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OS- 


REESE    LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


Received 


Accessions  No. 


C^. 


!. ^^k^^^ 


Shelf  No.. ^ 


COURSE  OF  LECTURES 


ON 


NATURAL  PHILOSOPHY 

AND  THE 

MECHANICAL  ARTS. 

BY  THOMAS  VOUNG,  M.D. 

\* 
FOR.  SEC.  K.  S.   F.L.S.  MEMBER  OF  EMMANUEL  COLLEGE,  CAMBRIDGE, 
AND   LATE   PROFESSOR  OF  NATURAL  PHILOSOPHY  IN  THE 
ROYAL    INSTITUTION    OF    GREAT    BRITAIN 

IN  TWO  VOLUxMES. 
VOLUME  L 


J,t)NIVElsj^    ' 


LONDON: 


PRINTED  FOR  JOSEPH  JOHNSON,    ST.   PAUL's  CHURCH  YARD, 

BY  WILLIAM  SAVAGE,    BEDFORD  BURY. 

1807. 


^<:)  2^ 


*f7 


J' 


i\ 


UU'i 


^ 


f7 


a-** 


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TO  THE  RIGHT  HONOURABLE  THOMAS  GRENVILLE 

A  MAN  EQUALLY  ESTEEMED  FOR  HIS  PRIVATE  VIRTUES 

AND  RESPECTED  FOR  HIS  DISTINGUISHED  TALENTS 

WHO  LATELY  PRESIDED 

AS  FIRST  LORD  OF  THE  ADMIRALTY 

OVER  THAT  DEPARTMENT  OF  THE  PUBLIC  SERVICE 

TO  WHICH  THE  PRINCIPLES  OF  MECHANICAL  SCIENCE 

MAY  WITH  THE  GREATEST  NATIONAL  BENEFIT 

BE  PRACTICALLY  APPLIED 

THIS  WORK  IS  DEDICATED 

BY  THE  AUTHOR. 


PREFACE. 


Having  undertaken  to  prepare  a  course  of  lectures  on  natural 
philosophy,  to  be  delivered  in  the  theatre  of  the  Ro3'.al  Institution,  I 
thought  that  the  plan  of  the  Institution  required  something  more  than 
a  mere  compilation  from  the  elementary  works  at  present  existing;  and 
that  it  was  my  duty  to  collect  from  oi'iginal  authors,  to  examine  with 
attention,  and  to  digest  into  one  system,  every  thing  relating  to  the 
principles  of  the  mechanical  sciences,  that  could  tend  to  the  improve-  . 
ment  of  the  arts  subservient  to  the  conveniences  of  life.  I  found  also, 
in  delivering  the  lectures,  that  it  was  most  eligible  to  conmiit  to  writ- 
ing, 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  uninterruptedly,  and  to  repeat 
the  explanation  during  its  exhibition.  Hence  it  became  necessary  th^t 
the  Avritten  lectures  should  be  as  clearly  and  copiously  expressed,  and 
in  a  language  as  much  adapted  to  the  comprehension  of  a  mixed  audi- 
ence, as  the  nature  of  the  investigations  would  allow ;  and  that  each 
experiment,  which  was  to  be  performed,  should  also  be  minutely  de- 
scribed in  them.  If  therefore  there  was  any  novelty  either  in  the  mat- 
ter 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  pubUcation. 

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 


VI  PREFACE. 

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  en- 
tirely with  this  view,  making  notes  of  the  principal  subjects  discussed 
in  them,  and  examining  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  informa- 
tion, constituted  no  small  part  of  the  collection,  which  was  thus  to  be 
reduced  into  one  body  of  science. 

'  With  the  addition  of  the  materials  acquired  in  making  this  compi- 
lation, and  of  the  results  of  many  original  investigations,  to  which 
they  had  given  rise,  it  became  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  discover  and  to  correct  every  obscurity  of  expression  or 
of  argument.  Drawings  were  also  to  be  made,  for  representing  to  the 
reader  the  apparatus  and  experiments  exhibited  at  the  time  of  deliver- 
ing the  lectures,  for  showing  the  construction  of  a  variety  of  machines 
and  instruments  connected  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  reason- 
ing, but  is  referred,  at  the  end  of  a  paragraph,  to  a  plate,  which  has 
always  a  sufficient  explanation  on  the  opposite  page.  .  >: 


PREFACE.  VH 

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  inclination  to  study  the  whole.  To  such  it  may  be 
desirable  to  have  those  subjects  pointed  out,  which  appear  to  the  au- 
thor to  be  the  most  deserving  of  their  notice. 

The  fundamental  doctrines  of  motion  have,  in  the  first  place,  been 
more  immediately  referred  to  axioms  simply  mathematical,  than  has 
hitherto  been  usual;  and  the  apphcation  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 
inunediate  importance  to  the  architect  and  to  the  engineer,  and  which 
appear  to  contradict  the  results  of  some  very  elaborate  calculations. 

The  theory  of  waves  has  been  much  simplified,  and  somewhat  ex- 
tended, 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  prin- 
ciple of  a  velocity,  corresponding  to  half  the  height  of  a  certain  modu- 
lus, being  shown  to  be  applicable  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  gene- 
ral 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 


VIU  PREFACE. 

the  images,  formed  by  lenses  and  mirrors,  has  been  correGtly  investi- 
gated, and  thcs  inaccuracy  of  some  former  Estimations  has  been  de- 
monstrated. 

In  the  department  of  physical  optics,  the  phenomena  of  halos  and 
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  distances  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  satisfacto- 
rily removes  almost  every  difficulty  that  has  hitherto  attended  the 
subject. 

I'he  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  assump- 
tions are  more  universally  applicable   to  the  facts,  than  those  which 
that  justly  celebrated  mathematician  has  employed.     I  have  also  at- 
tempted to  throw  some  new  light  on  the  general  properties  of  matter 
in  other  forms  :  and  on  the  doctrine  of  heat,  which  is  materially  con- 
cerned in  them  ;  and  to  deduce  some  useful  conclusions  from  a  com- 
parison of  various  experiments  on  the  elasticity  of  steam,  on  evapora- 
tion, and  on  the  indications  of  hygrometers.     I  have  enumerated,  in 
a  compendious  and  systematical  form,  the  principal  facts  which  have 


PREPACEv  IX 

%een  discovered  with  respect  to  galvanic  electricity  ,•  and  I  have  for- 
tunately been  able  to  profit  by  Mr.  Davy's  most  important  experi- 
ments, which  have  lately  been  communicated  to  the  Royal  Society, 
and  which  have  already  given  to  this  branch  of  science  a  much 
greater  perfection,  and  a  far  greater  extent,  than  it  before  possessed. 
The  historical  part  of  the  work  can  scarcely  be  called  new,  but  several 
of  the  circumstances,  Avhich  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 
examination  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  carpentry,  and  on  the  firmness  of  wedges  ;  and  an 
easy  mode  of  forming  a  kirb  roof:  for  the  purposes  of  machinery  of 
different  kinds,  an  arrangement  of  bars  for  obtaining  rectilinear  mo- 
tion ;  an  inquiry  into  the  most  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  fric- 
tion ;  a  chronometer  for  measuring  minute  portions  of  time  ;  a  clock 
«capement ;  a  calculation  of  the  effect  of  temperature  on  steel  springs; 
an  easy  determination  of  the  best  line  of  draught  for  a  carriage  ;  a« 
VOL.  I.  b 


X  PREFACE. 

investigation  of  the  resistance  to  be  overcome  by  a  wheel  or  roller  ? 
and  an  estimation  of  the  ultimate  pressure  produced  by  a  blow. 

In  the  hydraulic  and  optical  part,  may  be  enumerated  an  over- 
flowing lamp  ;  a  simplification  of  the  rules  for  finding  the  velocity  of 
running  water  ;  remarks  on  the  application  of  force  to  hydraulic  ma- 
chines ;  a  mode  of  letting  out  air  from  water  pipes  ;  an  analysis  of 
the  human  voice;  and  some  arrangements  for^olar  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  com- 
pass, 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  Philosophi- 
cal Transactions  and  elsewhere,  and  which  are  now  reprinted  with  cor- 
rections and  additions ;  others  are  summarily  investigated  in  the  ma- 
thematical elements,  which  form  a  part  of  the  second  volume,  or  in 
the  remarks,  which  are  inserted,  in  their  proper  places,  iatlie  catalogue 
of  references. 

The  arrangement  of  the  whole  work  is  probably  dififerent  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- 


PREFACE.  XI 

value,  especially  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  atford  them. 

It  will  not  be  thought  surprising,  that  the  execution  of  this  plan, 
allowino-  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  publica- 
tion of  the  work.  Some  part  of  it  is  in  its  nature  incapable  of  perma- 
nent perfection,  since  the  catalogue  must  require  to  be  continually  ex- 
tended 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  tolera- 
bly commensurate  to  the  state  of  the  sciences  for  a  much  longer  pe- 
riod; since,  in  investigations  so  intimately  connected  with  mathemati- 
cal principles,  the  essential  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  con- 
tains, 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  refer- 
ences 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 
observe,  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 


Xii  PREFACE. 


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  depart- 
ment of  medical  knowledge:  this  work  will  not,  however,  be  speedily 
ready  for  publication ;  it  will  be  comparatively  more  concise  than  thesa 
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. 


Wclbeck  Street, 
OOtb  March,    180?. 


CONTENTS. 


PART  THE   FIRST.    MECHANICS. 


Lecture  i.     Introduction ;    Page  1. 

Objects  of  the  Uoyal  Institution;  1.  Dissemina- 
tion of  eleraentary  knowledge  ;  2.  Education  of  fe- 
males ;  Theory  of  practical  mechanics,  and  of  manu- 
factures; 3.  Simplicity  of  useful  theory;  4.  Diffi- 
culty of  making  improvements;  Repository  of  the  In- 
stitution; Library;  Journals;  5.  Nature  of  the  lec- 
tures; Merits  of  En<;lish  philosophers;  6.  Delivery 
of  the  lectures;  7.  General  view;  8.  Division  of 
the  lectures;  Synthetical  metliod;  9..  14.  Induction; 
Causatiop ;  15.  Erroneous  inductions ;  10.  Newtonian 
rules  of  philosophizing;  Their  insufficiency;  17. 

Lectuhe  II.     On  motion  ;    18. 

Definition  of  motion;  18.  Absolute  and  relative 
motion  ;  All  motion  relative ;  19.  Quiescent  space ; 
Direction  of  motion;  20.  Laws  of  motion;  21.  Time; 
■  32.  Composition  of  motion;  Space  in  motion;  23. 
Result  of  two  motions ;  24.  Resolution  of  motion; 
25.     General  result  of  a  number  of  motions;  2(5. 

Lectuue  hi.  On  accelerating  forces; 

2.7. 

Definition  of  force;  27.  Action  of  force;  38.  Ac- 
celeration and  retardation;  Velocity;  29.  Uniform 
force;  Gravitation;  Laws  of  falling  bodits;  Atwood's 
machine;  30.  Space  described;  Law  of  Galileo; 
31.  General  law  of  velocities;  Ascent;  Velocity  due 
to  a  height;  32. 

Lecture  iv.     On  deflective  forces; 
33. 

Centrifugal  force;  Sling;  S.*?.  Motion  of  a  hoop; 
Whirling  table;  34.  Laws  of  central  forces;  35. 
Keplerian  laws;  36.  Ellipsis;  Projectiles;  37.  Re- 
solution of  oblique  motion;  38.  Horizontal  range; 
Best  elevation ;  Parabolic  path ;  39.  Practice  of  gui> 
Hery;  Experiments  of  Robins;  40,41. 
3 


Lecture  v.     On   confined  motion; 

42. 

Motion  limited  by  suspension,  or  by  a  smooth  sur-- 
face;  Effect  of  friction  and  of  rotatory  motion;  In- 
clined plane;  42.  Descent  in  the  chords  of  a  circle  ;. 
Velocity  of  descent;  43.  Ascending  force;  Energy; 
Cycloidal  pendulum;  44.  Laws  of  pendulums;  45. 
Swiftest  descent;  Circular  pendulums,  40.  Pendu- 
lums with  resistance;  Revolving  pendulums ;  Corapo-- 
sition  of  vibrations;  Regulator  for  steam  engines;  47» 
Circular  road;  Principle  of  the  least  action;  48,49. 

Lecture  vi.    On  the  motions  of  sim- 
ple masses ;  60. 

Definition  of  a  moveable  body,  without  regard  to  its- 
extension;  50.  Inertia;  Centre  of  inertia;  Its  pro- 
perties; 51.  Reciprocal  forces;  Quantity  of  motion;. 
52.  Momentum  ;  Centre  of  inertia  of  a  system ;  53. 
Motion  of  the  centre  of  inertia ;  54.  Action  and  re- 
action; Newton's  illustrations;  55.  Magnitude  of  re- 
ciprocal forces;  50.  Fall  of  a  feather  and  of  a  piece 
of  gold;  Lucretius;  Relation  between  forces  and  dis- 
tances; 57.  Displacement  of  the  earth  by  the  effect 
of  a  machine;  58. 

Lecture  vii.    On  pressure  and  equi- 
librium ;  59. 

Pressure,  a  force  couuteraoted ;  Pressure  and  mo- 
mentum incommensurable ;  59.  Laws  of  pressure  in- 
cluded in  those  of  motion;  Opposition  of  pressures; 
60.  Equilibrium  of  meckanical  po.wers ;  Centre  of 
gravity;  61.  Stability  of  equilibrium;  62.  Stabihty 
independent  of  equilibrium ;  63.  Situation  and  mo- 
tions of  tlie  centre  of  gravity  of  animals;  64.  Levers 
of  two  kinds;  Fundamental  property  of  the  lever;  65.. 
Series  of  levers ;  Bent  levers ;  Oblique  levers ;  66, 
^Ylle€l  and  axis;  Wheels  and  pinion* ;  Double  axis; 


XIV 


COKTENTS. 


^7.  Pullies;  68.  Blocks;  Smeaton's  pulUes;  69. 
Oblique  ropes ;  Inclined  plane ;  70.  Wedges;  Props,  or 
shores;  71.  Screws;  Nuts;  Hunter's  screw ;  72.  De- 
termination of  mechanical  power  from  virtual  veloci- 
ties ;  73,  74. 

Lecture  vlii.     On  collision  ;  75. 

Motions  of  various  bodies  acting  reciprocally; 
Elastic  bodies;  75.  Nature  of  repulsion;  Experiment  on 
nn  ivory  ball ;  Apparatus  for  experiments  on  collision; 
76.  Inelastic  bodies;  Energy;  78.  Measure  of  force  ; 
llelation  of  labour  to  energy;  79.  Preservation  of 
energy;  or  of  ascending  force;  Effect  of  a  blow;  30. 
Rotation;  Billiards;  Reflection;  81,82. 

Lecture  ix.  On  the  motions  of  con- 
nected bodies ;   83, 

Rotatory  power ;  83.  Consideration  of  the  square  of 
the  velocity  ;  Smeaton's  apparatus  ;  Centre  of  gyration; 
84.  Centre  of  percussion  and  of  oscillation ;  Free  ro- 
tation ;  85.  See  corrections.  Motion  of  a  stick  broken 
by  a  blow;  86.  Preponderance;  Greatest  effect  of 
machines ;  Experiments ;  87, 88.  Cautions  with  regard 
to  the  construction  of  machines ;  89.  Comparison  of 
animal  with  inanimate  force;  90.  Regulation  of  force  ; 
Small  momentum  of  machines;  Impossibility  of  a 
perpetual  motion ;  91,92. 

Lecture  x.     On  drawing,  writing, 
and  measuring ;  93. 

Subjects  preliminary  to  the  consideration  of  prac- 
tical mechanics;  Instrumental  geometry;  Statics;  Pas- 
sive strength ;  Friction;  93.  Drawing;  Outline;  Pen; 
Pencil;  Chalks;  94.  Crayons;  Indian  ink;  Water 
colours;  Body  colours;  95.  Miniatures;  Distemper; 
Fresco;  Oil;  96.  Encaustic  paintings;  Enamel;  Mo- 
saic work;  Writing;  97.  Materials  for  writing;  98. 
Pens;  Inks;  Use  of  coloured  inks  for  denoting  num- 
bers; 99.  Polygraph;  Telegraph;  Geometrical  in- 
struments; Rulers;  100.  Compasses;  Flexible  rul- 
ers; 101.  Squares;  Triangular  compas.ses;  Parallel 
rulers;  Marquois's  scales;  102.  Pantograph;  Pro- 
portional compasses;  103.  Sector;  Measurement  of 
angles;  104.  Theodolites ;  Quadrants;  Dividing  engine; 
Vernier;  Levelling;  105.  Sines  of  angles;  106.  Gun- 
ter's  scale ;  Nicholson's  circle ;  Dendrometer;  Arith- 
metical machines;  Standard  measures;  Quotation 
from  Laplace;   107.    New  measures;   Decimal  divi- 


sions; 108.  Length  of  the  pendulum,  Mid  of  the  tne- 
ridian  of  the  earth;  109.  Measure^f  time ;  Objec- 
tions; 110.  Comparison  of  measures!  Instruments  for 
measuring;  111.  Micrometrical  scales;  Log  lines;  11*. 

Lecture  xx.  On  modelling,  per- 
spective, engraving,  and  print- 
ing;  113. 

Copying  a  statue ;  Modelling;  Casting;  113.  Per- 
spective; Mechanical  perspective ;  114.  Geometri- 
ci>l  perspective;  115.  Orthographical  projection; 
116;  Projections  of  a  sphere;  117.  Invention  of  en- 
graving; Woodcuts;  118.  Mode  of  engraving;  Rul- 
ing; Mczzotinto;  Etching;  119.  Aqua  tinta;  120. 
Musical  characters ;  Printing;  Copying  letters ;  Prmt- 
ing  from  stones;  121.  Letterpress ;  Stereotype  print- 
ing; 122. 

Lecture  xii.     On  statics;    123. 

Weighing;  123.  English  and  French  weights ;  Ba- 
lances; 124.  False  balances;  125.  Weighing  ma- 
chines; Steelyards;  Bent  lever  balances;  126.  Spring 
steelyard;  Dynamometer;  127.  Animal t  actions ; 
Strength  of  muscles;  128.  Instances  of  strength; 
Progressive  motion  ;  129.  Running ;  Pulling ;  130. 
Sources  of  motion;  Work  of  a  labouring  man;  131. 
Temporary  exertions;  Horses;  132.  Wind;  Water; 
Steam;  133.  Gunpowder;  Measurement  of  small 
forces;  134. 

Lecture  xiii.     On  passive  strength 
and  friction ;    135. 

Immediate  effects  of  force  on  a  solid ;  135.  Exten- 
sion and  compression;  Rigidity;  136.  Measure  of 
elasticity ;  137.  Detrusion  ;  Lateral  adhesion  ;  Flex- 
ure; 138.  Cause  of  irregularities;  Stiffness;  139^ 
Stiffness  of  beams;  Hollow  beams;  Torsion;  140. 
Alteration;  Ductility;  141.  Temper  of  metals; 
Toughness;  Britileness;  142.  Fracture;  Strength; 
Resilience;  Effect  of  velocity ;  143.  Limit  of  strength 
or  resilience ;  144.  Qualities  of  natural  bodies;  Frac- 
ture by  simple  compression ;  145.  Strength  of  lateral 
adhesion  ;  Transverse  force ;  146.  Fracture  by  flex- 
ure; Comparative  strength  and  resilience;  14T. 
Uses  of  resistonces  of  different  kinds;  Coach  springs; 
148.  Comparison  of  direct  and  transverse  strength ; 
Beam  cut  out  of  a  tree ;  Hollow  masts;  149.  Strong- 
est forms  of  beams;    150.     Machine  for  measuring 


CONTENTS. 


XV 


jtrength ;  Strengtk  of  different  substances,  151.  In- 
convenience of  bulk  ;  Friction ;  Lateral  adhesion ; 
153.  Uniformity  of  friction,  153.  Usual  magnitude  of 
friction;  Best  direction  for  draught;  154.  Stability  of 
a  wedge  or  nail ;  155.  Resistance  lo  penetration ;  156. 

Lecture  xiv.     On  architecture  and 
carpentry ;   157. 

Architecture;  Form  of  a  column;  157.  Eddystone 
lighthouse;  158.  Wall;  159.  Joints;  Mortar;  Arch; 
160.  Oblique  pressure;  of  earth;  161.  Bridge;  162. 
Flat  arch;  Horizontal  thrust;  Piers;  163.  Black- 
friars  bridge ;  Dome  ;  164.  St.  Paul's  cathedral ;  Pan- 
theon; Orders  of  architecture;  165.  Gothic  architec- 
ture ;  Carpentry;  Joints;  166.  Scarfing  ;16T.  Jog- 
gles; Tenons;  Mortises;  Straps;  168.  Inconveni- 
ence of  transverse  strains;  Roofs;  169.  Kirb  roof ; 
Height  of  a  roof;  170.  Wooden  bridges;  Centres  of 
bridges;  Furniture;  Parker's  gates;  171. 

Lecture  xv.     On  machinerj';   172. 

Application  of  force;  172.  Levers;  Connected 
rods;  Hooke's  joint ;  Cranks;  173.  Winches;  Rec- 
tification of  circular  motion;  174.  Wlieelwork ; 
175.  Teeth  of  wheels ;  176.  Kinds  of  wheels;  177. 
Eccentric  wheels  ;  Sun  and  planet  wheels ;  Construc- 
tion of  wheels;  Weights  and  springs;  178.  Fly 
wheels;  Air  vessels;  179. 

Lecture    xvi.     On    the    union    of 
flexible  fibres  j   180. 

Chain  ;  Union  by  means  of  adhesion  ;  Friction  of  a 
rope  on  a  cylinder;  180.  Twisting;  Spinning;  Rope- 
making;  181.  Materials  of  ropes;  182.  Hemp;  Flax; 
183.  Cotton;  Silk;  184.  Wool;  Weaving;  185. 
Crape  ;  Cloth  ;  Felts;  136.     Hats;  Paper;  187. 

Lecture  XVII.  OnTimekeepers;  18S. 

Clepsydrae;  188.  Clocks;  Fly  clocks;  189.  Ba- 
lances; Chronometer  with  a  revolving  pendulum; 
190.  Measuremcntof  minute  intervals  of  time;  Pen- 
dulum; Balance  spring;  191.  Principal  requisites  of 
a  timekeeper;  Sustaining  force;  192.  Equalisation  of 
the  force;  Intermediate  spring  or  wheel;  Scapemcnt; 
Crank ;  193.  Crutch  scapement;  Common,  watch 
scapement ;  194.  Dead  beat  scapement  and  horizon- 
tal watch;  Friction  of  scapcments  ;  195.  See  correc- 
tions. Duplex  scapement;  Comma  scapement; 
Scapemcnts  of  Harrison,  Mudge,  Haley,  Cumming, 
and  Nicholson;  196.  Scapcments  of  Arnold  and 
Earnsliaw;  Isoclironism  of  vibrations ;  197.     Proper- 


ties of  springs,  198.  Expansion  of  pendulums  ;  Com- 
pensations for  clocks;  199.  Compensations  for 
watches;  200.  Resistance  of  the  air;  Striking  part ; 
201.  Supports  of  clocks ;  Mutual  influence  of  two 
clocks ;  202. 

Lecture  xviii.     On  raising  and  re- 
moving weights;  203. 

Counteraction  of  gravitation ;  Levers:  203.  Per- 
rault's  lever;  Axis  with  a  winch;  204.  Water  whim- 
sey;  Gin;  Capstan;  205.  Double  capstan;  Wheel- 
work;  String  of  buckets;  PuUies;  206.  Inclined 
plane;  Duke  of  Bcidgwater's  canal;  207.  Screws; 
Cranes ;  208.  Walking  wheels  ;  White's  crane  ;  209  ; 
Weighing  cranes  ;  Lewis;  Counterpoise  for  a  chain  ; 
Removing  weights ;  Porters;  210.  Distribution  of 
weight ;  211.  Simple  dray  ;  Effect  of  agitation ;  Oily 
substances;  212.  Rollers;  Friction  wheels ;  2 13.  Per- 
rault's  ropes;  Wheels  of  carriages;  214.  Magnitude 
of  wheels;  215.  Line  ofdraught;  Conical  wheels  ;  216  ; 
Effect  of  springs ;  217.  Attachment  of  horses  ;  Wheel 
ways;    218;  String  of  baskets  or  carts;  219. 

Lecture  xix.     On  modes  of  chang- 
ing the  forms  of  bodies ;  220. 

Compression;  Presses;  Effect  of  momentum;  220. 
Printing  press;  Sugar  mill;  221.  Oil  mills;  Ilam- 
meiing;  Ilydrostalic  press;  Extension;  Laminat- 
ing machine;  Glazier's  vice;  222.  Wire  drawing; 
Pottery;  Glassblowing;  Percussion;  223.  Forges; 
Goldbeating  ;  Coining;  Stamping;  Penetration;  224; 
Pile  driving  engine;  225.  Sling;  Bow  and  arrow ;  22S. 
Whip;  Division;  Cutting  instruments;  Slitting  milt ; 
227.  Lathes ;  Boring ;  228.  Agricultural  instru- 
ments; Mining;  Sawing;  229.  Stonecutting;  Grind- 
ing; 230.  Polishing;  231.  Trituration;  Powder 
mills;  Agitation;  Threshing  machines ;  232.  Corn 
mills;  933.  Kneading;  Levigating;  Demolition; 
Bolt  drawer ;  234.     Burning ;  -Blasting  ;  235. 

Lecture  XX.    On  the  history  of  me- 
chanics ;  236,. 

Origin  of  the  Grecian  learning  ir»  Egypt;  Tliale?  t 
230.  Ionian  school ;  Italiaivschool ;  Pythagoras  ;  237 ; 
Demooritus  ;  Invention  of  the  arch  ;  238.  See  correc- 
tions. Archytas  and  Eudoxus;  Aristotle;  Foundation 
of  Alexandria;  239.  Epicurus;  Archimedes;  240. 
Siege  of  Syracuse ;  241.  Athenaeus;  Ctesibius;  249. 
Vitruvius;  Middle  ages;  243.  British  manufactures ; 
244.     Anglonorman  atid  Gothic  architecture;    245, 


XVI 


CONTENTS. 


Roger  Bacon;  Clocks ;  Engrnving  and  printing;  246. 
Leonardo  da  Vinci;  Bacon  LordVerulam;  Galileo; 
Napier;  247.  Laws  of  collision;  Hooke;  Barrow; 
Newton;  248.    FoUowen  of  Newton ;  249.    Modern 


matliematiclans  and  mechanics;  250.  Timekeepers  4 
Journals;  Royal  Institution  ;  251.  Future  prospects; 
Use  of  a.  catalogue  of  references;  252.  Table  of  the 
chronology  of  mathematicians  and  mechanics;  253. 


PART  THE   SECOND,    HYDRODYNAMICS. 


Lecture  xxi.   On  hydrostatics ;  257. 

Hydrodynamics  more  dependent  on  experiment  than 
mechanics;  257.  Division  of  the  subject  into  Hy- 
draulics, Acustics  and  Optics;  258.  Hydrostatics; 
Definition  of  a  fluid  and  a  liquid;  259.  Surface  of  a 
gravitating  fluid  horizontal;  260.  Surface  of  a  re- 
volving fluid;  Pressure  of  a  fluid;  261.  Magnitude 
of  hydrostatic  pressure ;  262.  Hydrostatic  paradox ; 
J63.  Blowing  with  the  mouth  and  lungs;  Pressure 
on  the  bank  of  a  river ;  264.  Pressure  on  a  concave 
surface ;  Pressure  of  diflferent  fluids ;  Equilibrium  of 
fluids  with  solids  ;  265.  Floating  bodies ;  2C6.  Sta- 
biUty  and  oscillations  of  floating  bodies;  Buoyancy; 
267.  Bodies  falling  in  fluids;  Hooke's  hemisphere; 
Flexible  vessels  ;  268,  269. 

Lecture  xxii.   On  pneumatic  equili- 
brium; 270. 

Properties  of  tlie  air,  and  of  gases ;  Mercurial  co- 
lumn; 270.  Steams  and  vapours;  Weight  of  the  air  ; 
STl.'.  Experiments  with  the  air  pump;  Constitution 
of  the  atmosphere;  272.  See  Corrections.  Measure- 
ment of  heights;  Ascent  of  a  balloon-;  Pressure  of 
the  atmosphere;  273.  Magdeburg  hemispheres ;  Na- 
ture of  suction;  274.  Barometers;  275.  Compres- 
sibility of  liquids;  276. 

Lecture  xxiii.     On  the  theory  of 

hydraulics;  277- 

General  principle  of  ascending  force  ;  277.  Ber- 
•nouUi's  inferences;  278.  ^'elocity  of  a  jet  of  a  fluid ; 
Ajutages  of  different  kinds;  279.  Contraction  of  a 
jet;  Effect  of  a  short  pipe;  280.  Diverging  pipe; 
Experiments  of  Bernoulli,  Venturi,  and  Matthew 
Young;  281.  Discharge  through  large  apertures; 
Vessels  emptying  themselves ;  282.  Lodss;  Siphons; 
983.  Discharge  through  a  vertical  pipe;  284.  Ex- 
planation; Limit  of  velocity;  Whirlpool;  285.  In- 
termitting springs;  Ascending  jets;  286.  Oscilla- 
tions of  fluids  ;  Waves;  287.  Reflection  of  waves ; 
288;  Height  of  waves;  Experimental  exhibition  of 
waves;  289.  Divergence  of  waves;  Combinations  of 
waves;  Applications;  290.  Elastic  pipes;  Circula- 
tion of  the  blood;  29  L 


Lecture  xxiv.    On  tlic  friction  of 
fluids;  292. 

Experiments  of  Du  Buat;  Motions  of  rivers;  29*. 
Friction  and  resist;mce;  293.  Examples  of  the  velo- 
city of-  rivers;  Velocity  at  different  depths;  294. 
Weres;  295.  Changes  and  flexures  of  rivers;  Late- 
ral friction;  290.  Ven|uri's  experiments;  Ball  sup- 
ported by  a  jet;  297.  Discharge  of  long  pipes;  Bent 
pipes;  298.  Dilatations  of  pipes ;  Effect  of  tempera- 
ture; 299. 

Lecture  xxv.     On  hydraulic  pres-. 
sure;   300.' 

Pressure  of  fluids  in  motion;  300.  Counterprcs- 
sure ;  Magnitude  of  the  pressure  and  impulse  of  fluids; 
301.  Laws  of  hydraulic  pressure;  Particular  case  of 
■water  wheels;  Oblique  impulse;  302.  Distribution 
of  pressure;  303.  Elevation  and  depression  produced 
by  the  motion  of  a  floating  body;  Form  of  a  ship> 
Body  moving  below  the  surface;  304.  Convex  sup- 
faces;  Hydraulic  pressure  of  the  air;  305.  Concave 
surfaces;  Great  effect  of  an  increase  of  velocity; 
S06.     Reflection  of  a  ball  or  stone ;  307. 

Lecture  xxvr.  On  hydrostatic  in- 
struments, and  hydraulic  archi- 
tecture ;   308. 

Statics  and  architecture  of  fluids;  Hydrostatic  ba- 
lance; 308.  Hydrometer;  Glass  globules;  309.  Spe- 
cific gravities  of  particular  substances;  Mixtures; 
Spirit  level;  310.  Hydrostatic  lamps;  3]1.  Fjo- 
bmikments;  Dil^es:  Rivers;  312.  Reservoirs;  Flood 
gates;  313.  .  Strength  of  sluices  and  flood  gates; 
Friction;  314.     Canals;  Pirrs;  Harbours;  315. 

Lecture  xxvir.  On  the  regulation 
of  hydraulic  forces;  316. 

Machinery  of  fluids;  Watcrpipes;  Siphons;  310. 
Stopcocks  and  valves;  317.  Pitol's  tube ;  Hydromc" 
trie  fly;  Captain  Hamilton's  hydraulic  register;  318. 
Motions  of  the  air;  Weight  and  impulse  of  Jluids; 
Raising  weights  by  the  descent  of  water ;  319.  Effect 
4>{  velocity ;  Overshot  wheel ;  030.    Undershot  wheel ; 


CONTENTS. 


XVll 


Mechanical  power  of  a  stream ;  321.  Breast  wheel ; 
Second  wheel;  Oblique  wheels  and  windmills  ;  322, 
SIS.  Smoke  jack;  Kite;  Parent's  mill;  Seamanship  ; 
Side  wind;  S'ii.  Vovva  and  arrangement  of  a  vessel; 
325.     Stability  of  a  ship;  326. 

Lecture  xxviii.     On  hydraulic  ma- 
chines; 327. 

Machines  for  raising  water;  Noria;  Bucket  wheel ; 
Throwing  wheel ;  Rope  pump  :  32r.  Venturi's  drain  ; 
Spiral  pipes;  Screw  of  Archimedes;  .'528.  Water 
screw  ;  Wirtz's  spiral  pump  ;  329.  Centrifugal  pamp  ; 
330.  Pumps  ;  Plunger  pump  ;  331.  Forcing  pump  ; 
Mixed  pump  ;  Pistons ;  Bramah's  press ;  Sucking 
pump  ;  332.  Bag  pump  ;  Lifting  pump;  Sucking  and 
forcing  pnmp;  Air  vessel  ;  333.  Fire  engine  ;  Roll- 
er pumps  and  slider  pumps  ;  334.  Arrangement  of 
pipes  ;  Bead  pump  ;  Cellular  pump  ;  Chain  pump  ; 
Cranks ;  335.  Wheels  and  rollers  ;  Chinese  walking 
■wheels  ;  Inverted  pump  ;  Hydraulic  air  vessels  ;  336. 
Fountain  of  Hero ;  Atmospheric  machines ;  Hydraulic 
ram ;  337,  338. 

Lecture  XXIX.     On  pneumatic  ma- 
chines; 339- 

Counteraction  and  application  of  pneumatic  forces  ; 
Torricellian  vacuum  ;  Air  pump  ;  339.  Double  barrel  ; 
Smeaton's pump; Experiments; 340.  Gages  ;Peargage'; 
S4J.  Condensers  ;  Diving  bells  ;  342.  Bellows  ;  Gas- 
ometer! ;  343.  Shower  bellows  ;  Velocity  of  a  blast ; 
Ventilation;  344.  Corn  fan  ;  Chimnies ;  345.  Fur- 
naces ;  Balloons  ;  Steam  engines  ;  Saver/s  engine  ; 
346.  Newcomen's  and  Beighton's  engine  ;  347.  Watt's 
improvements ;  348.  Power  of  Boulton  and  Watt's 
machines  ;  Later  alterations  ;  Gunpowder  ;  349.  Cal- 
culations of  Bernoulli  and  of  Count  Rumford  ;  pro- 
perties of  a  gun ;  350.  Bullets  ;  Shot ;  Air  gun  ; 
351. 

Lecture  xxx.    On  the  history  of  hy- 
drauHcs  and  pneumatics ;  352. 

Discoveries  of  Archimedes  ;  352.  Ctesibius  ;  Hero ; 
Viti'uvius  ;  353.  Canals  ;  Gunpowder  ;  Galileo;  Tor- 
ricelli  ;  354.  Castelli ;  Mariotte ;  Guglielmini  ;  Gue- 
ricke;  Hooke  ;  355.  Marquis  of  Worcester;  356. 
Huygens  ;  Pardies  ;  Renaud  ;  James  and  John  Ber- 
noulli ;  Newton  ;  Poleni ;  357.  Bouguer ;  D.  Ber- 
noulli ;  358.  John  Bernoulli  ;  Maclaurin ;  359. 
VOL,  I. 


Robins  ;  Dalembert ;  Kaestncr  ;  360.  Eolcr  ;  Smea. 
ton  ;  Borda;  Watt ;  Specification  of  Mr.  Watt's  pa- 
tent;  361,  362.  Bossut ;  Juan  ;  Prony ;  363.  Chap_ 
man;  Romme  ;  Hutton  ;  Rumford;  Du  Buat ;  364. 
Black  ;  Montgolfier  ;  365.     Chronological  table  ;  366. 

Lecture  xxxi.    On  the  propagation 
of  sound  ;  367. 

Importance  of  acustics;  Division^f  the  subject;  De- 
finition of  sound;  367.  Propagation  of  sound  ;  Velocity 
ofsound;368.  Delineation  of  a  sound;  369.  Com- 
pressibility of  hard  bodies;  Transmission  of  sound  hy 
different  mediums;  370.  Correction  on  account  of 
heat;  371.  Transmission  in  gases  of  different  kinds; 
In  liquids ;  372.  In  solids  ;  Divergence  of  sound  ; 
373.  Reflection  of  sound;  874.  Illustration  by 
waves  of  water;  Speaking  trumpet  ;Whispering  gallery  ; 
375.  Invisible  girl ;  Partial  interception  of  sound  ; 
Decay  of  sound;  376,  377. 

Lecture  xxxii.   On  the  sources  and 
effects  of  sound ;  378. 

Origin  of  a  simple  sound ;  Of  a  continued  sound; 
378.  Musical  sounds  derived  from  vibrations;  Open 
pipes;  Stopped  pipes;  379.  Harmonic  sounds; 
Effect  of  temperature ;  Longitudinal  sounds  of  solids; 
Lateral  vibrations ;.  380.  Flexible  chords  and  mem- 
branes; 381.  Harmonic  sounds  of  chords;  382.  Loaded 
wire;  Revolutions  of  chords;  383.  Vibrations  of 
clastic  rods;  384.  Vibrations  of  plates,  rings,  and 
vessels;  Mixed  vibrations  of  solids  and  fluids  ;  385. 
Sympathetic  sounds;  Hearing;  386.  Description  of 
the  ear;  387.     Delicacy  of  the  car  ;  388. 

Lecture  xxxiii.  On  harmonics;  389. 

Theory  of  harmonics;  Combinations  of  sounds;  389. 
Beats;  390.  Grave  harmonics;  Concords;  391. 
Melody  ;  Rhythm  ;  Simple  compositions  ;  Diatonic 
scale;  399.  Half  notes  or  semitones;  393.  Minor 
mode;  Discords;  Rules  of  accompaniment;  394.  Tem- 
perament ;  395.     Distinction  of  the  notes  ;  396. 

Lecture  xxxiv.  On  musical  instru- 
ments; 397- 

Division  of  musical  instruments;  Harp;  Lyre;  397. 
Harpsichord;  Spinet;  Pianoforte;  Dulcimer;  Clavi- 
chord; Guitar;    398.     Violins    of   different    kinds; 
Vielle;  Trumpet  Marigni;  Aeolian  harp  ;  399. 
C 


XVlll 


CONTENTS. 


human  voice';  40{T.  Drum ;  Stacada ;  Bell ;  Harmo- 
nica; Vox  humana  pipe  ;  401.  Simple  wind  instru- 
ments; Mixed  wind  instruments;  402.  History  of 
music;  Lyre;  Hermes  ;  Terpander;  Pythagoras;  Si- 
raonides;403.  Tibia;  Aristotle;  Ctesibius;  Pope 
Gregory;  404.  Guido;  Bacon ;  Galileo ;  Mersennc ; 
Kircher  ;  Meibomius  ;  Wallis  ;  Newton ;  Brook  Tay- 
lor ;  Sauveur;  405.  Lagrange;  Euler;  Bernoulli; 
Dalembert;  Sounds  of  rods;  Grave  harmonics  of 
Romieu  and  Tartini ;  Sounds  of  pipes.  Chladni ;  406 . 
Laplace;  Chronological  table  ;  407. 

Lecture  xxxv.     On  the  theory  of 
optics ;  408. 

Importance  of  optics  ;  Division  of  tlie  subject ;  De- 
finition of  light ;  408.  Ray  of  light ;  Motion  of  light . 
Homogeneous  mediums  ;  409.  Reflection  ;  410.  Re- 
fraction ;  411.  Polished  surfaces  ;  Return  of  a  ray  ; 
Refractive  density  ;  412.  Index  of  refractive  power  ; 
Intermediate  refraction;  Total  reflection;  413.  Di- 
optrics and  catoptrics ;  Focus  ;  414.  Plane  speculum ; 
Principal  focus;  Convergence  by  reflection  ;  415.  Con- 
cave and  convex  mirrors  ;  Prism;  Multiplying  glass; 
Lens;  416.  Effects  of  lenses  ;  Focus  of  a  lens;  41T. 
Joint  focus;  Image  ;  Optical  centre  ;  418.  Curvature 
of  the  image;  419. 

