  either  perfectly  or  very  nearly  in  contact  with 
each  other,  but  also  between  all  other  particles  at  all  distances,  whatever 
obstacles  may  be  interposed  between  them.  Thus,  if  two  electrified  balls 
repel  each  other,  the  effect  is  not  impeded  by  the  interposition  of  a  plate  of 
glass  :  and  if  any  other  substance  interposed  appears  to  interfere  with  their 
mutual  action,  it  is  in  consequence  of  its  own  electrical  affections.  In 
these  respects,  as  well  as  in  the  law  of  their  variation,  the  electrical  forces 
differ  from  the  common  repulsion  which  operates  between  the  particles  of 
elastic  fluids,  and  resemble  more  nearly  that  of  gravitation.  Their 
intensity,  when  separately  considered,  is  much  greater  than  that  of 
gravitation,  and  they  might  be  supposed  to  be  materially  concerned  in  the 
great  phenomena  of  the  universe  ;  but  in  the  common  neutral  state  of  all 
bodies,  the  electrical  fluid,  which  is  every  where  present,  is  so  distributed, 
that  the  various  forces  hold  each  other  exactly  in  equilibrium,  and  the 
separate  results  are  destroyed ;  unless  we  choose  to  consider  gravitation 
itself  as  arising  from  a  comparatively  slight  inequality  between  the  elec- 
trical attractions  and  repulsions. 

The  attraction  of  the  electric  fluid  to  common  matter  is  shown  by  its 
communication  from  one  body  to  another,  which  is  less  copiously  supplied 


ON  ELECTRICITY  IN  EQUILIBRIUM.  509 

with  it,  as  well  as  by  many  other  phenomena ;  and  this  attraction  of  the 
fluid  of  the  first  body,  to  the  matter  of  the  second,  is  precisely  equal  to  its 
repulsion  for  the  quantity  of  the  fluid  which  naturally  belongs  to  the 
second,  so  as  to  saturate  the  matter.  For  the  excess  or  deficiency  of  the 
fluid  in  the  first  body  does  not  immediately  produce  either  attraction  or 
repulsion,  so  long  as  the  natural  distribution  of  the  fluid  in  the  second  body 
remains  unaltered. 

Since  also  two  neutral  bodies,  the  matter  which  they  contain  being 
saturated  by  the  electric  fluid,  exhibit  no  attraction  for  each  other,  the 
matter  in  the  first  must  be  repelled  by  the  matter  in  the  second  :  for 
its  attraction  for  the  fluid  of  the  second  would  otherwise  remain  uncom- 
pensated.  We  are,  however,  scarcely  justified  in  classing  this  mutual 
repulsion  among  the  fundamental  properties  of  matter  ;  for  useful  as  these 
laws  are  in  explaining  electrical  appearances,  they  seem  to  deviate  too  far 
from  the  magnificent  simplicity  of  nature's  works,  to  be  admitted  as 
primary  consequences  of  the  constitution  of  matter :  they  may,  however, 
be  considered  as  modifications  of  some  other  more  general  laws,  which  are 
yet  wholly  unknown  to  us. 

When  the  equilibrium  of  these  forces  is  destroyed,  the  electric  fluid  is 
put  in  motion  ;  those  bodies  which  allow  the  fluid  a  free  passage,  are  called 
perfect  conductors ;  but  those  which  impede  its  motion  more  or  less,  are 
nonconductors,  or  imperfect  conductors.  For  example,  while  the  electric 
fluid  is  received  into  the  metallic  cylinder  of  an  electrical  machine,  its 
accumulation  may  be  prevented  by  the  application  of  the  hand  to  the 
cylinder  which  receives  it,  and  it  will  pass  off  through  the  person  of  the 
operator  to  the  ground  ;  hence  the  human  body  is  called  a  conductor.  But 
when  the  metallic  cylinder,  or  conductor,  of  the  machine  is  surrounded 
only  by  dry  air,  and  supported  by  glass,  the  electric  fluid  is  retained,  and 
its  density  increased,  until  it  becomes  capable  of  procuring  itself  a  passage 
some  inches  in  length,  through  the  air,  which  is  a  very  imperfect  conductor. 
If  a  person,  connected  with  the  conductor,  be  placed  on  a  stool  with  glass 
legs,  the  electricity  will  no  longer  pass  through  him  to  the  earth,  but  may 
be  so  accumulated,  as  to  make  its  way  to  any  neighbouring  substance 
which  is  capable  of  receiving  it,  exhibiting  a  luminous  appearance  called  a 
spark  ;  and  a  person  or  a  substance,  so  placed  as  to  be  in  contact  with 
nonconductors  only,  is  said  to  be  insulated.  When  electricity  is  subtracted 
from  the  substance  thus  insulated,  it  is  said  to  be  negatively  electrified,  but 
the  sensible  effects  are  nearly  the  same,  except  that  in  some  cases  the  form 
of  the  spark  is  a  little  different. 

Perfect  conductors,  when  electrified,  are  in  general  either  overcharged  or 
undercharged  with  electricity  in  their  most  distant  parts  at  the  same  time; 
but  nonconductors,  although  they  have  an  equal  attraction  for  the  electric 
fluid,  are  often  differently  affected  in  different  parts  of  their  substance, 
even  when  those  parts  are  similarly  situated  in  every  respect,  except  that 
some  of  them  have  had  their  electricity  increased  or  diminished  by  a 
foreign  cause.  This  property  of  nonconductors  may  be  illustrated  by 
means  of  a  cake  of  resin,  or  a  plate  of  glass,  to  which  a  local  electricity 
n/ay  be  communicated  in  any  part  of  its  surface,  by  the  contact  of  an 


510  LECTURE  LIII. 

electrified  body  ;  and  the  parts  thus  electrified  may  afterwards  be  distin- 
guished from  the  rest,  by  the  attraction  which  they  exert  on  any  small 
particles  of  dust  or  powder  projected  near  them  ;  the  manner  in  which 
the  particles  arrange  themselves  on  the  surface,  indicating  also  in  some 
cases  the  species  of  electricity,  whether  positive  or  negative,  that  has 
been  employed ;  positive  electricity  producing  an  appearance  somewhat 
resembling  feathers ;  and  negative  electricity  an  arrangement  more  like 
spots.  The  inequality  in  the  distribution  of  the  electric  fluid  in  a  noncon- 
ductor may  remain  for  some  hours,  or  even  some  days,  continually 
diminishing  till  it  becomes  imperceptible. 

These  are  the  fundamental  properties  of  the  electric  fluid,  and  of  the 
different  kinds  of  matter  as  connected  with  that  fluid.  We  are  next  to 
examine  its  distribution,  and  the  attractive  and  repulsive  effects  exhibited 
by  it,  under  different  forms.  Supposing  a  quantity  of  redundant  fluid  to 
exist  in  a  spherical  conducting  body,  it  will  be  almost  wholly  collected  into 
a  minute  space  contiguous  to  the  surface,  while  the  internal  parts  remain 
but  little  overcharged.  For  we  may  neglect  the  actions  of  the  portion  of 
fluid  which  is  only  occupied  in  saturating  the  matter,  and  also  the  effect  of 
the  matter  thus  neutralised,  since  the  redundant  fluid  is  repelled  as  much 
by  the  one  as  it  is  attracted  by  the  other :  and  we  need  only  to  consider 
the  mutual  actions  of  the  particles  of  this  superfluous  fluid  on  each  other. 
It  may  then  be  shown,  in  the  same  manner  as  it  is  demonstrated  of  the 
force  of  gravitation,  that  all  the  spherical  strata  which  are  remoter  from 
the  centre  than  any  given  particle,  will  have  the  whole  of  their  action  on  it 
annihilated  by  the  balance  of  their  forces,  and  that  the  effective  repulsion 
of  the  interior  strata  will  be  the  same,  as  if  they  were  all  collected  in  the 
centre.  This  repulsion  will,  therefore,  impel  the  particles  of  the  fluid 
towards  the  surface,  as  long  as  it  exists,  and  nothing  will  impede  the 
condensation  of  the  redundant  fluid  there,  until  it  is  exhausted  from  the 
neighbourhood  of  the  centre.  In  the  same  manner  it  may  be  shown,  that 
if  there  be  a  deficiency  of  fluid,  it  will  be  only  in  the  external  parts,  the 
central  parts  remaining  always  in  a  state  of  neutrality  :  and  since  the 
quantity  of  electric  fluid  taken  away  from  a  body,  in  any  common  experi- 
ment, bears  but  a  very  small  proportion  to  the  whole  that  it  contains,  the 
deficiency  will  also  be  found  in  a  very  small  portion  of  the  sphere,  next  to 
its  surface.  And  if,  instead  of  being  spherical,  the  body  be  of  any 
other  form,  the  effects  of  electricity  will  still  be  principally  confined  to 
its  surface.  This  proposition  was  very  satisfactorily  investigated  by  Mr. 
Cavendish  ;*  and  it  was  afterwards  more  fully  shown,  by  Dr.  Gray'st 
experiments,  that  the  capacities  of  different  bodies  for  receiving  electricity, 
depend  much  more  on  the  quantity  of  their  surfaces,  than  on  their  solid 
contents :  thus,  the  conductor  of  an  electrical  machine  will  contain  very 
nearly  or  quite  as  much  electricity  if  hollow  as  if  solid. 

If  two  spheres  be  united  by  a  cylindrical  conducting  substance  of  small 
dimensions,  there  will  be  an  equilibrium,  when  the  actions  of  the  redundant 
fluid  in  the  spheres,  on  the  whole  fluid  in  the  cylinder,  are  equal ;  that  is, 
when  both  the  spheres  have  their  surfaces  electrified  in  an  equal  degree  : 

*  Ph.  Tr.  177G.     See  also  ibid.  1771,  p.  584.  f  Ibid.  1788,  p.  121. 


ON  ELECTRICITY  IN  EQUILIBRIUM.  511 

but  if  the  length  of  the  cylinder  is  considerable,  the  fluid  within  it  can 
only  remain  at  rest  when  the  quantities  of  redundant  fluid  are  nearly  equal 
in  both  spheres,  and  consequently  when  the  density  is  greater  in  the 
smaller.  And  for  a  similar  reason,  in  bodies  of  irregular  forms,  the  fluid 
is  always  most  accumulated  in  the  smallest  parts  ;  and  when  a  conducting 
substance  is  pointed,  the  fluid  becomes  so  dense  at  its  extremity,  as  easily 
to  overcome  the  forces  which  tend  to  retain  it  in  its  situation.  (Plate 
XXXIX.  Fig.  551.)* 

In  this  distribution  we  find  a  very  characteristic  difference  between  the 
pressure  of  the  electric  fluid  and  the  common  hydrostatic  pressure  of 
liquids  or  of  simple  elastic  fluids;  for  these  exert  on  every  surface 
similarly  situated  a  pressure  proportionate  to  its  magnitude ;  but  the 
electric  fluid  exerts  a  pressure  on  small  and  angular  surfaces,  greater,  in 
proportion  to  their  magnitudes,  than  the  pressure  on  larger  parts  :  so  that 
if  the  electric  fluid  were  in  general  confined  to  its  situation  by  the  pressure 
of  the  atmosphere,  that  pressure  might  easily  be  too  weak  to  oppose  its 
escape  from  any  prominent  points.  It  does  not  appear,  however,  that  this 
pressure  is  the  only  cause  which  prevents  the  escape  of  the  electric  fluid  ; 
nor  is  it  certain  that  this  fluid  can  pass  through  a  perfect  vacuum, 
although  it  has  not  yet  been  proved,  that  a  body  placed  in  a  vacuum  is 
perfectly  insulated.  Whatever  the  resistance  may  be,  which  prevents  the 
dissipation  of  electricity,  it  is  always  the  more  easily  overcome,  as  the 
electrified  substance  is  more  pointed,  and  as  the  point  is  more  promi- 
nent ;  and  even  the  presence  of  dust  is  often  unfavourable  to  the  success 
of  electrical  experiments,  on  account  of  the  great  number  of  pointed  termi- 
nations which  it  affords. 

The  general  effect  of  electrified  bodies  on  each  other,  if  their  bulk  is 
small  in  comparison  with  their  distance,  is,  that  they  are  mutually  repelled 
when  in  similar  states  of  electricity,  and  attracted  when  in  dissimilar  states. 
This  is  a  consequence  immediately  deducible  from  the  mutual  attraction  of 
redundant  matter  and  redundant  fluid,  and  from  the  repulsion  supposed  to 
exist  between  any  two  portions  either  of  matter  or  of  fluid,  and  it  may 
also  easily  be  confirmed  by  experimental  proof.  A  neutral  body,  if  it  were 
a  perfect  nonconductor,  would  not  be  affected  either  way  by  the  neighbour- 
hood of  an  electrified  body  :  for  while  the  whole  matter  contained  in  it 
remains  barely  saturated  with  the  electric  fluid,  the  attractions  and  repul- 
sions balance  each  other.  But  in  general,  a  neutral  body  appears  to  be 
attracted  by  an  electrified  body,  on  account  of  a  change  of  the  disposition 
of  the  fluid  which  it  contains,  upon  the  approach  of  a  body  either 
positively  or  negatively  electrified.  The  electrical  affection  produced  in 
this  manner,  without  any  actual  transfer  of  the  fluid,  is  called  induced 
electricity. 

When  a  body  positively  electrified  approaches  to  a  neutral  body,  the 
redundancy  of  the  fluid  expels  a  portion  of  the  natural  quantity  from  the 

*  On  charge  and  distribution  consult  Winkler,  Electr.  Kraft  des  Wassers,  Leipz. 
1746.     Beccaria,  Ph.  Tr.  1767,  p.  297.     Achard,  Hist,  et  Mem.  de  Berlin,  1780, 
*  p.  47.     Coulomb.  Hist,  et  Mem.   1785,  p.  612;  1786,  p.  67;  1787,  p.  421 ;  and 
the  Analytical  investigations  of  Poisson,  Mem.  de  1'Institut,  1811,  1,  163,  274  ;  and 
,  Essay,  4to,  Netting.  1828. 


512  LECTURE  LIU. 

nearest  parts  of  the  neutral  body,  so  that  it  is  accumulated  at  the  opposite 
extremity  ;  while  the  matter,  which  is  left  deficient,  attracts  the  redundant 
fluid  of  the  first  hody,  in  such  a  manner  as  to  cause  it  to  be  more  con- 
densed in  the  neighbourhood  of  the  second  than  elsewhere  ;  and  hence  the 
fluid  of  this  body  is  driven  still  further  off,  and  all  the  effects-  are  re- 
doubled. The  attraction  of  the  redundant  fluid  of  the  electrified  body  for 
the  redundant  matter  of  the  neutral  body,  is  stronger  than  its  repulsion 
for  the  fluid  which  has  been  expelled  from  it,  in  proportion  as  the  square 
of  the  mean  distance  of  the  matter  is  smaller  than  that  of  the  mean  dis- 
tance of  the  fluid  :  so  that  in  all  such  cases  of  induced  electricity,  an 
attraction  is  produced  between  the  bodies  concerned.  And  a  similar 
attraction  will  happen,  under  contrary  circumstances,  when  a  neutral 
body  and  a  body  negatively  electrified,  approach  each  other. 

The  state  of  induced  electricity  may  be  illustrated  by  placing  a  long 
conductor  at  a  little  distance  from  an  electrified  substance,  and  directed 
towards  it ;  and  by  suspending  pith  balls  or  other  light  bodies  from  it,  in 
pairs,  at  different  parts  of  its  length  :  these  will  repel  each  other,  from 
being  similarly  electrified,  at  the  two  ends,  which  are  in  contrary  states 
of  electricity,  while  at  a  certain  point  towards  the  middle,  they  will 
remain  at  rest,  the  conductor  being  here  perfectly  neutral.  It  was 
from  the  situation  of  this  point  that  Lord  Stanhope*  first  inferred  the  true 
law  of  the  electric  attractions  and  repulsions,  although  Mr.  Cavendish^ 
had  before  suggested  the  same  law  as  the  most  probable  supposition. 

The  attraction  thus  exerted  by  an  electrified  body  upon  neutral  sub- 
stances, is  strong  enough,  if  they  are  sufficiently  light,  to  overcome  their 
gravitation,  and  to  draw  them  up  from  a  table  at  some  little  distance : 
upon  touching  the  electrified  body,  if  it  is  a  conductor,  they  receive  a 
quantity  of  electricity  from  it,  and  are  again  repelled,  until  they  are 
deprived  of  their  electricity  by  contact  with  some  other  substance,  which, 
if  sufficiently  near  to  the  first,  is  usually  in  a  contrary  state,  and  there- 
fore renders  them  still  more  capable  of  returning,  when  they  have  touched 
it,  to  the  first  substance,  in  consequence  of  an  increased  attraction,  assisted 
also  by  a  new  repulsion.  This  alternation  has  been  applied  to  the  con- 
struction of  several  electrical  toys  ;  a  little  hammer,  for  example,  has  been 
made  to  play  between  two  bells  ;  and  this  instrument  has  been  employed 
for  giving  notice  of  any  change  of  the  electrical  state  of  the  atmosphere. 
The  repulsion,  which  takes  place  between  two  bodies,  in  a  similar  state  of 
electricity,  is  the  cause  of  the  currents  of  air  which  always  accompany  the 
discharge  of  electricity,  whether  negative  or  positive,  from  pointed  sub- 
stances ;  each  particle  of  air,  as  soon  as  it  has  received  its  electricity  from 
the  point,  being  immediately  repelled  by  it ;  and  this  current  has  also  been 
suppossd  to  facilitate  the  escape  of  the  electricity,  by  bringing  a  continual 
succession  of  particles  not  already  overcharged. 

If  two  bodies  approach  each  other,  electrified  either  positively  or 
negatively  in  different  degrees,  they  will  either  repel  or  attract  each  other, 
according  to  their  distance  :  when  they  are  very  remote,  they  exhibit  a 

*  Lord  Mahon's  Principles  of  Electr.  4to,  Lond.  1779.  * , 

f  On  the  Principal  Phenomena  of  Electr.  Ph.  Tr.  1771,  p.  584. 


ON  ELECTRICITY  IN  EQUILIBRIUM.  513 

repulsive  force,  but  when  they  are  within  a  certain  distance,  the  effects  of 
induced  electricity  overcome  the  repulsion  which  would  necessarily  take 
place,  if  the  distribution  of  the  fluid  remained  unaltered  by  their  mutual 
influence. 

When  a  quantity  of  the  electric  fluid  is  accumulated  on  one  side  of  a 
non-conducting  substance,  it  tends  to  drive  off  the  fluid  from  the  other 
side  ;  and  if  this  fluid  is  suffered  to  escape,  the  remaining  matter  exerts 
its  attraction  on  the  fluid  which  has  been  imparted  to  the  first  side,  and 
allows  it  to  be  accumulated  in  a  much  greater  quantity  than  could  have 
existed  in  an  equal  surface  of  a  conducting  substance.  In  this  state,  the 
body  is  said  to  be  charged ;  and  for  producing  it  the  more  readily,  each 
surface  is  usually  coated  with  a  conducting  substance,  which  serves  to 
convey  the  fluid  to  and  from  its  different  parts  with  convenience.  The 
thinner  any  substance  is,  the  greater  quantity  of  the  fluid  is  required  for 
charging  it  in  this  manner,  so  as  to  produce  a  given  tension,  or  tendency  to 
escape  :  but  if  it  be  made  too  thin,  it  will  be  liable  to  break,  the  attractive 
force  of  the  fluid  for  the  matter  on  the  opposite  side  overcoming  the 
cohesion  of  the  substance,  and  perhaps  forcing  its  way  through  the  tem- 
porary vacuum  which  is  formed. 

When  a  communication  is  made  in  any  manner  by  a  conducting  sub- 
stance between  the  two  coatings  of  a  charged  plate  or  vessel,  the  equili- 
brium is  restored,  and  the  effect  is  called  a  shock.  If  the  coatings  be 
removed,  the  plate  will  still  remain  charged,  and  it  may  be  gradually  dis- 
charged by  making  a  communication  between  its  several  parts  in  suc- 
cession, but  it  cannot  be  discharged  at  once,  for  want  of  a  common  con- 
nexion :  so  that  the  presence  of  the  coating  is  not  absolutely  essential  to 
the  charge  and  discharge  of  the  opposite  surfaces.  Such  a  coated  substance 
is  most  usually  employed  in  the  form  of  a  jar.  Jars  were  formerly  filled 
with  water,  or  with  iron  filings ;  the  instrument  having  been  principally 
made  known  from  the  experiments  of  Musschenbroek  and  others  at 
Leyden,  it  was  called  the  Leyden  phial ;  but  at  present  a  coating  of  tin 
foil  is  commonly  applied  on  both  sides  of  the  jar,  leaving  a  sufficient  space 
at  its  upper  part,  to  avoid  the  spontaneous  discharge,  which  would  often 
take  place  between  the  coatings,  if  they  approached  too  near  to  each  other ; 
and  a  ball  is  fixed  to  the  cover,  which  has  a  communication  with  the 
internal  coating,  and  by  means  of  which  the  jar  is  charged,  while  the 
external  coating  is  allowed  to  communicate  with  the  ground.  A  collection 
of  such  jars  is  called  a  battery,  and  an  apparatus  of  this  kind  may  be 
made  so  powerful,  by  increasing  the  number  of  jars,  as  to  exhibit  many 
striking  effects  by  the  motion  of  the  electric  fluid,  in  its  passage  from  one 
to  the  other  of  the  surfaces. 

The  conducting  powers  of  different  substances  are  concerned,  not  only 
in  the  facility  with  which  the  motions  of  the  electric  fluid  are  directed  into 
a  particular  channel,  but  also  in  many  cases  of  its  equilibrium,  and  par- 
ticularly in  the  properties  of  charged  substances,  which  depend  on  the 
resistance  opposed  by  nonconductors  to  the  ready  transmission  of  the  fluid. 
These  powers  may  be  compared,  by  ascertaining  the  greatest  length  of 
of  the  substances  to  be  examined,  through  which  a  spark  or  a  shock 

2L 


514  LECTURE  LIII. 

will  take  its  course,  in  preference  to  a  given  length  of  air,  or  of  any  other 
standard  of  comparison.  The  substances,  which  conduct  electricity  the 
most  readily,  are  metals,  well  burnt  charcoal,  animal  bodies,  acids,  saline 
liquors,  water,  and  very  rare  air.  The  principal  nonconductors  are  glass, 
ice,  gems,  dry  salts,  sulfur,  amber,  resins,  silk,  dry  wood,  oils,  dry  air  of 
the  usual  density,  and  the  barometrical  vacuum.  Heat  commonly  increases 
the  conducting  powers  of  bodies  ;  a  jar  of  glass  may  be  discharged  by  a 
moderate  heat,  and  liquid  resins  are  capable  of  transmitting  shocks, 
although  they  are  by  no  means  good  conductors :  it  is  remarkable  also  that 
a  jar  may  be  discharged  by  minute  agitation,  when  it  is  caused  to  ring  by 
the  friction  of  the  finger.  It  has  been  observed  that,  in  a  great  variety  of 
cases,  those  substances,  which  are  the  best  conductors  of  heat,  afford  also 
the  readiest  passage  to  electricity;  thus,  copper  conducts  heat  more 
rapidly,  and  electricity  more  readily,  than  iron,  and  platina  less  than 
almost  any  other  metal ;  glass  also  presents  a  considerable  resistance  to  the 
transmission  of  both  these  influences.  The  analogy  is,  however,  in  many 
respects  imperfect,  and  it  affords  us  but  little  light,  with  regard  either  to 
the  nature  of  heat,  or  to  that  of  the  electric  fluid. 


LECT.  LIII.— ADDITIONAL  AUTHORITIES. 

Treatises  on  Electricity. — Mortensson,  De  Electr.  4to,  Upsal,  1740.  Desa- 
guliers,  A  Dissertation  concerning  Electr.  1742.  Winckler's  Gedanke  von  der 
Elektr.  Leipz.  1744.  Eigenschaften  der  Elektr.  Materie,  1745.  Bose,  Recherches 
sur  la  Cause  de  1'Electr.  4to,  Berlin,  1745.  Tentamina  Electr.  4to,  Wittemb.  1747. 
Waitz,  Abhand.  von  der  Elektr.  4to,  Berlin,  1745.  Piderit,  De  Electr.  Marb.  1745. 
Watson's  Exp.  and  Obs.  with  Sequel,  1746.  Miiller,  Ursachund  Nutzen  der  Elektr. 
1746.  Nollet,  Essai  sur  1'Electr.  12mo,  Paris,  1746.  Recherches  sur  do.  4to, 
1749.  Lettres  sur  do.  12mo,  1753.  Martin  on  Electr.  Bath,  1748.  Jallabert  sur 
1'Electr.  1749.  Boulanger,  Traite  de  I7 Electr.  12mo,  1750.  Secondat,  Obser- 
vations Physiques,  12mo,  1750.  Verrati  sur  1'Electr.  12mo,  Montp.  1750. 
Buia,  Electr.  Effectuum  Explicatio,  1751.  Franklin,  Exp.  and  Obs.  4to,  1751- 
54.  Navarro,  Physica  Electr.  Madrid,  1752.  Klingenstierna,  Electr.  Stockholm, 
1755.  Beccaria,  Lettere  dell'  Elettr.  fol.  Bolog.  1758  (tr.),  Lond.  1776;  Ex- 
perimenta,  4to,  Turin,  1772.  Egelin,  De  Electr.  4to,  Utrecht,  1759.  Wesley's 
Electr.  made  plain,  12mo,  1760.  Saussure,  De  Electr.  Geneve,  1766.  Lullin, 
De  Electr.  Geneve,  1766.  Hartmann's  Versuche  in  leeren  Ratime,  Hanov. 
1766.  Priestley's  Introduction  to  Electr.  1769.  Ferguson's  Introduction  to 
Electr.  1771.  Sigaud  de  la  Fond,  Traite  de  1'Electr.  12mo,  1771.  Precis  des 
Phenomenes  Electr.  1781.  Jacquet,  Precis  de  1'Electr.  Vienna,  1775.  Gross, 
Elektrische  Pauschen,  Leipz.  1776.  Dubois,  Lettres  sur  1'Electr.  1776.  Bar- 
letti  (R.  S.)  1771.  Socin,  Anfangsgriinde  der  Elektr.  Hanau,  1777.  Gallitzin 
sur  1'Electr.  4to,  Petersb.  1778.  Lord  Mahon's  Principles  of  Electr.  4to,  1779. 
Wilson's  Short  View  of  Electr.  4to,  1780.  Lyons's  New  System  of  Electr.  4to, 

1780.  Marat,  Recherches  sur  1'Electr.  1782.         Lacepede  sur  1'Electr.  2  vols. 

1781.  Cuthbertson,  Van  der  Elektr.    Amst.    1782-94.     D'Inarre,   Naturlehre, 
Frankf.  1783.     Adams,  Essay  on  Electr.  1784.     Donndorff's  Lehre  von  der  Elektr. 
Erf.  1784.     Tressan  sur  la  Fluide  Electr.   2  vols.  1786.     Priestley's  Introd.  to 
Electr.  1787.     Beck,  Lehre  von  Electr.  1787.    Langenbucher's  Elektr.  Augs.  1788. 
Bennet's  Experiments,  Derby,  1789.    Briefe  iiber  die  Elektr.  von  C.  L.  Leipz.  1789. 
Brook  on  Electr.  1790.     Peart  on  do.  Gainsborough,  1791.     Lampadius,  Ueber 
Electr.  und  Warme,  Berlin,   1793.      Cavallo's   Electr.  3  vols.  1795.      Morgan's 
Lectures    on  Electr.  2  vols.  12mo.      Saxtorph,  Darstellung  der  Elektr.  2  vols. 
Copenh.  1803.     Deluc,  Traite  Elementaire  sur  le  Fluide  Electro-galvanique,  Milan, 
1804.     Sammlung  Elektr.  Spielwerke,  Niirnb.  1804.     Robison's  Mechanical  Phi- 
losophy.    Singer's  Elements  of  Electr.  1814.     Galle,  Beitrage  zur  Erweiterung  der 
Elektr.  2  vols.  Salzb.  1816.     Adams's  Electricity,  4to,  1823.     Roslin,  Priifungvler 


ON  ELECTRICITY  IN  EQUILIBRIUM.  515 

Electr.  Ulm,  1823.  Leschan,  Grundziige  der  Reinen  Elektr.  1826.  Farrar,  Ele- 
ments of  Electr.  Camb.  N.  E.  1826.  Fechner,  Lehrbuch  der  Galvanismus,  Leipz. 
1829.  Murphy's  (Mathematical)  Principles  of  Electr.  1833.  Becquerel,  Traite 
Experimentale  de  1' Electr.  et  du  Magnetisme,  7  vols.  Paris,  1834.  Nobili,  Nuovi 
Trattati,  Modena,  1838.  Roget's  Electr.  (Lib.  of  Useful  Knowledge).  Thomson's 
Heat  and  Electr.  1840.  Sturgeon,  Lect.  on  Electr.  1842.  Lardner  and  Walker's 
Electricity,  in  Cab.  Cyc.  2  vols.  Noad's  Electricity  (new  ed.)  1844. 

Memoirs. — Hauksbee's  Physico-Mech.  Experiments,  4to,  1709,  and  Ph.  Tr.  1706, 
p.  2277;  1707,  pp.2313,  2372;  1708,  pp.  82,  87;  1709,  pp.  391,  439;  1711, 
p.  328.  Gray's  Exp.  ibid.  1720,  p.  104;  1731,  p.  18;  1732,  p.  397.  Dufay's, 
Hist,  et  Mem.  1733,  pp.  23,  73,  233,  457 ;  1734,  pp.  341,  503  ;  1737,  pp.  86,  307. 
Schilling,  Mis.  fieri.  1734,  p.  334.  Desaguliers,  Ph.  Tr.  1739,  pp.  186,  200  ; 
1741,  p.  634;  1742,  pp.  14,  140.  Bose,  Hist,  et  Mem.  1743,  H.  45.  Nollet, 

ibid.   1745 1766  (various  memoirs).     Watson,   Ph.  Tr.  1745,  p.  481  ;  1747, 

pp.  388,  695,  704  ;  1751,  pp.  202,  362.  Hollmann,  ibid.  1745,  p.  239.  Lemonnier, 
ibid.  1746,  p.  290.  Dutour,  Mem.  des  Sav.  Etr.  i.  345,  ii.  246,  516,  537,  iii.  244. 
Wilson,  Ph.  Tr.  1753,  p.  347  ;  1763,  p.  436.  Canton,  ibid.  1753,  p.  350  ;  1754, 
p.  780.  Leroy,  Hist,  et  Mem.  1753,  p.  447,  H.  18  ;  1755,  p.  264,  H.  20. 
Franklin,  Ph.  Tr.  1755,  pp.  300,305  ;  1760,  p.  525.  Aepinus,  Hist,  et  Mem.  de 
Berlin,  1756.  Nov.  Com.  Petr.  vii.  277.  Delaval  on  the  Influence  of  Temp.  Ph. 
Tr.  1759,  p.  83  ;  1761,  353;  with  Canton's  Remarks,  1762,  p.  457.  Beccaria, 
1760,  pp.  514,  525.  Priestley,  ibid.  1769,  pp.  57,  63;  1770,  p.  192.  Cigna, 
Mis.  Taur.  ii.  31,  77,  iii.  31,  v.  I.  97.  Brydone,  Ph.  Tr.  1773,  p.  163.  Gallitzin, 
Acta  Petr.  i.  II.  H.  25.  Achard,  Jour,  de  Phy.  xix.  417,  xxv.  429.  Van  Marum, 
ibid.  xxxi.  343;  1788,  p.  148;  Experiences,  2  vols.  4to,  Haarlem,  1787,  1795. 
Gilbert's  Jour.  i.  239,  256,  x.  121.  Vassali  and  Zimmermann,  Mem.  della  Soc. 
Ital.  iv.  264.  Nicholson,  Ph.  Tr.  1789,  p.  265.  Deluc,  Jour,  de  Phy.  xxxvi.  450. 
Von  Arnim,  Gilb.  Jour.  v.  33,  vi.  116.  Remer,  ibid.  viii.  323.  Clos,  Jour,  de 
Phy.  liv.  316.  Wollaston,  Ph.  Tr.  1801,  p.  427.  Snow  Harris  on  the  Elementary 
Laws  of  Electr.  Ph.  Tr.  1834  ;  1836,  p.  417  ;  1839,  p.  215  ;  1842,  p.  165.  Riess, 
Repert.  der  Phys.  ii.  Pogg.  Ann.  xl.  321,  xliii.  47,  xlv.  1,  liii.  1.  Pfaff,  ibid.  xliv. 
332.  PouiUet  sur  1'Electr.  des  Fluides  Elastiques,  Ann.  de  Ch.  xxxv.  401. 
Knockerhauer,  Ueber  die  Gebundene  Elektr.  Pogg.  Ann.  xlvii.  444,  Iviii.  211,  391. 

Conducting  Powers.  —  Plot's  Catalogue  of  Electrics,  Ph.  Tr.  1698,  p.  384. 
Gray  on  the  Electr.  of  Water,  ibid.  1732,  p.  227.  Desaguliers,  ibid.  1741,  p.  661. 
Watson,  ibid.  1746,  p.  41.  Mazeas,  ibid.  1753,  p.  377.  Ammersin,  De  Electr. 
Lignorum,  24mo,  Luzern.  1754.  Priestley  on  the  Conducting  Power  of  Charcoal, 
ibid.  1770,  p.  211.  Harley  on  Vapour,  ibid.  1774,  p.  389  ;  on  Glass,  1778,  p.  1049. 
Cavendish,  ibid.  1776.  Achard,  Jour,  de  Phy.  xv.  117,  xxii.  245.  Bergman  on  the 
Conducting  Power  of  Water,  ibid.  xiv.  192.  Cavallo,  Ph.  Tr.  1783,  p.  495,  and 
Electricity.  Morgan  on  a  Vacuum,  ibid. 1785,  p.  272.  Volta,  Gilb.  Ann.  xiv.  257. 
Tremery,  Bulletin  de  la  Soc.  Philom.  No.  19.  Erman,  Gilb.  Jour.  xi.  143.  Snow 
Harris,  Ph.  Tr.  1827,  p.  18. 

Theory  of  Electricity.— Gordon,  Versuch  einer  Erklarung  der  Elektr.  Erf.  1745. 
Rosenberg,  Von  der  Ursachen  der  Elektr.  Bresl.  1745.  Werenberg,  Gedanken 
yon  der  Elektr.  1745.  Kratzenstein,  Theoria  Electr.  4to,  Hal.  1746.  Ellicott, 
Ph.  Tr.  1748,  p.  195.  J.  Euler,  De  Causa  Electr.  4to,  Petersb.  1755  ;  Hist, 
et  Mem.  de  Berlin,  1757,  p.  125.  Wilcke,  Dissertatio  Physica  de  Electr.  con- 
trariis,  4to,  Rostock,  1757  ;  Schwed.  Abhand.  xxxix.  68.  Symmer,  Ph.  Tr. 
1759,  p.  340.  Cigna  on  the  Analogy  of  Magnetism  and  Electr.  Mis.  Taur.  i. 
Aepinus,  Tentamen  Theorise  Electr.  et  Magnet.  4to,  Petersb.  1759  ;  Nov.  Com. 
Petr.  x.  296.  Dutour  sur  la  Matiere  Electr.  12mo,  Paris,  1760.  Bergmann 
on  the  Existence  of  Two  Fluids,  Ph.  Tr.  1764,  p.  84.  Bauer,  Theorie  der 
Elektr.  1770.  Herbert,  Theoria  Phenom.  Electr.  Vienna,  1778.  Euler's  Letters, 
ii.  34.  Barletti,  Mem.  de  la  Soc.  Ital.  i.  1,  ii.  1,  iv.  304,  vii.  444.  Coulomb, 
Hist,  et  Mem.  1784,  &c.  Haiiy,  Exposition  Theorique,  1787.  Biot,  Bulletin 
de  la  Soc.  Philom.  No.  51.  Tremery,  ibid.  No.  63.  Schrader,  Versuch  einer  neuen 
Theorie,  Altona,  1796.  Gren,  Grundriss  der  Naturlehre,  Halle,  1797,  sec.  1408. 
Heidmann,  Theorie  der  Elektr.  2  vols.  Wien.  1799.  Ritter,  Das  Elektr.  System 
der  Korper,  Leipz.  1805.  Winterl,  Gehlen  Jour.  vi.  1,  201.  Oersted,  Ansichtder 
Naturgesetze,  Berl.  1802.  Parrot,  Grundriss  der  Theoretischen  Physik,  ii.  3. 
Becquerel,  Annales  de  Chimie,  xlvi.  265,  337,  xlvii.  113,  xlix.  131.  Avogadro,  Jour, 
de  Phys.  Ixiii.  450.  Faraday's  Experimental  Researches  in  Electricity,  Ph.  Tr.  1832 
..f'f.  Republished,  2  vols.  1839,  1844. 

2  L2 


516 


LECTURE    LIV. 


ON  ELECTRICITY  IN  MOTION. 

THE  manner  in  which  the  electric  fluid  is  transferred  from  one  body  to 
another,  the  immediate  effects  of  such  a  transfer,  the  causes  which  origi- 
nally disturb  the  equilibrium  of  electricity,  and  the  practical  methods, 
by  which  all  these  circumstances  are  regulated  and  measured,  require  to  be 
considered  as  belonging  to  the  subject  of  electricity  in  motion.  Among 
the  modes  of  excitation  by  which  the  equilibrium  is  originally  disturbed, 
one  of  the  most  interesting  is  the  galvanic  apparatus,  which  has  been  of  late 
years  a  very  favourite  subject  of  popular  curiosity,  and  of  which  the  theory 
and  operation  will  be  briefly  examined,  although  the  subject  appears 
rather  to  belong  to  the  chemical  than  to  the  mechanical  doctrine  of 
electricity. 

The  progressive  motion  of  the  electric  fluid  through  conducting  sub- 
stances is  so  rapid,  as  to  be  performed  in  all  cases  without  a  sensible 
interval  of  time.  It  has  indeed  been  said,  that  when  very  weakly  excited, 
and  obliged  to  pass  to  a  very  great  distance,  a  perceptible  portion  of 
time  is  actually  occupied  in  its  passage  ;  but  this  fact  is  somewhat 
doubtful,  and  attempts  have  been  made  in  vain,  to  estimate  the  interval 
employed  in  the  transmission  of  a  shock  through  several  miles  of  wire. 
We  are  not  to  imagine  that  the  same  particles  of  the  fluid,  which  enter 
at  one  part,  pass  through  the  whole  conducting  substance,  any  more  than 
that  the  same  portion  of  blood,  which  is  thrown  out  of  the  heart  in  each 
pulsation,  arrives  at  the  wrist,  at  the  instant  that  the  pulse  is  felt  there. 
The  velocity  of  the  transmission  of  a  spark  or  shock  far  exceeds  the  actual 
velocity  of  each  particle,  in  the  same  manner  as  the  velocity  of  a  wave 
exceeds  that  of  the  particles  of  water  concerned  in  its  propagation ;  and 
this  velocity  must  depend  both  on  the  elasticity  of  the  electric  fluid,  and 
on  the  force  with  which  it  is  confined  to  the  conducting  substance.  If  this 
force  were  merely  derived  from  the  pressure  of  the  atmosphere,  we 
might  infer  the  density  of  the  fluid  from  the  velocity  of  a  spark  or  shock, 
compared  with  that  of  sound ;  or  we  might  deduce  its  velocity  from  a 
determination  of  its  density.  It  has  been  supposed,  although  perhaps 
somewhat  hastily,  that  the  actual  velocity  is  nearly  equal  to  that  of 
light* 

When  a  conducting  substance  approaches  another,  which  is  electrified, 
the  distribution  of  the  electric  fluid  within  it  is  necessarily  altered  by 
induction,  before  it  receives  a  spark,  so  that  its  remoter  extremity  is 
brought  into  a  state  similar  to  that  of  the  first  body :  hence  it  happens 
that  when  the  spark  passes,  it  produces  less  effect  at  the  remoter  end  of 
the  substance,  while  the  part  presented  to  the  electrified  body  is  most 

*  Watson's  Exp.  to  determine  the  Celerity  of  Electricity,  Ph.  Tr.  1748,  pp.  49, 
491.  Wheatstone,  ibid.  1834,  p.  583. 


ON  ELECTRICITY  IN  MOTION.  517 

affected,  on  account  of  its  sudden  change  to  an  opposite  state.  But  if 
both  ends  approach  bodies  in  opposite  states  of  electricity,  they  will  both 
be  strongly  affected  when  the  shock  takes  place,  while  the  middle  of  the 
circuit  undergoes  but  little  change. 

The  manner  in  which  the  electric  fluid  makes  its  way,  through  a  more 
or  less  perfect  nonconductor,  is  not  completely  understood  :  it  is  doubtful 
whether  the  substance  is  forced  away  on  each  side,  so  as  to  leave  a  vacuum 
for  the  passage  of  the  fluid,  or  whether  the  newly  formed  surface  helps  to 
guide  it  in  its  way  ;  and  in  some  cases  it  has  been  supposed  that  the 
gradual  communication  of  electricity  has  rendered  the  substance  more 
capable  of  conducting  it,  either  immediately,  or,  in  the  case  of  the  air,  by 
first  rarefying  it.  However  this  may  be,  the  perforation  of  a  jar  of  glass 
by  an  overcharge,  and  that  of  a  plate  of  air  by  a  spark,  appear  to  be 
effects  of  the  same  kind,  although  the  charge  of  the  jar  is  principally  con- 
tained in  the  glass,  while  the  plate  of  air  is  perhaps  little  concerned  in  the 
distribution  of  the  electricity. 

The  actual  direction  of  the  electric  current  has  not  in  any  instance  been 
fully  ascertained,  although  there  are  some  appearances  which  seem  to 
justify  the  common  denominations  of  positive  and  negative.  Thus,  the 
fracture  of  a  charged  jar  of  glass,  by  spontaneous  explosion,  is  well  defined 
on  the  positive,  and  splintered  on  the  negative  side,  as  might  be  expected 
from  the  passage  of  a  foreign  substance  from  the  former  side  to  the  latter  ; 
and  a  candle,  held  between  a  positive  and  a  negative  ball,  although  it 
apparently  vibrates  between  them,  is  found  to  heat  the  negative  ball  much 
more  than  the  positive.  We  cannot,  however,  place  much  dependence  on 
any  circumstance  of  this  kind,  for  it  is  doubtful  whether  any  current  of 
the  fluid,  which  we  can  produce,  possesses  sufficient  momentum  to  carry 
with  it  a  body  of  sensible  magnitude.  It  is  in  fact  of  little  consequence  to 
the  theory,  whether  the  terms  positive  and  negative  be  correctly  applied, 
provided  that  their  sense  remain  determined  ;  and  that,  like  positive  and 
negative  quantities  in  mathematics,  they  be  always  understood  of  states 
which  neutralise  each  other.  The  original  opinion  of  Dufay,*  of  the 
existence  of  two  distinct  fluids,  a  vitreous  and  a  resinous  electricity,  has  at 
present  few  advocates,  although  some  have  thought  such  a  supposition 
favoured  by  the  phenomena  of  the  galvanic  decomposition  of  water. 

When  electricity  is  simply  accumulated  without  motion,  it  does  not 
appear  to  have  any  effect,  either  mechanical,  chemical,  or  physiological,  by 
which  its  presence  can  be  discovered ;  the  acceleration  of  the  pulse,  and 
the  advancement  of  the  growth  of  plants,  which  have  been  sometimes 
attributed  to  it,  have  not  been  confirmed  by  the  most  accurate  experi- 
ments.t  An  uninterrupted  current  of  electricity,  through  a  perfect 
conductor,  would  perhaps  be  also  in  every  respect  imperceptible,  since  the 
best  conductors  appear  to  be  the  least  affected  by  it.  Thus,  if  we  place 

*  Ph.  Tr.  1733,  xxxviii.  258.     Hist,  et  Mem.  1733,  p.  457. 
t  Consult  Kies  et  Koestlin,  DeEffectibus  Electr.  4to,  Tubing.  1775.   Ingenhousz, 
Versuche   mit   Pflanzen,   3  vols.  Vienna,  1778-90.     Bertholon,    do.  Leipz.   1785. 

k,  De  1' Application  de  1'Electr.  4to,  Amst.  1788.     Van  Marum,  Proefne- 

met  Teylers  Electrisir  Maschine,  4to,  Haarlem,  1795. 


518  LECTURE  LIV. 

our  hand  on  the  conductor  of  an  electrical  machine,  the  electricity  will 
pass  off  continually  through  the  body,  without  exciting  any  sensation.  A 
constant  stream  of  galvanic  electricity,  passing  through  an  iron  wire  is, 
however,  capable  of  exciting  a  considerable  degree  of  heat,  and  if  it  be 
transmitted  through  the  hands  of  the  operator,  it  will  produce  a  slight 
numbness,  although  in  general  some  interruption  of  the  current  is  neces- 
sary in  order  to  furnish  an  accumulation  sufficient  to  produce  sensible 
effects  ;  and  such  an  interruption  may  even  increase  the  effect  of  a  single 
spark  or  shock  ;  thus,  gunpowder  is  more  readily  fired  by  the  discharge  of 
a  battery  passing  through  an  interrupted  circuit,  than  through  a  series  of 
perfect  conductors. 

The  most  common  effect  of  the  motion  of  the  electric  fluid  is  the  produc- 
tion of  light.  Light  is  probably  never  occasioned  by  the  passage  of  the 
fluid  through  a  perfect  conductor;  for  when  the  discharge  of  a  large 
battery  renders  a  small  wire  luminous,  the  fluid  is  not  wholly  confined  to 
the  wire,  but  overflows  a  little  into  the  neighbouring  space.  There  is 
always  an  appearance  of  light,  whenever  the  path  of  the  fluid  is  inter- 
rupted by  an  imperfect  conductor  ;  nor  is  the  apparent  contact  of  conduct- 
ing substances  sufficient  to  prevent  it,  unless  they  are  held  together  by  a 
considerable  force ;  thus,  a  chain,  conveying  a  spark  or  shock,  appears 
luminous  at  each  link,  and  the  rapidity  of  the  motion  is  so  great,  that  we 
can  never  observe  any  difference  in  the  times  of  the  appearance  of  the  light 
in  its  different  parts ;  so  that  a  series  of  luminous  points,  formed  by  the 
passage  of  the  electric  fluid,  between  a  string  of  conducting  bodies,  repre- 
sents at  once  a  brilliant  delineation  of  the  whole  figure  in  which  they  are 
arranged.  A  lump  of  sugar,  a  piece  of  wood,  or  an  egg,  may  easily  be 
made  luminous  in  this  manner  ;  and  many  substances,  by  means  of  their 
properties  as  solar  phosphori,  retain  for  some  seconds  the  luminous 
appearance  thus  acquired.  Even  water  is  so  imperfect  a  conductor,  that  a 
strong  shock  may  be  seen  in  its  passage  through  it ;  and  when  the  air  is 
sufficiently  moistened  or  rarefied  to  become  a  conductor,  the  track  of  the 
fluid  through  it  is  indicated  by  streams  of  light,  which  are  perhaps  derived 
from  a  series  of  minute  sparks  passing  between  the  particles  of  water  or  of 
rarefied  air.  When  the  air  is  extremely  rare,  the  light  is  greenish  ;  as  it 
becomes  more  dense,  the  light  becomes  blue,  and  then  violet,  until  it 
no  longer  conducts.  The  appearance  of  the  electrical  light  of  a  point 
enables  us  to  distinguish  the  nature  of  the  electricity  with  which  it  is 
charged ;  a  pencil  of  light,  streaming  from  the  point,  indicating  that  its 
electricity  is  positive,  while  a  luminous  star,  with  few  diverging  rays, 
shows  that  it  is  negative.  The  sparks,  exhibited  by  small  balls,  differently 
electrified,  have  also  similar  varieties  in  their  forms,  according  to  the 
nature  of  their  charges.*  (Plate  XL.  Fig.  552.) 

The  production  of  heat  by  electricity  frequently  accompanies  that  of 
light,  and  appears  to  depend  in  some  measure  on  the  same  circumstances. 
A  fine  wire  may  be  fused  and  dissipated  by  the  discharge  of  a  battery  ; 
and  without  being  perfectly  melted,  it  may  sometimes  be  shortened  or 

*  Consult  Doppelmayer,  Ueber  das  Elektr.  Licht.  1749.  Nairne,  Ph.  Tr.JL777, 
p.  614.  Nicholson,  ibid.  1789,  p.  265.  Davy  on  a  Vacuum,  ibid.  1822,  p.  64rv 


ON  ELECTRICITY  IN  MOTION.  519 

lengthened,  accordingly  as  it  is  loose  or  stretched  during  the  experiment. 
The  more  readily  a  metal  conducts,  the  shorter  is  the  portion  of  it  which 
the  same  shock  can  destroy ;  and  it  has  sometimes  been  found  that  a 
double  charge  of  a  battery  has  been  capable  of  melting  a  quadruple  length 
of  wire  of  the  same  kind.* 

The  mechanical  effects  of  electricity  are  probably  in  many  cases  the 
consequences  of  the  rarefaction  produced  by  the  heat  which  is  excited ; 
thus,  the  explosion  attending  the  transmission  of  a  shock  or  spark  through 
the  air,  may  easily  be  supposed  to  be  derived  from  the  expansion  caused 
by  heat ;  and  the  destruction  of  a  glass  tube,  which  contains  a  fluid  in  a 
capillary  bore,  when  a  spark  is  caused  to  pass  through  it,  is  the  natural 
consequence  of  the  conversion  of  some  particles  of  the  fluid  into  vapour. 
But  when  a  glass  jar  is  perforated,  this  rarefaction  cannot  be  supposed  to 
be  adequate  to  the  effect.  It  is  remarkable  that  such  a  perforation  may  be 
made  by  a  very  moderate  discharge,  when  the  glass  is  in  contact  with  oil 
or  with  sealing  wax ;  and  no  sufficient  explanation  of  this  circumstance 
has  yet  been  given. 

A  strong  current  of  electricity,  or  a  succession  of  shocks  or  sparks, 
transmitted  through  a  substance,  by  means  of  fine  wires,  is  capable  of 
producing  many  chemical  combinations  and  decompositions,  some  of  which 
may  be  attributed  merely  to  the  heat  which  it  occasions,  but  others  are 
wholly  different.  Of  these  the  most  remarkable  is  the  production  of 
oxygen  and  hydrogen  gas  from  common  water,  which  are  usually  extri- 
cated at  once,  in  such  quantities,  as,  when  again  combined,  will  reproduce 
the  water  which  has  disappeared  ;  but  in  some  cases  the  oxygen  appears  to 
be  disengaged  most  copiously  at  the  positive  wire,  and  the  hydrogen  at  the 
negative.t 

When  the  spark  is  received  by  the  tongue,  it  has  generally  a  subacid 
taste  ;  and  an  explosion  of  any  kind  is  usually  accompanied  by  a  smell 
somewhat  like  that  of  sulfur,  or  rather  of  fired  gunpowder.  The  peculiar 
sensation,  which  the  electric  fluid  occasions  in  the  human  frame,  appears 
in  general  to  be  derived  from  the  spasmodic  contractions  of  the  muscles 
through  which  it  passes  ;  although  in  some  cases  it  produces  pain  of  a  dif- 
ferent kind  ;  thus,  the  spark  of  a  conductor  occasions  a  disagreeable 
sensation  in  the  skin,  and  when  an  excoriated  surface  is  placed  in  the 
galvanic  current,  a  sense  of  smarting,  mixed  with  burning,  is  experienced. 
Sometimes  the  effect  of  a  shock  is  felt  most  powerfully  at  the  joints,  on 
account  of  the  difficulty  which  the  fluid  finds  in  passing  the  articulating 
surfaces  which  form  the  cavity  of  the  joints.  The  sudden  death  of  an 
animal,  in  consequence  of  a  violent  shock,  is  probably  owing  to  the  im- 
mediate exhaustion  of  the  whole  energy  of  the  nervous  system.  It  is 
remarkable  that  a  very  minute  tremor,  communicated  to  the  most  elastic 

*  Kinnersley  on  an  Electrical  Air  Thermometer,  and  on  the  Extension  of  Wire, 
Ph.  Tr.  1763,  p.  84.  Nairne  on  Shortening  Wires,  ibid.  1780,  p.  334.  Riess, 
Fogg.  Ann.  xl.  321 ;  xliii.  47  ;  xlv.  1. 

t  Consult  Cavendish,  Ph.  Tr.  1788,  p.  261.  Pearson,  ibid.  1797,  p.  142.  Wol- 
laston,  ibid.  1801,  p.  417.  Davy,  ibid.  1807,  p.  1.  Van  Trostwyk,  Gren's  Jour, 
i*.  130.  Schonbein,  Pogg.  Ann.  1.  616. 


620  LECTURE  LIV. 

parts  of  the  body,  in  particular  to  the  chest,  produces  an  agitation  of  the 
nerves,  which  is  not  wholly  unlike  the  effect  of  a  weak  electricity. 

The  principal  modes,  in  which  the  electric  equilibrium  is  primarily 
destroyed,  are  simple  contact,  friction,  a  change  of  the  form  of  aggrega- 
tion, and  chemical  combinations  and  decompositions.  The  electricity  pro- 
duced by  the  simple  contact  of  any  two  substances  is  extremely  weak,  and 
can  only  be  detected  by  very  delicate  experiments  :  in  general  it  appears 
that  the  substance  which  conducts  the  more  readily,  acquires  a  slight 
degree  of  negative  electricity,  while  the  other  substance  is  positively 
electrified  in  an  equal  degree.  The  same  disposition  of  the  fluid  is  also 
usually  produced  by  friction,  the  one  substance  always  losing  as  much  as 
the  other  gains  ;  and  commonly  although  not  always,  the  worst  conductor 
becomes  positive.  At  the  instant  in  which  the  friction  is  applied,  the 
capacities  or  attractions  of  the  bodies  for  electricity  appear  to  be  altered, 
and  a  greater  or  less  quantity  is  required  for  saturating  them  ;  and  upon 
the  cessation  of  the  temporary  change,  this  redundancy  or  deficiency  is 
rendered  sensible.  When  two  substances  of  the  same  kind  are  rubbed 
together,  the  smaller  or  the  rougher  becomes  negatively  electrified  ;  perhaps 
because  the  smaller  surface  is  more  heated,  in  consequence  of  its  under- 
going more  friction  than  an  equal  portion  of  the  larger,  and  hence  becomes 
a  better  conductor  ;  and  because  the  rougher  is  in  itself  a  better  conductor 
than  the  smoother,  and  may  possibly  have  its  conducting  powers  increased 
by  the  greater  agitation  of  its  parts  which  the  friction  produces.  The  back 
of  a  live  cat  becomes  positively  electrified,  with  whatever  substance  it 
is  rubbed ;  glass  is  positive  in  most  cases,  but  not  when  rubbed  with 
mercury  in  a  vacuum,  although  sealing  wax,  which  is  generally  negative, 
is  rendered  positive  by  immersion  in  a  trough  of  mercury.  When  a  white 
and  a  black  silk  stocking  are  rubbed  together,  the  white  stocking  acquires 
positive  electricity,  and  the  black  negative,  perhaps  because  the  black  dye 
renders  the  silk  both  rougher  and  a  better  conductor. 

Those  substances,  which  have  very  little  conducting  power,  are  some- 
times called  electrics,  since  they  are  capable  of  exhibiting  readily  the 
electricity  which  friction  excites  on  their  surfaces,  where  it  remains  accu- 
mulated, so  that  it  may  be  collected  into  a  conductor ;  while  the  surfaces 
of  such  substances,  as  have  greater  conducting  powers,  do  not  so  readily 
imbibe  the  fluid  from  others  with  which  they  are  rubbed,  since  they  may 
be  supplied  from  the  internal  parts  of  the  substances  themselves,  when 
their  altered  capacity  requires  it;  thus,  glass,  when  heated  to  110°  of 
Fahrenheit,  can  with  difficulty  be  excited,  becoming  an  imperfect  con- 
ductor :  but  a  thin  plate  of  a  conducting  substance,  when  insulated,  may 
be  excited  almost  as  easily  as  an  electric,  commonly  so  called. 

Vapours  are  generally  in  a  negative  state,  but  if  they  rise  from  metallic 
substances,  or  even  from  some  kinds  of  heated  glass,  the  effect  is  uncertain, 
probably  on  account  of  some  chemical  actions  which  interfere  with  it. 
Sulfur  becomes  electrical  in  cooling,  and  wax  candles  are  said  to  be  some- 
times found  in  a  state  so  electrical,  when  they  are  taken  out  of  their 
moulds,  as  to  attract  the  particles  of  dust  which  are  floating  near  them. 
The  tourmalin,  and  several  other  crystallized  stones,  become  electrics^ 


ON  ELECTRICITY  IN  MOTION.  521 

when  heated  or  cooled,  and  it  is  found  that  the  disposition,  assumed  by 
the  fluid,  bears  a  certain  relation  to  the  direction  in  which  the  stone  trans- 
mits the  light  most  readily ;  some  parts  of  the  crystal  being  rendered 
always  positively  and  others  negatively  electrical,  by  an  increase  of 
temperature. 

The  most  remarkable  of  the  phenomena,  attending  the  excitation  of 
electricity  by  chemical  changes,  are  those  which  have  lately  received  the 
appellation  of  galvanic.  Some  of  the  effects  which  have  been  considered 
as  belonging  to  galvanism  are  probably  derived  from  the  electrical  powers 
of  the  animal  body,  and  the  rest  have  been  referred  by  Mr.  Volta,  and 
many  other  philosophers  on  the  continent,  to  the  mere  mechanical  actions 
of  bodies  possessed  of  different  properties  with  regard  to  electricity. 
Thus,  they  have  supposed  that  when  a  circulation  of  the  electric  fluid  is 
produced  through  a  long  series  of  substances  in  a  certain  direction,  the 
differences  of  their  attractions  and  of  their  conducting  powers,  which 
must  remain  the  same  throughout  the  process,  keep  up  this  perpetual 
motion,  in  defiance  of  the  general  laws  of  mechanical  forces.  In  this 
country  it  has  been  generally  maintained,  that  no  explanation  founded  on 
such  principles  could  be  admissible,  even  if  it  were  in  all  other  respects 
sufficient  and  satisfactory,  which  the  mechanical  theory  of  galvanism  cer- 
tainly is  not. 

The  phenomena  of  galvanism  appear  to  be  principally  derived  from  an 
inequality  in  the  distribution  of  the  electric  fluid,  originating  from 
chemical  changes,  and  maintained  by  means  of  the  resistance  opposed  to 
its  motion,  by  a  continued  alternation  of  substances  of  different  kinds, 
which  furnishes  a  much  stronger  obstacle  to  its  transmission  than  any  of 
those  substances  alone  would  have  done.  The  substances  employed  must 
neither  consist  wholly  of  solids  nor  of  fluids,  and  they  must  be  of  three 
different  kinds,  possessed  of  different  powers  of  conducting  electricity; 
but  whether  the  difference  of  their  conducting  powers  is  of  any  other  con- 
sequence than  as  it  accompanies  different  chemical  properties,  is  hitherto 
undetermined.  Of  these  three  substances,  two  must  possess  a  power  of 
acting  mutually  on  each  other,  while  the  other  appears  to  serve  principally 
for  making  a  separate  connexion  between  them  :  and  this  action  may  be  of 
two  kinds,  or  perhaps  of  more ;  the  one  is  oxidation,  or  the  combination 
of  a  metal  or  an  inflammable  substance  with  a  portion  of  oxygen  derived 
from  water  or  from  an  acid,  the  other  sulfuration,  or  a  combination  with 
the  sulfur  contained  in  a  solution  of  an  alkaline  sulfuret. 

We  may  represent  the  effects  of  all  galvanic  combinations,  by  con- 
sidering the  oxidation  as  producing  positive  electricity  in  the  acting  liquid, 
and  the  sulfuration  as  producing  negative  electricity,  and  by  imagining 
that  this  electricity  is  always  communicated  to  the  best  conductor  of  the 
other  substances  concerned,  so  as  to  produce  a  circulation  in  the  direction 
thus  determined.  For  example,  when  two  wires  of  zinc  and  silver, 
touching  each  other,  are  separately  immersed  in  an  acid,  the  acid,  becoming 
positively  electrical,  imparts  its  electricity  to  the  silver,  and  hence  it  flows 
back  into  the  zinc :  when  the  ends  of  a  piece  of  charcoal  are  dipped  into 
water  and  into  an  acid,  connected  together  by  a  small  tube,  the  acid, 


522  LECTURE  LIV. 

becoming  positive,  sends  its  superfluous  fluid  through  the  charcoal  into  the 
water ;  and  if  a  wire  of  copper  be  dipped  into  water  and  a  solution  of 
alkaline  sulfuret,  connected  with  each  other,  the  sulfuret,  becoming  nega- 
tive, will  draw  the  fluid  from  the  copper  on  which  it  acts  ;  and  in  all  these 
cases  the  direction  of  the  current  is  truly  determined,  as  it  may  be  shown  by 
composing  a  battery  of  a  number  of  alternations  of  this  kind,  and  either 
examining  the  state  of  its  different  parts  by  electrical  tests,  or  connecting 
wires  with  its  extremities,  which,  when  immersed  into  a  portion  of  water, 
will  exhibit  the  production  of  oxygen  gas  where  they  emit  the  electric 
fluid,  and  of  hydrogen  where  they  receive  it.  These  processes  of  oxidation 
and  of  sulfuration  may  be  opposed  to  each  other,  or  they  may  be  combined 
in  various  ways,  the  sum  or  difference  of  the  separate  actions  being  ob- 
tained by  their  union ;  thus  it  usually  happens  that  both  the  metals 
employed  are  oxidable  in  some  degree,  and  the  oxidation,  which  takes  place 
at  the  surface  of  the  better  conductor,  tends  to  impede  the  whole  effect, 
perhaps  by  impeding  the  passage  of  the  fluid  through  the  surface.  The 
most  oxidable  of  the  metals,  and  probably  the  worst  conductor,  is  zinc  ; 
the  next  is  iron ;  then  come  tin,  lead,  copper,  silver,  gold,  and  platina. 
(Plate  XL.  Fig.  553.. .555.) 

In  the  same  manner  as  a  wire  charged  with  positive  electricity  causes 
an  extrication  of  oxygen  gas,  so  the  supply  of  electricity  through  the  more 
conducting  metal  promotes  the  oxidation  of  the  zinc  of  a  galvanic  battery  ; 
and  the  effect  of  this  circulation  may  be  readily  exhibited,  by  fixing  a  wire 
of  zinc,  and  another  of  silver  or  platina,  in  an  acid,  while  one  end  of  each 
is  loose,  and  may  be  brought  together  or  separated  at  pleasure  :  for  at  the 
moment  that  the  contact  takes  place,  a  stream  of  bubbles  rising  from  the 
platina,  and  a  white  cloud  of  oxid  falling  from  the  zinc,  indicate  both  the 
circulation  of  the  fluid  and  the  increase  of  the  chemical  action.  But  when, 
on  the  other  hand,  a  plate  of  zinc  is  made  negative  by  the  action  of  an 
acid  on  the  greater  part  of  its  surface,  a  detached  drop  of  water  has  less 
effect  on  it,  than  in  the  natural  state  :  while  a  plate  of  iron,  which  touches 
the  zinc,  and  forms  a  part  of  the  circle  with  it,  is  very  readily  oxidated  at  a 
distant  point :  such  a  plate  must  therefore  be  considered,  with  regard  to 
this  effect,  as  being  made  positive  by  the  electricity  which  it  receives  from 
the  acid  or  the  water  ;  unless  something  like  a  compensation  be  supposed 
to  take  place,  from  the  effects  of  induced  electricity.  Instead  of  the  ex- 
trication of  hydrogen,  the  same  causes  will  sometimes  occasion  a  deposition 
of  a  metal  which  has  been  dissolved,  will  prevent  the  solution  of  a  metal 
which  would  otherwise  have  been  corroded,  or  produce  some  effects  which 
appear  to  indicate  the  presence  of  an  alkali,  either  volatile  or  fixed.  All 
these  operations  may,  however,  be  very  much  impeded  by  the  interposition 
of  any  considerable  length  of  water,  or  of  any  other  imperfect  conductor. 
(Plate  XL.  Fig.  556.) 

It  is  obvious,  that  since  the  current  of  electricity,  produced  by  a  galvanic 
circle,  facilitates  those  actions  from  which  its  powers  are  derived,  the  effect 
of  a  double  series  must  be  more  than  twice  as  great  as  that  of  a  single  one  : 
and  hence  arises  the  activity  of  the  pile  of  Volta,  the  discovery  of  which 
forms  the  most  important  era  in  the  history  of  this  department  of  natural 


ON  ELECTRICITY  IN  MOTION.  523 

knowledge.  The  intensity  of  the  electrical  charge,  and  the  chemical  and 
physiological  effects  of  a  pile  or  battery,  seem  to  depend  principally  on  the 
number  of  alternations  of  substances  ;  the  light  and  heat  more  on  the 
joint  magnitude  of  the  surfaces  employed.  In  common  electricity,  the 
greatest  heat  appears  to  be  occasioned  by  a  long  continuation  of  a  slow 
motion  of  the  fluid  ;  and  this  is  perhaps  best  furnished  in  galvanism  by  a 
surface  of  large  extent,  while  some  other  effects  may  very  naturally  be 
expected  to  depend  on  the  intensity  of  the  charge,  independently  of  the 
quantity  of  charged  surface.  It  may  easily  be  imagined,  that  the  tension 
of  the  fluid  must  be  nearly  proportional  to  the  number  of  surfaces,  im- 
perfectly conducting,  which  are  interposed  between  the  ends  of  a  pile  or 
battery,  the  density  of  the  fluid  becoming  greater  and  greater  by  a  limited 
quantity  at  each  step  ;  and  it  is  easily  understood,  that  any  point  of  the 
pile  may  be  rendered  neutral,  by  a  connexion  with  the  earth,  while  those 
parts  which  are  above  it  or  below  it,  will  still  preserve  their  relations  un- 
altered with  respect  to  each  other  :  the  opposite  extremities  being,  like  the 
opposite  surface  of  a  charged  jar,  in  contrary  states,  and  a  partial  discharge 
being  produced,  as  often  as  they  are  connected  by  a  conducting  substance. 
The  various  forms  in  which  the  piles  or  troughs  are  constructed,  are  of 
little  consequence  to  the  theory  of  their  operation :  the  most  convenient 
are  the  varnished  troughs,  in  which  plates  of  silvered  zinc  are  arranged 
side  by  side,  with  intervening  spaces  for  the  reception  of  water,  or  of  an 
acid.  (Plate  XL.  Fig.  557.) 

It  is  unquestionable  that  the  torpedo,  the  gymnotus  electricus,  and  some 
other  fishes,  have  organs  appropriated  to  the  excitation  of  electricity,  and 
that  they  have  a  power  of  communicating  this  electricity  at  pleasure  to 
conducting  substances  in  their  neighbourhood.  These  organs  somewhat 
resemble  in  their  appearance  the  plates  of  the  galvanic  pile,  although  we 
know  nothing  of  the  immediate  arrangement,  from  which  their  electrical 
properties  are  derived ;  but  the  effect  of  the  shock,  which  they  produce, 
resembles  in  all  respects  that  of  the  weak  charge  of  a  very  large  battery. 
It  has  also  been  shown  by  the  experiments  of  Galvani,  Volta,  and  Aldmi, 
that  the  nerves  and  muscles  of  the  human  body  possess  some  electrical 
powers,  although  they  are  so  much  less  concerned  in  the  phenomena  which 
were  at  first  attributed  to  them  by  Galvani,  than  he  originally  supposed, 
that  many  philosophers  have  been  inclined  to  consider  the  excitation  of 
electricity  as  always  occasioned  by  the  inanimate  substances  employed,  and 
the  spasmodic  contractions  of  the  muscles  as  merely  very  delicate  tests  of 
the  influence  of  foreign  electricity  on  the  nerves. 

Such  is  the  general  outline  of  the  principal  experiments  and  conclusions 
which  the  subject  of  galvanism  afforded  before  Mr.  Davy's*  late  ingenious 
and  interesting  researches,  which  have  thrown  much  light,  not  only  on  the 
foundation  of  the  whole  of  this  class  of  phenomena,  but  also  on  the  nature 
of  chemical  actions  and  affinities  in  general.  Mr.  Davy  is  inclined  to  infer 
from  his  experiments,  that  all  the  attractions,  which  are  the  causes  of 
chemical  combinations,  depend  on  the  opposite  natural  electricities  of  the 

%  Outlines  of  a  view  of  Galvanism,  Jour,  of  the  Roy.  Inst.  i.  49.  Also,  Hi.  Tr. 
1807,  p.  1  ;  1808,  pp.  1,  333;  1809,  p.  1. 


524  LECTURE  LIV. 

bodies  concerned  ;  since  such  bodies  are  always  found,  by  delicate  tests,  to 
exhibit,  either  during  their  contact  or  after  separation,  marks  of  different 
species  of  electricity ;  and  their  mutual  actions  may  be  either  augmented 
or  destroyed,  by  increasing  their  natural  charges  of  electricity,  or  by 
electrifying  them  in  a  contrary  way.  Thus,  an  acid  and  a  metal  are  found 
to  be  negatively  and  positively  electrical  with  respect  to  each  other ;  and 
by  further  electrifying  the  acid  negatively,  and  the  metal  positively,  their 
combination  is  accelerated  ;  but  when  the  acid  is  positively  electrified,  or 
the  metal  negatively,  they  have  no  effect  whatever  on  each  other.  The 
acid  is  also  attracted,  as  a  negative  body,  by  another  positively  electrified, 
and  the  metal  by  a  body  negatively  electrified,  so  that  a  metallic  salt  may 
be  decomposed  in  the  circuit  of  Volta,  the  positive  point  attracting  the 
acid,  and  the  negative  point  the  metal ;  and  these  attractions  are  so  strong 
as  to  carry  the  particles  of  the  respective  bodies  through  any  intervening 
medium,  which  is  in  a  fluid  state,  or  even  through  a  moist  solid  ;  nor  are 
they  intercepted  in  their  passage,  by  substances  which,  in  other  cases,  have 
the  strongest  elective  attractions  for  them.  Alkali,  sulfur,  and  alkaline 
sulfurets,  are  positive  with  respect  to  the  metals,  and  much  more  with 
respect  to  the  acids  :  hence  they  have  a  very  strong  natural  tendency  to 
combine  with  the  acids  and  with  oxygen  :  and  hydrogen  must  also  be  con- 
sidered as  belonging  to  the  same  class  with  the  alkalis. 

Supposing  now  a  plate  of  zinc  to  decompose  a  portion  of  water ;  the 
oxygen,  which  has  a  negative  property,  unites  with  the  zinc,  and  probably 
tends  to  neutralise  it,  and  to  weaken  its  attractive  force  ;  the  hydrogen  is 
repelled  by  the  zinc,  and  carries  to  the  opposite  plate  of  silver  its  natural 
positive  electricity ;  and  if  the  two  plates  be  made  to  touch,  the  energy  of 
the  plate  of  zinc  is  restored,  by  the  electricity  which  it  receives  from  the 
silver  :  and  it  receives  it  the  more  readily,  as  the  two  metals,  in  any  case 
of  their  contact,  have  a  tendency  to  become  electrical,  the  zinc  positively, 
and  the  silver  negatively.  Mr.  Davy  therefore  considers  this  chemical 
action  as  destroying,  or  at  least  counteracting,  the  natural  tendency  of  the 
electric  fluid  to  pass  from  the  water  to  the  zinc,  and  from  modifications  of 
this  counteraction  he  explains  the  effects  of  galvanic  combinations  in  all 
cases.  Thus,  in  a  circle  composed  of  copper,  sulfuret,  and  iron,  the  fluid 
tends  to  pass  from  the  iron  towards  the  sulfuret,  and  from  the  copper  to 
the  iron,  in  one  direction,  and  in  the  opposite  direction  from  the  copper  to 
the  sulfuret,  with  a  force  which  must  be  equal  to  both  the  others,  since 
there  would  otherwise  be  a  continual  motion  without  any  mechanical 
cause,  and  without  any  chemical  change  ;  but  the  action  of  the  sulfuret  on 
the  copper  tends  to  destroy  its  electromotive,  or  rather  electrophoric,  power, 
of  directing  the  current  towards  the  sulfuret,  and  its  combination  with  the 
sulfur  makes  it  either  positively  electrical,  or  negatively  electrical  in  a  less 
considerable  degree ;  consequently  the  fluid  passes,  according  to  its  natural 
tendency,  from  the  copper  to  the  iron,  and  from  the  iron  to  the  sulfuret. 
In  a  third  case,  when  copper,  an  acid,  and  water,  form  a  circle,  the  natural 
tendency  is  from  the  acid  to  the  copper  on  one  side,  and  from  the  acid  to 
the  water,  and  from  the  water  to  the  copper  on  the  other  ;  here  we  niust 
suppose  the  first  force  to  be  only  a  little  weakened  by  the  chemical  action, 


ON  ELECTRICITY  IN  MOTION.  525 

while  the  third  is  destroyed,  so  that  the  first  overcomes  the  second,  and  the 
circulation  is  determined,  although  very  feebly,  in  such  a  direction,  that 
the  fluid  passes  from  the  acid  to  the  copper.  When,  in  the  fourth  place, 
the  combination  consists  of  copper,  sulfuret,  and  water,  the  tendencies  are, 
first,  from  the  copper  to  the  sulfuret,  and  from  the  water  to  the  copper ; 
and  secondly,  from  the  water  to  the  sulfuret :  in  this  instance  a  chemical 
action  must  be  supposed  between  the  oxygen  of  the  water  and  the  sulfuret, 
which  lessens  the  electromotive  tendency,  more  than  the  action  that  takes 
place  between  the  sulfuret  and  the  copper,  so  that  the  fluid  passes  from  the 
copper  to  the  sulfuret ;  and  the  current  has  even  force  enough  to  prevent 
any  chemical  action  between  the  water  and  the  copper,  which  would  tend 
to  counteract  that  force,  if  it  took  place. 

Mr.  Davy  has  observed  that  the  decomposition  of  the  substances 
employed  in  the  battery  of  Volta,  is  of  much  more  consequence  to  their 
activity  than  either  their  conducting  power,  or  their  simple  action  on  the 
other  elements  of  the  series  :  thus,  the  sulfuric  acid,  which  conducts  elec- 
tricity better,  and  dissolves  the  metals  more  readily,  than  a  neutral 
solution,  is,  notwithstanding,  less  active  in  the  battery,  because  it  is  not 
easily  decomposed.  Mr.  Davy  has  also  extended  his  researches,  and  the 
application  of  his  discoveries,  to  a  variety  of  natural  as  well  as  artificial 
phenomena,  and  there  can  be  no  doubt  but  that  he  will  still  make  such 
additions  to  his  experiments,  as  will  be  of  the  greatest  importance  to  this 
branch  of  science. 

The  operation  of  the  most  usual  electrical  machines  depends  first  on  the 
excitation  of  electricity  by  the  friction  of  glass  on  a  cushion  of  leather, 
covered  with  a  metallic  amalgam,  usually  made  of  mercury,  zinc,  and  tin, 
which  probably,  besides  being  of  use  in  supplying  electricity  readily  to 
different  parts  of  the  glass,  undergoes  in  general  a  chemical  change,  by 
means  of  which  some  electricity  is  extricated.  The  fluid,  thus  excited,  is 
received  into  an  insulated  conductor  by  means  of  points,  placed  at  a  small 
distance  from  the  surface  which  has  lately  undergone  the  effects  of  friction, 
and  from  this  conductor  it  is  conveyed  by  wires  or  chains  to  any  other 
parts  at  pleasure.  Sometimes  also  the  cushion,  instead  of  being  connected 
with  the  earth,  is  itself  fixed  to  a  second  conductor,  which  becomes  nega- 
tively electrified  ;  and  either  conductor  may  contain  within  it  a  jar,  which 
may  be  charged  at  once  by  the  operation  of  the  machine,  when  its 
internal  surface  is  connected  either  with  the  earth,  or  with  that  of  the 
jar  contained  in  the  opposite  conductor.  The  glass  may  be  either  in  the 
form  of  a  circular  plate  or  of  a  cylinder,  and  it  is  uncertain  which  of  the 
arrangements  affords  the  greatest  quantity  of  electricity  from  the  same 
surface ;  but  the  cylinder  is  cheaper  than  the  plate,  and  less  liable  to 
accidents,  and  appears  to  be  at  least  equally  powerful.  (Plate  XL.  Fig. 
558,  559.) 

The  plate  machine  in  the  Teylerian  museum,  employed  by  Van  Marum, 
when  worked  by  two  men,  excited  an  electricity,  of  which  the  attraction 
was  sensible  at  the  distance  of  38  feet,  and  which  made  a  point  luminous 
at  27  feet,  and  afforded  sparks  nearly  24  inches  long.  A  battery  charged 
by  it,  melted  at  once  twenty  five  feet  of  fine  iron  wire.  Mr.  Wilson  had 


526  LECTURE  LIV. 

also  a  few  years  ago,  in  the  Pantheon  in  London,  an  apparatus  of  singular 
extent;  the  principal  conductor  was  150  feet  long,  and  16  inches  in 
diameter,  and  he  employed  a  circuit  of  4,800  feet  of  wire.* 

The  electrophorus  derives  its  operation  from  the  properties  of  induced 
electricity.  A  cake  of  a  nonconducting  substance,  commonly  of  resin  or  of 
sulfur,  is  first  excited  by  friction,  and  becomes  negatively  electric  :  an 
insulated  plate  of  a  conducting  substance,  being  placed  on  it,  does  not  come 
sufficiently  into  contact  with  it  to  receive  its  electricity,  but  acquires  by 
induction  an  opposite  state  at  its  lower  surface,  and  a  similar  state  at  its 
upper  ;  so  that  when  this  upper  and  negative  surface  is  touched  by  a 
substance  communicating  with  the  earth,  it  receives  enough  of  the  electric 
fluid  to  restore  the  equilibrium.  The  plate  then  being  raised,  the  action  of 
the  cake  no  longer  continues,  and  the  electricity,  which  the  plate  has 
received  from  the  earth,  is  imparted  to  a  conductor  or  to  a  jar ;  and  the 
operation  may  be  continually  repeated,  until  the  jar  has  received  a  charge 
of  an  intensity  equal  to  that  of  the  plate  when  raised.  Although  the 
quantity  of  electricity,  received  by  the  plate,  is  exactly  equal  to  that 
which  is  emitted  from  it  at  each  alternation,  yet  the  spark  is  far  less 
sensible  ;  since  the  effect  of  the  neighbourhood  of  the  cake  is  to  increase 
the  capacity  of  the  plate,  while  the  tension  or  force  impelling  the  fluid  is 
but  weak  ;  and  at  the  same  time  the  quantity  received  is  sufficient,  when 
the  capacity  of  the  plate  is  again  diminished,  to  produce  a  much  greater 
tension,  at  a  distance  from  the  cake.  (Plate  XL.  Fig.  560.) 

The  condenser  acts  in  some  measure  on  the  same  principles  with  the 
electrophorus,  both  instruments  deriving  their  properties  from  the  effects  of 
induction.  The  use  of  the  condenser  is  to  collect  a  weak  electricity  from 
a  large  substance  into  a  smaller  one,  so  as  to  make  its  density  or  tension 
sufficient  to  be  examined.  A  small  plate,  connected  with  the  substance,  is 
brought  nearly  into  contact  with  another  plate  communicating  with  the 
earth  ;  in  general  a  thin  stratum  of  air  only  is  interposed ;  but  sometimes 
a  nonconducting  varnish  is  employed  ;  this  method  is,  however,  liable  to 
some  uncertainty,  from  the  permanent  electricity  which  the  varnish  some- 
times contracts  by  friction.  The  electricity  is  accumulated  by  the  attrac- 
tion of  the  plate  communicating  with  the  earth,  into  the  plate  of  the 
condenser ;  and  when  this  plate  is  first  separated  from  the  substance  to  be 
examined,  and  then  removed  from  the  opposite  plate,  its  electricity  is 
always  of  the  same  kind  with  that  which  originally  existed  in  the  sub- 
stance, but  its  tension  is  so  much  increased  as  to  render  it  more  easily 
discoverable.  This  principle  has  been  variously  applied  by  different 
electricians,  and  the  employment  of  the  instrument  has  been  facilitated  by 
several  subordinate  arrangements.  (Plate  XL.  Fig.  561.) 

Mr.  Cavallo's  multiplierf  is  a  combination  of  two  condensers  ;  the 
second  or  auxiliary  plate  of  the  first,  like  the  plate  of  the  electrophorus,  is 
moveable,  and  carries  a  charge  of  electricity,  contrary  to  that  of  the 
substance  to  be  examined,  to  the  first  or  insulated  plate  of  the  second 
condenser,  which  receives  it  repeatedly,  until  it  has  acquired  an  equal 

*  Wilson's  Account  of  his  Experiments,  4to,  1778.  \ 

t  Nich.  Jour.  i.  394. 


ON  ELECTRICITY  IN  MOTION.  527 

degree  of  tension ;  and  when  the  two  plates  of  this  condenser  are  sepa- 
rated, they  both  exhibit  an  electricity  much  more  powerful  than  that  of 
the  first  condenser.  The  force  is,  however,  still  more  rapidly  augmented 
by  the  instruments  of  Mr.  Bennet*  and  Mr.  Nicholson,t  although  it  has 
been  supposed  that  these  instruments  are  more  liable  to  inconvenience 
from  the  attachment  of  a  greater  portion  of  electricity  to  the  first  plate 
of  the  instrument,  which  leaves,  for  a  very  considerable  time,  a  certain 
quantity  of  the  charge  not  easily  separable  from  it.  Mr.  Bennet  employs 
three  varnished  plates  laid  on  each  other,  but  Mr.  Nicholson  has  substituted 
simple  metallic  plates,  approaching  only  very  near  together,  so  that  there 
can  be  no  error  from  any  accidental  friction.  In  both  of  these  instruments, 
the  second  plate  of  a  condenser  acquires  an  electricity  contrary  and  nearly 
equal  to  that  of  the  first,  by  means  of  which  it  brings  a  third  plate  very 
nearly  into  the  same  state  with  the  first ;  and  when  the  first  and  third 
plates  are  connected  and  insulated,  they  produce  a  charge  nearly  twice  as 
great  in  the  second  plate,  while  the  first  plate  becomes  at  the  same  time 
doubly  charged  ;  so  that  by  each  repetition  of  this  process,  the  intensity  of 
the  electricity  is  nearly  doubled  :  it  is  therefore  scarcely  possible  that  any 
quantity  should  be  so  small  as  to  escape  detection  by  its  operation.  (Plate 
XL.  Fig.  562,  563.) 

The  immediate  intensity  of  the  electricity  may  be  measured,  and  its 
character  distinguished,  by  electrical  balances,  and  by  electrometers  of 
different  constructions.  The  electrical  balance  measures  the  attraction  or 
repulsion  exerted  by  two  balls  at  a  given  distance,  by  the  magnitude  of  the 
force  required  to  counteract  it ;  and  the  most  convenient  manner  of  apply- 
ing this  force  is  by  the  torsion  of  a  wire,  which  has  been  employed  for  the 
purpose  by  Mr.  Coulomb.^  The  quadrant  electrometer  of  Henley  §  ex- 
presses the  mutual  repulsion  of  a  moveable  ball  and  a  fixed  column,  by  the 
divisions  of  the  arch  to  which  the  ball  rises.  These  divisions  do  not 
exactly  denote  the  proportional  strength  of  the  action,  but  they  are  still  of 
utility  in  ascertaining  the  identity  of  any  two  charges,  and  in  informing  us 
how  far  we  may  venture  to  proceed  in  our  experiments  with  safety;  and 
the  same  purpose  is  answered,  in  a  manner  somewhat  less  accurate,  by  the 
electrometer,  consisting  of  two  pith  balls,  or  of  two  straws,  which  are 
made  to  diverge  by  a  smaller  degree  of  electricity.  Mr.  Bennet's  electro- 
meter ||  is  still  more  delicate  ;  it  consists  of  two  small  portions  of  gold  leaf, 
suspended  from  a  plate,  to  which  the  electricity  of  any  substance  is  com- 
municated by  contact :  a  ve*y  weak  electricity  is  sufficient  to  make  them 
diverge,  and  it  may  easily  be  ascertained  whether  it  is  positive  or  negative, 
by  bringing  an  excited  stick  of  sealing  wax  near  the  plate,  since  its 
approach  tends  to  produce  by  induction  a  state  of  negative  electricity  in 
the  remoter  extremities  of  the  leaves,  so  that  their  divergence  is  either 
increased  or  diminished,  accordingly  as  it  was  derived  from  negative  or 
from  positive  electricity :  a  strip  of  gold  leaf  or  tin  foil,  fixed  within  the 

*  Ph.  Tr.  1787,  pp.  32,  288  ;  1794,  p.  266. 
t  Ibid.  1788,  p.  403.     Nich.  Jour.  i.  395  ;  ii.  370 ;  iv.  95. 
%  Hist,  et  Mem.  1785,  p.  569.  §  Ph.  Tr.  1772,  p.  359. 

1  Ph.  Tr.  1787,  p.  26. 


528  LECTURE  LIV. 

glass  which  covers  the  electrometer,  opposite  to  the  extremities  of  the 
leaves,  prevents  the  communication  of  any  electricity  to  the  glass,  which 
might  interfere  with  the  action  of  the  instrument.  When  the  balls  of  an 
electrometer  stand  at  the  distance  of  4  degrees,  they  appear  to  indicate  a 
charge  nearly  8  times  as  great  as  when  they  stand  at  one  degree  :  a  charge 
8  times  as  great  in  each  ball  producing  a  mutual  action  64  times  as  great 
at  any  given  distance,  and  at  a  quadruple  distance  a  quadruple  force  ;  in 
the  same  manner  a  separation  of  9  degrees  is  probably  derived  from  an 
intensity  27  times  as  great  as  at  1.  In  Lane's  electrometer*  the  magnitude 
of  a  shock  is  determined  by  the  quantity  of  air  through  which  it  is  obliged 
to  pass,  between  two  balls,  of  which  the  distance  may  be  varied  at  plea- 
sure ;  and  the  power  of  the  machine  may  be  estimated  by  the  frequency  of 
the  sparks  which  pass  at  any  given  distance.  It  appears  from  Mr.  Lane's 
experiments,  that  the  quantity  of  electricity  required  for  a  discharge  is 
simply  as  the  distance  of  the  surfaces  of  the  balls,  the  shocks  being  twice 
as  frequent  when  this  distance  is  only  -^  of  an  inch  as  when  it  is  TV  Mr. 
Volta  says,  that  the  indications  of  Lane's  and  Henley's  electrometer  agree 
immediately  with  each  other  ;  but  it  seems  difficult  to  reconcile  this  result 
with  the  general  theory.  Sometimes  the  force  of  repulsion  between  two 
balls  in  contact  is  opposed  by  a  counterpoise  of  given  magnitude,  and  as 
soon  as  this  is  overcome,  they  separate  and  form  a  circuit  which  discharges 
a  battery  ;  whence  the  instrument  is  called  a  discharger.  (Plate  XL.  Fig. 
564... 568.) 

It  must  be  confessed  that  the  whole  science  of  electricity  is  yet  in  a  very 
imperfect  state  :  we  know  little  or  nothing  of  the  intimate  nature  of  the 
substances  and  actions  concerned  in  it :  and  we  can  never  foresee,  without 
previous  experiment,  where  or  how  it  will  be  excited.  We  are  wholly 
ignorant  of  the  constitution  of  bodies,  by  which  they  become  possessed  of 
different  conducting  powers ;  and  we  have  only  been  able  to  draw  some 
general  conclusions  respecting  the  distribution  and  equilibrium  of  the  sup- 
posed electric  fluid,  from  the  laws  of  the  attractions  and  repulsions  that  it 
appears  to  exert.  There  seems  to  be  some  reason  to  suspect,  from  the 
phenomena  of  cohesion  and  repulsion,  that  the  pressure  of  an  elastic 
medium  is  concerned  in  the  origin  of  these  forces ;  and  if  such  a  medium 
really  exists,  it  is  perhaps  nearly  related  to  the  electric  fluid.  The  identity 
of  the  general  causes  of  electrical  and  of  galvanic  effects  is  now  doubted  by 
few  ;  and  in  this  country  the  principal  phenomena  of  galvanism  are 
universally  considered  as  depending  on  chemical  changes  ;  perhaps,  also, 
time  may  show,  that  electricity  is  very  materially  concerned  in  the  essen- 
tial properties,  which  distinguish  the  different  kinds  of  natural  bodies,  as 
well  as  in  those  minute  mechanical  actions  and  affections  which  are 
probably  the  foundation  of  all  chemical  operations  ;  but  at  present  it  is 
scarcely  safe  to  hazard  a  conjecture  on  a  subject  so  obscure,  although  Mr. 
Davy's  experiments  have  already  in  some  measure  justified  the  boldness  of 
the  suggestion. 

*  Ph.  Tr.  1767,  p.  451. 

.0* 


ON  ELECTRICITY  IN  MOTION.  529 


LECT.  LIV.— ADDITIONAL  AUTHORITIES. 

Excitation  of  Electricity.  By  simple  contact. — Weber,  Korper  ohne  Reiben  zu 
Elek.  1781.  Bennet,  Ph.  Tr.  1787,  p.  26;  Nich.  Jour.  8vo.  i.  144,  184.  Haiiy 
sur  FElect.  de  la  Pression,  Ann.  de  Ch.  v.  95.  Becquerel,  ibid.xxii.  91. 

By  Friction.— Hauksbee,  Ph.  Tr.  1705,  p.  2165.  Gray,  ibid.  1735,  p.  166. 
Symmer,  ibid.  1759,  p.  308.  Beccaria,  ibid.  1766,  p.  105.  Bergmann,  Schwed. 
Abhand.  xxv.  p.  344.  Henley,  Ph.  Tr.  1774,  p.  389  ;  1777,  p.  122.  Wilcke,  De 
Electr.  contrariis,  Gott.  1790.  Ritter,  Das  Elektr.  System  der  Korper.  Pereyro, 
Arch,  de  1'Electr.  ii.  395.  Lists  of  substances  which,  under  certain  conditions, 
produce  certain  kinds  of  electricity,  will  be  found  in  Erxleben's  Naturlehre  by  Lich- 
tenberg,  and  in  Cavallo's  Treatise  on  Electr. 

By  Steam. — Lavoisier  and  Laplace  sur  1'Electr.  qu'  absorbent  les  Corps  qui  se 
reduisent  en  Vapeurs,  Hist,  et  Mem.  1781,  p.  292,  H.  6.  Volta,  Del  Modo  di 
render  sensibilissima  la  piu  Debole  Elettr.  Appendice  Ph.  Tr.  1782,  p.  274.  Me- 
teorologische  Briefe,  Leipz.  1793,  p.  193.  Bennet,  Ph.  Tr.  1787.  Erman,  Abhand. 
der  Ak.  zu  Berlin,  1814,  p.  123.  Pouillet  sur  FElectr.  des  Fluides  Elastiques,  Ann. 
de  Ch.xxxv.  365,  401.  Armstrong,  Ph.  Mag.  xvii.  370,  452,  xviii.  51,  328,  xx.  5, 
xxii.  1,  xxiii.  194.  Pattinson,  ibid.  xvii.  376,  457.  Schafhautl,  ibid.  xvii.  449, 
xviii.  14,  95,  265.  Williams,  ibid,  xviii.  93.  Faraday,  Ph.  Tr.  1843,  p.  1. 

Electrical  Apparatus. — Bohnenberger's  Elektrisirmaschinen,  Stuttg.  1784. 
Guttle,  Instrumenten  Kabinet,  1790.  Kunze,  Schauplatz  der  Gemeinniitzigen  Ma- 
schinen. 

Electrical  Machines.  Otto  v.  Guericke,  Experimenta  Nova  de  Vacuo  Spatio, 
Amst.  1672,  p.  140.  Hauksbee  on  a  Glass  Globe  lined  with  Sealing  Wax,  Ph.  Tr. 
1708,  p.  219.  Hausen,  Novi  Profectus  in  Historia  Electr.  4to,  1743.  Winkler, 
Descriptio  Pyrorgani  sui  Electr.  Ph.  Tr.  1747,  p.  497.  Faure,  Congetture  intorno 
alia  Mach.  Elettr.  4to,  Rome,  1747.  Espinasse,  Ph.  Tr.  1767,  p.  186.  Leroy,  A 
Machine  for  producing  both  Species  of  Electr.  Hist,  et  Mem.  1772,  I.  499,  H.  9. 
Nooth  on  the  Cushion  and  Flap,  Ph.  Tr.  1773,  p.  333.  Nairne,  ibid.  1774,  p.  79, 
and  Treatise  on  do.  1787.  Planta's  Plate  Machine,  Allg.  Deutsche  Bibliot.  xxiv. 
549.  Ingenhousz,  do.  Ph.  Tr.  1769,  p.  659.  Schmidt,  Beschreibung  einer  Elek.  4to, 
Berlin,  1778.  Langenbiicher,  do.  Anspach,  1780.  Bohnenberger,  1784.  Rouland, 
Description  des  Machines  a  Taffetas,  Amst.  1785.  Van  Marum,  Description  d'une 
tres  Grande  Machine,  4to,  Haarlem,  1785.  Nicholson's  Exp.  Ph.  Tr.  1789,  p.  265. 
Cuthbertson,  Beschreibung  einer  Elektrisirmaschine  von  Deimann  und  Trostwyk, 
Leipz.  1790.  Wolff's,  Gilb.  Ann.  xii.  597.  Wolfram's,  ibid.  Ixxiv.  53.  Hare's, 
Sturgeon's  Ann.  i.  487.  Page's,  Silliman's  American  Journal,  xxvi.  110.  Dujar- 
din's,  Ann.  de  Ch.  N.  S.  ix.  111. 

Jars  and  Batteries. — Kriiger,  Geschichte  der  Erde,  Halle,  1746,  p.  177,  announces 
the  discovery  of  Von  Kleist,  of  the  power  of  charged  glass.  (Cuneus)  Musschen- 
broek,  Hist,  et  Mem.  1746,  p.  2.  Winkler,  Die  Starke  der  Elekt.  Kraft  des 
Wassers,  Leipz.  1746.  Wilcke,  Schwed.  Abhand.  1758,  p.  241  ;  1762,  pp.  213, 
253.  Wilkinson  on  the  Ley  den  Phial,  1798.  Dana,  Schweigg.  Jour,  xxiii.  257. 

Electrophorus. — Volta,  Lettere  sul  Elettroforo  Perpetuo,  Scelta  di  Opusculi 
Interessanti,  Milan,  viii.  127  (1775),  ix.  91,  x.  37.  Wilcke,  Schwed.  Abhand.  1777, 
pp.  54,  116,  200.  Ingenhouss,  Exp.  and  Theory  of  do.  Ph.  Tr.  1778,  p.  1027. 
Henley,  ibid.  1778,  p.  1049.  Kraft,  Acta  Petr.  1771,  p.  154.  Achard,  Hist,  et 
Mem.  de  Berlin,  1766,  p.  162.  Klindworth,  Goth.  Mag.  i.  II.  35.  Lichtenberg, 
ibid.  i.  II.  42.  Weber,  Beschreibung  des  Luftelektrophorus,  Augsb.  1779. 

Condensers. — Volta  on  the  Method  of  rendering  very  sensible  Small  Degrees  of 
Electr.  Ph.  Tr.  1 782,  p.  237.  Cavallo  on  manifesting  Small  Quantities  of  Electr.  ibid. 
1788,  p.  1.  His  Collector,  ibid.  1788,  p.  255.  Cuthbertson,  Nich.  Jour.  ii.  281. 
Read,  ibid,  ii.  495.  Bohnenberger,  Beschreibung  Elektritatsnerdoppeler,  Tubing. 
1798. 

Electrometers,  Sfc.— D'Arcy's  Electr.  Hist,  et  Mem.  1749,  p.  63,  H.  7.  Rich- 
mann's,  Nov.  Com.  Petr.  iv.  301.  Comus's,  Jour,  de  Phy.  vii.  520.  Canton's, 
Ph.  Tr.  xlviii.  350,  780.  Cavallo's,  ibid.  1777,  p.  388;  1780,  p.  15.  Brooke's, 
ibid.  1782,  p.  384.  Saussure's,  Voyages,  ii.  202.  Deluc's,  Nouvelles  Idees  sur  la 
Meteorologie,  p.  397.  Lawson's,  Ph.  Mag.  xi.  251.  Marechaux's,  Gilb.  Ann.  xv. 
93,  99i  xvi.  115,  xix.  476,  xx.  357,  xxii.  318,  xxv.  4,  18,  xxvi.  29,  123.  Behrens's, 
ibid.  <xxiii.  24.  Bohnenberger's,  ibid.  Ii.  390.  Oersted's,  Pogg.  Ann.  liii.  612. 
Harris's,  Ph.  Tr.  1836,  p.  447. 

2  M 


530  LECTURE  LIV. 

Galvanism. — Al.  Galvani,  De  Viribus  Electr.  inMotu  Musculari  Commentarius , 
Bolog.  1791 ;  Com.  Bon.  vii.  O.  363.  Mayer,  Abhand.  von  Galvani  und  Andern, 
2  vols.  Prague,  1793.  Creve,  do.  Frankf.  1793.  Volta  on  Galvani's  Discoveries, 
Ph.  Tr.  1793,  p.  10  ;  Annales  de  Ch.  xxiii.  270,  xl.  255  ;  Nich.  Jour.  8vo.  i.  135  ; 
on  the  Electr.  excited  by  contact.  Ph.  Tr.  1800,  p.  403  ;  on  the  Identity  of  the 
Electr.  and  Galv.  Fluids,  Brugnatelli's  Ann.  xix.  38,  163.  Collezione  dell'-Opere  di 
Volta,  3  vols.  Firenza,  1816.  Pfaff  on  Volta' s  Theory,  &c.  Gilb.  Ann.  x.  219,  Lxviii. 
273  ;  Schweigger's  Jour.  xlvi.  129  ;  Uebersicht  iiber  den  Voltaismus,  Stuttg.  1804  ; 
Ann.  de  Ch.  xli.  236.  Aldini,  De  Animali  Electr.  4to,  Bolog.  1794.  Esperienze  sul 
Galvanismo,  Bolog.  1802.  Essai  Theorique,  2  vols.  Paris,  1804.  Ritter,  Beitragezu 
Nahren  Kentniss  des  Galv.  Jena,  1800-5.  Experiments  and  Remarks,  Gilb.  Jour, 
ii.  vii.  viii.  386,  ix.  1,  212,  xiii.  1,  265,  xvi.  293  ;  Nich.  Jour.  vi.  223,  vii.  288. 
Sue,  Hist,  de  Galvan.  2  vols.  Paris,  1802.  Fourcroy's  Experiments,  Ann.  de  Ch. 
xxxix.  103.  Deluc,  Traite  Elem.  sur  le  Fluide  Electro-galvanique,  2  vols.  Paris, 
1804.  Wilkinson's  Elements  of  Galv.  2  vols.  1804.  Bellinger!,  Esp.  ed  Obs.  sul 
Galv.  4to,  Turin,  1816.  Bostock's  Hist,  of  Galv.  1818.  Parrot,  Handbuch  der 
Physik,  vol.  ii.  Muller,  Elemente  der  Elek.  und  Elektro  Chemie,  Berlin,  1819. 
Karsten,  Ueber  Contact  Electr.  Berlin,  1836.  Negro,  Experiment!,  4to,  Padova, 
1833.  Daniell's  Introd.  to  the  Study  of  Chem.  Phil.  1843.  Golding  Bird's  Nat.  Ph. 
184. .  Le  Journal  de  Physique,  Bulletin  de  la  Soc.  Philom.,  Annales  de  Ch.,  Gilbert's 
Annalen,  Schweigger's  do.,  Poggendorff's  do.,  Brugnatelli's  Jour.,  Nich.  Jour.,  and 
the  other  periodicals  of  the  period,  contain  numerous  accounts  of  experiments  and 
remarks  by  Volta,  Nicholson,  Carlisle,  Biot,  Cuvier,  Lehof,  Berzelius,  Fourcroy, 
Grimm,  Ritter,  Hermbstadt,  Hebebrand,  Pfaff,  Bourguet,  Davy,  Heidemann,  Rein- 
hold,  Curtet,  Bouvier,  Erman,  Aldini,  Pepys,  Jaeger,  Bunzen,  Brugnatelli,  Gilbert, 
Von  Arnim,  Friedlander,  Cruickshank,  Eandi,  Robertson,  Desormes,  Cuthbertson, 
Garboin,  Wilkinson,  Rossi,  Gautherot,  Fabroni,  and  others ;  whilst  the  more 
recent  periodicals,  such  as  the  Archives  de  1'Electr.,  Mem.  de  la  Soc.de  Philos.  et 
d'Hist.  Nat.  de  Geneve,  the  Comptes  Rendus,  Jameson's  Jour.,  the  Philosophical 
Mag.,  Quarterly  Journal  of  Science,  Silliman's  Jour.  &c.  contain  papers  by  Peclet, 
Belli,  Fechner,  Becquerel,  Henrici,  Martens,  Marianini,  Parrot,  Draper,  Grove, 
Daniell,  Hare,  De  la  Rive,  Oersted,  Schonbein,  Heer,  Andrews,  Seebeck,  Golding, 
Bird,  and  others. 

Mathematical  Theory  of  Galvanism, — Ohm,  Die  Galvanische  Kette  Mathema- 
tisch  bearbeitet,  Berlin,  1827;  translated  in  Taylor's  Scientific  Memoirs,  ii.  401  ; 
also  papers  in  Schweigg.  Jour,  xliv,  110,  xlix.  1,  Iviii.  393,  Ixiii.  1,  159,  385,  Ixiv. 
21,  138,  257,  Ixvii.  341  ;  Pogg.  Ann.  vi.  459,  vii.  45,  117;  Karsten's  Archiv,  vii. 
1,  452,  xiv.  475,  xvi.  1.  Fechner,  Maasbestimmungen  iiber  die  Galvanische  Kette, 
4to,  Leipz.  1831;  also  papers  in  Schweigg.  Jour.  Ivii.  9,  291,  Ix.  17,  Ixiii.  249; 
Henrici  in  Pogg.  Ann.  liii.  277;  Pogg.  in  Pogg.  Ann.  liv.  161,  Iv.  43,  Ivi.  353  ; 
Jacobi  in  do.  Ivii.  85  ;  Draper  in  Ph.  Mag.  xv.  206,  339.  Heer  in  Bullet,  des 
Sciences  Physiques  en  Neerlande,  1839,  p.  319  ;  1840,  p.  132  ;  Lenz  in  Pogg.  Ann. 
xlvii.  584,  lix.  203,  407. 

Galvanic  Apparatus. — Izarn,  Manuel  du  Galvanisme,  Paris,  1805.  Children, 
Ph.  Tr.  1809,  p.  32.  Cruickshank's,  Nich.  Jour.  4to,  187,  254.  Wollaston,  Thorn- 
son's  Annals,  vi.  209,  and  in  Children's  Account  of  Exp.  with  a  Large  Battery,  Ph. 
Tr.  1815,  p.  363.  Pepys.  ibid.  1823,  p.  187.  Hare's  New  Theory  of  Galvanism, 
Philadelph.  1819.  Silliman's  Journal,  vii.  347.  Zamboni,  L' Elettromotoro  Perpe- 
tuo,  2  vols.  Verona,  1820.  Faraday's  Exp.  Researches,  10th  series,  &c.  Daniell's 
Constant  Battery,  Ph.  Tr.  1836,  p.  117  ;  1837,  p.  141  ;  1838,  p.  41 ;  1839,  p.  89  ; 
1842,  p.  137.  Becquerel's  Battery,  Pogg.  Ann.  xxxvii.  429.  Karsten,  Ueber  Con- 
tactelekt.  Berlin,  1838.  Grove  on  a  Gas  Battery,  Ph.  Mag.  xxi.  417. 

Animal  Electricity.  See  also  Galvanism.  Torpedo.— Redi,  Exp.  Natur.  1666. 
Lorenzi,  Obs.  intorno  alii  Torp.  1678.  Reaumer,  Hist,  et  Mem.  1714,  p.  344, 
H.  19.  Walsh,  Ph.  Tr.  1773,  pp.  63,  461;  1775,  p.  465.  Hunter,  ibid.  1773, 
p.  481,  with  plates.  Pringle's  Discourse,  4to,  1775.  Cavendish's  Imitation  of  the 
Torp.  Ph.  Tr.  1776,  p.  196.  Spallanzani,  Op.  Scelt.  di  Milano,  1783.  Mem. 
della  Soc.  Ital.  ii.  603.  Girardi,  ibid.  iii.  553.  Langguth,  De  Torp.  4to,  Witt. 
1784.  Volta,  Brugnatelli's  Ann.  1805,  p.  223.  Humboldt,  Ann.  de  Ch.  1.  15. 
H.  Davy,  Ph.  Tr.  1829,  p.  15  ;  1832,  p.  259.  J.  Davy,  ibid.  1834,  p.  531.  Col- 
ladon,  Comptes  Rendus,  1836,  p.  490.  Linari,  ibid.  1836,  p.  46.  Matteuci,  Arch, 
de  1'Electr.  iii.  153.  Proceedings  of  the  Electrical  Society,  p.  512. 

Gymnotus.— Richer,  Hist,  et  Mem.  i.  116,  vii.  II.  92.  Berker,  Reisb  nach 
Rio,  1680.  Williamson,  Ph.Tr.  1775,  p.  94.  Garden,  ibid.  1775,  p.  102.  Hunter, 


ON  MAGNETISM.  531 

ibid.  1775,  p.  395.  Ginsan,  De  Gym.  Tubing.  1819.  Schonbein,  Arch,  de 
1'Electr.  i.  445.  Faraday,  Ph.  Tr.  1839,  p.  1.  Letheby,  Proceedings  of  the  Electr. 
Soc.  p.  367. 

Other  Animals.— Geoffroj  ( Anatomy),  Bullet,  dela  Soc.  Philom.  No.  70  ;  Mem. 
du  Musee  d'Hist.  Nat.  i.  392.  Rudolphi,  Abh.  der  Akad.  Berl.  1820,  p.  223. 
Marianini,  Soprala  Scossa  che  provano  gli  Animali,  Venice,  1S28.  DuBois,  Pogg. 
Ann.  pp.  Iviii.  1.  Quse  apud  Veteres  exstant  Argumenta,  Berl.  1843.  Nobili,  Delia 
Rana,  Mem.  i.  135.  Matteuci,  Arch,  de  1'Electr.  ii.  628,  419,  iii.  5.  Essai  sur 
les  Phe"n.  Electr.  des  Animaux,  Paris,  1840. 

Mineral  Electricity.— Wilson  on  the  Tourmaline,  &c.  Ph.  Tr.  1759,  p.  308 ; 
1762,  p.  443.  Due  de  la  Noya  Caraffa  sur  la  Tourmeline,  4to,  Paris,  1759.  Aepinus 
sur  do.  Petersb.  1762.  Miiller,  Au  Born.  4to,  Vienna,  1773.  Bergmann,  Ph.  Tr. 
1766,  p.  236.  Zallinger,  Vom  Tourm.  Vienna,  1779.  Haiiy,  Hist,  et  Mem.  1785, 
p.  206 ;  Ann.  de  Ch.  ix.  59  ;  Mem.  de  1'Inst.  i.  49  ;  Traite  des  Characters  des 
Pierres  Precieuses,  Paris,  1817,  p.  146  ;  Traite  de  Mineralogie,  1822,  p.  206. 
Becquerel,  Ann.  de  Ch.  xxxvii.  1,  355.  Brewster,  Ed.  Jour.  ii.  308.  Forbes,  Ed. 
Tr.  xiii.  27.  Riess  and  Rose,  Pogg.  Ann.  lix.  553. 

Thermo-Electricity.—Seebeck,  Abh.  der  Akad.  Berl.  1822  ;  Pogg.  Ann.  vi. 
pp.  1,  133,  253.  Yelin,  Der  Thermomagnetismus,  Munch.  1823.  Gumming, 
Camb.  Tr.  ii.  1.  Becquerel,  Ann.  de  Ch.  xxiii.  135,  xxxi.  371,  xli.  353.  Sturgeon, 
Ph.  Mag.  1831,  p.  1,  116.  Pouillet,  Comptes  Rendus,  v.  785.  Prideaux,  Ph. 
Mag.  iii.  205,  262,  398.  Andrews,  ibid.  x.  433.  Watkins,  ibid.  xi.  304.  Wheat- 
stone  on  the  Thermo-electric  Spark,  ibid.  x.  414.  Matteuci,  Bibliot.  Univ.  xv.  187  ; 
Arch,  de  1'Electr.  ii.  227. 


LECTURE   LV. 


ON  MAGNETISM. 

THE  theory  of  magnetism  bears  a  very  strong  resemblance  to  that  of 
electricity,  and  it  must  therefore  be  placed  near  it  in  a  system  of  natural 
philosophy.  We  have  seen  the  electric  fluid  not  only  exerting  attractions 
and  repulsions,  and  causing  a  peculiar  distribution  of  neighbouring  por- 
tions of  a  fluid  similar  to  itself,  but  also  excited  in  one  body,  and  trans- 
ferred to  another,  in  such  a  manner  as  to  be  perceptible  to  the  senses,  or  at 
least  to  cause  sensible  effects,  in  its  passage.  The  attraction  and  repulsion, 
and  the  peculiar  distribution  of  the  neighbouring  fluid,  are  found  in  the 
phenomena  of  magnetism  ;  but  we  do  not  perceive  that  there  is  ever  any 
actual  excitation,  or  any  perceptible  transfer  of  the  magnetic  fluid  from 
one  body  to  another  distinct  body  ;  and  it  has  also  this  striking  peculiarity, 
that  metallic  iron  is  very  nearly,  if  not  absolutely,  the  only  substance 
capable  of  exhibiting  any  indications  of  its  presence  or  activity. 

For  explaining  the  phenomena  of  magnetism,  we  suppose  the  particles  of 
a  peculiar  fluid  to  repel  each  other,  and  to  attract  the  particles  of  metallic 
iron  with  equal  forces,  diminishing  as  the  square  of  the  distance  increases  ; 
and  the  particles  of  such  iron  must  also  be  imagined  to  repel  each  other,  in 
a  similar  manner.  Iron  and  steel,  when  soft,  are  conductors  of  the  mag- 
netic fluid,  and  become  less  and  less  pervious  to  it  as  their  hardness  in- 
crea^es.  The  ground  work  of  this  theory  is  due  to  Mr.  Aepinus,*  but  the 

*  See  p.  515. 
2  M  2 


532  LECTURE  LV. 

forces  have  been  more  particularly  investigated  by  Coulomb*  and  others. 
There  are  the  same  objections  to  these  hypotheses  as  to  those  which  con- 
stitute the  theory  of  electricity,  if  considered  as  original  and  fundamental 
properties  of  matter :  and  it  is  additionally  difficult  to  imagine,  why  iron, 
and  iron  only,  whether  apparently  magnetic  or  not,  should  repel  'similar 
particles  of  iron  with  a  peculiar  force,  which  happens  to  be  precisely  a 
balance  to  the  attraction  of  the  magnetic  fluid  for  iron.  This  is  obviously 
improbable  ;  but  the  hypotheses  are  still  of  great  utility  in  assisting  us  to 
generalise,  and  to  retain  in  memory,  a  number  of  particular  facts  which 
would  otherwise  be  insulated.  The  doctrine  of  the  circulation  of  streams 
of  the  magnetic  fluid  has  been  justly  and  universally  abandoned,  and 
some  other  theories,  much  more  ingenious  and  more  probable,  for  instance 
that  of  Mr.  Prevost,t  appear  to  be  too  complicated,  and  too  little  supported 
by  facts,  to  require  much  of  our  attention. 