Lecture  xxxvi.     On  optical  instru- 
ments ;  420. 

Divergence  of  light;  Photometers ;  420.  Measure- 
ment of  refractive  densities;  Instruments  strictly 
optical ;  421.  Images  formed  by  lenses  and  mirrors  ; 
Magnifiers  ;  Simple  microscopes  ;  Globules  ;  429.  Il- 
lumination of  an  image  ;  Burning  Glasses ;  Materials 
of  lenses  and  mirrors  ;  423.  Images  visible  in  every 
direction;  Camera  obscura;  424.  Solar  microscope  ; 
425.  Lucernal  microscope  :  Phantasmagoria  ;  426. 
Astronomical  telescope ;  Double  microscope  ;  427. 
Galilean  telescope :  Common  day  telescope ;  Dr. 
Herschel's  telescope;  428.  Newtonian  reflector;, 
Gregorian  telescope  ;  Cassegrain's  telescope  ;  Smith's 
microscope;  Curvature  of  images  in  telescopes,  129; 
Magnifying  powers  of  telescopes  ;  Field  glass  ;  430. 
Double  magnifier;  Aberration  from  colour;  Achro- 
matic glasses;  431.  Achromatic  eyepiece;  Micro- 
meters ;  432.     Divided  speculum ;  433. 

Lecture  xxxvi.  On  physical  optics; 
434. 


Sources  of  light;  Combustion  ;  Slow  decomposition; 
434.  Electricity  ;  Friction  ;  Solar  phosphori ;  435. 
Emission'of  light;  Velocity  of  light ;  Apparent  aber- 
ration ;  436.  Oblique  reflection  ;  Diffraction  ;  Dis- 
persion ;  Colour;  437.  Division  of  the  spectrum; 
Light  of  diff'erent  kinds;  438.  Mixed  lights  ;  Imita- 
tion of  white  light ;  Primitive  colours ;  439.  Mixture 
of  colours  by  rapid  motion;  Combinations  ;  440.  At- 
mospherical refraction;  Horizontal  refraction;  441. 
Rainbows  ;  442.  Halos  and  parhelia  ;  443.  Refrac- 
tion of  ice  ;  Complicated  halos  ;  444.  Double  refrac- 
tion; Iceland  spar;  Second  refraction ;  Transparent 
plates  ;  445,  446. 

Lecture  xxxviii.    On  vision  ;  447. 

Description  of  the  eye  ;  447.  Image  on  the  retin*  j 
Advantages  of  the  arrangement ;  448.  Inversion  of 
the  image  ;  Instinct ;  449.  Sensibility  of  the  retina ; 
Focus  of  the  eye  ;  Accommodation  ;  450.  Change  in 
the  crystalline  lens  ;  Uses  of  the  iris  ;  451.  Optome- 
ter ;  Myopic  and  presbyopic  sight ;  452.  Single 
vision  ;  Judgment  of  distance  ;  453.  Apparent  mag- 
nitudes of  the  sun  and  moon ;  Aerial  perspective ; 
Painting;  454.  Panorama;  Duration  of  sensations; 
Ocular  spectra  ;  455,  456. 

Lecture  xxxix.     On  the  nature  of 
light  and  colours;  457. 

Theories  respecting  the  nature  of  light ;  457.  Sim- 
ple propagation  ;  Transparent  mediums;  458.  Uni- 
formity of  velocity  ;  459.  Reflection  and  refraction  ; 
Partial  reflection ;  460.  Total  reflection;  461.  Sources 
of  light  ;  Aberration ;  Double  refraction ;  462. 
Dispersion  ;  Colours  of  thin  plates;  463.  Alternate 
union  and  extinction  of  colours;  Light  admitted  by 
two  holes  ;  464.  Supposed  dimensions  of  undulations  ;. 
Correction  ;  Stripes  in  a  shadow  ;  465.  Light  passing 
through  a  narrow  aperture;  Colours  of  striated  sur- 
faces; 466.  Curved  stripes.af  colours;  Fringes  near 
a  shadow  ;  467.  Colours  of  thin  plates ;  468.  Co- 
lours of  natural  bodies ;  469.  Colours  of  mixed  plates  ; 
supernumerary  rainbows  ;  470.  Colours  of  concave 
mirrors  ;  Agreement  of  the  Iluygenian  theory  with 
the  phenomena  ;  471. 

Lecture    xl.     On    the   history   of 
optics ;  472. 

Knowledge  of   the  ancients ;  Empedocles ;    472^ 


CONTENTS. 


XIX 


Aristotle  ;  Archimedes  ;  Euclid ;  Ptolemy ;  Alhazen  j 
Vitellio  ;  R.  Bacon  ;  473.  Jansen  ;  Galileo  ;  Kepler; 
Scheiner ;  Rheita  ;  Maurolycus;  DeDoniinis;  Silel- 
lius ;  Descartes  ;  474.  Ferraat ;  Leibnitz  ;  Barrow ; 
Boyle  ;  Hooke  ;  475.  Newton ;  Grimaldi ;  476- 
Bartholin;  Huygens;  Roemcr  ,  Bradley  ;  477.    Bou- 

PART  THE  THIRD 

Lecture  xli.     On  the  fixed    stars; 
487. 

Division  of  the  subjects  of  physics  ;487.  Astronomy  ; 
488.  Empty  S|;ace  ;  fixed  stars  ;  489.  Light  of  the 
stars;  Figure;  Twinkling;  Number;  Magnitudes; 
490.  Distances  of  the  stars  ;  491.  Clusters  or  ne- 
bulae ;  492.  Arrangement  of  the  stars  in  general  ; 
Milky  way  ;  Proper  motions  of  the  ^stars  ;  493.  Dr. 
Herschel's  division  of  stars  and  nebulae  ;  Changes  of 
the  stars ;  494.  Constellations ;  495.  Representa- 
tions of  the  stars  ;  AUineations ;  496  .  .498. 

Lecture  xLir.    On  the  solar  system  ; 
^99- 

The  sun  a  star;  Progressive  motion  of  the  sun; 
499.  Orbit  of  the  sun  ;  Rotation  ;  500.  Spots ; 
Solar  heat ;  501.  Sun's  attraction ;  Solar  atmosphere ; 
502.  Planets ;  Ecliptics ;  503.  Change  of  position 
of  the  ecliptic  ;  Nodes ;  Keplerian  laws  ;  504.  Rota- 
tion of  the  planets  ;  Precession  of  the  equinoxes ;  505. 
Nutation  of  the  earth's  axis ;  Proportional  distances 
of  the  planets  ;  Mercury  ;  506.  Venus  ;  The  earth  ; 
Mars;  507.  Juno;  Pallas;  Ceres;  Jupiter ;  Saturn  ; 
608.  Georgian  planet ;  Unknown  planets;  Satellites; 
509.  Moon  ;  510.  Satellites  of  Jupiter ;  Ring  of 
Saturn  ;  511.  Comets  ;  512.  Number  and  orbits  of 
the  comets;  513. 

Lecture  xliii.     On  the  laws  of  gra- 
vitation ; 

Newton's  great  discovery ;  Attraction  of  spherical 
bodies;  515.  Extent  of  tiie  force  ofgravity  ;  5l6. 
Sun's  change  of  place  ;  Orbits  of  the  planets  ;  Kep- 
lerian laws  ;  517.  Universality  of  gravitation  ;  Mo- 
tions of  the  apsides  and  nodes;  Changes  of  the 
•cliptic  ;  Forms  of  the  planets  ;  518.  Precession  ; 
Nutation;  Lunar  motions;  519.  Disturbing  force  of 
the  Run  i  520.     Acceleration  of  the  moon's  motion ; 


guer ;  Porterfield  ;  Jurin  ;  Smith  ;  Doliond  ;  Hall  . 
478.  Euler ;  479.  Lambert ;  Mathematical  opti- 
cians;  Mazeas;  Dutour  ;  Comparetti  ;  Priestley; 
480.  Delaval  ;  R.  Darwin  ;  Atmospherical  refrac- 
tion ;  Wollaston;  Ritter  ;  Herschcl ;  481.  Laplace  J 
Attempts  of  the  author ;  482.  Chronological  table ;  483' 

..  PHYSICS ;  485. 

Moon's  rotation  ;  Orbits  of  comets;  521.  Predictions 
of  Halley  and  Clairaut ;  522.  Chronological  table;  433. 

Lecture     xliv.      On    the    appear- 
ances of  the  celestial  bodies;  523. 

Apparent  motions  to  be  described  after  the  real 
ones;  Motions  of  the  stars  and  sun  ;  Motions  of  the 
earth  ;  523.  Apparent  revolution  of  the  sun  ;  524. 
Sun's  apparent  diameter;  Length  of  summer  and  win- 
ter"; Day  and  night ;  Sun's  apparent  path  ;  525.  Cen- 
trifugal force  ;  Places  of  the  stars  ;  Twilight ,  526. 
Relative  positions  and  phases  of  the  planets;  527. 
Phases  of  the  moon:  Lunar  eclipses  ;  528.  Eclipses 
of  the  sun  ;  Series  of  eclipses  ;  529.  Harvest  moon  j 
Eclipses  of  Jupiter's  satellites  ;  530.  Comets;  Light 
of  the  heavenly  bodies  ;  Planetary  worlds  ;  531.  Fon- 
tenelle ;  Mercury  ;  Venus  ;  532.  Moon ;  533.  Mars ; 
Newly  discovered  planets  ;  Jupiter  ;  534.  Saturn  ; 
Georgian  planet ;  535. 

Lecture   xlv.     On   practical  astro- 
nomy ;  536. 

Real  motions  neglected  ;  Situation  of  a  point  in  the 
heavens  ;  Meridian  ;  536.  Astronomical  instruments : 
Time;  Sidereal  day;  .Solar  day;  Equation  of  time' 
537.  Dialling;  Chronology;  538.  Calendar;  539. 
Improvement  suggested  ;  Republican  calendar  ;  Me- 
tonic  cycle  ;  Golden  number ;  540.  Epact ;  Moon's 
age;  Julian  period;  Astronomical  time ;  Quadrants; 
Transit  instruments  ;  541.  Iladley's  quadrant ;  De- 
clinations ;  Refraction  and  parallax ;  542.  Latitudes: 
Longitudes ;  543.  Lunar  observations ;  Distance  of 
the  sun ;  Transits  ;  544.  Densities  of  the  sun  add 
planets;  Artificial  globe  ;  "  565".  Planispheres  ;;566- 
Orreries ;  567. 

Lecture  xlvi.  On  Geography;  568. 

Particular  account  of  the  earth;  Curvature  of  its 
surface;  Direction  of  the  plumb  line;  568.    Ellipti- 


XX 


CONTENTS, 


city ;  Mcasuremtnts  of  degrees ;  569.  Zones ;  570. 
Climates;  Sea  and  land;  Continents;  571.  Rivers; 
Elevations;  572.  Mountains;  573.  DifFcrent  orders 
of  mountains;  Internal  parts  of  the  earth;  574.  Den- 
sity of  the  earth ;  575. 

Lecture    xLvii.      On    the     tides; 
576. 

Tides  noticed  by  the  ancients ;  Daily  changes ;  570. 
Monthly  changes;  Yearly  clianges;  Connexion  with 
the  moon;  Effect  of  gravitation  on  a  fluid  sphere; 
577.  Primitive  lunar  tides;  Comparison  with  a  pen- 
dulum ;  578.  Direct  and  inverted  tides ;  Tides  of  a 
lake;  579.  Resistance;  Tides  of  the  Atlantic ;  580. 
Particular  modifications ;  58 1.  Tides  of  t'.ie  Channels, 
and  of  rivers;  582.  Inferior  and  superior  tides ;  Laws 
of  elevation  and  of  depression;  583.  Mode  of  ob- 
serving the  tides;  Solar  tides;  Combination  of  tides; 
584.  Retardation  of  spring  and  neap  tides;  585. 
Increased  height  in  converging  channels;  Combina- 
tions in  particular  ports;  586.  Currents;  Tides  of  the 
atmosphere ;  587,  588.  See  corrections. 

Lecture    xlviii.    On   the   history 
of  astronomy  ;  589. 

Earliest  astronomy ;  Signs  of  the  zodiac;  589.  Baby- 
lonian observations;  Chaldeans;  Hermes;  Egyptians; 
Chinese;  590.  Indians;  Greeks;  591.  Thales;  Py- 
thagoras; Meto;  Alexandrian  school ;  592.  Erato- 
sthenes; Hipparchus;  593.  Ptolemy;  594.  Arabians; 
Persians;  595.  Copernicus;  Tycho  Brahe;  596. 
Kepler;  59T.  Napier;  Huygeus;  Cassini;  Gravita- 
iJon;  598.  Newton's  discoveries;  Extract  from  Pem- 
berton;  599,600.  British  astronomers ;  Observatory 
at  Greenwich;  001.  Determination  of  the  longitude  ; 
Late  discoveries;  602,  603.  See  corrections.  Chrono- 
logical table ;  004. 

Lecture    xlix.      On  the  essential 
properties  of  matter ;  605. 

Importance  of  minute  objects;  605.  Definition  of 
mater;  Place  of  the  investigation;  006.  Essential 
and  accidental  properties  of  matter;  Extension;  Di- 
visibility; 607.  Actual  division  of  matter;  608. 
Impenetrability;  609.  Permeability;  Orders  of  sub- 
stances; 610.  Repulsion;  Apparent  contact;  611. 
Laws  of  repulsion;  612.      Dalton's  hypothesis;  Re- 


pulsion of  liquids  and  solids;  Reciprocality  of  repul- 
sion; 613.  Inertia;  Gravitation;  Cause  of  gravita- 
tion; 614.  Mathematical  conceptions;  Newton's 
opinion;  615.  Constitution  of  a  medium  capable  of 
producing  gravitation;   616.     Difficulties;  617. 

Lecture  l.     On  cohesion  ;  618. 

Accidental  properties  of  matter;  Laws  of  cohesion  ; 
618.  Modification  of  cohesion  by  heat;  Liquidity;  619i 
Superficial  cohesion;  620.  Bubbles;  Form  of  the  sur- 
face of  a  fluid  ;  021.  See  corrections.  Magnitude  of  the 
force  of  cohesion;  Ascent  between  two  plates;  622. 
Capillary  tubes ;  Horizontal  surface ;  623.  Detached 
portion  of  a  liquid ;  Lycopodium  ;  Attractions  and  re- 
pulsions of  floating  bodies;  024.  Apparent  cohesion 
of  plates ;  Drop  between  plates;  Oil  spreading  on 
water;  Sponge;  025.  Long  column  supported  by 
cohesion;  Cohesion  of  solids;  More  perfect  union; 
026.  Solidity;  627.  Cause  of  solidity ;  Elasticity;. 
028.  Stiffness;  Strength;  Softness;  Ductility;  629. 
Primary  cause  of  cohesion;  630. 

Lecture  li.     On  the  sources   and 
effects  of  heat;  631. 

Division  of  the  subject  of  heat ;  Definition  of  heat 
and  cold;  631.  Excitement  of  heat;  Condensation; 
Friction ;  Count  Rumford's  experiments ;  632.  Ef- 
fect of  velocity ;  633.  Pictet's  experiments ;  Heat 
from  combustion  ;  634.  Communication  of  heat  i 
Conducting  powers;  Fluids;  635.  Radiation  of  heat; 
Mr.  Leslie's  discoveries ;  636.  Differences  of  solar 
and  culinary  heat ;  Invisible  heat ;  Equilibrium  of  ra- 
diant heat ;  637.  Apparent  reflection  of  cold  ;  Re- 
frangibility  of  heat ;  638.  Blackening  rays ;  Effects 
of  heat;  Tejnporary  effects;  639.  Expansion  of 
gases;  Condensation;  640.  Expansion  of  fluids; 
Diminution  of  cohesive  powers;  Boiling;  Slow  eva- 
poration; 041.  Contraction;  Freezing;  Expansion 
of  solids;  042.  Liquefaction;  Cracks  from  heat; 
043.  Permanent  effects  of  heat;  Glass  drops;  Tem- 
pering of  metals  ;  644,  645. 

Lecture     lii.     On     the   measures 
and  the  nature  of  heat ;  646. 

Measures  of  expansion;  Pyrometer;  Scale  of  heat; 
646.  Mixtures;  Sun's  rays;  Expansion  of  solids  and 
fluids;  Tiiermometers ;  647.     Wedgwood's  thermo- 


CONTENTS. 


XXI 


meter  j  Different  scales ;  648.  Temporary  change  of 
a  thermometer;  Air  thermometers;  649.  Capacities 
for  heat;  Natural  zero ;  650.  Theory  of  capacities  ; 
651.  Chemical  effects;  Latent  heat;  C52.  Mr. 
Davy's  experiments;  Intimate  nature  of  heat;  Theory 
of  caloric;  Confutation;  653.  Heat  a  quality; 
Newton's  opinion  ;  Vibrations ;  654.  Mechanical  ef- 
fects of  vibrations ;  Chemical  effects ;  Comparison 
with  sound;  655.     General  inferences ;  656,657. 

Lecture     liii.     Ou  electricity    in 
equilibrium  ;  6o8. 

Utility  of  electrical  hypotheses;  Division  of  the 
subject;  658.  Supposed  electric  fluid;  Its  attrac- 
tions and  repulsions  ;  659.  Conductors  and  noncon- 
ductors ;  660.  Positive  and  negative  electricity ;  Lo- 
cal electricity;  Distribution  of  electricity;  661. 
Electricity  of  a  sphere;  Connected  spheres;  662. 
Difference  of  hydrostatic  and  electrical  pressure; 
Attractions  and  repulsions ;  663.  Induced  electri- 
city ;  Neutral  point ;  Effects  of  attraction  and  repul- 
sion; 664.  Currents  of  air;  Bodies  electrified  in  dif- 
ferent degrees;  Charge;  665.  Discharge;  Shock; 
Coated  jar;  Battery;  Comparison  of  conducting 
powers;  666,  667. 

Lecture     liv.     On    electricity    in 
motion ;  668. 

Effects  and  causes  of  electrical  motions,   and  elec- 
trical  apparatus;   Velocity;    668.     Spark;   Perfora- 
tion of  a  jar;  Direction  of  the  motion;  669.     Opini- 
ons respecting  positive  and  negative  electricity ;  Ef- 
fects of  electricity  ;  Accumulation  ;  Simple  current ; 
Electric  light ;  670.    Heat;  Mechanical  effects  ;  671. 
Chemical  effects;  Sensible  effects;  672.     Excitation 
of  electricity ;  Electrics;  673.  Vapours;  Tourmalin; 
Galvanic  electricity;  Chemical  chanws;  674.     G:»l- 
vanic  combinations  ;  General  laws  ;  675.     Particular 
facts;  Pile  of  Volta;  676.     Troughs;   Animal  elec- 
tricity ;  677.     Mr.  Davy's  discoveries  ;  Electrical  na- 
ture of  chemical  attractions ;  Theory  of  the  pile  ;  678. 
Efficacy  of  decomposable  substances;  679.  Electrical 
machines  ;  Teylenan  machine  ;  Electrophorus ;   680. 
Condenser;  681.     Multiplier;  Doublers ;  Electrical 
balance;  Quadrant  electrometer;  682.  Gold  kaf  elec- 
trometer ;  Lane's  electrometer ;  683.    General  obser- 
Tations;  684. 


Lecture  lv.  On  magnetism;  6SS. 

Resemblance  of  magnetism  and  electricity  ;  Theory  ; 

685.  Conducting  powers  ;   Magnetical   substances ; 

686.  Aurora  borealis;  North  and  South  poles  ;  At- 
tractions and  repulsions;  687.  Polarity;  Arrange- 
ment of  filings;  Directive  force;  688.  Terrestrial 
magnetism;  Compass;  Dipping  needle;  Illustra- 
tion ;  689.  Temporary  magnetism  :  Natural  magnet ; 
Magnetic  poles  of  the  earth  ;  690.  Diurnal  changes  j 
Variation  of  the  declination;  Line  of  no  declination; 
691.  Dip;  Artificial  magnets;  692.  Double  touch  ; 
Magnetic  paste  ;  Division  of  a  magnet ;  693.  Strik- 
ing and  ringing  a  magnet ;  Hammering  brass;  Solu- 
tion in  an  acid ;  694.  Resemblance  of  polarity  to 
crystallization ;  695. 

Lecture     lvi.      On     climates  and 
winds;  696. 

Meteorology;  Division  of  the  subject ;  Climates; 
Meteorological  thermometers ;  696.  Immediate  effects 
of  the  sun  ;  697.  Prevost's  calculations  ;  Variations 
of  temperature ;  Slow  changes  ;  698.  Heat  of  the 
sea ;  Effect  of  freezing  and  thawing  ;  Heat  of  the  at- 
mosphere ;  699.  Sunnner  and  winter ;  Temperatures 
of  different  places  ;  Local  variations  ;  700.  Winds  ; 
Periodical  winds ;  Trade  winds;  Had  ley  ;  701.  Hal- 
ley's  theory  ;  Atmosphere  of  Jupiter;  Greater  heat  of 
the  northern  hemisphere ;  702.  Westerly  winds ; 
Local  modifications;  Monsoons;  703;  Land  and  sea 
breezes;  Hurricanes;  Variations  of  the  barometer; 
704,  705. 

Lecture    lvii.     On    aqueous    and 
igneous  meteors  ;   7O6. 

Evaporation,  and  its  effects;  Theory  of  Deluc  and 
Dallon;  700.  Quantity  of  water  evaporating;  Preci-" 
pitation ;  707.  ^Moisture;  Mediterranean;  Currents 
at  the  Straights;  Attraction  of  moisture;  708.  B. 
Provost;  Hygrometers;  709.  Natural  hygrometer; 
Water  contained  in  air;  710.  Visible  vapour;  Dew; 
Mists;  711.  Ruin;  Indications  of  the  barometer; 
Effects  of  mountains;  712.  Periodical  rains;  Thun- 
der and  lightning;  713.  Atniospheiical  electricity; 
Thunderstorms;  714.  Conductors;  Sudden  conden- 
sations; 715.  Wall rspouts;- Aurora  borealis;  Earth- 
quakes and  Volcaiius;  716.  Volcanic  countries; 
Earthquakes  of  Calabria;  717.    Eruptions  of  Vesu- 


XXll 


CONTENTS. 


viiis;  718,  719.  Geological  changes ;  Reality  of  va- 
rious clianges ;  720.  Effects  of  rivers  and  of  the  sea  ; 
Shouting  stars;  721.     Falling  stones ;  722. 

Lectuhe  lviii.     On  vegetation; 
723. 

Sketchof natural  history ; Minerals; Vegetables ;  723. 
Animals  ;  724.  Distinctions  of  animals  and  vegetables; 
725.  Description  of  a  vegetable:  Germination j 
Parts  of  plants;  726.  Vessels;  727.  Motion  of  the 
sap;  728.  Mr.  Knight's  experiments ;  Grafting;  729. 
Diseases  of  plants;  Exposure  to  the  air;  Linnean 
system;  730,  731.     System  of  Jussieu;    732. 

Lecture    lix.      On  animal  life; 
733. 

Classification  of  aninuils,  according  to  Linn^ ;  733. 
Mammalia;  Birds;  734.  Amphibia;  Fishes;  735. 
Insects;  736.  Vermes;  737.  Senses;  Nutrition;  738. 
Nervous  system;  739.  Nature  of  the  nerves;  Dis- 
*asesj  740.  Natural  cures;  741. 


Lecture  lx.     On  the  history  of 
terrestrial  physics ;  742. 

General  retrospect ;  Knowledge  of  the  ancients ; 
742.  Chinese;  Numa;  Tliales;  Anaximander;  Anaxi- 
menes;  743.  Pyth.igoras;  Anaxagoras;  Democritus; 
Heraclitus;  Plato;  744.  Aristotle;  Epicurus;  745.  R. 
Bacon;  Discovery  of  tlie  compass;  Gesner;  Aldro- 
vandus ;  Gilbert  of  Colchester ;  746.  Variation  of 
the  compass;  F.Bacon;  Opinions  of  heat;  Drebel ; 
747.  Harvey ;  Circulation  of  the  blood  ;  Barometer ; 
Bauhins;  Ray;  Willughby ;  748.  Philosophical  so- 
cieties; Variation  charts;  749.  Electricity;  Lin- 
nean system ;  Discoveries  respecting  heat ;  750. 
Theory  of  magnetism  and  electricity;  Boscovich; 
Hygrometry;  751.  Galvanism;  Pile  of  Volta  ;  752. 
Mr.  Davy's  experiments;  Dalton;  Rumford;  753. 
Herschel ;  Leslie ;  Capillary  tubes ;  Laplace ;  754. 
Advantages  to  be  expected  from  modern  institutions ; 
755.     Chronological  table;  756. 


EXPLANATION  OF  THE  PLATES;    757- 


ADDITIONS  AND  CORRECTIONS. 


p.  40.    L.   5   from  the  bottom;    for  "therefore," 
read,  afterwards. 

P.  ri.-  L.  5  from  the  bottom;   for  "  IV,"  read,  V. 
P.  72.  L.  2,  for  "  IV,"  read,  V. 
P.  87.  After  1.  4,  insert. 

When  an  insulated  body  revolves  round  an  axis  in 
any  direction,  the  state  of  revolution  cannot  be  per- 
manent, unless  the  axis  be  so  situated,  that  the  cen- 
trifugal 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  rlifterent 
axes,  situated  at  right  angles  to  each  other,  round 
which  the  body  may  revolve  in  an  equilibrium  either 
stable  or  tottering.     It  may  also  be  shown  that  if  a 
body,  revolving  round  any  axis,  receive  at  the  same 
time  an  impulse  which  would  cause  it  to  revolve  round 
a  second  axis  in  another  direction,  the  two  revcrfutions 
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  perma- 
nent 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;  bnt  it  will 
never  pass  beyond  the  state  of  equilibrium,  as  in  many 
other  cases  of  deviation  from  such  a  state ;  since  the 
momentum,  produced   by   the  excess  of  centrifugal 
force  in  one  part  of  the  revolution,  is  destroyed  irf 
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  dis- 
turbing force,  which  might  be  sufficient  to  turn  it  into 
a  vertical  position  during  the  course  of  its  path,  will 
only  produce,  when  combined  with  the  rotatory  mo- 
tion, a  slight  change  of  the  direction  of  the  rotation, 
which  will  confine  the  deviation  of  the  stick  from  a 
horizontal  position  within  narrow  limits. 

P.  138.  L.  9,  after  "  concerned,"  insert,  it  has  in- 
deed 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  cas«,  be  sup- 
posed to  be  materially  increased. 


P.  146.  L.  3,  after  "  124,"  insert,  125. 

L.  8  from  the  bottom,  for  «  IX,"  read,  X. 
P.  169.  L.  7,  for  "XIV,  read,  XIII. 
P.    176.  L.  19,  for  "  the  circle,"  read,  a  second 
circle. 

P.  196.  L.  5  . .  2,  from  the  bottom,  for  "  If  the  fric- 
tion. .  to  obviate  this,"  read,  Since  friction  is  always 
increased  by  an  increase  of  pressure,  the  effect  of  any 
addition  to  the  sustaining  force  must  tend,  in  some  de- 
gree, to  retard  the  vibrations,  even  if  the  friction  be 
somewhat  less  increased  than  the  force  propelling  the 
balance.     In  order  to  obviate  this  retardation. 

P.  238.  L.  5  from  the  bottom,  after  "  arches,"  in- 
sert, since  they  must  have  left  too  small  a  space  for 
the  passage  of  the  water.  If,  however,  we  may  be- 
lieve Herodotus,  whom  Mr.  King  has  quoted,  this  was 
in  reality  a  kind  of  drawbridge.  According  to  thi» 
author,  it  was  built  by  Nitocris,  the  immediate  Suc- 
cessor of  Serairamis:  the  stones  were  united  by  iron 
and  lead,  and  beams  were  laid  across  them,  which 
viere  removed  at  night,  in  order  to  prevent  the  mutual 
depredations  of  the  inhabitants  of  difterent  parts  of 
the  city. 

P.  261.  L.  19,  for  "XX,"  read,  XIX. 
P.  267.  L.  18,  for  "  heel,"  read,  pitch. 
P.  273.  L.  3  from  the  bottom,  omit  "  logarithm  of." 
L.    2   from  the  bottom,   for   "  numbers," 
read,  corresponding  logarithms. 
P.  292.  L.  9,  for  "  de,"  read,  du. 
P.  420.  L.  *,  for  "more,"  read,  most. 
P.  424,  after  line  5,  insert. 

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  reflection  of  a  prism  of  glass,  of 
which  the  four  surfaces  are  ground  so  as  to  form  pro- 
per angles  with  each  other.  The  image  formed  by-, 
the  first  surface  is  inverted,  and  the  second  reflection 
restores  it  to  its  original  position,  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 
occupied  by  the  edge  of  the  prism,  the  remaining  part 
being  left  open,  or  simply  covered  with  a  lens,  for  the 
adraissjon  of  the  direct  rays  of  light,  by  which  we  may 


•xs.iv 


Acr>rTro?rs  and  coruections. 


see,  at  the  same  time,  the  paper  aud  the  pencil  to  be 
employed,  for  making  a  diawiug  or  a  copy  of  any  ob- 
ject placed  before  us. 

P.  425.  L.  1^,  for  "  XXVn,"  read,  XXVIII. 

P.  464.  L.  15,  for  "  other  points  at,"  read,  at  other 
points. 

P.  477.  Last  lino  but  one,  after  "  telescopes,''  in- 
sert, but  with  respect  to  the  theory  of  halos  and  par- 
helia, he  was  less  successful  than  Mariotte  had  been 
some  years  before. 

P.  335.  L.  7  from  the  bottom,  for  "  ecipses,"  read, 
species. 

P.  .545  .  . .  Running  title.  The  numbers  of  all  the 
pages  are  too  great  by  20. 

P.  587.  L.  15.  .  17,  for  " the  attraction  .  .  is  pro- 
duced," read,  a  current  is  observed  iu  its  most  ex- 
posed parts. 

P.  588.  L.  14,  15,  for  "  on  account  .  .  moon"  read. 
These  currents,  as  well  as  the  general  current  of  the 
sea,  have  been  attributed  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  disturbing  force 
of  the  sun  produces  this  effect  on  the  moon  only  iu  pro- 
portion as  it  increases  her  distance  from  the  earth  ; 
consequently  no  such  retardation  can  possibly  be  pro- 
duced by  the  force  of  gravitation  in  the  rotation  of  the 
sea  or  of  the  atmospliere,  and  the  whole  effect  must  be 
attributed  to  the  operation  of  meteorological  causes, 
producing  first  the  trade  winds,  and  secondly  occa- 
sionmg,  by  means  of  the  friction  of  these  winds,  a  simi- 
lar 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  rotation  of 
this  planet  being  extremely  rapid,  it  is  not  at  all  im- 
possible 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. 

P.  565,  L.  12,  for  "  Almamoun,  was  the  son",  read, 
Almamoun,  the  son. 

P.  003.  L.  2.  for  "  The  observations  of  the  transit  of 
Venus  were  twice  made  in  the  South  Seas",  read.  Ob- 
servations of  the  transit  of  Venus  were  made  with 
great  care  in  the  South  Seas. 

At  the  end,  insert.  For  tlie  latest  improvement 
that  has  been  made  in  astronomy,  we  are  also  indebted 
to  the  zeal  and  ingenuity  of  Dr>01bers,who,  in  pursuit 


of  an  opinion  which  be  had  formed,  respecting  the  ori- 
gin of  the  three  small  planets  from  the  separation  of 
a  larger  one  into  frngments,  has  been  in  the  habit  of 
of  examining  monthly  that  part  of  the  heavens,  io 
which  he  supposes  the  event  to  have  taken  place,  and 
through  whicli  each  of  the  bodies  must  necessarily  pass. 
He  has  had  the  good  fortune  to  discover,  in  this  man- 
ner, a  fburth  planet,  which  nearly  resembles  the 
throe  otiiers  in  its  appearance,  except  that  it  seem* 
to  be  considerably  larger. 

P.  C21.  L.  22,  after  "  descriptions,''  insert. 

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. 

P.  622.  L.  5  .  .  13,  for  "  It  may  also  .  .  densities," 
read.  This  mode  of  re.isoniiig  is  however  by  no  means 
sufficient  to  explain  all  the  phenoini  nu  ;  for  it  may  be 
inferred  from  it  that  when  the  attractive  power  of  tlie 
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,  instetvd  of  form- 
ing an  angle  with  it,  as  it  often  does  in  reality.  But 
the  difficulty  may  be  removed  by  reverting  to  the  ge- 
neral principle  of  superficial  cohesion,  and  by  com- 
paring the  common  surface  of  the  liquid  and  solid 
with  the  surface  of  a  single  liquid,  of  which  the  attrac- 
tive powfer  is  equal  only  to  the  difference  of  the  re- 
spective 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  iu  other  cases,  the  angle  of 
contact  will  be  greater,  in  proportion  as  the  solid  is  less 
attractive.  A  similar  comparison  is  also  equally  ap- 
plicable to  the  contact  of  two  liquids  of  different  den- 
sities. 

P.  630.  L.  11,  for  "  one,"  read,  we. 

P.  678.  L.  7.  for  "  when  in  contact,"  read,  cither 
during  their  contact,  or  after  separation. 

P.  702.  L.  9  .  .  28.  For  "  Astronomers  . .  years,'' 
read,  "  nor  can  any  sufficient  cause  be  found,  in  the 
attractions  of  the  celestial  bodies,  either  for  the 
general  easterly  trade  winds,  or  for  the  current  of  the  sea 
in  a  similar  direction,  which  appears  to  be  the  imme- 
diate effect  of  their  friction  on  the  surface  of  the  water." 

P.  770.  Fig.  172,  add.  The  strap  itself  must  how- 
ever be  made  stronger  when  in  the  situation  B. 


COURSE  OF  LECTURES 


ON 


NATURAL  PHILOSOPHY 


AND  THE 


MECHANICAL  ARTS 


PART  I. 


MECHANICS. 


COURSE  OF  LECTURES 


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  na- 
ture of  the  objects  which  its  founders  and  promoters  have  been  endeavouring 
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 
tlaat  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  journey,  may  know  precisely  what 
route  we  are  to  follow,  and  what  departments  will  more  particularly  arrest 
our  attention. 

Societies,  which  are  merely  literary  and  philosqphical,  have  in  general 
prmcipally  proposed  to  themselves,  to  enlighten  the  understanding  by  the 
discovery  of  unknown  phenomena,    and  to  exercise  the  reasoning  powers,  by 


VOL.   r. 


B 


2  tECTURE    I. 

opening  new  fields  for  speculation.  Other  associations  have  been  more  par- 
ticularly intended  for  the  encouragement  of  the  arts,  of  manufactures,  and 
of  commerce.  The  primary  and  peculiar  object  of  the  Royal  Institution  of 
Great  Britain  is  professedly  of  an  humbler,  but  not  of  a  less  interesting  na- 
ture. It  is,  to  apply  to  domestic  convenience  the  improvements  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  provinces  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  this  department  must,  in  the  natural  order 
of  arrangement,  be  anterior  to  the  application  of  the  sciences  to  practical 
uses.  To  exclude  all  knowledge  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  ob- 
servation, can  with  reason  be  declared  wholly  inapplicable  to  the  benefit 
of  mankind. 

It  has  therefore  always  appeared  to  me,  to  be  not  only  the  best  beginning, 
but  also  an  object  of  high  and  permanent  importance  in  the  plan  of  the  In- 
stitution, to  direct  the  public  attention  to  the  cultivation  of  the  elementary 
doctrines  of  natural  philosophy,  as  well  speculative  as  practical.  Those  who 
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  pur- 
poses they  are  applicable:  they  receive  a  sufficient  gratification  from  the  en- 
largement of  their  views  of  the  constitution  of  the  universe,  and  experience, 
in  the  immediate  pursuit  of  knowledge,  that  pleasure  which  others  wish  to 
obtain  more  circuitously.  by  its  means.  And  it  is  one  of  the  principal  advan- 
tages of  a  liberal  education,  that  it  creates  a  susceptibility  of  an  enjoyment 
so  elegant  and  so  rational. 


INTRODUCTION.  S 

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  civilised  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  satis- 
faction, to  the  improvement  of  the  mind,  and  to  the  acquisition  of  know* 
ledge,  than  to  such  amusements  as  are  only  designed  for  facilitating  the  in- 
sipid consumption  of  superfluous  time.  The  hours  thus  spent  will  unquestion- 
ably become,  by  means  of  a  little  habit,  as  much  more  agreeable  at  the  mo- 
ment, as  they  must  be  more  capable  of  affording  self  approbation  upon  re- 
flection. 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  enjoy- 
ment, 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  sub- 
ordinate 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  ob- 
jects of  the  Royal  Institution;  and  Ave  must  therefore  direct  our  attention 
more  particularly  to  the  theory  of  practical  mechanics,  and  of  manufactures. 
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  inventions  of  all  kinds, 
we  may  proceed  in  the  most  direct  manner  to  contribute  to  the  dissemination 
of  that  kind  of  knowledge  which  is  most  particularly  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  element- 
ary 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 


4  LECTURE    I. 

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,  sub- 
servient 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  supported  by  the  head  that  dir 
rects ;  and  much  labour  is  lost  for  want  of  a  little  previous  application  tp  the 
fundamental  doctrines  of  the  mechanical  sciences.  Npr  is  any  exorbitant 
portion  of  time  or  industry  necessary  for  this  purpose;  for  it  happens  singu- 
larly enough,  that  almost  all  practical  applications  of  science  depend  on  prin- 
ciples easily  learnt;  and,  except  in  astronomy  only,  it  has  seldom  been  fbund 
that  very  abstruse  investigations  have  been  of  great  importance  to  society. 
Our  most  refined  analytical  calculations  are  by  far  too  imperfect  to  apply  1;o 
all  possible  cases  of  mechanical  actions  that  caabe  proposed;  ai^d  those  pro- 
blems which  most  frequently  occur,  may  in  general  be  solved  by  metliods 
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  ap- 
plication. 

We  may  also  be  able  to  rendex.an  miportant  service  to  society,  and  to  con- 
fer, a  still  more  essential  benefit  on  individuals,  by  repressing  the  premature 
zeal  of  unskilful  inventors^  ,  Weuepd  g}}\y  read  over  the  monthly  accounts  of  pa- 
tents, intended  fo;?.  securing  the  pecuniajiy  advantages  of  useful  discoveries,  in 
order  to  be  convinced  what  expense  of  time  and  fortune  is  continually  lavishr 
ed  on  the  feeblest  attempts  to  innovate  and  improve.  If  we  can  be  successful 
in  convincing  siich  inconsiderate  enthusiasts  of  their  r^al  ignorance,  or  if  we 
can  show  them,  that  even  their  own  fairy  ground  has  been  preoccupied,  we 
may  save.thep}  from  impending  ruin,  and  may  relie,v.e  the  public  from  the 
distraction  of  having  its  attention  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  sujch  experimental  tests  as  cominou 


INTRODUCTION.  5 

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,  ninety 
at  least,  if  not  ninety  nine,  are  either  old  or  useless ;  the  object  of  our  re- 
gearches  is,  to  enable  ourselves  to  distinguish  and  to  adopt  the  hundredth. 
But  while  we  prune  the  luxuriant  shoots  of  youthful  invention,  we  must  re- 
member 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  fur- 
nished, 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  per- 
haps deserve  admission,  which  will  not  require  so  particular  an  explanation. 
To  those  who  have  profited  by  the  lectures,  or  who  are  already  too  far  ad- 
vanced to  stand  in  need  of  them,  our  rooms  for  reading  and  for  literary  con- 
versation may  be  a  source  of  mutual  instruction.  Our  Library  in  time  nuist 
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  occasion- 
ally be  given  in  the  lectures  on  those  sciences.  Our  Journals,  free  from  com- 
mercial shackles,  will  present  the  public,  from  time  to  time,  with  concise  ac- 
counts of  the  most  interesting  novelties  in  science  and  in  the  useful  arts  ;  and 
they  will  furnish  a  perpetual  incitement  to  their  editors  to  appropriate,  as  muck 
as  possible,  to  their  own  improvement,  whatever  is  valuable  in  the  jxiblications 
of  their  cotemporaries.  When  all  the  advantages,  which  may  reasonably  be 
expected  from  this  Institution,  shall  be  fully  understood  and  impartially  con- 
sidered, it  is  to  be  hoped  that  few  persons  of  liberal  minds  will  be  indifi'ercnt 
to  its  success,   or  unwilling  to  contribute  to  it  and  to  participate  in  it. 