The  distinction  between  conductors  and  nonconductors  is,  with  respect 
to  the  electric  fluid,  irregular  and  intricate  :  but  in  magnetism,  the  softness 
or  hardness  of  the  iron  or  steel  constitutes  the  only  difference.  Heat,  as 
softening  iron,  must  consequently  render  ,it  a  conductor :  even  the  heat  of 
boiling  water  affects  it  in  a  certain  degree,  although  it  can  scarcely  be  sup- 
posed to  alter  its  temper  ;  but  the  effect  of  a  moderate  heat  is  not  so  con- 
siderable in  magnetism  as  in  electricity.  A  strong  degree  of  heat  appears, 
from  the  experiments  of  Gilbert,  J  and  of  Mr.  Cavallo,§  to  destroy  com- 
pletely all  magnetic  action. 

It  is  perfectly  certain  that  magnetic  effects  are  produced  by  quantities 
of  iron  incapable  of  being  detected  either  by  their  weight  or  by  any 
chemical  tests.  Mr.  Cavallo  ||  found  that  a  few  particles  of  steel,  adhering 
to  a  hone,  on  which  the  point  of  a  needle  was  slightly  rubbed,  imparted  to 
it  magnetic  properties ;  and  Mr.  Coulomb^f  has  observed  that  there  are 
scarcely  any  bodies  in  nature  which  do  not  exhibit  some  marks  of  being 
subjected  to  the  influence  of  magnetism,  although  its  force  is  always  pro- 
portional to  the  quantity  of  iron  which  they  contain,  as  far  as  that  quan- 
tity can  be  ascertained  ;  a  single  grain  being  sufficient  to  make  20  pounds 
of  another  metal  sensibly  magnetic.  A  combination  with  a  large  propor- 
tion of  oxygen  deprives  iron  of  the  whole  or  the  greater  part  of  its 
magnetic  properties  ;  finery  cinder  is  still  considerably  magnetic,  but  the 
more  perfect  oxids  and  the  salts  of  iron  only  in  a  slight  degree  ;  it  is  also 
said  that  antimony  renders  iron  incapable  of  being  attracted  by  the  magnet. 
Nickel,  when  freed  from  arsenic  and  from  cobalt,  is  decidedly  magnetic, 
and  the  more  so  as  it  contains  less  iron.  Some  of  the  older  chemists  sup- 
posed nickel  to  be  a  compound  metal  containing  iron,  and  we  may  still 
venture  to  assume  this  opinion  as  a  magnetical  hypothesis.  There  is  in- 
deed no  way  of  demonstrating  that  it  is  impossible  for  two  substances  to 
be  so  united  as  to  be  incapable  of  separation  by  the  art  of  the  chemist ; 

*  Hist,  et  Mem.  1785,  pp.  569,  578  ;  1789,  p.  455.     Mem.  de  1'Instit.  iii.  176. 
f  De  1'Origine  des  Forces  Magnetiques,  Geneve,  1788. 
t  De  Magnete,  fol.  Lond.  1600. 

§  Ph.  Tr.  1787,  p.  6.  ||   Ibid.  1786,  p.  62. 

H  Bulletin  de  la  Soc.  Philom.  No.  61,  63.     Jour,  de  Phy.  liv.  240,  267,  454;    See 
Young,  Jour,  of  the  Roy.  Inst.  i.  134,  217. 


ON  MAGNETISM.  533 

had  nickel  been  as  dense  as  platina,  or  as  light  as  cork,  we  could  not  have 
supposed  that  it  contained  any  considerable  quantity  of  iron,  but  in  fact 
the  specific  gravity  of  these  metals  is  very  nearly  the  same,  and  nickel  is 
never  found  in  nature  but  in  the  neighbourhood  of  iron  ;  we  may  therefore 
suspect,  with  some  reason,  that  the  hypothesis  of  the  existence  of  iron  in 
nickel  may  be  even  chemically  true.  The  aurora  borealis  is  certainly  in 
some  measure  a  magnetical  phenomenon,  and  if  iron  were  the  only  sub- 
stance capable  of  exhibiting  magnetic  effects,  it  would  follow  that  some 
ferruginous  particles  must  exist  in  the  upper  regions  of  the  atmosphere. 
The  light  usually  attending  this  magnetical  meteor  may  possibly  be 
derived  from  electricity,  which  may  be  the  immediate  cause  of  a  change 
of  the  distribution  of  the  magnetic  fluid,  contained  in  the  ferruginous 
vapours,  that  are  imagined  to  float  in  the  air. 

We  are  still  less  capable  of  distinguishing  with  certainty  in  magnetism, 
than  in  electricity,  a  positive  from  a  negative  state,  or  a  real  redundancy  of 
the  fluid  from  a  deficiency.  The  north  pole  of  a  magnet  may  be  con- 
sidered as  the  part  in  which  the  magnetic  fluid  is  either  redundant  or  de- 
ficient, provided  that  the  south  pole  be  understood  in  a  contrary  sense  : 
thus,  if  the  north  pole  of  a  magnet  be  supposed  to  be  positively  charged, 
the  south  pole  must  be  imagined  to  be  negative  ;  and  in  hard  iron  or  steel 
these  poles  may  be  considered  as  unchangeable. 

A  north  pole,  therefore,  always  repels  a  north  pole,  and  attracts  a  south 
pole.  And  in  a  neutral  piece  of  soft  iron,  near  to  the  north  pole  of  a 
magnet,  the  fluid  becomes  so  distributed  by  induction,  as  to  form  a  tem- 
porary south  pole  next  to  the  magnet,  and  the  whole  piece  is  of  course 
attracted,  from  the  greater  proximity  of  the  attracting  pole.  If  the  bar  is 
sufficiently  soft,  and  not  too  long,  the  remoter  end  becomes  a  north  pole, 
and  the  whole  bar  a  perfect  temporary  magnet.  But  when  the  bar  is  of 
hard  steel,  the  state  of  induction  is  imperfect,  from  the  resistance  opposed 
to  the  motion  of  the  fluid  ;  hence  the  attraction  is  less  powerful,  and  an 
opposite  pole  is  formed,  at  a  certain  distance,  within  the  bar ;  and  beyond 
this  another  pole,  similar  to  the  first ;  the  alternation  being  sometimes  re« 
peated  more  than  once.  The  distribution  of  the  fluid  within  the  magnet  is 
also  affected  by  the  neighbourhood  of  a  piece  of  soft  iron,  the  north  pole 
becoming  more  powerful  by  the  vicinity  of  the  new  south  pole,  and  the 
south  pole  being  consequently  strengthened  in  a  certain  degree  ;  so  that  the 
attractive  power  of  the  whole  magnet  is  increased  by  the  proximity  of  the 
iron.  A  weak  magnet  is  capable  of  receiving  a  temporary  induction  of  a 
contrary  magnetism  from  the  action  of  a  more  powerful  one,  its  north  pole 
becoming  a  south  pole  on  the  approach  of  a  stronger  north  pole ;  but  the 
original  south  pole  still  retains  its  situation  at  the  opposite  end,  and 
restores  the  magnet  nearly  to  its  original  condition,  after  the  removal  of 
the  disturbing  cause. 

The  polarity  of  magnets,  or  their  disposition  to  assume  a  certain  direc- 
tion, is  of  still  greater  importance  than  their  attractive  power.  If  a  small 
magnet,  or  simply  a  soft  wire,  be  poised  on  a  centre,  it  will  arrange  itself 
in  such  a  direction,  as  will  produce  an  equilibrium  of  the  attractions  and 
repulsions  of  the  poles  of  a  larger  magnet ;  being  a  tangent  to  a  certain 


534  LECTURE  LV. 

oval  figure  passing  through  those  poles,  of  which  the  properties  have  been 
calculated  by  various  mathematicians.  This  polarity  may  easily  be 
imitated  by  electricity  ;  a  suspended  wire  being  brought  near  to  the  ends 
of  a  positive  and  negative  conductor,  which  are  placed  parallel  to  each 
other,  as  in  Nairne's  electrical  machine,  its  position  is  perfectly  similar  to 
that  of  a  needle  attracted  by  a  magnet,  of  which  those  conductors  repre- 
sent the  poles.  (Plate  XLI.  Fig.  569.) 

The  same  effect  is  observable  in  iron  filings  placed  near  a  magnet,  and 
they  adhere  to  each  other  in  curved  lines,  by  virtue  of  their  induced  mag- 
netism, the  north  pole  of  each  particle  being  attached  to  the  south  pole  of 
the  particle  next  it.  This  arrangement  may  be  seen  by  placing  the  filings 
either  on  clean  mercury,  or  on  any  surface  that  can  be  agitated  ;  and  it 
may  be  imitated  by  strewing  powder  on  a  plate  of  glass  supported  by 
two  balls,  which  are  contrarily  electrified.*  (Plate  XLI.  Fig,  570.) 

The  polarity  of  a  needle  may  often  be  observed  when  it  exhibits  no  sen- 
sible attraction  or  repulsion  as  a  whole ;  and  this  may  easily  be  understood 
by  considering  that  when  one  end  of  a  needle  is  repelled  from  a  given  point, 
and  the  other  is  attracted  towards  it,  the  two  forces,  if  equal,  will  tend  to 
turn  it  round  its  centre,  but  will  wholly  destroy  each  other's  effects  with 
respect  to  any  progressive  motion  of  the  whole  needle.  Thus,  when  the 
end  of  a  magnet  is  placed  under  a  surface  on  which  iron  filings  are  spread, 
and  the  surface  is  shaken,  so  as  to  leave  the  particles  for  a  moment  in  the 
air,  they  are  not  drawn  sensibly  towards  the  magnet,  but  their  ends,  which 
are  nearest  to  the  point  over  the  magnet,  are  turned  a  little  downwards,  so 
that  they  strike  the  paper  further  and  further  from  the  magnet,  and  then 
fall  outwards,  as  if  they  were  repelled  by  it.  (Plate  XLI.  Fig.  571.) 

The  magnets,  which  we  have  hitherto  considered,  are  such  as  have  a  sim- 
ple and  well  determined  form  ;  but  the  great  compound  magnet,  which 
directs  the  mariner's  compass,  and  which  appears  to  consist  principally  of 
the  metallic  and  slightly  oxidated  iron,  contained  in  the  internal  parts  of 
the  earth,  is  probably  of  a  far  more  intricate  structure,  and  we  can  only 
judge  of  its  nature  from  the  various  phenomena  derived  from  its  influence. 

The  accumulation  and  the  deficiency  of  the  magnetic  fluid,  which  deter- 
mine the  place  of  the  poles  of  this  magnet,  are  probably  in  fact  consider- 
ably diffused,  but  they  may  generally  be  imagined,  without  much  error  in 
the  result,  to  centre  in  two  points,  one  of  them  nearer  to  the  north  pole  of 
the  earth,  the  other-to  the  south  pole.  In  consequence  of  their  attractions 
and  repulsions,  a  needle,  whether  previously  magnetic  or  not,  assumes 
always,  if  freely  poised,  the  direction  necessary  for  its  equilibrium  ;  which, 
in  various  parts  of  the  globe,  is  variously  inclined  to  the  meridian  and  to 
the  horizon.  Hence  arises  the  use  of  the  compass  in  navigation  and  in 
surveying  :  a  needle,  which  is  poised  with  the  liberty  of  horizontal  motion, 
assuming  the  direction  of  the  magnetic  meridian,  which  for  a  certain  time 
remains  almost  invariable  for  the  same  place  ;  and  a  similar  property  is 
also  observable  in  the  dipping  needle,  which  is  moveable  only  in  a  vertical 
plane  ;  for  when  this  plane  is  placed  in  the  magnetic  meridian,  the  needle 

*  Bazin,  Descrip.  des  Courans  Mag.  en  15  Planches,  4to,  Strasb.  1753.  Roget, 
Jour,  of  the  Roy.  Inst.  1831,  p.  311. 


ON  MAGNETISM.  535 

acquires  an  inclination  to  the  horizon,  which  varies  according  to  the  situa- 
tion of  the  place  with  respect  to  the  magnetic  poles.  (Plate  XLI.  Fig.  572, 
573.) 

The  natural  polarity  of  the  needle  may  be  in  some  measure  illustrated 
by  inclosing  an  artificial  magnet  in  a  globe  ;  the  direction  of  a  small  needle, 
suspended  over  any  part  of  its  surface,  being  determined  by  the  position  of 
the  poles  of  the  magnet,  in  the  same  manner  as  the  direction  of  the  compass 
is  determined  by  the  magnetical  poles  of  the  earth,  although  with  much 
more  regularity.  In  either  case  the  whole  needle  is  scarcely  more  or  less 
attracted  towards  the  globe  than  if  the  influence  of  magnetism  were 
removed  ;  except  when  the  small  needle  is  placed  very  near  to  one  of  the 
poles  of  the  artificial  magnet,  or,  on  the  other  hand,  when  the  dipping 
needle  is  employed  in  the  neighbourhood  of  some  strata  of  ferruginous  sub- 
stances, which,  in  particular  parts  of  the  earth,  interfere  materially  with 
the  more  general  effects,  and  alter  the  direction  of  the  magnetic  meridian. 

A  bar  of  soft  iron,  placed  in  the  situation  of  the  dipping  needle,  acquires 
from  the  earth,  by  induction,  a  temporary  state  of  magnetism,  which  may 
be  reversed  at  pleasure  by  reversing  its  direction  ;  but  bars  of  iron,  which 
have  remained  long  in  or  near  this  direction,  assume  a  permanent  polarity ; 
for  iron,  even  when  it  has  been  at  first  quite  soft,  becomes  in  time  a  little 
harder.  A  natural  magnet  is  no  more  than  a  heavy  iron  ore,  which,  in  the 
course  of  ages,  has  acquired  a  strong  polarity  from  the  great  primitive 
magnet.  It  must  have  lain  in  some  degree  detached,  and  must  possess  but 
little  conducting  power,  in  order  to  have  received  and  to  retain  its  mag- 
netism. 

We  cannot,  from  any  assumed  situation  of  two  or  more  magnetic 
poles,  calculate  the  true  position  of  the  needle  for  all  places  ;  and  even  in  the 
same  place,  its  direction  is  observed  to  change  in  the  course  of  years,  accord- 
ing to  a  law  which  has  never  yet  been  generally  determined,  although  the 
variation  which  has  been  observed,  at  any  one  place,  since  the  discovery  of 
-the  compass,  may  perhaps  be  comprehended  in  some  very  intricate  expres- 
sions ;  but  the  less  dependence  can  be  placed  on  any  calculations  of  this 
kind,  as  there  is  reason  to  think  that  the  change  depends  rather  on  chemical 
than  on  physical  causes.  Dr.  Halley*  indeed  conjectured  that  the  earth 
contained  a  nucleus,  or  separate  sphere,  revolving  freely  within  it,  or  rather 
floating  in  a  fluid  contained  in  the  intermediate  space,  and  causing  the 
variation  of  the  magnetic  meridian  ;  and  others  have  attributed  the  effect 
to  the  motions  of  the  celestial  bodies  :  but  in  either  case  the  changes  pro- 
duced would  have  been  much  more  regular  and  universal  than  those  which 
have  been  actually  observed.  Temporary  changes  of  the  terrestrial  mag- 
netism have  certainly  been  sometimes  occasioned  by  other  causes ;  such 
causes  are,  therefore,  most  likely  to  be  concerned  in  the  more  permanent 
effects.  Thus,  the  eruption  of  Mount  Hecla  was  found  to  derange  the 
position  of  the  needle  considerably  ;  the  aurora  borealist  has  been  observed 
to  cause  its  north  pole  to  move  6  or  7  degrees  to  the  westward  of  its  usual 

*.?h.'Tr.  1693,  p.  563. 

f  See  Arago,  Ann.  de  Ch.  xxxix.  369.     Fox,  Ph.  Tr.  1831,  p.  199.     Sabine, 
Obs.  on  Days  of  unusual  Mag.  Disturbance,  4to,  1843. 


536  LECTURE  LV. 

position ;  and  a  still  more  remarkable  change  occurs  continually  in  the 
diurnal  variation.  In  these  climates  the  north  pole  of  the  needle  moves 
slowly  westwards  from  about  8  in  the  morning  till  2,  and  in  the  evening 
returns  again  ;*  a  change  which  has  with  great  probability  been  attributed 
to  the  temporary  elevation  of  the  temperature  of  the  earth,  eastwards 
of  the  place  of  observation,  where  the  sun's  action  takes  place  at  an  earlier 
hour  in  the  morning,  and  to  the  diminution  of  the  magnetic  attraction  in 
consequence  of  the  heat  thus  communicated.  In  winter  this  variation 
amounts  to  about  7  minutes,  in  summer  to  13  or  14. 

Important  as  the  use  of  the  compass  is  at  present  to  navigation,  it  would 
be  still  more  valuable  if  its  declination  from  the  true  meridian  were  con- 
stant for  the  same  place,  or  even  if  it  varied  according  to  any  discoverable 
law  ;  since  it  would  afford  a  ready  mode  of  determining  the  longitude  of  a 
place  by  a  comparison  of  an  astronomical  observation  of  its  latitude  with 
another  of  the  magnitude  of  the  declination.  And  in  some  cases  it  may 
even  now  be  applied  to  this  purpose,  where  we  have  a  collection  of  late  and 
numerous  observations.  Such  observations  have  from  time  to  time  been 
arranged  in  charts,  furnished  with  lines  indicating  the  magnitude  of  the 
declination  or  variation  at  the  places  through  which  they  pass,  beginning 
from  the  line  of  no  variation,  and  proceeding  on  the  opposite  sides  of  this 
line  to  show  the  magnitude  of  the  variation  east  or  west.  It  is  obvious 
that  the  intersection  of  a  given  parallel  of  latitude,  with  the  line  showing 
the  magnitude  of  the  variation,  will  indicate  the  precise  situation  of  the 
place  at  which  the  observations  have  been  made. 

The  line  of  no  variation  passed  in  1657  through  London,  and  in  1666 
through  Paris  :  its  northern  extremity  appears  to  have  moved  continually 
eastwards,  and  its  southern  parts  westwards ;  and  it  now  passes  through 
the  middle  of  Asia.  The  opposite  portion  seems  to  have  moved  more  uni- 
formly westwards  ;  it  now  runs  from  North  America  to  the  middle  of  the 
South  Atlantic.  On  the  European  side  of  these  lines,  the  declination  is 
westerly ;  on  the  South  American  side,  it  is  easterly.  The  variation  in 
London  has  been  for  several  years  a  little  more  than  24°.  In  the  West 
Indies  it  changes  but  slowly ;  for  instance  it  was  5°  near  the  island  of 
Barbadoes,  from  1700  to  1756.  (Plate  XLI.  Fig.  574  .  .  576.  Plate 
XLII.  XLIII.) 

The  dip  of  the  north  pole  of  the  needle  in  the  neighbourhood  of  London 
is  72°.t  Hence  the  lower  end  of  a  bar  standing  upright,  as  a  poker,  or  a 
lamp  iron,  becomes  always  a  north  pole,  and  the  temporary  south  pole  of 
a  piece  of  soft  iron  being  uppermost,  it  is  somewhat  more  strongly  attracted 
by  the  north  pole  of  a  magnet  placed  over  it,  than  by  its  south  pole  ;  the 
distribution  of  the  fluid  in  the  magnet  itself  being  also  a  little  more  favour- 
able to  the  attraction,  while  its  north  pole  is  downwards.  It  is  obvious 
that  the  magnetism  of  the  northern  magnetic  pole  of  the  earth  must 
resemble  that  of  the  south  pole  of  a  magnet,  since  it  attracts  the  north  pole  ; 

*  Graham,  Obs.  made  in  1722.  Ph.Tr.  xxxiii.  96,  383.  The  daily  variation  has 
been  more  accurately  observed  by  Christie,  Ph.  Tr.  1823-5-7  ;  and  at  Gottinge^  by 
Goldschmidt  and  others,  Res.  des  Mag.  Vereins,  v.  y. 

t  It  is  now  about  69°. 


ON  MAGNETISM.  537 

so  that  if  we  considered  the  nature  of  the  distribution  of  the  fluid,  rather 
than  its  situation  in  the  earth,  we  should  call  it  a  south  pole.  Although 
it  is  impossible  to  find  any  places  for  two,  or  even  for  a  greater  number  of 
magnetic  poles,  which  will  correctly  explain  the  direction  of  the  needle  in 
every  part  of  the  earth's  surface,  yet  the  dip  may  be  determined  with 
tolerable  accuracy,  from  the  supposition  of  a  small  magnet  placed  at  the 
centre  of  the  earth,  and  directed  towards  a  point  in  Baffin's  Bay,  about  75° 
north  latitude,  and  70°  longitude  west  of  London  ;  and  the  variation  of  the 
dip  is  so  inconsiderable,  that  a  very  slow  change  of  the  position  of  this 
supposed  magnet  would  probably  be  sufficient  to  produce  it ;  but  the  ope- 
ration of  such  a  magnet,  according  to  the  general  laws  of  the  forces  con- 
cerned, could  not  possibly  account  for  the  very  irregular  disposition  of  the 
curves  indicating  the  degree  of  variation  or  declination  ;  a  general  idea  of 
these  might  perhaps  be  obtained  from  the  supposition  of  two  magnetic  poles 
situated  in  a  line  considerably  distant  from  the  centre  of  the  earth  ;  but  this 
hypothesis  is  by  no  means  sufficiently  accurate  to  allow  us  to  place  any 
dependence  on  it.  (Plate  XLI.  Fig.  577,  578.) 

The  art  of  making  magnets  consists  in  a  proper  application  of  the  attrac- 
tions and  repulsions  of  the  magnetic  fluid,  by  means  of  the  different  con- 
ducting powers  of  different  kinds  of  iron  and  steel,  to  the  production  and 
preservation  of  such  a  distribution  of  the  fluid  in  a  magnet,  as  is  the  best 
fitted  to  the  exhibition  of  its  peculiar  properties. 

We  may  begin  with  any  bar  of  iron  that  has  long  stood  in  a  vertical 
position  ;  but  it  is  more  common  to  employ  an  artificial  magnet  of  greater 
strength.  When  one  pole  of  such  a  magnet  touches  the  end  of  a  bar  of  hard 
iron  or  steel ;  that  end  assumes  in  some  degree  the  opposite  character,  and 
the  opposite  end  the  same  character :  but  in  drawing  the  pole  along  the 
bar,  the  first  end  becomes  neutral,  and  afterwards  has  the  opposite  polarity ; 
while  the  second  end  has  its  force  at  first  a  little  increased,  then  becomes 
neutral,  and  afterwards  is  opposite  to  what  it  first  was.  When  the  opera- 
tion is  repeated,  the  effect  is  at  first  in  some  measure  destroyed,  and  it  is 
difficult  to  understand  why  the  repetition  adds  materially  to  the  inequality 
of  the  distribution  of  the  fluid  ;  but  the  fact  is  certain,  and  the  strength  of 
the  new  magnet  is  for  some  time  increased  at  each  stroke,  until  it  has 
acquired  all  that  it  is  capable  of  receiving.  Several  magnets,  made  in  this 
manner,  may  be  placed  side  by  side,  and  each  of  them  being  nearly  equal 
in  strength  to  the  first,  the  whole  collection  will  produce  together  a  much 
stronger  effect ;  and  in  this  manner  we  may  obtain  from  a  weak  magnet 
others  continually  stronger,  until  we  arrive  at  the  greatest  degree  of  polarity 
of  which  the  metal  is  capable.  It  is,  however,  more  usual  to  employ  the 
process  called  the  double  touch ;  placing  two  magnets,  with  their  opposite 
poles  near  to  each  other,  or  the  opposite  poles  of  a  single  magnet,  bent  into 
the  form  of  a  horseshoe,  in  contact  with  the  middle  of  the  bar  ;  the  opposite 
actions  of  these  two  poles  then  conspire  in  their  effort  to  displace  the  mag- 
netic fluid,  and  the  magnets  having  been  drawn  backwards  and  forwards 
repeatedly,  an  equal  number  of  times  to  and  from  each  end  of  the  bar,  with 
a  considerable  pressure,  they  are  at  last  withdrawn  in  the  middle,  in  order 
to  keep  the  poles  at  equal  distances. 


538  LECTURE  LV. 

Iron  filings,  or  the  scoriae  from  a  smith's  forge,  when  finely  levigated, 
and  formed  into  a  paste  with  linseed  oil,  are  also  capable  of  being 
made  collectively  magnetic.  A  bar  of  steel,  placed  red  hot  between  two 
magnets,  and  suddenly  quenched  by  cold  water,  becomes  in  some  degree 
magnetic,  but  not  so  powerfully  as  it  may  be  rendered  by  other  means. 
For  preserving  magnets,  it  is  usual  to  place  their  poles  in  contact  with 
the  opposite  poles  of  other  magnets,  or  with  pieces  of  soft  iron,  which,  in 
consequence  of  their  own  induced  magnetism,  tend  to  favour  the  accumu- 
lation of  the  magnetic  power  in  a  greater  quantity  than  the  metal  can 
retain  after  they  are  removed.  Hence  the  ancients  imagined  that  the  mag- 
net fed  on  iron. 

A  single  magnet  may  be  made  of  two  bars  of  steel,  with  their  ends  pressed 
into  close  contact ;  and  it  might  be  expected  that  when  these  bars  are 
separated,  or  when  a  common  magnet  has  been  divided  in  the  middle,  the 
portions  should  possess  the  properties  of  the  respective  poles  only.  But  in 
fact  the  ends  which  have  been  in  contact  are  found  to  acquire  the  properties 
of  the  poles  opposite  to  those  of  their  respective  pieces,  and  a  certain  point 
in  each  piece  is  neutral,  which  is  at  first  nearer  to  the  newly  formed 
pole  than  to  the  other  end,  but  is  removed  by  degrees  to  a  more  central 
situation.  In  this  case  we  must  suppose,  contrarily  to  the  general  prin- 
ciples of  the  theory,  that  the  magnetic  fluid  has  actually  escaped  by  degrees 
from  one  of  the  pieces,  and  has  been  received  from  the  atmosphere  by  the 
other. 

There  is  no  reason  to  imagine  any  immediate  connexion  between  mag- 
netism and  electricity,  except  that  electricity  affects  the  conducting  powers 
of  iron  or  steel  for  magnetism,  in  the  same  manner  as  heat  or  agitation. 
In  some  cases  a  blow,  an  increase  of  temperature,  or  a  shock  of  electricity, 
may  expedite  a  little  the  acquisition  of  polarity  ;  but  more  commonly  any 
one  of  these  causes  impairs  the  magnetic  power.  Professor  Robison  found, 
that  when  a  good  magnet  was  struck  for  three  quarters  of  an  hour,  and 
allowed  in  the  mean  time  to  ring,  its  efficacy  was  destroyed  ;  although  the 
same  operation  had  little  effect  when  the  ringing  was  impeded  ;  so  that  the 
continued  exertion  of  the  cohesive  and  repulsive  powers  appears  to  favour 
the  transmission  of  the  magnetic  as  well  as  of  the  electric  fluid.  The  inter- 
nal agitation,  produced  in  bending  a  magnetic  wire  round  a  cylinder,  also 
destroys  its  polarity,  and  the  operation  of  a  file  has  the  same  effect.  Mr. 
Cavallo*  has  found  that  brass  becomes  in  general  much  more  capable  of 
being  attracted  when  it  has  been  hammered,  even  between  two  flints ;  and 
that  this  property  is  again  diminished  by  fire  :  in  this  case  it  may  be  con- 
jectured that  hammering  increases  the  conducting  power  of  the  iron  con- 
tained in  the  brass,  and  thus  renders  it  more  susceptible  of  magnetic 
action.  Mr.  Cavallo  t  also  observed  that  a  magnetic  needle  was  more 
powerfully  attracted  by  iron  filings  during  their  solution  in  acids,  espe- 
cially in  the  sulfuric  acid,  than  either  before  or  after  the  operation  :  others 
have  not  always  succeeded  in  the  experiment ;  but  there  is  nothing  impro- 
bable in  the  circumstance,  and  there  may  have  been  some  actual  difference 
in  the  results,  dependent  on  causes  too  minute  for  observation.  In  subjects 
*  Ph.  Tr.  1786,  p.  62.  f  Ibid.  1787,  p.  6. 


ON  MAGNETISM.  539 

so  little  understood  as  the  theory  of  magnetism,  we  are  obliged  to  admit 
some  paradoxical  propositions,  which  are  only  surprising  on  account  of 
the  imperfect  state  of  our  knowledge.  Yet,  little  as  we  can  understand 
the  intimate  nature  of  magnetical  actions,  they  exhibit  to  us  a  number 
of  extremely  amusing  as  well  as  interesting  phenomena  ;  and  the  prin- 
ciples of  crystallization,  and  even  of  vital  growth  and  reproduction,  are 
no  where  so  closely  imitated,  as  in  the  arrangement  of  the  small  particles 
of  iron  in  the  neighbourhood  of  a  magnet,  and  in  the  production  of  a 
multitude  of  complete  magnets,  from  the  influence  of  a  parent  of  the 
same  kind. 

[Numerous  and  important  as  are  the  additions  which  have  been  recently 
made  to  our  knowledge  of  the  agencies  of  electric  and  magnetic  forces,  our 
limits  will  merely  suffice  us  to  mention  those  which  appear  to  constitute 
new  and  distinct  branches  of  science. 

In  1819,  Professor  Oersted,  of  Copenhagen,  discovered*  that  a  current 
of  voltaic  electricity  exerts  an  action  on  the  magnetic  needle,  which  differs 
in  its  character  from  the  other  forces  observed  in  nature,  inasmuch  as  it  is 
tangential  to  the  course  of  the  current.  This  will  be  best  understood  from 
an  inspection  of  the  accompanying  figures,  in  which  N  and  S  are  the  north 
and  south  poles  of  Tin  ± 

a  magnet,  cz  is  a  c 
wire,  along  which 
flows  a  current  of 
voltaic  electricity, 
the  end  c  being  in 
connexion  with  the 
positive  or  copper 
plate  of  the  simple 
battery,  and  the 

other  end  with  the 

~"c 
-  negative     or     zinc 

plate.  In  figure  1, 
where  the  wire  is  above  the  needle,  it  causes  the  north  pole  to  be  deflected 
towards  the  east,  as  at  n  ;  in  figure  2,  where  it  is  below,  towards  the  west. 
Were  the  wire  placed  in  the  same  horizontal  plane  with  the  needle,  the 
poles  of  the  latter  would  simply  suffer  elevation  or  depression.  The  effect 
of  this  force  on  the  north  pole  of  a  magnet  (that  on  the  south  pole  being 
of  course  the  reverse)  is  represented  by  the  following  diagram,  in  which 
the  repulsion  is  in  the 
direction  in  which  the 
hands  of  the  watch  are  ac-  •*  *•$  °- 

customed  to  move.  The 
science  which  is  built  on 
this  fact  is  termed  ELEC- 
TRO-MAGNETISM. 

Fro,m  the  nature  of  the  ^-j^^ 

*  Thomson's  Annals  of  Philosophy,  1820,  xvi.  273.  A.nn.  de  Ch.  xxii.  201. 
Schweigg.  Jour,  xxxii.  199  ;  xxxiii.  123. 


540  LECTURE   LV. 

action  which  we  have  de- 
scribed, it  is  evident  that  the 
effect  can  he  multiplied  al- 
most indefinitely  hy  simply 
coiling  the  wire  and  placing 
the  needle  within  the  coil  ; 
for  the  currents  on  each  side 
of  the  needle  all  tend  to  move 
it  in  the  same  direction. 

In  this  way  the  galvano- 
meter is  constructed.*  A 
small  needle  is  suspended  hy 
a  fibre  of  silk,  and  a  coil  of 
wire,  coated  with  sealing  wax 
or  silk,  causes  the  voltaic  current  to  circulate  in  directions  parallel  to  it. 
The  tangential  action  of  the  current  overcomes  the  magnetic  action  of  the 
earth  and  deflects  the  needle.  The  delicacy  and  value  of  this  instrument 
have  been  greatly  increased  by  the  inventions  of  Gumming  t  and  Nobili.J 
Instead  of  a  single  needle,  two  needles  are  used,  which  are  placed  with 
their  poles  opposite  ways,  so  that  the  directive  tendency  due  to  the  earth's 
action  is  completely  neutralized,  and  the  torsion  of  the  suspending  thread 
is  the  sole  impediment  to  motion.  In  the  figure  the  needles  are  ordi- 
nary sewing  needles  similarly  magnetized,  and  passed  parallel  to  each 
other  through  a  flat  bit  of  straw  which  is  attached  to  the  fibre  of  silk.  The 
coil  of  wire  passes  about  the  lower  needle,  having  in  its  upper  part  an 
opening  through  which  the  straw  passes  freely.  The  amount  of  force 
exerted  is  the  sum  of  the  actions  of  the  upper  and  lower  currents  on  the 
lower  needle,  together  with  the  difference  of  those  on  the  upper  wire. 
The  action  of  the  voltaic  current  on  a  magnetic  needle  is  very  similar  to 
the  action  of  one  magnetic  needle  on  another,  except  that  it  is  perpendi- 
cular to  the  direction  of  the  current.  Now  the  action  of  a  magnetic  needle 
produces  the  magnetic  state  in  a  bar  of  soft  iron,  and  hence  it  is  natural  to 
conclude  that  a  voltaic  current  should  produce  a  similar  state.  Accord- 
ingly, if  a  considerable  quantity  of  copper  wire  be  twisted  round  a  piece  of 
soft  iron  bent  into  the  form  of  a  horseshoe,  and  a  voltaic  current  be  passed 
along  the  wire,  the  result  is  the  formation  of  a  powerful  magnet.  On 
discontinuing  the  communication  with  the  voltaic  pile,  the  iron  is  instantly 
reduced  to  nearly  its  former  state.  This  presents  us  with  a  promising  field 
of  research  in  its  applicability  to  economical  purposes  as  a  moving  power. 
And  although  the  endeavours  of  Jacobi  §  and  others  have  as  yet  been  only 
partially  successful,  there  is  every  reason  to  suppose  that  time  will 

*  Schweigger,  in  his  Jour.  1821.  f  Camb.  Tr.  1821,  p.  281. 

J  Memorie  ed  Osservazioni  colla  Descrizione  de  suoi  Apparati,  2  vols.  Firenze, 
1834.  See  also  Melloni,  Arch,  de  1'Electr.  i.  165. 

§  Ritchie,  Phil.  Mag.  iv.  13.  Dal  Negro,  Nuova  Macchina  Elettro-Mag.  Ann. 
delle  Scienze  del  Regno  Lomb.  Venet.  1834.  Jacobi,  Mem.  sur  1' Application  de 
1'Electro-Mag.  au  Mouvement  des  Mach.  Potsdam,  1835.  Sturgeon,  in  Stuf.-Ann. 
i.  75 ;  viii.  81.  Davenport,  ibid,  ii.  284.  Davidson,  Mechanics'  Magazine,  Nov. 
1842. 


ON  MAGNETISM.  541 

develope  the  means  of  rendering  this  agent  one  of  the  great  assistants  to 
human  power.  An  attractive  force  can  be  created  and  destroyed  at  plea- 
sure, and  thereby  an  alternation'of  action,  so  necessary  to  dynamical  effects, 
can  be  produced.  The  electro-magnetic  telegraph  is  based  on  the  same 
principles.*  A  wheel  has  twenty-four  conductors  placed  on  its  circum- 
ference at  equal  intervals,  so  that  when  it  is  turned  through  a  complete 
revolution,  the  voltaic  circuit  is  completed  and  broken  twenty-four  times. 
This  wheel  is  placed  at  one  station,  and  another  wheel,  together  with 
an  electro-magnet,  at  the  other;  a  pair  of  wires  sufficing  to  effect  the 
communication  between  them.  When  the  circuit  is  complete,  the  electro- 
magnet is  in  action  and  causes  its  accompanying  circle  to  move  through 
one  division ;  that  is  to  say,  each  turn  of  the  one  wheel  causes  a  similar 
movement  in  the  other.  Now  to  every  division  is  attached  a  letter  of  the 
alphabet.  If  then  the  instrument  be  standing  at  C,  and  it  be  requi- 
site to  convey  the  letter  F,  the  first  wheel  must  be  turned  through  three 
divisions,  by  which  D,  E,  and  F  are  successively  presented  to  the  ob- 
server at  the  other  station  ;  the  last  of  which  only  is  suffered  to  rest. 
The  close  analogy  between  the  agents  which  produce  the  varied  forms  of 
electricity  and  magnetism  is  rendered  still  closer  by  the  beautiful  dis- 
coveries of  Faraday  and  others.  When  a  current  is  passing  along  a  wire, 
it  induces  a  similar  current  along  a  wire  placed  near  the  first,  at  the  times 
of  making  and  of  breaking  the  contact.  Now  we  have  seen  that  a  current 
of  electricity  passing  round  a  bar  of  iron  renders  it  a  magnet,  and  it  was 
easy  to  conjecture  that,  conversely,  a  magnet  should  produce  a  current  in 
a  coil  wound  about  it.  Faraday  f  proved  that  this  is  the  case  at  the  moment 
only  of  its  becoming  or  ceasing  to  become  a  magnet.  The  coil  was 
wrapped  round  a  piece  of  soft  iron,  the  extremities  of  which  could  be 
brought  simultaneously  in  contact  with  the  ends  of  a  horseshoe  magnet. 
At  the  instant  of  forming  this  contact  a  current  of  electricity  was  produced 
along  the  coil,  the  effect  of  which  was  sensible  to  the  galvanometer.  Soon 
after  this  discovery,  all  the  usual  electrical  effects  were  produced  in  this 
way,  and  in  1832  was  constructed,  by  M.  Pixii,  J  a  very  powerful  magneto- 
electric  machine.  This  machine,  as  improved  by  Saxton  §  and  Clarke,  || 
consists  of  a  compound  horseshoe  magnet  of  a  large  size  fixed  in  a  given 
position.  A  piece  of  soft  iron,  of  much  the  same  shape,  has  a  quantity  of 
insulated  copper  wire  wound  round  it,  and  is  so  placed  as  to  be  capable  of 
rapidly  presenting  its  ends  alternately  to  the  poles  of  the  fixed  magnet.  By 
this  means  it  becomes  constantly  magnetized,  demagnetized,  and  oppositely 
magnetized.  Thus  the  conditions  requisite  for  the  development  of  an 

*  Wheatstone,  Mech.  Mag.  1840.  Walker's  Electr.  Mag.  vol.  ii.  Sturgeon's 
Annals,  v.  337.  Steinheil,  Ueber  Teleg.  4to,  Munch,  1838.  Morse,  Ann.  de  Ch. 
Ixxii.  219.  Lenz,  Ueber  die  Praktischen  Anwendungen  des  Galv.  Petersb.  1839. 
De  Heer,  Theorie  de  la  Teleg.  Electr.  Bullet,  des  Sci.  Phys.  en  Neerland,  1839. 
Finlayson,  The  Application  of  the  Electric  Fluid  to  the  Useful  Arts.  For  the 
application  of  galvanism  to  gilding,  &c.  see  Jacobi,  Galvanoplastik,  St.  Petersb. 
1840.  Smee's  Metallurgy. 

t  F?*a*day,  Ph.  Tr.  1832.     Experimental  Researches  in  Electricity,  1839. 

J  Ann.  de  Ch.  1.  322.  §  Ph.  Mag.  ix.  262. 

||  Sturgeon's  Ann.  i.  145. 


542  LECTURE  LV. 

electric  current  are  attained,  and  very  little  ingenuity  is  requisite  to 
render  the  machine  available  as  a  powerful  electrical  machine  of  a  peculiar 
character. 

The  last  mode  of  developing  a  current  which  we  shall  mention  is  that 
discovered  by  M.  Arago.*  If  a  plate  of  copper  be  made  to  rotate  with 
considerable  rapidity  in  a  horizontal  plane,  a  magnetic  needle  placed  above 
or  below  it  tends  to  follow  its  motion,  and  that  quite  irrespective  of  the 
motion  of  the  air,  as  may  be  proved  by  interposing  a  plate  of  glass  or 
other  substance  between  them.  It  is  evident  that  this  effect  is  due  to  the 
evolution  of  a  current  of  electricity,  which  travels  from  the  centre  to  the 
circumference  of  the  plate.  For  further  information,  the  reader  is  referred 
to  Faraday's  Researches  ;  he  will  also  find  an  excellent  article  on  electro- 
magnetism,  by  Roget,  in  the  Library  of  Useful  Knowledge.] 


LECT.  LV.-ADDITIONAL  AUTHORITIES. 

Treatises. — Peregrinus,  De  Magnete,  4to,  Augsb.  1558.  Norman,  The  New 
Attractive,  4to,  1596.  Ridley,  On  Magn.  Bodies  and  Motions,  4to,  Lond.  1613. 
Cabseus,  Philosophia  Mag.  fol.  Ferrara,  1629.  Kircher,  Magnes,  4to,  Col.  1643. 
Lieutaud.  Magnetologia,  4to,  Lugd.  1668.  Dalance,  Traite  de  1'Aimant,  4to,  Liege, 
1691.  Eberhard's  Mag.  Theorie,  4to,  Leipz.  1720.  Becker,  Der  Mineralische 
Mag.  Miihlh.  1729.  Euler,  D.  and  J.  Bernoulli,  Dutour,  Pieces  qui  ont  rem- 
portees  la  prix  de  1'Acad.  4to,  Paris,  1748.  Du  Fay,  Amnerkungen,  Erf.  1748. 
Penrose  on  Mag.  1753.  Adams's  Essay,  4to,  1753.  Scarella,  De  Mag.  2  vols. 
4to,  Brescia,  1759.  Cooper's  Experimental  Mag.  1761.  Wilcke,  Tal  om  Mag. 
Stock.  1764.  Brugmann,  De  Materia  Magnetica,  4to,  Franeker,  1765.  Lo- 
vett's  Electr.  and  Mag.  1766.  Van  Swinden,  De  Phsen.  Mag.  Lugd.  1772. 
Recueil  de  Mem.  sur  1' Analogic  de  1'Electr.  et  du  Mag.  3  vols.  Haag.  1784.  Le- 
monnier,  Loix  du  Mag.  2  vols.  1776.  Gabler,  Theoria  Mag.  Ingolst.  1781. 
Cavallo  on  Mag.  1787.  Walker,  1794.  Lorimer,  4to,  1795.  Haiiy,  Expos,  de  la 
Theorie,  Altenb.  1801.  V.  Lowerrorn,  Ueber  den  Magnet.  Kopenhag.  1802.  Biot, 
Traite  de  Physique,  and  art.  Magnetism  in  Edin.  Encyc.  Roucher-Deratte,  Traite 
sur  1'Electr.  &c.  1803.  Meissen,  Ueber  den  Mag.  1819.  Barlow's  Essay  on  Mag. 
Attractions,  1823.  Peytavin,  Essai  sur  la  Constit.  des  Fluides  Magnetiques,  1830. 
Brewster's  Magnetism,  1837  ;  also  an  essay  in  many  treatises  on  electricity. 

Memoirs.— Du  Fay,  Hist,  et  Mem.  1728,  p.  355  ;  1730,  p.  142;  1731,  p.  417. 
Servington  Savery's  Mag.  Obs.  Ph.  Tr.  1730,  p.  295.  Lambert,  Hist,  et  Mem.  de 
Berlin,  1766,  pp.  22,  49.  Franklin,  Am.  Tr.  iii.  10.  Krafft,  Com.  Petr.  xii.  276. 
Kirwan,  Ir.  Tr.  vi.  177.  Ritter,  Gilb.  Ann.  iv.  1.  Kratzenstein,  Lichtenb.  Mag. 
iv.  132.  Poisson,  Mem.  de  1'Inst.  1821,  pp.  247,  448.  Ampere,  ibid.  1823, 
p.  175.  Harris,  Ed.  Tr.  vol.  xi.  Christie,  Ph.  Tr.  1828,  p.  325.  Blondeau,  Mem. 
de  Brest,  i.  385,  401.  Haldat,  Mem.de  1'Acad.  de  Nancy,  1830. .  1839  ;  Ann. 
de  Ch.  xlii.  53.  Scoresby,  Jameson's  Jour.  1832,  p.  319,  &c.  Kupfer,  Ann.  de 
Ch.  xxxvi.  50. 

Artificial  Magnets. — Leuwenhoek  on  the  Mag.  Quality  acquired  by  Iron  after 
standing  a  long  time  in  the  same  Posture,  Ph.  Tr.  xxxiii.  72.  Marcel,  ibid. 
1730,  p.  112.  Reaumer,  Hist,  et  Mem.  1723.  Duhamel,  ibid.  1735,  1745, 
p.  181.  Knight's  Method,  Ph.  Tr.  1744-5,  pp.  161,  361 ;  1776,  p.  591  ;  1779, 
p.  51.  Canton,  ibid.  1751,  p.  31.  Michell  on  Artificial  Magnets,  Camb.  1751. 
Klingenstierna,  De  Mag.  Artif.  Stock.  1752.  Riviere  sur  les  Aimans  Artificiels, 
1752.  Richmann,  Nov.  Com.  Petr.  iv.  235.  Nebel,  de  Mag.  Artif.  4to,  Utr.  1756. 
Antheaulme  sur  les  Aimans  Artificiels,  1760.  Coulomb,  Mem.  de  1'Inst.  vi.  399. 
Barlow,  Ed.  Jour.  i.  344.  Scoresby's  Exp.  on  the  Development  of  Magnetical 
Properties  in  Steel  and  Iron  by  Percussion,  Ph.  Tr.  1820,  p.  241.  Baden  Powell, 
Ann.  of  Phil.  1822,  p.  92.  Weber,  Magnetismus  des  Eisens  durch  die  Erde,  Res. 
des  Mag.  Ver.  1841,  p.  85. 

*  Ann.  deCh.  xxvii.  363  ;  xxviii.  325  ;  xxxii.  213. 


ON  MAGNETISM.  543 

Compensation  for  Local  Attraction. — Sabine,  Ph.  Tr.  1819,  p.  112.  Barlow, 
ibid.  1831,  p.  215.  Airy,  ibid.  1839,  p.  167. 

Instruments.  Mariner's  Compass. — Lous,  Tentamen  Exp.  ad  Compassum  per- 
ficiendum,  4to,  Hafnise,  1734.  Knight,  Ph.  Tr.  1750,  pp.  505,  513.  Duhamel, 
Hist,  et  Mem.  1750,  p.  154.  Bain  on  the  Compass,  1817.  Gilbert,  M'Culloch, 
and  Alexander's  Compass,  in  Barlow's  art.  Magnetism  in  Encyc.  Metr.  Kater,  Ph. 
Tr.  1821,  p.  104. 

Declination.— Lahire,  Hist,  et  Mem.  1716,  p.  7.  Lemonnier,  ibid.  1778,  p.  68. 
Coulomb,  ibid.  1785,  p.  560.  Wilcke,  Schwed.  Abhand.  1763,  p.  154.  Brander, 
Beschreibung  eines  Mag.  Dec.  und  Incl.  Augsb.  1779.  Cassini,  Mem.  de  1'Inst.  v. 
145.  Prony,  Jour,  de  Phy.  xliv.  474.  Troughton,  Nich.  Jour.  1806,  p.  179. 
Bidone,  Mem.  de  TurinJSll,  p.  141.  Bessel,  Schumacher's  Ast.  Nachr.  vi.  221. 
Weber,  Res.  des  Mag.  Ver.  1837,  p.  104.  Gauss,  ibid.  1841,  p.  1.  Simonoff, 
ibid.  62.  Report  of  the  Committee  of  Physics  of  the  Royal  Soc.  1840,  p.  30. 
Lamont,  Ann.  fur  Meteorolog.  und  Erdmagnet.  1842,  ii.  179.  Gambey  in  Pouillet's 
Physique,  pi.  xi.  fig.  266.  The  practical  processes  of  finding  the  variation  at  sea  will 
be  found  in  Raper's  Navigation  and  Nautical  Ast.  1840. 

Inclination.— Buache,  Hist,  et  Mem.  1732,  p.  377.  Nairne,  Ph.  Tr.  1772, 
p.  476.  Borda,  Gilb.  Ann.  iv.  449.  Robinson,  in  Sabine  Ph.  Tr.  1822,  p.  1. 
Weber,  Res.  der  Gott.  Ver.  1837,  p.  81.  Kreil,  Die  Mag.  Apparat.  zu  Prag.  ibid. 
1839,  p.  91.  Lloyd  on  the  Mag.  Obs.  at  Dublin,  4to,  1842. 

Intensity. — Coulomb,  Mem.de  1'Instit.  iii.  176.  Hansteen,  Beobachtungen  iiber 
die  Intensitat  des  Mag.  in  Nord  Europa,  Pogg.  Ann.  iii.  225.  Christie,  Ph.  Tr. 
1833,  p.  343.  Gauss,  Magnetometer,  4to,  Gott.  1833  ;  Res.  des  Mag.  Ver.  1837, 
p.  1,  20,  58  ;  1840,  p.  1.  Weber,  ibid.  1836,  p.  63  ;  1838,  p.  68 ;  1841,  p.  79; 
translated  in  Sci.  Mem.  vol.  ii.  Lamont,  Ueber  Bestimmung  der  Horizontal-Inten- 
sitat,  4to,  Munch.  Ueber  das  Mag.  Observatorium  bei  Miinchen,  4to,  1842. 

Theory  of  Terrestrial  Mag. — Whiston,  The  Latitude  and  Longitude  found  by  the 
Dipping  Needle,  1721.  Zegollstrom,  Theoria  Decl.  Mag.  Upsal,  1755.  Dunn's 
Mag.  Atlas,  1776.  Steinhauser,  De  Mag.  Telluris,  Wittenb.  1806.  Mollweide, 
Gilb.  Ann.  xxix.  1,  251,  Ixx.  26.  Humboldt  and  Biot,  Jour,  de  Phy.  xlix.  429. 
Quinet,  Theorie  de  1' Aimant,  4to,  Paris,  1809  ;  Expos£  des  Variations,  Mag.  1826. 
Hansteen,  Untersuchungen  iiber  den  Mag.  der  Erde,  4to,  Christiana,  1819 ;  Gilb. 
Ann.  Ixv.  313,  Ixx.  36,  110,  Ixxi.  273,  Ixxv.  145  ;  Pogg.  Ann.  iv.  277,  ix.  49,  229, 
xxviii.  473,  578.  Schumacher's  Ast.  Nach.  vii.  17.  Duperrey's  Chart,  Pogg.  Ann. 
xxi.  151.  Barlow,  Ph.  Tr.  1831,  p.  99.  Gauss,  Intensitas  Vis  Mag.  Terrest.  ad 
Mensuram  revocata,  Gott.  1833  ;  Sci.  Mem.  ii.  184,  313.  Res.  des  Magn.  Vereins, 
1838,  p.  1,  146;  1839,  p.  50.  Gauss  and  Weber's  Atlas,  4to,  Leipz.  1840. 
Sabine,  Ph.  Tr.  1840,  p.  129;  1841,  p.  11  ;  1842,  p.  9.  Bessel,  Schum.  Ast. 
Jahrb.  1843,  p.  117. 

Observations.— See  Christie's  Report  Br.  Ass.  1833 ;  Sabine's  Report,  vol.  vi.  ; 
or  Dove's  Repertor.  Band  v.  ;  from  which  the  preceding  list  is  for  the  most  part 
extracted  :  also  Kupfer  Recueil  d'Obs.  faites  a  St.  Petersb.  4to,  1837. . .  Annu- 
aire  Magnetique,  5  vols.  4to,  St.  Petersb.  1836. . .  Gauss  and  Weber,  Resultate, 
Leipz.  1836....  and  Scientific  Mem.  ii.  20.  Kreil,  Mag.  und  Meteor.  Obs.  zu 
Prag.  4to,  1839.  Lamont,  Ann.  der  Meteor,  und  des  Erdmagnetismus,  Munch. 
1842.  Quetelet,  Mem.  de  Brux.  xvi 

Electro-magnetism. — Kastner,  Obs.  de  Electro-mag.  Erlang.  1821.  Schrader, 
Dissertatio  de  Electro-mag.  Halse,  1821.  Erman ,  Umrisse  zu  Elektr.  Magn.  Berl. 
1821.  Seebeck,  Ueber  den  Magn.  des  Galvan.  Kette,  4to,  Berl.  1822.  Am- 
pere, Recueil  d'Obs.  Electro-magn.  1822  ;  Mem.  sur  la  Theorie  Math,  des  Phen. 
Electro-dyn.  Mem.  de  1'Instit.  1823,  vi.  175  ;  Ann.  de  Ch.  xv.  57.  Precis 
de  la  Theorie  des  Phsen.  Electro-dyn.  1824  ;  ExposS  Methodique  des  Phaen.  1824  ; 
Theorie  des  do.  4to,  1826.  Demonfernand's  Manuel,  1823  ;  translated  by  Gumming, 
with  additions,  Camb.  1827.  De  la  Rive,  Recherches  sur  la  Distribution  de  1'Electr. 
Dyn.  dans  les  Corps,  Geneve,  1825.  Pfaff,  Der  Electro-mag.  Hamburg,  1824 ; 
Gilb.  Ann.  Ixxiv.  249.  Guerin,  Action  Mutuelle  des  Fils  Conducteurs,  &c.  1828. 
Pohl,  Der  Electro-mag.  Theor.  Practisch  Dargestellt,  Berlin,  1830.  Fechner, 
Elementarlehrbuch  des  Elektr.  Leipz.  1830.  Watkins's  Electro-mag.  1832. 
Poisson,  Theorie  du  Mag.  en  Mouvement,  Mem.  de  1'Inst.  vi.  439.  Nobili, 
Question^  sul  Magnetismo,  Modena,  1838.  Antologia  di  Firenze,  Nos.  cxxxi.  &c. 
Marias4ni,  Mem.  di  Fisica  Sperimentale,  Modena,  1838.  Zantedeschi,  Relazione 
Storico-critica  Sperimentale  nell'  Elettro-mag.  Venice,  1840.  Matteuci,  Bibliot. 
Univ.  1840. 


544 


LECTURE    LVI. 


ON  CLIMATES  AND  WINDS. 

THE  science  of  meteorology  relates  principally  to  the  natural  history 
of  the  air,  and  to  such  temporary  changes  in  the  earth  and  sea  as  are 
produced  by  causes  not  mechanical  only.  The  subject  is  of  a  very  com- 
plicated and  intricate  nature ;  it  comprehends  many  effects  derived  from 
such  causes  as  belong  separately  to  every  department  of  physics  which  we 
have  hitherto  examined ;  and  although  it  lias  occupied  the  attention  of 
several  philosophers  of  considerable  eminence,  we  cannot  yet  boast  of 
having  made  any  great  advancement  in  it.  Whether  we  shall  ever  be  able 
to  carry  our  theories  to  so  high  a  degree  of  perfection,  as  to  furnish  us 
with  much  information  applicable  to  the  purposes  of  common  life,  to  agri- 
culture, or  to  medicine,  is  at  present  uncertain  ;  although  some  advantage 
has  already  been  derived  from  the  indications  of  meteorological  instru- 
ments ;  and  the  philosophy  of  the  science  is  in  many  respects  much  more 
advanced  than  has  commonly  been  supposed.  We  shall  divide  this  exten- 
sive subject  into  two  parts,  the  first  relating  principally  to  the  effects  of 
heat  on  the  atmosphere,  including  the  phenomena  of  winds ;  the  second 
to  the  nature  and  consequences  of  evaporation,  comprehending  atmo- 
spherical electricity,  and  to  the  effects  of  subterraneous  fires  and  igneous 
meteors. 

The  variations  of  temperature  in  different  parts  of  the  earth's  surface, 
require  to  be  examined  in  the  first  place ;  since  they  are  not  only  of  con- 
siderable importance  in  themselves,  but  are  also  among  the  principal  causes 
of  other  changes  in  the  state  of  the  winds  and  weather.  These  changes 
are  measured  by  thermometers,  of  various  kinds,  which  have  already  been 
described  ;  but,  for  meteorological  purposes,  some  additions  are  frequently 
made  to  the  simple  thermometer.  In  Six's  thermometer,*  the  tube  is 
twice  bent,  so  as  to  return  in  a  parallel  direction  :  the  bulb  is  in  the  form 
of  a  long  cylinder,  and  is  usually  filled  with  spirit  of  wine,  which  is  in 
contact  with  a  portion  of  mercury  occupying  the  lower  part  of  the  tube  ; 
and  this  is  succeeded  by  a  second  portion  of  spirit.  The  mercury  carries 
on  each  of  its  surfaces  an  index,  which  is  retained  in  its  remotest  situation 
by  means  of  a  weak  spring ;  and  consequently  shows  the  greatest  degree 
of  heat  or  of  cold  that  has  happened  since  the  last  observation.  The 
indexes  are  of  iron  or  steel,  and  may  be  brought  back  to  the  surface  at 
pleasure  by  means  of  a  magnet ;  they  are  carried  up  by  the  mercury,  more 
by  its  capillary  action,  than  by  the  difference  of  the  specific  gravities.  A 
similar  effect  is  obtained  in  Rutherford's  t  arrangement  of  a  pair  of  ther- 
mometers, one  with  mercury,  the  other  with  spirit  of  wine,  placed  in  a 
horizontal  position  ;  one  index  being  without  the  surface  of  the  mercury, 

*  Ph.  Tr.  Ixxii.     Six  on  Meteorology,  Maidst.  1794. 
f  Ed.  Tr.  iii.  247. 


ON  CLIMATES  AND  WINDS.  545 

the  other  within  that  of  the  spirit :  the  thermometers  being  in  contrary 
directions,  both  indexes  may  be  brought  back  to  their  places,  by  merely 
raising  the  end  of  the  instrument.  Self  registering  thermometers  have 
also  sometimes  been  constructed,  for  keeping  a  still  more  accurate  account 
of  all  the  variations  of  temperature  that  have  occurred,  by  describing  a 
line  on  a  revolving  barrel,  which  shows  the  height  for  every  instant  during 
the  whole  time  of  their  operation.  (Plate  XLI.  Fig.  579,  580.) 

The  climates  of  different  parts  of  the  earth's  surface  are  unquestionably 
owing  in  great  measure  to  their  position  with  respect  to  the  sun.  At  the 
equator,  where  the  sun  is  always  nearly  vertical,  any  given  part  of  the 
surface  receives  a  much  greater  quantity  of  light  and  heat,  than  an  equal 
portion  near  the  poles ;  and  it  is  also  still  more  affected  by  the  sun's  verti- 
cal rays,  because  their  passage  through  the  atmosphere  is  shorter  than  that 
of  the  oblique  rays.  As  far  as  the  sun's  mean  altitude  only  is  concerned, 
it  appears  from  Simpson's  calculations,  that  the  heat  received  at  the 
equator  in  the  whole  year  is  nearly  twice  and  a  half  as  great  as  at  the 
poles  ;  this  proportion  being  nearly  the  same  as  that  of  the  meridian  heat 
of  a  vertical  sun,  to  the  heat  derived,  at  the  altitude  23£°,  in  the  middle 
of  the  long  annual  day  at  the  poles.  But  the  difference  is  rendered  still 
greater,  by  the  effect  of  the  atmosphere,  which  interrupts  a  greater  portion 
of  the  heat  at  the  poles  than  elsewhere.  Bouguer  has  calculated,  upon  the 
supposition  of  the  similarity  of  the  affections  of  heat  and  light,  that  in 
latitude  45°,  80  parts  out  of  100  are  transmitted  at  noon  in  July,  and  55 
only  in  December.  The  heat  intercepted  by  the  atmosphere  is  perhaps 
not  wholly,  but  very  nearly,  lost  with  respect  to  the  climate  of  the  neigh- 
bouring places.  It  is  obvious  that,  at  any  individual  place,  the  climate 
in  summer  must  approach  in  some  degree  to  the  equatorial  climate,  the 
sun's  altitude  being  greater,  and  in  winter  to  the  climate  of  the  polar 
regions. 

While  the  earth  is  becoming  warmer  at  any  particular  spot,  the  heat 
thrown  off  by  radiation  into  the  atmosphere,  and  thence  into  the  empty 
space  beyond  it,  together  with  that  which  is  transmitted  to  the  internal 
parts  of  the  earth,  must  be  less  than  the  heat  received  from  the  sun  ;  and 
when  the  earth  is  growing  colder,  more  heat  must  pass  off  than  is  received  : 
but  whenever  the  heat  of  the  surface  is  stationary,  neither  increasing  nor 
diminishing,  as  at  the  times  of  the  greatest  and  least  heat,  it  is  obvious 
that  the  heat  received  from  the  sun  must  be  precisely  equal  to  the  heat 
which  is  thrown  off.  Now  this  quantity  may  be  estimated  by  the  degree 
of  refrigeration  in  the  night ;  and  hence  Mr.  Prevost*  has  very  ingeniously 
deduced  the  proportion  of  the  sun's  heat  arriving  at  the  surface  of  the  earth 
in  the  latitude  of  Geneva,  in  July,  and  in  December ;  which  he  finds  to  be 
as  7  or  8  to  1 ;  and  this  result  agrees  very  well  with  a  calculation  deduced 
from  the  length  of  the  day,  the  sun's  altitude,  and  the  interception  of  his 
rays  by  the  atmosphere. 

In  London  the  temperature  generally  varies,  in  the  course  of  the  day 
and  night,  somewhat  more  than  5°,  and  less  than  20°.     In  January,  the 
mean  diffrnal  variation  of  temperature  is  6°,  in  March  20°,  in  July  10°, 
*  Jour,  de  Phy.  xlii.  81. 
2  N 


546  LECTURE  LVI. 

and  in  September,  18°.  Hence,  says  Mr.  Kirwan,*  we  may  understand 
the  reason  of  the  great  frequency  of  colds  in  spring  and  in  autumn. 

Some  philosophers  have  supposed  the  earth  to  become  progressively 
warmer  in  the  course  of  ages,  while  others  have  imagined  that  its  heat 
is  exhausted.  Both  these  opinions  appear  in  general  improbable.  The 
greater  heat  the  earth  receives  by  day,  the  more  it  throws  off,  both  by 
day  and  by  night ;  so  that  in  the  course  of  a  few  ages  the  heat  must  pro- 
bably have  attained  its  maximum.  Local  changes  may  indeed  arise  from 
local  circumstances ;  thus,  the  climate  of  America  is  said  to  have  become 
considerably  warmer,  since  a  large  part  of  its  surface  has  been  cleared  from 
its  dense  forests  by  human  labour :  and  to  judge  from  the  descriptions  of 
the  ancients,  it  appears  that  even  in  Europe  the  winters  were  formerly 
much  colder  than  they  are  at  present.  If,  however,  Dr.  Herschel's  opinion 
of  the  variation  of  the  heat  of  the  sun  be  confirmed,  it  will  introduce  a 
great  uncertainty  into  all  theories  upon  the  subject :  since  in  these  calcula- 
tions the  original  heat  of  the  sun  has  always  been  supposed  unalterable. 

The  sea  is  less  heated  than  the  land,  partly  because  a  greater  quantity  of 
water  evaporates  from  it,  and  partly  because  the  sun's  rays  penetrate  to  a 
considerable  depth,  and  have  less  effect  on  the  surface,  while  the  water  is 
also  mixed,  by  the  agitation  of  its  waves  and  currents,  with  the  colder 
water  below.  It  is  also  more  slowly  cooled  than  the  land,  since,  when  the 
temperature  of  the  superficial  particles  is  depressed,  they  become  heavier, 
and  sink  to  the  bottom.  For  similar  reasons,  the  sea  is  colder  than  the 
land  in  hot  climates,  and  by  day,  and  warmer  in  cold  climates,  and  by 
night.  These  circumstances,  however,  nearly  balance  each  other,  so  that 
the  mean  temperatures  of  both  are  equal,  that  of  the  sea  being  only  less 
variable.  Although  the  process  of  evaporation  must  cool  the  sea,  yet  when 
the  vapours  are  condensed  without  reaching  the  land,  their  condensation 
must  compensate  for  this  effect  by  an  equal  extrication  of  heat. 

There  is  another  cause  which  perhaps  contributes  in  some  degree,  in  tem- 
perate climates,  to  the  production  of  cold  ;  that  is,  the  alternation  of  freez- 
ing and  thawing.  Mr.  Prevost  observes  that  congelation  takes  place  much 
more  suddenly  than  the  opposite  process  of  liquefaction  ;  and  that  of 
course  the  same  quantity  of  heat  must  be  more  rapidly  extricated  in  freez- 
ing than  it  is  absorbed  in  thawing ;  that  the  heat,  thus  extricated,  being 
disposed  to  fly  off  in  all  directions,  and  little  of  it  being  retained  by 
the  neighbouring  bodies,  more  heat  is  lost  than  is  gained  by  the  alternation : 
so  that  where  ice  has  once  been  formed,  its  production  is  in  this  manner 
redoubled.  This  circumstance  must  occur  wherever  it  freezes,  that  is,  on 
shore,  in  latitudes  above  35° ;  and  it  appears  that  from  about  30°  to  the 
pole,  the  land  is  somewhat  colder  than  the  sea,  and  the  more  as  it  is  further 
distant  from  it ;  and  nearer  the  equator  the  land  is  warmer  than  the  sea  : 
but  the  process  of  congelation  cannot  by  any  means  be  the  principal  cause 
of  the  difference,  and  it  is  probable  that  the  different  capacity  of  earth  and 
water  for  heat  is  materially  concerned  in  it. 

Since  the  atmosphere  is  very  little  heated  by  the  passage  of  the  sun's  rays 
through  it,  it  is  naturally  colder  than  the  earth's  surface ;  arf&vfor  this 
*  Ph.  Mag.  xvi.  212. 


ON  CLIMATES  AND  WINDS.  547 

reason,  the  most  elevated  tracts  of  land,  which  are  the  most  prominent,  and 
the  most  exposed  to  the  effects  of  the  atmosphere,  are  always  colder  than 
situations  nearer  the  level  of  the  sea.  The  northern  hemisphere  is  somewhat 
warmer  than  the  southern,  perhaps  because  of  the  greater  proportion  of 
land  that  it  contains,  and  also  in  some  measure  on  account  of  the  greater 
length  of  its  summer  than  that  of  the  southern  :  for  although,  as  it  was 
long  ago  observed  by  Simpson,  the  different  distance  of  the  sun  compen- 
sates precisely  for  the  different  velocity  of  the  earth  in  its  orbit,  with  respect 
to  the  whole  quantity  of  heat  received  on  either  side  of  the  equinoctial 
points,  yet  Mr.  Prevost  has  shown,  that  in  all  probability  the  same  quan- 
tity of  heat  must  produce  a  greater  effect  when  it  is  more  slowly  applied  ; 
because  the  portion  lost  by  radiation  from  the  heated  body  is  greater,  as 
the  temperature  is  higher.  Since,  therefore,  on  account  of  the  eccentricity 
of  the  earth's  orbit,  the  north  pole  is  turned  towards  the  sun  7  or  8  days 
longer  than  the  south  pole,  the  northern  winters  must  be  milder  than  the 
southern  :  yet  the  southern  summers,  though  shorter,  ought  to  be  some- 
what warmer  than  the  northern  :  but  in  fact  they  are  colder,  partly  per- 
haps from  the  much  greater  proportion  of  sea,  which  in  some  degree 
equalises  the  temperature,  and  partly  for  other  reasons.  The  compara- 
tive intensity  of  southern  summer  and  winter  is  not  exactly  known  ; 
but  in  the  island  of  New  Georgia  the  summer  is  said  to  be  extremely 
cold. 

The  northern  ice  extends  about  9°  from  the  pole  :  the  southern  18° 
or  20° ;  in  some  parts  even  30°  ;  and  floating  ice  has  occasionally  been 
found  in  both  hemispheres  as  far  as  40°  from  the  poles,  and  sometimes,  as 
it  has  been  said,  even  in  latitude  41°  or  42°.  Between  54°  and  60°  south 
latitude,  the  snow  lies  on  the  ground,  at  the  sea  side,  throughout  the  sum- 
mer. The  line  of  perpetual  congelation  is  three  miles  above  the  surface  at 
the  equator,  where  the  mean  heat  is  84°  ;  at  Teneriffe,  in  latitude  28°,  two 
miles ;  in  the  latitude  of  London,  a  little  more  than  a  mile  ;  and  in  latitude 
80°  north,  only  1200  feet.  At  the  pole,  according  to  the  analogy  deduced 
by  Mr.  Kirwan,*  from  a  comparison  of  various  observations,  the  mean 
temperature  should  be  31°.  In  London  the  mean  temperature  is  50°  ;  at 
Rome  and  at  Montpelier,  a  little  more  than  60°  ;  in  the  island  of  Madeira, 
70°  ;  and  in  Jamaica,  80°.f 

There  are  frequently  some  local  causes  of  heat  and  cold  which  are  inde- 
pendent of  the  sun's  immediate  action.  Thus,  it  has  been  observed,  that 
when  the  weather  has  been  clear,  and  a  cloud  passes  over  the  place  of  obser- 
vation, the  thermometer  frequently  rises  a  degree  or  two  almost  instanta- 
neously. This  has  been  partly  explained  by  considering  the  cloud  as  a 
vesture,  preventing  the  escape  of  the  heat  which  is  always  radiating  from 
the  earth,  and  reflecting  it  back  to  the  surface  :  the  cloud  may  also  have 
been  lately  condensed,  and  may  itself  be  of  a  higher  temperature  than 
the  earth.  Mr.  SixJ  has  observed  that  in  clear  weather,  the  air  is  usually 
some  degrees  colder  at  night,  and  warmer  by  day,  close  to  the  ground, 

*  Anjgstimate  of  the  Temperature  of  different  Latitudes,  Lond.  1787. 
f  O;i  Isothermal  Lines,  see  Humboldt,  Fragments  Asiatiques,  ii.  398.     Mem. 
d'Arcueil,  Hi.  462.  +  Ph.  Tr.  1784,  p.  428  ;  1788,  p.  103. 

2  N  2 


548  LECTURE   LVI. 

than  a  few  feet  above  it ;  but  that  in  cloudy  weather  there  is  less  differ- 
ence :  and  it  is  possible  that  this  circumstance  may  be  derived  from 
the  difference  of  the  quantity  of  evaporation  from  the  earth's  surface, 
which  occasions  a  different  degree  of  cold  in  different  states  of  the  atmo- 
sphere. 

The  motions  of  the  air,  which  constitute  winds,  are  in  general  dependent, 
in  the  first  instance,  on  variations  of  temperature.  They  are  so  accidental 
and  uncertain,  as  to  be  subjected  to  no  universal  laws  ;  as  far  however  as 
any  regularity  can  be  observed  in  their  recurrence,  it  may  in  most  cases 
be  sufficiently  explained.* 

The  principal  phenomena  of  the  periodical  winds  may  be  reduced  to  six 
distinct  heads  :  first  the  general  tendency  from  north  east  and  south  east 
towards  the  equator,  in  latitudes  below  30°  ;  secondly,  the  deviation  of  this 
.  tendency  from  the  precise  situation  of  the  equator  ;  thirdly,  the  prevalence 
of  westerly  winds  between  30°  and  40°  or  more,  especially  in  the  southern 
hemisphere  ;  fourthly,  the  local  modifications  to  which  these  general  effects 
are  subjected ;  fifthly,  the  monsoons,  which  vary  every  half  year ;  and 
lastly,  the  diurnal  changes  of  land  and  sea  breezes. 

With  respect  to  the  general  tendency  of  the  trade  winds  to  the  west,  it 
may  be  sufficiently  explained  by  Hadley's  theory  t  of  the  difference  of  the 
rotatory  motion  of  different  parts  of  the  atmosphere,  combined  with  the 
currents  occasioned  by  the  greater  heat  at  the  equator.  For  the  sun's  rays, 
expanding  the  air  in  the  neighbourhood  of  the  equator,  and  causing  it  to 
ascend,  produce  a  current  in  the  lower  parts  of  the  atmosphere,  which  rush 
southwards  and  northwards  towards  the  equator,  in  order  to  occupy  the 
place  of  the  heated  air  as  it  rises :  and  since  the  rotatory  motion  of  the 
earth  is  greatest  at  the  equator,  and  is  directed  eastwards,  the  air  coming 
from  the  poles  has  of  course  a  relative  motion  westwards  ;  and  hence  the 
joint  motion  of  the  current  is  directed,  in  the  northern  hemisphere,  from 
north  east  to  south  west,  and  in  the  southern,  from  south  east  to  north 
west.  [As  the  winds  on  both  sides  approach  the  equator,  the  friction  of 
the  earth's  surface  is  constantly  tending  to  give  them  an  easterly  direction ; 
and  since  the  lengths  of  the  diurnal  circles  increase  very  slowly  in  the 
immediate  vicinity  of  the  equator,  this  friction  is  even  more  effective  than 
the  change  of  latitude ;  and  the  westerly  direction  of  the  winds  is  gra- 
dually lessened.  Moreover,  the  northerly  and  southerly  currents,  coining 
here  into  opposition,  mutually  annihilate  each  other's  effects.  At  the  equa- 
tor, therefore,  the  trade  winds  lose  their  distinctive  character,  and  consti- 
tute only  currents  which  depend  on  the  preponderancy  of  local  causes,  and 
thus  vary  in  different  places.^]  Dr.  Halley§  supposed  that  the  air  was 
made  in  some  measure  to  follow  the  sun  round  the  earth,  simply  by  means 
of  the  expansion  of  the  atmosphere,  which  takes  place  immediately  under 
him,  and  accompanies  him  round  the  globe ;  but  it  does  not  seem  evident 
that  the  air  could  have  any  greater  tendency  to  follow  the  sun  that  to  meet 

*  See  Dove,  Meteorologische  Untersuchungen,  Berlin,  1837.  Fechner's  Reper- 
torium,  vol.  Hi.  f  Hadley,  Ph.  Tr.  1735,  xxxix.  $8. 

£  See  Hall's  Fragments  of  Voyages  and  Travels,  2nd  Series,  i.  162. 
§  Ph.  Tr.  xvi.  152. 


ON  CLIMATES  AND  WINDS.  549 

him.  Nor  can  any  sufficient  cause  be  found  in  the  attractions  of  the  celes- 
tial bodies,  either  for  the  general  easterly  trade  winds,  or  for  the  current  of 
the  sea  in  a  similar  direction,  which  appears  to  be  the  immediate  effect  of 
their  friction  on  the  surface  of  the  water. 

The  second  circumstance  is  easily  explained  by  the  greater  heat  of  the 
northern  than  of  the  southern  hemisphere  ;  so  that  instead  of  coinciding 
with  the  equator,  the  neutral  portion  of  the  atmosphere  lies  between  3° 
and  5°  of  north  latitude ;  the  north  east  wind  not  reaching  the  equator, 
and  the  south  east  continuing  about  3°  beyond  it.  But  the  situation  of  the 
neutral  portion  varies  with  the  sun's  decimation,  accordingly  as  different 
parallels  of  latitude  become  in  succession  somewhat  hotter  than  the  neigh- 
bouring parts.  Where  the  northern  and  southern  currents  meet,  their 
joint  effect  must  naturally  be  to  produce  a  due  east  wind  ;  but  in  some 
parts  of  the  ocean,  temporary  calms  and  irregular  squalls  have  been  ob- 
served to  take  place  of  this  easterly  wind,  which  generally  prevails  in  the 
neutral  parts  near  the  equator. 

The  third  fact,  that  is,  the  frequency  of  westerly  winds  between  the 
latitudes  30°  and  40°,  has  not  yet  been  sufficiently  explained.  The  most 
probable  cause  of  this  circumstance  is,  that  the  current  of  heated  air, 
which  we  have  hitherto  neglected,  and  which  passes,  in  the  upper  parts  of 
the  atmosphere,  from  the  equator  each  way  towards  the  poles,  and  which, 
being  the  converse  of  the  trade  wind,  must  be  a  south  west  and  north 
west  wind,  in  the  different  hemispheres,  becomes  here  sufficiently  cool  to 
descend  and  mix  with  the  lower  parts  of  the  atmosphere,  or  to  carry  them 
along  by  its  lateral  friction  :  and  while  it  descends  to  complete  the  circle, 
necessary  for  supplying  the  current  to  the  equator,  its  motion  with  respect 
to  the  horizon  must  become  at  a  certain  time  due  west,  since  the  cause 
which  stops  its  progress  northwards,  has  no  tendency  to  impede  its  motion 
eastwards.  The  outward  bound  East  India  ships  generally  make  their 
easting  in  about  36°  south  latitude.  It  is  probably  also  on  account  of  the 
rotatory  motion  of  the  earth,  that  south  west  winds  are  more  common  in 
our  latitudes  than  south  east,  and  north  east  than  north  west. 

Among  the  local  modifications  to  be  considered  in  the  fourth  place,  we 
may  reckon  the  greater  indistinctness  of  the  third  effect  in  the  northern 
than  in  the  southern  hemisphere,  a  circumstance  which  is  explained 
from  the  more  irregular  distribution  of  sea  and  land :  for  between  30° 
and  40°  south  latitude  the  ocean  is  scarcely  any  where  interrupted.  In 
lower  latitudes  also,  near  the  west  coast  of  Africa,  the  winds  are  so  much 
deflected  towards  the  land,  as  to  become  in  general  westerly  instead  of 
easterly. 

The  monsoons,  which  constitute  the  fifth  remarkable  circumstance,  are 
so  called  from  a  Malay  word,  denoting  season.  They  are  occasioned  by 
the  peculiar  situation  of  the  continent  of  Asia,  on  the  north  side  of  the 
equator.  From  April  to  September,  the  sun  having  north  decimation,  the 
heat  on  this  continent,  a  little  north  of  the  tropic,  is  very  intense,  and  the 
genera -^current  is  consequently  towards  the  north.  The  air,  therefore, 
coming  from  south  latitudes  towards  the  equator,  becomes,  on  account  of  the 
deficiency  of  rotatory  motion,  a  south  east  wind,  as  usual,  which  is  found 
to  prevail  between  Madagascar  and  New  Holland,  as  far  as  the  equator. 


550  LECTURE  LVI. 

In  consequence  perhaps  of  friction  in  its  passage,  it  gradually  loses  its  im- 
petus towards  the  west,  and  at  the  equator  is  nearly  a  south  wind  ;  but  in 
proceeding  north  from  the  equator,  it  becomes,  from  an  excess  of  rotatory 
motion,  a  south  west  wind,  which  blows  into  the  Arabian  gulf  and  the  bay 
of  Bengal.  Both  these  winds  are  however  variously  modified  by  the  par- 
ticular situations  of  the  islands  and  continents.  From  October  to  March, 
on  the  contrary,  the  sun  having  south  declination,  the  south  east  trade  wind 
stops  at  10°  south  latitude ;  the  trade  winds  on  the  north  side  of  the  equator 
are  as  usual  north  east ;  and  beyond  the  equator  they  become  for  some 
degrees  north  west,  the  circumstances  being  the  reverse  of  those  which 
happen  in  the  summer  months,  at  greater  distances,  on  the  other  side  of 
the  equator.  (Plate  XLII.  XLIII.) 

The  last  fact  is  the  simplest  of  all.  The  land  and  sea  breezes  are  pro- 
duced by  the  ascent  of  the  air  over  the  land  in  the  day  time,  while  the  land 
is  hotter  than  the  sea  ;  and  its  descent  at  night  when  the  land  is  become 
colder  :  hence  the  breeze  comes  from  the  sea  by  day,  and  from  the  land  by 
night. 

The  violent  agitations  of  the  air,  which  constitute  hurricanes  and  whirl- 
winds, occur  more  commonly  in  tropical  climates  than  in  others.  The 
causes  of  these  storms  are  little  understood  :  their  course  is  said  to  be  gene- 
rally opposite  to  that  of  the  trade  winds  ;  but  tornados,  which  are  less  re- 
gular hurricanes,  originate  indifferently  from  every  quarter. 

The  variations  of  the  weight  of  the  air,  wrhich  occasion  the  winds,  and 
other  changes  in  its  density,  which  are  the  effects  of  the  winds  themselves, 
are  indicated  by  the  height  of  the  barometer,  which  is  in  general  the  more 
variable  as  the  winds  are  more  liable  to  sudden  changes.  Hence  in  the  neigh- 
bourhood of  the  equator  the  height  of  the  barometer  is  scarcely  ever  a  quarter 
of  an  inch  more  or  less  than  30  inches,  which  is  very  nearly  its  mean  height  on 
the  level  of  the  sea  in  every  part  of  the  globe  :  in  Great  Britain  it  is  some- 
times as  low  as  28  inches,  but  never  higher  than  31.  We  have  already 
seen  that  the  elevation  of  any  place  above  the  sea  reduces  the  height  of  the 
barometer  according  to  a  law  which  is  determined  by  the  general  properties 
of  elastic  fluids :  thus,  at  an  elevation  of  1  mile  above  the  sea,  the  mean 
height  of  the  barometer  is  24%  inches,  and  at  2  miles,  20  inches  only.  The 
use  of  the  barometer,  in  foretelling  variations  of  weather,  is  perhaps  more 
limited  than  has  sometimes  been  supposed  ;  but  by  a  careful  observation, 
conclusions  may  be  drawn  from  it,  which  may  in  many  cases  be  of  con- 
siderable utility  :  and  it  has  even  been  applied  with  success,  by  some  late 
navigators,  to  the  prediction  of  changes  of  wind,  at  times  when  they  could 
not  have  been  suspected  from  any  other  circumstances.* 


LECT.  LVI.— ADDITIONAL  AUTHORITIES. 

Meteorology  in  general. — Richard,  Hist.  Naturelle  de  1'Air  et  des  Meteores,  10 
vols.  12mo,  Paris,  1770-1.  Toaldo,  Saggio  Meteorologico,  4to,  Padova,  1770. 
La  Meteor.  Applicata,  4to,  "Venezia,  1786.  Deluc,  Idees  sur  la  Metgprologie, 
2  vols.  1786-7.  Cotte,  Traite  de  Met.  4to,  Paris,  1774;  Mem.  sur  IziMeteor. 
2  vols.  4to,  1778.  Horrebow,  Tractatus  Historico-meteorologicus,  4to,  Copenhag. 


See  D'Alcmbert,  Reflexions  sur  la  Cause  Generate  des  Vents,  4to,  1747. 


ON  AQUEOUS  AND  IGNEOUS  METEORS.  551 

1780.  Saussure,  Voyages  dans  les  Alpes,  4  vols.  4to,  Neuchatel,  1796. . .  Dalton's 
Essays,  1793.  Forster  on  Atmospheric  Phenomena,  1823.  Schouw,  Beitrage  zur 
Vergleichenden  Klimatologie,  Copenhag.  1827;  Ed.  Jour,  of  Science,  viii.311.  Bailly 
de  Merlieux  ;  Resume  complet  de  Meteor.  32mo,  1830.  Rigaud.  Harvey's  Meteor, 
in  Encyc.  Metrop.  Kamtz,  Lehrbuch  der  Meteor.  3  vols.  1831-6.  Course  of 
Meteorology  (trans.},  Lond.  1845.  Howard's  Climate  of  London,  3  vols.  1833. 
Quetelet,  Aper£u  Historique  des  Obs.  de  Meteorologie  faites  en  Belgique,  4to,  Brux. 
1834.  Forbes's  Reports  on  Meteorology,  Br.  Ass.  1834,  1840 ;  translated  into 
German,  and  amplified  by  Mahlmann,  Leipz.  1836.  Dove's  Repertorium,  1839, 
vol.  iii.  Daniell's  Meteor.  Essays,  var.  ed.  Front's  Bridgwater  Treatise,  1834. 

Storms. — Redfield,  Silliman's  Journal,  1831,  p.  17.  Reid  on  the  Law  of  Storms, 
Lond.  1833;  Edin.  Review,  Ixviii.  406.  Espy  on  do.  Dove,  Scientific  Mem. 
part  ix. 


LECTURE   LVIT. 


ON  AQUEOUS  AND  IGNEOUS  METEORS. 

THE  phenomena  originating  from  the  evaporation  of  water  constitute  a 
large  proportion  of  the  subjects  of  meteorology:  they  are  materially 
influenced  by  the  diversities  of  climates  and  winds,  which  we  have  lately 
considered  ;  and  they  appear  to  contribute  to  the  electrical  changes,  which 
form  a  principal  part  of  luminous  or  igneous  meteors  :  nor  is  the  action  of 
water  wholly  unconcerned  in  many  of  the  effects  of  subterraneous  fires, 
which  have  also  a  slight  connexion  with  atmospherical  electricity ;  and  it 
has  been  conjectured  that  the  only  igneous  meteors,  which  appear  wholly 
independent  of  any  of  these  phenomena,  may  originate  from  volcanic 
commotions  in  other  worlds. 

The  action  of  heat  appears  to  detach  continually  from  the  surface  of 
water,  and  perhaps  of  every  other  liquid,  and  even  solid,  a  certain  quantity 
of  vapour,  in  the  form  of  an  invisible  gas  ;  but  when  the  space  above  the 
liquid  is  already  charged  with  as  much  vapour  as  can  exist  in  it  at  the 
actual  temperature,  the  vapour,  thus  continually  thrown  off,  either  remains 
suspended  in  the  form  of  visible  particles,  or  falls  back  immediately  into 
the  liquid.  This  is  the  simplest  mode  of  explaining  the  continuance  of 
evaporation,  under  the  pressure  of  any  dry  gas,  however  dense,  and  its 
apparent  suppression  in  the  presence  of  moist  air,  however  rare.  Some- 
times also,  when  the  temperature  of  the  liquid  is  elevated,  so  that  minute 
globules  either  of  steam  or  of  air  rise  through  it,  some  visible  particles  are 
projected  upwards  by  each  globule,  and  continue  to  float  in  the  air  ;  this 
appears,  however,  to  be  an  irregularity  unconnected  with  the  principal 
process  of  slow  evaporation.  • 

The  quantity  of  vapour,  which  can  exist  in  the  space  above  any  portion 
of  water,  has  been  supposed  by  Deluc,*  Volta,t  and  Dalton,^  to  be  wholly 
independent  of  the  nature,  the  density,  or  even  the  presence  of  the  air  or 
gas  wMeh  that  space  contains  :  and  we  may  easily  imagine  that  the 
smallest  distance  at  which  the  particles  of  water,  constituting  vapour,  can 

*  Ph.  Tr.  1792,  p.  400.  f  Gren's  Journal,  iii.  479. 

t  See  Ph.  Tr.  1826. 


552  LECTURE  LVII. 

exist,  without  coming  within  the  reach  of  their  mutual  cohesion,  is  the 
same,  whatever  other  particles  may  be  scattered  through  the  interven- 
ing space.  It  appears,  however,  more  consistent  with  some  experiments, 
to  suppose,  that  the  presence  of  air  of  the  usual  density  allows  the  particles 
of  water  to  approach  a  little  nearer  together  without  cohering,  so  that  the 
utmost  quantity  of  moisture  that  can  be  contained  in  a  cubic  foot  of  air 
at  a  given  temperature  is  not  exactly  the  same  as  would  make  a  cubic  foot  of 
pure  vapour,  but  always  in  a  certain  proportion  to  it ;  and  it  seems  to  fol- 
low,, from  the  experiments  of  Saussure,  compared  with  those  of  Pictet,  that 
the  weight  of  the  vapour  contained  in  a  cubic  foot  of  air  is  about  one  half 
greater  than  that  of  a  cubic  foot  of  pure  vapour  at  the  same  temperature. 

When  the  air,  in  the  neighbourhood  of  the  surface  of  the  water,  has 
become  thus  saturated  with  moisture,  the  evaporation  proceeds  very  slowly, 
the  vapour  being  precipitated  as  soon  as  it  rises :  but  if  the  air  be  continu- 
ally changed,  so  that  the  moistened  portion  may  be  removed,  and  dry  air 
substituted  for  it,  the  process  will  be  greatly  expedited ;  and  such  a  change 
may  be  effected  either  by  wind,  or  by  the  natural  circulation,  occasioned 
by  any  elevation  of  temperature  communicated  by  the  water  to  the  neigh- 
bouring air ;  but  when  this  circulation  is  prevented,  the  evaporation  is 
much  diminished,  although  the  temperature  may  be  considerably  elevated. 
In  moderate  exposures,  the  depth  of  the  quantity  of  water,  evaporating  in 
24  hours  from  any  surface,  is  expressed,  according  to  Mr.  Dalton's  experi- 
ments, by  the  height  of  the  column  of  mercury  equivalent  to  the  force  of 
steam  at  the  given  temperature,  deducting,  however,  the  effect  of  the  elas- 
ticity of  the  moisture  already  existing  in  the  air. 

Since  the  quantity  of  moisture,  which  the  air  [or  rather  a  given  space^ 
is  capable  of  receiving,  is  greater  as  its  temperature  is  greater,  we  may 
obtain  a  natural  measure  of  the  quantity  which  it  contains  by  reducing 
it  to  the  temperature  at  which  the  moisture  begins  to  be  deposited.  Thus, 
if  we  take  a  glass  of  cold  water,  and  add  to  it  some  common  salt,  or  some 
muriate  of  lime,  we  may  cool  the  air  near  it  so  much  as  to  cause  it  to 
deposit  a  part  of  its  moisture  on  the  glass  :  and  by  measuring  the  tempera- 
ture of  the  water  when  the  precipitation  begins,  Mr.  Dalton  estimates  the 
true  state  of  the  air  with  respect  to  moisture.  Thus,  if  the  glass  begins  to 
be  moistened  when  the  water  is  at  40°,  he  infers  from  the  known  elasticity 
of  steam  at  that  temperature,  that  the  quantity  of  moisture  contained  in 
the  air  is  equivalent  to  the  pressure  of  a  column  of  mercury  about  a 
quarter  of  an  inch  in  height ;  and  if  the  actual  temperature  of  the  air  be 
50°,  the  corresponding  elasticity  of  steam  being  a  little  more  than  one  third 
of  an  inch,  the  daily  evaporation  in  such  air  will  amount  to  about  one 
ninth  of  an  inch,  making  40  inches  in  the  whole  year.  In  fact,  however, 
the  air  is*  usually  moister  than  this,  and  the  mean  evaporation  of  all 
England  is,  according  to  Mr.  Dalton,*  about  23  inches  only. 

In  hotter  climates,  and  in  particular  situations,  the  evaporation  may  be 
considerably  greater.  The  Mediterranean  Sea,  being  surrounded  by  land, 
is  more  heated  than  the  ocean,  and  the  winds  which  blow  ovens^t  are 
drier ;  consequently  its  evaporation  is  greater  than  that  of  the  Atlantic, 
and  its  specific  gravity  is  increased  by  the  increased  proportion  of  salt ; 
*  Manch.  Mem.  v.  346. 


ON  AQUEOUS  AND  IGNEOUS  METEORS.  553 

so  that  at  the  straights  of  Gibraltar,  a  current  runs  inwards  at  the  surface 
and  outwards  near  the  bottom,  for  the  same  reason  as  the  air,  when  it  is 
denser  in  a  passage  than  in  the  adjoining  room,  blows  a  candle  towards  the 
room  at  the  lower  part  of  the  door,  and  draws  it  towards  the  passage  at  the 
upper.  Had  there  been  a  continual  current  inwards  through  the  Straights, 
at  all  parts,  the  Mediterranean  must  in  the  course  of  ages  have  become  a 
rock  of  salt.  It  is  indeed  remarkable  that  all  lakes,  into  which  rivers  run 
without  any  further  discharge,  are  more  or  less  salt,  as  well  as  lakes  in 
general  near  the  sea  :  but  where  a  river  runs  through  a  lake  into  the  sea, 
it  must  necessarily,  in  the  course  of  time,  have  carried  the  salt  of  the  lake 
with  it,  if  it  had  ever  existed. 

Experiments  on  the  deposition  of  moisture,  like  those  of  Mr.  Dalton,  are 
liable  to  a  slight  inaccuracy,  on  account  of  the  effects  of  an  apparent 
elective  attraction,  by  means  of  which,  some  substances  seem  to  attract 
humidity  at  a  temperature  a  little  higher  than  others.  Thus,  a  surface  of 
metal  often  remains  dry,  in  the  neighbourhood  of  a  piece  of  glass  which  is 
covered  with  moisture.  It  is  certain  that  some  substances  attract  moisture 
from  the  air,  even  when  the  quantity  which  it  contains  is  incomparably 
less  than  that  which  would  saturate  it,  since  it  is  on  this  circumstance 
that  the  construction  of  hygrometers  depends ;  and  it  is  probably  by  a 
property  somewhat  similar,  that  even  surfaces  of  different  kinds  possess 
different  attractive  powers  for  moisture  nearly  ready  to  be  deposited.  It  is, 
however,  only  necessary  to  employ,  for  Mr.  Dalton's  experiment,  a  sub- 
stance which  has  a  very  weak  attraction  for  moisture ;  and  any  kind  of 
metal  will  perhaps  be  found  sufficiently  correct  in  its  indications. 

It  has  been  observed,  that  a  piece  of  metal,  placed  on  glass,  usually  pro- 
tects also  the  opposite  side  of  the  glass  from  the  deposition  of  dew ;  and 
Mr.  Benedict  Prevost  has  shown,  that  in  general,  whenever  the  metal  is 
placed  on  the  warmer  side  of  the  glass,  the  humidity  is  deposited  more 
copiously  either  on  itself,  or  on  the  glass  near  it ;  that  when  it  is  on  the 
colder  side,  it  neither  receives  the  humidity,  nor  permits  its  deposition  on 
the  glass  ;  but  that  the  addition  of  a  second  piece  of  glass,  over  the  metal, 
destroys  the  effect,  and  a  second  piece  of  metal  restores  it.  It  appears  that, 
from  its  properties  with  respect  to  radiant  heat,  the  metallic  surface  pro- 
duces these  effects,  by  preventing  the  ready  communication  either  of  heat 
or  of  cold  to  the  glass.* 

The  quantity  of  invisible  moisture,  contained  in  air,  may  be,  in  some 
degree,  estimated  from  the  indications  of  hygrometers,  although  these  in- 
struments have  hitherto  remained  in  a  state  of  great  imperfection.  A  sponge, 
a  quantity  of  caustic  potash,  or  of  sulfuric  acid,  or  a  stone  of  a  peculiar 
nature,  has  sometimes  been  employed  for  determining  the  degree  of  moisture 
of  the  air,  from  which  it  acquires  a  certain  augmentation  of  its  weight. 
A  cord  dipped  in  brine,t  or  the  beard  of  an  oat,  is  also  often  used  for  the 
same  purpose  :  the  degree  in  which  it  untwists,  from  the  effect  of  moisture, 
being  shown  by  an  index.  But  the  extension  of  a  hair,  or  of  a  slip  of 
•  -' 

*  B.  Prevost  on  Dew,  Ann.  de  Chimie,  xliv.  75. 
t  Smeaton,  Ph.  Tr.  1771,  p.  198. 


554  LECTURE  LVII. 

whalebone,  which  have  been  employed  by  Saussure*  and  Deluc,t  appear 
to  be  more  certain  and  accurate  in  their  indications.  The  hair  hygrometer 
acquires  more  speedily  the  degree  corresponding  to  any  given  state  of  the 
air,  but  it  seems  to  reach  the  utmost  extent  of  its  scale  before  it  arrives  at 
perfect  humidity :  while  the  whalebone  hygrometer  appears  to  express  a 
greater  change  upon  immersion  in  water  than  from  the  effect  of  the  moist- 
est  transparent  air,  which  has  also  been  considered  by  some  as  an  imper- 
fection. Both  these  instruments  are  impaired  by  time,  and  acquire  contrary 
errors,  so  that  a  mean  between  both  is  more  likely  to  be  correct  than  either 
separately.  Their  indications  are  at  all  times  widely  different  from  each 
other,  and  the  mean  appears  to  approach  much  nearer  to  a  natural  scale 
than  either  of  them.  Mr.  Leslie  J  employs  a  very  delicate  thermometer,  of 
which  the  bulb  is  moistened,  for  measuring  the  drjoiess  of  the  air,  by  the 
cold  produced  during  evaporation,  when  the  thermometer  is  exposed  to  it ; 
but  this  mode  of  estimating  the  quantity  of  moisture  appears  to  be  liable 
to  considerable  uncertainty.  (Plate  XLI.  Fig.  581.) 

In  order  that  the  scale  of  a  hygrometer  should  be  perfectly  natural,  it 
ought  to  express,  at  all  temperatures,  the  proportion  of  the  quantity  of 
moisture  in  the  air  to  that  which  is  required  for  its  saturation  ;§  thus,  at 
100  degrees,  it  should  imply  that  the  slightest  depression  of  temperature 
would  produce  a  deposition  ;  at  50  degrees,  that  the  air  contains  only  half 
as  much  water  as  would  saturate  it,  or,  supposing  the  thermometer  at  52°, 
that  a  deposition  would  be  produced  in  it  by  a  depression  of  17°.  And 
if  we  know  the  actual  temperature,  and  the  temperature  at  which  the  depo- 
sition takes  place,  we  may  find  the  height  of  the  natural  hygrometer,  by 
the  proportion  of  the  corresponding  elasticities  of  steam.  The  mean 
height  of  the  natural  hygrometer  in  London  is  probably  about  80°  ;  that 
of  Deluc's  hygrometer,  with  proper  corrections,  being  nearly  70°:  so 
that  a  depression  of  6°  must  usually  be  sufficient  to  cause  a  deposition  of 
moisture. 

The  quantity  of  water  actually  contained  in  a  cubic  foot  of  air,  satu- 
rated with  moisture,  appears  to  be  about  2  grains  at  the  freezing  point, 
4  grains  at  48°,  6  at  60°,  and  8  at  68° ;  and  the  density  of  the  vapour, 
thus  mixed  with  air,  is,  according  to  Saussure's  experiments,  about  three 
fourths  as  great  as  that  of  the  air  itself ;  so  that  moist  air  is  always  a  little 
lighter  than  dry  air  ;  and  the  more  so  as  the  air  is  warmer,  provided  that 
it  be  saturated  with  moisture  by  means  of  the  presence  of  water.  It  follows 
from  the  properties  of  moisture  thus  determined,  that  if  any  two  portions 
of  perfectly  humid  air,  at  different  temperatures,  be  mixed  together,  there 
must  be  a  precipitation  :  thus,  a  cubic  foot  of  air  at  32°  being  mixed  with 
another  at  60°,  their  common  temperature  must  be  46°  ;  if  they  are  satu- 

*  Essai  sur  1'Hygrometrie,  Neuch.  1783.     Jour,  de  Phy.  xxxii.  24,  98. 

t  Ph.  Tr.  1791,  1,  389.     Jour,  de  Ph.  xxx.  437  ;  xxxii.  132. 

J  Nich.  Jour.  iii.  401.  A  short  Account  of  Instruments  depending  on  the  Rela- 
tions of  Air  to  Heat  and  Moisture,  Edin.  1813.  Descrip.  of  Instrs.  for  Improving 
Meteor.  Obs.  Edin.  1820.  See  on  this  subject  Forbes's  Supplementary  Report  on 
Meteor.  Brit.  Ass.  1840,  p.  95. 

§  This  phrase  must  not  be  supposed  to  imply  any  combination  between  the  air 
and  vapour. 


ON  AQUEOUS  AND  IGNEOUS  METEORS.  555 

rated  with  moisture,  they  must  contain  8  grains  of  water  when  separate  ; 
but  when  mixed  they  will  he  too  cold  by  2°  to  contain  the  same  quantity  ; 
since  air  at  48°  can  only  contain  four  grains  for  each  foot ;  and  it  has  been 
supposed  that  such  mixtures  frequently  occasion  a  precipitation  in  nature. 
Thus,  it  often  happens  that  the  breath  of  an  animal,  which  is  in  itself 
transparent,  becomes  visible  when  mixed  with  a  cold  atmosphere ;  and  in 
such  cases  the  deposition  may  perhaps  be  facilitated  by  the  cooling  of  the 
warmer  air  to  a  certain  degree,  even  before  a  perfect  mixture  has  taken 
place.* 

When  visible  vapour  has  been  thus  deposited  from  transparent  air,  by 
means  either  of  cold  or  of  mixture,  it  generally  remains  for  some  time  sus- 
pended, in  the  form  of  a  mist  or  of  a  cloud  :  sometimes,  however,  it  appears 
to  be  at  once  deposited  011  the  surface  of  a  solid,  in  the  form  of  dew  or  of 
hoar  frost ;  for  it  is  not  probable  that  the  crystallized  form,  in  which  hoar 
frost  is  arranged,  can  be  derived  from  the  union  of  the  particles  already 
existing  in  the  air  as  distinct  aggregates.t 

The  dew,  which  is  commonly  deposited  on  vegetables,  is  partly  derived, 
in  the  evening,  from  the  vapours  ascending  from  the  heated  earth,  since  it 
is  then  found  on  the  internal  surface  of  a  bell  glass  ;  and  towards  the  morn- 
ing, from  the  moisture  descending  from  the  air  above,  as  it  begins  to  cool. 
Sometimes,  however,  in  warmer  weather,  the  dew  begins  to  descend  in  the 
evening  ;  this  the  French  call  serein  :  the  humidity  deposited  by  mists  on 
trees,  and  by  moist  air  on  windows,  generally  within,  but  sometimes  with- 
out, they  call  givre.  [The  cause  of  the  deposition  of  dew  has  been  satis- 
factorily assigned  by  Dr.  Wells.  ^  It  is  traceable  to  two  circumstances,  the 
radiation  of  heat,  and  the  condensation  of  vapour  by  cold.  Owing  to  the 
former  circumstance,  different  substances  on  the  earth's  surface  become 
cool  with  different  degrees  of  rapidity,  according  to  their  mechanical  tex- 
ture, or  their  position,  or  whatever  it  may  be.  When  they  have  cooled 
down  to  such  a  point  that  the  existing  vapour  in  the  atmosphere  near  them 
can  no  longer  be  retained  in  its  elastic  state,  it  becomes  water,  and  is  depo- 
sited on  their  surface.  The  cause  of  deposition  is  the  previous  cooling 
of  the  substance  on  which  it  takes  place.  Dr.  Wells  found,  as  Mr.  Six 
had  done  before  him,  that  a  thermometer  laid  on  a  grass  plot  in  a  clear 
night,  indicates  a  cold  many  degrees  lower  than  a  thermometer  hung  at 
some  height  from  the  ground.  This  is  owing  to  the  fact  that  grass  radiates 
heat  well;  and  accordingly  it  receives  a  copious  deposition  of  dew,  which 
a  worse  radiator  would  not  do.  Moreover,  if  the  sky  becomes  overcast,  or 
if  any  substance  be  interposed  between  it  and  the  grass,  radiation  is  checked, 
or  it  may  be  that  the  grass  receives  more  heat  from  the  surrounding  objects 
or  clouds  than  it  radiates,  and  thus  its  temperature  becomes  raised.  Under 
these  circumstances  the  deposition  of  dew  ceases.] 

Mists  are  said  to  consist  sometimes  of  other  particles  than  pure  water : 
these  are  called  dry  mists,  and  they  have  been  supposed  to  blight  vege- 

*  Hatton,  Dissertation  on  various  Subjects  of  Natural  Philosophy,  4to,  Edin. 
1792. 

t  See  Howard's  Essay  on  the  Modification  of  Clouds,  1832. 
:  Wolls  on  Dew,  1814. 


556  LECTURE  LVII. 

tables.  Such  mists  are  sometimes  attended  by  a  smell,  resembling  that 
which  is  occasioned  by  an  electric  spark.  Rain  falling  after  a  dry  season 
deposits,  when  it  has  been  suffered  to  stand,  some  particles  of  foreign 
matter  which  it  has  brought  down  from  the  atmosphere.  There  must  in- 
deed frequently  be  a  multiplicity  of  substances  of  various  kinds  floating  in 
the  air ;  the  wind  has  been  found  to  carry  the  farina  of  plants  as  far  as  30 
or  40  miles,  and  the  ashes  of  a  volcano  more  than  200.  It  only  requires 
that  the  magnitude  of  the  particles  of  any  substance  be  sufficiently  reduced 
in  size,  in  order  to  render  them  incapable  of  falling  with  any  given  velo- 
city ;  and  when  this  velocity  is  very  small,  it  may  easily  be  overpowered 
by  any  accidental  motions  of  the  air.  The  diameter  of  a  sphere  of  water, 
falling  at  the  rate  of  one  inch  only  in  a  second,  ought  to  be  one  six  hundred 
thousandth  of  an  inch,  which  is  about  the  thickness  of  the  upper  part  of 
a  soap  bubble  at  the  instant  when  it  bursts  ;  but  the  particles  of  mists  are 
incomparably  larger  than  this,  since  they  would  otherwise  be  perfectly 
invisible  as  separate  drops :  the  least  particle  that  could  be  discovered  by 
the  naked  eye,  being  such  as  would  fall  with  a  velocity  of  about  a  foot  in 
a  second,  if  the  air  were  perfectly  at  rest.  But  it  is  very  probable  that  the 
resistance,  opposed  to  the  motion  of  particles  so  small,  may  be  considerably 
greater  than  would  be  expected  from  a  calculation  derived  from  experi- 
ments made  on  a  much  larger  scale,  and  their  descent  consequently  much 
slower. 

When  the  particles  of  a  mist  are  united  into  drops  capable  of  descending 
with  a  considerable  velocity,  they  constitute  rain  ;  if  they  are  frozen 
during  their  deposition,  they  exhibit  the  appearance  of  a  perfect  crystal- 
lization, and  become  snow  :  but  if  the  drops  already  formed  are  frozen, 
either  by  means  of  external  cold,  or  on  account  of  the  great  evaporation 
produced  by  a  rapid  descent  through  very  dry  air,  they  acquire  the  cha- 
racter of  hail,  which  is  often  observed  in  weather  much  too  hot  for  the 
formation  of  snow. 

It  cannot  be  doubted  but  that  there  is  a  connexion  betwen  the  descent  of 
the  barometer  and  the  fall  of  rain  ;  but  no  satisfactory  reason  has  yet  been 
assigned  for  the  circumstance  ;  nor  is  it  possible  to  foretel,  with  certainty, 
that  rain  will  follow  any  changes  in  the  height  of  the  barometer  that  have 
been  observed.  The  immediate  dependence  of  rain,  or  of  any  other  atmo- 
spherical phenomena,  on  the  influence  of  the  moon,  appears  to  be  rendered 
highly  improbable,  not  only  by  mathematical  calculations  of  the  effects  of 
the  moon's  attraction,  but  also  by  the  irregularity  of  the  very  observations 
which  have  been  adduced  in  favour  of  such  a  connexion.  But  however 
uncertain  the  ultimate  causes  of  rain  may  be  in  general,  their  effects  in 
some  places  are  sufficiently  constant  to  be  attributed  to  permanent  local 
circumstances,  and  in  particular  to  the  periodical  recurrence  of  similar 
winds. 

In  low  and  level  countries,  clouds  may  often  begin  to  descend  from  the 
upper  regions  of  the  atmosphere,  and  may  be  redissolved  by  the  warmer 
air  below ;  but  when  they  descend  in  an  equal  degree  among  mountains, 
they  fall  on  the  earth  ;  and  besides  the  quantity  of  water  which  they  fur- 
nish for  vegetation,  and  that  which  is  carried  off  by  evaporation,  they 


ON  AQUEOUS  AND  IGNEOUS  METEORS.  557 

afford,  by  means  of  springs  and  rivers,  a  constant  supply  for  the  use  of 
man  and  of  other  animals  in  distant  parts.  The  upper  regions  of  the 
atmosphere  are  however  by  no  means  the  principal  sources  of  rain  in  ordi- 
nary climates,  since  a  gage  placed  on  a  very  high  building  seldom  collects 
more  than  two  thirds  as  much  rain  as  another  standing  on  the  ground 
below  :*  and  the  effects  of  mountains  in  collecting  rain  are  perhaps 
chiefly  derived  from  the  ascending  currents  which  they  occasion,  and  by 
which  the  air  saturated  with  moisture  is  carried  to  a  higher  and  a  colder 
region. 

The  Abyssinian  rains  are  the  causes  of  the  inundation  of  the  Nile  :  they 
last  from  April  to  September ;  but  for  the  first  three  months  the  rain  is 
only  in  the  night.  The  inundation,  in  Egypt,  begins  at  present  about 
the  17th  of  June  ;  it  increases  for  40  days,  and  subsides  in  the  same  time  ; 
but  the  ancient  accounts,  as  well  as  some  modern  ones,  assign  a  longer 
duration  to  it.  The  river  Laplata  rises  and  falls  at  the  same  times  as  the 
Nile.  The  Ganges,  the  Indus,  the  Euphrates,  the  river  of  Ava  or  Pegu, 
and  many  other  large  rivers,  have  also  considerable  inundations  at  regular 
periods.  In  many  other  countries  there  are  seasons  at  which  the  rains 
seldom  fail  to  recur ;  and  sometimes  the  periodical  rains  are  different  in 
different  parts  of  the  same  country.  Thus  the  coast  of  Malabar,  which  is 
to  the  west  of  the  Gate  mountains,  or  Gauts,  enjoys  summer  weather, 
without  rain,  from  September  to  April,  while  that  of  Coromandel,  which 
is  on  the  eastern  side,  experiences  all  the  rigours  of  its  winter ;  being  at 
this  time  exposed  to  the  influence  of  the  north  east  trade  wind.  Vicissi- 
tudes of  a  similar  nature  are  also  observed  on  the  north  and  south  sides  of 
the  island  of  Jamaica.  The  mean  fall  of  rain  in  London  is  about  23 
inches ;  at  Exeter,  which  is  nearer  to  the  Atlantic,  33 ;  the  average  of 
England  and  Wales  is  31. 

The  evaporations  and  precipitations,  and  probably  also  the  condensations 
and  expansions,  which  take  place  on  a  large  scale  in  the  atmosphere,  and 
in  the  clouds,  cannot  fail  of  producing  changes  in  their  electrical  qualities, 
and  these  changes  appear  to  be  the  principal  sources  of  the  phenomena  of 
thunder  and  lightning.  The  clouds,  when  electrified,  being  more  or  less 
insulated  by  the  interposition  of  the  air,  exhibit  attractive  and  repulsive 
effects,  and  are  discharged  by  explosions,  either  among  themselves,  or 
communicating  with  the  earth,  in  the  same  manner  as  bodies  which  have 
been  electrified  by  artificial  means  ;  they  also  sometimes  produce,  in  the 
neighbouring  parts  of  the  earth,  and  in  the  animals  on  its  surface,  a  state 
of  induced  electricity  ;  and  in  this  case  the  returning  stroke,  or  the  sudden 
restoration  of  the  equilibrium,  when  the  electricity  of  the  nearest  clouds  is 
imparted  to  the  more  remote,  may  be  fatal,  without  any  appearance  of  an 
immediate  discharge,  at  the  place  where  the  animal  stands. 