To  that  regulation,  which  forbids  the  intFoduction  of  any  discussions  con- 
nected with  the  learned  professions,  I  shall  always  most  willingly  submit,  and 
most  punctually  attend.  It  requires  the  study  of  a  considerable  portion  of  a 
man's  life  to  qualify  hirh  to  be  of  use  to  mankind  in  any  of  them ;  and  nothing- 
can  be  more  pernicious  to  individuals  or  to  society,  tlian  the  attempting  to 
proceed  practically  upon  an  imperfect  conception  of  a  few  iirst  principles  only. 


6  LECTURE    I.  , 

In  physic,  the  wisest  can  do  but  little,  and  the  ignorant  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 
foi-  the  advancement  of  science  and  for  the  improvement  of  the  mind,  I  thought 
it  in  the  first  place  an  indispensable  duty  to  present  the  Royal  Institution,  in 
my  Syllabus,  with  a  connected  system  of  natural  philosophy,  on  a  plan  seldom, 
if  ever,  before  executed  in  the  most  copious  treatises.  Proceeding  from  the 
simplest  axioms  of  abstract  mathematics,  the  syllabus  contains  a  strict  demon- 
stration of  eveiy  proposition  which  I  have  found  it  necessary  to  employ  through, 
out  the  whole  extent  of  natural  philosophy.  In  the  astronomical  part  only, 
some  observations  occur,  unsupported  by  mathematical  evidence:  here,  how- 
ever, it  was  as  impracticable,  as  it  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  ac- 
curacy, all  the  steps  of  the  demonstrations  on  which  the  doctrines  of  the  me- 
chanical 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 
anight  fail  to  excite  sufficient  attention. 

This  combination  of  experimental  with  analogical  arguments,  constitute^ 
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  congra- 


INTRODUCTION.  7 

tulate  my  audience,  on  the  decided  superiority  of  our  own  country,  in  the  first 
establishment,  and  in  the  subsequent  cultivation,  of  the  true  philosophy  of  the 
operations  of  nature.  I  grant  that  we  have  at  times  been  culpably  negligent 
of  the  labours  of  others ;  tliat  we  have  of  late  suffered  our  neighbours  to  ex- 
cel us  in  abstract  mathematics,  and  perhaps,  in  some  instances,  in  patient 
and  persevering  observation  of  naked  phenomena.  We  have  not  at  this  mo- 
ment a  Lagrange  or  a  Laplace :  what  we  have,  I  do  not  think  it  necessary 
to  enumerate:  but  there  is  a  certain  combination  of  theoretical  reasonins:  with 
experimental  inquiry,  in  which  Great  Britain,  from  the  time  of  the  reforma- 
tion 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  fol- 
lowers 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  philosophy,  has,  in  a  considerable  part  of  Europe,  again  been 
threatening  it.  It  was  in  this  country  that  Newton  advanced,  with  one  gi- 
gantic stride,  from  the  regions  of  twilight  into  the  noon  day  of  science.  A 
Boyle  and  a  Hooke,  w^ho  would  otherwise  have  been  deservedly  the  boast  of 
their  century,  served  but  as  obscure  forerunners  of  Newton's  glories.  After 
these,  a  crowd  of  eminent  men  succeeded,  each  of  great  individual  merit;  but, 
absorbed  in  the  prosecution  of  the  Newtonian  discoveries,  they  chose  rather 
to  be  useful  by  their  humble  industry,  than  to  wander  in  search  of  the  brilli- 
ancy of  novelty.  It  is  difficult  to  judge  of  our  cotemporaries ;  but  we  appear 
at  present  to  be  in  possession  of  more  than  one  philosopher,  whose  names- 
posterity  will  be  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  bd  wholly  unknown,  we  can  have 
little  curiosity :  a  short  sketch  of  the  progress  of  each  branch  of  natural 
philosophy  will  be  more  properly  introduced,  after  we  have  finished  our  inves- 
tigation of  the  principal  doctrines  belonging  to  it. 

With  regard  to  the  mode  of  delivering  these  lectures,   I  shall  in  general  in- 
treat  my  audience  to  pardon  the  formality  of  a  written  discourse,  in  favour  of 


8  LECTURE    r. 

the  advantage  of  a  superior  degree  of  order  and  perspicuity.  It  would  un- 
questionably be  desirable  that  every  syllable  advanced  should  be  rendered  per- 
fectly easy  and  comprehensible  even  to  the  most  uninformed ;  that  the  most 
inattentive  might  find  sufficient  variety  and  entertainment  in  what  is  submit- 
ted 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  recon- 
ciling these  various  objects,  I  shall  esteem  it  better  to  seek  for  substantial 
utility  tlian  temporary  amusement ;  for  if  we  fail  of  being  useful  for  want  of 
being  sufficiently  popular,  we  remain  at  least  respectable:  but  if  we  are 
imsuccessful  in  our  attempts  to  amuse,  we  immediately  appear  trifling  and  con- 
temptible. It  shall  however  at  all  times  be  my  endeavour  to  avoid  each  ex- 
treme ;  and  I  trust,  that  I  shall  then  only  be  condemned,  when  I  am  found  ab- 
struse 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  bear- 
ing 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  th£  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  rriy  audience  may  be  disposed  to  make. 

We  have  to  extend  our  views  over  the  whole  circle  of  natural  and  artificial 
knowledge,  to  consider  in  detail  the  principles  and  application  of  the  philoso- 
phy 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  necessar}"^,  in  order  to  obtain  a  distinct  conception 
ot  the  foundation  and  relation  of  each  subdivision,  to  pay  particular  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  unnecessary;  for  however 
superfluous  we  may  deem  the  scholastic  forms  of  rhetoric,  it  is  confessedly 
advantageous  to  the  judgment  as  well  as  to  the  memory,  to  unite  those  things 
which  are  naturally  connected,  and  to  separate  those  which  are  essentially  dis- 
tinct.    When  a  traveller  is  desirous  of  becoming  acquainted  with  a  city  or 


INTncDUCTIOX.  <^ 

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  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  enlai'ge,  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  accuracy.  The 
public  opinion  is  rather,  on  the  contrary,  in  danger,  at  least  in  some  paits  of 
the  world,  of  being  too  exclusively  biassed  in  favour  of  natural  philosophy  j 
and  has  sometimes  been  mclined  to  a  devotion  too  much  limited  to  science, 
without  a  sufficient  attention  to  such  literature  as  an  elegant  mind  always  de- 
sires to  see  united  with  it.  As  to  the  practical  importance  of  philosophical 
tlieories  of  the  arts,  it  may  have  been  overrated  by  some,  but  no  person  is 
authorised  to  atTirm,  rhat.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,  Avill  never  have  reason  to  complain  of  their  fallacy. 

The  division  of  the  whole  course  of  lectures  into  three  parts,  was  originally 
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,  inclftding  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    t^' 


4.1  j-i 


■  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 

VOL.    I.  c 


10  LECTURE    I. 

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  re- 
tained in  the  memory  by  its  relation  to  the  rest  as  a  connecting  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  in- 
sulated 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  phenomena  of  nature  resemble  the  scatter- 
ed leaves  of  the  Sibylline  prophecies;  a  Avord  only,  or  a  single  syllable,  is 
written  on  each  leaf,  which,  when  separately  considered,  conveys  no  in- 
struction 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  hai-monious  language. 

Proceeding  therefore  in  the  synthetical  order,  we  set  out  from  the  abstract 
doctrines  of  mathematics,  relating  to  quantity,  space,  and  number,  which  we 
pass  over,  as  supposed  to  be  previously  understood,  or  as  sufficiently  explained 
in  the  mathematical  elements,  and  go  on  to  their  immediate  application  to 
mechanics  and  hydrodynamics,  or  to  such  eases  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  mathe- 
matical 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  nature  and  of  art,  and 
to  lay  down  such  laws,  as,  to  an  uninformed  person,  it  would  appear  to  be  be- 
yond the  powers  of  reason  to  determine,  without  the  assistance  of  experiment. 
The  affections  of  falling  bodies,  and  of  projectiles,  the  phenomen*^  of  bodies 
revolving  round  a  centre,  the  motions  of  pendulums,  the  properties  of  the  centre 
of  gravity,  the  equilibrium  of  forces  in  machines  of  diflferent  kinds,  the  laws 
of  preponderance,  and  the  efi'ects  of  collision ;  all  these  are  wholly  referable  to 
axiomatical  evidence,  and  are  frequently  applicable  to  important  uses  in  prac- 
tice. Upon  these  foundations,  we  shall  proceed  to  the  general  principles  of 
machinery,  and  the  application  of  forces  of  different  kinds :  we  shall  inquire 
what  are  the  principle  sources  of  motion  that  we  can  subject  to  our  command, 
and  what  advantages  are  peculiar  to  each  of  them ;   and  then,  according  to 


INTRODUCTION*.  H 

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  suhservient 
to  mathematical  purposes,  will  be  the  first  in  order,  including-  all  the  meclian- 
ism  of  literature,  the  arts  of  writing,  engraving,  and- printing,  in  their  various 
branches,  and  the  comparison  of  measures,  with  each  other  and  with  differ- 
ent standards ;  the  principles  of  perspective  will  also  form  a  useful  appendage 
to  the  description  of  geometrical  instruments.  The  determination  of  weights, 
and  of  the  magnitude  of  moving  forces  of  various  kinds,  constituting  the  sci- 
ence of  statics,  will  be  the  next  subject,  and  will  be  followed  by  the  con- 
sideration 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  complicated 
as  not  to  admit  of  regular  arrangement  without  some  difficulty:  they  may 
however  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  gravitation :  these  compre- 
hend the  employments  of  the  mason,  the  bricklayer,  the  joiner,  the  cabinet 
maker,  and  the  locksmith.  In  these  departments  it  is  often  of  the  utmost  im- 
portance to  the  mechanic,  to  recur,  especially  in  works  of  magnitude,  to  philoso- 
phical principles ;  and  in  many  other  cases,  where  there  is  no  need  of  much 
calculation,  we  may  still  be  of  service,  by  collecting  such  inventions  of  in- 
genious artists,  as  are  convenient  and  elegant,  and  which,  although  simple  in 
their  principles,  are  not  obvious  in  their  arrangements;  and  in  the  same  man- 
ner we  may  be  able,  in  taking  a  general  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  alter- 
ation, by  joints  of  various  kinds,  by  wheelwork,  and  by  cordage,  and  its 
equalisation  by  means  of  timekeepers.  The  subject  of  wheehvork  gives  con- 
siderable scope  for  mathematical  research,  and  requires  the  more  notice,  as  it 


H  N  LECTURE    I. 

has  often  been  inaccurately  treated:  the  consideration  of  cordage  leads  us  to- 
that  of  union  by  twisting,  and  by  intermixture  of  fibres;  including  the  im- 
portant arts  of  carding,  combing,  spinning,  ropemaking,  weaving,  fulling, 
felting,  and  papermaking;  which  constitute  the  employment  of  many  mil- 
lions of  manufacturers,  of  all  ages  and  sexes,  in  every  part  of  the  world,  and 
by  which  the  animal  and  vegetable  productions  of  a  large  portion  of  the  sur- 
face of  the  globe,  are  made  to  contiibute,  as  well  to. the  power  and  riches  of 
the  individuals  wlio  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  pe- 
culiarly interesting  department  of  practical  mechanics,  it  affords  employment 
for  mathematical  investigation,  for  experimental  inquiry,  and  for  ingeni6us  in- 
vention; and  the  perfection,  wliich  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  engaged  in  it.. 

To  counteract  the  powers  of  gravitation  and  of  friction,  is  the  object  of 
such  machines  as  are  vised  for  raising  and  removing  weights :  cranes,  friction 
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  machinery  intended  for 
compression,  extension,  penetration,  attrition,  trituration,  agitation,  and  de- 
molition. 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  turn- 
ing; mills  of  various  kinds,  threshing  mills,  corn,  mills,  oil  mills,  and  powder 
mills;  besides  the  chemical  agents  concerned  in  blasting  rocks,  and  in  the  opei*^ 
ations  of  artillery.  All  these  arts  are  comprehended  in  the  department  of  me- 
chanics, which  constitutes  the  first  division  of  this  course.  Not  that  we  shall 
be  able  to  enter  at  large  into  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  hydrodvnamics  relate  to  the  motions  and  affections  of 


INTRODUCTION.  Iti 

fluids,  in  which  we  no  longer  consider  each  distinct  particTe  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  the  affections 
of  liquids  at  rest,  pneumatostatics,  or  the  properties  of  clastic  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  ad- 
vantage, the  draining  of  lands  and  mhies,  the  supply  of  water  for  domestic 
convenience,  the  manoeuvres  of  seamanship,  the  construction  of  the  steam 
engine,  are  all  dependent  upon  hydrodynamical  principles,  and  are  often  con- 
sidered as  comprehended  in  the  science  of  hydraulics.  Harmonies  and  optics, 
the  remaining  parts  of  this  division,  are  more  insulated :  the  doctrine  of 
sound,  the  theory  of  music,,  and  the  construction  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  indis- 
pensable necessity  to  the  navigator,  to  tire  naturalist,  to  the  physiologist,  and 
evert  to  the  man  of  business  or  pleasure.  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  ex- 
plained hereafter. 

The  contemplation  of  the  particular  phenomena  of  nature,  as  they  are  dis- 
played in  the  universe  at  large,  contributes  perhaps  less  to  the  perfection  of 
any  of  the  arts,  which  are  immediately  subservient  to  profit  or  convenience,, 
than  the  study  of  mechanics  and  hydrodynamics.  But  the  dignity  and  mag'^ 
niiicence  of  some  of  these  phenomena,  and  the  beauty  and  variety  of  others, 
render  them  highly  interesting  to  the  philosophical  mind,  at  the  same  tinle 
that  some  of  them  are  of  the  utmost  importance  in  their  application  to  the 
purposes  of  life.  In  ail  these  respects  the  science  of  astronomy  holds  the  first 
rank ;  its  uses  in  assisting  navigation,  and  in  regulating  chronology,  are  be- 
yond all  calculation.  Geography,  and  hydrography,  or  the  particular  histories 
of  the  earth  and  sea,  are  immediately  connected  with  astronomy.  The  discus- 
iion  of  the  properties  of  matter  in  general,    and  of  the  alterations  of  tempera-- 


,14  LECTURE    I. 

tuie  to  which  all  bodies  are  hable,  has  not  hitherto  received  a  distinct  appel- 
lation as  a  science ;  but  both  these  subjects  require  a  separate  consideration,  and 
afford  a  vast  scope  for  speculation  and  for  observation.  Electricity  and  magne- 
tism 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  utihty  of  the  philosophy  of  electricity 
is  sufKciently  exemplified  in  the  general  introduction  of  conductors  for  secur- 
ing us  against  lightning,  to  say  nothing  of  the  occasional  employment  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; 
notwithstanding  many  difltuse  treatises  which  relate  to  them,  we  cannot  boast 
of  having  reduced  them  to  any  determinate  laws ;  and  yet  there  are  some  me- 
teorological 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  philo- 
sophy 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  experiments  with  which  the  labours  of  our 
cotemporaries  have  presented  us,  and  which  will  be  exhibited  in  the  theatre 
of  the  Royal  Institution  by  the  Professor  of  Chemistry,  are  sufhcient  to 
make  this  department  of  natural  philosophy  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  ana  sciences,  comprehended  in  it,  are  principally  applicable. 


INTRODUCTION.  15 

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  em- 
ployed, 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  en- 
sue, is  the  most  general  and  most  important  law  of  nature;  it  is  the  founda- 
tion 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  cau- 
sation, 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  fol- 
lowed 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  bow- 
string 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  supported;  and 
the  pressure  of  the  string  to  be  the  cause  of  the  arrow's  motion,  and,  that  if 
we  shoot,  the  arrow  will  fly ;  if  we  hesitated  to  make  these  conclusions,  "we 
should  often  pay  de:ir  for  our  scepticism.  This  explanation  is  sufficient  to 
show  the  identity  of  the  two  expressions,  that  like  causes  produce  like  effects, 
and,  that  in  similar  circumscances  similar  consequences  ensue.  And  such  is 
the  ground  of  argument  from  experience,  the  simplest  principle  of  reasoning, 
after  pure  nK! them atical  truths;  which  appear  to  be  so  far  prior  to  experi- 
ence, as  their  contradiction  always  implies  an  absurdity  repugnant  to  the 
imaginatioco 

In  the  application  of  induction,  the  greatest  caution  and  circmnspection 
are  necessary ;  for  it  is  obvious  that,  before  we  can  infer  with  certainty  the 
complete  similarity  of  two  ^ents,  we  must  be  perfectly  well  assured  that  we 
are  acquainted  with  every  circumstance  which  can  have  any  relation  to  their 
causes.     The  error  of  some  of  the  ancient  schools  consisted  principally  in  the 


]()  LECTURE    I. 

want  of  sufficient  precaution  in  this  respect;  for  although  Bacon  is,  with 
great  justice,  consiclered  as  the  author  of  the  most  correct  method  of  induc- 
tion, yet,  according  to  his  own  statement,  it  was  chiefly  the  guarded  and  gra- 
dual application  of  the  mode  of  argument,  that  he  laboured  to  introduce.  He 
remarks,  that  the  Aristotelians,  from  a  hasty  observation  of  a  few  concurring 
facts,  proceeded  immediately  to  deduce  universal  principles  of  science,  and 
fimdamental  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.  Wd 
observe,  that,  in  general,  heavy  bodies  fall  to  the  ground  unless  tliey  are  Sjup- 
ported;  it  was  therefore  concluded  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  em- 
ployed in  observing  the  effects  of  fluids  on  falling  and  on  floating  bodies,  in 
examining  the  relations  of  flame  to  the  circumambient  atmosphere,  and  in  as- 
certaining 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  pheno- 
menon. , 

■"  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, 


INTRODUCTION.  -  17 

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  in- 
creased nor  diminished,  and  which  are  found  in  all  bodies  within  the  reach  of 
our  experiments,  are  to  be  considered  as  general  qualities  of  all  bodies  exist- 
ing:" fourthly,  "in  experimental  philosophy,  propositions  collected  by  induc- 
tion from  phenomena,  are  to  be  esteemed  cither  accurately  or  veiy  nearly  true, 
notwithstanding  any  contrary  hypotheses,  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  instance 
from  the  subject  of  electricity.     Supposing  that  we  wish  to  determine,  whe- 
ther or  no  the  electric  fluid  has  weight ;    we  are  to  inquire  whether  or  no  gra- 
vitation 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  di- 
minution 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  comprehensive  a  scale,    that  we  shall  find  it 
more  secure  to  be  contented  to  proceed  gradually  by  closer  inductions  in  par- 
ticular cases.     We  shall  however  seldom  be  much  embarrassed  in  the  choice 
of  a  mode  of  argumentation.     The  laws  of  motion,    Avhich  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  satis- 
factory manner,  by  means  of  our  general  axiom,    from  reasonings  purely  ma- 
thematical,  which,    wherever  they  are  applicable,    are  unquestionably  prefer- 
able to  the  imperfect  evidence  of  the  senses,  employed  in  experimental  inves- 
tigations. 

VOL.    I.  D 


18 


LECTURE  ir. 


ON    MOTION. 


TL  HE  whole  science  of  mechanics  depends  on  the  laws  of  motion,  either  ac- 
tually existing,  or  suppressed  by  the  opposition  of  the  forces  which  tend  to 
produce  it.  The  nature  of  motion  requires  therefore  to  be  particularly  ex- 
amined 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 
ijeldom  capable  of  receiving  much  immediate  illustration  from  the  objects  of 
sense,  yet  we  shall  find  it  indispensable  to  our  progress  in  the  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, 
i?.  said  to  have  walked  across  the  room,  and  to  have  answered,  you  see  it,  but 
what  it  is,  1  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  resoliition 
of  a  complex  idea  int,o  the  more  simple  elements  which  compose  it;  and,  in  the 
present  instance,  these  elements  are,  the  existence  of  two  points  at  a  certain 
^stance^  and  after  a  certain  interval  of  time,  the  existence  of  the  same  points 
at.a  different  distance;  the  difterence  of  the  distances  being  supposed  to  be  as- 
certained according  to  that  postulate  of  geometry,  which  has  in  general  been 
tacitly  understood,  but  which  I  have  expressly  inserted  iri  the  geometrical  part 
of  my  syllabus ;  requiring  that  the  length  of  a  line  be  capable  of  being  identi- 
fied, whether  by  the  effect  of  any  object  on  the  senses,  or  merely  in  ima- 
gination. 

Motion,  therefore,  is  the  change  of  rectilinear  distance  between  two  points. 
Allowing  the  accuracy  of  this  definition,    it  appears  that  two  points  are  ne- 

\ 


ox    MOTION.  \Q 

cessary  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  consequence  of  our  de- 
finition, and  the  paradox  is  only  owing  to  the  difficulty  of  imagining  the  ex- 
istence 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  relative  mo- 
tion. For  the  definition  of  motion,  as  the  change  of  rectilinear  distance  be- 
tween two  points,  appears  to  be  the  definition  of  what  is  commonly  called  re- 
lative motion ;  but,  on  a  strict  examination,  we  shall  find,  that  what  we  usu- 
ally 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  perpe- 
tually in  motion,  and  that  in  very  various  directions :  nor  are  any  material 
objects  accessible  to  our  senses,  which  we  can  consider  as  absolutely  motion- 
less, or  even  as  motionless  with  regard  to  each  other;  since  the  continual  va- 
riation 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  ex- 
ists a  body  absolutely  at  rest,  in  as  strict  a  sense  as  an  absolutely  straight  line 
may  be  conceived  to  exist,  we  cannot  positively  affinn;  and  if  such  a  quies- 
cent body  did  exist,  we  have  no  criterion  by  which  it  coidd  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  revolv- 
ing round  the  axis  of  the  earth,  and  with  the  earth  round  the  sun;    and  with 


20  LECTURE    II. 

the  sun  and  the  whole  solar  system,  he  would  be  slowly  movmg  among  the 
starry  worlds  which  surround  them.  Now  with  respect  to  any  ettects  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  determining  those  effects.  In  the  same  manner,  if  the  ship 
appear,  by  comparison  with  the  water  only,  to  be  moving  through  it  with  the 
velocity  of  three  miles  an  hour,  ami  the  water  be  moving  at  the  same  time  in 
a  contrary  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  sTifficient  to  observe  the  increase  or  decrease  of  distance  of  a  mov- 
ing point  from  another  single  point  only:  we  must  compare  its  successive  si- 
tuations with  many  other  points  surrounding  it;  and  for  this  purpose  these 
points  must  be  at  rest  among  themselves,  in  order  to  be  considered  as  belong- 
ing to  a  quiescent  space  or  surface ;  which  may  be  defined  as  a  space  or  sur- 
face, 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  influ- 
ence of  a  centripetal  force,  which"renders  it  improper  for  determining  the  af- 
fections 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  re- 
mains 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  definition,  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 


ON    MOTIOK.  21 

tangent:  for  it  meets  the  curve,  but  does  not  cut  it,  provided  that  the  curva- 
ture 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  derivable 
from  the  essence  of  the  definitions  that  have  been  premised.  The  first  is,  that 
a  moving  point  never  quits  the  line  of  its  direction  without  a  disturbing  cause : 
-for  a  right  line  being  the  same  witb  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  in- 
dependent of  experimental  proof.  It  was  once  proposed  as  a  prize  question 
by  the  academy  of  sciences  at  Berlin,  to  determine  whether  the  law&  of  mo- 
tion were  necessary  or  accidental;  that  is,  whether  they  were  to  be  consider- 
ed as  mathematical  or  as  physical  truths.  Maupertuis,  then  president  of  the 
academy,  wrote  an  elaborate  dissertation,  in  which  he  endeavoured  to  deduce 
them  from  a  complicated  principle  of  the  prodtiction  of  every  eifect  in  the 
manner  which  requires  the  least  possible  action^  a  principle  which  he  sup- 
poses to  be  most  consistent  with  the  wise  economy  of  nature.  But  this  prin- 
ciple has  itself  been  shown  to  be  capable  of  accommodation  to  any  other 
imaginable  laws  of  motion,  and  the  intricacy  of  the  theory  tends  only  to  en- 
velope the  subject  in  unnecessary  obscurity;  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  produce  like  effects.  If,  however,  any  person 
thinks  differently,  he  is  at  liberty  to  call  these  laws  experimental  axioms,  col- 
lected from  a  comparison  of  various  phenomena;  for  we  cannot  easily  reduce 
them  to  direct  experiments,  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  ex- 
amine. 

Having  established  the  rectilinear  direction  of  undisturbed  motion,   we 


22  LFXTURE    ir. 

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  it  is  obvious  that  the  results  of  an  intellectual 
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  ob- 
jects will  often  make  a  week  appear,    upon  retrospection,    as  long  as  a  month 
spent  in  a  continuation  of  such  employments  as  are  uniform,  without  being  la- 
borious ;   the  multitude  of  new  impressions  not  only  serving  to  increase  the  ap- 
parent magnitude  of  the  interval,  by  filling  up  its  vacuities,  but  tending  also 
to  diminish  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  ob- 
jects: of  these  changes,  the  simplest  and  most  convenient  is  the  apparent  mo- 
tion of  the  sun,  or  rather  of  the  stars,  derived  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  mo- 
tion, which,  with  the  former  law,  constitutes  Newton's  first  axiom  or  law  of 
motiort:  "  that  every  body  perseveres  in  its  state  of  rest  or  uniform  rectilineaf 
motion,  except  so  far  as  it  is  compelled  by  some  force  to  change  it."  It  ap- 
pears that  this  second  law  is  strictly  deducible  from  the  axioms  and  definitions 
which  have  been  premised,  and  principally  from  the  consideration  of  the  re- 
lative nature  of  motion,  and  the  total  deficiency  of  a  criterion  of  absolute  mo- 
tion. For,  since  the  velocity  of  a  body,  moving  without  resistance  or  disturb- 
ance, 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  efi^ect 
on  the  velocity  of  the  first  body,  however  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 


oil    UOTlOVt.  ^3 

motions  of  those  bodies  may  be,  when  compared  with  the  surrounding  objects; 
and  these  relations  can  only  be  preserved  by  its  continuance  in  uniform  recti- 
linear motion.  Tills  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  to- 
tally exempt  from  the  operation  of  all  accelerating  or  retarding  causes;  and 
the  deductions  from  such  experiments  as  we  can  make,  would  require  in  ge- 
neral, 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 
forthedisturbingforceof  gravitation,  which  so  modifies  the  effect,  tliat  the  bo- 
dy deviates  from  a  right  line,  but  remains  in  the  same  vertical  plane ;  whence 
we  may  infer,  that,  in  the  absence  of  the  force  of  gravitation,  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  common  intersection,  which  could  only 
be  a  straight  line:  so  that  by  thus  combining  arguments  Avith  observation,  we 
may  obtain  a  confirmation  of  the  law  of  the  rectilinear  direction  of  undisturb- 
ed motion,  partly  founded  on  direct  experiments 'Its  uniformity  is  however 
still  less  subjected  to  immediate  examination;  ytf,  from  a  consideration  of  the 
natiue  of  friction  and  resistance,  combined  with  the  laws  of  gravitation,  we 
thay  ultimately  show  the  perfect  Coincidence  of  the  flieory  with  experiment. 
The  tendency  of  matter  to  persevere  in  this  manner'  in  the  state  of  rest  or 
of  uniform  rej^tilinear  motion,  is  called  its  inertia. 

In  all  thicse  cases  it  is  of  importahcfe  to  attend  to  the  composition  of  motion, 
or  the  joint  effieCt  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  combina- 
tion or  separation  of  relations  that  is  considered:  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  walk- 
ing 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 


24  JLECTURE    H, 

motion,   and  to  examine  how  it  may  mov£  in  tlie  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  rectiUnear  distance  of  each,  from  each  of  the  rest,  re- 
mains 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  re- 
spect to  the  other.  This  is  easily  exemphfied  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  square  is  made  to  slide  along  the 
straight  edge'  of  a  board,  the  surface  of  the  square  is  in  rectilinear  motion 
Avith  respect  to  the  board.     (Plate  L  ¥ig.  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  respect  to  the 
other  plane,  the  one  in  common  with  its  plane,  and  the  other  peculiar  to  it- 
self; and  the  joint  effect  of  these  motions  with  respect  to  the  second  plane  is 
called  the  result  of  the  two  motions.  Thus,  when  a  carriage  moves  on  a  per- 
fectly 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  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  whatever  position  the  arm  be  fixed.  Here  we  have 
two  motions  in  the  slider,  one  in  common  with  the  arm,  and  the  other  pecu- 
liar to  itself,  which  may  be  either  equal  or  unequal  to  the  first;  and  by  trac- 
ing a  line  on  a  fixed  plane,  with  a  point  attached  to  the  slide/,  we  may  easily 
examine  the  joint  result  of  both  the  motions.     (Plate  I.  Fig.  6.) 


ON    MOTION.    .  25 

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  motions ; 
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 
coexistence  of  two  motions  in  the  sense  that  has  been  defined;  it  is  also  ca- 
pable of  a  complete  illustration  by  means  of  the  apparatus  that  has  been  de- 
scribed.    (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  mo- 
tion. 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  mathematical 
quantities,  and  we  must  relinquish  the  prejudice;  derived  from  our  own  feel- 
ings, 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 
from  the  original  words  of  Aristotle,  in  his  mcclianical  problems.  He  says, 
that  if  a  moving  body  has  two  motions,  bearing  a  constant  proportion  to 
each  other,  it  must  necessarily  describe  the  diameter  of  a  parallelogram,  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  weshould  scarce- 
ly have  expected,  that,  from  the  time  at  which  the  subject  began  to  be  so  clcar- 

VOJL.     I.  E 


q6  lecture  II. 

ly  understood,  two  thousand  years  would  have  elapsed,  before  this  law  began 
to  be  applied  to  the  determination  of  the  velocity  of  bodies  actuated  by  de- 
flecting 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  parallelogram  by 
two  forces  acting  conjointly,  in  the  same  time  in  which  it  would  describe  its 
sides  by  the  same  forces  acting  separately."  It  appears,  however,  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,  repre- 
sented by  the  sides  of  a  polygon,  that  is,  of  a  figure  consisting  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  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  southwards,  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  ele- 
vation of  its  path,  and  its  velocity  in  the  direction  of  its  motion. 


27 


LECTURE  III. 


ON    ACCELERATING    FORCES. 


l^E  have  hitherto  only  considered  motion  as  ah-eady  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  catise  which  pr6duc'es  motion  in  a  body  at  res't,  or 
which  increases,  diminishes,  oi*  modifies  it  in  a  body  which  -tvas  before  in  mo- 
tion. 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  re- 
tarding 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  motion  with  respect  to  a  quiescent  space.  For  if  the  change  were 
only  in  the  relative  motion  of  two  points,  it  might  happen  without  the  opera- 
tion of  any  force:  thus,  if  a  body  be  moving  Without  disturbance,  its  motion 
with  respect  to  another  body,  not  in  thehneofits  direction,  will  be  perpetually 
changed ;  and  this  change,  considered  alone,  would  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  con- 
sequence of  the  centrifugal  effect  of  a  rotatojy  motion.     (Plate  I.  Fig.  9-> 


iJ8  LECTURE    III. 

The  exertion  of  an  animal,  the  unbending  of  a  bow,  and  the  commun?Ca- 
tion  of  motion  by  impulse,  are  familiar  instances  of  the  actions  of  forces.  Wc 
must  not  imagine  that  the  idea  of  force  is  naturally  connected  with  that  of  la- 
bour or  difficulty;  this  association  is  only  derived  from  habit,  since  our  vo- 
luntary 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  ta 
produce  motion;  for  instance,  by  what  means  the  earth  causes  a  stone  to  gra- 
vitate towards  it.  In  some  cases,  indeed,  we  are  disposed  to  imagine  that  we 
understand  better  the  nature  of  the  action  of  a  force,  as,  when  a  body  in  mo- 
tion strikes  another,  we  conceive  that  the  impenetrability  of  matter  is  a  suffi- 
cient cause  for  the  communication  of  motion,  since  the  first  body  cannot  con- 
tinue its  course  without  displacing  the  second;  and  it  has  been  supposed  that 
if  we  could  discover  any  similar  impulse  that  might  be  the  cause  of  gravita- 
tion, we  should  have  a  perfect  idea  of  its  operation.  But  the  fact  is,  that 
even  in  cases  of  apparent  impulse,  the  bodies  impelling  each  othcF  are  not  ac- 
tually in  contact;  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  Professor  Robison  has  estimated  this  force  at  a  thousand  pounds  for  every 
square  inch.  These  extremely  minute  intervalsiiave  been  ascertained  by  ob- 
servations 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  mi- 
croscope, 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  dimensions  accordingly.  Hence  it  is  obvious, 
that  whenever  two  pieces  of  glass  strike  each  other,,  without  exerting  a  pres- 
sure 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  ac- 

i 


ON    ACCZLERATIXG    FOUCES.  <>9 

knowledge  our  total  ignorance  of  the  intimate  nature  of  forces  of  every  kind; 
and  we  are  first  to  examine  the  eftect  offerees,  considering  only  their  magni- 
tude and  direction,  without  any  regard  to  their  origin. 

It  was  truly  asserted  by  Descartes,  that  the  state  of  motion  is  equally  na- 
tural with  that  of  rest.  When  a  body  is  once  in  motion,  it  requires  no  fo 
reign  power  to  sustain  its  velocity.  If  therefore  a  moving  body  is  subjected 
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  ston*,  for 
instance,  beginning  to  fall,  or  projected  downwards,  by  uo  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  destroying  whatever  opposes  its  progress.  In 
the  same  manner,  when  a  ball  is  thrown  upwards,  it  gradually  loses  its  motion 
by  the  operation  of  gravitation,  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  ve- 
locity; 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  (juantity  or  degree  of  its  motion,  independently  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  instance  a  second,  if 
there  were  no  other  motions  than  undisturbed  or  uniform  motions :  but  the  ve- 
locity 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  ele- 
ments 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  velocity,  is  this,  that  the  change  produced  in  the  velocity, 
tluring  so  short  an  interval  of  time,  must  be  absolutely  inconsiderable  in  com- 
parison with  the  whole  velocity,  and  the  element  of  space  becomes  a  true  mea- 
sure of  the  temporary  velocity,  in  the  same  manner  as  any  larger  portion  of 
space  may  be  the  measure  of  a  uniform  velocity. 


30  LECTURE  nr. 

Wlieu  the  increase  or  diminution  of  the  velocity  of  a  moving  body  is  uni- 
form, 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 
1)ody  Avould  describe  one  foot  and  ten  feet  in  the  respective  seconds,  if  undis- 
turbed, and  the  spaces  actually  described  become  two  feet  and  eleven  feet,  each 
being  increased  one  foot,  the  accelerating  force  must  be  denominated  uniform. 

•  The  power  of  gravitation,  acting  at  or  near  the  earth's  surface,  may,  with- 
out 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  correctly  l6-fV, 
in  tile  first  second ;  if  it  begins  a  second  with  a  velocity  of  SSI  feet,  it  describes 
.'32  and]  6,  or  4  H  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 
fj^iteptible,  iit  any  heights  within  our  reach,  by  the  nicest  tests  that  we  can 
employ.  . 

The  velocit}'  produced  by  any  uniformly  accelerating  force,  is  proportional 
to  the  magnitude  of  the  force,  and  the  time  of  its  operation  conjointly.  When 
tlie  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 
diifer,  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  se- 
parate forces  or  motions,  approach  to  each  other,  and  at  last  coincide  in  direc- 
tion, the  diagonal  of  the  parallelogram,  representing  their  joint  effect,  becomes 

equal  to  the  sum  of  the  sides,     (Plate  I.  Fig.  10.) 

./<:'•   DV  -Mi  n't  -:  ^ 

The  machine  invented  by  Mr.  Atwood  furnishes  us  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  sub- 
mitted to  experimental  examination;  but  by  means  of  this  apparatus,  we  can 

2 


ON    ACCELERATING    FORCE?.  JJ 

diminish  it  in  any  degree  that  is  required.  Two  boxes,  which  are  attached  to  a 
thre  1(1  passing  over  a  pulley,  may  be  filled  with  different  vveights,  wliich  coun- 
terbalance 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  lialf  second  pendulum,  the  space  de- 
scribed being  ascertained  by  the  place  of  a  moveable  stage,  against  which  the 
bottom  of  the  descending  box  strijses:  and  when  we  wish  to  determine  imme- 
diately the  velocity  acquired  at  any  point,  by  measuring  the  space  uniforndy 
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  uni- 
form 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  conveni- 
ent mode  of  letting  the  weights  go,  without  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  pendulum.     (Plate  I.  Fig.  11.) 

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  uni- 
form accelerating  force,  .may  be  shown  by  placing  the  moveable  ring  so  as  to 
intercept  the  same  bar  successively  at  two  different  points:  thus  the  spact; uni- 
formly 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  gcDcrated  in  a  given  time  is  proportional  to  the  force 
employed. 

We  are  neJit  to  determine  the  magnitude  of  the  whole  space  described  in  a 
given  time  with  a  velocity  thus  uniformly  increasing.  The  la;W  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,  is  one  of  the  most  useful  and  interesting  propositions 
in  the  whole  science  of  mechanics.  Its  truth  is  easily  shown  from  mathema- 
tical considerations,  by  comparing  the  time  with  the  base,  and  the  velocity 
with  the  perpendicular  of  a  triangle  gradually  increasing,  of  which  the  area 


St  LECTURE    IV. 

Standing  its  weiglit,  to  the  sling  which  is  above  it,  in  consequence  of  the  ex- 
cess of  the  centrifugal  force  abo\e  the  force  of  gravitation. 

It  is  also  a  centrifugal  force  that  is  thp  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  Avhcn  it  is  moving  forwards,  a  slight  inclination  towards 
either  side  causes  the  parts  to  acquire  amotion  towards  that  side,  those  which 
are  uj)permost  being  most  affected  Iry  it;  and  this  lateral  motion,  assisted 
sometimes  by  the  curvature  of  the  surface  of  the  hoop,  causes  its  path  to  de- 
viate 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  po- 
sition, its  tendency  to  fall  still  further  is  counteracted  by  the  centrifugal  force, 
and  it  generally  makes  several  complete  revolutions  before  it  falls.  The  mo- 
tion of  a  bowl,  with  its  bias,  is  of  a  similar  nature;  the  centrifiigal  force 
counteracting  the  tendency  to  curvilinear  motion,  so  as  to  diminish  it  very  con- 
siderably, until  the  velocity  is  so  much  reduced,  as  to  suifer  it  to  describe  a  path 
evidently  curs'ed,   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  tliat  which  it  would  acquire,  in  falling,  by 
means  of  the  same  force,  if  uniform,  through  half  the  radius,  tliat  is,  through 
one  fourth  of  the  diameter.  This  proposition  affords  a  very  Convenient  me- 
thod of  comparing  the  effects  of  central  forces  with  those  of  simple  accele- 
rating forces,  and  deserves  to  be  retained  in  memory.  We  may  in  some  mea- 
sure demonstrate  its  truth  by  means  of  the  whirling  table:  an  apparatus  which 
is  arranged  on  purpose  for  exhibiting  the  properties  of  central  forces,  although 
it  is  more  calculated  for  showing  their  comparative  thati  their  absolute  magni- 
tude; 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  pvdlies  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  gra- 
dually increased,   produces  a  sufiicient  centrifugal  force,  both  stages  may  raise 

2 


ox    DEFLECTIVE    FORCES.  35 

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  measured 
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  ac- 
quired by  any  heavy  body  in  falling  through  a  height  equal  to  half  the  dis- 
tance from  the  centre,  and  as  much  greater  as  is  sufficient  for  overcoming  the 
friction  of  the  machine.     (Plate  I,  Pig.  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  gra- 
vity. 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 
he  eight  feet  in  a  second,  since  eight  times  the  square  root  of  1  is  eight;  and 
this  must  be  its  velocity  at  the  highest  ])oint;  with  this  velocity  it  would  per- 
form 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. 
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; 
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  distances. 

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  performed  in 
the  sajne  time. 


3Q  i^EcruRE  IV. 

In  general,  the  forces  are  a&  tlie  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  iucceased  to,  half  of  its  ori- 
ginal magnitude. 