We  can,  however,  by  no  means  precisely  ascertain  in  what  manner  all 
the  electrical  phenomena  of  the  atmosphere  are  produced.  It  appears  from 

*  From  the  observations  of  Prof.  Phillips  at  York,  the  fall  of  rain  during  twelve 
months  ^as  25'7  in.  on  the  ground,  19'8  in.  44  feet  above  the  ground,  and  not  quite 
15  in.  213  feet  above  it.  Rep.  of  Br.  Ass.  1834,  p.  560. 


558  LECTURE  LVII. 

the  experiments  of  Beccaria*  and  Cavallof  that  the  air  is  in  general 
positively  electrical,  and  most  so  in  cold  and  clear  weather  ;  in  cloudy- 
weather  more  slightly  :  and  that  during  rain,  the  air  is  generally  in  a  nega- 
tive state.  Mr.  Read  J  has  found  that  air  charged  with  putrid  vapours  of 
any  kind,  and  in  particular  the  air  of  close  rooms,  is  almost  always  nega- 
tively electrified.  The  electricity  is  more  readily  communicated  to  an 
electrometer  in  an  elevated  situation,  and  in  damp  weather,  than  in  other 
circumstances  ;  a  candle  is  also  very  useful  in  collecting  it.  When  a  wire 
is  connected  with  a  kite,  being  continued  along  the  string,  we  may  fre- 
quently ohtain  from  it  sparks  a  quarter  of  an  inch  long. 

We  find  a  complete  and  interesting  description  of  the  effects  of  a  violent 
thunder  storm  in  a  paper  by  Mr.  Brereton,  inserted  in  the  Philosophical 
Transactions^  The  circumstance  happened  in  September  1780,  at  East 
Bourn,  in  a  house  occupied  by  Mr.  Adair  :  it  was  built  of  stone,  and  stood 
facing  the  sea.  About  nine  o'clock,  in  a  very  stormy  morning,  a  black 
cloud  approached  the  house  ;  several  balls  of  fire  were  seen  to  drop  from  it 
successively  into  the  sea,  and  one  in  particular,  appearing  like  an  immense 
sky  rocket,  broke  against  the  front  of  the  house  in  different  directions. 
Mr.  Adair  was  standing  at  a  window  on  the  first  floor,  with  his  hands 
clasped  together,  and  extended  against  the  middle  of  the  frame  :  his  hands 
were  forced  asunder,  he  was  thrown  several  yards  off  on  the  floor,  and 
remained  for  some  time  speechless  and  motionless,  although  not  insensible  5 
his  clothes  were  much  torn  ;  several  articles  of  metal  about  his  person  were 
partially  melted,  while  others,  apparently  in  similar  circumstances,  and  in 
particular  a  silver  buckle,  escaped  ;  and  his  skin  was  in  many  parts  much 
scorched  and  lacerated.  The  whole  of  the  glass  in  the  window,  and  a  pier 
glass  near  it,  were  completely  destroyed,  and  scattered  about  the  room  ; 
most  of  the  furniture  was  broken  to  pieces,  and  all  the  bell  wires  were 
melted.  In  the  room  above  this,  a  lady  and  her  maid  were  driven  to  a 
distant  part,  and  rendered  insensible  for  some  time,  but  not  hurt ;  in  the 
room  below,  two  servants,  who  were  near  the  windows,  were  struck  dead  : 
both  the  bodies  were  turned  black  :  one  of  them  had  a  wound  near  the 
heart ;  and  neither  of  them  became  stiff  after  death  ;  a  third  servant,  who 
was  a  little  behind  one  of  them,  escaped  with  the  loss  of  a  telescope,  which 
he  held  in  his  hand,  and  with  the  sensation  of  a  violent  pressure  on  his 
head  and  on  his  back.  A  large  stone  was  forced  out  of  the  wall  near  them, 
and  thrown  into  the  room,  and  some  other  similar  effects  were  observed, 
which  marked  the  progress  of  the  explosion. 

For  guarding  against  accidents  so  dreadful,  Dr.  Franklin's  great  invention 
of  metallic  conductors  may  be  very  advantageously  employed :  for,  when 
properly  fixed,  they  afford  a  degree  of  security  which  leaves  very  little  room 
for  apprehension.  A  conductor  ought  to  be  continued  deep  into  the  earth, 

*  Delia  Elettricita  Terrestre  Atmosferica,  4to,  Torino,  1775. 
f  Ph.  Tr.  1776,  p.  407  ;  1777,  p.  48. 

J  Jour,  of  Electricity,  Ph.  Tr.  1792,  p.  225  ;  1794,  pp.  185,  266.     Treatise  on 
Atmospheric  Electricity,  1793.     See  Arago,  Annuairefor  1838. 
§  1781,  p.  42. 


ON  AQUEOUS  AND  IGNEOUS  METEORS.  559 

or  connected  with  some  well  or  drain :  it  should  be  of  ample  dimensions, 
and  where  smallest,  of  copper,  since  copper  conducts  electricity  more  readily 
than  iron.  In  one  instance  a  conductor  of  iron,  four  inches  wide  and  half 
an  inch  thick,  appears  to  have  heen  made  red  hot  by  a  stroke  of  lightning. 
It  seems  to  be  of  some  advantage  that  a  conductor  should  be  pointed,  but 
the  circumstance  is  of  less  consequence  than  has  often  been  supposed.* 
Mr.  Wilson  exhibited  some  experiments  in  which  a  point  was  struck  at  a 
greater  distance  than  a  ball,  and  therefore  argued  against  the  employment 
of  pointed  conductors.  Mr.  Nairne,  f  on  the  contrary,  showed  that  a  ball 
is  often  struck  in  preference  to  a  point.  But  it  has  been  observed,  that  if  a 
point  attracts  the  lightning  from  a  greater  distance,  it  must  protect  a  greater 
extent  of  building.  It  is  easy  to  show,  by  hanging  cotton  or  wool  on  a  con- 
ductor, that  a  point  repels  light  electrical  bodies,  and  that  a  pointed  con- 
ductor may,  therefore,  drive  away  some  fleecy  clouds  ;  but  this  effect  is 
principally  derived  from  a  current  of  air  repelled  by  the  point ;  and  such 
a  current  could  scarcely  be  supposed  to  have  any  perceptible  effect  on  clouds 
so  distant  as  those  which  are  concerned  in  thunder  storms.  In  order  to 
escape  personal  danger  in  a  thunder  storm,  the  best  precautions  are,  to  avoid 
eminences,  and  all  exposed  situations,  as  well  as  a  near  approach  to  conduc- 
tors. The  neighbourhood  of  windows,  looking-glasses,  fire-places,  and  trees, 
must  always  be  considered  as  hazardous. 

It  has  been  supposed  that  a  sudden  condensation  of  the  air,  arising  from 
cold,  accompanied  by  a  deposition  of  moisture,  and  propagated  by  a  con- 
tinuation of  the  cause,  by  means  of  the  cold  occasioned  by  expansion,  pro- 
duces frequently  the  noise  of  thunder,  without  any  lightning,  and  without 
any  electrical  agitation  :  but  it  does  not  appear  that  the  opinion  is  well 
established.  J 

The  phenomena  of  waterspouts,  if  not  of  electrical  origin,  appear  to  have 
some  connexion  with  electrical  causes.  A  waterspout  generally  consists  of 
large  drops  like  a  dense  rain,  much  agitated,  and  descending  or  ascending 
with  a  spiral  motion,  at  the  same  time  that  the  whole  spout  is  carried  along 
horizontally,  accompanied  in  general  by  a  sound  like  that  of  the  dashing 
of  waves.  Spouts  are  sometimes,  although  rarely,  observed  on  shore,  but 
generally  in  the  neighbourhood  of  water.  They  are  commonly  largest 
above  ;  sometimes  two  cones  project,  the  one  from  a  cloud,  the  other  from 
the  sea  below  it,  to  meet  each  other,  the  junction  being  accompanied  by  a 
flash  of  lightning  :  and  when  the  whole  spout  has  exhibited  a  luminous 
appearance,  it  has  perhaps  served  to  conduct  electricity  slowly  from  the 
clouds  to  the  earth.  Some  of  these  circumstances  may  be  explained  by 
considering  the  spout  as  a  whirlwind,  carrying  up  drops  of  water,  which  it 
has  separated  from  the  surface  of  the  waves ;  and  the  remainder  may  per- 

*  See  Report  of  Committee  appointed  to  consider  of  a  Method  for  securing  Pow- 
der Magazines  ;  with  Mr.  B.  Wilson's  Dissent,  Ph.  Tr.  1773,  Ixiii.  42.  See  also 
ibid.  liv.  247;  Ixviii.  999.  Cavallo,  ibid.  1788,  p.  1.  Murray's  Treatise  on  At- 
mospheric Electr.  1828.  Harris,  On  the  Utility  of  fixing  Lightning  Conductors  in 
Ships,  Plymouth,  1830.  Annals  of  Electr.  iv.  310  ;  v.  41. 

t  Ph?Tr.  1774,  p.  79;  1778,  p.  823. 

J  See  Harris's  Essay  on  Thunderstorms,  1843. 


560  LECTURE  LVII. 

haps  be  deduced  from  the  cooperation  of  electricity,  already  existing  in  a 
neighbouring  cloud. 

It  is  doubtful  whether  the  light  of  the  aurora  borealis  may  not  be  of  an 
electrical  nature  :  the  phenomenon  is  certainly  connected  with  the  general 
cause  of  magnetism  ;  the  primitive  beams  of  light  are  supposed  to  be  at  an 
elevation  of  at  least  50  or  100  miles  above  the  earth,  and  every  where  in  a 
direction  parallel  to  that  of  the  dipping-needle  ;  but  perhaps,  although  the 
substance  is  magnetical,  the  illumination,  which  renders  it  visible,  may  still 
be  derived  from  the  passage  of  electricity,  at  too  great  a  distance  to  be  dis- 
covered by  any  other  test. 

Earthquakes*  and  volcanos  appear  to  originate  in  chemical  changes, 
which  take  place  within  the  substance  of  the  earth :  they  have  probably 
little  further  connexion  with  electricity,  than  as  causes  which  occasionally 
destroy  the  electrical  equilibrium ;  for  although  some  authors  have  inferred, 
from  the  great  velocity  with  which  the  shock  of  an  earthquake  is  trans- 
mitted from  place  to  place,  that  its  nature  must  be  electrical,  yet  others 
have,  with  greater  probability,  attributed  the  rapid  succession  of  the  effects 
to  the  operation  of  a  single  cause,  acting  at  a  great  distance  below  the  earth's 
surface.  There  are  however  some  circumstances,  which  indicate  such  a 
connexion  between  the  state  of  the  atmosphere  and  the  approach  of  an 
earthquake,  as  cannot  easily  be  explained  by  any  hypothesis. 

The  shocks  of  earthquakes  and  the  eruptions  of  volcanos,  are  in  all 
probability  modifications  of  the  effects  of  one  common  cause :  the  same 
countries  are  liable  to  both  of  them  ;  and  where  the  agitation  produced  by 
an  earthquake  extends  further  than  there  is  any  reason  to  suspect  a 
subterraneous  commotion,  it  is  probably  propagated  through  the  earth 
nearly  in  the  same  manner  as  a  noise  is  conveyed  through  the  air.  Volca- 
nos are  found  in  almost  all  parts  of  the  world,  but  most  commonly  in  the 
neighbourhood  of  the  sea  ;  and  especially  in  small  islands  ;  for  instance,  in 
Italy,  Sicily,  Iceland,  Japan,  the  Caribbees,  the  Cape  Verd  islands,  the 
Canaries,  and  the  Azores  :  there  are  also  numerous  volcanos  in  Mexico  and 
Peru,  especially  Pichincha  and  Cotopaxi.  The  subterraneous  fires,  which 
are  continually  kept  up  in  an  open  volcano,  depend  perhaps  in  general  on 
sulfureous  combinations  and  decompositions,  like  the  heating  of  a  heap  of 
wet  pyrites,  or  the  union  of  sulfur  and  iron  filings  :  but  in  other  cases  they 
may  perhaps  approach  more  nearly  to  the  nature  of  common  fires.  A 
mountain  of  coal  has  been  burning  in  Siberia  for  almost  a  century,  and 
must  probably  have  undermined  in  some  degree  the  neighbouring  country. 
The  immediate  cause  of  an  eruption  appears  to  be  very  frequently  an 
admission  of  water  from  the  sea,  or  from  subterraneous  reservoirs  ;  it  has 
often  happened  that  boiling  water  has  been  discharged  in  great  quantities 
from  a  volcano  ;  and  the  force  of  steam  is  perhaps  more  adequate  to  the 
production  of  violent  explosions,  than  any  other  power  in  nature.  The 
consequence  of  such  an  admission  of  water,  into  an  immense  collection  of 

^  *  Bertrand,  M£moires  Historiques  et  Physiques  sur  lea  Tremblemens  de  Terre.  A 
1  Haye,  1757.  Michell,  Conjectures  concerning  the  Cause  of  Earthquakes^  Ph.  Tr. 


ON  AQUEOUS  AND  IGNEOUS  METEORS.  561 

ignited  materials,  may  in  some  measure  be  understood,  from  the  acci- 
dents which  occasionally  happen  in  founderies ;  thus  a  whole  furnace  of 
melted  iron  was  lately  dissipated  into  the  air  in  Colebrook  Dale,  by  the 
effect  of  a  flood,  which  suddenly  overflowed  it. 

The  phenomena  of  earthquakes  and  volcanos  are  amply  illustrated  by 
the  particular  accounts,  transmitted  to  the  Royal  Society  by  Sir  William 
Hamilton,  of  those  which  have  happened  at  different  times  in  Italy.*  The 
earthquake,  which  desolated  Calabria,  in  1783,  was  fatal  to  about  40,000 
persons,  continuing  its  ravages  for  more  than  three  months ;  it  destroyed 
the  towns  and  villages  occupying  a  circle  of  nearly  50  miles  in  diameter, 
lying  between  38  and  39  degrees  latitude,  and  extending  almost  from  the 
western  to  the  eastern  coast  of  the  southernmost  point  of  Italy,  besides 
doing  considerable  damage  to  places  at  much  greater  distances  from  its 
origin,  which  is  supposed  to  have  been  either  immediately  under  the  town 
of  Oppido,  in  the  centre  of  this  circle  ;  or  under  some  part  of  the  sea, 
between  the  west  of  Italy,  and  the  volcanic  island  of  Stromboli.  This 
island,  as  well  as  Mount  Etna,  had  smoked  less  than  usual  before  the 
earthquake,  but  they  both  exhibited  appearances  of  an  eruption  during  its 
continuance  ;  Etna  towards  the  beginning,  and  Stromboli  at  the  end. 
Before  each  shock  the  clouds  were  usually  motionless  for  a  certain  time, 
and  it  rained  violently ;  frequently  also  lightning  and  sudden  gusts  of 
wind  accompanied  the  rain.  The  principal  shocks  appeared  to  consist  in  a 
sudden  elevation  of  the  ground  to  a  considerable  height,  which  was  propa- 
gated somewhat  like  a  wave,  from  west  to  east :  besides  this,  the  ground 
had  also  a  horizontal  motion  backwards  and  forwards,  and  in  some  mea- 
sure in  a  circular  direction.  This  motion  was  accompanied  by  a  loud 
noise  ;  it  continued  in  one  instance  for  ten  seconds  without  intermission ; 
and  it  shook  the  trees  so  violently  that  their  heads  nearly  reached  the 
ground.  It  affected  the  plains  more  strongly  than  the  hills.  In  some 
places  luminous  exhalations,  which  Sir  William  Hamilton  thinks  rather 
electrical  than  igneous,  were  emitted  by  the  earth  :  the  sea  boiled  up  near 
Messina,  and  was  agitated  as  if  by  a  copious  discharge  of  vapours  from  its 
bottom  ;  and  in  several  places  water,  mixed  with  sand,  was  thrown  up  to 
a  considerable  height.  The  most  general  effect  of  these  violent  commotions 
was  the  destruction  of  buildings  of  all  kinds,  except  the  light  barracks  of 
wood  or  of  reeds,  into  which  the  inhabitants  retreated  as  soon  as  they  were 
aware  of  their  danger  :  the  beds  of  rivers  were  often  left  dry,  while  the 
shock  lasted,  and  the  water  on  its  return  overflowed  their  banks  :  springs 
were  sometimes  dried  up,  and  new  ones  broke  out  in  other  places.  The  hills 
which  formed  the  sides  of  steep  vallies  were  often  divided  by  deep  chasms 
parallel  to  the  vallies  ;  and  in  many  cases  large  portions  of  them  were  sepa- 
rated, and  removed  by  the  temporary  deluge  to  places  half  a  mile  or  a  mile 
off ;  with  the  buildings  and  trees  still  standing  on  them  ;  and  in  this 
manner  hills  were  levelled,  and  vallies  were  filled  up.  But  the  most  fatal 
accident  of  this  kind  happened  at  Scilla,  where  so  large  a  portion  of  a  cliff 

*  Ph.Tr.  1767,  Ivii.  192  ;  1768,  Iviii.  1 ;  lix.  18  ;  1780,  Ixx.  42  ;  1783,  p.  169: 
and  Count  Ippolito,  ibid.  p.  209,  1795,  73.  See  also  Hamilton's  Observations  on 
the  Volcanos  of  the  Two  Sicilies,  2  vols.  fol.  1776. 

2  o 


502  LECTURE   LVII. 

was  thrown  into  the  sea,  that  it  raised  an  immense  wave,  which  carried  oft* 
more  than  2000  inhabitants  who  were  collected  on  the  beach,  and  even 
extended  its  formidable  effects  to  the  opposite  coast  of  Sicily,  where  several 
persons  perished  by  it  in  a  similar  manner. 

The  eruptions  of  volcanos  are  usually  attended  by  some  shocks  like  those 
of  earthquakes,  although  commonly  less  violent.  Open  volcanos  con- 
tinually throw  out,  in  more  or  less  abundance,  smoke,  ashes,  and  pumice 
stones,  or  light  cinders  ;  but  their  most  formidable  effects  are  produced  by 
a  torrent  of  ignited  lava,  which,  like  a  vast  deluge  of  liquid  or  semiliquid 
fire,  lays  waste  the  country  over  which  it  runs,  and  buries  all  the  works  of 
human  art.  In  March,  1767,  Vesuvius  began  to  throw  out  a  considerable 
quantity  of  ashes  and  stones,  which  raised  its  summit  in  the  course  of  the 
year  no  less  than  200  feet,  forming  first  a  little  mountain  of  pumice  stones 
within  the  crater,  which  by  degrees  became  visible  above  its  margin.  The 
smoke,  which  was  continually  emitted,  was  rendered  luminous  at  night,  by 
the  light  derived  from  the  fire  burning  below  it.  In  August  some  lava  had 
broken  through  this  mountain,  and  in  September  it  had  filled  the  space 
left  between  it  and  the  former  crater.  On  the  13th  and  14th  of  October 
there  were  heavy  rains,  which  perhaps  supplied  the  water  concerned  in  the 
eruption  that  shortly  followed.  On  the  morning  of  the  19th,  clouds  of 
smoke  were  forced,  in  continual  succession,  out  of  the  mouth  of  the  vol- 
cano, forming  a  mass  like  a  large  pine  tree,  which  was  lengthened  into  an 
arch,  and  extended  to  the  island  of  Caprea,  28  miles  off ;  it  was  accom- 
panied by  much  lightning,  and  by  an  appearance  of  meteors  like  shooting 
stars.  A  mouth  then  opened  below  the  crater,  and  discharged  a  stream  of 
lava,  which  Sir  William  Hamilton  ventured  to  approach  within  a  short 
distance,  imagining  that  the  violence  of  the  confined  materials  must  have 
been  exhausted  ;  but  on  a  sudden  the  mountain  opened  with  a  great  noise 
at  a  much  lower  point,  about  a  quarter  of  a  mile  from  the  place  where  he 
stood,  and  threw  out  a  torrent  of  lava,  which  advanced  straight  towards 
him,  while  he  was  involved  in  a  shower  of  small  pumice  stones  and  ashes, 
and  in  a  cloud  of  smoke.  The  force  of  the  explosions  was  so  great,  that 
doors  and  windows  were  thrown  open  by  them  at  the  distance  of  several 
miles  :  the  stream  of  lava  was  in  some  places  two  miles  broad,  and  60  or 
70  feet  deep  ;  it  extended  about  six  miles  from  the  summit  of  the  moun- 
tain, and  remained  hot  for  several  weeks.  In  1794  a  still  more  violent 
eruption  occurred  :  it  was  expected  by  the  inhabitants  of  the  neighbour- 
hood, the  crater  being  nearly  filled,  and  -the  water  in  the  wells  having 
subsided.  Showers  of  immense  stones  were  projected  to  a  great  height ; 
and  ashes  were  thrown  out  so  copiously,  that  they  were  very  thick  at 
Taranto,  250  miles  off ;  some  of  them  also  were  wet  with  salt  water.  A 
heavy  noxious  vapour,  supposed  to  be  carbonic  acid,  issued  in  many  places 
from  the  earth,  and  destroyed  the  vineyards  in  which  it  was  suffered  to 
remain  stagnant.  A  part  of  the  town  of  Torre  del  Greco  was  overwhelmed 
by  a  stream  of  lava,  which  ran  through  it  into  the  sea  ;  yet  notwithstand- 
ing the  frequency  of  such  accidents,  the  inhabitants  had  so  strong,  a  predi- 
lection for  their  native  spot,  that  they  refused  the  offer  of  a  safer  situation 
for  rebuilding  their  houses. 


ON  AQUEOUS  AND  IGNEOUS  METEORS.  5G3 

Convulsions  of  these  kinds  must  have  very  materially  influenced  the 
disposition  of  the  strata  of  the  earth,  as  well  as  the  form  of  its  surface  ; 
but  it  is  by  no  means  fully  determined  how  far  such  causes  have  been 
concerned,  or  how  far  the  effects  are  to  be  attributed  to  the  intermediation 
of  water  only.  Mineralogists  and  geologists  have  been  principally  divided 
into  two  classes  with  respect  to  their  theories  of  the  earth,  some  maintain- 
ing the  Vulcanian,  and  some  the  Neptunian  hypothesis.  It  appears  to  be 
impossible  to  decide  with  any  certainty  between  these  opposite  opinions  ; 
nor  is  it  perhaps  of  much  consequence  for  any  purpose  of  practice,  or  even 
of  science.  The  Neptunians  are  certainly  able  to  establish  their  own 
theory  positively,  and  to  prove  that  the  fluid  parts  of  the  earth  and  sea 
must  have  been  very  materially  concerned  in  producing  the  changes  which 
have  happened  to  the  solid  parts  ;  but  it  may  be  difficult  for  them  to  con- 
fute the  assertion,  that  heat,  whether  caused  by  volcanos  or  otherwise,  has 
also  been  a  very  powerful  agent  in  these  operations,  and  in  some  cases  the 
joint  effects  of  heat  and  of  increased  pressure  appear  to  have  been  con- 
cerned in  giving  to  minerals  of  different  kinds  their  actual  form  ;  although 
on  the  whole  it  seems  probable  that  the  operation  of  heat  has  been  much 
more  limited  than  that  of  aqueous  solutions  and  precipitations.  Mr. 
Davy  has  also  very  justly  inferred,  from  his  experiments  with  the  battery 
of  Volta,  that  the  effects  of  the  electricity  excited  by  means  of  chemical 
changes  within  the  earth,  have  probably  been  very  materially  concerned  in 
the  gradual  formation  of  a  variety  of  mineral  productions. 

The  arguments  for  establishing  the  general  fact,  that  great  convulsions 
have  actually  happened  to  the  earth,  are  too  well  known  to  require  minute 
examination  :  the  variety  of  fossil  substances,  many  of  them  marine  pro- 
ductions, and  some  almost  preserving  a  recent  appearance,  that  are  found 
in  mountains  remote  from  the  sea,  are  undeniable  proofs  that  the  levels  of 
the  earth's  surface  must  have  undergone  considerable  changes ;  although 
some  philosophers  are  of  opinion,  that  such  of  the  primary  mountains  as 
are  above  6  or  700  feet  high,  have  never  been  wholly  covered  by  the  sea. 
It  is  not  at  all  easy  to  explain  the  change  of  climate,  which  some  of  these 
circumstances  appear  to  indicate  ;  the  remains  of  animals  inhabiting  hot 
countries,  and  the  marine  productions  of  hot  climates,  which  are  frequently 
found  in  high  northern  latitudes,  would  induce  us  to  suspect,  that  the  posi- 
tion of  the  earth's  axis  was  at  a  former  time  very  different  from  its  pre- 
sent position :  and  we  can  scarcely  assign  any  other  probable  cause  for 
this  change,  than  the  casual  interference,  and  perhaps  incorporation,  of  a 
comet  with  the  earth.  The  probabilities  of  such  an  event,  in  the  whole 
course  of  time,  are  however  so  small,  that  we  have  no  reason  to  be  appre- 
hensive of  the  chance  of  its  occurring  in  future,  for  it  is  not  enough  that  a 
comet  should  approach  so  near  to  the  earth  as  to  be  very  powerfully  at- 
tracted by  it,  its  motion  must  also  be  directed  almost  in  a  straight  line 
towards  the  earth  ;  otherwise  it  might  only  be  inflected  into  a  new  orbit, 
and  go  off  again,  without  having  caused  any  other  disturbance  than  a 
partial  overflow  of  the  sea. 

The  face  of  the  globe  has  also  been  very  materially  changed  in  the 
course  of  ages,  by  the  gradual  operation  of  the  sea  and  of  rivers.  The  sea 

2  o2 


564  LECTURE  LVII. 

has  incroached  in  particular  parts,  and  retired  from  others  ;  and  the 
mouths  of  large  rivers,  running  through  low  countries,  have  often  been 
variously  modified,  by  a  deposition  and  transfer  of  the  matter  washed 
down  from  the  land.  At  Havre  the  sea  undermines  the  steep  coast,  and 
recedes  at  Dunkirk,  where  the  shore  is  flat :  in  Holland  the  Zuyder  Zee 
was  probably  formed  in  the  middle  ages  by  continual  irruptions  of  the 
sea,  where  only  the  small  lake  Flevo  had  before  existed  ;  and  the  mouths 
of  the  Rhine  have  been  considerably  altered,  both  in  their  dimensions  and 
in  their  directions.  The  mud,  deposited  by  large  rivers,  generally  causes  a 
Delta,  or  triangular  piece  of  land,  to  grow  out  into  the  sea  ;  thus  the 
mouth  of  the  Mississippi  is  said  to  have  advanced  above  50  miles  since  the 
discovery  of  America ;  and  the  sea  has  retired  from  Rosetta  above  a  mile 
in  40  years.  The  mouths  of  the  Arno  and  of  the  Rhone  consist  also  in 
great  measure  of  new  land.* 

The  meteors  denominated  shooting  stars  are  observed  to  move  in  all 
directions,  as  well  upwards  as  downwards,  although  they  frequently  seem 
to  have  a  tendency  towards  a  particular  quarter  in  the  course  of  the  same 
evening.  Their  height  is  seldom  less  than  20  miles,  and  sometimes  as 
much  as  100  or  200,  but  usually  about  50  ;  their  velocity  is  commonly 
about  20  miles  in  a  second,  which  differs  very  little  from  that  of  the  earth 
in  its  orbit.  The  rapidity  of  their  motion,  as  well  as  its  occasional  devia- 
tion from  a  right  line,  has  generally  been  considered  as  a  reason  for  sup- 
posing that  they  depend  on  electricity ;  but  the  opinion  is  by  no  means 
fully  established. 

Other  igneous  meteors,  which  nearly  resemble  in  their  appearance  the 
largest  of  these,  are  sometimes  observed  to  fall  on  the  earth,  either  entire 
or  divided  ;  and  after  their  fall,  certain  stones  have  been  found,  which  have 
been  supposed  to  have  descended  in  an  ignited  state.t  Mr.  Howard  J  has 
ascertained  that  almost  all  these  stones  agree  in  their  general  characters, 
and  in  their  chemical  analysis,  especially  in  the  circumstance  of  containing 
nickel.  It  has  been  conjectured,  both  in  this  country  and  on  the  con- 
tinent, that  they  have  been  emitted  by  lunar  volcanos,  and  it  has  been 
observed,  that  since  they  would  find  little  or  no  resistance  from  the  very 
rare  atmosphere  of  the  moon,  they  would  require  a  velocity  of  projection 
only  four  times  as  great  as  that  which  a  cannon  ball  sometimes  receives,  in 
order  to  rise  into  the  sphere  of  the  earth's  attraction.  Their  heat  and 
combustion  may  not  improbably  be  derived  from  the  great  condensation 
which  they  must  occasion  in  the  air  immediately  before  them,  and  even 
their  friction  might  easily  produce  enough  of  electric  light,  to  render  them 
visible  in  the  dark.  Among  many  such  substances  projected  from  the 
moon,  it  is  probable  that  a  few  only  would  be  directed  towards  the  earth, 
and  many  more  would  be  made  to  revolve  in  ellipses  round  it,  and  become 
little  satellites,  too  small  for  human  observation,  except  when  they  enter 

*  The  reader  is  referred  to  Lyell's  or  Ansted's  Geology. 

t  On  meteoric  stones,  see  Chladni  on  the  Siberian  iron,  Riga,  1794  ;  Ueber 
Feuer-Meteore,  Vienna,  1819,  with  App.  by  Schreibers ;  and  art.  Stones  (Meteor.)* 
Encyc.  Metrop. 

J  Ph.  Tr.  1802,  p.  168. 


ON  VEGETATION.  665 

far  enough  into  the  atmosphere  to  produce  an  appearance  of  light,  re- 
sembling that  of  a  shooting  star ;  but  it  is  scarcely  probable  that  their 
velocity  could  ever  be  at  all  comparable  with  that  which  has  been  attri- 
buted to  these  meteors.  There  is,  however,  no  difficulty  in  supposing,  on 
the  other  hand,  that  the  wandering  substances,  which  may  be  moving 
through  empty  space,  with  a  velocity  equal  to  that  of  the  shooting  stars, 
may  be  so  much  retarded,  when  they  penetrate  deep  into  our  atmosphere, 
as  to  make  but  a  moderate  impression  by  their  fall  on  the  ground  ;  and  if 
we  suppose  the  meteors  to  be  of  one  kind  only,  they  must  be  referred 
rather  to  the  description  of  shooting  stars  than  to  that  of  the  productions 
of  lunar  volcanos;  although  the  undulatory  motion,  sometimes  observed  in 
these  meteors,  seems  to  be  in  some  measure  inconsistent  with  the  progress 
of  a  heavy  body,  moving  by  means  of  its  natural  inertia  in  a  straight  line. 


LECTURE   LVIII. 


ON  VEGETATION. 

IT  may  appear  idle  to  some  persons,  to  attempt  to  reduce  the  outlines 
of  natural  history  into  so  small  a  compass,  as  is  required  for  their  becom- 
ing a  part  of  this  course  of  lectures ;  and  it  would  indeed  be  a  fruitless 
undertaking  to  endeavour  to  communicate  a  knowledge  of  the  particular 
subjects  of  this  science,  even  in  a  much  longer  time  than  we  shall  bestow 
on  it.  But  many  naturalists  have  spent  a  great  portion  of  their  lives  in 
learning  the  names  of  plants  and  animals,  and  have  known  at  last  less  of 
the  philosophy  of  the  science,  than  might  have  been  told  them  in  a  few 
hours,  by  persons  who  had  observed  with  more  enlarged  views,  and  who 
had  reasoned  on  general  principles.  And  we  shall  perhaps  find  it  possible 
to  collect  into  a  small  compass  the  most  useful  information,  that  has 
hitherto  been  obtained,  respecting  the  laws  of  animal  and  vegetable  life,  as 
well  as  the  foundations  of  the  methods,  by  which  the  most  received  syste- 
matical classifications  have  been  regulated. 

The  surface  of  the  earth,  as  well  sea  as  land,  is  occupied  by  innumerable 
individuals,  constituting  an  immense  variety  of  distinct  species  of  animated 
and  inanimate  beings,  comprehended  in  the  three  grand  divisions  of  natural 
bodies.  The  mineral  kingdom  consists  of  such  substances  as  are  composed 
of  particles  either  united  without  any  regular  form,  or  collected  together  by 
accretion  or  external  growth  only.  When  mineral  substances  crystallize, 
they  often  imitate  the  form,  and  almost  assume  the  external  appearance  of 
vegetables :  but  their  particles  are  never  extended  to  admit  others  between 
them,  aad  to  be  thus  enlarged  in  all  their  dimensions ;  their  growth  is  only 
performed  by  the  addition  of  similar  particles,  upon  the  surface  of  those 
that  have  been  already  deposited. 


566  LECTURE   LVIII. 

Vegetables  derive  their  existence,  by  seeds,  or  otherwise,  from  a  parent 
stock,  their  parts  are  extended  and  evolved  from  within,  and  they  imbibe 
their  nutriment  by  superficial  absorption  only.  There  is  indeed  in  the 
crystallization  of  minerals  a  slight  resemblance  to  a  reproduction  or  genera- 
tion, when  a  small  portion  of  the  substance  serves  as  a  basis  for  the  forma- 
tion of  subsequent  crystals  :  but  this  portion  becomes  a  constituent  part  of 
the  crystal,  while  it  preserves  its  original  form  ;  a  seed,  on  the  contrary,  is 
a  substance  naturally  and  completely  detached  from  the  plant,  and  con- 
taining within  itself  the  simplest  rudiments  of  a  new  individual,  which  is 
afterwards  evolved  and  enlarged.  Sometimes,  however,  vegetables  are  pro- 
pagated by  means  of  bulbs,  or  by  spreading  roots,  by  slips,  or  by  ingrafted 
scions,  without  a  seed  detached  in  the  regular  manner ;  but  in  these  cases 
the  new  plant  is  much  more  identical  with  the  old  one,  than  when  it  is 
raised  from  a  seed,  being  as  it  were  a  continuation  of  the  same  existence. 
Plants  are  nourished  in  great  measure  by  means  of  their  roots  ;  and  some- 
times, where  they  are  without  roots,  their  nutriment  is  probably  absorbed 
by  all  parts  of  their  surface. 

Animals  are  distinguished  from  vegetables  by  the  reception  of  their 
food,  for  digestion  and  assimilation,  into  an  internal  cavity  constituting  a 
stomach.  The  existence  of  a  stomach,  calculated  for  the  digestion  of  food, 
appears  to  be  the  best,  if  not  the  only  criterion  of  an  animal.  Some  vegeta- 
bles, indeed,  have  a  power  of  catching  and  detaining  animals,  by  curling 
up  their  leaves  so  as  to  cover  them,  as  the  drosera  or  sundew,  and  the 
dionaea  muscipula,  or  catchfly ;  but  this  mechanism  can  scarcely  be 
intended  for  their  immediate  nutriment,  at  least  the  leaf  can  scarcely  be 
supposed  to  assume  the  character  of  a  stomach.  It  is  true  that  we  imagine 
all  animals  to  have  sensation,  and  all  plants  to  be  without  it ;  and  if  it  were 
possible  to  discriminate  decisively  between  sensation  and  irritation,  the  dis- 
tinction would  supersede  every  other :  but  in  many  cases  it  is  extremely 
difficult  to  say  where  sensation  is  present,  and  where  irritation  only  pro- 
duces the  same  apparent  effects.  We  cannot  be  sure  that  the  hydra,  or 
fresh  water  polypus,  or  the  trichurus  sol,  an  animalcule  described  by 
Dr.  Shaw,  suffers  any  sensation  of  pain  when  it  is  divided  into  two  parts  ; 
at  least  the  pain  seems  to  agree  remarkably  well  with  its  constitution,  for 
it  lives  and  thrives  with  increased  vigour,  as  two  distinct  animals.  On  the 
other  hand,  many  plants  are  easily  stimulated  to  perform  motions,  which 
have  the  appearance  of  muscular  actions,  influenced  by  sensation  :  the  sen- 
sitive plants  close  or  depress  their  leaves,  in  consequence  of  agitation  or  of 
electricity ;  the  stamina  of  the  barberry  and  of  the  pellitory  are  thrown 
into  motion,  when  touched  with  a  needle,  and  those  of  rue,  and  of  the 
grass  of  Parnassus,  have  at  times  alternate  motions  without  any  apparent 
cause.  A  zoophyte  is  an  animal  absolutely  fixed  to  one  place  ;  and  the 
vallisneria  is  a  vegetable  possessed  of  a  certain  limited  power  of  locomotion. 
A  plant  chooses  in  preference  to  turn  towards  the  light ;  and  it  has  been 
known  that  an  ash  tree  on  a  wall,  when  incapable  of  being  any  longer  sup- 
ported by  the  wall  only,  has  concentrated  all  its  force  in  the  production  of 
one  large  root,  descending  to  the  ground.  Some  of  these  circumstances 
may  be  explained  without  recurring  to  any  thing  like  volition ;  but,  as 


ON  VEGETATION.  567 

far  as  we  know,  the  same  explanations  might  be  applied  to  some  animal 
motions;  and  although  it  is  very  possihle  that  there  may  be  a  certain 
limit,  where  the  influence  of  mind  and  sensation  terminates,  and  the  laws 
of  vegetable  life  only  prevail ;  yet  the  place  of  the  division  is  not  strongly 
enough  marked,  to  allow  it  to  form  a  characteristic  in  an  artificial  system. 
It  has  been  asserted  that  some  worms  are  nourished  by  absorption  only, 
without  the  assistance  of  a  stomach ;  thus  hydatids,  which  are  supposed 
to  be  of  an  animal  nature,  appear  to  be  simply  bags  of  a  fluid  without  any 
visible  opening ;  but  a  few  doubtful  cases  of  this  kind  can  scarcely  be 
sufficient  to  invalidate  the  general  position,  that  all  bodies  decidedly 
animal  have  a  cavity  for  the  reception  of  food.  There  are  usually  also 
some  chemical  distinctions  in  the  component  parts  of  animals  and  vegeta- 
bles ;  animal  substances  commonly  containing  greater  proportions  of  azote 
or  nitrogen,  and  of  phosphoric  acid  ;  but  there  are  some  exceptions  to  this 
observation ;  thus  the  carica  papaya,  or  papaw,  contains  nearly  the  same 
principles  as  are  usually  found  in  substances  of  animal  origin.  In  general 
we  may  readily  distinguish  a  small  portion  of  an  animal  from  a  vegetable 
substance,  by  the  smell  produced  in  burning  it.  According  to  common 
language,  we  say,  that  minerals  have  growth  only,  but  not  always ;  that 
vegetables  grow  and  live  also  ;  and  that  animals  have  sensation,  as  well  as 
life  and  increase  of  magnitude. 

Mineralogy  is  a  branch  of  natural  history  so  nearly  allied  to  chemistry, 
that  it  cannot  be  completely  understood  without  a  previous  knowledge  of 
that  science.  It  may  therefore  be  more  properly  considered  as  belonging 
to  a  course  of  chemical  than  of  physical  lectures. 

The  vegetable  kingdom  presents  to  us  a  spectacle  highly  interesting  by 
its  variety  and  by  its  elegance  ;  but  the  economy  of  vegetation  appears  to 
be  little  diversified,  although  little  understood.  With  respect  to  the  appa- 
rent perfection  of  their  functions,  and  the  complication  of  their  structure, 
we  may  consider  all  vegetables  as  belonging  to  two  principal  divisions,  in 
one  of  which  the  seed  is  prepared  with  the  assistance  of  a  flower,  having 
its  stamina  and  its  pistils,  with  petals  or  a  calyx  ;  while  in  the  other,  the 
preparation  of  the  seed  is  less  regular  and  conspicuous,  and  hence  such 
plants  are  called  cryptogamous.  In  some  of  these  there  is  a  slight  resem- 
blance to  the  flowers  of  other  vegetables,  but  on  the  whole,  the  class 
appears  to  form  one  of  the  connecting  links  between  the  three  kingdoms  of 
nature  ;  its  physiology  is  probably  simple,  but  it  has  been  little  examined. 
The  herbs,  palms,  shrubs,  and  trees,  which  constitute  the  numerous  genera 
of  flowering  vegetables,  exhibit  the  greatest  diversity  in  the  forms  and  dis- 
positions of  the  organs  of  fructification,  while  they  have  all  a  general  resem- 
blance in  their  internal  economy. 

Every  vegetable  may  be  considered  as  a  congeries  of  vessels,  in  which,  by 
some  unknown  means,  the  aqueous  fluids,  imbibed  by  its  roots,  are  sub- 
jected to  peculiar  chemical  and  vital  actions,  and  exposed  in  the  leaves  to 
the  influence  of  the  light  and  air ;  so  as  to  be  rendered  fit  for  becoming 
constituent  parts  of  the  plant,  or  of  the  peculiar  substances  contained 
within  it. 

The  first  process  in  the  germination  of  a  seed  is  its  imbibing  moisture, 


568  LECTURE  LVIII. 

and  undergoing  a  chemical  fermentation,  in  which  oxygen  is  absorbed, 
and  a  part  of  the  mucilage  contained  in  the  seed  is  converted  into  sugar ;  a 
substance  probably  more  nutritive  to  the  young  plant.  The  radicle  shoots 
downwards,  and  the  seed  leaves,  or  cotyledons,  which  are  generally  two, 
although  sometimes  more  or  less  numerous,  raise  themselves  above  the 
ground,  till  in  a  short  time  they  die  and  drop  off,  being  succeeded  by  the 
regular  and  more  adult  leaves. 

In  every  transverse  section  of  a  vegetable,  we  commonly  discover  at  least 
four  different  substances.  The  parts  next  to  the  axis  of  the  tree  or  branch 
consist  of  medulla  or  pith,  which  is  supposed  by  some  to  be  the  residence 
of  the  vegetable  life  of  the  plant ;  but  a  tree  may  live  for  many  years  after 
being  in  great  measure  deprived  of  its  medulla.  The  pith  is  of  a  loose  and 
light  spongy  texture ;  it  sends  a  ramification  into  each  branch  and  each 
leaf,  where  it  appears  to  serve  also  as  a  reservoir  of  moisture.  The  pith  is 
surrounded  by  the  woody  part,  composed  of  fibres  more  or  less  strongly 
compacted  together,  but  not  actually  ramifying  into  each  other  in  any 
great  degree,  although  there  is  reason  to  suspect  some  lateral  communica- 
tions between  them.  They  are  interrupted,  at  certain  intervals,  in  many 
trees,  by  fibres,  in  a  radiating  direction,  forming  what  is  called  the  silver 
grain.  Like  the  bones  in  animals,  the  wood  constitutes  the  strongest  part 
of  the  vegetable  ;  and  like  them  too  it  is  in  a  certain  degree  furnished  with 
vessels.  It  has  even  been  supposed  by  some,  that  the  fibres  themselves  are 
distinct  tubes,  and  by  others,  that  the  interstices  between  them  serve  the 
purpose  of  vessels,  but  neither  of  these  opinions  is  at  present  generally 
received  •.  The  wood  consists  of  a  number  of  concentric  layers  or  strata, 
formed  in  successive  years  ;  the  external  part,  which  is  last  formed,  is 
called  the  alburnum,  or  white  wood,  and  this  part  is  the  most  vascular. 
The  bark  encompasses  the  wood  ;  and  this  also  consists,  in  trees,  of  several 
layers,  which  are  produced  in  as  many  different  years  ;  the  external  parts 
usually  cracking,  and  allowing  us  at  their  divisions  to  observe  their  num- 
ber, the  inner  layer  only  being  of  immediate  use.  This  layer  is  called  the 
liber,  and  since  this  material  was  once  used  instead  of  paper,  the  Romans 
called  a  book  also  liber.  The  bark  consists  of  fibres  of  the  same  kind  as 
the  wood,  but  more  loosely  connected.  It  is  covered  by  the  cuticle,  which 
extends  itself  in  a  very  great  degree,  as  the  growth  of  the  vegetable 
advances,  but  at  last  cracks,  and  has  its  office  supplied  by  the  outer  layers 
of  bark.  Between  the  bark  and  the  cuticle  a  green  pulpy  substance,  or 
parenchyma,  is  found,  which  seems  to  be  analogous  to  the  rete  mucosum, 
interposed  between  the  true  skin  and  the  cuticle  in  animals.  Mr.  Desfon- 
taines*  has  observed,  that  in  palms,  and  in  several  other  natural  orders  of 
plants,  the  annual  deposition  of  new  matter  is  not  confined  to  the  external 
surface,  but  that  it  takes  place  in  various  parts  of  the  plant,  as  if  it  were 
composed  of  a  number  of  ordinary  stems  united  together. 

There  are  three  principal  kinds  of  vessels  in  the  different  parts  of  vege- 
tables :  the  sap  vessels,  which  are  found  both  in  the  wood  and  in  the  bark, 
although  their  nature  appears  to  require  further  examination :  secondly, 
the  air  vessels,  or  tracheae,  which  are  composed  of  single  threads  wound 
*  Mem.  de  1'Instit.  i.  478. 


ON  VEGETATION.  569 

into  a  spiral  tube,  like  the  spring  of  a  bell,  and  capable  of  being  easily 
uncoiled  ;  these,  though  they  have  been  called  air  vessels,  and  supposed  by 
some  to  serve  the  purposes  of  respiration,  are  described  by  others  as  con- 
taining, during  the  life  of  the  plant,  an  aqueous  fluid  :  and  they  are  pro- 
bably little  more  than  sap  vessels,  with  an  additional  spiral  coat ;  they  are 
not  found  in  the  bark,  nor  in  all  species  of  plants  ;  and  it  has  thence  been 
inferred  that  they  are  not  immediately  necessary  to  the  growth  of  the 
plant.  The  third  kind  are  the  proper  vessels  of  the  plant,  which  are  gene- 
rally disposed  in  concentric  circles,  and  appear  to  be  unconnected  with  the 
sap  vessels,  and  to  contain  the  milky,  resinous,  and  other  peculiar  juices, 
which  are  found  in  different  kinds  of  plants  ;  for  the  sap  is  nearly  the  same 
in  all,  at  least  it  is  independent  of  the  gums  and  resin,  which  often  distin- 
guish particular  plants  ;  it  contains  a  certain  portion  of  mucilage,  and  pro- 
bably in  some  plants,  as  the  sugar  maple,  a  considerable  quantity  of  sugar. 
Mr.  Mirbel*  has  also  made  a  number  of  still  more  accurate  distinctions 
respecting  the  structure  of  the  different  kinds  of  vessels.  The  circulation 
of  the  sap  is  not  completely  understood  ;  when  an  orifice  is  made  near  the 
root  of  a  tree,  it  flows  most  copiously  from  above  :  when  near  the  summit, 
from  below.  Dr.  Hope  actually  reverted  the  natural  course  of  the  juices 
of  a  tree,  without  changing  its  position ;  by  inoculating  a  willow  with  two 
others,  he  completely  united  its  existence  with  theirs,  and  then,  removing 
its  roots,  he  found  that  its  vegetation  was  supported  by  the  juices  of  the 
two  others.  A  tree  may  also  be  actually  inverted,  and  the  upper  part  will 
strike  root,  the  lower  putting  out  branches  and  leaves. 

Plants  perspire  very  considerably,  and  also  emit  a  quantity  of  gases  of 
different  kinds ;  they  generate  a  slight  degree  of  heat,  which  may  be 
observed  by  means  of  the  thermometer,  and  by  the  melting  of  snow  in  con- 
tact with  them.  The  growth  of  every  tree  takes  place  at  the  internal  sur- 
face of  the  bark,  not  only  the  bark  itself  being  formed  there,  but  the  wood 
also  being  deposited  by  the  bark  ;  for  Dr.  Hope  separated  the  whole  of  the 
bark  of  a  branch  of  willow  from  the  wood,  leaving  it  connected  only  at  the 
ends,  so  as  to  constitute  a  hollow  cylinder,  parallel  to  the  wood ;  and  he 
found  that  new  layers  were  formed  within  the  bark  ;  and  in  another  expe- 
riment a  part  of  the  wood,  deprived  of  the  bark,  although  protected  from 
the  air,  was  only  covered  with  new  bark  as  it  grew  over  from  the  old  bark 
above  and  below.  The  layers  of  wood,  which  are  added  in  successive 
seasons,  and  keep  a  register  of  the  age  of  the  tree,  are  very  easily  observed 
when  it  is  cut  across  ;  sometimes  as  many  as  400  have  been  found  in  firs, 
and  oaks  are  said  to  have  lived  1000  years. 

Mr.  Knight  f  has  inferred,  from  a  great  variety  of  experiments,  that  the 
sap,  either  usually  or  universally,  ascends  through  the  wood  into  the 
leaves,  and  then  descends  through  the  bark  to  nourish  the  plant.  The 
leaves  seem  to  be  somewhat  analogous  to  lungs,  or  rather  to  the  gills  of 

*  Bullet,  de  la  Soc.  Philom.  No.  60.  Journal  de  Phy.  lii.  336.  Anatomie  et  Phy- 
siologic Vgget.  2  vols.  Paris,  1815. 

•f  His  papers  are  in  the  Ph.  Tr.  1795,  p.  290;  1799,  p.  195  ;  1801,  p.  333  ; 
1803,  p.  277;  1804,  p.  183. 


570  LECTURE  LVIII. 

fishes  :  for  plants  have  need  of  air,  and  it  has  been  found,  that  even  seeds 
will  not  germinate  in  a  vacuum.    As  the  lungs  of  animals  appear  to  be 
concerned  in  forming  the  blood,  so  it  may  be  inferred  from  Mr.  Knight's 
experiments,  that  the  sap  first  ascends  to  the  leaves  through  the  external 
fresh  wood  of  alburnum,  and  through  the  central  vessels  of  the  young 
leaves  and  branches,  derived  from  the  alburnum,  and  accompanied  by  the 
spiral  tubes  ;  and  after  being  perfected  by  exposure  to  light  and  air  in  the 
leaves,  it  descends  in  the  bark,  and  serves  for  the  secretion  of  the  alburnum, 
and  of  the  internal  layers  of  the  bark,  being  conveyed  probably  by  two 
distinct  sets  of  vessels.     The   sap,  thus  prepared  by  the  leaves  in  the 
summer  and  autumn,  is  supposed  to  leave  its  extractive  matter  in  the  tree 
throughout  the  winter,  in  such  a  state  as  to  be  ready  to  unite  with  the 
aqueous  juices,  which  ascend  from  the  root  in  the  succeeding  spring.     The 
internal  parts  of  the  wood,  having  served  the  purposes  of  vegetation,  are  har- 
dened, and  perhaps  dried  up,  so  as  to  be  afterwards  principally  subservient 
to  strength  alone.    By  subsequent  experiments,  Mr.  Knight  has  also  found, 
that  when  a  branch  hangs  downwards,  the  sap  still  appears  to  proceed 
from  the  part  of  the  bark  which  is  uppermost ;  so  that  the  direction  of  the 
force  of  gravity  seems  to  be  concerned  in  determining  that  of  the  motion  of 
the  sap.     There  appears  also  to  be  some  reason  to  suppose  that  mechanical 
means  assist  in  the  protrusion  of  the  sap,  and  the  consequent  growth  of  the 
tree  ;   for  if  a  tree  be  more  agitated  by  the  wind  in  one  direction  than  in 
another,  its  diameter  will  be  greatest  in  that  direction. 

The  process  of  grafting  depends  on  a  remarkable  property  of  the  growth 
of  vegetables ;  if  the  cut  surface  of  the  inner  bark  of  a  small  branch,  or 
cutting,  be  placed  in  contact  with  that  of  the  branch  of  another  tree,  they 
will  unite  sufficiently  for  the  nourishment  of  the  cutting  ;  provided,  how- 
ever, that  the  nature  of  the  plants  be  not  too  different.  Something  of  the 
same  kind  occurs  in  animal  life,  where  a  tooth  has  been  transplanted  into 
the  socket  of  another,  or  where  the  spur  of  a  cock  has  been  inserted  into  his 
comb. 

Plants  have  their  natural  periods  of  life,  either  of  a  few  days,  as  in  the 
case  of  some  of  the  fungi,  of  a  year,  of  a  few  years,  or  of  many  centuries. 
They  have  also  their  diseases  ;  they  are  often  infested  by  insects,  as  in  the 
gall  of  the  oak,  and  the  woodruff  of  the  rose,  or  by  animalcules  of  a  still 
lower  order,  which  are  either  the  causes  of  the  smut  of  corn,  or  constant 
attendants  on  it.  From  unnatural  and  too  luxuriant  culture,  they  become 
sterile,  and  produce  double  flowers  instead  of  fruits  and  seeds.  When 
deprived  of  sufficient  moisture,  or  nipped  by  frost,  their  leaves  and  branches 
often  die ;  and  if  the  plants  recover  their  vigour,  a  separation  is  effected 
by  a  natural  process,  resembling  the  sloughing  of  decayed  parts  of  animals  ; 
but  when  the  whole  plant  sinks,  the  dead  leaves  continue  to  adhere  to  it. 
The  annual  fall  of  leaves  in  autumn  appears  to  be  a  natural  separation 
nearly  of  the  same  kind,  which  takes  place  when  the  leaves  are  no  longer 
wanted  ;  the  growth  of  the  plant  being  discontinued,  and  their  functions 
being  no  longer  required. 

Succulent  plants  generally  die  when  the  cuticle  is  removed,  but  not  all 


ON  VEGETATION.  571 

other  plants.  The  air  appears  to  be  injurious  to  vegetables  where  it  is  not 
natural ;  hence  arises  the  benefit  of  Mr.  Forsyth's*  method  of  completely 
excluding  the  air  from  the  wounded  parts  of  trees,  by  means  of  which 
their  losses  are  often  in  great  measure  repaired,  and  they  acquire  new 
strength  and  vigour.  Sometimes  a  diminution  of  the  magnitude  of  a  tree 
immediately  increases  its  fertility  ;  its  force  being  more  concentrated  by 
lopping  off  its  useless  branches  and  leaves,  it  produces  a  larger  quantity  of 
fruit,  with  the  juices  which  would  have  been  expended  in  their  nourish- 
ment. 

The  Linnean  system  of  vegetables  is  confessedly  rather  an  artificial  than 
a  natural  one  ;  but  it  is  extremely  well  adapted  for  practice,  and  its  uni- 
versal adoption  has  been  productive  of  the  most  important  improvements 
in  the  science  of  botany.  Of  the  24  classes  into  which  Linne  has  divided 
the  vegetable  kingdom,  23  are  distinguished  by  the  forms  of  the  flowers  and 
fruit,  and  the  24th  by  the  want  of  a  regular  florescence.  The  first  10  are 
named  from  monandria,  in  order,  to  decandria  ;  then  follow  dodecandria  ; 
icosandria,  and  polyandria  ;  the  names  expressing  the  number  of  the 
stamina,  or  filaments,  surrounding  the  seed  vessel ;  and  the  orders  are 
deduced  in  a  similar  manner  from  the  number  of  pistils  or  little  columns 
immediately  connected  with  the  seed  vessel ;  and  denominated  mono- 
gynia,  digynia,  and  so  forth,  as  far  as  polygynia.  These  classes  differ 
little  in  general  with  respect  to  their  natural  habits,  except  the  twelfth, 
icosandria,  which  is  characterized  by  the  attachment  of  the  filaments  to 
the  green  cup,  surrounding  the  flower,  and  which  comprehends  the  most 
common  fruit  trees  :  this  class  has,  however,  been  incorporated  by  some 
later  botanists  with  the  next.  In  the  third  class  we  find  most  of  the 
natural  order  of  grasses  ;  the  fifth,  pentandria,  is  by  far  the  most  numerous 
of  any  :  the  sixth  contains  the  lilies,  and  many  other  bulbous  plants.  The 
14th  class,  didynamia,  is  known  by  two  longer  and  two  shorter  filaments  ; 
it  is  perfectly  natural,  and  comprehends  flowers  similar  in  their  structure 
to  the  foxglove  and  the  deadnettle.  The  15th  also,  tetradynamia,  is  a  class 
of  plants  strongly  characterized  even  by  chemical  properties ;  two  of  the 
filaments  are  here  shorter  than  the  other  four  :  cresses,  radishes,  and  many 
other  acrid  and  ammoniacal  vegetables,  belong  to  this  class,  as  well  as  the 
turnip  and  cabbage,  which,  when  cultivated,  become  mild  and  nutritious. 
The  class  monadelphia  contains  a  few  plants  similar  to  the  mallow ;  they 
are  known  by  the  union  of  the  filaments  at  their  bases  into  a  cylinder  : 
those  of  the  next  class  have  generally  nine  united,  and  one  separate,  whence 
the  class  is  named  diadelphia ;  it  contains  the  papilionaceous  flowers,  some- 
what resembling  a  butterfly  in  their  form,  like  the  pea,  and  other  legu- 
minous plants,  the  broom,  the  furze,  and  the  acacia.  The  18th  class,  poly- 
adelphia,  has  the  filaments  of  its  flowers  united  into  several  masses  or 
bundles,  as  the  hypericum  or  tutsan.  The  next  class  is  perfectly  natural, 
and  contains  the  composite  flowers,  which  have  a  peculiar  union  of  the 
summits  of  the  filaments  ;  it  is  named  syngenesia  :  sunflowers,  daisies,  and 
artichokes,  are  familiar  examples  of  the  plants  of  this  class.  The  20th 
class,  gynandria,  though  it  contains  the  natural  family  of  the  orchides,  has 
*  On  the  Diseases  of  Forest  Trees,  1791. 


572  LECTURE  LVIII. 

been  omitted  by  some  late  botanists ;  here  the  filaments  are  fixed  on  the 
pistil ;  or  more  properly,  in  the  arums,  within  the  pistils.  The  three  fol- 
lowing classes,  monoecia,  dioecia,  and  polygamia,  differ  from  the  rest  in 
having  some  flowers  with  filaments  or  chives,  and  some  with  pistils  only, 
either  on  the  same  plant,  or  on  different  plants,  or  mixed  with  flowers  of 
the  more  common  construction.  Most  of  the  forest  trees  belong  to  these 
classes,  but  the  distinctions  which  separate  them  from  other  classes  are  not 
always  very  uniformly  preserved,  and,  for  this  reason,  many  later  botanists 
have  disused  them.  The  plants  of  the  last  class,  cryptogamia,  are  exceed- 
ingly numerous  ;  the  families  of  ferns,  mosses,  algae,  or  membranous  weeds, 
and  fungi  or  mushrooms,  fill  up  its  extensive  departments ;  some  have  also 
separated  a  part  of  the  algae  under  the  name  of  hepaticae,  or  gelatinous 
weeds.  In  this  class  the  fructifications  are  extremely  various ;  some  of 
the  fuci  and  confervae  approach  so  much  in  their  general  appearance  and 
mode  of  growth  to  corallines  and  zoophytes,  that  they  seem  to  form  an 
obvious  connexion  between  the  lowest  ranks  of  the  vegetable  and  animal 
kingdoms  ;  while  other  plants  of  the  class  are  scarcely  distinguishable  by 
their  appearance  from  some  of  the  productions  of  the  mineral  kingdom. 

The  French  have  introduced  into  very  general  use  the  botanical  system 
of  Jussieu.  The  most  prominent  feature  in  this  system  is  the  division  of 
all  the  genera  into  a  hundred  natural  orders,  which  are  also  arranged  in 
fifteen  classes.  Jussieu  begins,  like  Linne,  with  the  separation  of  crypto- 
gamic  from  phanerogamic  plants;  the  seeds  of  the  cryptogamic  plants, 
which  form  the  first  class,  being  without  cotyledons  or  seed  leaves,  and  all 
other  plants  being  distinguished  into  such  as  have  seeds  with  one  and  with 
two  cotyledons.  Accordingly  as  the  stamina  or  filaments  are  inserted 
below  the  pistil,  on  the  calyx,  or  on  the  seed  vessel,  the  first  description  of 
seeds  affords  three  distinct  classes.  The  plants  which  have  two  cotyledons 
follow,  and  are  divided  into  apetalous,  monopetalous,  and  polypetalous, 
from  distinctions  respecting  the  corolla  or  flower  leaves,  which  are  some- 
what arbitrarily  understood  ;  and  lastly  diclinous,  from  the  separation  of 
the  stamina  and  pistils.  The  three  first  of  these  divisions  are  subdivided 
according  to  the  insertion  of  the  stamina,  and  the  union  or  separation  of 
the  antherae,  which  they  support,  into  ten  classes,  making,  with  the  four 
already  mentioned,  fourteen,  to  which  the  diclinous  plants  add  a  fifteenth. 
The  orders  are  determined  without  any  particular  limitation  of  the  parts 
from  which  the  characters  are  taken.  This  system  is  of  acknowledged 
merit  as  a  philosophical  classification  of  the  natural  orders  of  plants ; 
such  vegetables  as  nearly  agree  in  their  habits  and  appearances  being 
brought  more  uniformly  together  than  in  the  system  of  Linne.  Hence, 
in  the  arrangement  of  a  botanical  garden,  or  in  a  treatise  on  the  chemical 
or  medical  properties  of  plants,  it  might  be  employed  with  advantage  :  but 
for  the  practical  purposes  of  botanical  investigation  it  appears  to  be  utterly 
unfit,  since  its  author  has  sacrificed  all  logical  and  systematical  laws 
to  the  attempt  to  follow  nature,  in  analogies,  which  are  often  discoverable 
only  with  great  difficulty,  and  which  are  seldom  reducible  to  methodical 
definitions. 


ON  ANIMAL  LIFE.  673 

LECT.  LVIIL— ADDITIONAL  AUTHORITIES. 

A   FEW    OF   THE    MORE    IMPORTANT   WORKS    ONLY   ARE    GIVEN. 

Botany  in  general. — Smith's  Introduction,  1807,  &c.  Decandolle,  Theorie  Elem. 
de  la  Bot.  1819.  Link,  Elementa  Philos.  Bot.  Berol.  1824.  Lindley's  Introduc- 
tion, 1835.  Henslow's,  12mo,  1836.  Achille  Richard,  Nouv.  Elem.  de  la  Bo- 
tanique. 

Vegetable  Physiology.— Willoughby,  Ph.  Tr.  1669,  p.  963  ;  1670,  p,  1165 

Malpighius,  Anatome  Plantarum,  fol.  Lond.  1675-9.  Grew  on  the  Anatomy  of 
Veget.  12mo,  1671,  fol.  1682.  Hales,  Vegetable  Staticks,  1727.  Duhamel,  Phy- 
sique des  Arb  res,  2  vols.  4to,  Paris,  1758.  Hedwig,  Descrip.  Muscorum,  fol.  Leipz. 

1792 and  other  works.  Darwin's  Phytologia  4to,  Lond.  1800.  Senebier, 

Physiologic  Vegetale,  5  vols.  Geneve,  1801.  Saint-Hilaire,  Mem.  sur  les  Plantes 
auxquelles  on  attribue  un  Placenta  Central  Libre,  4to,  Paris,  1816.  A.  Brogniart, 
Turpin,  and  other  writers  in  the  Annales  des  Sciences  Naturelles  ;  Du  Petit-Thouars, 
Cours  de  Phytologie.  Dutrochet,  Recherches  sur  la  Structure  intime  des  Vegdtaux, 
Paris,  1824.  L' Agent  du  Mouvement  Devoile",  1826.  Nouvelles  Recherches  sur 
1'Endosmose  et  1'Exosmose,  1828.  Cassini,  Opuscules  Phytologiques,  2  vols.  Paris, 
1826.  Decandolle,  Organographie  Vegetale,  2  vols.  Paris,  1827.  Cours  de  Bota- 
nique,  3  vols.  1832.  Brown's  Microscopic  Obs.  1829,  and  various  other  works. 
Slack,  Trans,  of  the  Soc.  of  Arts,  vol.  xlix.  Viviani,  Organi  Elementari  delle 
Piante,  Geneva,  1831.  Roget's  Animal  and  Vegetable  Physiology,  2  vols.  1834. 
Liebig's  Agricultural  Chemistry,  8vo.  1843. 

Systematic  Botany. — Ray,  Historia  Generalis  Plantarum,  fol.  Lond.  1686-8. 
Tournefort's  History  of  Plants  (trans,  by  Martyn),  2  vols.  1732.  Linnaeus  Genera 
Plantarum,  var.  ed.  Jussieu's  Natural  System,  Hist,  et  Mem.  1773,  p.  214,  H.  34  ; 
1774,  1775  :  Genera  Plant.  Turici,  1791.  English  Botany,  or  Coloured  Figures  of 

British  Plants,  by  Sowerby,  35  vols.  Lond.  1790 Withering's  British  Plants 

(Linnsean),  4  vols.  1796.  Decandolle,  Regni  Vegetabilis  Systema  Naturale,  1818- 
21,  &c.  Smith's  English  Flor.  (Linmean),  4  vols.  1824-8.  Vol.  v.  Crypogamia,  by 
Hooker.  Hooker's  British  Flora  (Linnaean),  1836  ;  (Natural)  1844.  Lindley's 
Synopsis  (Nat.)  12mo,  1835.  Loudon's  Encyclopaedia  of  Plants. 


LECTURE    LIX. 


ON  ANIMAL  LIFE. 

THE  functions  of  animal  life  are  not  only  more  complicated  in  the  same 
individual  than  those  of  vegetation,  but  also  more  diversified  in  the  different 
classes  into  which  animals  are  divided ;  so  that  the  physiology  of  each 
class  has  its  peculiar  laws.  We  are  indebted  to  Linne  for  the  first  enlarge- 
ment of  our  views  of  the  different  classes  of  animals,  and  perhaps  for  the 
most  convenient  arrangement  of  the  animal  kingdom;  although  his 
method  has  never  been  universally  adopted  by  our  neighbours  on  the  con- 
tinent. 

A  considerable  portion  of  the  bulk  of  all  animals  is  composed  of  tubular 
vessels,  which  originate  in  a  heart ;  the  heart  propels  through  the  arteries, 
with  the  assistance  of  their  own  muscular  powers,  either  a  colourless 
transparent  fluid,  or  a  red  blood,  into  the  extremities  of  the  veins  ;  through 
which  i*  again  returns  to  the  origin  of  its  motion.  Both  insects,  and 
vermes,  or  worms,  have  their  circulating  fluids  a  little  warmer  than  the 
surrounding  medium,  and  generally  colourless  ;  hut  insects  have  legs  fur- 


574  LECTURE  L1X. 

nished  with  joints,  and  worms  have  nothing  but  simple  tentacula  at  most 
in  the  place  of  legs.  Fishes  have  cold  red  blood,  which  is  exposed  to  the 
influence  of  the  air  contained  in  water,  by  means  of  their  gills.  The 
amphibia  receive  the  air  into  their  lungs,  but  their  blood  is  cold,  like  that 
of  fishes,  and  in  both  these  classes  the  heart  has  only  two  regular  cavi- 
ties, while  that  of  animals  with  warm  blood  has  four ;  the  whole  contents 
of  one  pair  being  obliged  to  pass  through  the  lungs,  in  order  to  arrive  at 
the  other  pair.  Of  animals  with  warm  blood,  the  oviparous  are  birds,  and 
are  generally  covered  with  feathers,  the  viviparous  are  either  quadrupeds 
or  cetaceous  animals,  and  are  furnished  with  organs  for  suckling  their 
young. 

Each  of  these  classes  of  animals  is  subdivided  by  Linne  into  different 
orders,  of  which  we  shall  only  be  able  to  take  a  very  cursory  view.  The 
first  class,  denominated  mammalia,  from  the  female's  suckling  its  young, 
comprehends  all  viviparous  animals  with  warm  blood.  These,  with  very 
few  exceptions,  have  teeth  fixed  in  their  jaw  bones  ;  and  from  the  form  and 
number  of  these  teeth,  the  orders  are  distinguished,  except  that  of  ceta- 
ceous fishes,  which  is  known  by  the  fins  that  are  found  in  the  place  of  feet. 
The  distinctions  of  the  teeth  are  somewhat  minute,  but  they  appear  to 
be  connected  with  the  mode  of  life  of  the  animal,  and  they  are  tolerably 
natural.  The  first  order,  primates,  contains  man,  monkeys,  and  bats  ;  the 
second,  bruta,  among  others,  the  elephant,  the  rhinoceros,  the  ant  eater, 
and  the  ornithoryhncus,  an  extraordinary  quadruped,  lately  discovered  in 
New  Holland,  with  a  bill  like  a  duck,  and  sometimes  teeth  inserted  behind 
it ;  but  there  are  some  suspicions  that  the  animal  is  oviparous.  The  order 
ferae  contains  the  seal,  the  dog,  the  cat,  the  lion,  the  tiger,  the  weasel,  and 
the  mole,  most  of  them  beasts  of  prey;  the  opossum  and  the  kangaroo  also 
belong  to  this  order,  and  the  kangaroo  feeds  on  vegetables,  although  its 
teeth  are  like  those  of  carnivorous  animals.  The  fourth  order,  glires,  com- 
prehends beavers,  mice,  squirrels,  and  hares ;  the  fifth,  pecora,  camels,  goats, 
sheep,  and  horned  cattle.  The  sixth  order,  belluae,  contains  the  horse,  the 
hippopotamus,  and  the  hog.  The  cetaceous  fishes,  or  whales,  form  the 
seventh  and  last  order  ;  they  reside  in  the  water,  enveloped  in  a  thick 
clothing  of  fat,  that  is,  of  oily  matter,  deposited  in  cells,  which  enables 
their  blood  to  retain  its  temperature,  notwithstanding  the  external  contact 
of  a  dense  medium  considerably  colder. 

Birds  are  distinguished  from  quadrupeds,  by  their  laying  eggs ;  they 
are  also  generally  feathered,  although  some  few  are  rather  hairy  ;  and 
instead  of  hands  or  fore  legs  they  have  wings.  Their  eggs  are  covered  by 
a  calcarious  shell ;  and  they  consist  of  a  white,  or  albumen,  which  nourishes 
the  chick  during  incubation,  and  a  yolk,  which  is  so  suspended  within  it, 
as  to  preserve  the  side  on  which  the  little  rudiment  of  a  chicken  is  situated, 
continually  uppermost,  and  next  to  the  mother  that  is  sitting  on  it.  The 
yolk  is  in  great  measure  received  into  the  abdomen  of  the  chicken  a  little 
before  the  time  of  its  being  hatched,  and  serves  for  its  support,  like  the 
milk  of  a  quadruped,  and  like  the  cotyledons  of  young  plants,  until  the 
system  is  become  sufficiently  strong  for  extracting  its  own  food  out  of  the 
ordinary  nutriment  of  the  species. 


ON  ANIMAL  LIFE.  575 

Birds  are  divided,  according  to  the  form  of  their  bills,  into  six  orders : 
accipitres,  as  eagles,  vultures,  and  hawks;  picae,  as  crows,  jackdaws, 
humming  birds,  and  parrots ;  anseres,  as  ducks,  swans,  and  gulls ;  grallae, 
as  herons,  woodcocks,  and  ostriches ;  gallinae,  as  peacocks,  pheasants, 
turkies,  and  common  fowls ;  and,  lastly,  passeres,  comprehending  sparrows, 
larks,  swallows,  thrushes,  and  doves. 

The  amphibia  are  in  some  respects  very  nearly  allied  to  birds :  but  their 
blood  is  little  warmer  than  the  surrounding  medium.  Their  respiration  is 
not  necessarily  performed  in  a  continual  succession  of  alternations,  since 
the  whole  of  their  blood  does  not  pass  through  the  lungs,  and  the  circula- 
tion may  continue  without  interruption  in  other  parts,  although  it  may  be 
impeded  in  these  organs,  for  want  of  the  motion  of  respiration.  They  are 
very  tenacious  of  life ;  it  has  been  asserted  on  good  authority  that  some  of 
them  have  lived  many  years  without  food,  inclosed  in  hollow  trees,  and 
even  in  the  middle  of  stones ;  and  they  often  retain  vestiges  of  life  some 
days  after  the  loss  of  their  hearts.  Their  eggs  are  generally  covered  with  a 
membrane  only.  They  have  sometimes  an  intermediate  stage  of  existence, 
in  which  all  their  parts  are  not  yet  developed,  as  we  observe  in  the  tadpole ; 
and  in  this  respect  they  resemble  the  class  of  insects.  They  are  now  uni- 
versally considered  as  divided  into  two  orders  only ;  reptilia,  as  the  tortoise, 
the  dragon,  or  flying  lizard,  the  frog  and  the  toad  ;  all  these  have  four  feet ; 
but  the  animals  which  belong  to  the  order  serpentes  are  without  feet. 
Most  of  the  serpentes  are  perfectly  innocent,  but  others  have  fangs,  by 
which  they  instil  a  poisonous  fluid  into  the  wounds  that  they  make.  In 
England  the  viper  is  the  only  venomous  serpent ;  it  is  known  by  its  dark 
brown  colour,  and  by  a  stripe  of  whitish  spots  running  along  its  back ;  but 
to  mankind  its  bite  is  seldom,  if  ever,  fatal. 

The  first  three  classes  of  animals  have  lungs,  as  we  have  already  seen, 
for  respiration,  and  receive  air  by  the  mouth ;  those  which  have  gills,  and 
red  blood,  are  fishes,  residing  either  in  fresh  or  in  salt  water,  or  indif- 
ferently in  both ;  their  eggs  are  involved  in  a  membrane,  and  have  no 
albumen.  Of  the  six  orders  of  fishes,  four  have  regular  gills,  supported 
by  little  bones ;  and  they  are  distinguished,  according  to  the  place  of  their 
ventral  fins,  into  apodes,  as  the  eel  and  lamprey;  jugulares,  as  the  cod; 
thoracici,  as  the  sole  and  perch,  and  abdominales,  as  the  salmon  and  pike ; 
distinctions  which  appear  to  be  perfectly  artificial,  although  useful  in  a 
systematic  arrangement.  The  two  remaining  orders  are  without  bones  in 
the  gills,  those  of  the  one  being  soft,  and  of  the  other  cartilaginous  or 
gristly.  These  are  the  branchiostegi  and  chondropterygii  of  Artedi,  which 
Linne,  from  a  mistake,  classed  among  the  amphibia.  The  sun  fish,  the 
lump  fish,  the  fishing  frog,  and  the  sea  horse,  are  of  the  former,  and  the 
sturgeon,  the  skate,  and  the  shark,  of  the  latter  order. 

Insects  derive  their  name  from  being  almost  always  divided  into  a  head, 
thorax,  and  abdomen,  with  very  slender  intervening  portions :  although 
these  divisions  do  not  exist  in  all  insects.  They  are  usually  oviparous  : 
they  respire,  but  not  by  the  mouth  ;  they  have  a  number  of  little  orifices 
on  each  side  of  the  abdomen,  by  which  the  air  is  received  into  their  rami- 
fied tracheae  ;  and  if  these  are  stopped  with  oil,  they  are  suffocated.  In- 


576  LECTURE  LIX. 

stead  of  bones,  they  have  a  hard  integument  or  shell.  Their  mouths  are 
formed  on  constructions  extremely  various,  but  generally  very  complicated : 
Fabricius*  has  made  these  parts  the  basis  of  his  classification  ;  but  from 
their  minuteness  in  most  species,  the  method  is,  in  practice,  insuperably 
inconvenient ;  and  the  only  way,  in  which  such  characters  can  be -rendered 
really  useful,  is  when  they  are  employed  in  the  subdivision  of  the  genera, 
as  determined  from  more  conspicuous  distinctions.  Insects  have  most  fre- 
quently jaws,  and  often  several  pairs,  but  they  are  always  so  placed  as  to 
open  laterally  or  horizontally.  Sometimes,  instead  of  jaws,  they  have  a 
trunk,  or  proboscis.  In  general,  they  pass  through  four  stages  of 
existence,  the  egg,  the  larva,  or  stage  of  growth,  the  pupa,  or  chrysalis, 
which  is  usually  in  a  state  of  torpor  or  complete  inactivity,  and  the  imago, 
or  perfect  insect,  in  its  nuptial  capacity.  After  the  last  change,  the  insect 
most  frequently  takes  no  food  till  its  death. 

The  Linnean  orders  of  insects  are  the  coleoptera,  with  hard  sheaths  to 
their  wings,  generally  called  beetles  ;  the  hemiptera,  of  which  the  sheaths 
are  of  a  softer  nature,  and  cross  each  other,  as  grasshoppers,  bugs,  and 
plant  lice  ;  the  lepidoptera,  with  dusty  scales  on  their  wings,  as  butterflies 
and  moths  ;  the  neuroptera,  as  the  libellula,  or  dragon  fly,  the  may  fly, 
and  other  insects  with  four  transparent  wings,  but  without  stings  ;  the 
hymenoptera,  which  have  stings,  either  poisonous  or  not,  as  bees,  wasps, 
and  ichneumons  ;  the  diptera,  with  two  wings,  as  common  flies  and  gnats, 
which  have  halteres,  or  balancing  rods,  instead  of  the  second  pair  of  wings  ; 
and  lastly  the  aptera,  without  any  wings,  which  form  the  seventh  order, 
comprehending  crabs,  lobsters,  shrimps  and  prawns,  for  these  are  properly 
insects  ;  spiders,  scorpions,  millepeds,  centipeds,  mites,  and  monoculi. 
The  monoculus  is  a  genus  including  the  little  active  insects  found  in  pond 
water,  which  are  scarcely  visible  to  the  naked  eye,  as  well  as  the  Molucca 
crab,  which  is  the  largest  of  all  insects,  being  sometimes  six  feet  long. 
Besides  these  there  are  several  genera  of  apterous  insects  which  are 
parasitical,  and  infest  the  human  race  as  well  as  other  animals. 

The  vermes  are  the  last  and  lowest  of  animated  beings,  yet  some  of  them 
are  not  deficient  either  in  magnitude  or  in  beauty.  The  most  natural  divi- 
sions of  vermes  is  into  five  orders ;  the  intestina,  as  earth  worms  and 
ascarides,  which  are  distinguished  by  the  want  of  moveable  appendages,  or 
tentacula,  from  the  mollusca  ;  such  as  the  dew  snail,  the  cuttle  fish,  the 
sea  anemone,  and  the  hydra,  or  fresh  water  polype.  The  testacea  have 
shells  of  one  or  more  pieces,  and  most  of  them  inhabit  the  sea,  and  are 
called  shell  fish,  as  the  limpet,  the  periwinkle,  the  snail,  the  muscle,  the 
oyster,  and  the  barnacle.  The  order  zoophyta  contains  corallines,  sponges, 
and  other  compound  animals,  united  by  a  common  habitation,  which  has 
the  general  appearance  of  a  vegetable,  although  of  animal  origin  ;  each  of 
the  little  inhabitants,  resembling  a  hydra,  or  polype,  imitating  by  its 
extended  arms  the  appearance  of  an  imperfect  flower.  The  last  order, 
infusoria,  is  scarcely  distinguished  from  the  intestina  and  mollusca  by  any 
other  character  than  the  minuteness  of  the  individuals  belonging  to  it,  and 
their  spontaneous  appearance  in  animal  and  vegetable  infusions,  where  we 
*  Entomologia  Systematica,  6  vols.  Hafniae,  1792-8. 


ON  ANIMAL  LIFE.  577 

can  discover  no  traces  of  the  manner  in  which  they  are  produced.  The 
process,  by  which  their  numbers  are  sometimes  increased,  is  no  less  astonish- 
ing than  their  first  production  ;  for  several  of  the  genera  often  appear  to 
divide  spontaneously,  into  two  or  more  parts,  which  become  new  and  dis- 
tinct animals,  so  that  in  such  a  case  the  question  respecting  the  identity  of 
an  individual  would  be  very  difficult  to  determine.  The  volvox,  and  some 
of  the  vorticellae  are  remarkable  for  their  continual  rotatory  motion, 
probably  intended  for  the  purpose  of  straining  their  food  out  of  the  water  : 
while  some  other  species  of  the  vorticella  resemble  fungi  or  corallines  in 
miniature. 

Among  the  animals  of  these  different  classes,  the  more  perfect  are  in- 
formed of  the  qualities  of  external  objects  by  the  senses  of  touch,  taste, 
smell,  hearing,  and  vision.  A  few  quadrupeds  are  incapable  of  seeing  : 
the  mole  has  an  eye  so  small  as  to  be  with  difficulty  distinguishable  ;  and 
the  mus  typhlus,  supposed  to  be  the  aspalax  of  Aristotle,  has  its  eye  com- 
pletely covered  by  the  skin  and  integuments,  without  any  perforation. 
Birds  have  hearing,  but  no  external  ears,  or  auriculae.  Insects  appear  to 
want  the  organs  of  smell ;  but  it  is  not  impossible  that  their  antennae  may 
answer  the  purpose  of  hearing.  Many  of  the  vermes  are  totally  destitute 
of  sight,  and  some  of  all  the  organs  of  sense :  none  of  them  have  either 
ears  or  nostrils.  The  external  senses  of  animals  with  warm  blood  are 
usually  liable  to  a  periodical  state  of  inactivity  in  the  night  time,  denomi- 
nated sleep.  It  is  said  that  fishes  never  sleep ;  and  it  is  well  known  that 
some  animals  pass  the  whole  of  the  severest  part  of  the  winter  in  a  state 
nearly  resembling  their  usual  sleep. 

In  animals  which  approach,  in  their  economy,  to  that  of  the  human 
system,  the  process  for  supporting  life  by  nutrition  begins  with  the  masti- 
cation of  the  food,  which  has  been  received  by  the  mouth.  The  food  thus 
prepared  is  conveyed  into  the  stomach  by  the  operation  of  swallowing  ; 
but  in  ruminating  cattle,  it  is  first  lodged  in  a  temporary  receptacle,  and 
more  completely  masticated  at  leisure.  In  the  stomach,  it  undergoes 
digestion,  and  being  afterwards  mixed  with  the  bile  and  other  fluids, 
poured  in  by  the  liver  and  the  neighbouring  glands,  it  becomes  fit  for 
affording  the  chyle,  or  nutritive  juice,  which  is  separated  from  it  by  the  ab- 
sorbents of  the  intestines,  in  its  passage  through  the  convolutions  of  a  canal 
nearly  forty  feet  in  length.  Together  with  the  chyle,  all  the  aqueous  fluids, 
which  are  swallowed,  must  also  be  absorbed,  and  pass  through  the  thoracic 
duct  into  the  large  veins  entering  the  heart,  and  thence  into  the  general  cir- 
culation, before  they  can  arrive  at  the  kidneys,  by  which  the  superfluous 
parts  are  rejected.  The  chyle  passes  unaltered,  with  the  blood,  through 
the  right  auricle  and  ventricle  of  the  heart,  and  enters  the  lungs,  to  be 
there  more  intimately  mixed  with  it,  and  perhaps  to  be  rendered  animal 
and  vital ;  while  the  blood  receives  from  the  air,  in  the  same  place,  a 
supply  of  oxygen,  with  a  small  portion  of  nitrogen,  and  emits  some  super- 
fluous carbonic  matter,  in  the  form  of  carbonic  acid.  The  blood,  thus 
rendered  arterial,  returning  to  the  left  side  of  the  heart,  is  distributed 
thence  to  every  part  of  the  system,  supplying  nutriment  throughout, 
while  the  glands  and  arteries  secrete  from  it  such  fluids,  as  are  become 


578  LECTURE  LIX. 

redundant,  and  such  as  are  required  for  particular  purposes  subservient 
to  the  animal  functions.  It  is  probably  in  these  processes  that  heat  is 
evolved  ;  for  by  experiments  on  living  animals,  it  has  been  found,  that  the 
Wood,  returning  from  the  lungs,  is  not  warmer  than  before  its  entrance 
into  them  :  we  must  therefore  suppose,  that  when  the  florid  arterial  blood 
is,  by  some  unknown  means,  converted,  in  the  extreme  ramifications  of 
the  arteries,  into  the  purple  venous  blood,  to  return  to  the  heart  by  the 
converging  branches  of  the  veins,  there  is  a  much  more  considerable  extri- 
cation of  heat,  than  in  the  conversion  of  venous  into  arterial  blood,  by  the 
absorption  of  oxygen  and  nitrogen  in  the  lungs.  If  the  chyle  is  actually 
converted  into  blood  in  the  lungs,  it  is  here  that  we  must  look  for  the 
formation  of  the  red  globules,  those  singular  corpuscles,  to  which  the  blood 
owes  its  colour,  as  it  does  its  power  of  coagulation  to  a  glutinous  lymph, 
mixed  with  a  less  coagulable  serum.  The  red  particles  in  the  human  blood 
are  about  ^Vu-  of  an  inch  in  diameter,  somewhat  oblong,  and  flattened ; 
they  have  usually  the  appearance  of  a  dark  point  in  the  centre  ;  but  there 
is  some  reason  to  suspect  that  this  is  merely  an  optical  deception.  In  a 
few  animals  they  are  a  little  smaller,  but  in  most  of  the  amphibia,  much 
larger  and  flatter  than  in  man.  While  the  lymph  remains  fluid,  after  the 
blood  has  been  withdrawn  from  the  vessels,  these  globules  tend  to  subside, 
and  to  leave  it  semitransparent :  hence  arises  the  appearance  of  a  buff 
coat  on  blood  left  to  coagulate,  which  is  thinner  or  thicker,  accordingly  as 
the  globules  are  sooner  or  later  arrested  in  their  descent. 

The  muscles  are  probably  furnished  by  the  blood  with  a  store  of  that 
unknown  principle,  by  which  they  are  rendered  capable  of  contracting,  for 
producing  locomotion  or  for  other  purposes,  in  obedience  to  the  influence 
transmitted  by  the  nerves  from  the  sensorium ;  the  brain  and  nervous 
system  in  general  are  also  sustained,  by  means  of  the  vascular  circulation, 
in  a  fit  state  for  transmitting  the  impressions,  made  by  external  objects 
on  the  senses,  to  the  immediate  seat  of  thought  and  memory,  in  the 
sensorium ;  and  for  conveying  the  dictates  of  the  will,  and  the  habitual 
impulses  almost  independent  of  volition,  to  the  muscular  parts  of  the 
whole  frame. 

In  what  manner  these  reciprocal  impressions  are  transmitted  by  the 
nerves,  has  never  yet  been  fully  determined :  but  it  has  long  been  conjec- 
tured that  the  medium  of  communication  may  bear  a  considerable  analogy 
to  the  electrical  fluid ;  and  the  extreme  sensibility  of  the  nerves  to  the 
slightest  portion  of  electrical  influence,  as  well  as  the  real  and  apparently 
spontaneous  excitation  of  that  influence  in  animal  bodies,  which  have  been 
of  late  years  evinced  by  galvanic  experiments,  have  added  very  materially 
to  the  probability  of  the  opinion.  An  extremely  slender  fibre,  of  a  sub- 
stance capable  of  conducting  electricity  with  perfect  freedom,  enveloped  in 
a  sheath  of  a  perfect  nonconductor,  would  perhaps  serve  to  communicate 
an  impulse,  very  nearly  in  the  same  manner,  as  the  nerves  appear  to  do. 
Indeed  nothing  can  be  more  fit  to  constitute  a  connecting  link  between 
material  and  immaterial  beings,  than  some  modification  of  a  fluid,  which 
appears  to  differ  very  considerably,  in  its  essential  properties,  from  the 
common  gross  matter  of  the  universe,  and  to  possess  a  subtility  and 


ON  ANIMAL  LIFE.  579 

an  activity,  which  entitle  it  to  a  superior  rank  in  the  order  of  created 
substances. 

When  all  the  functions  of  animal  life  are  carried  on  in  their  perfect  and 
natural  manner,  the  animal  is  said  to  be  in  health :  when  they  are  dis- 
turbed, a  state  of  disease  ensues.  The  diseases  to  which  the  human  frame 
is  liable  are  so  various  and  irregular,  that  they  cannot  easily  be  reduced 
to  any  systematical  order.  Dr.  Cullen  has  divided  them  into  four  classes. 
Febrile  diseases,  which  constitute  the  first  class,  consist  principally  in  an 
increase  of  the  frequency  of  the  pulsations  of  the  heart  and  arteries,  toge- 
ther with  an  elevation  of  the  temperature,  the  whole  animal  economy 
being  at  the  same  time  in  some  measure  impaired  :  they  are  often  accom- 
panied by  unnatural  or  irregular  actions  of  the  vessels  of  particular  parts, 
constituting  local  inflammations,  which  were  formerly  considered  as  a 
derivation  of  diseased  humours,  falling  on  those  parts :  thus,  a  pleurisy 
is  a  fever,  with  an  inflammation  of  the  membrane  lining  the  chest.  The 
incapacity  of  a  part  to  perform  its  functions,  upon  the  application  of  a 
natural  stimulus,  or  perhaps  more  frequently  the  incapacity  of  the  nerves 
to  transmit  to  it  the  dictates  of  the  mind,  constitutes  a  palsy :  such 
derangements,  and  others,  by  which  the  actions  of  the  nervous  system  are 
peculiarly  impaired,  form  the  class  of  neuroses,  including  spasmodic  affec- 
tions, madness,  melancholy,  and  epilepsy.  A  general  derangement  of  the 
system,  without  fever,  or  any  peculiar  debility  of  the  nerves,  constitutes 
the  class  of  cachectic  diseases,  such  as  atrophy,  consumption,  scrofula, 
and  dropsy.  Besides  these  diseases,  we  have  a  fourth  class,  consisting  of 
local  affections  only,  such  as  blindness,  deafness,  tumours,  and  luxations. 

Notwithstanding  the  labours  of  men  of  the  greatest  learning  and  genius, 
continued  for  many  centuries,  it  must  be  confessed  that  the  art  of  healing 
diseases  is  still  in  a  state  of  great  imperfection.  Happily,  however,  for 
mankind,  we  may  observe  in  almost  all  cases,  where  the  offending  cause  is 
discoverable,  and  where  the  system  is  not  at  once  overwhelmed  by  its  mag- 
nitude, a  wise  and  wonderful  provision  for  removing  it,  by  a  mechanism 
admirably  simple  and  efficacious ;  and  it  is  reasonable  to  conclude,  where 
the  cause  is  more  obscure,  that  the  same  benevolent  Providence  has  em- 
ployed agents  equally  well  adapted  for  counteracting  it,  although  their 
operations  are  utterly  beyond  the  reach  of  human  penetration. 


On  the  subjects  embraced  in  this  Lecture,  the  reader  may  consult  Roget's  Bridg- 
water  Treatise ;  Darwin's  Zoonomia,  4  vols.  1804  ;  or  the  great  works  of  Buffon, 
Histoire  Naturelle,  127  vols.  Paris,  1799-1808,  and  Cuvier,  Le  Regne  Animal, 
translated,  in  16  vols.  Lond.  1824-33.  Liebig's  Animal  Chemistry,  8vo.  1843. 


2  P2 


580 


LECTURE    LX. 


ON  THE  HISTORY  OF  TERRESTRIAL  PHYSICS. 

THROUGHOUT  the  whole  of  nature,  we  discover  a  tendency  to  the  mul- 
tiplication of  life,  of  activity,  and  of  enjoyment :  man  is  placed  at  the  head 
of  terrestrial  beings,  the  only  one  that  comprehends,  and  that  can  trace,  in 
a  faint  outline,  the  whole  plan  of  the  universe.  We  have  seen  the  innumer- 
able luminaries  which  enliven  the  widely  expanded  regions  of  immeasur- 
able space,  with  their  brilliant,  but  distant  emanations  of  light  and  heat. 
Revolving  round  them  at  lesser  intervals,  and  cherished  by  their  fostering 
influences,  are  their  planets  and  their  comets  ;  those  preserving  their  dis- 
tances nearly  equal,  and  these,  ranging  more  widely  from  the  upper  to  the 
lower  regions,  without  limits  to  their  numbers  or  to  their  motions.  Having 
conjectured  what  might  possibly  exist  on  other  planetary  globes,  we 
descended  to  our  own,  and  examined  its  structure  and  the  proportions  of 
its  parts.  Next  we  studied  the  general  properties  of  the  matter  within  our 
reach,  and  then  the  particular  substances  or  qualities  that  are  either 
not  material,  or  are  distinguished  by  very  remarkable  properties  from 
other  matter,  as  we  found  them  concerned  in  the  phenomena  of  heat,  of 
electricity,  and  of  magnetism ;  and  we  afterwards  examined  the  combi- 
nations of  all  these,  in  the  great  atmospherical  apparatus  of  nature,  which 
serves  for  the  exhibition  of  meteorological  phenomena.  The  forms  and  the 
laws  of  animal  and  vegetable  life  have  been  the  last  objects  of  our  inqui- 
ries ;  but  the  magnitude  of  some  departments  of  natural  history,  and  the 
obscurity  of  others,  have  prevented  our  entering  more  than  superficially 
upon  any  of  them. 

Of  the  gradual  advancement  of  astronomy  we  have  already  taken  a  his- 
torical view.  With  respect  to  the  other  sciences  comprehended  under  the 
denomination  of  proper  physics,  the  progress  of  discovery  has  generally 
been  slow,  and  frequently  casual.  The  ancients  had  little  or  no  substantial 
knowledge  of  any  part  of  physics,  except  astronomy  and  natural  history  : 
their  opinions  were  in  general  mere  speculations,  derived  from  fancy,  and 
inapplicable  to  the  real  phenomena  of  nature.  Opinions  such  as  these  will 
only  require  to  be  so  far  examined,  as  to  enable  us  to  trace  the  imperfect 
rudiments  of  discoveries,  which  were  only  completed  after  intervals  of  many 
ages. 

The  Chinese  are  said  to  have  been  acquainted  with  the  use  of  the  com- 
pass above  3000  years  ago  ;  but  in  such  accounts,  it  is  impossible  to  ascer- 
tain how  far  the  spirit  of  national  vanity  may  have  induced  a  historian  to 
falsify  his  dates.*  It  has  been  conjectured  that  the  death  of  Numa,  like 
that  of  Professor  Richmann,  was  occasioned  by  some  unguarded  experi- 
ments on  the  electricity  of  the  atmosphere,  which  drew  on  him  the,  effects 

*  Consult  Davies  on  the  History  of  Magnetical  Discovery,  British  Annual,  1837. 
Klaproth,  Lettre  a  M.  de  Humboldt  sur  1' Invention  de  la  Boussole. 


ON  THE  HISTORY  OF  TERRESTRIAL  PHYSICS.         581 

of  a  thunderstorm  that  was  passing  by.  If,  however,  the  fact  was  such, 
the  experiments  must  probably  have  been  suggested  rather  by  an  accidental 
discovery  of  the  light  on  the  point  of  a  spear,  than  by  any  rational  opinions 
respecting  the  nature  of  the  ethereal  fire. 

Thales  is  the  most  ancient  of  the  Grecian  philosophers,  who  appear  to 
have  seriously  studied  the  phenomena  of  nature.  He  supposed  water  to  be 
the  general  principle  from  which  all  material  things  are  formed,  and  into 
which  they  are  resolved ;  an  opinion  which  was  without  doubt  suggested 
to  him  by  the  obvious  effects  of  water  in  the  nutrition  of  plants  and  of 
animals.  He  particularly  noticed  the  properties  of  the  magnet,  which  had 
been  before  observed  to  attract  iron,  as  well  as  the  effect  of  friction  in  ex- 
citing the  electricity  of  amber  ;  and  he  attributed  to  both  of  these  substances 
a  certain  degree  of  animation,  which  he  considered  as  the  only  original 
source  of  motion  of  any  kind. 

Anaximander  appears  to  have  paid  some  attention  to  meteorology ; 
he  derived  the  winds  from  the  rarefaction  of  the  air,  produced  by  the 
operation  of  heat :  thunder  and  lightning  he  attributed  to  the  violent 
explosion  or  bursting  of  the  clouds,  which  he  seems  to  have  considered  as 
bags,  filled  with  a  mixture  of  wind  and  water.  The  same  mistaken  notion 
was  entertained  by  Anaximenes,  who  compared  the  light  attending  the 
explosion,  to  that  which  is  frequently  exhibited  by  the  sea,  when  struck 
with  an  oar. 

Pythagoras,  great  as  he  was  in  some  other  departments  of  science,  rea- 
soned respecting  physical  effects  in  a  manner  too  mathematical  and  vision- 
ary, to  allow  him  much  claim  to  be  ranked  among  those  who  have  studied 
to  investigate  the  minute  operations  of  nature. 

Anaxagoras  was  so  far  from  confining  himself  to  the  supposition  of  four 
elements,  which  was  most  generally  received  by  the  philosophers  of  anti- 
quity, that  he  imagined  the  number  of  elements  nearly  if  not  absolutely 
infinite.  He  conceived  that  the  ultimate  atoms,  composing  every  sub- 
stance, were  of  the  same  kind  with  that  substance,  and  his  system  was 
thence  called  the  homoeomeria  ;  it  erred  perhaps  less  from  the  truth  than 
many  of  the  more  prevalent  opinions.  Democritus,  adopting  the  senti- 
ments of  Leucippus,  proposed  a  still  more  correct  theory  of  the  consti- 
tution of  matter,  supposing  it  to  be  ultimately  so  far  homogeneous,  that 
the  weight  of  its  atoms  was  proportional  to  their  bulk.  He  asserted  that 
the  forms  of  these  atoms  were  different  and  unalterable  ;  that  they  were 
always  in  motion,  and  that  besides  their  primitive  difference  of  form,  they 
were  also  susceptible  of  a  variety  in  the  mode  of  their  arrangement.  The 
space  not  occupied  by  the  atoms  of  matter,  he  considered  as  a  perfect 
vacuum. 

As  Thales  had  supposed  water  to  be  the  first  principle  of  all  things, 
and  Anaximenes  air,  so  Heraclitus  fixed  on  fire  as  the  foundation  of  his 
system,  attributing  to  it  the  property  of  constant  motion,  and  deriving 
all  kinds  of  grosser  matter  from  its  condensation  in  different  degrees. 
This  Doctrine  was  wholly  unsupported  by  any  thing  like  reason  or  obser- 
vation. 

Plato  introduced  into  philosophy  a  variety  of  imaginations,  which  resem- 


682  LECTURE  LX. 

bled  the  fictions  of  poetry  much  more  than  the  truths  of  science.  He 
maintained,  for  example,  that  ideas  existed  independently  of  the  human 
mind,  and  of  the  external  world,  and  that  they  composed  beings  of  different 
kinds,  by  their  union  with  an  imperfect  matter.  It  is  observed  by  Bacon, 
in  his  essay  on  the  opinions  of  Parmenides,  that  the  most  ancient'  philo- 
sophers, Empedocles,  Anaxagoras,  Anaximenes,  Heraclitus,  and  Demo- 
critus,  submitted  their  minds  to  things  as  they  found  them  ;  but  that  Plato 
made  the  world  subject  to  ideas,  and  Aristotle  made  even  ideas,  as  well  as 
all  other  things,  subservient  to  words  ;  the  minds  of  men  beginning  to  be 
occupied,  in  those  times,  with  idle  discussions  and  verbal  disputations,  and 
the  correct  investigation  of  nature  being  wholly  neglected.  Plato  enter- 
tained, however,  some  correct  notions  respecting  the  distinction  of  denser 
from  rarer  matter  by  its  greater  inertia ;  and  it  would  be  extremely  unjust 
to  deny  a  very  high  degree  of  merit  to  Aristotle's  experimental  researches, 
in  various  parts  of  natural  philosophy,  and  in  particular  to  the  vast  col- 
lection of  real  information  contained  in  his  works  on  natural  history. 
Aristotle  attributed  absolute  levity  to  fire,  and  gravity  to  the  earth,  consi- 
dering air  and  water  as  of  an  intermediate  nature.  By  gravity  the  ancients 
appear  in  general  to  have  understood  a  tendency  towards  the  centre  of  the 
earth,  which  they  considered  as  identical  with  that  of  the  universe  ;  and  as 
long  as  they  entertained  this  opinion,  it  was  almost  impossible  that  they 
should  suspect  the  operation  of  a  mutual  attraction  in  all  matter,  as  a  cause 
of  gravitation.  The  first  traces  of  this  more  correct  opinion  respecting  it 
are  found  in  the  works  of  Plutarch. 

Epicurus  appears  to  have  reasoned  as  justly  respecting  many  particular 
subjects  of  natural  philosophy,  as  he  did  absurdly  respecting  the  origin  of 
the  world,  and  of  the  animals  which  inhabit  it.  He  adopted  in  great  mea- 
sure the  principles  of  Democritus  respecting  atoms,  but  attributed  to  them 
an  innate  power  of  affecting  each  other's  motions,  and  of  declining,  in  such 
a  manner,  as  to  constitute,  by  the  diversity  of  their  spontaneous  arrange- 
ments, all  the  varieties  of  natural  bodies.  He  considered  both  heat  and 
cold  as  material ;  the  heat  emitted  by  the  sun  he  thought  not  absolutely 
indentical  with  light,  and  even  went  so  far  as  to  conjecture  that  some  of 
the  sun's  rays  might  possibly  possess  the  power  of  heating  bodies,  and  yet 
not  affect  the  sense  of  vision.  In  order  to  explain  the  phenomena  of 
magnetism,  he  supposed  a  current  of  atoms,  passing,  in  certain  directions, 
through  the  magnet  and  through  iron,  which  produced  all  the  effects  by 
their  interference  with  each  other.  Earthquakes  and  volcanos  he  derived 
from  the  violent  explosions  of  imprisoned  air. 

Among  all  these  opinions  and  conjectures,  there  is  scarcely  any  one 
which  was  scientifically  established  upon  sure  foundations.  Some  insulated 
observations  had  a  certain  degree  of  merit ;  and  we  find  many  interesting 
facts  relating  to  different  departments  of  natural  knowledge,  not  only  in 
Aristotle,  but  also  in  Theophrastus,  Dioscorides,  and  Pliny,  as  well  as  in 
some  of  the  historical  writers  of  antiquity.  Protagorides  of  Cyzicum,  who 
is  quoted  by  Athenaeus,  relates  that  in  the  time  of  king  Antiochus,  it  was 
usual,  as  a  luxury,  to  cool  water  by  evaporation  ;  and  it  is  not  impossible 
that  the  custom  may  have  been  introduced  from  the  east,  where  even  ice 


ON  THE  HISTORY  OF  TERRESTRIAL  PHYSICS.         583 

is  frequently  made  at  present  by  a  similar  process  ;  others  of  the  ancients 
had  remarked,  according  to  Dr.  Falconer,*  that  water  usually  froze  the 
more  readily  for  having  been  boiled  ;  and  it  is  possible  that  some  other 
detached  observations  of  a  similar  nature  may  occur  to  those  who  have  the 
curiosity  to  make  them  objects  of  research. 

The  thirteenth  century  may  be  considered  as  the  date  of  the  revival,  if 
not  of  the  commencement,  of  physical  discoveries.  Our  countryman, 
Roger  Bacon,  was  one  of  its  principal  ornaments :  he  appears  to  have 
anticipated  in  his  knowledge  of  chemistry,  as  well  as  of  many  other  parts 
of  natural  philosophy,  the  labours  of  later  times.  The  polarity  of  the 
magnetic  needle  is  described  in  some  lines  which  are  attributed  to  Guyot,  a 
French  poet,  who  lived  about  1180  ;  but  some  persons  are  of  opinion  that 
this  description  was  actually  written  by  Hugo  Bertius,  in  the  middle  of 
the  succeeding  century ;  and  it  is  generally  believed  that  the  compass  was 
first  employed  in  navigation  by  Gioja  of  Amain,  about  the  year  1260  ;  he  is 
said  to  have  marked  the  north  with  a  fleur  de  lis,  in  compliment  to  a 
branch  of  the  royal  family  of  France,  then  reigning  at  Naples.  The 
declination  of  the  needle  from  the  true  meridian  is  mentioned  by  Peter 
Adsiger,  the  author  of  a  manuscript  which  bears  the  date  1269.  The  poet 
Dante,  who  flourished  at  the  close  of  this  century,  distinguished  himself 
not  only  by  his  literary,  but  also  by  his  philosophical  pursuits ;  and  we 
find  among  his  numerous  works  an  essay  on  the  nature  of  the  elements. 

The  learned  and  voluminous  labours,  by  which  Gesner  and  Aldrovandus 
enriched  the  various  departments  of  natural  history,  may  be  considered  as 
comprehending  the  greatest  part  of  what  had  been  done  by  the  ancients  in 
the  investigation  of  the  economy  of  the  animal  world  ;  but  their  works 
have  too  much  the  appearance  of  collections  of  what  others  had  asserted, 
rather  than  of  original  observations  of  their  own. 

The  first  of  the  moderns  whose  discoveries  respecting  the  properties  of 
natural  bodies  excite  our  attention,  by  their  novelty  and  importance,  is 
Dr.  Gilbert,  of  Colchester  :  his  work  on  magnetism,  published  in  1590,  con- 
tains a  copious  collection  of  valuable  facts,  and  ingenious  reasonings.  He 
also  extended  his  researches  to  many  other  branches  of  science,  and  in 
particular  to  the  subject  of  electricity.  It  had  been  found,  in  the  preced- 
ing century,  that  sulfur,  as  well  as  amber,  was  capable  of  electric  excitation, 
and  Gilbert  made  many  further  experiments  on  the  nature  of  electric 
phenomena.  The  change  or  variation  of  the  declination  of  the  needle  is 
commonly  said  to  have  been  discovered  by  Gellibrand,  a  professor  at 
Gresham  college,  in  the  year  1625  ;  but  it  must  have  been  inferred  from 
Gunter's  observations,  made  in  1622,  if  not  from  those  of  Mair,  or  of  some 
other  person,  as  early  as  1612  ;  for  at  this  time  the  declination  was  con- 
siderably less  than  Burrows  had  found  it  in  1580.f 

In  the  beginning  of  the  seventeenth  century,  Lord  Bacon  acquired,  by 
his  laudable  efforts  to  explode  the  incorrect  modes  of  reasoning,  which  had 
occupied  the  schools,  the  just  character  of  a  reformer  of  philosophy ;  but 

*  On  the  Knowledge  of  the  Ancients,  Manch.  Mem.  i.  261 ;  iii.  278. 
f  Burroughs's  Dissertation  in  Norman's  New  Attractive,  3rd  edit.     Gellibrand, 
on  the  Variation  of  the  Mag.  Needle,  1635.     See  Robison,  Mec.  Ph.  iv.  354. 


584  LECTURE  LX. 

his  immediate  discoveries  were  neither  striking  nor  numerous.  In  1620, 
he  proposed,  with  respect  to  heat,  an  opinion  which  appears  to  have  been 
at  that  time  new,  inferring,  from  a  variety  of  considerations,  which  he  has 
very  minutely  detailed  in  his  Novum  Organum,  that  it  consisted  in  "  an 
expansive  motion,  confined  and  reflected  within  a  body,  so  as  to  'become 
alternate  and  tremulous ;  having  also  a  certain  tendency  to  ascend."  A 
similar  opinion,  respecting  the  vibratory  nature  of  heat,  was  also  sug- 
gested, about  the  same  time,  by  David  Gorlaeus,  and  it  was  afterwards 
adopted  by  Descartes,*  as  a  part  of  his  hypothesis  respecting  the  constitu- 
tion of  matter  ;  which  he  imagined  to  consist  of  atoms  of  different  forms, 
possessing  no  property  besides  extension,  and  to  derive  all  its  other  qualities 
from  the  operation  of  an  ethereal  and  infinitely  elastic  fluid,  continually 
revolving  in  different  orders  of  vortices. 

A  much  more  important  step,  than  the  proposal  of  any  hypothesis  con- 
cerning the  nature  of  heat,  was  also  made  about  the  year  1620,  by  Cornelius 
Drebel,  who  appears  to  have  been  the  original  inventor  of  the  method  of 
measuring  the  degrees  of  heat  by  a  thermometer.  The  utility  of  the  instru- 
ment remained,  however,  much  limited,  for  want  of  an  accurate  method  of 
adjusting  its  scale,  and  it  was  not  till  the  close  of  the  century,  that  Dr. 
Hooke's  discovery,  of  the  permanency  of  the  temperature  of  boiling 
water,  afforded  a  correct  and  convenient  limit  to  the  scale  on  one  side, 
while  the  melting  of  snow  served  for  fixing  a  similar  point  on  the  other ; 
although  there  would  have  been  no  great  difficulty  in  forming  a  scale  suffi- 
ciently natural,  from  the  proportion  of  the  expansion  of  the  fluid  contained 
in  the  thermometer  to  its  whole  bulk. 

It  was  about  the  year  1628,  that  Dr.  Harvey  1*  succeeded  in  demon- 
strating, by  a  judicious  and  conclusive  train  of  experiments,  the  true 
course  of  the  circulation  of  the  blood,  through  the  veins  and  arteries,  both 
in  the  perfect  state  of  the  animal,  and  during  its  existence  as  an  embryo. 
Servetus  had  explicitly  asserted,  in  his  work  on  the  Trinity,  as  early  as 
the  year  1553,  that  the  blood  performed,  in  its  passage  through  the  lungs, 
a  complete  revolution,  beginning  and  ending  in  the  heart ;  and  Cisalpinus 
had  even  expressed,  in  1569,  some  suspicions  that  the  circulation  of  the 
whole  body  was  of  a  similar  nature ;  but  neither  of  these  authors  had 
advanced  any  satisfactory  proofs  in  confirmation  of  his  opinions. 

In  the  middle  of  the  seventeenth  century,  the  barometer  was  invented  by 
Torricelli ;  the  variation  of  the  atmospheric  pressure  was  discovered  by 
Descartes  ;  and  Pascal  made  several  experiments  on  the  difference  of  its 
magnitude  at  different  places,  which  tended  to  illustrate  the  principles,  on 
which  the  method  of  determining  heights  by  barometrical  observations  is 
founded. 

What  Gesner  and  Aldrovandus  had  before  done  with  regard  to  the 
animal  kingdom,  was  performed,  a  century  later,  for  the  vegetable  world 
by  John  and  Caspar  Bauhin,  whose  works,  as  collections  of  all  that  was  to 
be  found  on  record  respecting  ftie  distinctions  and  properties  of  plants, 

*  Princip.  PLilos.  Part  IV.   §  29. 

f  Exercitatio  Anatomica  de  Motu  Cordis  et  Sanguinis,  Francof.  1628  :  his  expe- 
riments were  made  in  1616.  Consult  Cuvier,  Le?ons  sur  1'Hist.  des  Sci.  Nat. 


ON  THE  HISTORY  OF  TERRESTRIAL  PHYSICS.        585 

have  not  yet  been  superseded  by  the  latest  publications.  Our  country- 
men, Ray  and  Willughby,  contributed  also  to  add  much  new  matter  to 
the  stores  of  natural  history,  in  all  its  departments  ;  and  their  labours, 
as  well  as  those  of  Tournefort  and  Re'aumur,  are  of  the  more  value,  as  they 
were  far  more  studious  than  their  predecessors  to  discriminate  truth  from 
fiction. 