From  these  principles  we  may  deduce  the  law  which  was  discovered  by 
Kepler  in  the  motions  of  the  planetary  bodies,  but  which  was  first  demon 
strated  by  Newton  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  revohition  are  proportional  to  the  cubes  of  the  dis- 
tances. Thus  if  the  distance  of  one  body  be  four  times  as- great  as  that  of 
another,  the  cube  of  4  being  G4,  which  is  the  scjuai^e  o-f  8,  the  time^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  simples 
laws  which  have  already  been  laid  down. 

Hitherto  we  have  supposed  the  orbit  of  a  revolving  body  to  be  a  perfect 
circle;  but  it  ol ten  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  disco- 
vered by  Kepler;  that  the  right  line  joining  a  revolving  body  and  its  centre 
of  attraction,  always  describes  equal  aieas  in  Cfjual-  times,  and  the  velocity  of 
the  body  is  therefore  always  inversely  as  the  peri>endicular  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 
Wallis  greatly  advanced,  and  which  Newton  brought  near  to  perfection.  Its 
truth  may  be  in  some  measure  shown  by  an  experiment  on  tlie  revolution  of 
a  ball  suspended  Ijy  a  long  thread,  and  drawn  towards  a  point  immediately 
under  the  point  of  suspension  by  another  thread,  which  may  either  be  held 
in  the  hand,  or  have  a  weight  attached  to  it.  The  ball  being  made  to  re- 
volve, its  motion  becomes  evidently  more  rapid  when  it  is  drawn  by  the  ho- 


ON    DEFLECTIVE    FORCES.  37 

rizontal  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  maybe  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  tbe  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 ;  that  is,  that  the 
force  directed  to  its  focus  must  be  inversely  as  the  square  of  the  distance. 
We  have  no  other  expcrimentul  proof  of  this  theorem  than  astronomical  ob- 
servations, which  are  indeed  perfectly  decisive,  but  do  not  require  to  be  here 
anticipated.     (Plate  II.  Fig.  16.) 

There  is  another  general  proposition  which  is  sometimes  of  use  in  the  com- 
parison of  rectilinear  and  curvilinear  motions.  Two  bodies  being  attracted  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  re- 
main always  equal  at  equal  distances,  whatever  be  their  directions.  For  in- 
stance, if  one  cannon  ball  be  slxot  oblitjuely  upwards,  and  anotlier  perpendi- 
cularly 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  lias  usually  been  made  a  step  in  tbe  demonstra- 
tion 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  fuom  the 
earth's  surface,  the  actual  weight  of  a  body  is  diminished  about  a.  two  thour 
sandth  part,  or  three  grains  and  a  half  for  every  pound,  and  w.e  may  discover 
this  inequality  by  means  of  the  vibrations  of  pendulutns,   which  become  a  lit- 


38  LFXTURE    IV. 

tic  slower  when  they  are  placed  on  the  summits  of  very  high  mountains.  On 
the  other  hand,  a  body  not  specifically  heavier  thau  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, 
liut  both  these  differences  ma}-,  in  all  common  calculations,  be  wholly  disre- 
garded. The  direction  of  gravity  is  always  exactly  perpendicular  to  the  ho- 
rizon, that  is,  to  the  surface  of  the  earth,  which  is  somewhat  curved,  on  ac- 
count 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. 

The  oblique  motion  of  a  prqjectile  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  tilie  composition  of  motion, 
that  the  horizontal  velocity  will  not  be  aflPected  by  the  force  of  gravitation 
acting  in  a  direction  perpendicular  to  it,  and  that  it  will  therefore  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  projectile 
will  rise,  by  finding  the  height  from  Avhich  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,  consequently  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  re- 
tarded by  the  air,  that  it  docs  not  attain  the  height  of  a  single  mile. 


ON    DEFLECTIVE    FORCES.  S^ 

Wc  may  easily  find  the  time  of  the  body's  ascent  from  its  initial  velocity ; 
for  the  time  of  ascent  is  directly  proportional  to  the  velofcity,  and  may  be  found 
in  seconds  by  dividing  the  vertical  velocity  in  feet  by  32;  or  if  we  divide  by 
16  only,  we  sllall  have  the  time  of  ascent  and  descent;  and  then  the  horizontal 
rano-e  mavl>e: found,  by  calculating  the  distance  described  in  this  time,  with  the 
imiform  horizontal  velocity.  Thus,  in  the  example  that  wc  have  assumed,  di- 
vidino-  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  horizontal  range  is  31  times  886,  that  is, 
nearly  28000  feet,  or  above  5  miles.  Biit  the  resistance  of  the  air  will  reduce 
this  distance  also  to  less  than  one  mile. 

It  may  be  demonstrated  that  the  horizontal  rat>ge  of  a  body,  projected  with  a 
given  velocity,  is  always  proportional  to  the  sine  of  twice  the  angle  of  elevation  r 
that  is,  to  the  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;  sup- 
posing thebody  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  obseive  in  the  track  of  a 
bomb.  '  For  both  these  reasons,  the  best  elevation  is  somewhat  less  than  45°, 
andsometijnes,  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  ex- 
tent of  the  range,  provided  that  it  contiftu'e  between  the  limits  of  45"  and  35°; 
and  for  theisanve  reason^  the  angular  adjtistmettt  requires,  less  accuracy  in  this- 
position  than  in  any  other,  "Which  besides  the  economy  of  powder,  makes  it 
the  best  elevation  for  practice.     (PlatC' 11.  Fig.  I7,    18.) 

Tlie  path  of  a  projectile,  supposetl  to  move  without  resistance,  is  always  a: 
parabola.  This  interesting  proposition  was  first  discovered  by  Galileo;  it  fol- 
lows very  readily  from  the  doctrine  of  the  composition  of  motion,  combined 
with  the' laws  which  that  philosopher  established  concerning  the  fall  of  heavy 
bodies.  If  from  any  points  of  a  given  right  liTie,  as  many  lines  be  drawn, 
parallel  to  each  other,  and  proportional  to  the  squares  of  tlie  corresponding 


40  LECTURE    IV. 

segments  of  the  fiist  line,  the  curve  in  wliich  all  their  extremities  arc  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  eft'ect  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  ex- 
tremity of  the  vertical  line  corresponding  to  the  time  elapsed,  and  will  there- 
fore describe  a  parabola.     (Plate  II.  Fig.  17,  ^9-) 

It  is  easy  to  show  by  experiment,  that  the  path  of  a  projectile  is  a  parabola : 
if  we  only  let  a  ball  descend  from  a  certain  point,  along  a  groove,  so  as  to  ac- 
quire 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,  wliere  the  velocity  of  a  projectile  is 
considerable,  the  resistance  of  the  atmosphere,  is  so  great  as  to  render  the  Ga- 
lilean propositions  of  little  or  no  use ;  and  a  complete  determination  of  the 
path,  mcluding  all  the  circumstances  which  may  influence  it,  is  attended 
with  difficulties  almost  insuperable.  It  appears  from  Robins's  experiments, 
that  the  resistance  of  the  air  to  an  iron  ball  of  4-4:  inches  in  diameter,  moving 
at  the  rate  of  800  feet  in  a  secqnd,  is  equal  to  four  times  its  weight,  and  that 
where  the  velocity  is  much  greater,  the  resistance  increases  far  more  rapidly. 
I3ut  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  J^Ir.  Robins,  that  a  ball  sometimes  deviates  three  or  four  hundred  yards 
laterally,  without  any  apparent  reason;  bo  that  we  cannot  be  absolutely  cer- 
tain to  come  within  this  distance  of  our  mark  in  any  direction.  The  circum- 
stance is  probably  owing  to  an  accidental  rotatory  motion  communicated  to 
the  ball  in  its  passage  through  the  piece,  causing  therefore  a  greater  friction 
from  the  air  on  one  side  than  on  the  other;  and  it  may  in  some  measure  be  re- 
medied by  employing  a  rifle  barrel,  which  determines  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  tlie  ball  is  turned  in  succession  every  way.     For  the  ordinary 


ON    DEFLECTIVE    FORCES.  41 

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  experiment.  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. 


VOL.    I. 


LECTURE  V. 

ON    CONFINED    MOTION. 


\VE  have  hitherto  considered  the  princiijal  cases  of  motion,  either  undisturb- 
ed, or  simply  subjected  to  the  action  of  an  accelerating,  retarding,  or  deflec- 
tive force.  We  now  proceed  to  examine  the  effects  of  an  additional  modifica- 
tion, 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  surface  by  its  attach- 
ment to  a  thread,  or  still  more  narrowly  restricted,  by  means  of  two  threads, 
which  allow  it  to  move  only  in  a  given  line.  Suspension  is  the  most  conveni- 
ent mode  of  making  experiments  on  confined  motion  ;  but  it  is  not  always  easy 
to  cause  the  body  to  remain  in  the  surface  that  is  required  ;  and  to  confine  it  in 
this  manner  to  a  perfectly  plane  surfiice,  is  impossible.  When  we  suffer  a  body 
to  slide  along  any  surface,  there  is  a  loss  of  force  from  friction,  from  the  pro- 
duction of  rotatory  motion,  or  from  both  these  causes  combined.  The  effect 
of  friction  is  obvious  and  well  known ;  and  we  may  be  convinced  of  the  re- 
tardation attendant  on  the  production  of  rotatory  motion,  by  allowing  two  cy- 
linders, of  equal  dimensions,  to  roll  down  an  inclined  plane  ;  the  one  being  co- 
vered with  sheet  lead,  the  other  having  an  equal  weight  of  lead  in  its  axis, 
<^nd  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  11.  Fig.  20.) 

When  a  body  is  placed  on  an  inclined  plane,  the  force  urging  it  to  de- 
scend, 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  principles 
pf  the  composition  of  motion,  and  may  also  be  shown  experimentally  with 


ON    CONFINED    MOTION.  4$ 

great  accuracy,  when  we  consider  the  doctrine  of"  the  cquihbrium  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  ou 
it  in  two  seconds,   instead  of  64  feet,  somewhat  less, than  two  feet. 

It  may  be  deduced  from  the  laws  of  acccleraiting  forces,  that  when  bodies 
descend  on  any  inclined  planes,  of  equal  heights,  but  of  different  inclinations, 
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  ov  in  an  oblique  direction; 
but  tlie  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  sliown  by  experi- 
ment, as  nearly  as  the  obstacles  already  mentioned  will  permit,  the  times  be- 
ing measured  by  a  pendulum,  or  by  a  stop  watch.     (Plate  H..  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.  32.) 

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  Avhen  the  surface 
is  a  plane,  but  also  when  it  is  a  continued  curve,  in  which  the  body  is  retain- 
ed by  its  attachment  to  a  thread,  or  is  supported  by  any  regular  surface,  sup- 
posed to  be  free  from  friction.  We  may  easily  sliow,  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 
fonn  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  succes- 
sion temporary  centres  of  motion;  and  we  shall  find,  in  all  cases,  that  the  body 
ascends  to  a  height  equal  to  that  from  which  it  descendetl,  with  a  small  de- 
duction on  account  of  friction,     (Plate  II.  Fig.  23.) 


44  LECTURE   V. 

Hence  is  derived  the  idea  conveyed  by  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- 
fiices,  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.  Galileo  was  the  first  that  considered  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.  It  was 
Huygcns  that  first  demonstrated  the  properties  of  the  cycloidal  pendulum, 
which  are  of  still  more  importance  in  the  solution  of  various  mechanical  pro- 
blems, than  for  the  immediate  purposes  of  timekeepers,  to  which  that  emi- 
nent 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  denomi- 
nated isochronous,  or  of  equal  duration.  This  equality  may  be  shown  by  let- 
ting go  two  pendulous  balls  at  tlie  same  instant,  at  different  points  of  the  curve, 
and  observing  that  they  meet  at  the  lowest  point.     (Plate  II.  Fig.  24.) 


ON    CONFIXED    MOTION.  45 

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  ia 
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.  Sil4.) 

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  differ- 
ent 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  '4v  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  cy- 
cloidal  curve,  may  be  represented,  by  supposing  another  pendulum  to  revolve 
imiformly  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  vibrat- 
ing 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,  provided  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  dis- 
tance 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  vi- 
brations are  isochronous,  and  the  space  described  corresponds  to  the  versed 
sine  of  a  circular  are  increasing  uniformly,  that  is  to  tlie  height  of  any  point 


A6  ^ECTUUE    V. 

*  of  a  wheel  revolving  uniformly  on  its  axis,  or  rolling  uniformly  on  a  horizontal . 
l^laue. 

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.  It  mav 
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  uti- 
lity; the  proposition  was  formerly  considered  as  somewhat  difficult  to  be 
demonstrated,  but  of  late,  from  the  invention  of  new  modes  of  calculation, 
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  complicated 
apparatus  necessary  to  introduce  a  cycloidal  motion,  for  the  pendulums  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  tliat  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  e(}ual  distances  from  the  lowest  point.  • 
This  may  be  shown  by  a  comparison  of  two  equal  pendulums,  vibrating  in  arcs 
of  different  extent :  if  may  also  be  observed,  by  an  experiment  with  two  simple 
pendulums  of  different  lengths,  that  their  times  of  vibration,  like  those  of  cy- 
cloidal 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  pen- 
dulum, to  be  referred  to  one  point,  since  we  are  not  at  present  prepared  to  ex- 
amine the  effect  of  tlie  slight  difference  between  the  situations,  and  the  velocities 
of  the  different  parts  of  the  substances,  employed  in  our  experiments.  The  na- 
ture of  rotatory  motion  requires  to  be  more  fully  understood,  before  we  can 
attend  to  the  determination  of  the  centres  of  oscillation  of  bodies  of  various 


ON    CONFINED    MOTION.  '  4f 

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  in- 
terference 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  re- 
volution  of  balls  suspended  from  a  fixed  point.  If  a  body,  suspended  by  <l 
-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  rcvo>- 
lution  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.  lig.  26".)  lUifjiq 

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 ;  consequently 
all  the  revolutions  will  be  nearly  isochronous,  while  the  threqds  or  wires 
deviate  but  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  pen- 
dulum 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  al- 
ways proportional  to  the  distance  fiom  that  centre.     (Plate  II.  Fig.  27.) 

The  near  .approach  of  these  revolutions  to  isochronism  has  sometimes  been 


48  LECTUEE    V. 

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  inclination  of  a 
circular  road,  capable  of  counteracting  the  centrifugal  force  of  a  horse,  running 
round  it :  for  the  horse,  like  the  ball  of  the  revolving  pendulum,  has  a  cen- 
trifugal 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  completely  counteracted  by  the  force  of  the  thread  or 
wire,  and  must  therefore  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  perpendicular  to 
them;  otherwise  its  materials  will  naturally  be  forced  outwards,  until  they  pro- 
duce 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  revolutions  in  an  hour,  and  half  a  revo- 
lution in  3  seconds  and  a  half.  Now  the  length  of  a  pendulum  vibrating  in 
34-  seconds,  must  be  39  inches  multiplied  by  the  square  of  34^,  or  a  little  more 
than  80  feet :  the  road  must  therefore  be  perpendicular  to  the  direction  of  a 
line  drawn  to  it  from  a  point  80  feet  above  the  centre  of  the  ring;  and  its  ex- 
ternal circumference  must  be  higher  than  its  internal  circumference  by  one 
fourth  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  curvihnear  motion,  which  is  in  itself  of  lit- 
tle 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. 


ON    CONFINED    MOTION.  49 

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  every 
where  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  velocitj^,  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  in- 
ference from  the  simpler  laws  of  motion,  and  if  those  laws  were  even  dilFerent 
from  what  they  are,  the  principle  would  be  true  in  another  form,  and  in  ano- 
ther sense  of  the  word  action. 


VOL.    I.  H 


50 


LECTURE  VI. 


ON    THE    MOTIONS    OF    SIMPLE    MASSES. 


JfXlTHERTO  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  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  conveni- 
ent to  define  a  moveable  body,  as  a  moveable  point  or  particle,  composed  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,  Ave  are  obliged  to  have  recourse  to 
material  bodies,  and  although  such  bodies  differ  considerably  from  this  defini- 
tion 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  mathematical  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.  Indeed  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  ^f  their 
effects,  in  examining  the  laws  and  affections  of  motion.  The  forces  of  cohe- 
sion and  repulsion,  for  example,  act,  in  general,  in  a  very  complicated  manner,  in 
almost  all  cases  of  the  communication  of  motion;  but  to  consider  these  opera- 
tions minutely  in  treating  of  collision,  would  be  to  involve  the  subject  in  very 
great  and  veiy  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 


ON    THE    MOTIONS    OP    SIMPLE    MASSES.  51 

matter ;  but  in  the  mean  time  we  must  have,  for  our  experimental  illustrations, 
some  measure  of  the  mass  or  bulk  as  here  defined.  We  might  employ  spheri- 
cal bodies,  composed  only  of  homogeneous  substances,  that  is,  of  substances  of 
the  same  kind,  and  we  might  estimate  the  mass  by  the  comparative  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  numberino- 
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  rectilinear 
motion,  is  a  property  attached  to  all  matter,  and  may  be  considered  as  propor- 
tional to  the  mass  or  weight  of  a  body.  When  the  motions  of  a  system  of  bo- 
dies are  considered,  their  inertia  may  in  some  respects  be  referred  to  a  single 
point,  which  is  called  the  centre  of  inertia.  The  centre  of  inertia  of  two  bo- 
dies is  that  point,  in  the  right  line  joining  them,  M'hich  divides  it  into  two  such 
portions,  that  the  one  is  to  the  other,  as  the  mass  of  the  remoter  body  to  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  ftom  the  larger :  and 
the  distance  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  its 
distance  are  equal :  thus  two  multiplied  by  one,  is  equal  to  one  multiplied  by 
two.     (Plate  II.  Fig.  39.) 

This  point  is  most  commonly  called  the  centre  of  gravity ;  it  has  also  some- 
times been  denominated  the  centre  of  position.  Since  it  has  many  properties 
independent  of  the  consideration  of  gravity,  it  ought  not  to  derive  its  nam<5 
from  gravitation,  and  the  term  centre  of  inertia  begins  now,  with  great  propri- 
ety, to  be  generally  adopted. 

The  centre  of  inertia  of  any  two  bodies  initially  at  rest,  remain's  at  rest,  not- 
withstanding any  reciprocal  action  of  the  bodies  ;  that  is,  notwithstanding  any 
action  which  aftccts  the  single  particles  of  both  equally,  in  increasing  or  diniif- 


52  LECTURE  vr. 

iiishing  their  distance.  For  it  may  be  shown,  from  the  principles  of  the  compo- 
sition 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, 
Avhich  therefore  still  remains  the  centre  of  inertia,  and  is  at  rest.  And  it  fol- 
lows also,  that  if  the  centre  of  inertia  is  at  first  in  motion,  its  motion  will  not 
be  aftected  by  any  reciprocal  action  of  the  bodies. 

This  important  property  is  very  capable  of  experimental  illustration  ;  first 
observing,  that  all  kr^^wn  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  remains  unaltered.  They  may  either  be  made  to 
float  on  water,  or  may  be  suspended  by  long  threads ;  the  spring  may  be  de- 
tached by  burning  a  thread  that  confines  it,  and  it  may  be  observed  whe- 
ther or  no  they  strike  at  the  same  instant  two  obstacles,  placed  at  such  dis- 
tances as  the  theory  requires ;  or  if  they  are  suspended  as  pendulums,  the  arcs 
■\^'hich  they  describe  may  be  measured,  the  velocities  being  always  nearly  pro- 
portional 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  placedourselves  in  a  small  boat,  and  pulled  a  rope  tied  to  a 
much  larger  one,  we  should  draw  ourselves  towards  the  large  boat  with  a  mo- 
tion as  much  more  rapid  than  that  of  the  large  boat,  as  its  weight  is  greater 
than  that  of  our  own  boat;  arid  the  two  boats  would  meet  in  their  common 
centre  of  inertia,  supposing  the  resistance  of  the  water  inconsiderable. 

Having  established  this  property  of  the  centre  of  inertia,  as  a  law  of  motion, 
we  may  derive  from  it  the  true  estimate  of  the  quantity  of  motion  in  differ- 
ent bodies,  in  a  much  more  satisfactory  manner,  than  it  has  usually  been  ex- 
plained. 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 

2 


ON    THE    MOTIONS    OF    SIxAIPLE    MASSES,  53 

the  quantity  of  motion  naust  always  be  measured  by  the  joint  ratio  of  mass  to 
mass,  and  velocity  to  velocity  ;  that  is,  by  the  ratio  of  the  products,  obtained 
by  multiplying  the  weight  of  each  body  by  the  number  expressing  its  velo- 
city ;  and  these  products  are  called  the  momenta  of  the  bodies.  \Vc  appear  to 
have  deduced  this  measure  of  motion  from  the  most  unexceptionable  argu- 
ments ,  and  we  shall  have  occasion  to  apply  the  momentum  thus  estimated  as 
a  true  measure  of  force ;  at  the  same  time  that  we  allow  the  practical  import- 
ance 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  velo- 
city. Thus  a  body  weighing  one  pound,  moving  with  a  velocity  of  a  hundred 
feet  in  a  second,  has  the  same  momentum,  and  the  same  (juantity  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  !^fr.  Atwood's  ma- 
chine, that  the  same  momentum  is  generated,  in  a  given  time,  by  the  same 
preponderating  force,  whatever  may  be  the  quantity  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  com- 
pare the  centrifugal  forces  of  bodies  revolving  in  the  same  time,  at  diflerent 
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  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  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  com- 


54  LECTURE    VI. 

mon  centre  of  inertia ;  determining  the  centre  of  inertia  of  this  iniaginarj 
body  and  tlie  tliird  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,  we  shall  be  able  to  pro- 
duce an  experimental  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  of  a  system, 
of  moving  bodies,  by  supposing  their  masses  to  be  united  into  one  body,  and 
tliis  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  imaginary  body  to 
three  given  directions,  and  collecting  all  the  results,  into  three  sums,  which 
will  represent  the  motion  .of  the  centre  of  inertia  of  the  s-ystenu 

We  have  already  presupposed  this  proposition,  when  we  have  employed  ma- 
terial 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  thoseof  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  mo- 
tions, thus  collected,  must  also  be  a  uniform  and  rectilinear  motion.  The 
centre  of  inertia  of  a  system  of  bodies  moving  without  disturbance,  is,  there- 
fore, 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  from  the  same  plane.     And  the  proposition  will  be 


ON    THE    MOTIONS    OF    SIMPLE    MASSES.  55 

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  applicable  to  the  consideration  of  the 
centre  of  gravity,  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  of  two  bodies 
is  not  affected  by  any  reciprocal  action  between  tliem ;  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  obtain- 
ing the  conclusion  would  be  somewhat  complicated. 

All  the  forces  in  nature,  with  which  we  are  acquainted^  act  reciprocally  be- 
tween different  masses  of  matter,  so  that  any  two  bodies  repelling  or  attracting 
each  otlier,  are  made  to  recede  or  approach  with  equal  momenta.  This  cir- 
cumstance is  generally  expressed  by  the  third  law  of  motion,  that  action  and 
reaction  are  equal.  There  would  be  something  peculiar,  and  almost  incon- 
ceivable, in  a  force  which  could  affect  unequally  the  similar  particles  of  mat- 
ter ;  or  in  the  particles  themselves,  if  they  could  be  possessed  of  such  differ- 
ent 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  equilibrium  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  thenij 
and  it  is  difficult  to  conceive  that  they  should  approach  each  other  with  une- 
qual velocities  in  consequence  of  magnetic  attraction,  or  of  anj'  other  natural 
force.  The  reciprocality  of  force  is  therefore  a  necessary  law  in  the  mathe- 
matical consideration  of  mechanics,  and  it  is  also  perfectly  warranted  by  ex- 
perience. The  contrary  supposition  is  so  highly  improbable,  that  the  princi-. 
pie  may  almost  as  justly  be  termed  a  necessary  axiom,  as  a  phenomenon  col- 
lected 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  contraiy  ways."     He  proceeds,  "  if  any  body 


56  LECTURE    VI. 

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  n  M'eight  tied  to  a  rope,  the  horse  is  also  equally  drawn  back- 
wards towards  the  weight :  for  the  rope,  being  distended  throughout,  will  iu 
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  tiling  pressed,  but  the  stone  would  not  sensibly  advance 
into  the  place  of  the  finger,  if  it  were  removed  ;  and  in  the  same  manner  we 
imderstand,  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  intirely  cease; 
in  these  senses,  therefore,  we  cannot  say,  that  the  stone  presses,  or,tliat  the  weight 
pulls,  and  we  have  no  reason  to  ofi^end  the  just  prejudices  of  a  beginner,  by 
introducing  paradoxical  expressions  without  necessity.  Yet  it  is  true  in  both 
cases,  that  if  all  friction,  and  all  connexion  with  the  surrounding  bodies,  could 
be  instantaneously  destroyed,  the  point  of  the  finger  and  the  stone  would  re- 
cede 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  re- 
ciprocality  of  forces,   or  the  equality  of  action  and  reaction. 

The  quantity  of  action  of  two  attractive  or  lepulsive  bodies  on  each  other 
is  partly  dependent  on  their  magnitude.  When  the  bodies  are  of  the  same 
kind,  their  mvitual  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  contain- 
ing two  inches,  the  other  ten,  of  the  same  matter,  then  the  mutual  attraction 
or  repulsion  of  these  will  be  expressed  by  20  grains  ;  for  each  of  the  10  inches 
is  attracted  by  each  of  the  two  with  a  force  of  a  grain.  And  the  mutual  ac- 
tion of  3  and  10  will  be  30,  of  4  and  10,  40;    so  that  when  one  of  the  bodies 


ON    THE    MOTIONS    OF    SIMPLE    MASSES.  57 

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  the  same  kind.  For  the  apparent  difference 
in  the  velocity,  Avith  which  different  substances  fall  through  the  atmosphere, 
is  only  owing  to  the  resistance  of  the  air,  as  is  sometimes  shown  by  an  ex- 
periment 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  ma- 
chine,  and  it  is  distinctly  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  sliould  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  particles 
contained  in  a  given  space,  independently  of  any  other  characters  that  may 
constitute  the  specific  diff^erences  of  those  substances. 

In  some  cases  it  is  necessary  to  consider  the  sum  of  the  masses  of  two  bo- 
dies, 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  ceutre  of  iner- 
tia, which  are  inversely  in  the  same  ratio.  This  consideration  is  sometimes 
of  use  in  determining  the  action  of  the  sun  on  the  seveial  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  distances  from 
their  common  centre  of  inertia.  Thus,  in  the  planetarj' 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 

VOL.    I.  I 


58  LECTURE   VI. 

detenuine  the  effect  of  the  attraction  as  directed  to  a  fixed  point,  \vc  consider 
the  force  as  residing  in  the  common  centre  of  inertia  of  the  two  bodies,  whicli 
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  reci- 
procal forces  of  two  bodies  may  therefore  be  considered  as  tending  to  or  from 
their  common  centre  of  inertia,  as  a  fixed  point;  but  it  often  happens  that,  the 
dift'erence  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  bis  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  eruption  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  unneces- 
sary condition:  "  give  me,"  said  he,  "  but  a  firm  support,  and  I  will  move  the 
earth;"  but  granting  him  his  support,  he  could  only  have  displaced  the  earth 
insensibly  by  the  properties  of  his  machines;  and  without  any  such  sup- 
port, when  he  threw  rocks  upon  the  ships  of  Marcellus,  he  actually  caused 
the  walls  of  Syracuse  and  theisland  of  Sicily  to  move  northwards,  with  as  much 
momentum,  as  carried  his  projectiles  southwards  against  the  Roman  arma- 
ments. 


■"fO 


LECTURE  VIl. 


ON    PRESSURE    AND    EQUILIBRIUM. 


We  have  now  examined  the  principal  cases  in  whicli  a  simple  force  is  em- 
ployed in  the  production  of  motion;  it  is  pf  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  weight,  up- 
on 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  antients,  that  pressure  and  motion  are  ab- 
solutely incommensurable  as  effects;  for  according  to' the  definition  of  pres- 
sure, the  force  appears  to  he  what  is  called  in  logic  a  potential  cause,  M'hich 
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  ex- 
actly 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  time.  Plencc  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 


60  LECTURE    VII. 

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  dilficulty  in  extending  the  laws  of  the  composition  of  motioa 
to  the  composition  of  pressure.  For  since  we  measure  forces  by  the  motions, 
which  they  produce,  it  is  obvious  that  the  composition  of  forces  is  included 
in  the  doctrine  of  the  composition  of  motions;  and  Avhen  we  combine  three 
fprces  according  to  the  laws  of  motion,  there  can  be  no  question  but  that  the 
resulting  motion  is  truly  determined  in  a:Il  cases,  whatever  may  be  its  magni- 
tude; nor  can  any  reason  be  given*  why  it  should  be  otherwise,  when  this  mo- 
tion is  evanescent,  and  the  force  becomes  a  pres^re.  The  case  is  similar  to 
that  of  a  fraction,  which  may  still  retain  a  real  valud,  when  both  its  numerator 
and  denominator  become  less  than  any  assignable  quantity.  Some  authors 
on  mechanics,  and  indeed  the  most  eminent,  Bernoulli,  Dalembert,  and  La- 
place, have  deduced  the  laws  of  pressure,  more  immediately,  from  the  principle 
of  the  equality  of  the  eifects  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  intricate. 

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  e()ual  or  proportion- 
ate 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  con- 
trary 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  otl>ers,  when  it  would  produce  a  mo- 
mentum, ccjual  and  contrary  to  the  momentum  which  would  be  derived  from 
the  joint  result  of  the  other  forces.  For,  supposing  each  of  two  forces  op- 
posed 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  con- 
tinuedactionof  each  force ;  consequently,  since  the  halves  completely  counteract 

2 


ON    PRESSUBE    AND    EQUILIBRIUM.  61 

each  other,  the  'vholes  will  do  the  same.     And  a  similar  mode  of  reasoning 
may  be  extended  to  any  number  of  forces  opposed  to  each  other. 

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  represented  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  completely  shown  by  experi- 
ment. We  attach  three  weights  to  as  many  threads,  united  in  one  point,  and 
passing  ovev  three;  pulliies ;  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  lof  each  weight,  by  the  length  of  the  side  of  the  triangle 
corresponding  to  its  thread.     (.P.late  III.  Fig.  33.) 

The  most  important  of  the  problems  relating  to  equilibrium  are  such  as  con- 
cern the  machines  which  are  usually  called  mechanical  povj^ers.  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  theirmotion  requires  additional  Considerations,  and  their  application  to  prac- 
tice belongs  to  another  subdivision  of  our  subject. 

There  is  a  general  law  of  mechanical  ecjuilibrium,  which  includes  tlie  prin- 
cipal properties  of  most  of  these  machines.     If  two  or  more  bodies,  con- 
nected together,'  be  suspended  from  a  given  point,  they  will  be  at  rest  when 
their  centre  of  inertia  is  in  the  vertical  line  passing  through  the  point  of  suS" 
pension.    The  truth  of  this  proposition  may  easily  be  illustrated,  by  the  actual 
suspension  of  any  body,  or  systenl  of  bodies,  from  or  upon  a  fixed  point ;   the 
whole  remaining  in  equilibrium,  when  the  centre  of  inertia  is  either  vertically 
below  the  point  of  suspension,   or  above  the  point  of  support,   or  when  the 
fixed  point  coincides  with  the  centre  of  inertia.     And  whatever  may  be  the  - 
form  of  a  Compound  body,    it  may  be  considjered.as  a  system  of  bodies  cour 
nected  together,  the  situation  of  the  common  centre  of  the  inertia  determining 
the  quiescent  position  of  the  body.     (Plate  III.  Fig.  S^-.JS.) 
♦ 

Hence  the  centpe  of  inertia  is  called  the  centre  of  gravity ;,  and  it  may  be 
practically  found,  by  determining  the  intersection  of  two  lines  which  bccohie 


6S     .  LECTURE    Vir, 

vertical  in  any  two  positions  in  which  the  body  is  at  rest.  Thus,  if  we  sus- 
pend a  board  of  an  irregular  form  from  any  two  points  successively,  and  mark 
the  situation  of  the  vertical  line  in  each  position,  we  may  find  by  the  inter- 
section the  place  of  the  centre  of  gravity:  and  it  will  appear  that  this  in- 
tersection will  be  the  game,  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  quantities, 
the  stability  may  be  positive,  negative,  or  evanescent.  ''jTbe^  Equilibrium  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  lirte:  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  gravity  coincides  with 
the  centre  of  motion,  or  when  its  path  would  be  a  hoiizontal  right  line,  the 
equilibrium  has  been  called  insensible,  but  may  more  properly  be  termed  neu- 
tral, and  the  body  will  rest  in  any  position,  without  tending  either  to  tall,  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  equili- 
brium, 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. 
13ut  the  equilibrium  of  a  circle  or  a  sphere  is  always  neutral,  foi',  when  dis- 
turbed, it  neither  recovers  its  first  position,  nor  deviates  further  from  it.  A  flat 
body,  resting ort  a'sphere,  will  have  its  equilibrium  tottering  or  stable,  accord- 
ingly as  its  centre  of  gravity  is  more  or  less  than  the  semidiamcter  of  the 
sphere  above  the  point  of  Contact.     (Plate  III.  Fig.  41,  42.) 


ON    PRESSURE    AND    EQUILIBRIUM.  63 

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  niove  either  way,  it  -must  begin  its  motion  in  an  inclined  direction, 
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  tot- 
tering equilibrium ;  and  if  the  inclination  be  still  further  continued,  the  body 
will  tall.     (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  aft'ect  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  M-eight  of 
hay;  supposing  the  inequality  of  the  road,  of  any  accidental  obstacle,  to  ele- 
vate one  side  of  the  waggon,  it  will  always  recover  its  position,  provided  that 
the  centre  of  gravity  remain  within  the  vertical  line,  passing  tlirough  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  perfectly  erect, 
and  the  centre  of  gravity  of  the  carriage,  with  its  pas.sengers,  Avill  be  some- 
what more  elevated,   than  it  would  be  on  this  supposition. 

The  direction  of  the  initial  motion  of  the  centre  of  gravity  readily  explains 
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 ; 


-Ci  LECTURE   VXl. 

for  although  the  bucket  seems  suspended  by  its  handle,  yet  if  the  handle  be- 
gan to  descend,  the  centre  of  gravity  would  be  obliged  to  rise ;  consequently 
the  whole  will  retain  its  position,  and  remain  at  rest.     (Plate  III,  Tig.  45.) 

The  apparent  ascent  of  a  loaded  cylinder  on  an  inclined  plane,  and  tjie  mo- 
tion of  a  roller  composed  of  two  united  cones,  with  a  coynnpu  axis,  resting  on 
the  edge  of  a  triangle  which  is  inclined  to  the  horizon,  may  bq  easily  under- 
stood from  the  same  consideration.     (Plate  III.  Fig.  46.) 

We  may  also  observe,  in  tJie  equilibrium  of  animals,  many  circumstances  il- 
lustrative of  the  properties  of  the  centre  of  gravity.  W  hen  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  when  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 
Jcept  in  a  state  of  perpetual  vibration,  without  ever  attaining  such  a  position  as 
would  give  it  any  degree  of  positive  stabiUty;  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  flex- 
ure, and  by  the  changes  of  the  position  of  the  extremities  :  hence,  b}'  habit,  the 
arts  of  ropedancers  and  balancers  are  acquired.  Sometimes,  however,  the  po- 
sition of  the  balancer  ^is  not  so  dilhcult  to  be  preserved  as  it  appears,  the  cur- 
vature of  the  wire  in  contact  with  the  foot  tending  materially  to  assist  him. 

When  we  attempt  to  rise  from  a  scat,  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. 


ON    PRESSURE    AND    EQUILIBRIUM.  65 

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  re- 
sumed their  activity.  Some  authors  have  thought  it  impossible  that  a  qua- 
druped 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  definition  of 
this  point,  that  if  two  bodies  be  attached  to  a  straight  rod  of  inconsiderable 
weight,  they  may  be  sustained  in  equilibrium,  by  a  fixed  point,  or  fulcrum, 
which  divides  their  distance  into  portions  which  are  inversely  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  aie  applied,  in  contrary  di- 
rections,  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,  Newton, 
Maclaurin,  Dr.  Hamilton,  and  Mr.  Vince,  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  ge- 
neral antl  natural  as  one  of  Dr,  Hamilton's,  nor  so  simple  and  convincing  as " 
Maclaurin's,  which  it  may  be  worth  our  while  to  notice.  Supposing  two 
equal  weights,  of  an  ounce  each,  to  be  fixed  at  the  ends  of  the  ecpial  arms  of 
a  lever  of  the  first  kind;  in  this  case  it  is  obvious  that  there  will  be  an  equi- 
librmm,  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 

VOL.    I.  K 


()6  LECTURE    VII. 

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  remaining  at  the  other  end  of  the  lever  counter- 
balances a  force  of  two  ounces,   acting  at  half  the  distance  from  the  new  ful- 
crum ;  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 
suihciently  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 
manner  the  demonstration  may  be  extended  to  any  commensurable  proportion 
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  whatever,  even 
if  they  happen  to  be  incommensurable,  such  as  the  side  of  a  square,  compared 
to  it§  diagonal,  which  cannot  be  accurately  expressed  by  any  numbers  what- 
ever; 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 
otlier,   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  man- 
ner 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  fulcrum  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  forc'G  applied  trans- 
versely 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  ecpial  advantage  on  the  side  of  the  rope  and  the  other 
lever  to  which  it  is  attached.     When  therefore  a  great  force  is  required  in  the 
beginning  of  the  motion,  and  afterwards  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  j\Ir.  Watt  has  very  ingeniously 
applied  this  arrangement  of  levers  to  the  purpose  in  his  steam  engines.     In  the 


ON    PRESSURE   AND    EQUILIBRIUM.  67 

same  manner,  it  is  necessary  that  tlie  platten  of  a  printing  press,  or  the  part 
which  presses  the  pap^^i'-  on  the  types,  should  descend  from  a  considerable 
height,  blrt'jft  is  Only  at;  the  imtant  of  taking  off  the  impression  that  a  great 
force  is  required;  and  both  these' ca'ds  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. .  i|",.twd 
threads,  or  perfectly  flexible  and  inextensible  lines,  be  wound- in  contrary  di- 
rections round  two  cylinders,  drums,  or  rollers,  moveable  tog-ether  on  ".the 
$ame  axis,  there  will  be  an  eciuilibrium,  when  the  weights  attached  to  thft 
threads,  or- the  forces  operating  on  tlienij-  are  inversely  as  the  radii  of  the  cy- 
linders, 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  cy- 
linders, 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  immediately  deduced  from 
the  position  of  the  centre  of  gravity,  immediately  below  the  axis  of  the  cy- 
linders, 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  levea-  or 
winch,  and  in  this  case  the  radius  of  tire  cy.linder  is  to  be  compared  with  the 
Jeagth-of  the  lever ipr;wi<ieh.     (Plate  III.  Fig.  50.) 

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  produce 
a  difference  in  their  action,  which  will  be  mentioned  when  the  practical  con- 
struction 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  rimning  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  dia- 
meter equal  to  half  the  difference  of  the  diameters  of  the  double  axis.     The 


68  LECTURE    VII. 

machine  is,   however,   much  stronger  than  such  a  cyhnder  would  be,  and  does 
not  require  so  great  a  curvature  in  the  ropes  employed.     (Plate  IV".  Fig.  51.) 

The  laws  of  the  efjuilibrium  of  puUies  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  attached  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  equilibrium  are  axioraatically 
evident,  without  any  further  reasoning;  and  in  more  complicated  cases,  the  cal- 
culations proceed  on  perfectly  different  grounds.  We  are,  therefore,  to  con- 
sider 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  perfectly 
smooth  surface,  it  communicates  the  whole  force  acting  on  it;  for  the  resist- 
ance 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  perpendicular  to  it, 

A  fixed  pulley,  therefore,  has  no  effect  in  gaining  a  mechanical  advantage ; 
but  by  means  of  a  moveable  pulley,  it  is  obvious  that  a  weight  may  be  sup- 
ported 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  equilibrium  will  continue  unimpair- 
ed, each  portion  of  the  thread  still  supporting  one  half  of  tlie  original  weight; ' 
so  that,  by  means  of  a  single  moveable  pulley,  one  body  may  retain  in  equili- 
brium 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  portions  which  help 


OJf    PRESSURE    AND    EQUILIBRIUM.  GQ 

to  support  the  moveable  block,  each  of  them  bearing  a  weight  equivalent  to 
the  force  \yhich  is  applied  at  the  end  of  the  thread.  In  the  common  ship's 
blocks,  the  pullies  or  shieves  are  equal  in  magnitude,  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,  imeuted  a  system  of  pullies,  arranged  in  two  rows  in  each 
block,  one  larger,  and  the  other  smaller  :  the  force  being  applied  in  the  mid- 
dle, the  rope  passes  on  the  larger  pullies,  till  it  arrives  at  the  last,  then  re- 
turns 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  friction  may,  per- 
haps,  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  tlic  threads  of  this  pulley  be  similarly 
arranged,  the  weight  will  be  counterpoised  by  a  power,  which  is  found  by 
halving  it  as  many  times  as  there  are  moveable  pullies;  for  it  is  obvious  that 
each  of  the&e  pullies  doubles  the  efilxt  of  the  power.    (Plate  IV.  Fig.  58.) 