The  foundation  of  the  most  celebrated  of  the  philosophical  societies  of 
Europe  renders  the  latter  half  of  the  seventeenth  century  a  very  interesting 
period  in  the  history  of  natural  knowledge.  The  Royal  Society  of  London, 
and  the  Academy  of  Sciences  of  Paris,  have  always  been  the  most  distin- 
guished of  these  :  and  the  Florentine  Academy  del  Cimento,  although  its 
labours  were  not  of  long  duration,  produced  at  first  in  a  short  time 
a  very  copious  and  interesting  collection  of  experiments,  relating  to  various 
subjects  of  physical  research.  In  the  Royal  Society,  Boyle,  Hooke,  and 
Newton  were  the  most  industrious,  as  well  as  the  most  successful  inves- 
tigators of  natural  phenomena  :  the  elementary  doctrines  of  chemistry,  the 
nature  of  combustion,  the  effects  of  heat  and  cold,  and  the  laws  of  attrac- 
tion, repulsion,  and  cohesion  were  attentively  examined  and  discussed. 
The  expansion  of  water,  by  a  reduction  of  its  temperature,  near  the  freez- 
ing point,  was  first  observed  by  Dr.  Croune ;  although  his  experiments 
were  considered  by  Dr.  Hooke  as  inconclusive.*  The  attention  of  the 
society  was  directed  by  Newton  to  the  phenomena  of  electricity,  some  of 
which  had  been  a  short  time  before  particularly  noticed  by  Guericke  ;  the 
mode  of  making  electrical  experiments  was  greatly  improved  by  Hauks- 
bee  ;  this  accurate  observer  investigated  also  the  nature  of  capillary  attrac- 
tion with  considerable  success.  Early  in  the  succeeding  century,  many  of 
the  members  of  the  Academy  of  Petersburg  followed  the  example  of  other 
societies  with  great  industry  ;  and  the  experiments  of  Richmann  on  heat 
were  among  the  first  and  best  fruits  of  their  researches. 

Dr.  Halley  employed  himself,  with  the  most  laudable  zeal,  in  procuring 
information  respecting  the  variation  of  the  compass ;  he  undertook  a 
voyage  round  the  world,  for  the  express  purpose  of  making  magnetical 
observations  ;  and  he  published  a  chart  of  variation,  adapted  to  the  year 
I700.f  He  also  collected  many  particulars  respecting  the  trade  winds  and 
monsoons,  and  he  endeavoured  to  explain  them  by  a  theory  which  has 
been  adopted  by  some  of  the  latest  authors,  but  which  is  in  reality  much 
less  satisfactory  than  the  hypothesis  proposed  some  time  afterwards  by 
Hadley.^  His  magnetical  investigations  were  continued  with  great  dili- 
gence by  Montaigne  and  Dodson,  who  published,  at  different  periods,  two 
charts  representing  the  successive  states  of  the  variation.  Euler,§  Mayer, || 
and  others  have  attempted,  in  later  times,  to  discover  such  general  laws  as 
might  be  sufficient  to  determine  the  magnitude  of  the  variation  for  every 
part  of  the  globe  ;  but  their  success  has  been  very  much  limited. 

The  science  of  electricity  was  diligently  cultivated  in  the  middle  of  the 
last  century  by  Stephen  Gray,  Dufay,  Winkler,  Nollet,  Musschenbroek, 

*  Birch,  iv.  26,  253.  f  Ph.Tr.xxiii.  1106.  J  See  p.  681. 

§  Hist,  et  M£m.  de  Berlin,  1755,  p.  107  ;  1757,  p.  175 ;  1766,  p.  213. 
II  Gott.  Anz.  1760,  p.  633  ;  1762,  p.  377. 


686  LECTURE  LX. 

and  Franklin.  As  early  as  1735  it  was  remarked  by  Gray,  that  "the 
electric  fire  seemed  to  be  of  the  same  nature  as  lightning,"*  and  their 
identity  was  afterwards  more  strongly  asserted  by  Winkler,  and  experi- 
mentally demonstrated  by  Franklin.  The  shock  of  a  charged  jar  was  first 
discovered  by  Kleist,  in  1745  ;  and  the  experiment  was  repeated  by  Lalla- 
mand  and  Musschenbroek,  who  described  its  disagreeable  effects  on  the 
sensations  with  an  exaggeration  not  the  most  philosophical.  The  theory  of 
the  nature  of  the  charge  was  the  second  great  improvement  made  by 
Dr.  Franklin  in  this  science. 

The  introduction  of  the  Linnean  system  of  botany  and  zoology  is  to  be 
considered  as  bringing  near  to  perfection  the  logic  and  phraseology  of 
natural  history  ;  nor  has  its  celebrated  author  wholly  neglected  the  philo- 
sophy of  the  science.  The  number  and  the  diligence  of  his  successors  have 
already  furnished  to  the  different  departments  of  natural  history  a  much 
ampler  store  of  observations  than  could  easily  have  been  expected  from  the 
short  time  which  their  labours  have  occupied.  Buffon  had  merit  of  a  dif- 
ferent kind,  and  though  his  fancy  was  too  little  regulated  by  mathematical 
accuracy,  the  elegance  of  his  writings  have  made  their  subjects  highly 
interesting  to  the  general  reader.  Among  other  modern  naturalists  of 
great  respectability,  Spallanzani,  Daubenton,  Degeer,  Geoffrey,  Pennant, 
the  Jussieus,  Lacepede  and  Haiiy,  have  particularly  distinguished  them- 
selves by  the  importance  of  their  discoveries,  and  the  accuracy  of  their 
descriptions. 

.  The  absorption  of  heat,  during  the  conversion  of  ice  into  water,  appears 
to  have  been  separately  observed  by  Deluc,  Black,  and  Wilke,  about  the 
year  1755.  On  this  experiment  Dr.  Black  principally  founded  his  doc- 
trine of  latent  heat,  supposed  to  be  retained  in  chemical  combination  by  the 
particles  of  fluids.  Dr.  Irvine  and  Dr.  Crawford  explained  the  circum- 
stances somewhat  differently,  by  the  theory  of  a  change  of  capacity  for 
heat  only.  Bergmann,t  Lavoisier,  Laplace,  Kirwan,  Seguin,  and  many 
other  philosophers  have  illustrated,  by  experiments  and  calculations,  the 
various  opinions  which  have  been  entertained  on  this  subject ;  and  few 
chemists,  from  the  times  of  Boerhaave,  Stahl,  and  Scheele  to  those  of 
Priestley  and  other  later  authors,  have  left  the  properties  of  heat  wholly 
unnoticed. 

The  elegant  hypothesis  of  Aepinus,  respecting  magnetism  and  electricity, 
founded  in  great  measure  on  the  theory  of  Franklin,  was  advanced  in  1759  ; 
our  venerable  countryman,  Mr.  Cavendish,  had  invented  a  similar  theory, 
and  had  entered  in  many  respects  more  minutely  into  the  detail  of  its  con- 
sequences, without  being  acquainted  with  Aepinus's  work  ;  although  the 
publication  of  his  paper  on  the  subject  was  12  years  later.  Lambert, 
Mayer,  Coulomb,  and  Robison  have  also  pursued  inquiries  of  a  similar 
nature,  both  theoretically  and  experimentally,  with  great  success.  The 
electrophorus  of  Wilke,  and  the  condenser  of  Volta,  are  among  the  earliest 
fruits  of  the  cultivation  of  a  rational  system  of  electricity,  and  Mr. 
Cavendish's  investigation  of  the  properties  of  the  torpedo  may  'serve  as 

*  Ph.  Tr.  xxxix.  24. 

t  Opuscula  Physica  et  Chemica,  6  vols.  Upsalise. 


ON  THE  HISTORY  OF  TERRESTRIAL  PHYSICS.         587 

a  model  of  accuracy  and  precision  in  the  conduct  of  experimental 
researches. 

The  speculations  of  Boscovich  respecting  the  fundamental  properties  of 
matter,  and  the  general  laws  of  the  mutual  action  of  bodies  on  each  other, 
have  been  considered  by  some  candid  judges  as  deserving  the  highest  com- 
mendation ;  they  remain  however  almost  in  all  cases  speculations  only ; 
and  some  of  the  most  intricate  of  them,  being  calculated  for  the  explanation 
of  some  facts,  which  have  perhaps  been  much  misunderstood,  must  con- 
sequently be  both  inaccurate  and  superfluous. 

The  attention  of  several  experienced  philosophers,  who  are  now  living, 
has  been  devoted,  with  much  perseverance,  to  the  difficult  subject  of 
hygrometry.  Deluc's  experiments  have  offered  us  a  very  useful  compari- 
son of  the  hygrometrical  qualities  of  various  substances :  Saussure  has 
investigated,  with  great  labour,  the  indications  of  the  hygrometer  and  the 
thermometer,  as  connected  with  the  presence  of  a  certain  portion  of  vapour, 
contained  in  air  of  various  densities;  and  Pictet  has  ascertained  some 
similar  circumstances  respecting  vapours  of  different  kinds  wholly  un- 
mixed with  any  air.  The  hypotheses,  which  have  usually  accompanied 
the  relation  of  most  of  these  experiments,  have  however  been  in  general 
too  little  supported  by  facts  to  be  entitled  to  universal  adoption. 

For  some  years  past,  the  philosophical,  as  well  as  the  unphilosophical 
world  has  been  much  occupied  and  entertained  by  the  discoveries  of  Gal- 
vani,  Volta,  and  others,  respecting  the  operations  of  the  electric  fluid.  The 
first  circumstance  that  attracted  Galvani's  attention  to  the  subject  of 
animal  electricity,  was  the  agitation  of  a  frog,  that  had  a  nerve  armed, 
that  is,  laid  bare  and  covered  with  a  metal,  when  a  spark  was  taken  in 
its  neighbourhood.  A  person  acquainted  with  the  well  known  laws  of 
induced  electricity  might  easily  have  foreseen  this  effect :  it  proved,  how- 
ever, that  a  frog  so  prepared  was  a  very  delicate  electrometer,  and  it  led 
Galvani  to  further  experiments.  It  has  been  shown  by  Volta,  that  an 
entire  frog  may  be  convulsed  by  a  degree  of  electricity  which  affects 
an  electrometer  but  very  weakly ;  but  that  when  prepared  in  Galvani's 
manner,  it  will  be  agitated  by  an  electricity  one  fiftieth  part  as  great, 
which  cannot  be  discovered,  by  any  other  means,  without  the  assistance 
of  a  condenser.  Galvani,  however,  found  that  a  communication  made 
between  the  armed  nerve  and  its  muscle,  by  means  of  any  conducting 
substance,  was  sufficient  to  produce  a  convulsion,  without  the  presence  of 
foreign  electricity :  hence  he  concluded  that  the  nerve  and  muscle,  like 
the  opposite  surfaces  of  a  charged  jar,  were  in  contrary  states  of  electri- 
city, and  that  the  communication  produced  a  discharge  between  them. 
He  observed,  however,  a  considerable  difference  in  the  effects,  when  dif- 
ferent metals  were  employed  for  forming  the  circuit ;  and  this  circum- 
stance led  to  the  discovery  of  the  excitation  of  electricity  by  means  of  a 
combination  of  different  inanimate  substances  only,  which  Mr.  Davy 
attributes  to  Fabroni,  Creve,  and  Dr.  Ash.  It  was,  however,  still  more 
satisfactorily  demonstrated  by  Volta ;  and  he  at  first  supposed  that  all 
the  phenomena  observed  by  Galvani  were  derived  from  effects  of  this 
kind,  but  on  further  examination  he  was  obliged  to  allow  the  independent 


588  LECTURE  LX. 

existence  of  animal  electricity.  This  industrious  and  ingenious  philo- 
sopher has  the  sole  merit  of  the  invention  of  the  pile  or  battery,  which  has 
rendered  every  other  mode  of  exciting  the  galvanic  action  comparatively 
insignificant. 

No  sooner  was  Volta's  essay  communicated  to  the  Royal  Society,  than 
a  pile  was  constructed  by  Mr.  Carlisle,  and  its  singular  effects  in  the 
decomposition  of  water  were  jointly  observed  by  himself  and  Mr.  Nichol- 
son. The  original  existence  of  animal  electricity,  as  asserted  by  Galvani 
and  Volta,  has  been  in  some  degree  confirmed  by  the  experiments  of 
Aldini,  the  nephew  of  Galvani.  A  number  of  detached  observations,  of 
considerable  merit,  have  also  been  made  by  Pfaff,  Ritter,  Cruikshank, 
Wollaston,  Fourcroy,  and  many  other  chemists,  both  in  this  country  and 
on  the  continent.  But  Mr.  Davy's  late  experiments  must  be  considered 
as  exceeding  in  importance  every  thing  that  has  been  done  upon  the  subject 
of  electricity,  since  the  discovery  of  the  pile  of  Volta.  The  conclusions 
which  they  have  enabled  him  to  form  respecting  the  electrical  properties 
of  such  bodies  as  have  the  strongest  tendencies  to  act  chemically  on  each 
other,  and  the  power  of  modifying  and  counteracting  those  tendencies 
which  the  electric  fluid  possesses,  have  greatly  extended  our  views  of  the 
minute  operations  of  nature,  and  have  opened  a  new  field  for  future  inves- 
tigations. I  hope  that  I  shall  be  pardoned  by  astronomers  for  having 
inserted,  on  this  occasion,  in  a  vacant  space  among  the  constellations,  in 
the  neighbourhood  of  Pegasus,  the  figure  of  a  galvanic  battery ;  which 
must  now  be  allowed  to  have  as  great  pretensions  to  such  a  distinction  as 
the  electrical  machine  and  the  chemical  furnace. 

The  late  experiments  and  speculations  of  Mr.  Dalton,  on  various  sub- 
jects, belonging  to  different  branches  of  physics,  have  tended  to  place  some 
parts  of  the  science  of  meteorology  in  a  new  light.  It  is  true  that  many 
of  his  hypotheses  are  very  arbitrarily  assumed ;  some  of  them  are  mani- 
festly contrary  to  experiment,  and  others  to  analogy  and  probability ;  at 
the  same  time  his  remarks  appear  in  some  cases  to  be  either  perfectly  cor- 
rect, or  to  lead  to  determinations  which  are  sufficiently  accurate  for  every 
practical  purpose.  I  have  attempted  to  borrow  from  Mr.  Dalton' s  ideas  some 
hints,  which  I  have  incorporated  with  a  less  exceptionable  system  ;  and  by 
a  comparison  of  his  experiments  with  those  of  many  other  philosophers,  I 
have  deduced  some  methods  of  calculation  which  may  perhaps  be  practi- 
cally useful ;  in  particular  a  simple  rule  for  determining  the  elasticity  of 
steam,  and  a  mode  of  reducing  the  indications  of  hygrometers  of  different 
kinds  to  a  natural  scale. 

Count  Rumford's  establishment  of  a  prize  medal,  to  be  given  every  three 
years  by  the  Royal  Society  to  the  author  of  the  most  valuable  discovery 
respecting  heat  or  light,  forms  an  era  less  remarkable,  than  the  first  adjudi- 
cation of  the  medal  to  himself,  and  the  second  to  Mr.  Leslie.  Count 
Rumford's  numerous  experiments  on  the  production  and  communication  of 
heat  are  highly  important,  both  for  the  utility  which  may  be  derived  from 
their  economical  application,  arid  for  the  assistance  which  they  afford  us  in 
the  investigation  of  the  intimate  nature  of  heat.  Mr.  Leslie's  discovery  of 
the  different  properties  possessed  by  surfaces  of  different  kinds,  with  regard 


ON  THE  HISTORY  OF  TERRESTRIAL  PHYSICS.         589 

to  emitting  and  receiving  radiant  heat,  is  in  every  respect  highly  interesting  ; 
and  the  multiplicity  and  diversity  of  his  experiments  would  have  entitled 
him  to  still  higher  commendation  than  he  has  obtained,  if  they  had  heen 
more  simply  and  circumstantially  related.  Perhaps,  however,  none  of 
the  modern  improvements  in  speculative  science  deserves  a  higher  rank 
than  Dr.  Herschel's  discovery  of  the  separation  of  heat  from  light  by  re- 
fraction. Mr.  Prevost  has  made  some  just  remarks  on  the  experiments  of 
other  philosophers  respecting  heat ;  and  his  own  theory  of  radiant  heat, 
and  his  original  investigations,  on  the  effect  of  the  solar  heat  on  the  earth, 
have  tended  materially  to  illustrate  the  subject  of  his  researches. 

The  general  laws  of  the  ascent  and  descent  of  fluids  in  capillary  tubes, 
and  between  plates  of  different  kinds,  had  long  ago  been  established  by 
the  experiments  of  Hauksbee,  Jurin,  and  Musschenbroek  ;  many  other 
circumstances,  depending  on  the  same  principles,  had  been  examined  by 
Taylor,  Achard  and  Guyton ;  and  some  advances  towards  a  theory  of  the 
forms  assumed  by  the  surfaces  of  liquids,  had  been  made  by  Clairaut, 
Segner,  and  Monge.  In  an  essay  on  the  cohesion  of  fluids,  read  before 
the  Royal  Society  in  the  year  1804,  I  have  reduced  all  effects  of  this 
nature  to  the  joint  operation  of  a  cohesive  and  repulsive  force,  which 
balance  each  other ;  assuming  only  that  the  repulsion  is  more  augmented 
by  the  approach  of  the  particles  to  each  other  than  the  cohesion ;  and  I 
have  had  the  satisfaction  of  discovering  in  this  manner  a  perfect  corre- 
spondence between  many  facts,  which  had  not  been  supposed  to  have  the 
slightest  connexion  with  each  other.  Almost  a  year  after  the  publication 
of  this  paper,  Mr.  Laplace  read  to  the  National  Institute  a  memoir  on  capil- 
lary tubes,  in  which,  as  far  as  he  has  pursued  the  subject,  he  has  precisely 
confirmed  the  most  obvious  of  my  conclusions;  although  his  mode  of 
calculation  appears  to  be  by  no  means  unexceptionable,  as  it  does  not  in- 
clude the  consideration  of  the  effects  of  repulsion.  Had  my  paper  been  so 
fortunate  as  to  attract  Mr.  Laplace's  attention  before  his  memoir  was  pre- 
sented to  the  Institute,  he  would  perhaps  have  extended  the  results  of  my 
theory  with  the  same  success,  which  has  uniformly  distinguished  his 
labours  in  every  other  department  of  natural  philosophy. 

When  we  reflect  on  the  state  of  the  sciences  in  general,  at  the  beginning 
of  the  seventeenth  century,  and  compare  it  with  the  progress  which  has 
been  since  made  in  all  of  them,  we  shall  be  convinced  that  the  last  two 
hundred  years  have  done  much  more  for  the  promotion  of  knowledge,  than 
the  two  thousand  that  preceded  them  :  and  we  shall  be  still  more  encouraged 
by  the  consideration,  that  perhaps  the  greater  part  of  these  acquisitions 
has  been  made  within  fifty  or  sixty  years  only.  We  have  therefore  the 
satisfaction  of  viewing  the  knowledge  of  nature  not  only  in  a  state  of  ad- 
vancement, but  even  advancing  with  increasing  rapidity ;  and  the  universal 
diffusion  of  a  taste  for  science  appears  to  promise,  that,  as  the  number  of 
its  cultivators  increases,  new  facts  will  be  continually  discovered,  and  those, 
which  are  already  known,  will  be  better  understood,  and  more  beneficially 
applied. .  The  Royal  Institution,  with  other  societies  of  a  similar  nature, 
will  have  the  merit  of  assisting  in  the  dissemination  of  knowledge,  and  in 
the  cultivation  of  a  taste  for  its  pursuit ;  and  the  advantages  arising  from 


I  > 

690  LECTURE  LX. 

the  general  introduction  of  philosophical  studies,  and  from  the  adoption 
of  the  practical  improvements  depending  on  them,  will  amply  repay  the 
labours  of  those,  who  have  been  active  in  the  establishment  and  support 
of  associations  so  truly  laudable. 


LECT.  LX.— ADDITIONAL  AUTHORITIES. 

History  of  Electricity.— Hausen,  Novi  Perfectus  in  Hist.  Electr.  4to,  Leipz. 
1734.  Gralath,  Geschichte  der  Elektr.  Abhand  der  Natur.  Gesellsch.  in  Danzig, 
1747,  i.  23.  Hist.  Generate  et  Particuliere  de  1'Electr.  Paris,  1752.  Dalibard,  do. 
abrege*e,  2  vols.  1766.  Priestley's  Hist,  of  Electr.  with  Original  Experiments,  4to, 
1764  ;  Additions,  4to,  1770.  Kriinitz,  VerzeichnissderVornehmsten  Schriften  von 
der  Elektr.  Leipz.  1769.  German  trans,  of  Priestley,  4to,  fieri.  1772.  Kiibu, 
Geschichte  der  Medicinischen  und  Phys.  Elektr.  2  vols.  Leipz.  1783  and  1796. 
Eyewater,  Essay  on  the  Hist,  of  Electr.  1810.  De  la  Rive,  Esquisse  Histor.  des 
Principals  Decouvertes  faites  dans  1'Electr.  depuis  quelques  Annees,  Geneve,  1833. 
Ann.  de  1'Electr.  i.  1.  Wartmann,  ibid.  i.  31. 

Galvanism. — Ritter,  Beitrage  zur  Nahern  Kenntniss  des  Galv.  Jena,  1800-5. 
Sue",  Hist,  der  Galv.  4  vols.  Paris,  1802-5.  Tromsdorff,  Geschichte  des  Galv. 
Erfurt,  1808.  Bostock's  Hist,  of  Galv.  1818. 


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INDEX. 


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• 


INDEX. 


AARON  Reschid,  456. 

Aberration  from  colour,  337. 

Aberration  of  light,  363,  PI.  29. 

Aberration  of  the  stars,  341,  342,  379. 

Abutments,  125. 

Academicians,  289. 

Academy  del  Cimento,  489,  585. 

Academy  of  Paris,  191,  192,  279,  280,  585. 

Academy  of  Petersburg,  585. 

Accelerated  motion,  PI.  1. 

Accelerating  forces,  21. 

Acceleration,  22. 

Acceleration  of  the  moon's  motion,  414. 

Acceleration  of  tides,  447,  448. 

Accidental  properties  of  matter,  465. 

Accommodation  of  the  eye,  353. 

Accompaniment,  308. 

Accumulation  of  electricity,  517« 

Achard,  589. 

Achernar,  395. 

Achromatic  eye  piece,  337. 

Achromatic  glasses,  337« 

Achromatic  telescopes,  379,  PI.  28. 

Acids,  524. 

Acoustics,  195,  287- 

Acting  pump,  PI.  23. 

Action  of  water  on  lead,  277- 

Actual  focus,  324. 

Adair,  558. 

Adhesion,  112,  117,  119,480. 

Adsiger,  583. 

Advancement  of  science,  589. 

Aeolian  harp,  299,  312. 

Aepinus,  507,  531,  586. 

Aerial  perspective,  356. 

Africa,  437. 


Aggregation,  480. 
Agitation,  163,  178. 


Agricultural  instruments,  175. 

Air,  232.    Buoyancy  of  the  air,  29.    Resistance 

of  the  air,  30,  31,  154,  232,  260,  261,  284. 
Air  consumed,  486. 
Air  gun,  173,  269,  PI.  24. 
Air  pump,  205,  260,  278,  PL  24. 
Air  thermometer,  498,  PL  39. 
Air  vents,  241. 
Air  vessel,  138,  255. 
Ajutages,  212,  213. 
Albategni,  456. 
Albertus,  285. 

Albinus,  88,  90;  b.  1683,  d.  1771. 
Alcohol,  497. 
Aldebaran,  395- 
Aldini,  523,  588. 

Aldrovandus,  583,  584;  b.  1525,  d.  1605. 
Alembert.    See  Dalembert. 
Alexander,  182,  454. 
Alexandria,  75,  183. 
Alexandrian  school,  453,  454. 
Alfred,  186. 
Algenib,  394,  395. 
Algol,  393,  394,  395. 
Alhazen,  375;  fl.  1072. 
Alkalis,  524. 
Allineations,  394,  395. 
Almagest,  456. 
Almamoun,  456;  4a33. 


Alteration,  105,  109. 

Alternate  motion,  PL  14. 

Alternation  of  motion,  257- 

Altitude,  PL  35. 

Alva.    Duke  of  Alva,  187- 

Amontons,  191,  256,278;  b.  1663,  d.  1705. 

Amphibia,  575. 

Anatomy  of  plants,  568. 

Anaxagoras,  581,  582. 

Anaximander,  581 ;  b.  611,  d.  547,  B.  c. 

Anaximenes,  581,  582. 

Anchor.    Weighing  an  anchor,  158. 

Andr6,  93. 

Andromeda,  395. 

Aneurisms,  227- 

Angles,  80. 

Angles  of  incidence  and  reflection,  322. 

Anglonorman  architecture,  187- 

Animal  actions,  98. 

Animal  electricity,  523. 

Animal  force,  69. 

Animal  life,  573. 

Animal  light,  340. 

Animal  motions,  49. 

Animals,  566. 

Anne,  190. 

Annealing,  494. 

Anoria,  PL  22. 

Antares,  395. 

Anthelia,  347- 

Antimony,  532. 

Antiochus,  582. 

Anvil,  61. 

Anvils,  170. 

Anvil  of  the  ear,  302. 

Apollodorus,  186 ;  fl.  120. 

Apollonius  Pergaeus,  183, 455 ;  fl.  242,  B.C. 

Apparent  attractions,  repulsions,  and  cohesions, 
PL  39. 

Apparent  diameter  of  the  sun,  416. 

Apparent  motion  of  the  sun,  416. 

Apparent  motions,  425. 

Apparent  motions  of  the  stars,  416. 

Appearances  of  the  celestial  bodies,  415. 

Apsides,  PL  34. 

Aquarius,  401. 

Aqua  tinta,  93. 

Aqueous  humour,  350. 

Aquila,  395. 

Arabians,  186, 188,  456. 

Arago,  372,  542. 

Aratus,  463 ;  b.  300,  B.C. 

Arch,  123,  182,  PL  11. 

Archimedes,  28,  44,  50, 184,  185,  189, 190,  236, 
251,  275,  276,  375,  433,  454,  PL  22 ;  d.  212,  B.C. 

Architecture,  121, 182,  187.    Hydraulic  architec- 
ture, 235,  237,  238. 

Arch  lute,  312. 

Archytas,  182 ;  b.  442,  d.  352,  B.C. 

Arcs  of  circles,  PL  6. 

Arcturus,  392,  395,  397- 

Are,  84. 

Aretin,  the  monk,  316. 

Argo,  395. 

Aries,  395,  401. 

Aristarchus,  454 ;  fl.  264,  B.C. 

Aristophanes,  374. 
2  Q 


r>94 


INDEX. 


Aristotelians,  12. 

Aristotle,  5,  19,  183,  275,  315,  316,  374,  442,  577, 

582,  PL  22;  b.  385,  d.  322,  B.C. 
Aristyllus,  454. 
Arkwright,  101,  142,  187- 
Arnault,  146. 
Arnold,  151,  154,  PL  16. 
Arrangement  of  particles,  480. 
Arrangement  of  the  stars,  392. 
Arrow,  173. 
Arrowsmith,  PI.  42,  43. 
Arsenic,  532. 
Artedi,  575. 
Arteries,  220. 
Artificial  globe,  432. 
Artificial  magnets,  537- 
Arytaenoid  cartilages,  312,313. 
Ascent,  25. 

Ascent  of  a  double  cone,  PI.  3. 
Ascent  of  a  loaded  cylinder,  PI.  3. 
Ascent  of  water,  PI.  39. 
Ash,  587. 

Astronomer  Royal,  461. 
Astronomical  instruments,  426. 
Astronomical  telescope,  334. 
Astronomical  time,  429. 
Astronomy,  387.    Practical  Astronomy,  425. 
Athenaeus,  185,  582  ;  fl.  136. 
Atmosphere,  206,  546,  PL  19,  24. 
Atmosphere  of  Jupiter,  450,  548. 
Atmosphere  of  the  sun,  399,  400. 
Atmospherical  pressure,  207. 
Atmospherical  refraction,  345,  PL  29. 
Atmospheric  machine,  258. 
Atmospheric  tides,  450. 
Atoms,  469,  581. 
Attachment  of  horses,  167. 
Attalus,  186. 

Attraction  of  a  sphere,  410. 
Attraction  of  moisture,  553. 
Attractions  and  repulsions  of  electrified  bodies, 

511. 

Attractions  of  floating  bodies,  478,  513. 
Attractions  of  solids  and  fluids,  476. 
Attractions  of  the  electric  fluid,  508. 
Attrition,  120. 

Atwpod's  machine,  23,  41,  118,  PL  1. 
Auriga,  394. 

Aurora  boreal  is,  533,  560. 
Avicenna,  147. 
Avoirdupois,  96. 
Axes  of  rotation,  66. 
Axis  and  wheel,  51. 
Axis  and  winch,  157. 
Axles,  116. 
Azimuth  compass,  PI.  41. 


.'),'.    - 

Babylonian  observations,  452. 

Bacon.    Roger  Bacon,  188,  227,  375,  583  ;  b.  1214, 

d.  1292. 
Bacon.  Lord  Verulam,  5,  12,  189,  316,  458,  582, 

583;  b.  1560,  d.  1626. 
Bag,  203. 

Bag  pump,  254,  PL  23. 
Bailly,  452. 
Baily,  440. 

Balance,  146,  PL  8,  9. 
Balance.    Hydrostatic  balance,  235. 
Balances,  96. 
Balance  spring,  147. 
Ballast,  249. 
Balloon,  206,  265. 
Bank,  200. 
Banking,  153. 
Banks,  238. 
Bark,  569. 
Barlow,  95. 

Barometer,  550,  556,  584,  PI.  19. 
Barometers,  208. 

Barrel  chronometer,  146. 
Barrow,  190,  377;  b.  1630,  d.  1677- 
Bartholin,  378  ;  b.  1616,  d.  1680. 
Barton,  PL  4. 
Baskets,  168. 
Bass,  312. 
Batsha,  449,464. 
Battering  ram,  179. 


Battery,  513. 

Battery  of  Volta,  563,  588. 

Bauhin,  584.    J.  Bauhin,  b.  1541,  d.  1613.    C. 

Bauhin,  b.  1560,  d.  1624. 
Bayer,  394. 
Bead  pump,  256. 
Beads  in  equilibrium,  PL  11. 
Beam,  114,  115. 
Beam  compasses,  78,  PL  6. 
Beams,  PL  10. 

Beams  in  equilibrium,  PI.  11. 
Bear,  394. 
Beat,  PL  25. 
Beats,  305. 
Beccaria,  558. 
Becquerel,  504. 
Beguelin,  381. 

Beighton,  266,  279,  282,  PI.  24. 
Bell,  314. 

Bell.    Henry  Bell,  271. 
Bellows,  200,  262,  PL  24. 
Benedetti,  189. 
Bennet,  109,  110,  527,  PL  40. 
Bent  columns  and  bars,  PL  9. 
Bent  lever,  PL  3. 
Bent  lever  balance,  96,  98,  PL  9. 
Bent  pipes,  227- 
Bent  straps,  PL  13. 
Berard,  504. 

Bergmann,  586  ;  b.  1735,  d.  1784. 
Bernoulli,  46,  155,  203,  228,  268.     D.  Bernoulli, 

191,  210,  213,  280,  281,  296,  300,  317,  498,  PL 

20,  22,  39.    Ja.  Bernoulli,  191,  279  ;  I*.  1654,  d. 

1705.    Jo.  Bernoulli,  191,  279,  281,   282;    b. 

1667,  d.  1748. 
Berthoud,  153,  155. 
Bertius,  583. 
Bessel,  390,  404. 
Beudant,  291. 

Bevilled  wheels,  136,  PL  15. 
Bianconi,  290. 
Biceps,  99. 
Billiard  balls,  PL  5. 
Billiards,  62. 
Biot,  285,  371. 
Bird,  461. 
Birds,  574,  575. 
Birmingham,  187. 
Biscop,  186. 
Bissextile,  427. 
Bistre,  73. 
Bito,  186. 

Black,  285,  501,  586;  b.  1728,  d.  1799. 
Blackening  rays,  490. 
Blackfriars  bridge,  126,  PL  12,  14. 
Blasting,  180. 
Blast  of  air,  200. 
Blocks,  53,  176,  PI.  4. 
Blood,  573,  574,  578. 
Blow,  61. 

Board  of  longitude,  192,461. 
Board  perforated,  1  12. 
Bode,  433. 

Body.    Moveable  body,  38. 
Body  colours,  73. 

Boerhaave,  498,  586  ;  b.  1668,  d.  1738. 
Boiling,  492. 
Bolognan  jars,  494. 


Bolts, 


Bones  of  the  ear,  PI.  25. 

Bootes,  395. 

Borda,  84,  85,  282;  b.  1733,  d.  1797- 

Borelli,  99. 

Boring,  175. 

Boscovich,  359,  360,  3C2,  381,  471,  587;  b.  1711, 

d.  1787- 
Bossut,  284. 
Botany,  586. 

Bottom  of  a  cistern,  PL  19. 
Bouguer,  280,  342,  379,  381,  421,545;  b.  1698, 

d.1758. 

Boulton,  103, 117,  259,  267,  2G9.         , 
Bovillus,  34. 
Bow,  173. 
Boyle,    5,  278,    377,    585,    PL   1<);     b.  1027. 

d.  1691. 
Braces,  130,  PL  13. 


INDEX. 


595 


Bradley,  341,  379,  402,  413,  416,  461 ;  b.  1622, 

d.  1762. 

Brahe.    See  Tycho. 
Bramah,  170,  256. 
Bramah's  press,  199,  254,  PI.  23. 
Brass,  538. 

Breast  wheel,  246,  PL  22. 
Brereton,  558. 
Brewster,  371. 
Bridge,  125,  PI.  11. 
Bridges,  PI.  14. 
Bridgewater.    Duke  of  Bridgewater,   157,  159, 

PL  17. 

Briggs,  189;  b.  1561,  d.  1631. 
British  manufactures,  186. 
Brittleness,  110. 
Brouncker,  34. 
Brunau,  278. 

Buat.    Chevalier  de  Buat,  222,  223,  243,  285. 
Bubble,  476. 
Buchanan,  101. 
Bucket  revolving,  198. 
Bucket  wheel,  250. 
Buffon,  375,  489,  586. 
Bull,  395. 
Bullets,  268. 
Buoyancy,  202. 
Burg,  461. 

Burning  glasses,  330,  374, 
Burning  mirror,  375. 
Burning  rocks,  179. 
Burnisher,  92. 
Burrows,  583. 

Cabbage:ieaf,  478. 

Cable,  114. 

Caesar,  186,  277,  427,  428,  442,  455  ;  b.  99,  d.  43, 

Calabria,  561. 

Calendar,  427,  456. 

Calendering  mill,  170. 

Calking,  72. 

Caloric,  501. 

Camden,  187. 

Camera  lucida,  331. 

Camera  obscura,  331,  PL  28. 

Camper,  90. 

Canal,  PL  21. 

Canals,  238,  240,  277. 

Cancer,  401. 

Candles,  486. 

Cnno  n,  175, 

Cannon  ball,  179,  233. 

Canopus,  395. 

Canterbury  cathedral,  188. 

Canton,  209,  291. 

Capacity  for  heat,  499. 

Capella,  394,  395. 

Capes,  437. 

Capillary  action,  475. 

Capillary  attraction,  227. 

Capillary  tubes,  477,  589. 

Capstan,  158,  PL  3,  4. 

Capricornus,  401. 

Carbonic  acid  gas,  289. 

Carisbrook  castle,  160. 

Carlisle,  588. 

Carpentry,  121,  128. 

Carriages,  PI.  18. 

Carrying,  102. 

Cartes.    See  Descartes. 

Cartesian  devils,  PL  19. 

Cartilages  of  the  larynx,  PL  26. 

Carts  connected,  168. 

Cart  with  a  crane,  161. 

Caspian  Sea,  43?. 

Cassegrain,  335,  338. 

Cassegrain's  telescope,  335,  PL  28. 

Cassini,  34,  147,  399,  456,  458,  PL  33.  C.  F. 
Cassini,  b.  1714,  d.  1784.  D.  Cassini,  b.  1625, 
d.  1712.  J.  Cassini,  b.  1677,  d.  1756. 

Cassiopeia,  393,  394,  395. 

Castelli,  2J7;  b.  ab.  1575,  d.  1644. 

Casting,  87- 

Castor,  397. 

Catalogue  of  references,  193. 

Catchfly,  566. 

Catenaria,  124. 


Catoptrics,  324. 

Causation,  11. 

Caustics,  PL  28. 

Cavalleri,  28,  190,  256. 

Cavallo,  526,  532,  538,  558,  PL  40. 

Cavendish,  348,  440,  507,  510,  512,  586. 

Caxton,  189. 

Ceiling,  114. 

Cellular  pump,  256. 

Celsius,  498. 

Centaur,  395. 

Central  forces,  PL  1,  2. 

Centre,  32?. 

Centre  of  a  bridge,  PI.  14. 

Centre  of  gravity,  40,  47,  PL  3. 

Centre  of  gyration,  64. 

Centre  of  inertia,  39,  PL  2,  3. 

Centre  of  oscillation,  64. 

Centre  of  percussion,  64. 

Centre  of  position,  40. 

Centre  of  pressure,  202. 

Centres  of  bridges,  131 . 

Centrifugal  bellows,  PI.  24. 

Centrifugal  force,  26,  417. 

Centrifugal  pump,  253,  PL  23. 

Centrifugal  regulator,  37. 

Cepheus,  395. 

Ceres,  404, 424. 

Chain,  139,  PL 7. 

Chain  loaded,  PL  11. 

Chain  pump,  256. 

Chains,  86. 

Chair,  131. 

Chaldeans,  452. 

Chalk,  112. 

Chalks,  72. 

Changeable  stars,  393. 

Change  of  climate,  546. 

Changes  of  form,  169. 

Chapman,  284. 

Charcoal,  486. 

Charge,  513. 

Charles,  294. 

Charles  II.,  460. 

Charts,  394. 

Chase,  94. 

Chemical  attractions,  523,  524. 

Chemical  effects  of  electricity,  519. 

Chemical  electricity,  521. 

Chemistry,  11. 

Chemists,  504. 

Chersiphron,  182. 

Childers,  102. 

Childrey,  399. 

Chimney,  265. 

Chimney  pipes,  314,  PI.  26. 

Chimnies,  277. 

Chinese,  74,  91,  452,  580. 

Chinese  pumps,  257. 

Chiron,  453. 

Chladni,  292, 297,  300,  317,  318,  PL  25. 

Chord,  PL  25. 

Chords  of  a  circle,  33,  PL  2. 

Choroid  coat,  351. 

Christian  era,  427. 

Chromatic  aberration,  337- 

Chromatic  scale,  307. 

Chronology,  427. 

Chronology  of  acoustics,  319. 

Chronology  of  astronomers,  463. 

Chronology  of  authors  on  hydrodynamics,  286. 

Chronology  of  mathematicians  and  mechanics. 

See  194. 

Chronology  of  optical  authors,  385. 
Chronology  of  physical  authors.    See  590. 
Chronometer  with  a  barrel,  146. 
Churchman,  PL  41. 
Chyle,  577,  578. 
Cicero,  456. 

Cimabue,  188 ;  b.  1240,  d.  1300. 
Cimento.     Academicians    del    Cimento,     290, 

489. 

Circle.    Graduated  circle,  81. 
Circle  in  perspective,  PL  8. 
Circles,  77,  PL  6. 
Circular  pendulum,  36. 
Circular  slider,  PL  7. 
Circulation  of  the  blood,  220,  584. 
Cisalpinus,  584. 
Cisterns,  239. 

2  Q  2 


.598  INDEX. 

Electrical  attraction  and  repulsion,  524. 
Electrical  balance,  527,  PL  40. 
Electrical  light,  340,  518. 
Electrical  machines,  525,  PL  40. 
Electrical  pressure,  511. 
Electric  fluid,  508. 
Electricity,  13,  508,  531,  585. 
Electricity  in  equilibrium,  507. 
Electricity  in  motion,  516. 
Electrics,  520. 
Electrified  spheres,  PI.  39. 
Electro-magnetic  telegraph,  541. 
Electro-magnetism,  539. 
Electrometers,  527,  PL  40. 
Electrophorus,  526,  PL  40. 
Elevation  of  a  projectile,  30. 
Elevation  of  liquids,  477,  PL  39. 
Elevations,  438,  PL  38. 
Ellicott,  153. 

Ellipsis,  29,  37,  89,  293,  PL  2. 
Ellipticity  of  the  earth,  435. 
Elliptic  motion  of  a  pendulum,  37- 
Elliptic  orbits,  401. 
Elliptic  vibrations,  PL  2. 
Elongation,  418. 
Elongation  of  Venus,  PL  34. 
Elvius,  282. 

Embankments,  237,  PL  21. 
Emery,  149. 
Emission  of  light,  341. 
Empedocles,  374,  582;  b.  473,  d.  413,  B.C. 
Encaustic  paintings,  74. 
Encroachments  of  the  sea,  563,  564. 
Encyclopaedia  Britannica,  32,  46. 
Encyclopedic,  192. 
Energy,  59,  172. 
Englefield,  490. 
English  foot,  85. 
English  philosophers,  5. 
Engraving,  71,  91,  188. 
Engymeter,  82. 
Epact,  429. 
Epicureans,  12,  458. 
Epicurus,  183,  582;  b.  342,  d.  270,  B.C. 
Epicycles,  455. 

Epicycloidal  teeth,  135,  PI.  15. 
Epiglottis,  312. 
Eprouvette,  103. 
Equal  areas,  PL  1. 
Equalization  of  force,  148. 
Equated  clocks,  427. 
Equation  of  time,  426. 

Equilibrium,  45,  PL  3,  8.    Stability  of  equili- 
brium, 198. 

Equilibrium  of  animals,  49. 
Equilibrium  of  electricity,  PL  39. 
Equilibrium  of  fluids,  PL  19. 
Equilibrium  of  gases,  204. 
Equilibrium  of  radiant  heat,  489. 
Equinoctial  tides,  442. 
Equinox,  PL  34. 
Eratosthenes,  401,  454. 
Eridanus,  395. 
Eskinard,  378. 

Essential  properties  of  matter,  464. 
Etching,  92. 

Ethereal  medium,  362,  472,  482. 
Euclid,  183,  375. 
Eudoxus,  182. 
Euler,  66,  191,  282,  300,  317,  360,  379,  380,  415, 

421,  432, 461,  585.    L.  Euler,  b.  1707,  d.  1783. 
Eumenes,  75. 
Evaporation,  492,  551. 
Excitation  of  electricity,  587- 
Excitement  of  heat.  484. 
Expanse  of  the  universe,  389. 
Expansion,  491. 
Expansion  of  pendulums,  153. 
Expansion  of  the  air,  PI.  24. 
Expansions,  496. 
Experiment  oh  elasticity,  22. 
Explosions,  560. 
Extension,  105,  106,  170,  465. 
Extension  of  a  column,  PL 9. 
Extinction  of  light,  364. 
Eyck.    Van  Eyck,  73,  188;  b.  1371,  d.  1441. 
Eye,  350,  PL  30. 
Eyepiece,  336,  PL  28. 
Eytelwein,  285. 


Fabricius,  5/6. 

Fabroni,  587- 

Fahrenheit,  485,  498. 

Falconer,  582. 

Fall  in  a  fluid,  203. 

Fall  of  a  heavy  body,  23,  85. 

Fall  of  a  feather,  44. 

Fall  of  leaves,  571. 

Fan  for  corn,  264. 

Faraday,  541,  542. 

Fata  Morgana,  346. 

Faunius,  276. 

Felt,  143. 

Felting,  143. 

Fermat,  376,  458. 

Fidler,  PI.  8. 

Field  glass,  336,  PL  28. 

Figure  of  the  earth,  435,  PL  34. 

Fire,  488. 

Fire  engines,  255,  276,  PL  23. 

Fishes,  231,  395,  575. 

Fixed  ecliptic,  400,  PL  32. 

Fixed  stars,  387,  PL  36,  37. 

Flageolet,  314. 

Flakes  of  snow,  348. 

Flame,  12. 

Flamsteed,  460,  461 ;  b.1646,  d.1719- 

Flax,  141. 

Flemish  weavers,  187. 

Flexible  fibres,  138. 

Flexible  vessels,  203. 

Flexure,  ]05,  107,  112,  113,  480,  482. 

Flexure  of  columns  and  bars,  PL  [). 
Floating  bodies,  201,  478,  PL  19. 

Floodgates,  239,  PL  21. 

Floor,  114. 

Flower,  567- 

Fluid,  196. 

Fluids,  195. 

Fluoric  acid,  92. 

Fluor  spar,  341. 

Flute,  314. 

Flute  pipe,  PI.  26. 

Fluxions,  191. 

Fly,  101. 

Fly  clocks,  145. 

Fly  wheels,  137. 

Focus,  324. 

Focus  of  a  lens,  326. 

Focus  of  the  eye,  353. 

Fomalhaut,  395. 

Fondeur,  146. 

Fontenelle,  190,  422. 

Foot,  85. 

Forbes,  505,  506. 

Force,  19,  26,  60.  Accelerating  force,  21.  Cen- 
trifugal force,  26.  Definition  of  force,  21. 
Deflective  force,  26.  Regulation  of  force,  69. 

Force  of  electricity,  104. 

Force  of  magnetism,  104. 

Forces.    Regulation  of  hydraulic  forces,  241. 

Forcing  pump,  254,  276,  PL  23. 

Forge  hammer,  PL  18. 

Forges,  171. 

Forging,  110. 

Form  of  the  sky,  356. 

Forms  of  the  planets,  412. 
I     Formulae  for  elasticity  of  steam,  272. 
|     Forsyth,  571. 

Fossils,  563. 
I     Fourcroy,  588. 
I     Fracture,  105,  110,  113. 

Fracture  from  heat,  494. 

Frame  for  rectilinear  motion,  PL  14. 

Frame  saw,  PL  4. 

Franc,  96. 

Franklin,  507,  558,  586;  b.  1706,  d.  1791. 
Fraunhofer,  343,  505. 
Frederick  II.,  145,  457- 
Freezing,  493,  546. 
French  measures,  85. 

French  weights,  96. 

Fresco,  73. 

Friction,  71,  117,  485,  514.    Avoiding  friction, 

156,  163. 

Friction  of  fluids,  222,  PI.  20,  21. 
Friction  of  ice,  501. 
Friction  of  scapements,  150. 
Friction  of  sluices,  240. 


INDEX. 


599 


Friction  wheels,  164,  PI.  14,  18. 

Frigid  zone,  436. 

Fringes  of  colours,  366,  367- 

Frisi,  192. 

Fulling,  143. 

Fulton,  271. 

Furnaces,  265. 

Fusee  of  a  watch,  148,  PI.  15,  16. 

Fusorius,  188 ;  fl.  1450. 

Fust,  189. 


Gages  for  air  pumps,  261,  PI.  22. 

Galen,  352. 

Galilean  telescope,  334,  336,  PL  28. 

Galileo,  24,  31,  34,  147,   189,  190,  207,  277,  316, 

376,  458;  b.  1562,  d.  1642. 
Gallon,  85. 

Galvani,  523,  587,  588 ;  b.  1737,  d.  1798. 
Galvanic  battery,  PL  40. 
Galvanic  circuit,  PL  40. 
Galvanic  electricity,  521. 
Galvanism,  587- 
Galvanometer,  540. 
Ganges,  223,  224. 
Garnerin,  233. 
Garnet,  PI.  17. 
Gases,  291,  4?0. 
Gasometer,  263,  PL  24. 
Gates,  131. 
Gay  Lussac,  285. 
Gellibrand,  583;  b.  1597,  d.  1636- 
Gemini,  401. 
Gemma,  393. 
Geneva,  545. 
Gensfleisch,  188. 
Geoffrey,  586. 
Geography,  435. 
Geology,  563. 

Geometry.    Instrumental  geometry,  71. 
Geometry  of  mechanics,  /I. 
Georgian  planet,  398, 405,  424. 
Germination,  567. 
Gerstner,  227- 

Gesner,  583,  584 ;  b.  1516,  d.  1565. 
Gilbert,  532,  583. 
Gin,  157- 
Gioja,  583. 
Givre,  555. 
Glass,  477. 
Glass  blower,  200. 
Glass  blowing,  171. 
Glass  drops,  494. 
Glass  vibrating,  301. 
Glauber's  salts,  493. 
Glazier's  vice,  1?!,  PL  18. 
Globe,  432. 
Globes,  394. 

Globules  for  finding  specific  gravities,  236. 
Globules  for  microscopes,  330. 
Glottis,  312,  313,  PL  26. 
Going  fusee,  with  an  intermediate  spring,  148, 

PL  16. 

Golden  number,  429. 
Gold  leaf,  322. 
Gong,  314. 
Gorlaeus,  584. 

Gothic  architecture,  127,  187- 
Gothic  roof,  PL  12. 
Grafting,  570. 
Graham,  85,  150,  153,  461. 
Grain,  95. 
Gramme,  96. 
Granite,  176,  177- 
Grave  harmonics,  306,  317. 
Gravesande.    See  S'Gravesande. 
Gravitation,  23,  29,  409,411,  458, 471,  508,  PL  34. 
Gravitation  of  light,  361. 
Gravity,  582. 

Gray.    Stephen  Gray,  510,  585,  586  ;  d.  1736. 
Grecian  year,  427- 
Greeks,  74,  181,  453. 
Greenwich,  150,  460. 
Gregorian  calendar,  428. 
Gregorian  telescope,  335,  PL  28. 
Gregory,  335,  378,  458.    Pope  Gregory,  316,  428. 
Gridiron  pendulum,  PL  16. 
Grimaldi,  342,  366,  377. 


Grinding,  176. 

Groups  of  stars,  392. 

Growth,  539. 

Guericke,  207,  260,  278,  585 ;  b.  1602,  d.  1686. 

Guglielmini,  2785  b.  1655,  d.  1710. 

Guido  of  Arezzo,  316;  fl.  1026. 

Guitar,  311. 

Guldinus,  189. 

Gulf  stream,  449. 

Gun,  268. 

Gunnery,  31- 

Gunpowder,  103,  268,  277- 

Gunter,  189,  583 ;  b.  1581,  d.  1626. 

Gunter's  scale,  82. 

Gutenberg,  188. 

Guyot,  583. 

Guy  ton,  589. 

Gwynn,  256,  PI.  23. 

Gymnotus  electricus,  523. 


Hadley,  548,  585;  d.  1744. 

Hartley's  quadrant,  80, 82,  430,  Pi.  35. 

Hair  hygrometer,  554. 

Hales,  278;  b.  1677,  d.  1761. 

Haley,  151. 

Halifax,  190. 

Hall,  379. 

Halley,  191,  389,  406,  408,  414,  432,  459,  460,  535, 

548,  585;  b.  1660,  d.  1742. 
Halos,  347,  PL  29. 
Hamilton,  50.    Captain  T.  Hamilton's  gage,  243, 

PL  22.    Sir  W.  Hamilton,  561,  562. 
Hammer,  61,  158. 
Hammering,  110, 170. 
Hammering  brass,  538. 
Hammer  of  the  ear,  302. 
Hanin,  98. 
Harbours,  240. 
Hard  bodies,  289. 
Harding,  404,  462. 
Harmonica,  314. 
Harmonic  curve,  289. 
Harmonics,  196,  304. 
Harmonic  sounds,  296,  298. 
Harmony,  306. 
Harness,  PL  18. 
Harp,  311. 
Harpsichord,  311. 

Harrison,  150, 153,  192,  461 ;  b.  16iM,  d.  1776. 
Harvest  moon,  421. 
Harvey,  584 ;  b.  1578,  d.  1657- 
Hats,  143. 
Hatton,  85. 

Hauksbee,  225,  227,  278,  585,  589. 
Hautboy,  314. 
Hauy,  586. 
Hawser,  140. 
Hearing,  301,  303. 
Hearing  trumpet,  PI.  25. 
Heart,  220. 

Heat,  474,  484,  514,  532,  582,  584,  589,  589,586, 
PL  39. 

Effect  of  heat  on  sound,  289. 

Effect  of  heat  on  vibrations,  297- 

Nature  of  heat,  496. 
Heat  from  electricity,  518. 
Heat  from  mirrors,  330. 
Heat  of  different  latitudes,  545. 
Heat  of  mixtures,  496. 
Heat  producing  a  draught,  264. 
Hecla,  535. 

Height  of  mountains,  206. 
Height  of  tides,  448. 
Heights,  PI.  38. 
Helfqstate,  333. 

Hemispherical  counterpoise,  203. 
Hemp,  140. 
Henderson,  390. 
Henley,  527,  528,  PL  40. 
Henry  the  Sixth,  188. 
Heraclitus,  581,  582 ;  fl.  506,  B.C. 
Hercules,  395,  397. 
Hermann,  191 ;  b.  1678,  d.  1733. 
Hermes,  315,  452. 

Hero,  145,  158, 185,  186,  258,  276  ;  fl   130,  B.C. 
Herodotus,  182. 
Hero's  cupping  instrument,  PL  24. 


600 


INDEX. 


Hero's  fountain,  258,  PI.  23. 

Herschel,  334,  335,  337,  342,  357,  382.  389,  390, 

391,  392,  393,  397,  &99,  403,  404,  405,  406,  407, 

410,  421,  423,  424,461,  489,  490,  546,  589,  PI.  31, 

33,39. 

Hessian  bellows,  264. 
Hevelius,  458. 
Hiero,  184,  276. 
High  pressure  engine,  2/2. 
H  igh  water,  442. 

Hipparchus,  393,  402,  413,  451,  454,  455. 
History  of  astronomy,  451. 
History  of  hydraulics  and  pneumatics,  275. 
History  of  mechanics,  180. 
History  of  music,  315. 
History  of  optics,  374. 
History  of  terrestrial  physics,  580. 
Hoar  frost,  555. 
HOI1,  PI.  23. 
HOll's  machine,  257. 
Hoffmann,  489. 
Hogshead,  95. 
Hofiow  beams,  108. 
Hollow  masts,  115. 
Homogeneous  medium,  321. 
Hooke,  5,  76,  106,  123,  145,  147,  159,  190,  203, 

205,  256,  265,  278,  282,  377,  378,  382,  416,  430, 

458,  459, 460,  584,  585,  PI.  6 ;  b.  1635,  d.  1703. 
Hooke's  counterpoise,  237,  PI.  19. 
Hooke's  joint,  133,  PI.  14. 
Hoop,  26. 
Hope,  569. 
Horizon,  I'l.  35. 
Horizontal  moon,  356,  PI.  3u. 
Horizontal  range,  30,  PI.  2. 
Horizontal  refraction,  346. 
Horizontal  scapement,  PI.  16. 
Horizontal  surface,  197. 
Horizontal  watch,  150. 
Horn,  314. 
Hornsby,  392. 
Horrox,  432. 

Horse,  102.    Positions  of  a  horse's  legs,  37. 
Horses,  167,  PL  18. 
Hour  glasses,  144. 
Howard,  425,  564. 
Huddart,  140,  141,  382. 
Human  voice,  312. 
Humboldt,  395. 
Humidity,  553. 
Humming  top,  314. 
Hunter's  screw,  55,  160,  169. 
Hurdy-gurdy,  312. 
Hutton,  284. 
Huygens,  34,  50,  146,  147, 190,  210,  279,  280, 347, 

349,  360,  361,  363,  3<>8,  371,  378,  379,  380,  382, 

391,  411,  433,  458;  b.  1629,  d.  1695. 
Hydra,  566. 