There  are  also  other  arrangements,  by  which  the  eflfect  of  pullies  may  be  in- 
creased 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 


70  tECTonE  vii» 

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  tlie  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  determine  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  obli(}uely  round  the  axis,  it  will  require,  in  order  to  preserve 
the  equilibrium,  a  force  as  much  greater  than  would  be  sufficient,  if  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  perpendicidarly. 
This  remark  may  be  in  some  measure  illustrated  by  considering  the  method 
used  by  joiners  and  stonecutters  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,  without 
friction,  when  the  first  is  to  the  second  as  the  height  of  the  plane  to  its  ob- 
lique 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  rnay  be  measured  experimentally,  by  substituting  for  the  resistance 
of  the  plane,  that  of  a  thread  perpendicular  to  it.   (Plate  IV.  Fig.  63.) 


ON    PRESSURE    AND    EQUILIBUIUM.  7r 

The  same  principles  are  applicable  to  the  ecpiilibrium  of  the  wedge.  A 
we<ige  is  a  solid  which  has .  tla-ee  plane  faces  inclined  to  each  other,  and 
two  triangular  ends ;  and  we  suppose  the  faces  perfectly  polislied,  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  other- 
wise they  will  not  be  completely  opposed  to  each  other,  and  a  rotatory  mo- 
tion will  be  produced.     (Plate  IV.  Tig.  64.) 

If  each  face  of  the  wedge  were  conceived  to  be  capable  of  receiving  a  pres- 
sure, not  only  in  a  perpendicular  direction,  but  in  any  other  direction  at  plea- 
sure, as  some  authors  have  supposed,  the  instrument  wowld  lose  its  essential 
character  as  a  wedge ;  but  in  such  cases,  the  proportion  of  the  forces  required 
for  the  state  of  ecjuilibrium,  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  foice,  acting  in  a  direction  more  qr  less 
ohli(]ue,  as  when  a  heavy  body  rests  on  one  of  the  faces  of  tlie  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  tlie  wedge 
being  prevented  by  a  horizontal  force.  A  wedge  so  situated,  and  supposed  to 
be  capable  of  sliding  without  friction  on  a  horizontal  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,  tlie  magnitude  of  the  forces  must  be  determined 
from  the  general  law  of  the  composition  of  three  pressures.   (Plate  I V.Fig 65.) 

If  a  prop  or  bar,  leaning  against  a  smooth  vertical  surface  or  wall,  be  em- 
ployed to  support  or  to  raise  a  weight,  by  means  of  a  force  which  draws  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  perpcn- 


72  LECTURE   VII. 

dicular  height.     And  from  similar  principles,  the  conditions  of  the  equilibrium 
of  arches,  domes,  and  roofs  may  be  determined.     (Plate  IV.  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  horizontally  to  the  base  of 
the  wedge,  and  the  weight  which  is  to  be  raised  as  acting  vertically  on  its  in- 
clined surfice:  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,  provided  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  equilibrium.     (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  to- 
gether, 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  di- 
vides 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  circum- 
ference, without  any  diminution  of  its  power.  Sometimes  the  spires  of  a 
?crew  are  made  to  act  on  the  teeth  of  a  wheel,  when  a  very  slow  motion  of 
the  wbeel,  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;  which  is  somewhat  similar,  in  its  opera- 
tion, 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 


ON    PRESSURE    AND    EQUltlBUIUM.  7J 

little  more  or  less  than  the  internal  screw  which  perforates  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  ecjual  to  the  difference 
of  the  height  of  the  two  coils.  Here  the  machine  is  analogous  to  a  very  thip 
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  a<lvantage. 
It  might  in  some  cases  he  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  gi«at  impediment  to  their  opera- 
tion.    (Plate  V.  Fig.  71.) 

In  all  the  kinds  of  equilihrium  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  f  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  ve- 
locity 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  inclined  plane,  of  which  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,  re- 
duced 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  affordins:  a  fundamental  demon- 


o 


stration  of  the  conditions  of  equilibrium  in  all  possible  cases.     For  since, 
wherever  two  weights  are  in  equilibrium,  if  one  of  them  descended,  the  other 

VOL.    I.  T 


74  LECTURE    VII. 

must  ascend  Avith  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  tp  establish  its  trutk 


75 


LECTURE  VIII. 


ON    COLLISION.  X 


Having  inquired  into  the  laws  and  properties  of  tlie  motions  and  rest  of 
single  bodies,  under  the  operation  of  one  or  more  forces,  and  into  the  equili- 
brium 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  re- 
collect the  general  principle  already  laid  down,  respecting  the  centre  of  in- 
ertia, 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  velocities  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  eajth  in  its  descent  towards  the  sun,  is  the  same  as  its  velocity 
of  ascent  in  its  return,  although,  at  different  distances,  its  velocity  has  under- 
gone considerable  changes.  In  this  case,  the  force  acts  continually,  and  at- 
tracts the  bodies  towards  eacli  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  tlie  effects 


76  LECTURE    VI I r. 

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. 

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  reassume  their  primitive  form,  and  separate  with  a  velocity  equal  to  that 
with  which  they  before  approached  each  other.  Strictly  speaking,  the  repul- 
sion commences  a  little  before  the  moment  of  actual  contact,  but  only  at  a 
distance  which  in  common  cases  is  imperceptible.  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  witli  black  lead,  or 
printing  ink ;  or  by  suffering  it  to  fall  from  various  heights :  the  degree  of 
compression  will  then  be  indicated  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  conveni- 
ent 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  velocities  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  com- 
monly divided  into  equal  parts,  although  it  would  l^e  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 


ON    COLLISION.  77 

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  vest  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  velo- 
city of  the  moving  ball  before  they  begin  to  act  on  the  succeeding  ones;  they 
will  then  transmit  tlie  whole  velocity  to  the  succeeding  balls,  and  remaui  en- 
tirely 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  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  Avere  at  rest:  so  that  the  same  number 
of  balls  will  fly  off  together  on  one  side,  as  descended  to  strike  the  rcw  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  comparatively 
inconsiderable,  it  rebounds  with  a  velocity  nearly  as  great  as  the  velocity  of 


"76  LECTURE    Vllt. 

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. 

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  tlie  bodies  are  perfectly  elastic, 
they  reassume  their  primitive  form,  and  separate  with  a  velocity  equal  to  that 
with  which  they  before  approached  each  other.  Strictly  speaking,  the  repul- 
sion commences  a  little  before  the  moment  of  actual  contact,  but  only  at  a 
distance  which  in  common  cases  is  imperceptible.  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  indicated  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  conveni- 
ent 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  velocities  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  com- 
monly divided  into  equal  parts,  although  it  would  \)e  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  tsvo  equal  balk 


ov  coLLisiaN.  77 

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  eqnal  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  velo- 
city of  the  moving  ball  before  they  begin  to  act  on  the  succeeding  ones ;  they 
will  then  transmit  tlie  whole  velocity  to  the  succeeding  balls,  and  remain  en- 
tirely 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  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  Avere  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  comparatively 
inconsiderable,  it  rebounds  with  a  velocity  nearly  as  great  as  the  velocity  of 


78  LECTURE  vrri. 

its  impulse,  and  tlie  second  body  acquires  a  momentum  nearly  twice  as  great 
as  that  of  the  first.  When  a  larger  body  strikes  a  smaller  one,  it  communi- 
cates 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  cliange  of  form ;  such  bodies  receiving  and 
retaining  a  depression  at  the  point  of  contact  When  the  velocity  is  too 
Mnall  to  produce  this  change  of  form,  the  bodies,  however  inelastic^  may 
usually  be  observed  to  rebound  a  little. 

Bodies,  which  ai-e  perfectly  inelastic,  remain  in  contact  after  collision;  they 
must  therefore  proceed  with  tlie  same  velocity  as  the  centre  of  inertia  had 
before  •colHsion.  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  un- 
equal dimensions,  the  joint  velocity  is  as  much  smaller  than  that  of  the  strik- 
ing 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,  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  re- 
duced 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  direc- 
tions, remains  also  unaltered. 

The  tenn  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  ve- 
locity. Thus,  if  a  weight  of  one  ounce  moves  Avith  a  velocity  of  a  foot  in  a 
second,  we  may  call  its  energy  1 ;  if  a  second  body  of  two  ounces  have  a  ve- 
locity 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  ascending  force, 


ON    COLLISION.  7g 

since  the  height  of  the  body's  vertical  ascent  is  in  proportion  to  it;  and  some 
liave  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  denomination.  After  the  considerations  and  demon- 
strations which  have  been  premised  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  alloAving  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,  antl  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 
eft'ects  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  etjual  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  consider 
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  destruction.  Thus  also  " 
when  the  resistance,  opposed  by  any  body  to  a  force  tending  to  break  it,  is  to 
be  overcome,  the  space  through  which  it  may  be  bent,  before  it  breaks,  being- 
given,  Jis  well,  as:  the  force  exerted  aticvery  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  disadvantage, 
when  the  velocity  is  already  considerable.     For.  instance,  if  it  be  necessary  to 


go  LECTURE    VIII. 

obtain  a  certain  velocit}',  by  means  of  tbe  descent  of  a  beavy  body  fiom  a 
beigbt,  to  wliicb  we  carry  it  by  a  fligbt  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  manuer,  if  we  press  with  a 
g-iven  force  on  the  shorter  end  of  a  lever,  in  order  to  move  a  weight  at  a 
greater  distance  on  the  other  side  of  the  fulcrum,  a  certain  portion  of  the 
force  is  expended  i.n  the  pressure  which  is  supported  by  tlie  fulcrum,  and  we 
by  no  means  produce  the  same  momentum,  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  ma}-  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  Avill  then  be  expressed  by  2, 
and  that  of  the  second  by  16,  making  together  18,  as  before.  The  momentum 
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  di- 
minished. 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  im- 
mediately 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  one  fifth  as  great  as 


ox    COLLISION'.  ,  81 

tliat  of  the  hammer,  besides  some  further  dimmution,  on  accoiiut  of  the  want 
of  perfect  elasticity,  and  from  the  effect  of  the  larger  surface  of  the  anvil,  in 
dividing  the  pressure  occasioned  hy  the  blow,  so  as  to  enable  a  greater  por- 
tion 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  borly  is  spherical,  and  its  surface  perfectly  polish- 
ed; 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 
imptdse  in  a  direction  perpendicular  to  this  surface,  while  the  first  receives, 
from  its  reaction,  an  equal  impulse  in  a  contrary  direction,  which  is  com- 
bined with  its  primitive  motion.  The  magnitude  of  this  impulse  may  be  de- 
termined by  resolving  the  motion  of  the  first  ball  into  two  parts,  the  one  pa- 
rallel to  the  surface  of  contact,  and  the  other  perpendicular;  the  first  part  re- 
maining always  unaltered,  the  second  being  modified  by  the  collision.  If,  for 
example,  the  balls  were  equal,  this  second  part  of  the  motion  would  be  de- 
stroyed, and  the  remaining  motion  would  be  in  the  direction  of  the  surface 
of  contact,  and  perpendicular  to  that  of  the  ball  impelled. 

Hence  it  follows,  that  if  we  wish  to  impel  a  billiard  ball  in  a  given  direc- 
tion, by  the  stroke  of  another  ball,  we  have  only  to  imagine  a  third  ball  to 
be  placed  in  contact  Avith  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  determine 
its  path,  when  it  is  refiected  from  a  fixed  obstacle.  That  part  of  the  motion, 
which  is  in  a  direction  parallel  to  the  surface  of  the  obstacle,  remains  undi- 
minished: the  motion  perpendicular  to  it  is  changed  for  an  equal  motion 
in  a  contrary  direction,  and  the  joint  result  of  these  constitutes  a  motion, 
in  a  direction,  which  is  equally  inclined  to  the  surface,  with  the  first  motion, 

VOL.    I.  M 


S2  LECTURE    VIII. 

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  re- 
bounds 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  reflection,  with  a  direct  im- 
pulse. 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  col- 
lision becomes  very  intricate,  and  the  problem  is  scarcely  applicable  to  any 
practical  purpose.  Those  who  are  desirous  of  pursuing  the  investigation  as  a 
mathematical  amusement,  will  find  all  the  assistance  that  they  rec[uire  in  the 
profound  and  elegant  works  of  Maclaurin. 


S3 


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  coUision,  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  rotatory 
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  mechanical  arrange^ 
ments,  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,  Avill  have  three  times  as  great 
an  effect  on  a  system  of  bodies,  to  which  its  whole  force  is  communicated,  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  demon- 
strable, 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  mo- 


84  LECTURE    IX. 

menta  are  proportional  to  the  weights,  but  the  products  obtained  by  multiply- 
ing them  by  the  distances  from  the  centre,  at  which  they  act,  are  equal  r 
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  angvdar  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  multiphed  by  the  square  of  the  velocity,  since  the 
velocity  is  in  tWs  case  proportional  to  tli€  distance  from  the  centre ;-  and  this 
product  is  the  same  that  I  have  denominated  the  energy  of  a  moving  body. 

These  propositions  are  of  great  use  in  all  inquiries  respecting  the  operations- 
of  machines;  and  it  is  of  importance  to  bear  in  mind,  that  although  the  equi- 
librium 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  mvdtiplied  by  the  square  of  the  distance,, 
or  of  the  velocity.  For  this  reason,  together  with  some  others,  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,  oa  which  the  whole  theory  pf  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  pur- 
pose 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  ap- 
plied 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  mag- 


OS    THE    MOTIONS    OF    CONNECTED    BODIES.  85 

nitude,  is  made  to  revolve  round  a  centre,  it  is  sometimes  necessary  to  in- 
quire, 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  eftect  of  the  mo- 
mentum 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  tlie  circumference.- 

There  is  another  point,  of  which  the  determination  is  of  considerable  utility 
in  manv  meclianical  problems:  this  is  the  centre  of  percussion  ;  or  the  point 
at  which  an  obstacle  nuist  be  applied,  in  order  to  receive  the  whole  eftect  of  a 
stroke  of  a  body,  which  is  revolving  round  a  given  centre,  without  producing 
any  pressure,,  or  strain,  on  the  centre,  or  axis  of  motion.  In  a  straight  line, 
or  a  slender,  rod,  iixed  at  one  extremity,  the  distance  of  this  point,  from  the 
centre  of  motion,  is  two  thirds  of  the  whole  length. 

The  same  point  is  also  the  centre  of  oscillation,  the  distance  of  which  de- 
termines 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  extremity,  vi- 
brates in  the  same  time  as  a  ball  suspended  by  a  ducd<  ,  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.  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  considereol 
in,  this  place,  but  the  subject  involves  in  its  whole  extent  some  intricacy  of 
calculation,  and,  except  in  astronomy,  the  investigation  is  scarcely  applicable 
to  any  problems  which  occur  in  practice.  We  may,  however,  examine  a  few 
of  the  simplest  cases.     If  two  bodies  be  supposed  to  be  connected  by  an  in- 


86  LECTURE    IX. 

flexible  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  othcf  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  tlie  other  gain  velocity,  since  the  quantity 
of  rotatory  power  will  always  remain  unaltered:  that  point  only  which  "is  de- 
nominated the  centre  of  oscillation  retaining  its  original  velocity.  Now  the 
same  inequality  in  the  motion  of  the  bodies,  and  consequently  the  same  an- 
;giilar  velocity  of  rotation  will  be  produced,  if  the  connected  bodies  be  ini- 
tially at  rest,  and  tlie  fulcrum  be  applied  to  them  with  the  same  relative  velo- 
city. For  example,  if  a  straight  rod  or  wire  receive  an  impulse  at  one  end  in 
a  transverse  direction,  the  centre  of  oscillation,  Avhich  is  at  the  distance  of 
two  thirds  of  the  length  from  the  end  struck,  will  at  the  first  instant  remain 
at  rest,  conseciuently  the  centre  will  move  with  on^  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  al- 
ways with  an  equable  velocity  in  a  right  line,  while  the  whole  rod  Avill  also 
revolve  equably  roimd  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  communicate 
to  it  at  one  bloM'  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.directcd 
towards  it,  have  obviously  been  mistaken.  The  centre  of  oscillation  is  the 
only  point  which  remains  at  rest  with  regard  to  the  first  eflPcct  of  the  stroke, 
and  the  centre  of  gravity,  which  nev^r  coincides  with  the  centre  of  oscilla- 
tion, moves  in  the  direction  of  the  impulse,  while  the  parts  beyond  the  cen- 
tre 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,  without  injuring  the 
glasses  on  which  it  is  supported:  for  the  ends  of  the  stick,  instead  of  being 
depressed  by  the  stroke,  would  rise  Avith  half  the  velocity  of  the  body  wtich 


ON    THE    MOTIONS    OF    CONNECTED    BODIES.  87 

strikes  them,  if  the  two  portions  were  separated  without  tlie  loss  of  any  force. 
But  unless  some  art  has  been  previously  employed  in  producing  a  partial  se- 
paration, it  will  fre(juently  be  found,  that  the  stick  has  strength  enough  to 
break  the  glasses  before  it  gives  way. 

The  subject  of  preponderance,  or  of  the  action  of  "weights  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  opera- 
tion of  forces,  of  the  conditions  of  equilibrium,  and  of  the  estimation  of  rota- 
tory power.  The  consideration  of  the  effects  of  preponderance  enables  us  to 
determine,  in  some  circumstances,  the  best  possible  proportions  of  the  powers 
of  machines,  for  producing  the  required  effects  in  the  most  advantage- 
ous 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  consequence  to  know  what 
portion  of  the  power  must  be  employed  in  each  way,  in  order  that  the  great- 
est effect, may  be  produced  in  a  given  time.  We  are  sometimes  told,  that 
what  we  gain  in  power,  we  lose  in  time.  In  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  perform- 
ance 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,  sup- 
ported 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 


S8  LECTURE    I?C. 

equal  weights,  connected  with  the  former  three,  by  threads  passing  over  pul- 
lies.  The  length  of  one  of  the  planes  is  twice  its  height,  that  of  anothei 
considerably  more,  and  that  of  a  third  less:  if  the  M'eights  begin  to  rise  at 
the  same  time,  the  first  A\ill  arrive  at  the  top,  before  cither  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,  puUies,  or  any  similar  powers,  the 
greatest  eftect  will  be  produced,  if  the  acting  weight  be  capable  of  sustaining, 
in  equilibrium,  a  weight  about  twice  and  a  half  as  great  as  itself.  This  pro- 
position may  be  very  satisfactorily  illustrated  by  an  experiment.  Three  double; 
puUies  being  placed,  independently  of  each  other,  on  an  axis,  round  which 
they  move  freely,  the  diameters  of  the  two  cylindrical  portions,  which  com- 
pose the  iirst,  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  weig-hts  arc  attaclicd  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  Ave  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  weight 
the  fastest ;  and  consequently,  tliat  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  proportion  to  the  descending  weight,  the  ar- 
rangement 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  ohtaijied  in  this  case,  by  making  tlie  descend- 
ing weight  capable  of  holding  in  equilibrium  a  M'cight  one  ninth  as  great  as 
itself.     (Plate  Vf.  Fig.  77.)  ^ 

The  proportion  required  for  the  greatest  effect  is  somewhat  different,  when 
the  heights,  through  which  Ijoth  the  weights  are  to  move,  arc  limited,  as  they 
usually  must  be  in  practical  cases.  Here,  if  we  suppose  the  operation  to  be 
continually  repeated,  the  cfi'ect  will  be  greatest  in  a  given  time,  when  the 
ascending  weight  is  between  two  thirds  arul  one  half,  of  the  exact  countci- 
poise  to  the  descending  Aveiglit.  If,  however,  the  force  were  accunudated 
daring  the  action  of  the  machine,  there  would  be  no  limit  to  the  advantage  of 


ON    THE    MOTIONS    OF    CONNECTED    BODIES.  89 

a  slow  motion.  Thus,  if  we  have  a  stream  of  water,  fiUing  a  single  reservoir, 
which  is  to  raise  a  weight  by  means  of  its  descent,  the  proportion  here  as- 
signed 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  proportion  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  reascent  of  the  other. 

In  all  these  cases,  if  great  accuracy  were  required,  it  would  be  necessaiy 
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  gjTation 
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  attentive 
consideration  from  those  who  are  engaged  in  practical  mechanics ;  and  it  is 
natural  to  suppose  that  the  proportions  laid  down  may  be  adopted  w^th  safety, 
and  employed  with  success,  and  that  we  may  sometimes  derive  important  ad- 
vantages from  their  application.  But  on  more  mature  consideration,  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  destroy- 
ed; 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  arc  by  no  means  uniformly 
accelerating  forces,   like  that  of  gravitation,  to  which  the  propositions  which 

VOL.    I.  N 


go  LECTURE    IX. 

we  have  been  considering  are  adapted  :  they  are  not  only  less  active  when  a 
certain  velocity  has  once  been  att:uned,  but  they  are  often  capable  of  a  tem- 
porary increase  or  diminution  of  intensity  at  pleasure.  We  have  seen  the  in- 
convenience of  producing  a  great  final  velocity,  on  account  of  its  endanger- 
ing the  structure  of  the  machine :  if  therefore  our  permanent  force  be  calcu- 
lated according  to  the  common  rule,  so  as  to  be  able  to  maintain  the  equili- 
brium, and  overcome  the  friction,  the  niomentum  or  inertia  of  the  weights, 
when  once  set  in  motion,  will  be  able  to  sustain  that  motion  equably;  and  it 
will  not  be  dithcult  to  give  them  a  sufficient  momentum,  by  a  greater  exer- 
tion 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  ve- 
locity 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  mo&t  advantageous, 
when  its  velocity  is  one  third  of  that  of  the  stream :  but  it  will  hereafter  ap- 
pear, that  this  estimation  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  float- 
boards  of  a  water  wheel,  the  strength  which  can  be  exerted  may  be  repre- 
sented, 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  ; 
consequently  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  some- 
what greater  than  this. 


ON    THE    MOTION'S    01'    CONNECTED    BODIES.  91 

Where  a  uniformly  accelerating  force,  like  that  of  gravitation,  is  employed 
in  machines,  it  might  often  be  of  advantage  to  regulate  its  operation,  so  that 
it  might  act  nearly  in  the  same  manner  as  the  forces  that  we  have  been  con- 
sidering ;  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  modifica- 
tion 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  por- 
tion of  the  moving  force  is  expended  in  producing  momentum ;  the  velocity 
of  3  miles  an  hour,  would  be  generated  in  a  heavy  body,  descending  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  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  jus- 
tified by  a  more  profound  investigation. 

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  ob- 
serve 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  considera- 
tion of  the  properties  of  the  centre  of  gravity:  we  have  only  to  examine  whe- 
ther it  will  begin  to  descend  or  to  ascend,  when  the  machine  moves,  or  whe- 
ther it  will  remain  at  rest.     If  it  be  so  placed,  that  it  must  either  remain  at 


p2  LECTURE    IX. 

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  de- 
luded, 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  couuterbalancci 
each  other.     (Plate  VI.  Fig.  78.) 


95 


LECTURE  X. 


ON    DRAWING,    WRITING,     AND    MEASURING. 


JEXAVING  investigated  all  the  general  principles  and  laws  of  motion,  and 
of  mechanical  power,  we  may  now  proceed  to  the  consideration  of  particular 
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  definitioa" 
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  draw- 
ing, we  require  a  number  of  geometrical  instruments,  whicli  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  positioa 
of  the  lines  which  are  to  form  the  picture.  The  productions  of  the  arts  of 
drawing  and  writing  are  multiplied  and  perpetuated  by  means  of  engraving 
and  printing;  inventions  which  have  been  the  sources  of  inestimable  advantage 
in  the  instruction  and  civilisation  of  mankind. 


§♦  ,  LECTURE    X. 

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  en- 
larged, when  it  is  required.  But  a  copy  may  sometimes  be  more  expeditiously 
made,  by  tracing  immediately  from  the  original,  when  the  materials  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  of  points  through  it,  so 
as  to  mark  the  copy,  either  at  once,  or  by  means  of  charcoal  powder  inibbed 
through  the  holes,  which  is  called  stenciling:  and  for  this  purpose,  an  inter- 
mediate copy  may  be  fonned  on  semitransparent  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  cover- 
ed 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  carpenter  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  well  as  for  assisting  the  efiect  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  engrav- 
ings ;  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 


ON    DRAWING,    WRITING,    AND    MJ^AStJRINS.  f)5 

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  draw- 
ings with  chalk,  however,  the  advantage  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,  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  advantage  in  the  mode  of  pro- 
ducing its  liglits  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  prin- 
cipal 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  materials  employed  are 
Indian  ink,  the  black  liquor  of  the  cuttle  fish,  or  bistre,  which  is  extracted 
from  soot:  both  these  last  produce  a  browner  and  richer  tint  than  the  Indian 
ink.  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 


56  ^  LECTURE    X. 

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  required.  For  water  colours  of  all 
descriptions,  a  certain  quantity  of  gum  is  used,  and  sometimes  a  size  made  of 
isinglass,  with  a  little  sugarcandy.  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  boil- 
ing shreds  of  untanned  leather,  or  of  parchment,  for  several  hours :  this  me- 
thod is  chiefly  employed  for  colouring  walls  or  paper,  but  sometimes  for  paint- 
ing on  cloth.     For  delicate  purposes,  the  size  may  be  made  with  isinglass. 

When  a  wall  or  cieling  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  visually  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  antients,  which  have  been  preserved, 
were  executed  in  fresco. 

The  art  of  painting  in  oil  was  first  discovered  by  Van  Eyck  of  Bruges,  to- 
wards the  end  of  the  14th  century:  it  has  now  become  almost  the  only  man- 
ner 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  the 
occasianal  addition  of  other  oily  and  resinous  substances.  The  work  may  be 
fjxecuted  on  wood,  cloth,  silk,  paper,  marble,  or  metals:   these  substances 


ON    DRAWING,    WRITING,    AND    MEASURING.  97 

l>eing  first  washed  with  size,  and  then  primed  with  an  oil  colour,  which  is  usu- 
ally white,  but  sometimes  dark.  Some  painters  have,  however,  preferred  a 
ground  of  distemper.  The  glare  of  the  oil  colours,  or  of  tlie  varnish,  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  api)lied  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  ap])lied  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:  in  tapes- 
try, 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  countries, 
and  certainly  in  some,  of  a  later  date  than  that  of  drawing  representations  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  in- 
tended as  hieroglyphics ;  that  is,  like  the  antient  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  ob- 
jects, 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  froni  a  few  hundred  radical  characters  expressive  of  the  most  simple 
ideas.  The  art  of  writing  with  alphabetical  letters  must  have  been  suffici- 
ently understood,  in  the  age  of  Moses,  to  serve  the  purpose  of  the  promulga- 
tion of  laws  and  of  religion :  it  is  generally  supposed  to  have  been  invented 

VOL.    I.  o 


gS  LECTURE    X. 

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  riglit  side;  the  other  eastern  na- 
tions have  always  written  from  right  to  left.  The  most  ancient  Greek  in- 
scriptions are  turned  alternately  backwards  and  forwards,  the  letters  being  re- 
versed in  the  lines  which  begin  on  the  right  side;  but  the  Greeks  soon  con- 
fined themselves  to  that  mode,  which  has  been  since  adopted  by  all  European 
nations,  and  which  appears  to  be  in  itself  the  most  natural,  at  least  for  writ- 
ing 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  continued  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 
papyius  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  mem- 
brana  pergamena.  To  make  the  best  paper,  the  widest  and  finest  leaves  of  the 
papyrus  were  matted  together,  united  b}'  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  membrane  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  cpiality  of  the  paper,  by  filling  up  its 
pores. 

2 


ON    DRAWING,    WRITING,    AND    MEASURING.  99 

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  in- 
struction 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  Avriting  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. 

The  inks  of  the  ancients  arc  said  to  have  been  made  of  a  carbonaceous  sul)- 
stance,  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  abundance  of 
the  gallic  acid  produces  a  much  blacker  colour,  than  is  obtained  where  this  acid 
is  used  in  a  smaller  proportion.  Mr.  Kibaucourt'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,  having  strained  the  decoction, 
to  add  to  it  four  ounces  of  sulfate  of  iron,  one  of  sulfate  of  copper,  three  of 
gum  arable,  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  arable,  half  an  ounce  of  green  sulfate  of  iron,  or  cop- 
peras, and  a  drachm  of  sulfate  of  copper,  or  blue  vitriol,  or  even  a  much 
smaller  quantity  of  gvim  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  diffiL'rent  colours  for  indicating  different 
lumibcrs;  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 


100  LECTURE    X. 

drawn  in  clIfFerent  directions,  so  that  each  Avord,  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  polygraph,  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.  In  this  manner  five  copies  may  be  made  at  once  with  tolerable  facility, 
and  themethod  may  perhaps  hereafter  be  extended  to  a  much  greater  number. 

A  mode  of  Avriting,  perfectly  different  from  any  of  those  which  have  been 
mentioned,  is  performed  by  means  of  the  telegrapli,  which  is  justly  consider- 
ed 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  afterwards,  with  some  variations,  in  this  coun« 
try.  Dr.  Hooke  proposed  the  employment  of  alphabetical  and  other  arbitrary- 
characters  ;  at  present  it  is  usual  to  have  six  boards,  each  turning  on  its  axis 
■so  as  to  appear  or  disappear  at  pleasure:  these  admit  of  sixty  four  combina- 
tions, 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  ta 
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 


ON    DRAWING,    WRITING,    AND    MEASURING.  101 

a  right  line,  besides  that  it  is  guided  by  the  flatness  of  its  lower  surface.  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,  bniss)  or  ivory,  have  a  material  advantage  over  those 
of  wood,  as  they  are  not  liable  to  be  spoilt  by  warping,  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  draAV  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  twa- 
points.^ 

For  drawing  a  circle  of  a  gfven  radius,  we  use  compasses,  with  one  pofnt 
generally  of  metal,  the  other  of  various  descriptions.  Compasses  are  some- 
times 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  the  other; 
and  when  great  accuracy  is  required,  hair  compasses  may  be  employed,  having 
ajoint  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  graduated  scale,  so  as  to  indi- 
cate 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  dia- 
meter, 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  together,  so  as  to  form  an  angle,  are  made  tojslide 
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,  appli^ 


102  LECTURE    X. 

ed  to  difterent  parts  of  its  concavitj'  :  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  cir- 
cular 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  convenience 
in  making  the  square  to  slide  on  its  margin.  Rulers  also,  of  various  descrip- 
tions, are  commonly  made  rectangular,  in  order  to  answer  occasionally  the 
same  purpose. 

Triangular  compasses  are  sometimes  used,  for  laying  down  a  triangle  equal 
to  a  given  triangle;  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  oblifjuity  of 
one  of  the  two  motions  may  be  made  to  correct  that  of  the  other.  A  simple 
cyhnder,  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  accuracy;  but  where  the  dis- 
tances 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,  bevilledj  it  may  be  employed  for  the  same  purpose, 


ON     DRAWING,    WRITING,    AND    MEASURING.  103 

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  complicat- 
ed 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  {wo  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  b\  the  pencil  will  be  similar  to  that  which  is  described 
by  the  tracing  point.  And  instead  of  holes  in  the  rulers,  they  may  be  fur- 
nished 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  difterent  scale.  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  portions  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  irrstrument 
might  be  much  improved  by  inserting,  in  the  common  scale,  fractional  or  de- 
cimal divisions,  between  the  whole  numbers,  so  that  the  legs  might  be  di- 


^- 


104  LECTURE    X. 

vided,for  example,  in  the  ratio  of  2  to  3,   3  to  4,  or  4  to  5,  or  of  10  to  1 1,   !S 
oris,  at  pleasure.     (Plate  VI.  Fig.  90.) 

The  use  of  the  sector  depends  also  on  the  properties  of  similar  triangles.  The 
scale  of  equal  parts,  which  is  laid  down  on  each  leg,  beginning  from  the  cen- 
tre, 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  corresponding  points  are  neces- 
sarily 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  ex- 
tend 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  mag-nitude  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  construction  of  instruments; 
for  instance,  in  one  of  the  arcs  of  the  mural  quadrant  of  the  observatory  at 
Greenwich,  the  right  angle  is  divided  into  96  parts,  by  the  continual  bisec- 
tion of  one  sixth  of  the  circle.  There  arc  also  some  practical  methods  of  di- 
viding angles  into  three  or  more  equal  parts,  which  are  sufliciently  accurate 
for  many  purposes,  although  it  is  well  known  that  in  theory  the  perfect  tri- 
section  of  an  angle  is  beyond  the  reach  of  plain  geometry.  This  trisection  is, 
necessary  in  the  common  division  of  tlie  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  can- 


Oy    DRAWING,    WETTING,    AND    MEASURING.  105 

not  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  calculation,  beyond 
the  common  method,  and  its  execution  in  practice  must  be  much  more 
ditHcult. 

Whole  circles,  or  theodolites,  divided  into  degrees  and  their  parts,  quadrants 
and  sextants,  are  usually  employed  in  measuring  angles;  and  protractors,  se- 
micircles, 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  prin- 
ciples, each  degree  of  the  arc  is  reckoned  for  twc 

For  the  graduation  of  all  instruments  of  this  kind,  of  moderate  dimensionSy 
Mr.  Ramsden's  dividing  engine  is  of  great  utility  ;  the  instrument  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  J°  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  substitute  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  apparatus  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  arc  to  be  added 
to  that  of  the  intire  divisions.      (Plate  VII.  Fig,  92.) 

There  are  several  ways  of  measuring  the  angular  elevation  of  an  object 

YOL.    I.  B 


106  LECTURE    X. 

above  the  horizon;  at  sea,  the  apparent  horizon,  formed  by  the  surfiice  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  correction  is  therefore  re- 
quired according  to  the  height.  In  the  open  sea  this  correction  may  be  de- 
termined by  measuring  the  whole  angle  above  and  below  the  apparent  horizon, 
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  ac- 
count of  its  perfect  fluidity,  to  be  the  best  liquid  for  a  spirit  level.  An  arti- 
ficial horizon  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  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  em- 
ploy the  sine  or  cosine  of  an  angle  than  the  angle  or  arc  itself.  It  is,  how- 
ever, 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  employed 


ON    DRAWITffO,    WRITING,    AND    MEASURING.  lOT 

according  to  the  properties  of  similar  triangles,  in  the  computation  of  propor- 
tions. 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  cm- 
ployed  mechanically  in  the  same  manner  as  a  table  of  logarithms  is  used  arith- 
metically, 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  distances 
in  the  dendrometer  or  engymeter;  a  part  of  the  instrument  forms  a  base  of 
known  dimensions,  and  the  angle  at  each  extremity  of  this  base  being  mea- 
sured 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  two  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  subtended  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  na- 
ture, have  been  invented  and  constructed  with  great  labour  and  ingenuity;  but 
they  are  rather  to  be  considered  as  mathematical  toys,  than  as  instruments 
capable  of  any  useful  application. 

An  angle,  when  once  measured,  can  be  verbally  and  numerically  described, 
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  there- 
fore necessary  to  establisli  some  arbitrary  standard  with  which  any  given 
lengths  and  surfaces  may  be  compared.  It  might  be  of  advantage  in  the  com- 
munication between  different  countries  to  fix  one  single  standard  to  be  em- 
ployed throughout  the  world,  but  this  does  not  appear  to  be  practically  pos- 
sible, even  if  it  were  determined  what  the  standard  ought  to  be.  "  The  ob- 
servation of  the  isochronism  of  the  small  vibrations  of  a  pendulum,  and  the 
ease  and  certainty  with  which  the  length  of  a  pendulum  vibrating  secomls- 


108  LECTURE    X. 

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  ca- 
pricious and  inconvenient  divisions,  the  difficulty  of  determining  and  com- 
paring them,  the  embarrassment  and  the  frauds  which  they  occasion  ,in  com- 
merce, without  regarding,  as  one  of  the  greatest  benefits,  that  the  improve- 
ments of  the  sciences  and  the  ordinances  of  civil  governments  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  fundamental  magnitude  indicated  by 
nature  itself.  A  nation  that  would  introtluce  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  ob- 
stacles that  are  opposed  to  a  measure,  of  which  the  convenience  is  universally 
felt,  -Such  were  the  motives  that  determined  the  constituent  assembly  to  in- 
trust tlifi  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  information  of  several  members  of  the  national  representa- 
tion. 

"  The  ideiitity  of  the  calculation  of  decimal  fractions  and  of  whole  num- 
bers, leaves  no  doubt  with  respect  to  the  advantage  of  the  division  of  mea- 
sures 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  con- 
cerned, a  facility  that  becomes  still  greater  by  means  of  logarithms,  of  which 
the  use  may  also  be  rendered  extremely  popular  by  simple  and  cheap  instru- 
ments. The  decimal  division  was  therefore  adopted  without  hesitation;  and 
in  order  to  preserve  the  uniformity  of  the  whole  system,  it  was  resohed  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 
v/liich  the  name  of  metre  was  to  be  given. 


ox    DRAWING,    WRITING,    AND    MEASURING.  IOl> 

"  The  length  of  the  pendulum,  and  that  of  a  meridian  of  the  earth,  are  the 
two  principal  standards  thdt  nature  affords  us,  for  fixing  the  unit  of  linear 
measures.  Both  of  these  being  independent  of  moral  revolutions,  they  can- 
not experience  a  sensible  alteration  without  very  great  changes  in  the  physical 
constitution  of  the  earth.  The  first  method,  which  is  of  easy  execution,  li?,s 
the  inconvenience  of  making  the  measure  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  is  wholly  arbitrary. '  It 
was  resolved,  therefore,  to  employ  the  second  method,  which, "  says  Mr.  La- 
place, "  appears  to  be  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  sj)ace  to 
the  entire  circumference  of  the  earth.  This  method  has  also  the  advantage  of 
making  nautical  measures  correspond  at  once  with  celestial  ones.  The  navi- 
gator 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  consequence  that  these  measures  should  be  readily  obtained  from 
each  other,  by  altering  only  the  place  of  the  units.  But,  for  this  purpose, 
the  fundamental  unit  of  linear  measures  must  be  an  aliquot,  part  of  the  ter- 
restrial 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 
xmit  of  angular  measure,  and  the  right  angle,  as  constituting  the  limit  of  the 
inchnation  of  two  lines  to  each  other,  was  considered  as  entitled  to  the  pre- 
ference. 

"  The  arc,  Mdiich  was  measured  in  1740,  from  Dunkirk  to  the  Pyrenees, 
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  M^chain 
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  measurement  of  the  arc  in  Peru, 
the  quadrant  was  determined  to  be  equal  to  5130740  of  the  iron  tojse  used  at 
the  equator,  its  temperature  being  6]  ■^°  of  Fahrenheit:  the  ten  millionth  part 


110  LECTURE    X. 

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  pendulum  vibrating  seconds,  and  this  has  been 
done  with  great  care  by  Borda,  at  the  observatory  of  Paris.  The  unit  of  mea- 
sures of  land  is  the  are,  or  1 00  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 
liours,  the  hour  into  a  hundred  minutes,  and  the  minute  into  a  hundred  se- 
conds. 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,  have  suspended  its  in- 
troduction for  the  present.  We  may,  however,  expect  that  it  will  ultimately 
be  brQught  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  whe- 
ther a  standard  has  been  first  adjusted  according  to  the  circumference  of  tiie 
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  inde- 
pendent of  any  ulterior  comparison,  than  to  seek  for  an  ideal  perfection  in  at- 
tempting- to  copy  from  a  more  magnificent  original :  to  say  nothing  of  the  un- 
certainty with  regard  to  the  ellipticity  of  the  earth,  and  the  probable  irregu- 
larity of  its  form  in  various  respects.  On  the  other  hand,  it  must  be  allowed, 
that  the  correct  determination  of  the  length  of  the  pendulum  has  sometimes 


ox    DRAWING,    WRITING,    AND    MEASURING.  Ill 

been  found  more  difficult  than  Mr.  Laplace's  statement  would  lead  us  to  sup- 
pose 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',i^^  English  inches,  measured,  as  it  has  been  usual  in  this  country, 
on  a  standard  scale  of  brass,  at  the  temperature  of  62°  of  Fahrenheit;  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  pen- 
dulum vibrating  seconds  in  London,  was  found  by  George  Graham,  from  a 
mean  of  several  experiments,  all  agreeing  very  nearly  together,  to  be  39-r^ 
inches.  This  is  also  nearly  a  mean  between  the  length  which  may  be  de- 
duced, with  proper  corrections,  from  Borda's  experiments  at  Paris,  and  Mr. 
Whitehurst's  experiments  made  in  London,  with  the  apparatus  invented  by 
Mr.  Hatton,  where  the  length  ascertained  is  the  diiference  between  the  lengths 
of  two  pendulums  vibrating  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  76  -,^0^  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. 