Hydraulic  air  vessels,  257,  PI.  23. 
Hydraulic  architecture,  235,  237,  238. 
Hydraulic  bellows,  PI.  24. 
Hydraulic  forces,  241. 
Hydraulic  machines,  250. 
Hydraulic  measures,  243. 
Hydraulicostatics,  228. 
Hydraulic  pressure,  46,  228,  279. 
Hydraulic  ram,  259. 
Hydraulics,  195,  196,  210. 
Hydrodynamics,  195. 
Hydrometer,  236,  PL  21. 
Hydrometrical  fly,  243,  PL  22. 
Hydrostatic  balance,  235,  PL  21. 
Hydrostatic  instruments,  235. 
Hydrostatic  parodox,  199. 
Hydrostatic  press,  170. 
Hydrostatic  pressure,  511. 
Hydrostatics,  195,  196,  197,  PL  19. 
Hygrometer,  55.'i,  587,  PL  41. 
Hygrometry,  587- 
Hypatia,  276. 
Hyperbola,  477. 
Hyperbolic  fringes,  PL  30. 
Hypotheses  of  electricity,  507- 


Ibn  Junis,  14?,  456. 
Ice,  348,  442,  546,  582. 

348,  353,  3n> 


Idioelectrics.    See  electrics. 

Igneous  meteors,  564. 

Ignis  fatuus,  340. 

Illumination,  330. 

Illumination  of  the  planets,  PL  34. 

Image,  327,  329,  PL  27,  28. 

Image  on  the  retina,  351,  355,  PL  30. 

Impenetrability,  467. 

Impenetrability  of  matter,  21. 

Impulse  of  a  fluid,  46. 

Impulse  of  a  jet,  229. 

Inanimate  force,  69. 

Inclinations  of  the  planetary  orbits,  401. 

Inclined  plane,  33,  54,  PI.  4,  5,  17. 

Index,  76. 

Index  of  refraction,  323. 

Indian  ink,  73. 

Indians,  452. 

Indivisibles,  28. 

Induced  electricity,  512. 

Induction,  12. 

Inelastic  bodies,  57,  59. 

Inertia,  17,  26,  39,  470. 

Inferior  tides,  446. 

Infinites,  28. 

Inflammable  bodies,  323. 

Ink,  76,  93. 

Insects,  575. 

Instinct,  352. 

Instruments.     Musical  instruments,  310. 

tical  instruments,  328. 
Insulated  stars,  392. 
Intensity  of  electricity,  527. 
Intensity  of  light,  328. 
Interception  of  light,  321. 
Interception  of  sound,  294. 
Interference  of  light,  364,  370. 
Intermediate  spring,  148. 
Intermitting  springs,  216. 
Inundations  of  large  rivers,  557. 
Inverted  pump,  257. 
Inverted  tide,  443. 
Invisible  girl,  294. 
Invisible  heat,  489. 
Involutes  of  circles,  PL  15. 
Ionian  school,  181,  453. 
Ionic  column,  PL  12. 
Iris,  351,  354. 
Iron,  117,  174,  187,  531. 
Iron  filings,  534,  538,  PL  41. 
Iron  wheelways,  167- 
Irvine,  499,  500,  586. 
Italian  school,  181. 


Jack,  PL  17.    Kitchen  jack,  137. 

Jacobi,  540. 

Jamaica,  547- 

Janson,  375,  376. 

Jars,  517. 

Jeaurat,  381 ;  b.  1704,  d.  1803. 

Jet,  211,  212,  PL  20. 

Jet  with  a  ball,  226. 

Jewelling,  148. 

Jew's  harp,  314. 

Joggles,  129,  PL  13. 

Joint  focus,  327- 

Joints,  123,  128. 

Joints  for  beams,  PL  13. 

Joints  of  stones,  PL  11. 

Journal  de  Physique,  192. 

Journals,  191,  192. 

Juan,  284;  b.  1713,  d.  1773. 

Judgment  of  distance,  355. 

JUrgen,  187- 

Julian  period,  429. 

Juno,  404,  424. 

Jupiter,  404,  422,  424,  PL  33. 

Jupiter's  satellites,  421. 

Jurin,  379,  589;  b.  1680,  d.  1750. 

Jussieu,  572,  586;  b.  1699,  d.  1777. 


Ka? stner,  282. 
Kant,  391. 
Keel,  248. 
Keir's  lamp,  227. 
Kclland,  488,  506. 
Kcmpe,  187. 


Op- 


INDEX. 


601 


Kempelen,  313. 

Kepler,  28,  29,  375,  376,  381,  393,  401,  457,  458, 

459;  b.  1571,  d.  1630. 
Keplerian  laws,  401,  402,  411,  PI.  1. 
Key  note,  306. 
King,  182,489. 
Kingdoms  of  nature,  565. 
Kingpost,  130,  PI.  12. 
King's  College  Chapel,  188,  PL  12. 
Kirb  roof,  130,  PI.  13. 
Kircher,  316;  b.  1601,  d.  1680. 
Kirwan,  546,  547,  586. 
Kite,  247,  PL  22. 
Kleist,  586. 

Klingenstierna,  379,  380. 
Klugel,  38). 
Kneading,  179. 
Knight,  569,  570. 
Knives,  174. 
Kramp,  191. 

Kratzenstein,  313,  PI.  26. 
Kunze,  PL  39. 


Labour,  60,  253,  254. 

Labour  of  a  man,  101. 

Lacepede,  586. 

Lafaille,  189. 

Lagrange,  5, 121, 192,  218,  317,  401,  415. 

Lahire,  100, 191 ;  b.  1640,  d.  1718. 

Lahire's  pump,  254,  266,  PL  23. 

Lake,  444. 

Lalande,  398,  428,  458,  PL  33. 

Lallamand,  586. 

Lambert,   293,  318,  380,  381,  390,  391,  418,  421, 

489,586;  b.  1728,  d.  1777. 
Laminating  machine,  170. 
Lamp,  PL  21. 
Lamps,  237. 
Land,  437. 
Land  breezes,  550. 
Landen,  192 ;  b.  1719,  d.  1790. 
Lane,  528,  PL  40. 
Langsdorf,  285. 
Laplace,  5,  46,  83,  84,  85,  191,  192,  289,  318,  345, 

361,  382,  402,  404,  414,  415,  429,  432,  444,  450, 

451,  452,  486,  501,  586,  589. 
Larynx,  PL  26. 
Latent  heat,  501. 
Lateral  adhesion,  107,  480. 
Lateral  friction  of  fluids,  225. 
Lathe,  174. 
Latitude,  425,  430. 
Laurie,  PL  24. 

Lavoisier,  486,  501,  586;  b.  1743,  d.  1?94. 
Laws  of  gravitation,  409. 
Laws  of  refraction,  324. 
Leaden  pipes,  242. 
Lean,  269. 
Leaves,  570. 
Lee,  187. 
Lee  way,  248. 
Legs,  PL  9. 

Leibnitz,  60,  191,280,  376;  b.  1646,  d.  1716. 
Lens,  326. 
Lenses,  331,  374,  PL  27-    Grinding  lenses,  177- 

Leslie,  291,488,  498,  554,  588. 

Leslie's  thermometer,  498,  PL  34. 

Letherland,  149. 

Letterpress,  94. 

Leucippus,  581. 

Leupold,  191 ;  d.  1727- 

Level.    Spirit  level,  237. 

Levelling,  81. 

Levels,  438. 

Lever,  50,  PL  3,  4. 

Levers,  133,156. 

Levigating,  179. 

Levity,  207- 

Lewis,  161,  PL  17. 

Lexell,  40a 

Leyden  phial,  513. 

Libra,  3&S,  401. 

Libration  of  the  moon,  414,  419. 

Life,  567- 

Life  of  plants,  570. 

Lifting  pump,  255,  PL  23. 

Light,  320,  359, 389,  502,  503,  582,  PL  39. 


Light  from  electricity,  518. 

Light  from  friction,  340. 

Light-house,  122,  PL  11. 

Lightning,  557,  581,  586. 

Light  of  a  candle,  344. 

Light  of  the  heavenly  bodies,  421. 

Light  of  spirits,  344. 

Light  of  the  stars,  389. 

Lincoln  cathedral,  188. 

Lines,  77- 

Lines  or  hatches,  PL  6. 

Linne,  571,  5?2,  573,  575,  586. 

Linnean  system,  571,  586. 

Lintearia,  PL  19. 

Lion,  395. 

Liquefaction,  493. 

Liquid,  196. 

Liquid  adhering  to  a  solid,  478. 

Liquidity,  475. 

Liquids,  425,  470,  PL  39. 

Loaded  chain,  PL  11. 

Loaded  cylinder,  PL  3. 

Loaded  waggon,  PL  3. 

Lock  filled  from  a  reservoir,  214. 

Locomotive  engine,  272-  -275. 

Log,  86,  PL  22.   Hydraulic  log,  243. 

Logarithmic  circle,  PL  7. 

Logarithmic  curve,  PL  10. 

Logarithms,  82,  206,  458. 

Lohmeier,  285. 

London,  356,  547. 

Longitude,  192,  425,  431,  461. 

Longitudinal  sounds,  297. 

Looming,  346. 

Louis  XV.,  460. 

Lowitz,  PL  29. 

Low  water,  442. 

Lucernal  microscope,  333. 

Lucid  disc  micrometer,  337- 

Luc.    See  Deluc. 

Lucretius,  12,  44,  183,  389,  458. 

Luminous  bodies,  320. 

Lunar  globe,  423. 

Lunar  motions,  413,  PL  34. 

Lunar  observations,  431. 

Lunar  rainbow,  347. 

Lunar  volcanos,  565. 

Lute,  312. 

Lycopodium,  478. 

Lyonnet,  466. 

Lyra,  395. 

Lyre,  311,  315. 


Machin,  191. 

Machine  for  measuring  strength,  116. 

Machinery,  132,  PL  14. 

Machinery  of  fluids,  241. 

Machines,  68. 

Maclaurin,  50,  62,  191,  247,  280,  281  ;    b.  1698, 
d.  1746. 

Macrobius,  442. 

Madeira,  547. 

Magdeburg  hemispheres,  207,  483. 

Magic  lantern,  333,  375. 
I     Magnet,  534,  535,  581. 
I     Magnetical  attractions  and  repulsions,  533. 
1     Magnetical  curves,  PL  41. 

Magnetical  effects,  PI.  41. 

Magnetical  paste,  538. 

Magnetical  substances,  532. 

Magnet  in  a  globe,  535. 

Magnetism,  531,  586. 

Magnetism  by  induction,  535. 

Magneto-electric  machine,  541. 

Magnifier.    Double  magnifier,  336. 

Magnifying  powers,  330. 

Magnifying  powers  of  telescopes,  334,  336. 

Magnitude  of  the  planets,  PL  34. 

Magnitude  of  the  stars,  389. 

Mair,  583. 

Mairan,  399. 

Maire,  335. 

Malebranche,  380. 

Malta,  450. 

Malus,  371. 

Mammalia,  574. 

Manchester,  18?. 

Mandoline,  312. 


G02 


INDEX. 


Mangles,  170. 

Manilius,  463. 

Mansard  roof,  130,  PL  13. 

Manufactures,  186. 

Map  of  the  world,  PI.  42. 

Marble,  176, 177- 

Marcellus,  45,  184,  185. 

Marigni,  312. 

Marine  engines,  271,  272. 

Marine  octant,  PI.  35. 

Mariotte,  278,  284,  347,  348,  353,  379  ;  d.  1684. 

Marquois's  scales,  78,  PI.  6. 

Mars,  403,  423,  PI.  32. 

Marum.    See  Van  Marum. 

Maskelyne,  392, 440,  PI.  28. 

Masses,  38. 

Masts,  115. 

Mathematici  veteres,  182, 183,  184,  185. 

Matrix,  94. 

Matter,  464.    Impenetrability  of  matter,  21 . 

Matthesius,  278. 

Maupertuis,  16,  393. 

Maurolycus,  376. 

Mayer,  461,  585,  586  ;  T.  Mayer,  b.  1723,  d.  1762. 

Mazeas,  381. 

M'Culloch,  PI.  41. 

Measurement  of  the  earth,  454. 

Measurements  of  degrees,  436. 

Measure  of  force,  60. 

Measures  of  heat,  496. 

Measuring,  71. 

Measuring  instruments,  86. 

Mechain,  84. 

Mechanical  force,  60. 

Mechanical  power,  245. 

Mechanics.    History  of  mechanics,  180. 

Mediterranean,  449,  552. 

Medusa's  head,  394. 

Meibomius,  316. 

Melloni,  504,  505,  506. 

Melody,  306. 

Membranes.    Vibrations  of  membranes,  297. 

Meniscus  lens,  326. 

Menkar,  395. 

Mercurial  column,  204. 

Mercurial  thermometer,  49?. 

Mercury,  the  metal,  208,  209,  477,  497,  PL  39. 

Pressure  of  mercury,  201. 
Mercury,  the  planet,  403,  422. 
Meridian,  83,  426,  PL  35. 
Mersenne,  316;  b.1588,  d.1648. 
Messenger,  158. 
Messier,  PL  31. 
Metacentre,  202. 
Metallic  surface,  553. 
Metals,  322,  524,  525. 
Meteorology,  544,  586. 
Meteors,  564,  565. 
Meto,  428,  454. 
Metre,  84. 
Mexicans,  74. 
Mezzotinto,  92. 
Michael  III.,  456. 
Michell,  391,  392,  440. 
Micrometer,  337,  PL  28. 
Micrometrical  scale,  PL  7. 
Microscopes,  PL  28.    Double  microscopes,  334. 

Simple  microscopes,  330.    Solar  microscopes, 

332. 

Middle  ages,  186. 
Milky  way,  391,  394,  PL  31. 
Mills,  177,  178,  244,  PL  18. 
Mineralogy,  567. 
Minerals,  565. 
Miniatures,  73. 
Mining,  175. 
Minor  scale,  308. 
Mirage,  346. 
Mirbel,  569. 
Mirror,  325,  PL  27. 
Mirrors,  331,  PL  28. 
Mists,  555. 
Mixed  gases,  470. 
Mixed  plates,  369,  PL  30. 
Mixed  pump,  254. 
Mixture,  236. 

Mixture  of  colours,  344,  345. 
Modelling,  87- 

Modulus  of  elasticity,  106,  288. 
Moeris,  181. 


Moon's  age,  429. 
Moon's  phases,  PL  34. 


Moisture,  552. 
Moivre.    See  Demoivre. 
Momentum,  41,  45,  169,  PL  2. 
Monge,  589. 
Monnier,  392. 

Monsoons,  549,  585,  PL  42,  43. 
Montaigne,  585. 
Montbret,  93. 

Montgolfier,  259,  285,  PL  23. 
Montpelier,  547- 

Moon,  356,  405,  406, 419,  423,  PL  33. 
Moon  as  causing  tides,  442. 
Moons,  405. 
I's  age 

I's  pha      , 

Moon's  surface,  PL  34. 

Mortar,  123. 

Mortar  mill,  1/7. 

Mortise,  129. 

Mosaic  work,  74. 

Moses,  74. 

Motion,  13,  PL  1.    Composition  of  motion,  18. 

Confined  motion,  32.    Measure  of  motion,  60. 

Perpetual  motion,  70.    Quantity  of  motion, 

40.    Resolution  of  motion,  19. 
Motion  of  light,  321. 
Motions  of  the  stars,  411. 
Mountainous  countries,  556. 
Mountains,  438,  PL  38. 
Mouths  of  rivers,  564. 
Mudge,  150,  151,  PL  16. 
Multiplier  of  electricity,  526,  PL  40. 
Multiplying  glass,  326,  PL  27. 
Mural  quadrant,  PL  35. 
Murray,  Lord  G.,  77- 
Muscles,  98,  578. 
Music.    History  of  music,  315. 
Musical  characters,  93. 
Musical  chord,  PL  25. 
Musical  instruments,  319. 
Musical  pen,  PL  6. 
Musical  sounds,  295. 
Musschenbroek,   117,   191,  498,  513,    585,    586, 

589;  b.1692,  d.  1761. 
Myopic  sight,  354. 


Nail,  119. 

Nairne,  559,  PL  40. 

Nairne's  machine,  534. 

Napier,  189,  458;  b.  1555,  d.  1622. 

Nativity  of  Christ,  427. 

Natural  history,  565, 582,  586. 

Natural  hygrometer,  554. 

Natural  orders  of  plants,  572. 

Natural  zero,  499,  500. 

Nature  of  light,  359. 

Nautical  almanac,  461. 

Neap  tide,  442. 

Nebula,  391,  392,  393. 

Nebula  in  Orion,  391,  PL  31. 

Nebulosity,  393. 

Needle,  583. 

Negative  electricity,  509. 

Neptunian  theory,  563. 

Nerves,  578. 

Nettis,  PL  29. 

Newcomen,  266,  279,  PL  24. 

Newton,  5,  19,  22,  28,  29,  34,  36,  43,  50,  63,  190, 
218,  279,  280,  316,  317,  323,  342,  343,  344,  359, 
360,  362,  363,  366,  368,  369  370,  371,  377,  378, 
379,  380,  381,  382,  388,  402,  409,  410,  411,  415, 
430,  435,  440,  442,  449,  453,  458,  459,  460,  461, 
466,  467,  468,  471,  472,  490,  502,  585;  b.  1642, 
d.  1727. 

Newtonian  reflector,  335. 

Newtonian  rules  of  philosophy,  12. 

Newtonian  telescope,  PL  28. 

Nicetas,  453,  456. 

Nicholson,  85,  151,  154, 174,  527,  588- 

Nicholson's  circle,  82. 

Nickel,  532. 

Night,  417. 

Nile,  557. 

Nilometer,  454. 

Nitocris,  182. 

Nitre,  486,  501. 

Nobili,  504,  505,  540. 

Nodes,  401,  PL  34. 

Nodes  of  the  planets,  PL  32. 


INDEX. 


603 


Nollet,  585  ;  b.  1700,  d.  1770. 

Nonconductors,  513. 

Noria,  250,  PI.  22. 

North,  398. 

Northern  crown,  395. 

Northern  hemisphere  warmer,  549. 

North  pole,  533. 

Norwood,  460. 

Notes  of  music,  309. 

Nucleus  of  a  comet,  407. 

Numa,  580. 

Number  of  the  stars,  389. 

Nut,  55,  PI.  5. 

Nutation,  402. 

Nutation  of  the  earth's  axis,  402,  412. 

Nutrition  of  animals,  577. 


Oblique  float  boards,  246,  247. 

Oblique  forces,  PI.  3. 

Oblique  impulse  of  fluids,  230. 

Oblique  reflection,  342. 

Obliquity  of  the  ecliptic,  412,  454. 

Observatory,  114. 

Observatory  of  Greenwich,  150,  4GO. 

Octave,  307. 

Octant,  PI.  35. 

Ocular  spectra,  357,  PI.  30. 

Oersted,  539. 

Oil  mill,  170. 

Oil  paintings,  73. 

Oil  spreading  on  water,  479. 

Oily  substances,  163. 

Olbers,  404,  462. 

Opposition,  418. 

Opposition  of  forces,  PI.  3. 

Optical  centre,  327,  352. 

Optical  instruments,  328. 

Optic  nerve,  351. 

Optics,  195,  196,  320. 

Optometer,  354. 

Orbit  of  the  sun,  398. 

Orbits  of  comets,  414. 

Orders  of  architecture,  12?. 

Orders  of  plants,  572. 

Organ,  314,  316. 

Organ  pipes,  301, 313,  314,  PI.  26. 

Orion,  395. 

Orreries,  433. 

Orthographical  projection,  89,  PL  8. 

Oscillations  of  fluids,  217. 

Osiris,  315. 

Overflowing  lamp,  PI.  21. 

Overshot  wheel,  244,  PI.  22. 

Ovid,  181. 

Oxid,  495. 

Oxygen,  340. 

Oxygen  gas,  486. 


Painting,  356. 

Palladio,  PI.  11 ;   b.  1508,  d.  1580. 

Pallas,  404,  424. 

Panorama,  356. 

Pantheon,  127,526,  PI.  12. 

Pantograph,  79,  PI.  6. 

Paper,  75,  144,  186. 

Papin,  264,  290- 

Pappus,  J85,  186;  fl.  383. 

Papyrus,  75. 

Parabola,  31,  293,  PI.  2. 

Parabolas,  PI.  10. 

Parabolic  jet,  217. 

Parabolic  orbit,  414. 

Parachutes,  233. 

Paradox.    Hydrostatic  paradox,  199. 

Parallax,  430. 

Parallax  of  the  sun,  431,  432. 

Parallel  motion,  PI.  14. 

Parallelogram,  18. 

Parallel  rulers,  78,  PI.  14. 

Pardies,  J79,  380  ;  b.  1636,  d.  1673. 

Parent,  191,  248  ;  b.  1666,  d.  1716. 

Parent's  mill,  248, 253. 

Parhelia,  347,  PI-  29. 

Paris,  356. 

Parisian  academy,  191, 192,  279,  280. 


Parker,  131. 

Partial  electricity,  509. 

Partial  reflection,  362. 

Pascal,  504  ;  b.  1623,  d.  1662. 

Passive  strength,  71,  104,  PI.  11. 

Paternoster  work,  256. 

Path  of  the  centre  of  gravity,  PI.  3. 

Path  of  the  sun,  417. 

Paths  of  the  planets,  PI.  34. 

Pear  gage,  262,  PI.  24. 

Pearson,  433. 

Pedestrian,  100. 

Pegasus  ,395,  588. 

Pemberton,  191,459. 

Pen,  72. 

Pencil,  72,  73. 

Pencil  of  light,  320,  PL  26. 

Pendulum,  34,  35,  83,  147,  PL  2,  5,     Circular 

pendulum,  36. 
Pendulums,  417,  443. 
Penetration,  111,  120,  172. 
Pennant,  586  ;  b.  1726,  d.  1798. 
Pens,  75. 

Pens  for  lines,  77. 
Penumbra,  419. 

Perception  of  external  objects,  351. 
Percussion,  171. 
Perforation  of  ajar,  517. 
Periodical  winds,  548. 
Periods  of  the  planets,  402,  PL  32. 
Periscopic  spectacles,  332. 
Permeability  of  matter,  468. 
Perpetual  motion,  70,  PL  6. 
Perrault,  157, 191 ;  b.  1613,  d.  1688. 
Perrault's  ropes,  164. 
Perseus,  394. 
Persians,  428,  456. 
Perspective,  71,  88,  PL  7,  8. 
Perturbations,  412. 
Petit,  488. 
Pfaff,  588. 

Phantasmagoria,  333,  PI.  28. 
Phases  of  planets,  418. 
Phases  of  the  moon,  419. 
Phenicians,  74. 

Pherecydes,  181;  b.  600,  d.  515,  B.C. 
Philip  III.,  460. 
Philo,  183,  185,  276. 
Philolaus,  453. 
Philosophizing,  12. 
Phosphorus,  486. 
Phosphorus  of  Bologna,  341. 
Photometers,  329,  PI.  27. 
Physical  astronomy,  387. 
Physical  optics,  340. 
Physics,  387. 
Physiology,  5?a 
Pianoforte,  311. 
Piazzi,  404,  462. 
Picard,  34,  435,  460  ;  d.  1682. 
Pictet,  289,  486,  487>  489,  552,  587- 
Piers,  126,  240. 
Pile  engine,  137,  173,  PL  1* 
Pile  of  Volta,  522,  588. 
Pin,  119. 

Pinion,  136,  PL  15. 
Pipe.    Effect  of  a  short  pipe,  212,  213.    Vertical 

pipe,  215. 

Pipes,  222,  277-    Musical  pipes,  296. 
Pipes  of  lead,  242. 
Pipes  of  pumps,  256. 
Pisces,  401. 
Pise,  123. 
Piston,  PL  28. 
Pistons,  254. 
Pitot,  243. 

Pittacus,  181 ;  b.  652,  d.  570,  B.C. 
Pixii,  541. 

Plain  astronomy,  387. 
Plane  mirror,  325. 
Planetarium,  433. 
Planetary  worlds,  422. 
Planets,  400,  PL  32. 
Planispheres,  433. 
Planks,  PL  10. 
Planoconcave  lens,  326. 
Planoconvex  lens,  326. 
Plant,  568. 
Plaster  of  Paris,  87- 
Plate  machine,  525,  PL  40. 


604  INDEX. 

Platina,  467- 

Plato,  183,  581,  682 ;  b.  429,  d.  348,  B.C. 

Pleiades,  395. 

Plempius,  489. 

Pliny,  182,  420,  442,  464,  582 ;  b.  24,  d.  79. 

Plough,  PI.  18. 

Plungers,  253,  PL  23. 

Plurality  of  worlds,  422. 

Plutarch,  183,  184,  458,  582. 

Pneumatic  equilibrium,  204,  PI.  19. 

Peneumatic  machines,  259. 

Pneumatics,  275,  276. 

Pneumatostatics,  196,  PI.  19. 

Poetry,  422. 

Polar  circles,  436. 

Polarity,  533. 

Polarization  of  heat,  505. 

Polarization  of  light,  371,  3?2,  505. 

Poleni,  280;  b.  1683,  d.  1761. 

Poles,  436. 

Pole  star,  394. 

Polished  surface,  322. 

Polishing,  176. 

Polycrates,  181. 

Polygon,  20. 

Polygraph,  76. 

Pores,  467. 

Porosity,  360. 

Porterfield,  354,  379. 

Porters,  102,  162,  PI.  17. 

Positive  electricity,  509. 

Pottery,  171. 

Pound,  96. 

Powder  mill,  177. 

Powder  proof,  103. 

Powell,  505,  506. 

Power.    Mechanical  power,  245. 

Practical  astronomy,  425. 

Precession  of  the  equinoxes,  402,  412. 

Preponderance,  66,  PI.  5,  6. 

Presbyopic  sight,  355. 

Press.    Bramah's  press,  199,  PI.  23. 

Presses,  169,  170. 

Pressure,  45. 

Pressure  of  a  fluid,  198. 

Pressure  of  earth,  124. 

Pressure  of  fluids,  PI.  19. 

Pressure  of  the  atmosphere,  207. 

Prevost,  489,  532, 545,  546, 547, 589.    B.  Prevost, 

553. 

Priestley,  381,  586;  b.  1733,  d.  1804. 
Primary  mountains,  439. 
Printing,  71,  91,  93,  188. 
Printing  from  stones,  93. 
Printing  press,  169. 
Prism,  324,  326,  343,  PL  26,  27- 
Prismatic  spectrum,  PL  29. 
Proclus,  186. 
Procyon,  395. 
Progressive  motion,  100. 
Projectiles,  17,  26,  29,  217,  PI-  2. 
Projection  of  a  sphere,  90,  PL  8. 
Projection  of  light,  361. 
Prony,  284. 
Proofs,  494. 

Propagation  of  light,  359. 
Proper  motions  of  the  stars,  392. 
Properties  of  matter,  464,  509. 
Prop  or  shore,  55,  PL  5. 
Proportional  compasses,  79,  PL  6. 
Props  of  reservoirs,  238. 
Prosperin,  408. 
Protagorides,  582. 
Ptolemaic  system,  PL  38. 
Ptolemy,  75,  3?5,  393,  401,  420,  452,  453,  454, 

455,  456  ;  fl.  160. 
Ptolemy  Philadelphus,  454. 
Ptolemy  Soter,  454. 
Pullies,  52, 159,  PL  4. 
Pulse,  220. 
Pump,  253. 
Pumping,  102. 
Pumps,  PL  23. 
Pupil,  354. 
Pyramids,  454. 
Pyrometers,  496. 
Pythagoras,   181,  182,  315,  316,   453,  458,  581; 

b.  568,  d.  497,  B.C. 
Pythagorian  system,  PL  38. 


Quadrant,  80. 

Quadrant  electrometer,  527. 

Quadrants,  429,  PL  35. 

Quarter,  95. 

Quays,  240. 

Queen  post,  130,  PL  12. 

Quiescent  space,  15. 


Radiation  of  heat,  488. 

Rafter,  113. 

Rafters  in  equilibrium,  PL  11. 

Railroads,  272. 

Rain,  556,  557- 

Rainbows,  346,  369,  PL  29,  30. 

Raising  weights,  156. 

Ramelli,  189,  256,  PL  23- 

Rammelsberg,  179. 

Ramsden,  80,  86,  97,  336,  338,  381,  461,  PI.  7,  8, 
28 ;  b.  1730,  d.  1800. 

Range  of  a  projectile,  30,  217. 

Rarefaction,  484. 

Ravenna,  450. 

Ray,  585;  b.  1628,  d.  1705. 

Ray  of  light,  320,  PL  26. 

Reaction,  42. 

Read,  558. 

Reaumur,  485,  498,  585;  b.  1683,  d.  175?. 

Reciprocal  action,  40,  42,  43. 

Reciprocal  force,  470,  PL  2. 

Recorde,  375. 

Rectification  of  motion,  134,  PL  14. 

Rectilinear  motion,  PL  1. 

Redern,  381. 

Red  light,  365. 

Red  Sea,  449. 

References,  193. 

Reflecting  surface,  325. 

Reflecting  telescopes,  334,  337,  378. 

Reflection,  62,  342,  361,  374,  PL  5,  26. 

Reflection  of  a  stone,  233. 

Reflection  of  cold,  489. 

Reflection  of  light,  321. 

Reflection  of  sound,  293,  PL  25. 

Reflection  of  waves,  219,  293. 

Refraction,  321,322,  361,  375,  430,  433,  PL  26, 

29. 

Refraction  of  crystals,  348. 
Refraction  of  the  atmosphere,  345. 
Refractive  densities,  323,  329,  375,  PL  27. 
Refrangibility  of  heat,  490. 
Refrigeration,  545. 
Regaforgan  pipe,  314,  PL  26. 
Regulation  of  force,  69. 
Regulation  of  hydraulic  forces,  241. 
Regulator,  PL  2. 
Regulus,  395. 
Reich,  440. 

Relative  motion,  PL  1. 
Remote  tide,  444. 
Removing  earth,  168. 
Removing  weights,  156,  161. 
Renaud,  279;  b.  1652,  d.  1719. 
Reproduction,  539,  566. 
Republican  calendar,  428. 
Repulsion,  58,  468,  502,  5<)3,  PL  39. 
Repulsions  of  floating  bodies,  478. 
Repulsions  of  the  electric  fluid,  508. 
Reservoirs,  238. 
Resilience,  110,  114,  482. 
Resinous  electricity,  517. 
Resistance  of  fluids,  222,  230,  PL  21. 
Resistance  of  the  air,  30,31,154,232,  260,  261, 

284. 

Resistance  to  the  tides,  444. 
Resolution  of  motion,  19. 
Respiration,  575. 
Retardation,  22. 
Retina,  351. 

Retrograde  motions,  418. 
Returning  stroke,  557- 
Return  of  light,  323. 
Revolutions  of  cords,  299. 
Revolving  doubler,  PL  40, 
Revolving  pendulums,  36,  PL  2. 
Rheita,  334,  376,  PL  28. 
Rhinland  foot,  85. 
Rhythm,  306. 
Ribaucourt,  76. 


INDEX. 


00,5 


Riccati,  300,  317- 

Richmann,  278,  580,  585  ;  d.  1753. 

Rifle  barrels,  31,  268. 

Right  ascension,  425,  430. 

Ringing,  101. 

Ringing  a  magnet,  538. 

Ring  of  Saturn,  404,  407,  458. 

Ritter,  342,  382,  490,  588. 

Rise  and  fall  of  the  tides,  446,  447. 

Rising  and  setting,  433. 

Rivers,  222,  238,  438, 563.    Tides  of  rivers,  446. 

Road.    Circular  road,  37. 

Robertson,  334. 

Roberval,  458- 

Robins,  31,  281,  284,  285 ;  b.  1707,  d.  1751. 

Robison,  22,  32,  101,  112,  192,  223,  253,  264,  285, 

291, 469,  481,  507.  538,  586  ;  b.  1739,  d.  1804. 
Rochon,  93,  490. 
Rock  salt,  504. 

Rods,  86,  PI.  9,  14.    Sounds  of  rods,  300. 
Roemer,  341,  378;  b.  1644,  d.  1710. 
Roget,  542. 
Roller,  PL  17- 
Roller  pump,  256,  PI.  23. 
Rollers,  163. 
Rolling,  PI.  2. 
Romans,  91,  186. 
Roman  year,  427- 
Rome,  547. 
Romieu,  317- 
Romme,  284. 
Roof,  55, 130,  PI.  5. 
Roofs,  PI.  13. 
Rope  making,  139. 
Rope  pump,  250,  PI.  21. 
Ropes,  140. 
Rosetta,  564 
Rosnier,  285. 
Rotation,  32,  61,  65. 
Rotation  of  billiard  balls,  PI.  5. 
Rotation  of  the  earth,  417,  548. 
Rotation  of  the  moon,  406,  414. 
Rotation  of  the  planets,  402. 
Rotation  of  the  sun,  398. 
Rotatory  motion,  PI.  5. 
Rotatory  power,  63,  PI.  2. 
Rotatory  pump,  253. 
Rowing,  101. 
Roy,  8<i. 
Royal  Institution,  131, 192,  589.    Objects  of  the 

Royal  Institution,  1. 
Royal  Society,  5,  97, 161, 190, 191,  585. 
Rudder,  249. 
Rudders,  114. 
Rudolph,  457. 
Rulers,  77. 

Rules  of  philosophy,  12. 
Ruling  machine,  91. 
Rumford.    Count  Rumford,  268,  284,  285,  329, 

485, 487,  500, 588. 
Running,  100,  PI.  9. 
Rupert.  Prince  Rupert,  256.  Prince  Rupert's 

drops,  494. 
Russell,  423. 
Rutherford,  544. 
Rutherford's  thermometer,  PI.  41. 


Sagittarius,  401. 

Sail,  PI.  22. 

Saint  Paul's  cathedral,  127. 

Saint  Pierre,  460,  461. 

Sanctorius,  147,189,498;  b.  1561,  d.  1636. 

Sap,  569. 

Saracens,  145,  187, 188. 

Saros,  452. 

Satellites,  405,  406,  PI.  33. 

Saturn,  404,  424,  PI.  33. 

Saturn's  ring,  404,  407,  458. 

Saussure,  489,  552,  554,  587. 

Sauveur,  317- 

Savery,  265,  279,  PL  24. 

Saw,  PL  4. 

Sawing?  1?5. 

Saxton,  541. 

Scale  of  heat,  496. 

Scale  of  musical  notes,  307- 

Scaliger,  429. 

Scapement,  148. 


Scapements,  PL  16. 

Scarfing,  129,  PL  13. 

Schaeffer,  189. 

Scheele,  586;  b.  1742,  d.  1786. 

Scheiner,  376 ;  b.  1573,  d.  1650. 

Schemnitz,  257,  258,  PI.  23. 

Schott,  278. 

Schroeter,  403,  PL  33. 

Scorpio,  395,  401. 

Screen  of  glass,  489. 

Screw,  55, 160,  PI.  5. 

Screw  of  Archimedes,  251,  252,  PL  22. 

Screws,  160. 

Sculling,  101. 

Sculpture,  71. 

Sea,  437,  443,  444,  546,  563. 

Sea  breezes,  550. 

Seamanship,  248. 

Seasons,  417,  PL  34. 

Secants,  82. 

Secondary  mountains,  439. 

Section  of  a  canal,  PL  21. 

Sector,  79,  PL  7. 

Seebeck,  371,  490. 

Segner,  66,  589. 

Seguin,  586. 

Self  registering  thermometers,  545. 

Semaphore,  77- 

Semimaterial  existences,  468. 

Semiramis,  182. 

Semitone,  307. 

Semivowels,  313. 

Seneca,  182,  374,  442  ;  b.  8,  d.  65. 

Sensation,  567. 

Sensation  of  colours,  345. 

Sensation  of  light,  320. 

Senses,  577. 

Sensibility  of  the  retina,  352. 

Sensible  effects  of  electricity,  519. 

Sensible  effects  of  the  celestial  motions,  415. 

Serein,  555. 

Series  of  eclipses,  420. 

Series  of  rods,  PI.  14. 

Serpent,  314. 

Serpentarius,  393,  395. 

Serpentes,  575. 

Servetus,  584. 

Serviere,  PL  23. 

S'Gravesande,  191 ;  b.  1688,  d.  1742. 

Shadow,  367,  PI.  30. 

Shaw,  566. 

Sheffield,  187. 

Shehallion,  440. 

Ship,  114,  248,  249,  PI.  22. 

Ships,  231. 

Ship's  sails,  281. 

Ship's  way,  PL  22. 

Shooting  stars,  564. 

Shore,  PL  5. 

Short,  461. 

Shot,  268. 

Shower  bellows,  263,  PL  24. 

Showers  of  stones,  562. 

Shroud,  140. 

Sidereal  day,  426. 

Signs  of  the  ecliptic,  401. 

Signs  of  the  zodiac,  451. 

Silk,  142. 

Silkworm's  thread,  104. 

Simonides,  315;  b.  579,  d.  469,  B.C. 

Simple  sounds,  295. 

Simpson,  191,  379,  545,  547 ;  b.  1711,  d.  1761. 

Sine  of  an  angle,  81. 

Single  vision,  355. 

Siphon,  215. 

Siphon  of  Hero,  145. 

Siphons,  241. 

Sirius,  391,  392,  395,  397- 

Sisson,  461. 

Six,  547,  555. 

Six's  thermometer,  544,  PI.  41. 

Size,  73,  144. 

Sky,  356,  PI.  30. 

Slider  pump,  256,  PI.  23. 

Sliding  rule,  PL  7. 

Sling,  26,  17a 

Slitting  mill,  174,  PL  18. 

Sloughing,  570. 

Sluice,  PL  21. 

Sluices,  239. 

Smeaton,  53,  60,  64,  122, 123,  129,  159,  KB,  240, 


006 


INDEX. 


245,  247,  260,  262,  278,  282,  PI.  5,  11 ;  b.  1724, 

d.  1792. 

Smeaton's  blocks,  PI.  4. 
Smith,  335,  3/9 ;  d.  l/W. 
Smith's  microscope,  335,  PI.  28. 
Smoke,  356. 
Smoke  jack,  247- 
Smoky  chimnies,  265. 
Snellius,  376  ;  b.  1591,  d.  1626. 
Snow,  348,  556,  PI.  29. 
Society  for  the  encouragement  of  arts,  192. 
Socrates,  181. 
Softness,  482. 

Solar  and  culinary  heat,  488. 
Solar  atmosphere,  PI.  31. 
Solar  day,  426. 

Solar  microscope,  332,  PI.  28. 
Solar  phosphori,  341. 
Solar  system,  397,  PL  32. 
Solar  tides,  447- 
Solidity,  480. 
Solids,  470. 

Solution  of  iron  filings,  538. 
Sorge,  317. 
Sosigenes,  455. 
Sothic  period,  452. 
Sound,  287,  503. 
Sounding  board,  311. 
Sounds  of  rods,  317. 
Sources  of  heat,  484. 
Sources  of  light,  340. 
Sources  of  motion,  68,  69,  101. 
Sources  of  sound,  295. 
South,  398. 
South  America,  74. 
South  pole,  533. 
Space,  15,  388. 

Spallanzani,  586 ;  b.  1?29,  d.  1799. 
Spark,  516,  PI.  40. 
Speaking  trumpet,  293,  294,  PI.  25. 
Specific  gravities,  236. 
Specific  gravities  of  gases,  291. 
Spectrum,  343,  PI.  29. 
Sphere,  90. 

Sphere  charged  with  electricity,  510. 
Spheres,  410. 
Spheres  connected,  510. 
Spheroid,  442. 
Spica  Virginis,  395. 
Spider's  thread,  104. 
Spider's  web,  109. 
Spinet,  311. 
Spinning,  139. 
Spinning  wheel,  187- 
Spiral  pipes,  251. 
Spiral  pump,  252,  PI.  22. 
Spirit,  544. 

Spirit  level,  81,237,  PL  21. 
Spirit  of  wine,  291,475. 
Spirit  thermometer,  497. 
Spiritual  substances,  468. 
Sponge,  479. 

Spots  of  the  sun,  398,  PL  31. 
Spring,  PL  2,  10. 
Spring  of  a  coach,  114. 
Springs,  137,  166. 
Springs  of  water,  216,  PL  20. 
Spring  steelyard,  98,  PI.  9. 
Spring  tides,  442,  447- 
Spur  wheel,  136,  PL  15. 
Squares,  78. 

Stability  of  a  balance,  PL  8. 
Stability  of  a  wedge,  119. 
Stability  of  equilibrium,  47,  198,  PI.  3. 
Stability  of  floating  bodies,  202,  PL  19. 
Stability  of  fluids,  PL  19. 
Stability  of  ships,  249. 
Stacada,  313. 
Stadium,  454. 

Stahl,  586  ;  b.  1660,  d.  1734. 
Stamping,  172. 
Standard  measures,  82. 
Standard  weights,  95. 
Stanhope,  51,  252,507,  512. 
Star  Lyra,  PI.  31. 
Stars,  356,  387,  PI.  36,  37- 
Statical  baroscopes,  PL  19. 
Statics,  71,  95. 
Statics  of  fluids,  235. 
Stationary  planets,  PL  34. 


Statuary's  compass,  PL  7- 

Steam,  205,  474. 

Steam  boat,  PI.  29. 

Steam  engine,  37,  103,  265, 282,  283,  PI.  -24. 

Steam  vessels,  271. 

Steel,  174,531. 

Steelyards,  96,  97,  PL  8,  9. 

Steelyard  with  a  crane,  161. 

Stencilling,  72. 

Stereographical  projection,  90,  PL  8. 

Stereotype  printing,  94. 

Stevin,  286. 

Stevinus,  189 ;  d.  1633. 

Stick  broken  by  a  blow,  65. 

Stiffness,  108,  482. 

Stile,  75. 

Stirrup,  302. 

Stockings,  187. 

Stodart,  174. 

Stone,  116. 

Stone  cutting,  176,  177. 

Stones  fallen,  564. 

Stones  joined,  PI.  11. 

Stopcocks,  242,  PI.  21. 

Strabo,  442. 

Strain,  130. 

Strand,  140. 

Strap,  129. 

Straps  for  beams,  PL  13. 

Straps  for  wheels,  PL  15. 

Stray  Park  engine,  269. 

Stream,  245. 

Stream  of  a  fluid,  PL  20. 

Stream  of  air,  PL  21. 

Stream  of  electricity,  517. 

Streams  of  air  from  electricity,  512. 

Strength,  110,  111,  482. 

Strength  of  a  column,  PI.  10. 

Strength  of  different  substances,  116. 

Strength  of  flood  gates,  239. 

Strength  of  joints,  PI.  13. 

Strength  of  materials,  PI.  11. 

Strength  of  muscles,  98. 

Strength  of  ropes,  141. 

Striking  a  magnet,  538. 

Striking  part,  155. 

String  of  baskets,  168. 

Stripes  of  colours,  365,  PL  30. 

Strongest  forms,  114,  115,  PL  10. 

Sturm,  291. 

Subdominant,  307. 

Subterraneous  fires,  560. 

Sucking  and  forcing  pump,  255. 

Sucking  pump,  254,  PL  23. 

Suction,  207. 

Sugar  mill,  170,  PL  18. 

Sulfate  of  soda,  493. 

Sulfuric  acid,  525. 

Sulfurets,  524,  525. 

Summer,  417,  547. 

Sun,  356,  397. 

Sun  and  planet  wheel,  137,  267- 

Sun's  motion,  411. 

Sun's  parallax,  431. 

Sun's  path,  PI.  34. 

Sun's  rays,  325,  496,  545. 

Sun's  spots,  PL  31. 

Superficial  cohesion,  475. 

Superior  tides,  446. 

Supernumerary  rainbows,  369. 

Support,  PL  3. 

Supports  for  clocks,  155. 

Surface  of  a  fluid,  197- 

Surface  of  a  liquid,  476. 

Surface  of  the  sea,  435. 

Surfaces  of  fluids,  PI.  39. 

Surging  the  messenger,  158. 

Suspension,  32. 

Suspension  of  a  weight,  PL  3. 

Swan,  394. 

Swig,  53,  PL  4. 

Swiftest  descent,  35. 

Symington,  246,  271,  PI.  24. 

Sympathetic  sounds,  301. 

Sympathy  of  clocks,  155.  , 

Synchronous  tide,  443. 

Synthetical  order,  7- 

Syrinx,  341. 

System  of  Ptolemy,  455. 

Systems  of  the  world,  PI.  38. 


INDEX. 


007 


Tackle,  PI.  4, 17- 

Tails  of  comets,  407,  PI.  33. 

Tambourine,  313. 

Tangent,  PL  1. 

Tangents,  82. 

Tarquin,  181. 

Tartalea,  189;  d.  1557- 

Tartini,  317. 

Taurus,  401. 

Taylor,  317,  379,  589. 

Teeth  of  wheels,  135,  PL  15. 

Telegraph,  76,  PL  6. 

Telescope,  375. 

Telescopes,  334-  -338,  PL  28. 

Temper,  110. 

Temperament,  309,  PI.  25. 

Temperate  zones,  436. 

Temperature,  544. 

Temperature  of  running  water,  227. 

Tempering  of  metals,  494. 

Temper  of  iron,  480. 

Tenacity,  482. 

Tenerifle,  547. 

Tenon,  129. 

Tertiary  mountains,  439. 

Terpander,  315. 

Terrella,  or  magnet  in  a  globe,  535. 

Terrestrial  magnetism,  534. 

Terrestrial  refraction,  346. 

Teylerian  machine,  525. 

Thales,  181,  182,453,  581 ;  b.  636,  d.  546,  B.C. 

Thames  tunnel,  271. 

Thawing,  546. 

Theodolite,  80. 

Theon,  463. 

Theophrastus,  582;  b.  373,  d.  288,  B.C. 

Theories  of  light,  359. 

Theory  of  electricity,  507- 

Theory  of  optics,  320. 

Thermometers,  497.  544,  584. 

Thermomultiplier,  504. 

Thermoscope,  PL  39. 

Theuth,  181. 

Thick  plates,  369,  PL  30. 

Thin  plates,  368,  PL  30. 

Thoth,  181. 

Threshing  machines,  178. 

Threshing  mill,  PI.  18. 

Throwing  a  stone,  173. 

Throwing  wheels,  250,  PL  22. 

Thunder,  557. 

Thunderstorm,  558,  559. 

Thyreoid  cartilage,  312. 

Tibiae,  315. 

Tide  machine,  258. 

Tides,  441,  PL  38. 

Tides  of  the  Atlantic,  444. 

Tie  beam,  130. 

Time,  16,  144,  426. 

Timekeepers,  144,  461. 

Timocharis,  402,  454. 

Tint,  PL  6. 

Ton,  95. 

Topham,  99. 

Torpedo,  523. 

Torre  del  Greco,  562. 

Torricelli,  207,  277,  584 ;  b.  1608,  d.  1647- 

Torricellian  vacuum,  260,  2/7. 

Torrid  zone,  436. 

Torsion,  105,  108. 

Total  reflection,  324,  362. 

Tottering  equilibrium,  PL  3. 

Toughness,  110,  482. 

Tourmalin,  371,  372,  520. 

Tournefort,  685  ;  b.  1656,  d.  1708. 

Trachea,  312. 

Tracheae  of  plants,  568. 

Trade  winds,  548,  585,  PL  42,  43. 

Transit  circle,  PL  35. 

Transit  instruments,  429,  PL  35. 

Transverse  strain,  130. 

Trevithick,  257,  267,  272. 

Triad,  307. 

Triangle,  representing  forces,  PL  3. 

Triangular  compasses,  78,  PL  6. 

TrichuVus,  566. 

Triple  stars,  393. 

Trithemius,  145. 


Trituration,  177. 

1,  18,  PL  1. 


Trochoid, 


Trombone,  314. 

Tropical  year,  427. 

Tropics,  436. 

Troughton,  PL  7,  8. 

Trumpet,  314. 

Trumpet  Marigni,  312,  PL  25. 

Tubes,  108. 

Tun,  95. 

Tuning  fork,  314,  503. 

Tuscan  column,  PL  12. 

Twilight,  418,  433,  PL  34. 

Twinkling,  389. 

Twins,  395. 

Twisted  ropes,  53. 

Twisting,  104,  108,  139. 

Tycho  Brahe,  457;  b.  1546,  d.1601. 

Tychonic  system,  PL  38. 

Tympanum,  302. 

Type  metal,  94. 


Ubaldi,  189. 

Ulloa,  284,  406 ;  b.  1716,  d.  1795. 

Ulugh  Beigh,  456. 

Umbrella,  294. 

Undershot  wheel,  245,  PL  22. 

Undulations  of  light,  365. 

Undulatory  theory  of  light,  370. 

Unequal  balance,  PL  8. 

Union,  480. 

Union  of  flexible  fibres,  138. 

Union  of  lights,  364. 

Unit  of  engine  power,  103. 

Uranus,  405. 

Uvea,  351. 


Valerius,  189. 

Valves,  242,  PL  21. 

Valves  of  canals,  240. 

Vandelli,  284. 

Van  Eyck.    See  Eyck. 

Van  Marum,  525. 

Vapour,  551,  555. 

Vapours,  205,  558. 

Vapours  negatively  electrical,  520. 

Variation  chart,  585,  PL  41,  42,  43. 

Variation  in  London  and  in  the  West  Indies 
536. 

Variation  of  the  compass,  536,  583,  585,  PL  41. 

Variations  of  temperature,  544,  545. 

Varro,  75. 

Vegetable  anatomy,  567- 

Vegetables,  566. 

Velocities  of  the  planets,  PL  32. 

Velocity,  22,  244.  Effect  of  velocity  in  overcom- 
ing strength,  111. 

Velocity  due  to  a  height,  25. 

Velocity  of  a  blast,  263. 

Velocity  of  an  impulse,  111. 

Velocity  of  descent,  33. 

Velocity  of  electricity,  516. 

Velocity  of  fluids,  211. 

Velocity  of  friction,  486- 

Velocity  of  sound,  289,  291,  292. 

Velocity  of  light,  341. 

Vena  contracta,  PI.  20.. 

Ventilation,  264. 

Venturi,  213,225,  226,  251,  PI.  20. 

Venus,  403,  418,  419, 422,  431,  PL  33. 

Vera,  PL  22. 

Vermes,  576. 

Vernier,  81,  PL  7. 

Vertical  pipe,  216,  PL  20. 

Vessel,  248. 

Vessels  of  plants,  568. 

Vesta,  400,  404. 

Vestibule,  302. 

Vesuvius,  562. 

Vibrating  cord,  PL  25. 

Vibrations,  295,  305,  PL  25. 

Vibrations  of  cords,  297. 

Vibrations  of  fluids,  217. 

Vibrations  of  heat,  502. 

Vibrations  of  sounding  bodies,  147. 

Vices,  170. 

Vielle,  312. 

Vince,  50,  117,  382. 


<)08 


INDEX. 


Vinci.    Da  Vinci,  189  ;  b.  U4.r,,  d.  1520. 

Viola  diGamba,  312. 

Violin,  312. 

Violoncello,  312. 

Viper,  575. 

Virgo,  401. 

Virtual  focus,  324. 

Virtual  image,  329,  PI.  27- 

Virtual  velocities,  56. 

Viscosity,  482. 

Vision,  350. 

Vitellio,  375;  fl.  1269. 

Vitreous  electricity,  517- 

Vitreous  humour,  351. 

Vitruvius,  145,  186,  276,  277,  PI.  22;  fl.  15,  B.C. 

Voice,  312,  PJ.  26. 

Volcanos,  560. 

Volcanos  in  the  moon,  423. 

Volta,  521,  523,  524,  528,  661,  563,  586,  587,  588, 

PI.  40. 

Voltaic  current,  539,  549. 
Voltaire.    See  194 ;  b.  1694,  d.  1778. 
Vowels,  313. 

Vox  humana  pipe,  314,  PI.  26. 
Vulcanian  theory,  563. 


Waggon  overturning,  PI.  3. 

Wain,  394. 

Walking,  100,  PI.  9. 

Walking  wheels,  160,  257- 

Wall,  122. 

Wallace,  79. 

Wallingford,  145,188;  fl.  1326. 

Wallis,  28,  190,  316 ;  b.  1616,  d.  1713. 

Walter  of  Coventry,  188;  fl.  1213. 

Waring,  192. 

Watches,  192. 

Watch  scapements,  PI.  26. 

Water,  209,  291,  323,  475,  477- 

Water  colours,  73. 

Water  in  air,  554. 

Waterloo  Bridge,  271. 

Water  mill,  103. 

Water  pipes,  241,  PL  21. 

Water  screw,  251,  PI.  22. 

Water  snail,  251. 

Waterspouts,  559. 

Water-wheels,  230,  244,  282,  PL  22. 

Water  whimsey,  157. 

Watt,  37,  51,  101,  103,  187,  192,  265,  266,  267, 

269,  282,  283,  PL  24. 

Waves,  218,  PL  20.    Combinations  of  waves,  220. 
Wax  candle,  486. 
Weather,  550. 
Weaving,  142. 
Wedge,  54,  119,  PL  4. 
Wedge  moving  in  water,  230. 
Wedges  for  stones,  PL  11. 
Wedgwood,  192,  497  ;  <L  1795. 
Weidler,  406. 
Weighing,  95. 

Weighing  machines,  97,  PI.  9. 
Weight,  12,  PL  3. 
Weight  of  air,  207. 
Weight  in  air,  29. 
Weight  of  animals,  117- 
Weights  of  clocks,  137. 
Wells,  655. 
Were,  224. 
West,  398. 
Westerly  winds,  549. 


Westgarth,  257- 

Westminster  Abbey,  188. 

Wet  leather,  482. 

Whale,  395. 

Whalebone  hygrometer,  554. 

Wheat,  95. 

Wheel,  PL  1,  14. 

Wheel  and  axis,  51,  PL  3. 

Wheel  carriages,  164,  PL  18. 

Wheel  cutting  machine,  137. 

Wheelcutters,  PL  15. 

Wheel  of  Orfyreus,  PL  6. 

Wheels,  164,  165,  166. 

Wheels  and  pinions,  52. 

Wheels  with  straps,  PL  15. 

Wheelways  of  iron,  167- 

Wheelwork,  134. 

Whimsey,  157. 

Whip,  174. 

Whirling  table,  27,  198,  PL  1. 

Whirlpool,  216. 

Whispering  gallery,  294. 

Whistling,  314. 

Whitehurst,  85,  145, 146,  259. 

White  light,  342. 

White's  crane,  161,  PL  17- 

Wilfrid,  186. 

Wilke,  586. 

Wilkins,  285 ;  b.  1614,  d.  1672. 

William  of  Sens,  188. 

William  IV.,  457. 

Willughby,  585  ;  b.  1635,  d.  1672. 

Wilson,  399,  525,  559,  PL  31. 

Winch,  101,  134,  157,  PL  3. 

Wind,  246,  550. 

Wind  and  water,  246. 

Wind  gages,  243. 

Windmills,  103,  246,  247,  277,281. 

Winds,  544,  548. 

W  inkier,  585,  586;  b.  1703,  d.  1770. 

Winter,  417,  547. 

Wire,  187. 

Wire  drawing,  171. 

Wirtz,  252,  253,  PL  22. 

Wollaston.    Dr.  Wollaston,  329,  331,  332,  342, 

343,  346,  348,  349,  382,  490,  588,   PL  27.  29,  39. 

Rev.F.  Wollaston,  PL  35. 
Woltman,  PL  22. 
Wood,  116. 
Wood  cuts,  91. 
Wooden  bridges,  131,  PL  14. 
Wool,  142. 

Woollen  manufactures,  186. 
Worcester.   Marquis  of  Worcester,  265, 278, 279 ; 

d.  1667. 

Work  of  a  labourer,  101,  178,  253. 
Wren,  190,  459,  461 ;  b.  1632,  d.  1723. 
Writing,  71,  74,  75. 
Wunsch,  292. 


York  Minster,  188. 
Young.    M.  Young,  213. 
Young,  Dr.  T.,  270,  370,  371. 


Zenith  sectors,  429,  PL  35. 

Zero,  500. 

Zodiacal  light,  399,  PL  31. 

Zones,  436. 

Zucchius,  381. 

Zuyder  Zee,  564. 


THE   END. 


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