A  variety  of  instruments  are  used  for  the  immediate  comparison  of  the 
standard  measure,  or  its  parts,  with  other  lengths  or  distances.  Such  arc 
scales,  simple  and  diagonal,  verniers,  micrometer  screws,  beam  compasses, 
rods,  lines,  chains,  and  measuring  wheels.  The  greatest  accuracy  has  ge- 
nerally 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,  however,  found 
that  a  steel  chain  was  as  little  liable  to  error,  as  any  mode  that  he  could  em- , 


112  LECTURE    X. 

ploy;  and  those  whq  have  continued  the  extensive  survey  which  he  began, 
even  prefer  it  to  every  other.  For  the  comparison  of  standards,  and  for  de- 
termining 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,  corres- 
ponding 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  suf- 
ficiently 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,  suc- 
ceeded in  making  simple  scales,  which  are  accurate  enough  to  measure  the  ten 
thousandth  of  an  inch.  lie  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  powerful  microscope :  but  those  which  are  at  the  distance  of 
the  five  thousandth  of  an  inch  are  much  more  correct  and  distinct.  For  di- 
viding rectilinear  scales  of  all  kinds,  ]\Ir.  Ramsden  constructed  a  machine 
which  acts  by  the  turns  of  a  screw:  others  have  employed  an  apparatus  re- 
sembling Marquois'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  ecjual  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 
jship  and  the  water,  and  discharging  at  the  same  time  a  small  stream  into  a 
reservoir,  with  a  velocity  proportional  to  that  of  the  sliip. 


rn 


LECTURE  XL 

ON    MODELLING,    PERSPECTIVE,    ENGRAVING,    Aljijy 

PRINTING. 

\y  E  have  examined  die  principal  instrupicnts  and  materials  employed  for 
<lra>yingand  for  measuring;  we  ^ve  now  to  consider,  fust,  the  methods  of  co- 
pying solids,  and  of  projecting  their  images  on  a  plane  surface  ;  5ind  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 
.^xample,  of  a  sta.tue,  we  jnust  xletexmine  the  situation  of  a  sufficient  number 
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  pait  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  nlaster  of  Paris,  since  the  clay  would  crack  and  change 
its  form  in  drying.  This  mode  of  copying,  by  means  of  plaster,  is  exceed- 
ingly 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,  fornv  a 
mould  for  the  ultimate  cast.  Sometimes  a  small  figure  is  first  modelled  in  a 
mixture  of  wax,  turpentine,  and  oil;  and  a  mould  being  formed  on  this, 
VOL.  r.  ■    Q, 


!I4  LECTURE    XI. 

the  ultimate  cast  is  made  either  of  plaster,  or  of  a  composition  pf  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  an}'  kind,  than  to  represent  its  appearance  by  means  of  perspective 
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  merits  -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  embodying  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  suffi- 
cient, without  a  recurrence  to  mathematical  principles.  To  architects  there- 
fore, and  to  mechanics  in  general,  a  knowledge  of  perspective  is  almost  in- 
dispensable, whenever  they  Avish  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 
MS,  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  suffici- 
■  ent  distinctness.  The  paper  being  furnished  with  corresponding  lines,  we 
may  observe  in  what  division  of  the  frame  any  conspicuous  point  of  the  ob- 
ject 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  suflicient  number  of  points,  we  may  complete  the  figures  by  the  addition  of 


ON    MODELLING,     PERSPECTIVE,     EKGUAVING,     AND    PRINTING.       115 

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  our  picture 
as  a  reduced  copy  of  a  projection  formed  on  an  imaginary  plane,   which,   a.» 
well  as  the  picture,  is  generally  supposed  to  be  in  a  vertical  situation,  and 
which  stands  on  the  horizontal  plane,   at  the  point  where  the  objects  to  be 
represented  begin.     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  be  a  right  line  di- 
rected to  this  point,  but  never  passing  it.     When  the  lines  to  be  represented 
are  parallel  to  the  picture,   the  distance  of  their  vanishing  point  becomes  in- 
finite,  and  their  images  are  also  parallel  to  the  lines  and  to  each  other.     The 
centre  of  the  picture,   or  that  point  v/hich  is  nearest  to  the  eye,  is  the  vanish^ 
ing  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,  cou- 
siderijig  the  picture  as  a  horizontal  surface,   we  may  find  the  vanishing  point 
of  each  of  it  s  lines,  by  drawing  a  line   parallel  to  it   through    the    point 
of  distance,     until   it   meets    the   horizontal   vanishing   line.     (Plate   VII. 
rig.  100,    101.)  , 

In  order  to  find  the  position  of  the  image  of  a  given  point  of  a  line,   wc 
must  divide  the  whole  image  in  such  a  manner,  that  its  parts  may  be  to  each 


Il6  LECTURE    Xr. 

other,  in  tlie  same  proportion  as  the  distance  of  the  given  point,  and  of  tl)e 
eye,  from  the  plarie  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  in  the  poitit 
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  VIIL 
rig.  103.) 

The  projection  of  curvilinear  figures  is  most  conveniently  effected,  by  draw- 
ing across  them  parallel  lines,  which  form  small  squares  or  rectangles,  throwing 
these  divisions  into  perspective,  and  tracing  a  curve  through  the  correspond- 
ing points.  There  are  also  methods  of  determining  mathematically,  or  of 
drawing  mechanically  the  ellipsis,  which  results  from  the  projection  of  a  circle, 
in  a  given  position,  but  they  are  considerably  intricate,  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  magnitude, 
and  to  give  them  as  much  as  possible  the  appearance  of  an  imitation  of  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  other.  In  order  to  re- 
present 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  be  parallel,  and  another  for  that  of  the  point  of 
tlistance,  by  means  of  which  we  may  measure  the  first  lines,  as  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.) 


ON    MODELLING,     PERSPECTIVE,    ENGRAVING,    AND    PRINTING.       117 

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  re- 
presented would  have  had  less  of  tlie  appearance  of  nature,  if  they  had  been 
projected  orthographically,  nor  Avould  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  si- 
tuated 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  im- 
portant advantage,  that  the  image  of  every  circle,  greater  or  lesser,  still  re- 
mains a  circle.  This  point  is  in  the  surface  itself,  at  the  extremity  of  the  di- 
ameter 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  spherical  trigonometry.  The  pro- 
jection 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  mea- 
sure 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.  rig.  106.)  •  • 

For  projecting  figures  on  curved  or  irregular  surfaces,  the  readiest  methotl 


lis  LECTURE    xr. 

is  to  trace  cross  lines  on  them,  with  the  assistance  of  such  a  frame  as  lias  been 
described  for  drawing  in  perspective,  representing  the  appearance  of  uniform 
squares  or  rectangles,  and  to  delineate  in  each  of  these  the  corresponding 
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 
their  performance,  and  perpetuated  in  their  duration,  by  means  of  engraving 
and  printing.  If  there  is  any  one  circumstance  to  which  we  can  peculiarly  at- 
tribute the  more  rapid  progress  of  general  civilisation  in  modern  than  in  ancient 
times,  it  is  the  facility  of  qiultiplying  copies  of  literary  productions  of  all 
kinds,  by  the  assistance  of  these  arts.  The  distinguishing  character  of  print- 
ing 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  on  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 
Avere  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  introduced  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  \vorks,  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,  how- 
ever, at  present  in  a  high  degree  of  perfection  in  this  country,  and  blocks  are 
still  frequently  used  for  mathematical  diagrams  andother  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. 

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, 


ON    MODELLI^'G,     PERSPECTIVE,    ENGRAVING,    AND    PRINTING.      IIQ 

the  chawing,  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  draw- 
ing 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  characters  are  to  be  en- 
graved, 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  the  appearance  of  stiffness. 
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  rub- 
bed off  by  anothei-  tool.  Sometimes  a  number  of  detached  excavations  are 
formed  by  a  pointed  instrument,  and  the  projections  are  afterwards  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  Avholly  dark ;  the  lights  are  then  inserted,  by  re- 
moving 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  cop- 
per, is  the  process  of  etching.     The  plate,  being  covered  with  a  proper  var- 


ISO  l.i:G.TUiB;E  .XI. 

iiisli,  is  usually  blackened  with  smoke,  giitltlie  drawing  is  placed  on  it,  with  the 
interposition  of  a  paper  nibbed  over  with  red  chalk,  which,  when  the  drawing 
is  traced  with  a  wooden  point,  adheres  to  the  varnish,  in  the  form  of  the  out- 
line: or  if  it  is  re(iuired  that  the  ultimate  impression  be  turned  the  same  way 
as  the  drawing,  an  intermediate  outline  must  be  procured  in  the  same  man- 
ner on  a  separate  paper,  and  then  transferred  to  the  plate.  All  the  outlines 
thus  marked  are  traced  with  needles,  which  make  as  inany  furrows  in  the 
varnish,  and  leave  the  copper  bare:  tjie  shades  are  inserted  with  the  assist- 
ance of  the  ruling  machine,  wherever  parallel  lines  can  be  employed.  The 
plate  tlms  prepared,  and  furnished  with  an  elevated  border  of  a  proper  con- 
sistence, is  subjected  to  the  action  of  the  diluted  nitric  acid,  until  all  the 
parts  arc  sufficiently  eorroded,  care  being  taken  in  the  mean  time  to  sweep 
off  the  air  bubbles  as  they  collect,  and  to  stop  out,  oi;  cover  with  a  new  ya,r- 
nish,  the  lighter  parts,  which  aje  soonest  completed.  When  the  varnish  is  re- 
moved, the  finishing  touches  are  added  with  the  graver:  and  if  the  plate  re- 
quires further  corrosion,  the  varnish  jnay  sometimes  be  replaced,  without  fill- 
ing up  the  lines,  by  applying  it  on  a  ball  or  cushion,  taking  care  to  avoid 
any  oblique  motion.  It  is  said  that  the  acid  sometimes  operates  so  as  to  un- 
dermine the  metal  on  each  aide,  adad  to  render  the  furrows  wider  as  they  be- 
come deeper,  and  that  for  this  reason  in  etchings,  as  well  as  in  mezzotintos, 
the  later  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  cor- 
roded in  a  similar  rjaanner  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  varnish 
then  adheres  to  the  back  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  been  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 
iicid.     Sometimes  a  little  resin,   very  finely  powdered,   is  sifted  on  the  plate, 
•whioh  is:then  sufficiently  warmed  to  make  the  particles  adhere  to  it;    some- 


ON    MODELLING,     PERSPECTIVE,    ENGRAVING,    AND    PRINTING.      121 

times  it  is  varnished  with  a  spirituous  solution  of  resin,  which  cracks  through- 
out in  drying ;  and  if  a  strong  hue  be  any  where  required,  it  may  be  traced 
with  a  mixture  of  whiting  with  some  adhesive  substance,  before  the  varnish 
is  laid  on;  this  Avill  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  tliem  from  the  acid.  This  mode  of  engraving  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  in- 
vented 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  ffannels,  and  strongly  pressed  in  pass- 
ing between  two  wooden  rollers.  By  frequent  use  the  plate  loses  its  sliarpness, 
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,  e\cn 
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. 

A  simple  and  elegant  method  of  multiplying  drawings  has  been  lately  in- 
troduced by  Mr.  Andr^.  The  drawings  are  made  with  an  unctuous  compo- 
sition,  in  the  form  of  a  crayon  or  of  an  ink,  on  a  soft  stone  of  4  calcarious 

VOL.     I.  li 


122  LECTURE    XI, 

nature,  somewhat  like  a  stone  maiie.  When  the  drawing  is  finished,  the 
stone  is  moistened,  and  imbibes  so  much  water,  that  the  printing  ink  will 
not  adhere  to  it,  except  at  tlie  parts  where  the  crayon  or  the  ink  has  been 
applied;  and  in  this  manner  an  impression  is  procured,  which  has  much  of 
the  freedom  and  spirit  of  an  original  drawing.  When  tlie  ink  is  used,  a  little 
'  acid  is  afterwards  applied  to  the  stone,  in  order  to  corrode  its  intermediate 
parts  ;  and  the  bold  stile  of  the  impression  much  resembles  that  of  the  old 
wooden  cuts. 

The  art  of  printing  with  separate  types  was  invented  soon  after  the  in- 
troduction of  wooden  blocks  into  Europe.  Tlie  improvement  was  great  and 
important.  The  year  144'3,  or  1444,  is  considered  as  the  date  of  the  oldest 
printed  book ;  but  the  precise  time  and  place  of  the  invention  remain  some- 
what 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  starhped,  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  arrajiging  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  oflf  the  im- 
pression, are  entirely  calculated  for  the  simplicity  and  convenience  of  the 
manual  operations  concerned,  and  require  little  or  no  detailed  explanation.. 


123 


LECTURE    XII. 


ON    STATICS. 


f 


The  examination  of  the  magnitude  of  the  various  forces,  employed  in  prac- 
tical mechanics,  constitutes  the  doctrine  of  statics.  The  term  statics,  in  a 
strict  sense,  implies  the  determination  of  weights  only;  but  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  immediately  introductory  to 
the  particular  constructions  and  uses  of  machinery,  and  nearly  coimected 
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  velocities, 
and  from  the  effects  of  their  collision,  we  might  determine  their  comparative 
momenta,  and  the  proportion  of  their  masses;  but  it  is  obvious  that  this  pro- 
cess 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  dimensions ;  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  immediately 


124  LECTURE    XII. 

« 

Avith  otlier  weights  of  known  dimensions:  but  sometimes  the  flexure  of  a. 
spring  is  employed  for  the  comparison.  Standard  weights  hav"  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  2524-  grains.  A  hogshead  of  water,  wine 
measure,  weighs,  therefore,  525  pounds,  and  a  tun  2100  pounds,  which  is 
nearly  equal  to  a  ton  weight.  i\Ir.  Barlow  supposes  that  the  tun  measure  of 
water  contained  originally  S2  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  624-  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  equiva- 
lent to  a  ton,  although  it  now  weighs  nearly  half  as  much  more.  But  at  the 
mean  temperature  of  this  climate,  or  52°,  a  cubic  foot  of  distilled  Mater 
weighs  only  9.9S  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  1 5^  English  grains :  hence 
tlie  chiliogramme  is  2-j-  pounds,  and  five  myriogrammes  are  nearly  a  hundred 
weight.  Five  grammes  of  silver,  including  one  tenth  of  alloy,  make  a  franc, 
Avhich  is  one  eightictli  better  than  the  old  franc  or  livre,  _^«tl  is  intrinsically 
worth  nearly  ninepen^e  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  \vhich 
are  smaller,  in  a  certain  proportion,  than  those  which  they  represent :  in  the 
steelyard,  a  single  weight  acquires  different  values  at  different  parts  of  tlie 
arm,  and  in  the  bent  lever  balance,  the  position  of  the  arms  determines  the 
magnitude  of  the  counterpoise.  The  spring  steelyard  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 


ON    STATICS.  12,5 

scales,  being  freely  suspended  from  fixed  points  in  the  beam,  act  on  them  al- 
ways in  the  direction  of  gravity ;  and  the  effect  is  the  same  as  if  the  whole 
weight  were  concentrated  in  those  points.  The  beam  supports  the  scales,  and 
is  itself  supported,  by  means  of  line  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  ba- 
lance 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  equilibrium  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  equili- 
brium is  the  most  usual  and  the  best,  because  it  gives  us  an  opportunity  of 
determining  the  degree  of  inequality  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,  however,  the  fulcrum  be  too  much  elevated  above  the  centre  of 
gravity,  the  equilibrium  may  be  too  stable,  and  may  retjuire  too  great  an  in- 
equality, 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  tottering,  the  lower  scale  will  not  rise,  even  if  it  be  somewhat  less 
loaded  than  the  upper;  and  sieelyards  of  this  construction  have  scmietimes 
been  employed,  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  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  fulcrum  as 
may  be  required  for  the  occasion.  IVfr.  llamsden'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  .  •  IO9.) 

The  arms  of  a  balance  have  sometimes  been  made  imequal  for  fraudulent 
purposes,  the  weight  being  placed  nearer  to  the  fulcrum  than  the  substance 


1^6  .Z.ECTURE  xri. 

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  counterpoise 
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  suffi- 
cient 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  fcH"  this  purpose  the  instrument  should  be  in  equilibrium  without  any 
weight.  In  such  cases,  great  accuracy  may  be  obtained  by  applying  a  small 
weight  at  the  end,  in  the  form  of  a  micrometer  screw.    (Plate  IX.  Fig.  1 12.) 

The  arms  of  a  balance,  though  constant  in  length,  may  vary  in  effect  with- 
out 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  per- 


ON    STATICS.  127 

fectly  vertical,  since,  in  this  position,  the  weight  may  be  overpowered  by 
the  minutest  counterpoise  acting  on  the  other  arm.  The  centre  of  gravity 
being,  in  the  common  balance,  very  nearly  in  a  right  line  between  the  weights, 
in  order  that  it  may  be  immediately  below  the  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  de- 
termined are  large,  tiie  scale  becomes  very  much  contracted,  and  the  instru- 
ment requires  to  be  levelled  with  great  accuracy.  A  counterjioise  acting  on 
a  spiral  or  conical  barrel,  has  also  been  applied  to  a  similar  purpose ;  it  is  ca- 
pable of  a  scale  somewhat  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  supported  by  the  hook. 
This  instrument  is  called  a  spring  steelyard.  Mr.  Ilanin's  spring  steelyard 
has  a  long  index,  which  revolves  on  a  centre,  and  shows  at  once  the  weight 
according  to  the  standards  of  different  countries.  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  curva- 
ture, 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  ecpial  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  abcmt  one  part  in  five  thousand  from  the  apparent  weight  in- 
dicated by  the  spring  steelyard.     (Plate  IX.  Fig.  114.) 

The  spring  steelyard  affords  us  the  most  convenient  method  of  measunng 
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 


128  LECTURE    XII.  '     . 

animal,  which  is  employed  in  drawing  a  distant  boat  or  carriage,  by  the  in- 
clination 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  extend* 
to  the  point  where  the  curve  becomes  horizontal. 

All  animal  actions,  or,  at  least,  all  the  external  actions  of  animals,  are  ulti- 
mately dependent  on  the  contractions  and  relaxations  of  the  flesliy  parts,  - 
which  are  called  muscles.  The  operation  of  the  particular  muscles  belongs 
properly  to  the  Iscience  of  physiology  ;  but  their  mechanism  may  in  general 
be  understood  from  the  properties  of  the  lever  and  of  the  centre  of  gravity. 
^\\t  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  is  little  if  at  all  diminish- 
ed: when  it  relaxes  itself,  it  is  merely  passive,  for  the  fibres,  being  extremely 
flexible,  can  have  little  or  no  effect  in  separating  the  parts  to  which  they  are 
attached;  this  separation  is  generally  performed  by  the  action  of  other  mus- 
cles, which  are  called  the  antagonists  of  the  first,  but  sometimes  by  clastic 
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  me- 
chanical disadvantage  with  regard  to  rotatory  power;  but  it  is  more  conve- 
nient in  the  animal  economy  to  produce  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  ^pace ; 
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  pro- 
jection 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 

2 


ON    STATICS.  129 

would  be  formed  by  cutting  the  muscle  across;  and  it  i*  not  improbable  that 
the  contractile  force  of  the  muscles  of  a  healthy  man  is  equivalent  to  about 
500  pounds  for  each  s(}uare  inch  of  their  section.  The  Avcakcst  man  can  lift 
with  his  hands  about  1125  pounds,  a  strong  man  400.  Topham,  a  carpenter, 
mentioned  by  Desaguliers,  could  lift  800  pounds.  lie  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  bis  neck  ;  and  snapped  a  liempen  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 
liimself  as  a  pedestrian  by  going  gO  miles  in  IQ  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  exhibited 
by  men  who  have  not  really  been  possessed  of  any  material  superiority.  De- 
saguliers 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  sus- 
tained a  cannon,  weighing  two  or  three  thousand  pounds.  In  all  these  cases 
the  muscles  principally  employed  are  the  extensors  of  the  legs  and  thighs,  but 
tliQ^  passive  strength  of  the  bones  is  more  concerned  than  the  active  force  of 
the  muscles.  In  the  instance,  mentioned  by  Lahirc,  of  a  young  man  who 
raised  an  ass  from  the  ground,  by  cords  tied  to  the  hair  of  his  head,  the  sensi- 
bility 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  pro- 
gressive 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  n)Ost  ad\  antageously  obtained  from  their 
exertions.  In  walking,  the  centre  of  gravity  is  moved  forwards  Avith  a  ve- 
locity nearly  uniform.     If  the  legs  were  perfectly  inflexible,  the  centre  of 

VOL.    I.  s 


130  J^ECTUBE    XII. 

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  between  walk- 
ing and   running  is  this,   that  in  running,    one  foot  is  removed  from  the 
ground  before  the  other  touches  it ;    while  in  walking,   the  hindmost  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 
iegs  makes  the  progressive  motion  much  more  uniform,  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  impossible,  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  ^yhich  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  direc- 
tion of  the  line  of  draught:  but  we  much  more  usually  draw  or  \n\\l  in  an  as- 
cending direction,  so  that  our  whole  muscular  force  may  be  exerted  Avithout 
any  limit  of  this  kind. 


ON    STATICS.  131 

It  happens,  however,  very  frequerttly,  that  we  have  occasion  foi'  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  hantl  and  lingers  gi\'es  the  human  spe- 
cies a  great  superiority  overall  other  auinmls,  although  by  no  means,  as  some 
authors  have  supposed,  an  advantage  equivalent  to  that  of  the  higher  perfec- 
tion of  the  intellectual  powers.  It  is  true,  as  we  may  observe  in  the  manu- 
factories of  this  country,  that  machinery  has  been  invented  by  which  a  jjower 
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  diffi- 
cult 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  whieh  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  consenient  unit  for  the  comparison 
of  moving  powers  of  all  kinds.     It  may  be  most  easily  rememl)ered  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  da\-.    The  actual  velocity 
of  the  man's  motion  must  vary  according  to  the  mode  in  which  his  force  is  ap- 
plied ;    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.    Desaguliers  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  sup- 
port of  his  estimate.     Professor  Robison,  however,  mentions  a  hydraulic  ma- 
chine 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  wliich  the  water  nuist  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  ]\fr.  Buchanan's  ex-. 
perinients,an  action  like  that  of  ringing  bells  produced  an  effect  about  one  third 
greater  than  turning  a  winch,  and  the  actir)n  of  rowing,  an  effect  four  ninths 
greater;    but  it  does  not  appear  that  these  experiments  were  continued  for  a 


19S  LECTURE    XII. 

whole  day ;  and  the  greatest  number  of  observations  make  the  daily  per- 
formance of  workmen  considerably  less.  It  is  indeed  seldom  that  the 
muscles  employed  in  progressive  motion  arc  so  much  exerted  as  in  the  ar- 
rangement described  by  Professor  Robison.  A  Chinese,  in  the  operation  call- 
ed sculling,   is  said  to  beat  a  European  at  his  oar. 

For  a  sliort  time  a  much  greater  effect  than  this  may  be  produced  by  a  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  per- 
haps 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  em- 
ployed, 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  inconsiderable. 

The  action  of  carryijig  a  load  horizontally  requires  an  exertion  of  a  differ- 
ent kind,  and  admits  of  no  direct  comparison  with  the  application  of  a 
constant  force  to  overcome  the  gravitation  of  a  weight,  or  any  other  im- 
mediate resistance.  The  work  of  a  labourer  thus  employed  is  however 
confined  within  moderate  limits.  A  strong  porter  can  carry  §00  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  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  immediate 


ON    STATICS.     .  133 

force  is  something  greater,  but  it  cannot  support  the  labour  of  more  thati  8 
hours  a  day,  when  drawing  with  a  force  of  200  pounds,  or  of  6  hours  when 
with  a  force  of  240,  Avalking  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  ex- 
pensive as  that  of  men.  The  horse  Childers  is  said,  although,  perhaps,  with- 
out 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  him  on  an  inclined  plane  witliout  friction,  or  in  a 
very  long  sling,   to  the  perpendicular  height  of  1 20  feet. 

A  large  windmill,  on  which  Mr.  Coulomb  made  many  experiments,  was 
capable,  on  an  average,  of  working  eight  hours  a  day;  its  whole  performance 
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  convenient,  because  more 
regular,  than  that  of  the  wind. 

A  steam  engine  of  the  best  construction,  with  a.  thirty  inch  cylin<ler  has 
the  force  of  40  horses  ;  and,  since  it  acts  without  intermission,  will  perforin 
the  work  of  120  horses,  or  of  600  men,  each  square  inch  of  the  piston  being 
nearly  equivalent  to  a  labourer.  According  to  IVIr.  Boulton,  the  consumption 
of  a  bushel,  or  84  pounds  of  coals,  will  raise  48000  cubic  feet  of  water  10  feet 
high,  which  is  ecjuivalent  to  the  daily  labour  of  8  4-  nien,  or  perhaps  more : 
the  value  of  tliis  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  spmewhat  more  than  half  as  expensive  as  the  number 
of  horses  for  which  it  is  substituted.     According  to  other  accounts,  a  24  inch 


1J4  LECTURE    Xir. 

cylinder,  being  equivalent  to  about  1%  horses,   requires  ouly  a  chaldron  of 
coals  in  a  day,  each  bushel  doing  the  w6rk  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  ex- 
tremely 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  l>y  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  ac- 
curacy, 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  re- 
quired to  cause  the  beam  to  make  one  or  more  revolutions  being  ascertained^ 
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  sus- 
pended by  the  thread  of  a  silkworm,  or  of  a  spider,  we  may  compare  its 
magnitude  Avith  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. 


135 


LECTURE  XIII. 


ON    PASSIVE    STRENGTH    AND    FRICTION. 


XriE  passive  strength  of  the  materials  employed  in  the  mechanical  arts  de- 
pends on  the  cohesive  and  repulsive  forces  of  their  particles,  and  on  the 
rigidity  of  their  .structure.  The  consideration  of  the  intimate  nature  of  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  circum- 
stances, is  of  undeniable  importance  to  practical  mechanics,  and  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  considerations. 

The  principal  effects  of  any  force,  acting  on  a  solid  body,  may  be  reduced  to 
Seven  denominations;  extension,  compression,  detrusion,  flexure,  torsion, 
alteration,  and  fracture.  When  a  Aveight  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  pri- 
marily by  a  repulsive  force,  bvit  secondarily  also  by  its  rigidity.  The  eflfect 
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  principally  the  rigidity, 
or  lateral  adhesion  of  the  strata  of  the  substance,  but  it  could  scarcely  be 
effectual  without  some  degree  of  cohesive  and  repulsive  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 


156  LECTURE    XIII. 

are  detruded,  or  displaced,  in  opposite  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  tak- 
ing a  set.  But  the  limit  of  all  these  effects  is  fracture,  which  is  the  conse- 
quence of  the  application  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  di- 
vided into  two  kinds,  simple  pressure,  and  impulse  ;  but  it  is  only  with  re- 
gard to  fracture  that  it  will  be  necessary  to  Lake  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  re- 
pulsive forces,  which  resist  these  effects,  depend  almost  as  mucli  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  repidsive  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  particles  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  probably  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  and  thickness  are  diminished. 

If  the  rigidity  of  a  body  were  infinite,  and  all  lateral  motions  of  its  par- 
ticles 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  exten^jion  or 
compression  is  moderate,  and  no  permanent  alteration  of  form  is  produced; 
and  within  these  limits  these  substances  may  be  called  perfectly  elastic.     If 

2 


ON    PASSIVE    STRENGTH    AND    FRICTION.  137 

the  cohesion  and  repulsion  were  infinite,  and  the  rigidity  limited,  the  only 
effect  of  force  would  be  to  produce  alteration  of  fonn :  and  such  bodies  would 
be  perfectly  inelastic,  but  they  would  be  harder  or  softer  according  to  the  de- 
gree of  rigidity. 

It  is  found  by  experiment,  that  the  measure  of  the  extension  and  compres- 
sion of  uniform  elastic  bodies  is  simply  proportional  to  the  force  which  oc- 
casions 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  substance 
by  the  weight  of  a  certain  column  of  the  same  substance,  which  may  be  de- 
nominated 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  substance  of  equal  dia- 
meter. 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  accurately  99000,  which  is  to  100000  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  di- 
minish it,  in  the  same  ratio  that  the  equivalent  force  Avould  extend  any  por- 
tion of  the  substance.  The  heigJit  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  experiments,  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 
VOL.    I.  T 


'138  LECTURE    XIII. 

also  that  a  force  capable  of  extending  it  to  twice  its  length  will  only  com- 
press it  to  two  thirds.  In  this  substance,  and  others  of  a  similar  nature,  the 
resistance  appears  to  be  much  diminished  by  the  faciUty  by  which  a  contrary 
change  is  produced  in  a  different  direction;  so  that  the  cohesion  and  repul- 
sion thus  estimated  appears  to  be  very  weak,  unless  when  the  rigidity  is  in- 
creased by  a  great  degree  of  cold.  It  would  be  easy  to  ascertain  the  specific 
gravity  of  such  a  substance  in  different  states  of  tension  and  compression, 
and  some  light  might  be  thrown,  by  the  comparison,  on  the  nature  and  oper- 
ation of  the  forces  which  are  concerned. 

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  pro- 
duce a  temporary  derangement  of  this  kind  has  ever  been  examined :  it  may 
be  inferred,  however,  from  the  properties  of  twisted  substances,  that  tl>e 
force  varies  in  the  simple  ratio  of  the  distance  of  the  particles  from  their 
natural  position,  and  it  must  also  be  simply  proportional  to  the  magnitude  of 
the  surface  to  which  it  is  applied. 

The  most  usual,  as  well  as  the  most  important  effect,  produced  by  the  ap- 
plication 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  compression  or  ex- 
tension 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  curvature  of  the  axis  at  any  point 
will  always  be  proportional  to  its  distance  from  the  line  of  direction  of  the 
force,  not  only  while  the  column  remains  nearly  straight,  but  also  when  it  i* 


ON    PASSIVE    STREKCTII    ANT)    FRICTION.  129 

bent  in  any  degree  that  the  nature  of  tlie  substance  will  allow.  If  the  co? 
lumn  was  originally  bent,  any  force,  however  small,  applied  to  the  extre- 
mities 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  longitudinal  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  re- 
semble a  tottering  equilibrium,  in  which  a  body  may  remain  at  rest  until 
some  external  cause  disturbs  it.  The  figure  of  a  column  naturally  straight, 
but  bent  a  little  by  a  longitudinal  force,  will  coincide  with  that  of  the  har- 
monic 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  longitudinal 
foi  ces  ;  and  there  is  no  doubt  but  that  some  of  them  were  occasioned  by  the 
difKculty  of  applying  the  force  precisely  at  the  extremities  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  position, 
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  supported  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 


140  lECTURE    XIII. 

of  the  beam,  and  Inversely  as  the  cube  of  its  length.  Thus  if  we  have  & 
beam  which  is  twice  as  long  as  another,  we  must  make  it,  in  order  to  ob- 
tain 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  firndy  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  re- 
semble 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  se- 
parate beams  fixed  at  their  extremitii^s :  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  cohe- 
sion 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  detrnsion,  of 
the  opposite  parts  of  a  solid,  in  opposite  directions,  the  central  particles  only 
remaining  in  their  natural  state.  We  might  consider  a  wire  as  composed  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 


ON    PASSIVE    STRENGTH    AND    FRICTION,  141 

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  re- 
mained 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  de- 
termined by  experiment,  varies  simply  as  the  angle  of  torsion;  it  cannot, 
therefore,  be  explained  by  the  action  of  longitudinal  fibres  only;  but  it  ap- 
pears rather  to  depend  principally,  if  not  intirely,  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  dia- 
meter, 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,  al- 
most 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  alteration 
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  silvei',  lead,  annealed  iron  and  copper, 
wax  Avhen  warm,  glass  when  red  hot,  and  clay  when  moist,  possess  consider- 
able 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 


142  tECTURE    Xirf. 

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  increased 
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  jjower  of  returning  to  its  original  state,  without  any  permanent 
alteration  of  form,  it  would  never  acquire  the  power  of  returning  more  than 
half  a  revolution,  however  it  might  be  twisted.  From  a  want  of  attention  to 
this  consideration,  a  late  respectable  author  has  called  in  question,  without 
sufficient  reason,  tlie  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  tem])er,   resists  flexure 
with  equal  force,  when  the  deviations  from  the  natural  state  are  small:  but 
at  a  eeitain  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  mo- 
derate, it  is  capable  of  a  much  greater  curvature  without  either  permanent 
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  ap- 
parent difference  in  the  stiffness  of  some  substances  in  different  states,  arising 
from  the  greater  facility  with  which  their  dimensions  are  extended  in  one  di- 
rection 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  temperature ;  but  the  change  pro- 
duced 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,  Avhich  is  lessened  by  the  opera- 
tion.    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  irregularity  in  the  action  of.  the  acid. 


ON    PASSIVE    STREKGTH    AND    FRICTION.  H3 

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  elasticity,  and  of 
its  toughness,  or  the  degree  in  which  it  may  be  extended,  compressed,  or 
otherwise  deranged,  without  a  separation  of  its  parts.  'I  he  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  break- 
ing it,  or  of  the  mass  and  the  height  from  which  it  must  fall  in  order  to  ac- 
quire 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  Avithout  a  per- 
manent alteration  of  form;  when  this  has  been  produced, the  same  force,  if  its 
action  is  continued,  is  generally  capable  of  causing  a  total  solution  of  conr 
tinuity;  and  sometimes  a  separation  takes  place  without  any  previous  altera- 
tion of  this  kind  that  can  be  observed. 

It  follows  from  the  nature  of  resilience,  that  a  body  of  a  pound  weight, 
falling  from  the  height  of  a  yard,  Avill  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  ca- 
pable 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 


144  LECTURE    XIII. 

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  sub- 
stance 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  ir- 
regularities 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  cither  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  bod}^,  which  must  not  be  disregarded 
•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  cer- 
tain 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  im- 
pulse, 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  15000  feet  in 
a  second,  and  it  be  susceptible  of  compression  to  the  extent  of  -^-l-g-  <*f  its 
length,  the  greatest  velocity  that  it  can  resist  will  be  75  feet  in  a  second, 
which  is  equal  to  that  of  a  body  faliing  from  a  height  of  about  90  feet.  And 
by  a  similar  comparison  we  may  determine  the  velocity  which  will  be  suffici- 
ent to  penetrate  or  to  break  oft' a  substance  in  any  other  manner;  if  we  calcu- 
late the  velocity  required  to  convey  the  impulse  frOm  one  part  of  the  substance 


ON    PASSIVE    STRENGTH    AXD    FUICTIOV.  lAS 

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  na- 
tural bodies  with  respect  to  hardness,  softness,  toughness,  and  brittleness. 
A  column  of  chalk,  capable  of  supporting  only  a  pound,  will  perhaps  be  com- 
pressed 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  pres- 
sure, 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  a  second,  a  weight  of  .rV  of  ^ 
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  -r4-5-  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  rect- 
angular 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,  sup- 
posing the  resistance  arising  from  the  lateral  adhesion,  in  the  direction  of  any 
surface  or  section,   to  be  simply  proportional  to  that  section :  but  if  this  force, 

VOL.    I.  U 


146  LECTURE    XIII. 

like  that  of  friction,  is  increased  by  a  pressure  which  tends  to  bring  the  parts 
into  closer  contact,  the  angle  left  after  fracture  must  be  more  acute.  (Plate 
X.  Fig.  124.) 

The  power  of  the  force  of  lateral  adhesion,  in  resisting  fracture,  is  consider- 
ed 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  frac- 
ture takes  place  in  the  surface  of  least  resistance.  It  is,  however,  seldom 
that  the  strength,  with  which  a  body  resists  compression,  is  in  so  great  a  pro- 
portion as  this  to  its  cohesive  strength;  and  where  the  substance  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  increased  in  a  greater  proportion; 
jind  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  tliat  the  additional  pressure  of  their  own 
weight  on  the  lower  parts,  requires  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  convex  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  IX.  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  somewhat  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. 

2 


ON    PASSIVE    STRENGTH    AND    FRICTION.  147 

Flexure  is  the  most  usual  manner  in  Avhich  fracture  is  produced ;  tlie  super- 
ficial parts  on  the  convex  side  are  most  extended,  and  usually  give  way  fiist; 
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  be- 
comes 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  rafteris  broken  by  the  operation  of  a  longitudinal  pres- 
sure, 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  con- 
sequence, than  their  strength  in  resisting  transverse  fracture. 

The  strength  of  beams  of  the  same  kind,  and  fixed  in  the  same  manner,  in 
resisting  a  transverse  force,  is  simply  as  their  breadth,  as  the  square  of  their 
depth,  and  inversely  as  their  length.  Thus  if  a  beam  be  twice  as  broad  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  the  number 
of  the  resisting  particles,  but  also  gives  each  of  them  a  double  power,  by  in- 
creasing 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  ad- 
vantage 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  leno;th  is  increased. 


's' 


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  agiiin  doubled  if  both  the  ends  are 
firmly  fixed. 

The  resilience  of  a  prismatic  beam,  resisting  a  transverse  impulse,  follows 


i48  LECTURE    XIII, 

.  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.  Tims  a  beam 
ten  feet  long  will  support  but  half  as  great  a  pressure,  without  breaking,  as 
a  beam  of  the  same  breadth  and  depth,  which  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  cicling,  stiffness  would  be  princi- 
pally desirable ;  for  a  door,  strength;  for  the  floor  of  a  ball  room,  resilience; 
for  a  coach  spring,  resilience  and  flexibility,  that  is,  resilience  witliout  stift- 
pess.  An  observatory  should  be  as  stiff'  as  possible,  a  ship  as  strong  as  pos- 
fsible,   a  cable  as  resilient  as  possible. 

It  is  a  common  remark  that  a  floor  which  shakes  is  the  strongest ;  and,  im- 
probable 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  effiects  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,  with- 
out being  broken,  the  momentum  of  the  carriage,  arising  from  sudden  eleva- 
tions 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  stiff'ness  and  strength  may  be  in- 
creased by  binding  it  very  firmly  with  hoops.  . 


ON    PASSIVE    STRENGTH    AXD    FRICTION.  liQ 

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  resist 
compression  more  strongly  than  extension:  for  their  immediate  repulsive 
force  is  probably  not  greater  than  their  cohesive  force,  when  their  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  substance  is  less  capable 
of  resisting  compression  than  extension,  the  concave  surface  gives  way  first, 
and  the  strength  depends  immediately  on  the  repulsive  strength  of  the  sub- 
stance. This  is  perhaps  the  reason,  that,  in  experiments  on  beams  of  oak, 
the  transverse  strength  has  seldom  been  tbund  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  flat- 
tening its  sides,  we  shall  gain  the  greatest  stiflPness  by  making  the  breadth  or 
thickness  6  inches,  and  the  depth  104^,  the  greatest  strength  by  making  the 
breadth  7  inches  and  the  depth  9-1,  and  the  greatest  resilience  by  making  the  ' 
beam  square.  The  stiffness  and  the  strength  of  the  beam  may  be  much  in- 
creased 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  bean>  will  be  rather  diminished  than  increased  by  the  operation. 

The  adoption  of  the  hollow  masts  and  beams  which  an  ingenious  mechanic 
has  lately  introduced,  requires,  therefore,  some  caution.  For  where  an  im- 
pulse 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  pres- 
sure than  a  finite  impulse,  except  when  a  sudden  scpiall  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  architecture:  it  is  a 
common  opinion,  and  perhaps  a  well  founded  one,  that  flexibility  is  of  great 


150         ■  LECTURE    XIII. 

ad^'antag•e  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  com- 
pared, to  be  prismatic,  that  is,  of  equal  breadth  and  thickness  throughout, 
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  advantageous  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  frac- 
ture 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  materials  is  capable  of  affording  in  a  beam  of 
given  length,  the  form  must  be  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  curvature  is  greater.  It  is  also  necessaiy  to 
consider  whether  the  substance  is  likely  to  be  crushed,  and  whether  it  is  li- 
able 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,  accord- 
ing 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  tri- 
angle 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 


ON    PASSIVE    STRENGTH    AND    FRICTION.  151 

kinds:  but  there  is  seldom  occasion  to  determine  their  absolute  strength  in 
resisting  a  force  thus  applied :  if  they  are  sufficiently  stiif,  their  parts  arc  not 
often  separated  by  any  violent  efforts. 

In  Older  to  investigate  the  strength  of  the  various  substances  employed  for 
the  purposes  of  the  mechanical  arts,  it  is  most  convenient  to  use  a  ma- 
chine furnished  with  proper  supports,  and  gripes,  or  vices,  for  holding  the  ma- 
terials, and  with  steelyards  for  ascertaining  the  magnitude  of  the  force  ap- 
plied, 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  cHrection  of  the  force,  when  the  flexure  of  the  ma- 
terials 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  dimensions, 
is  about  3  million  pounds;   hence  it  follows,  that  when  a  square  inch  of  steel 
is  torn  asunder  by  a  weight  of    150000  pounds,  its  length  is  first  increa.sed  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  repidsive 
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.cuiva- 
ture  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  circum- 
ference, but  in  the  middle  between  both;  and  in  Europe  it  is  generally  thicker 


152  tECTURE    XIIX. 

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,  itgives  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  ho- 
nesty of  the  workman  for  its  soundness.  Wood,  when  it  is  crippled,  com- 
plains, 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 
increases  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  rigidity, 
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  con- 
sidered 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  examine  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,  and  many  of  their  results  have  been  confirmed 
by  Mr.  Vince,  in  a  simple  and  elegant  manner. 


OK    TASSIVZ    STRENGTH    AND    FRICTION.  15* 

With  a  few  exceptions,  the  friction  of  all  solid  bodies  is,  either  perfectly,  or 
Very  nearly,  a  uniformly  retarding  force,  neither  increasing  nor  diminishing 
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,  however,  the  mo- 
tion is  wholly  extinct,  and  the  bodies  remain  in  contact  with  each  other, 
their  adhesion  is  usually  greater  than  the  friction,  and  by  a  continuation  of 
the  contact,  it  may  become  twice  or  even  thrice  as  great,  especiidly  where  the 
surfaces  are  large,  and  the  substances  but  moderately  hard. 

The  truth  of  tlie  assertion,  that  friction  is  a  uniformly  retarding  force,  may 
be  shown  very  conveniently  by  means  of  Atwood's  machine  for  experiments 
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  diflerent  methods;  and  we  shall  find  that  the 
motions  of  the  boxes  still  indicate  the  action  of  a  uniformlv  acceleratinir 
force,'  the  spaces  described  being  always  proportional  to  the  squares  of  the 
times  of  descent;  it  follows,  therefore,  that  since  the  operation  of  gravity  is 
uniform,  th^t  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  acceleration. 

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  sub- 
stances concerned  into  contact,  independently  of  the  magnitude  of  their  sur- 

VOL.    I.  X 


154  LECTURE    XIII- 

faces :  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  calculatina: 
these  forces  separately,  we  may  probably  always  ascertain  the  whole  resist- 
iince  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  effiscts  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  na- 
ture 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  motion,  they  must 
be  first  separated,  and  then  allowed  to  move  on  each  other,  while  the  vhole 
apparatus  is  gently  agitated.  The  friction  will  then  be  to  the  pressure,  as  the 
height  of  the  inclined  plane  to  its  horizontal  length,  Avhcn  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  propor- 
tionate 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  direction  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  determine  the  incli- 
nation of  a  road  which  is  barely  sufficient  for  a  carriage  to  descend  on  it  by 
its  own  weight,  tlie  same  inclination  will  be  the  best  possible  for  the  appli- 


ON    PASSIVE    STRENGTH    AND    FRICTION.  155 

cation  of  any  force  by  Avhich  the  can'iage  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  pro- 
portion, and  continues  always  sufticient  to  prevent  the  relative  motion  of  the 
weight  and  the  inclined  plane.  Two  such  planes,  put  together,  would  con- 
stitute 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  adhesion  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  fourtli.  Such  a  wedge  Avould 
therefore  possess  a  perfect  stability  with  respect  to  any  forces  acting  on  its 
inclined  surfaces.  But  the  effects  of  agitation,  and  the  minute  tremors  pro- 
duced 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  afford- 
ing 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  friction:  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  introducing  it;  and  this  kind  of  stability,  together 
with  that  of  a  wedge  or  nail  resisting  a  lateral  pressure,  constitutes  the  se- 
curity of  the  lighter  structures  of  carpentry,  while  those  of  architecture  re- 
ceive a  great  part  of  their  firmness  from  the  accumulation  of  weight,  which 


156  .         •  LECTURE    XIII. 

makes  the  resistance  of  their  lower  parts  to  any  lateral  motion  almost  in- 
superable. 

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  con- 
sidered, 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  de- 
pend 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,  whatever  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  mo- 
mentum. 


157 


LECTURE  XIV. 


ON    ARCHITECTURE    AND    CARPENTRY. 


X  HE  subjects,  which  we  have  lately  examined,  are  to  be  considered  as  pre- 
liminary to  the  particular  departments  of  practical  mechanics.  The  first  di- 
vision of  these  is  to  consist  of  such  as  are  employed  in  resisting  forces  of  various 
kinds,  but  they  may  almost  all  be  referred,  without  inconvenience,  to  the  ge- 
neral heads  of  architecture  and  carpentry,  of  which  the  principal  business  is,  to 
resist  the  force  of  gravitation.  Architecture,  in  its  most  extensive  sense,  mav 
be  understood  as  comprehending  carpentry,  but  the  term  is  more  usually  ap- 
plied to  the  employment  of  those  materials,  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  beins 
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  deter- 
mine the  most  eligible  form  for  a  column.  The  length  and  weight  being  sup- 
posed to  be  given,  it  is  of  importance  to  investigate  the  form  which  affords 
the  greatest  possible  strength  ;  but  it  is  somewhat  difficult  tQ^. ascertain  the 
precise  nature  and  direction  of  all  the  forces  which  are  to  be  resisted.  If  we 
considered  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  power- 
ful enough  to  do  more  than  overcome  tlie  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  appeat  to  be  sufficiently  eligible.     ]\Ir.  La- 


158  LECTURE    XIV. 

grange  seems  to  have  been  misled  by  some  intricacies  of  mathematical  investi- 
gation, 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  thickness.  The  force  may  therefore  be  considered  as  tend- 
ing only  to  crush  the  column ;  and  since  the  inferior  parts  must  support 
the  Aveight  of  the  superior  parts,  in  addition  to  the  load  which  presses  on 
the  whole  column,  their  thickness  ought  to  be  somewhat  increased ;  and  it 
appears  from  a  consideration  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,  althougli  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  ;  some- 
times 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  resist- 
ed, Mr.  Smeaton  chose  a  curve  with  its  concavity  turned  outwards.  If  we 
calculated  what  would  be  the  best  form  for  a  wooden  pillar,  intended  to  re- 
main always  ipimersed  >n  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 

2 


ON    ARCHITECTURE    AND    CARPENTRV.  159 

considerable.  But  in  the  case  of  a  building  of  stone,  the  strength  often  de- 
pends 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  whicli  the  outline  is  a 
parabola,  concave  towards  the  axis:  and  for  procuring,  by  means  of  the 
weight,  a  lateral  adhesion  which  is  every  where  proportional  to  the  force,  the 
form  must  be  cylindrical.  So  that  in  a  building  circumstanced  as  we  have  sup- 
posed the  pillar  to  be,  there  appears  to  be  no  reason  for  making  either  portion 
of  the  outline  taken  separately,  convex  towards  the  axis,  although  the  angu- 
lar 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  ex- 
posed to  the  action  of  the  waves,  fhe  water  being  sometimes  thrown  up  to  a 
much  greater  height  than  that  of  the  light  house:  so  that  it  may  be  consider- 
ed as  exposed  to  the  force  of  a  fluid  more  and  more  powerful  as  it  is  nearer  to 
the  foundation;  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  diminishecl;  and  if  the  wall  is  a  part  of  a  house,  it  must  be  reduced- 
in  a  still  greater  degree,  since  the  load,  which  is  to  be  supported  by  it  at  dif- 
ferent 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  re- 
commended that  where  a  well  is  wanted,  it  should  be  dug  before  the  founda- 
tions 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  obviously  greatest  when  all  the 


160  tECTURE    XIV. 

surfaces  are  either  horizontal  or  vertical;  for  if  they  are  oblique,  thej'  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  ma- 
terials 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  circum- 
stance 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  mechanically, 
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 
ufility  depends  principally  on  the  firmness  and  cohesive  strength  that  it  ac- 
quires in  consequence  of  its  chemical  properties.  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  pis6  are  of  a  si- 
milar nature.     (Plate  XL  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  con- 
venient, especially  towards  the  middle,  if  the  depth  be  any  where  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  hangs  in  such  a  form,  that  the  weight  of 


ON    ARCHITECTURE    AND    CARPENTRY.  l6l 

each  link  is  held  in  equilibrium  by  the  result  of  the  two  forces  acting  at  its  ex- 
tremities ;  and  these  forces  or  tensions  are  produced,  the  one  by  the  weight  of 
the  portion  of  the  chain  below  the  link,  the  other  by  ^:he  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  constitute  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  equili- 
brium renders  an  ;iccurate  experimental  proof  of  the  proposition  somewhat 
difficult ;  but  it  may  be  shown  that  a  slight  degree  of  friction  is  sufficient  for 
retaining  in  equilibrium  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  ecjual;  the  same  method  may 
be  applied  to  the  determination  of  the  form  requisite  for  an  equilibrium,  what- 
ever 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  cir- 
cumstance into  the  experiment,  by  suspending  proportional  weights  from 
different  parts  of  the  chain.  Thus  we  may  employ  Avires  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  forni 
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 
XL  Fig.  152  .  .  154.) 

But  the  supposition  of  an  arch  resisting  a  weight,  which  acts  only  in  a  ver- 
tical direction,  is  by  no  means  perfectly  applicable  to  cases  which  generally 
occur  in  practice.     The  pressure  of  loose  stones  and  earth,  moistened  as  they 

VOL.    I.  y 


15S  LECTURE    XIV. 

frequently  are  by  rain,  is  exerted  very  nearly  in  the  same  manner  as  the  pres- 
sure 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  tlms  produce 
a  pressure  of  a  similar  nature,  notwithstanding  the  precaution  recommended 
by  some  authors,  of  making  the  surfaces  of  the  arch  stones  vertical  and  hori- 
zontal 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  exercising  the  skill  of  the  architect.  The  effect  of  such  a  pres- 
sure 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  weight  of  the  parts  beyond  it.  This 
property  belongs  to  the  curve  denominated  logarithmic,  the  length  cor- 
responding to  the  logarithm  of  the  depth.  If  the  strength  were  afforded 
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  maybe  composed  of  parabolic  arcs,  having  their 
convexity  turned  towards  each  other.  This  remark  also  would  be  only  ap- 
plicable to  the  arch  stones,  if  they  afforded  the  whole  strength  of  the 
bridge,  but  it  must  be  extended  in  some  measure  to  tlie  whole  of  the 
materials  forming  it. 

If  therefore  we  combine  together  the  curve  best  calculated  for  resisting  the 

2 


ON    ARCHITECTURE    AND    CARPENTRY.  163"" 

pressure  of  a  fluid,  which  is  nearly  elliptical,  the  logarithmic,  and  the  pa-' 
rabolic  curves,  allowing  to  each  its  due  proportion  of  influence,  we  may 
estimate,  from  the  comparison,  which  is  the  fittest  form  for  an  arch  intended 
to  support  a  road.  And  in  general,  whether  the  road  be  horizontal,  or  a 
little  inclined,  Ave  may  infer  that  an  ellipsis,  not  diff'ering  much  from  a 
circle,  is  the  best  calculated  to  comply  as  much  as  possible  with  all  the  con- 
ditions.    (Plate  XL  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  siimmit,  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  calculation  will  enable  an  ar- 
chitect 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  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  direc- 
tion of  the  pressure  be  so  much  disturbed,  as  to  exceed  at  some  part  the  li- 
mits of  these  surfaces,  before  the  blocks  can  be  displaced.  When  this  curve, 
indicating  the  general  pressure  which  results  from  the  efiect  of  a  disturb- 
ing 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 


164  LECTURE    XIV. 

kind  which  support  an  arched  or  vaulted  roof,  wherever  there  is  no  oppor- 
tunity 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  usually  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  pressure  for  securing  the  stabiUty  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  etfort  to  over- 
set it,  and  in  order  that  the  pier  may  stand,  the  sum  of  these  weights,  act- 
ing 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,  indicat- 
ing 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  caus- 
ing 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  situ- 
ated on  each  side.  A  dome  may  therefore  be  erected  witliout  any  tempo- 
rary 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  re- 
sisted, by  the  collateral  parts  of  the  same  horizontal  tier,  to  prevent  the  pos- 
sibility 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  in  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  as  the  span 
becomes  eleven  fourteenths  of  the  whole  diameter.     But  if  the  thickness  of 


ON    ARCHITECTURE    AND    CARPENTRY.  l€^ 

the  dome  be  diminislied  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  be- 
comes 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  stability,  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  aflPord  sufficient  resistance  to  their  pressure :  they  are  sup- 
ported by  walls  of  gVeat  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  busi- 
ness 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,  Avithout  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  enveloping  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,  tlie 
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.) 


\Q6  LECTURE    XIV. 

The  Gothic  architects  appear  to  have  been  superior  to  tlie  Greeks 
in  the  mechanical  arrangement  of  the  parts  of  their  edifices,  so  as  to 
produce  the  most  advantageous  effect  in  preserving  the  general  equi- 
librium. They  made  every  essential  member  of  their  buildings  a  constituent 
part  of  their  system  of  ornament,  and  even  those  embellishments,  which,  by  a 
superficial  observer, might  be  deemed  useless  or  prejudicial,  are  frequently  cal- 
culated, either  by  their  strength,  or  by  their  weight,  to  serve  some  beneficial 
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  sufficient  attention  to 
mechanical  principles,  have  conunitted  such  errors  in  their  attempts  to  pro- 
cure an  equilibrium,  as  have  been  followed  by  the  most  mischievous  conse- 
quences. 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  occasioned  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  princi- 
pally calculated  to  Avithstand  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  ar- 
ranged in  a  different  manner.  The  general  principle,  that  three  forces,  in 
order  to  retain  each  other  in  equilibrium,  must  be  proportional  to  the  sides 
of  a  triangle  corresponding  to  their  directions,  is  sufficient  for  determining 
the  distribution  of  pressure  in  almost  all  cases  that  can  occur.  The  conclu- 
sions which  have  been  drawn  from  this  principle,  and  from  other  similar  con- 
siderations, 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  intro- 
duces a  difficulty  which  scarcely  exists  in  architecture.     Tavo  blocks,  placed 


ON    ARCHITECTURE    AND    GARPENTRT.  -  1^7 

on  each  other,  resist  the  force  of  a  weight  compressing  them,  as  effectually  as  if 
they  formed  hat  one  piece:  biit  they  have  no  sensible  cohesion  to  enable  them 
to  withstand  a  force  tending  to  separate  them,  and  if  they  are  required  to  co- 
operate by  tlieir  cohesive  strength,  some  mode  of  uniting  them  must  be  found. 
For  this  purpose,  it  is  generally  necessary  to  sacriiice  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  jjrocure  a  firm  adhesion  between  them  by 
means  of  external  pressure,  or  to  employ  the  natural  adhesion  of  some  parts 
which  are  made  to  project  beyond  the  rest  in  each  piece,  and  receive  in  their 
interstices  the  corresponding  projections  of  the  other  piece. 

Where  the  adhesion  is  produced  by  external  pressure  only,  it  is  of  advan- 
tage 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,  fol- 
lowing each  other  in  the  same  line,  as  distant  as  possible  from  any  other 
junction;  for  in  this  manner,  the  loss  of  strength  may  be  diminished  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  pro- 
portion 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,, 
and  they  must  be  as  Httle.  prominent  as  possible,  partly  because  the  contigu- 
ous piece  nuist  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  resist  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 


16>8  ■        LECTURE    XIV. 

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  re- 
sult 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  somewhat  increased  by  the  operation,  supposing  the  two 
ends  to  meet  each  other  without  any  connexion.  Such  pieces  require,  how- 
ever, 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  se- 
cured still  more  firmly  by  a  stiap  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  moisture  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  adviseable  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  together  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  pur- 
pose 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  assist- 
ance 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  for 


ON    ARCHITECTURE    AND    CARPENTRY.  16«> 

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  is  bent  in  any  di- 
rection, 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  XtV.  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  trans- 
verse force,  to  its  primitive  cohesive  or  rcpulsive  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  re- 
quiring 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  woodcut 
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,  bat 
which  may  still  destroy  the  greater  part  of  the  strength,  by  causing  the  re- 
sistances 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  sub- 
jects 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  arc  again  erected  from  the  bottom  of  the  king  post,   to  sup- 

VOL.    I.  z 


170  LECTURE    XIV. 

port  the  middle  of  the  rafters.  Somethnes  a  flat  or  less  inclined  portion  is 
placed  in  the  middle,  forming  a  kirb  or  mansard  roof,  somewhat  resembling  ai*. 
arch ;  this  form  has  the  advantage,  when  it  is  properly  proportioned,  of  lessening 
the  transverse  strain  on  the  rafters,  by  making  them  shorter;  but  this  pur- 
pose is  answered  equally  well  by  the  addition  of  the  braces  which  have  been 
already  mentioned.  A  kirb  roof  aftbrds,  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  perpendicularly  from  the 
joints ;  and  the  place  of  the  king  post  may  be  supplied  by  a  cross  beam  unitr 
ing  the  heads  of  the  queen  posts  and  keeping  them  at  a  proper  distance;  this 
beam  may  also  be  suspended  by  a  shorter  kingpost  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  diiferenf 
climates:  in  Italy  the  height  is  generally  less  than  one  fourth  of  the  breadth; 
in  England  it  was  formerly  three  fourths,  but  it  now  commonly  approaches 
much  more  to  the  Italian  proportion.  In  northern  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  pro- 
portional to  the  length  of  a  line  perpendicular  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  bearing  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  through- 
out the  length,  we  neither  gain  nor  lose  force  by  lengthening  the  beam  and  rais- 
ing it  higher,  while  the  horizontal  span  continues  the  same,  since  the  obli- 
quity lessens  the  effect  of  tlie  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 


ON    ARCHITECTURE    AND    CARPENTRV.  •  l/I 

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  equilibrium  of  elastic  substances. 

Wooden  bridges,  and  the  temporary  centres  on  which  arches  of  stone  arc 
supported  during  their  construction,  depend  nearly  on  the  same  principles  as 
roofs:  the  external  parts  usually  support  a  thrust,  and  the  internal  act  as 
ties;  but  the  abutments  are  generally  capable  of  withstanding  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  di- 
rection of  chords,  bearing  immediately  on  the  abutments.  (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  conveni- 
ence 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  employment  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  consideration,  improvements  might  be  made  in 
all  of  them.  Mr.  Parker  has  devoted  much  time  and  labour  to  the  subject  of 
gates,  with  their  hinges  and  fastenings,  and  has  presented  to  the  Royal  In- 
stitution a  very  useful  collection  of  models,  which  show  the  result  of  his  in- 
vestigations. 


172 


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  applyinor 
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  metliods  by  which  the  union  of 
flexible  fibres  in  general  may  be  effected  ;  and  ir^  the  third  place,  the  regula- 
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  employ- 
ed: 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  to 
ascend ;  and  that  of  other  animals,  by  a  horizontal  arm  projecting  from  a  ver- 
tical 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  how- 
ever 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  nlotion  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, 


ON    MACHINERY.  17S 

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  iu  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  ettect  of  the  force  to  a  considerable  distance ;  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  ac- 
count of  the  alternation  of  the  motion  of  the  rods ;  for  if  they  are  suspend- 
ed at  equal  distances  from  a  number  of  fixed  points,  they  will  move  back- 
wards 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  changiug  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.  Hookc's  universal  joint  is 
sometimes  of  use,  especially  when  the  inclination  is  not  required  to  be  ma- 
terially changed ;  but  if  the  obli(juity  is  great,  the  rotation  is  not  commu- 
nicated 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 
Ayhich  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  revolution  the  force  exert- 
ed 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 


174  LECTURE    XV. 

irregular,  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  op- 
posing another  force,  so  as  to  produce  equilibrium  only,  the  other  in  generat- 
ing momentum.  With  respect  to  the  first  portion,  a  single  crank  has  the 
inconvenience  of  changing  continually  the  mechanical  advantage  of  the  ma- 
chine; with  respect  to  the  second,  its  motion  in  the  second  quarter  of  its  re- 
volution is  accelerated,  instead  of  being  retarded,  by  the  inertia  which  this 
portion  of  the  force  is  intended  to  overcome:  and  from  a  combination  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  comunicated  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  obliquely,  would 
answer  sufiiciently  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  Avhich 
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  oj^osite  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 

2 


ON    MACHINERY.      '  173 

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  use- 
ful is  the  employment  of  wheelwork,  which  is  capable  of  varying  its  direc- 
tion 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  them;  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.  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  mak- 
ing the  middle  prominent:  the  reason  of  this  may  be  understood  by  ex- 
amining the  manner  in  which  a  tiglit  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.  rig.  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  circum- 
ferences; and  sometimes»i.an  endless  screw  is  substituted  for  one  of  the 
wheels.  Informing  the  teeth  of  wheels,  it  is  of  consequence  to  determine 
the  curvature  which  will  procure  an  equable  communication  of  motion,  with 
the  least  possible  friction.  For  the  e(juable  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,  tliat  is,  of  a  curve  described  by  a  point  of  a 


176  LECTURE    XV. 

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  pro- 
duce 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  de- 
monstrated, that  an  equable  motion  is  produced  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  the  circle.  It  has  been  supposed  by  some  of  the  best  authors  that  the 
epicycloidal  tooth  has  also  the  advantage  of  completely  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  dura- 
bility ;  for  the  'effect  of  friction  always  increases  with  the  distance  of  the 
point  of  contact  from  the  line  joining  the  centres  of  the  wheels.  In  calcu- 
lating 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  resist- 
ance is  not  at  all  increased  by  increasing  the  relative  velocity;  but  the 
cflect  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  ve- 
locity 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  dimi- 
nished in  the  proportion  of  the  difference  of  the  diameters  to  their  sum.     If 


on    MACHINERY.  177 

the  face  of  the  teetli,  where  they  are  in  contact,  is  too  much  inchned  to  the 
radius,  their  mutual  friction  is  not  much  affected,  but  a  great  pressure  on  their 
axes  is  produced ;  and  this  occasions  a  strain  on  the  machinery,  as  well  as  a4» 
increase  of  the  friction  on  the  axes. 

If  it  is  desired  to  produce  a  great  angular  Velocity  with  the  smallest  possible 
quantity  of  wheel  work,  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  imj)els  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  resulting  from  the  calcu- 
lation ;  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  apinion  of  one  tooth,since  it  propels  the  wheel 
through  the  breadth  of  one  tooth  only  in  each  revolution.  For  a  piiiion  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  recur- 
rence of  friction.  It  has  been  proposed,  for  the  coarser  kinds  of  wheelwork, 
to  divide  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  rela- 
tive magnitude  of  the  wheels,  the  angle  of  the  bevil  must  be  different,  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  di- 
rected to  the  point  where  the  axes  would  meet.     (Plate  XV.  Tig.  193,  194.) 

VOL.    I.  A  a 


178  LECTURE    XV. 

In  cases  where  a  motion  not  quite  equable  is  required,  as  it  sometimes  hap- 
pens 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  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  be  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,  tlie  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  distance  of  the  centres  of 
the  two  wheels:  consequently,  when  the  wheels  are  equal,  the  central  wheel 
makes  two  revolutions,  every  time  that  the  exterior  wheel  travels  round  it. 
If  the  central  wheel  be  fixed,  and  the  exterior  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  ma- 
chine; the  wheel  is  fixed  on  an  axis,  which  also  carries  a  plate  furnished  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  application 


1    ,  ON    MACHINERY.  l/y 

of  a  given  force,  or  to  reserve  a  part  of  it  for  future  use.  Tiiis  is  generally 
effected  by  suffering  a  weight  to  descend,  which  has  been  previously  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  common  kitchen 
jack  is  also  employed  for  protracting  and  equalising-the  operation  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  operation 
of  any  part  of  the  force  which  happens  to  be  superfluous,  and  its  rotatory 
power  serving  to'continue  the  motion  when  the  force  is  diminished  or  with- 
drawn. Thus,  when  a  man  turns  a  winch,  he  can  exert  twice  as  nxiich  force 
in  some  positions  as  in  others,  and  a  fly  enables  him  in  some  cases  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  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  compressed  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. 


180 


LECTURE  XVI. 


ON    THE    UNION    OF    FLEXIBLE    FIBRES. 


JLlIE  strength  of  cordage,  and  of  other  substances  which  ai"e  employed  in 
the  communication  of  motion,  where  flexiblHty  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  fre- 
quently subservient  to  the  communication  of  motion,  and  the  machinery,  usually 
employed  for  producing  it,  belonging  immediately  to  the  subject  of  the  mo- 
dification of  motion,  we  may  with  propriety  consider  at  present,  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  ad- 
hesion, 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  processes  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  him- 
self from  a  window  in  cases  of  fire,  the  pressure  on  the  whole  circumference 

1 


ON    THE    UNION    OP    FLEXIBLE    FIBRES.  181 

is  to  the  weight,  as  twice  the  circumference  to  the  diameter;  supposing,  for 
example,  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  dif- 
ferent, the  adhesion  may  be  a  little  greater  or  less  than  in  this  proportion, 
according  to  the  manner  in  ■'.vhich  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  otker  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  obli- 
quity 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  directioii  of  the  rope:  so  that  after  employing  as  much  ob- 
liquity and  as  much  tension,  as  is  sutBcient  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  en- 
gage their  extremities  as  much  as  possible  in  the  centre;  for  it  is  obvious 
that  if  any  fibre  were  Avholly  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  con- 
nected by  twisting,  and  we  have  no  need  of  spinning.  In  both  cases  such 
machinery  has  been  invented  for  performing  the  necessary  operations,  as  is 
both  honourable  and  lucrative  to  the  British  nation. 

A  single  thread  or  yarn,  consisting  of  fibres  twisted  together,  has  a  ten- 
dency to  untwist  itself;  the  external  ptrts  are  the  most  strained  in  the  opera- 
tion, and  at  first  shorten  the  thread,  until  the  internal  parts  have  no  lonj?;er 
roam  for  spreading  out  laterally,  as,  they  must  necessarily  do  when  their 


182  LECTURE    XVI. 

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  hy  the  opposition  of  the  equal  forces  acting  in  contrary  directions, 
and  becomes  the  centre,  round  which  both  threads  are  carried  by  the  remain- 
ing forces,  so  that  they  continue  to  twist  round  each  other  till  the  new  com- 
bination 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  disadvantage  of  being  hollow  in  the  centre,  or  of  re- 
quiring 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  com- 
plicated combinations  are  not  v^ry  easily  determined  by  calculation ;  but  it  is 
found  by  experience  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  ex- 
ample 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 

2 


ON    THE    UNION    OF    FLEXIBLE    FIBRES.  183 

male  and  female  flowers  of  liemp  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  back- 
wai-ds,  draws  out  the  fibres  with  his  hands.  When  one  length  of  the  walk 
lias  been  spun,  it  is  immediately  reeled,  to  prevent  its  untwisting.  The  ma- 
chines employed  in  continuing  the  process  of  ropemaking  are  of  simple  con- 
struction, but  both  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  ex- 
ternal 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  lao  yards,  in  the  ratio  of  6  to  5.  The  difference  is  owing  partly 
to  the  obliquity  of  the  fibres,  and  partly  to  the  unecjual  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  experiments  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  ad- 
hesions between  some  of  the  fibres,  which  cause  them  to  be  disproportionully 
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  be- 
cause 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  cultiva- 


184  LECTURE    XVt. 

tion  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  cliange,  Avhich  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  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  thteads  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  Avorms  are  fed,   is  kept  at  the  temperature  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 


ON    THE    UNION    OF    FLEXIBLE    FIBUES,  ]  85 

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  re- 
moving 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  re- 
peatedly drawn  from  one  comb  to  the  other,  heat  being  used  in  the  process, 
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  stuifs,  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  sufficient 
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  depresses  the 
threads  in  succession  by  means  of  treadles,  moved  by  the  feet,  in  an  order 
which  is  d liferent,  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 

VOL.    I.  B  b 


1^6  LECTURE    XVI. 

wire  or  reeds,  while  the  piece,  in  proportion  as  it  is  completed,  is  rolled  up- 
on a  second  beam,  opposite  to  the  first. 

Crape  is  composed  of  threads  which  are  so  strongly  twisted,  as  to  have  a  dis- 
position 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  pro- 
.  bably  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,  however,  much  inferior 
to  that  of  cloth ;  partly  because  the  fibres  are  in  general  nmch  shorter,  and 
partly  because  their  arrangement  is  less  accurately  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  proportions,  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  opera- 
tion of  bowing,  which  depends  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 


ON    THE    UNION    OF    FLEXIBLE    flBRES.  187 

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  con- 
centric 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  serves  as  a  mould 
for  the  cylindrical  part.  The  black  dye  is  composed  of  logwood,  sulfate  of 
iron,  and  a  little  acetite  of  copper,  or  verdigris;  and  the  stiftening  is  a  thiu  < 
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  with  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. 


1S8 


T.ECTURE  XVII. 


ON    TIMEKEEPERS. 


X  HE  measurement  of  time  by  clocks  and  watches  is  a  very  important  and  in- 
teresting department  of  practical  mechanics.  The  subject  is  intimately  con- 
nected with  the  consideration  of  astronomical  instruments,  but  it  is  not  essen- 
tially 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  un- 
disturbed, and  consequently  uniform,  is  rendered  unattainable  by  the  resist- 
ances inseparable  from  the  actual  constitution  of  material  substances.  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  circumstances,  and  even  then  they  as- 
sist 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  ap- 
pears from  Vitruvius's  account  that  wheelwork  was  employed,  and  the  hour 
was  shown  on  a  graduated  scale;  the  graduations  were  also  probably  so  ad- 
justed as  to  correct  the  error  arising  from  the  inequality  of  the  velocity  oc- 
casioned 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 steam,  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 

2 


ON    TIMEKEEPERS.  189 

semicylindrical  counterpoise,  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  whicli  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  regulat- 
ed by  a  pendulum  or  a  balance.  Watches  differ  from  clocks,  in  being  port- 
able, 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.  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  Frederic  II.  Wallingford,  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  ra- 
pidly when  the  velocity  is  increased,  and  therefore  prevents  any  great  ine- 
quality in  the  motion,  as  long  as  the  moving  power  varies  but  little;  and  if 
the  action  of  the  weight  were  transmitted  with  perfect  regularity  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  however  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  instru- 
ment. Mr.  Whitehurst's  apparatus  for  measuring  the  time  occupied  in  the 
descent  of  heavy  bodies,  is  governed  by  a  fly ;  the  index  is  stopped  by  the 


igO  LECTURE    XVII. 

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  produc- 
ing a  degree  of  uniformity  in  the  motion  of  the  wheel;  for  the  force  operat- 
ing on  the  pallet  is  consumed  in  destroying  a  velocity  in  one  direction,  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  ad- 
dition of  a  balance  to  a  clock  was  made  soon  after  the  year  1400,  for  Ar- 
nault, 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  ba- 
lance provided  with  a  spring;  if  the  balance  spring  of  a  common  watch  be  re- 
moved, the  hands  will  pass  over  the  space  of  about  twenty  eight  minutes  in 
an  hour. 

It  i|  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,  wliich  rose  higher,  and  increased  the  resistance,  whenever  an  aug- 
mentation 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  pre- 
serve the  equality  of  the  revolutions. 

A  chronometer  maybe  constructed  on  this  principle  for  measuring  small  por- 
tions 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  pendu- 
lums 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  sur- 


ON    TIMEKEEPEnS.  191 

face,  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  up- 
per part,  and  this  string  may  serve  as  a  support  to  a  barrel,  sliding  on  a 
square  part  of  the  axis,  which  will  consequently  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  chord  or  rod,  or  any  other  moving  substance-  In  this 
manner,  supposing  a  barrel  a  foot  in  circumference  to  revolve  in  two  se- 
conds, 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  ne- 
cessary.    (Plate  XV.  Fig.  198.) 

By  means  of  tliis  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  vibrations 
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  fiequency,  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 


192  LECTURE    XVII. 

obsert^ations,  by  the  vibrations  of  pendulums;  but  they  never  connected 
them  with  machinery.  The  equaUty  of  the  times  occupied  by  these  vibra- 
tions, 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  in- 
strument to  which  he  had  himself  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;  and  soon  after,  he  conceived  the  idea  of  improving  timekeepers  suffi- 
ciently for  ascertaining  the  longitude  at  sea,  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  vi- 
brations are  in  their  nature  as  nearly  isochronous  as  possible.  In  clocks,  the 
sustaining  force,  being  generally  derived  from  a  weight,  is  already  sufficiently 
equable,  provided  that  care  be  taken  that  the  line  by  which  it  is  suspended  may 
be  of  equal  thickness  throughout,  and  may  act  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  Brussels:  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  general  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  alto- 
gether, the  curve  being  that  which  is  denominated  a  hyperbola;  but  the 
workmen  have  in  general  no  other  rule  than  a  habitual  estimation.  (Plate 
XV.  Fig.  199.) 


ON    TIMEKEEPERS.  193 

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  disturb- 
ances, 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  ne- 
cessity 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  continue  the  motion. 
(PlateXVI.  Jig.  200.) 

The  scapement,  by  which  the  sustaining  force  is  communicated  to  the  pen- 
dniiim  or  balance,  demands  a  greater  exertion  of  skill  and  accuracy  than  any 
other  part  of  a  timekeeper.  Sometimes  the  alternate  motion  of  the  pendu- 
lum has  been  produced  by  the  action  of  a  crank,  but  this  construction  sub- 
jects it  too  much  to  the  irregularities  of  the  Vvdieelwork,  and  is  liable  to  se- 
veral other  objections.  A  crank  cannot  properly  be  called  a  scapement,  for 
according  to  the  etymology  of  the  term,  the  pendulum  must  escape  for  a 
time  from  the  action  of  the  wheelwork,   and  in  general,   the   more  indcpen- 

VOL.    I.  c  c 


194-  LECTURE    XVII. 

dent  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  improvements  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  pen- 
dulum 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  ac- 
tion of  the  teeth,  to  retire  from  the  centre  of  the  wheel :  and  great  care  i& 
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.  £01.) 

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  circumference  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  ap- 
plied principally  at  the  extremities  of  the  vibrations,  disturbs  their  isochronism, 
or  the  equality  of  the  times  in  which  they  are  performed,  by  partially  in- 
creasing 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  subjectetl  to  its 

9 


ox    TIMEKEEPERS.  IQS 

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  application  of  springs  to  balances:  it  requires  a 
considerable  extent  of^  motion  in  the  balance,  and  cannot  therefore  well  be 
applied  to  clocks  with  such  pendulums  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  succeeded  very  well.  , 

To  avoid  the  inconveniences  of  the  recoiling  scapements,  Mr.  Graham  in- 
vented 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  in- 
clined plane  for  a  short  time  only,  in  the  middle  of  each  vibration;  so  that  a 
change  of  the  sustaining  power  scarcely  produces  a  sensible  derangement  of 
the  isochronism  ;  for  which  ever  way  we  turn  the  key  of  a  horizontal  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  observatory  at  Green- 
wich, 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  cylinder 
or  pallet,  and  the  tenacity  of  the  oil,  where  it  is  employed,  may  interfere  in 
a  slight  degree  with  the  time  of  vibration,  especially  by  the  irregularities  to 
which  they  are  liable.  If  the  friction  were  perfectly  uniform,  it  would 
scarcely  disturb  the  isochronism,  but  friction  is  always  increased  by  an  in- 
crease of  pressure ;  hence,  therefore,  the  effect  of  any  addition  to  the  sus- 
taining force  must  tend  in  some  degree  to  retard  the  vibrations ;  and  to  ob- 
viate this,  the  surfaces,  on  which  the  teeth  rest,    have  sometimes  been  so 


196'  LECTURE    XVII. 

» 

formed  as  to  create  a  slight  recoil;  but  this  construction  docs  not  appear  to 
have  been  very  successful  in  practice.  The  friction  may,  however,  be  con- 
siderably 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  receiving  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.  Tlie  French  have  sometimes  em- 
ployed 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 
jsurface  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  a  larger  teeth,  each  of 
which  is  to  be  finished  with  great  accuracy :  but  watches  on  these  construc- 
tions, especially  those  with  the  comma  scapement,  are  too  liable  to  be  stopped 
by  any  sudden  motion,  although  the  duplex  scapement  begins  to  be  fre- 
quently 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,  exce])ting  a  short  interval,  when  it  is  unlocked  in 
order  to  impel  the  pallets.  Mr.  Mudge  employed  a  detached  scapement,  ac- 
tuated by  a  subsidiary  spring,  of  which  the  force  is  scarcely  liable  to  any  va- 
riation; 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  ac- 
tion, which  may  sometimes  produce  a  slight  irregularity.  These  construc- 
tions are,  however,  much  too  delicate  for  common  ppcket  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  immedi- 
ately 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,  therefore,  produce  a  very  slight  inequality  in  the  motion 
of  the  pendulum.     Mr.  Nicholson  has  attempted  to  remove  this  cause  of 


ON    TIMEKEEPERS.  197 

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.  Cumming'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  opposite 
side,  at  the  moment  that  It  ceases  to  act  on  the  pendulum,  and  remaining  in- 
active 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;  Mr.  Earnshaw 
makes  .ji  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  littledifFerence  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 svich  a  motion  in  practice  is  much  greater  than  the  advantage  deriv- 
ed 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  Sic 
of  three  degrees,  would  gain  13^  seconds  if  the  arc  were  very  much  con- 
tracted or  made  cycloidal,  and  would  lose  104^  seconds  by  having  the  vibra- 
tion 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. 


198  LECTURE   xvir. 

The  elasticity  of  this  spring  adds  a  minute  force  to  the  power  of  gravitation, 
which  acts  o*\  the  pendulum,  and  this  force  mxist  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  per- 
fectly 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  inequalities  of  the 
sustaining  power;  and  in  large  excursions.  Dr.    Hooke's  law  is  not  so  pre- 
cisely 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  calcula- 
tion of  the  properties  of  the  vibration.     Yet  it  has  been  found  by  experiment 
that  a  certain  length  may  be  determined  for  almost  every  spring,   which  will 
afford  vibrations  cither  perfectly  or  very  nearly  isochronous.     In  orcler  that 
the  weight  or  inertia  of  the  spring  may  interfere  the  less  with  the  regularity 
of  its  motion,  it  is  sometimes    tapered,  and  made  thinner  at  the  extremity : 
it  is    now   also  usual  in  th.e  best   watches  to  employ  a  spring  coiled  into  a 
cylindrical  form,   like  that  of  the  spring  of  a  bell,  of  which  the  motion  ap- 
pears to  be   somewhat   more  regular  than  that  of  a  flat  spiral.     This  was  in- 
deed the  original  construction,   but  was  probably  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  ob- 
serves, 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  em- 
ploying 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 
compensation,  as  far  as  possible,   independent  of  circumstances  foreign  to 


ON    TIMEKEEPERS.  199 

the  cause  of  the  error.  The  strength  of  the  spring  is  found  to  be  less  im- 
paired by  use  when  it  is  hardened  than  when  the  steel  is  softer.  It  some- 
times happens,  that  from  a  sudden  motion,  or  from  some  other  accidental 
circumstance,  the  balance  of  a  timekeeper  may  be  thrown  beyond  the  point 
at  which  the  pallets  are  impelled  by  the  scape  wheels,  and  the  whole  motion 
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  pro- 
gress of  the  balance,  by  intercepting  a  pin  which  projects  from  it.  This  ar- 
rangement is  called  banking  the  balance. 

We  have  already  seen  that  the  squares  of  the  times  of  vibration  of  two  pen- 
dulums are  proportional  to  their  lengths ;  so  that  if  we  add  to  a  pendulum 
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  ex- 
pansion has  a  similar  elFcct  in  the  motion  of  a  balance,  and  the  increase  of 
temperature  produces  also  a  diminution  of  the  elastic  force  of  the  spring  it- 
self. There  is,  however,  a  great  ditt'erencc  in  the  expansibilities  of  various 
substances;  dry  deal  is  one  of  the  least  expansible,  and  is  therefne  often 
used  for  the  rods  of  pendulums.  Brass  expands  one  part  in  a  hundred 
thousand  for  every  degxee  of  Fahrenheit,  or  a  little  more  or  less  tloan  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  84-  seconds  in  a  day;  a  ba- 
lance 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  Bertlioud 
informs  us,  that  where  a  clock,  probably  with  a  pendulum  of  steel,  loses  20 
seconds  by  heat,  a  watch  loses  eight  minutes. 

Mr.  Graham  appears  to  have  been  the  first  tliat  attempted  to  compensate 
for  the  effects  of  temperature  by  the  different  expansibilities  of  various  sub^ 


200  LECTURE    XVir. 

Stances.  He  employed,  for  a  pendulum,  a  tube  partly  filled  with  mercury  ; 
when  the  tube  expanded  by  the  effect  of  heat,  the  mercury  expanded  much 
more;  so  that  its  surface  rose  ai.  little  more  than  the  end  of  the  pendulum  was 
depressed,  and  the  centre  of  oscillation  remained  stationary.  This  mode  of 
compensation  is  still  sometimes  practised  with  success;  but  the  gridiron  pen- 
dulum is  more  commonly  used:  it  was  the  invention  of  Harrison,  who  com- 
bined seven  bars,  of  iron  or  steel,  and  of  brass,  in  such  a  manner,  that  tlie  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  ex- 
tremity of  a  lever,  which  was  supported  by  a  pillar  of  brass,  much  nearer 
to  the  fulcrum ;  as  the  pendulum  expanded,  the  end  of  the  lever  was  raised 
in  the  same  degree,  and  the  weight  remained  at  its  original  distance  from 
the  point  of  suspension,  which  was  determined  by  a  fixed  plate,  transmitting 
the  slender  spring,  as  usual,  between  two  opposite  edges.  The  same  efl'ect  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  fix- 
ed 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  sup- 
port of  the  bar,  is  determined  by  materials  which  may  be  considered  as 
nearly  of  an  invariable  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  Avhole  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  itselfj 
fixing  a  weight  on  its  extremity,  which  is  brought  nearer  to  the  centre,  by 
the  increase  of  curvature  of  the  plate,  whenever  the  expansion  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  com- 


ON    TIMEKEEPERS.  201 

pensate  not  only  for  the  expansion  produced  by  heat,  but  also  for  the  dimi- 
"nution  of  the  elasticity  of  the  spring.  Sometimes  also  a  plate  has  been  ap- 
plied 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  chp  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.) 

Tlie  flexure  of  a  compound  plate  has  also  been  applied  in  a  simple  and  ele- 
gant 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  horizon- 
tally, 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  ad- 
justed with  great  accuracy,  so  that  when  the  temperature  is  increased,  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  deter- 
mines 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  atmosphere 
must  therefore  also  produce  some  irregularities  in  timekeepers:  they  are,how- 
ever,  too  small  to  be  sensible.  Derham  found  that  the  resistance  of  the  air 
accelerated  the  motion  of  a  half  second  pendulum  about  four  vibrations  in 
an  hour,  by  diminishing  the  arc  in  which  it  vibrated:  and  when  the  vibra- 
tions were  restored  to  their  original  magnitude,  the  resistance  of  the  air  pro- 
duced a  retardation  of  eight  vibrations  in  the  same  time.  But  a  heavy  pen- 
dulum, vibrating  in  a  small  arc,  is  very  little  affected  by  this  resistance. 
i 

Besides  these  more  essential  parts  of  the  watchmaker's  art,  there  are  se^ 
veral  subordinate  considerations  which  require  his  attention  ;  the  striking  part 
in  particular  occupies,  in  clocks,  and  in  repeating  watches,  no  inconsiderable 
portion  of  the  bulk  of  the  machine.  But  the  apparatus  employed  on  these  oc- 
casions  requires  neither  refinement  of  invention  nor  delicacy  of  execution. 

VOL.    I.  D  d 


go*  LECTURE    XVir. 

In  old  clocks,  the  number  of  hours  struck  is  usually  determined  by  the  revo- 
lution 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  produced  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  pen- 
dulum,  and  enlarges  the  diameter  of  the  circle  of  which  the  pendulum  de- 
scribes an  arc;  it  must,  therefore,  tend  in  general  to  retard  the  motion  of  the 
clock.     Sometimes,  however,  an  unsteady  support  may  he  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  etfect  on 
each  other's  vibrations,  so  as  to  continue  going  for  several  days,  without  va- 
rying 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  vi- 
brations 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  companion  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  influenx-e 
each  other's  vibrations  in  such  a  manner  as  to  produce  exactly  the  same  note 
when  they  sound  together. 


fUV 


203 


LECTURE    XVIII. 


ON    RAISING    AND    REMOVING    WEIGHTS, 


The  methodical  arrangement  of  our  subject  leads  us,  after  having  consi- 
dered 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"^r  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  mat- 
ter, 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  remaining  part  relates  to  the  machinery  in- 
tended'ifor  overcoming  the  other  corpuscular  powers  of  bodies,  by  such  opera- 
tions as  are  calculated  to  change  their  external  forms. 

Machines  for  raising  Aveights,  which  involve  only  the  mechanics  of  solid 
bodies,  are  principally  levers,  capstans,  wheels,  puUies,  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  distinguished 
into  two  principal  kinds,  accordingly  as  the  power  and  weight  are  on  differ- 
ent 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 


204  LECTURE    XVIII. 

the  end  of  the  lever,  and  the  utmost  force  that  he  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  now  draw  the  end  of  the  lever  up- 
wards. 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  be  more  fatigued  by  raising  even  the  same  weight  by  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  workmen  to  stand  on  them  with  advantage  at  once. 
A  bent  lever  operates  precisely  with  the  same  power  as  a  straight  one,  provid- 
ed 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  preponder- 
ance 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  detain- 
ed 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  rest- 
ing 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  continual  intermission  of  the  motion.  (Plate  XVII. 
Fig.  £13.) 

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 


'  ON    RAISING    AND    REMOVING    M'EIGHTS.  205 

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 
a,rm  of  the  lever. 

Sometimes  the  weight  of  a  reservoir  or  bucket  of  water  is  employed  for  rais- 
ing another  bucket,  filled  with  coals  or  other  mateiials,  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  consi- 
derablepreponderance  may  be  advantageously  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  cor- 
ruption 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  contrary  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  end- 
less rope,  called  the  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  neces- 
sary 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  interposition  of  friction  wheels  ; 
a  patent  has  been  taken  out  for  the  invention,  and  it  has  already  been  intro- 


206"  ^  LECTURE    XVIII.  \ 

duced  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  suffi- 
cient 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  con- 
nected 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.  51.) 

Wheel  work  is  employed  in  avariety  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  succession  on  the 
teeth  of  the  next  wheel.  The  simplest  combination  of  wheelwork  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  barulcus  described  by  Hero  was  a  machine  of  this  nature. 

(fif  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  supported  by  the  axis  of  the  wheel. 

PuUies,  and  their  combinations  in  blocks,  are  universally  employed  on 
hoard  of  ships.  They  are  very  convenient  where  only  a  moderate  increase  of 
power  is  required ;  but  in  order  to  procure  a  very  gxeat  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  friction  and  the 


ON    RAISING    AND    REMOVING    WEIGHTS.  207 

ligidity  of  the  ropes.  The  inconvenience  resulting  from  a  large  number  of 
puUies,  may,  however,  as  we  have  already  seen,  be  considerably  lessened 
when  they  are  arranged  in  Mr.  Smeaton's  manner,  the  acting  rope  being  in- 
troduced in  the  middle,  so  as  to  cause  no  obliquity  in  the  block.  Tackles, 
or  combinations  of  pullies  for  raising  weights,  are  most  conveniently  sup- 
ported 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  employed,  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  ap- 
paratus 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  scaffolding,  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  cir- 
cumstances 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 
cf  Bridgwater's  canal.  This  canal  is  extended,  above  ground,  for  forty 
miles  on  one  level;  an  underground  navigation  twelve  miles  long  joins  it  at 
Worsiey,  leading  to  the  coal  mines  under  VValkden  moor.  At  a  height  of 
354-  yards  above  this,  is  another  subterraneous  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  cani;il.     The  inclined  plane  is   fixed   in  a  stratum  of  stone,   which 


208  LECTURE   xviir. 

fortunately  has  the  most  eligible  inclination  of  1  in  4,  and  is  33  yards  in 
thickness,  affording  the  most  advantageous  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  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  formation  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  advantageously  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  has  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 
Avheelwork.  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  re(juired  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- 
mediately, or  with  the  interposition  of  wheelwork,  by  a  winch,  by  the  hori- 
zontal 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  advantageous  mode 
of  employing  the  str.ength  of  a  labourer,  but  the  bulk  of  the  machine  is 


ON    RAISING    AN»    REMOVING    WEIGHTS.  20i) 

sometimes  inconvenient  and  detrimental:  when,  however,  the  man  walks 
upon  the  wheel,  and  not  within  it,  this  objection  is  in  great  measure  obvi- 
ated. A  walking  wheel  requires  to  be  provided  with  some  method  of  pre- 
venting 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  tlic  man  may  support  him- 
self with  his  hands,  and  other  similar  precautions  have  been  adopted.  Some- 
times the  plane  of  a  walking  wheel  is  but  little  inclined  to  tlie  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  disadvantageous,  sinae  nmch  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  work  was  performed  by  the  same  individual  ass  for  the  wliole  of 
forty  five  years  preceding  1771.  Walking  wheels  have  also  been  invented,  on 
which  horses  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  direction;  but 
probably  after  all  they  might  be  more  advantageo\isly  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  mcfie  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  re- 
moved 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, 

VOL.    I.  EC 


glO  tECTUR£    XVIII. 

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  some- 
what larger  than  its  own,  was  turned  slowly,  and  therefore  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  behind  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  to 


OV    RAISING    AND    RJEMOVING    WEIGHTS.  1211 

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  de- 
termine the  most  advantageous  burden  for  a  porter  to  carry,  but  the  experi- 
ence 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  immedi- 
ately or  very  nearly  over  some  part  of  the  ground  between  their  feet.  The 
difiiculty  of  carrying  a  weight  at  the  extremity  of  a  long  rod  is  easily  under- 
stood from  the  properties  of  the  lever,  and  the  same  principles  will  enable  us 
to  deteruMne  the  distribution  of  a  load  between  two  porters,  in  Avhatever  way 
they  may  carry  it.  Supposing  the  weight  to  be  placed  on  a  porter's  horse,  or 
hand  barrow,  and  at  equal  distances  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  distributed  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  re- 
main 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  inclinatiou  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  perpendicularly  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  continue  parallel  to  each  other;  but  the  inequality 
wovdd  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  un- 


312  LECTURE    XVIII. 

equally  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  witli  the  same  velocity: 
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  friction  may  also  be  somewhat  further  dimi- 
nished by  making  the  outline  of  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  diminishing  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  consider- 
ably 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  increase  the  ad- 
hesion. 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,  however,  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 
tliat  of  the  rod. 

Friction  may  in  general  be  considerably  diminished  by  the  interposition  of 


ON    RAISING    AND    REMOVING    WJEIGHTS,  213 

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  ac- 
curacy. Tallow  is  liable  to  lose  its  lubricating  quality,  unless  it  be  frequently 
renewed.  Between  surfaces  of  wood,  soap  is  sometimes  applied,  but  more 
commonly  black  lead,  which  becomes  highly  polished.  The  advantages  of 
canals,  and  of  navigation  in  general,  are  principally  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  tlie  appli- 
cation of  fluids.  Supposing  the  surfaces  to  be  flat  and  parallel,  a  roller 
moves  between  them  without  any  friction:  but  it  has  still  to  overcome  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  Avant  of  elasticity  in  the  materials  concerned.  The  continued  change 
of  place  of  the  rollers  is  often  a  material  objection  to  their  employment;  their 
action  may  in  some  cases  be  prolonged  by  fixing  wheels  on  their  extremities, 
as  well  as  by  some  other  arrangements;  but  thcKse  methods  are  too  compli- 
cated to  afford  much  practical  utility.  Rollers  may  also  be  placed  betwceu 
two  cylinders,  the  one  convex  and  the  other  concave,  and  the  friction  may 
in  this  manner  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  propor- 
tion as  the  velocity  of  the  parts  sliding  on  each  other  is  diminished,  it  is  ob- 
vious that  by  reducing  £lie  dimensions  of  the  axis  of  a  wheel  as  much  as  possi- 
ble, 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; 


•14  LECTURE    XVIII. 

for  in  this  manner  tlie  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,  ft  is  necessary  that  the  friction  wheels  be 
very  strong,  and  very  accurately  formed;  for  if  their  surface  were  irregu- 
lar, 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  oweagreat  part  of  their  utility  to  the  diminution  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  in- 
creased 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  consequently  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  cui"vature  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  XVIlt.  Fig.  225,  226.) 


ON    RAISING    AKD    REMOVING    WEIGHTS.  215 

Tiie  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  elasticity,  but  undergo  a  per- 
manent 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  perfect'ly  hori- 
zontal, 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  car- 
riage. Thus,  if  the  materials  were  perfectly  inelastic,  acting  only  on  the  pre- 
ceding half  of  the  immersed  portion  of  the  wheel,  and  their  immediate  pres- 
sure or  resistance  were  simply  proportional  to  the  depth,  like  thatof  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  in- 
creased 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 
consider  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  arc  in  any  degree  elastic,  the  resist- 
ance will  be  lessened  accordingly.  But  on  any  of  these  suppositions,  it  may  be 
shown  that  the  resistance  may  be  reduced  to  one  half,  either  by  making  a  wheel 
a  little  lessi  than  three  times  as  high,  or  about  eight  times  as  broad  as  the  given 
wheel.  This  consideration  is  of  particular  consequence  in  soft  and  boggy  soils, 
as  well  as  in  sandy  countries  ;  thus,  in  moving  timber  in  a  moist  situation,  it  be- 
comes extremely  advantageous  to  employ  very  high  wheels,  and  they  have  the 
additional  convenience  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.  Tig.  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  overturn- 
ing 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  Avheel  which  might  interfere  with  the  body 
of  the  carriage.  It  is  also  of  advantage  that  the  draught  of  a  horse  should  be  in 


216  LECTURE  xvnr. 

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  direci- 
tion  of  a  line  passing  through  tlie  point  of  contact  of  his  hind  feet  with  the 
groiind.  But  a  reason  equally  strong,  for  having  the  draught  in  this  direc- 
tion, is,  that  a  part  of  the  force  nicay  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  thi.'?  manner  to  both 
pairs  of  wheels,  where  there  are  four,  the  line  of  draught  ought  to  be 
directed  to  a  point  half  way  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  immedi- 
ately through  this  axis,  the  pressure  on  the  hind  wheels  will  remain  un- 
altered; 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  com- 
mon 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  direc- 
tion 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  be- 
longs. 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  in  clination  of  the  body  of  the  carriage,  a 


OV    EAISING    AND    REMOVING    WEIGHTS.  Sl/ 

g-reater  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  horizontal,  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.  2Q8.) 

It  has  been  proposed  to  fix  the  wheels  to  their  respective  axles,  to  continue 
the  axles  as  far  as  the  middle  of  the  carriage  only,  and  to  cause  them  to  turn  oa' 
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  necessary.  If  both  opposite  wheels 
were  fixed  to  a  single  axis,  one  of  them  would  be  dragged  backwards  and  the 
other  forv/ards,  whenever  the  motion  deviated  from  a  straight  line;  and  a -si- 
milar 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, 
b]^  causing  every  change  to  be  more  gradually  communicated  to  it,  by  means 
of  the  flexibility  of  the  springs,  and  by  consuming  a  certain  portion  of  every 
sudden  impulse  in  generating  a'degree  of  rotatory  motion.  This  rotatory  mo- 
tion depends  on  the  oblique  position  of  the  straps  suspending  the  carriage, 
which  prevents  its  swinging  in  a  parallel  direction;  such  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  ob- 
liquity of  the  straps  tends  also  in  some  measure  to  retain  the  carriage  in  a  ho^ 
rizontal  position  :  for  if  they  were  parallel,  both  being  vertical,  the  lower 
one  would  have  to  support  the  greater  portion  of  the  weight,  at  least  accord- 
ing 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  consequently  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  hori- 

VOL.    I.  F  f 


S18  LECTURE   xviir. 

zontal  portions  of  the  fcirces  may  be  equal,  the  more  inclined  to  the  horizon 
must  be  the  greater:  the  upper  spring  will,  therefore,  be  a  httle  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  whee  Is, 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  re- 
quire 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  some- 
times 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  perpendicular  to  the  direc- 
tion of  his  force,  and  gives  him  a  greater  power,  while  the  opposite  arm  be- 
comes more  oblique,  and  causes  the  other  horse  to  act  at  a  disadvantage:  so 
that  there  is  a  kind  of  stability  in  the  equilibrium.  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  wliich  they  are  to  pass;  and  this 
practice  has  of  late  been  extended  in  some  cases  as  a  substitute  for  the  con- 
struction of  navigable  canals.  Where  there  is  a  turning,  the  carriages  are 
usually  received  on  a  frame,  supported  by  a  pivot,  which  allows  them  to  be 


ON    RAISING    AND    REMOVING    WEIGHTS,  210 

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  coutrivcnces  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  tlie 
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  expeditious  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  pullics  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  httle  carts  has  been  con- 
nected 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. 


220 


LECTURE  XIX. 


ON    M01>ES    OF    CHANGING    THE    FORMS    OF    BODIES. 


I  HE  corpuscular  forces  by  which  bodies  retain  their  peculiar  forms  of  aggre- 
gation, 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  aug-ment  their  dimensions  in  a  particular  direction,  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  referable  to  the  effects  of  compression, 
extension,  penetration,  division,  attrition,  digging,  boring,  agitation,  tritura- 
tion and  demolition.  The  two  first  of  these  articles  depend  on  such  a  change 
as  we  have  examined,  in  considering  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  ma- 
chine; but  it  isof  usein  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  friction  would  render  it  al- 
most 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.  Wherever  a  force  is  so  employed  as  to  produce  an  im- 
pulse which  acts  on  any  b.ody,  the  momentum,  which  is  the  result  of  the 
action  of  the  force  for  a  certain-  time,  is  usually  much  more  powerful  than  the 


ON    MODES    OF    CHANGING    THE    FORMS    OF    BODIES.  221 

simple  pressure;  the  degree  of  its  efficacy  depends,  however,  on  the  degree  of 
compressibility  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  toller  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  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  w.hich  the  materials  arc 
glazed. 

The  copper  plate  printing  press,  and  the  m-achi«e  for  copying  letters,  are  com- 
posed 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  roLer,  and  partly  by  external  force. 

The  rollers,  by  which  sugav  canes  are- pressed,  are  in  general  situated  verti- 
cally, 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  in- 
terstices 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  regularity  and  greater  force, 
than  the  action  of  a  single  roller  would  do.  For  this  reason,  it  may  be  ad- 
visable 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.., 
Bg.  231.) 


222  ,  LECTURE       XIX. 

'  In  oil  mills,  a  still  greater  momentum  is  applied  to  the  purpose  of  compres- 
sion than  in  the  printing  press:  hammers,  or  long  wooden  beams,  placed  ver- 
tically, 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  hammering: 
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  pre- 
serve its  ductility, it  must  be  frequently  annealed  by  exposure  to  heat.  Anvils 
and  vices  are  necessary  appendages  to  the  hammer;  their  use  depends  princi- 
pally 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  ap- 
plied a  well  known  law  of  hydrostatics  to  the  construction  of  a  very  useful  press, 
which  is  simple,  powerful,  and  portable. 

Extension  is  seldom  performed  by  forces  that  tend  immediately  to  increase 
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  em- 
ployed 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,  are  rolled  into  plates,  and  a  thin  plate 
of  silver  being  soldered  to  a  thicker  one  of  copper,  the  compound  plate  is  sub 
mitted  again  to  the  Action  of  the  press,  and  made  so  thin  as  to  be  afforded  at 
a  qioderate  expense.  The  glazier's  vice  U  a  machine  of  the  same  nature,  for 
forming  window  lead:    the  softness  of  the  lead  enables  it  to  assume  the  re- 


ON    MODES    or    CHANeiNG    THE    FORMS    OF    BODIES.  223 

quired  shape,  in  consequence  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  corresponding  elevations.     (Plate  XVIIL  Fig.  232.)    , 

In  drawing  wire,  the  force  is  originally  applied  in  the  direction  of  the  ex- 
tension, 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  mo- 
mentum 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 
ship's  bottoms.  Silver  wire,  thinly  covered  with  gold,  is  rendered  extremely 
fine,  and  then  flattened,  in  order  to  be  fit  for  making  gold  thread :  the  thick- 
ness 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  pot- 
ter's wheel  consists  in  great  measure  of  compression  and  extension,  performed 
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  immediately  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  com- 


f24  '  LECTURB    XIX. 

mon  operation  of  the  Bmith's  hammer.  In  forges,  the  hammers  are  raised  by 
macliinery,  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  hLimmer,  Such  forges  are  used  in  making  malleable  iron,  in  forming- 
copper  plates,  a:id  in  manufacturing  steel.     (Plate  XVIII.  Fig.  233.) 

Gold  is  beaten  between  the  intestines  of  animals,  on  a  marble  anvil;  for 
tliis  purpose  it  is  alloyed  with  copper  or  silver.  It  is  reduced  to  the  thick- 
ness of  little  more  than  the  three  hundred  thousandth  of  an  inch.  Silver 
leaf  is  about  the  hundred  and  sixty  thousandths  it  is  made  of  silver  without 
alloy. 

The  operation  of  coining  depends  also  principally  on  an  extension  of  the 
metal  into  the  recesses  of  the  die  ;  it  is  performed  by  a  strong  pressure,  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  re- 
quired, 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  con- 
tact, 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 
anode  of  uniting  metals  is  actually  employed  in  some  manufactures. 

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 


ON    MODES    OF    CHANGING    THE    FORM%    OF    BODIES.  225 

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,  Avhich  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  energ-y  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  pro- 
portion 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  em- 
ployed in  generating  momentum  ;  by  much  the  greatest  part  is  spent  in  over- 
coming 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  facilitat- 
ing penetration,  that  soft  substances,  moving  very  swiftly,  will  readily  per- 
forate much  harder  ones  ;  and  for  the  same  reason  a  gunshot  wound,  and 
even  the  loss  of  a  limb,  takes  place  with  so  little  disturbance  of  the  neigh- 
bouring parts,  that  it  is  sometimes  scarcely  felt.  The  advantage  of  an  impulse, 
however  inconsiderable,  above  a  pressure,  however  great,  may  be  easily  under- 
stood 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  suthcient 
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 

VOL.    I.  G  g 


Q26  *  LECTURE    XIX. 

fFect  in  d  riving  it,  but  it  would  be  absolutely  impossible  in  practice  to  con- 
struct macbiuery  strong  enougb  for  tbe  purpose,  and  if  it  were  possible,  tbere 
would  be  an  immense  loss  of  force  from  tbe  friction.  For  example,  supposing- 
a  weight  of  500  pounds,  falling  from  a  beigbt  of  50  feet,  to  drive  the  pile 
2  inches  at  each  stroke;  then,  if  the  resistance  be  considered  as  nearly  uni- 
form, its  magnitude  must  be  about  150  thousand  pounds,  and  the  same  mov- 
ing 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  fol- 
lower, 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,  uncoiling  the  rope  from  the  drum,  and 
the  force  of  the  horses  is  employed  in  turning  a  fly  wheel,  until  the  con- 
nexion with  the  weight  is  again  restored.     (Plate  XVIII.  Fig  234.) 

When  we  throw  a  stone,  or  a  missile  weapon  of  any  kind,  with  the  hand, 
the  stone  can  acquUe  no  greater  velocity  than  the  hand  itself,  accompanied 
by  the  neighbouring  part  of  the  arm:  so  that  the  whole  velocity  must  be  pro- 
duced 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  consider- 
able. An  elastic  bow,  furnished  Avith  a  strong  and  light  string,  enables 
us  to  apply  to  an  arrow  or  to  a  ball  the  whole  force  of  our  arms,  unencum- 
bered with  any  considerable  portion  of  matter,  that  requires  to  be  moved  with 
the  arrow;  hence  a  very  great  velocity  may  be  obtained  in  this  maflner.  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  im- 
mense force  in  the  form  of  an  inconceivably  hght  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 


ON    MODES    OF    CHANGING    THE    FORMS    OF    BODIES.  227 

the  bowstring  acts  on  it,  as  the  greatest  force  applied  in  drawing  the  bow  is 
greater  thantwice  the  weight  to  be  moved. 

The  action  of  a  whip,  either  on  the  air,  or  on  a  solid  body,  depends  on 
the  int;rease  of  velocity,  occasioned  by  the  successive  transmission  of  the  mo- 
tion 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  capability  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  instru- 
ment 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.  Stodart's 
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  rect"- 


228  LECTURE    XIX. 

angular  grooves,  and  which  are  placed  close  to  each  other,  so  that  the  pro- 
minent 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  transversely  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.  Orna- 
mental lathes  admit  of  a  great  variety  of  mechanical  contrivance,  but  they  are 
of  little  practical  use,  except  for  amusement.  Picture  frames  are,'  however, 
sometimes  turned  in  oval  lathes;  and  in  the  manufacture  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  a  screw,  a  screw  of  any  dia- 
meter 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,  com- 
municated 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  constitutes  the  can- 
non, assists  in  defining  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  outsid^  is  also  turned  into  its  intended  shape  by 
the  application  of  proper  instruments.     Cylinders  for  steam  engines  are  cast 


> 


ON    MODES    OF    CHANGING    THE    FORMS    OF   BODIES,  £29 

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  in- 
struments, resemble  in  their  operation  the  chisel  and  the  wedge  :  the  numer- 
ous diversities  in  their  form  and  the  complications  of  their  structure,  are  de- 
termined more  by  the  various  modifications  of  their  action,  required  for  par- 
ticular 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,  ashaft  is  sunk  through  the  up- 
permost 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  ma- 
chinery; 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  Avood  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  crank, 
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  circumference  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  mak- 


^ 


230  LECTURE    XIX. 

ing  blocks,  in  the  Royal  dock  yard  at  Portsmouth,  has  been  lately  much  im- 
proved 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  re- 
volves continually,  appears  to  be  very  considerable,  since  a  much  greater  velo- 
city 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,  tlie  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  pro- 
cesses of  this  kind  might  be  performed  Avith  advantage  under  water;  it  is  well 
known  that  glass  maybe  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,  instruments 
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 
arc  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;  audit  has  been  conjectured  that  the  cold  continually  occasion- 
ed 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  po- 
lishingsteel,  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  hori- 
zontally on  a  circular  surface,  and  in  order  that  the  action  may  be  equally  di- 


ON    MODES    OF    CHANGiyG    THE    FORMS    OF    BODIES.  231 

vided  throughout  the  surface,  it  is  allowed  to  revolve  on  an  axis  hy  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  poHshing  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,  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  interposi- 
tion of  sand;  the  polishing  blocks  are  sometimes  caused  to  revolve  by  machi- 
nery 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.  Tlie  tool  is  sometimes  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  appears  to  move;  a  circle  is  then 
described,  as  it  revolves,  in  order  to  mark  its  outline. 

4 


232  LECTURE    XIX. 

Machines  for  trituration,  by  means  of  which  the  larger  niasses-of  matter  are 
crushed,  broken,  or  ground,  into  smaller  parts,  are  in  general  comprehended 
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  with  iron 
or  steel.  But  barks  and  seeds  are  more  usually  ground  by  the  repeated  pres- 
sure of  two  wheels  of  stone,  rolling  on  an  axis  which  is  forced  in  a  hori- 
zontal direction  round  a  fixed  point.  A  nobleman  of  distinguished  rank  and 
talents  has  lately  employed  for  a  moj^ar  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  revolving 
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  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  countr}',  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 


ON    MODES    OF    CHANGING    THE    FORMS    OF    BODIES.  233 

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  revolv- 
ing axis,  which  strike  against  the  orifice ;  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  reduced  to  powder,  it  is  discharged  at  the  circum- 
ference, 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  eft'ectually  on  the  corn.  The  re- 
sistance, in  grinding  wheat,  has  been  estimated  at  about  a  thirty  fifth  of  the 
weight  of  the  millstone.  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 
20160  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,  tlie  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  the  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,  which  consists  of  a 

VOL.    1.  H  h  , 


334  LECTURE    XIX. 

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  oft"  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  collected 
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  besieging  a  town, 
are  now  generally  superseded  by  the  introduction  of  artillery,  although 
they  may  perhaps  still  aftbrd,  in  some  cases,  a  more  economical  and 
equally  powerful  mode  of  operation.  The  same  momentum,  and  the  same 
energy,  may  be  given  to  a  battering  ram  at  a  less  expense  tlian  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  sustain  without  giving  way,  inde- 
pendently 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  fi«mly,  and  sometimes 


ON    MODES    OF    CHANGING    THE    TORMS    OF    BODIES.  235 

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  em- 
ployed, 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  appli- 
cation of  fire,  as  in  the  mine  of  Ramraelsberg,  in  the  Hartz,  where  the  stra- 
tum containing  the  ore  is  of  such  a  nature,  partly,  perhaps,  on  account  of  the 
combustible  matter  which  enters  into  its  composition,  that,  by  the  effect  of 
a  large  quantity  of  fuel, which  is  burntin  the  vast  excavation,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  communication  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  gunpow- 
der, belong  to  a  department  of  philosophy  which  it  is  not  our  business  to  in- 
vestigate: 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. 


236 


LECTURE  XX. 


ON    THE    HISTORY    OF    MECHANICS. 


J-  HE  order  which  we  have  pursued,  in  considering  the  various  departments 
of  mechanical  science,  has  been  in  great  measure  synthetical,  dictated  by 
the  plan  of  proceeding  logically  from  the  most  simple  principles  to  their  more 
complicated  combinations,  so  as  to  build  at  every  step  on  foundations  which 
had  been  firmly  laid  before:  and  this  method  is  unquestionably  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  w.is  originally 
obtained,  and  to  what  individuals  mankind  is  indebted  for  each  improvement 
that  has  been  successively  made.  Hence,  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  mathematics  on  which  it  immediately 
depends. 

It  is  universally  allowed  that  the  Greeks  derived  the  elements  of  mathema- 
tical, mechanical,  and  astronpmical  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  Pytha- 
goras 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  foundations  of  geome- 
try; 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 


ON    THE    HISrORY    OF    MECHAlTlCS.  23T 

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  them- 
selves 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;  al- 
though 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  speculations, 
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  mathe- 
matical and  mechanical  researches,  it  does  not  appear  that  either  of  his  teach- 
ers had  made  any  improvements.  On  his  return  from  his  travels  in  Egypt  and 
th'fe  East,  in  the  time  of  the  last  Tarquin,  about  500  years  before  Christ,  he 
found  his  native  country  Samos  under  the  dominion  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. " 

However  erroneous  the  opinion  may  be,  that  Pythagoras  was  acquainted 
with  the  laws  of  gravitation,  it  is  certain  that  he  made  considerable  improve- 


g38  LECTURE    XX. 

ments  both  in  mathematics  and  in  mechanics,  and  in  particular  that  he  dis- 
covered 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  proposition  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,  beseems  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  possess- 
ed 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  introduction  in  building  was  of  much 
later  date.  Architecture,  and  other  mechanical  arts  had  however  been  con- 
siderably advanced  some  time  before  this  period,  if  it  is  true  that  Ctesiphon 
or  Chersiphron,  who  built  the  temple  of  Ephesus,  was  cotemporary  with 
Croesus  and  Thales.  It  is  uncertain  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  opi- 
nion, that  they  passed  over  bridges  which  already  existed.  Curtius  speaks  of  a 
bridge  of  stone  over  the  F.uphrates  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. 
We  are  informed  by  Pliny  that  Ctesiphon  lowered  his  large  blocks  of  stone  by 
placing  them  on  ])eaps  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. 


ON    THE    HISTORY    OF    MECHANICS.  239 

Archytasof  Tarentum,  and  Eiicloxus  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  pul- 
ley and  the  screw.  They  lived  nearly  150  years  after  Pythagoras,  and  geo- 
metry had  made  in  the  mean  time  very  rapid  advances,  for  the  properties  of 
the  conic  sections  were  well  known  to  these  philosophers.  "  The  first  per- 
sons," 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  solu- 
tions of  problems,  which,  if  more  mathematically  treated,  are  complicated 
and  difficult:  each  of  them  invented  a  method  of  determining  in  this  manner 
the  magnitude  of  two  mean  proportionals  between  two  given  lines,  by  the  as- 
sistance of  certain  curves  and  sections.  Plato  by  no  means  approved  of  their 
mode  of  proceeding,  and  reprehended  them  severely,  as  giving  up  and  pervert- 
ing the  most  essential  advantages  of  geometry,  and  causing  the  science  to 
revert  from  pure  and  incorporeal  forms  to  the  qualities  of  sensible  bodies, 
subjected  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  lulf  a  century  after  Archytas;  he  was  perhaps  the  author  of  no  ori- 
ginal 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.  Dino- 
crates  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 


3.40  LECTUUE    XX. 

this  well  known  work  is  arranged,  and  the  precision  and  accuracy  which  reign 
in  every  part  of  it,  demand  ahnost  as  great  a  share  of  praise  as  is  due  to  ori- 
ginal discovery. 

Epicurus  was  a  cotemporary  of  Euclid,  and  is  considered  as  the  last  of  the 
Pythagorean  or  Italian  philosophers.  The  penetration  that  he  discovered  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  amongthe  manuscripts  of  Ilerculaneum.  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 
warHke  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 
the  centre  of  gravity;  for  the  discovery  of  the  laws  of  h3'drostatics,  and  of  the 
modes  of  determining  the  specific  gravities  of  bodies;  for  the  construction  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   inven- 
tions 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  materinl    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  disco- 
verable only  to  the  reasoning  faculty.     Archimedes,  who  was  a  friend  and  a 


ox    THE    HISTORY    OF    MKCHANICS.  241 

relation  of  Hiero,  had  asserted  that  any  weight  wliatever  might  be  moved  by 
any  given  power:  and  depending  on  tlie  vahdity  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:  up.on  this  Archimedes  procured  a  ship,  which  was  with  great 
labour  drawn  up  on  the  shore,  and  having  completely  manned  and  freighted 
lier,  he  seated  himself  at  a  distance,  and  by  lightly  touching  the  first  move- 
ment 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- 
tlie  powers  of  mechanical  art,  prevailed  on  Archimedes  to  construct  such  en- 
gines both  of  defpnce  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. valua- 
ble 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  con- 
stituted but  a  part  of  Archimedes's  corporeal  macliinery,  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  annoy- 
ance 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 
macliine  of  Archimedes, and  immediately  fled;  so  that  Marcellus  at  last  deter- 
mined 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 
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,  un conta- 
minated by  the  imperfections  of  the  material  world:  works  that  are  comparable 
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  o»€ 

VOL.    I.  J  i 


242  LECTURE    XX. 

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'wlth  ease.  For  we  might 
ourselves  search  in  vain  for  a  demonstration  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  fas- 
cinated 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;  de- 
riving, like  a  true  votary  of  the  muses,  every  pleasure  from  an  intellectual 
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;  re- 
questing of  his  friends  that  they  would  place  on  his  tomb  a  cylinder  contain- 
ing 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  happened  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  centuries. 

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  Mathematicl  Veteres.  Ctesibius  of 
Alexandria  was  about  a  century  later  than  Archimedes;  he  enriched  hydrau- 
lics with  several  valuable  machines;  although  he  contributed  little  to  the  ad- 


/        ON    THK    HISTORY    OP    MECHANICS.  243 

vancement  of  theoretical  investigation.  Hero  was  of  the  same  school,  and  his  pur- 
suits 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 
liad  referred  the  properties  of  the  lever,  the  wheel  and  axis,  the  pulley,  the 
wedge,  and  the  screw,  to  the  same  fundamental  principle ;  so  that  (he  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  Attains,   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.  ApoUodorus  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  himself  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  stilj  extant. 
The  rudiments  of  algebraical  notation  and  calculation  may  be  found  in  the  work* 
of  Diophantus  ;  but  the  Arabians  appear  to  have  first  practised  the  method  of 
denoting  quantities  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  barbarians  were  as  effectual 
in  suppressing  the  refinements  of  civilisation,  as  in  checking  the  pursuit  of  li- 
terary 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 


244  LECTURE    XX. 

wlio  have  excelled  in  them  ;  and  the  improvements  which  have  been  made, 
within  a  few  centuries,  in  the  British  manufactures,  liave  obtained  for  them  a 
celebrity  unrivalled  by  those  of  any  other  nation.  The  ancient  Britons  are  sup- 
posed 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,  which 
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  great  measure 
forgotten  soon  after  they  left  the  country.  In  the  seventh  century,  several 
architects  and  workmen  were  brought  from  the  continent  by  Wilfrid  and 
Biscopj  they  restored  the  practice  of  building  with  stone,  which  had  been 
generally  superseded  by  wood,  and  laid  the  foundation  for  other  improve- 
ments. In  the  time  of  king  Alfred,  the  English  goldsmiths  began  to  excel, 
and  before  the  conquest,  the  woollen  manufactures  had  acquired  a  consider- 
able degree  of  perfection.  The  paper  now  in  use  vras  introduced  about  the 
year  1100;  it  was  probably  imported  from  the  continent,  since  the  linen 
manvifacture  was  little  advanced  in  England  till  150  years  later;  but  em- 
broidery was  much  practised,  although  in  the  12th  century  silks  were  princi- 
pally 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 
inventioli  of  the  method  of  drawing  wire,  which  was  first  introduced  at  Nu- 
remberg. In  the  succeeding  century,  the  increasing  number  of  hands  em- 
ployed in  various  manufactures,  suggested  to  some  mind  of  superior  penetra- 
tion 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  manufacture,  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  per- 
secutions in  Flanders,  and  before  the  end  of  the  century  a  new  modification 
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 


.       -  ox    THE    HISTORY    OF    MECHANICS.  245 

for  slitting  iron  were  also  first  erected  in  the  sixteenth  century ;  Birming- 
ham and  Sheifield  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 
astonisli  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  inventions  of  Arkwright  and  his  followers,  which  have  also 
been  introduced  in  many  other  parts  of  the  united  kingdom.  The  import- 
ance 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  Avhite 
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  stile  prevailed  in  this  country  from  the 
conquest  to  the  beginning  of  the  thirteenth  century;  the  arch  was  frequently 
employed,  and  its  form  was  semicircular.  The  Gothic  architecture,  dis-" 
tinguished  by  its  pointed  arches,  which  is  said  to  have  originated  from  the 
Saracens,  was  first  introduced  into  England  about  the  year  1170,  and  was 
more  and  more  generally  adopted  fo^  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  afterwards;  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- 
Hot  be  equal  to  either  of  them. 


246  LECTURE    XX. 

In  the  midst  of  an  age  of  darkness,  an  insulated  individual  arrests  our  at- 
tention by  merits  of  no  ordinary  kind.  Roger  Bacon  was  burn  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  au 
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  pur- 
suits; he  declares  that  he  had  seen  chariots  which  could  move  with  incredible 
rapidity,  without  the  helpof  animals  ;  he  describes  a  diving  bell;  and  he  says 
that  he  had  been  informed,  on  good  authority,  that  machines  had  been  made, 
by  tlie  assistance  of  which  men  might  fly  through  the  air,  Cimabue,  who 
first  began  to  revive  the  long  neglected  art  of  painting,  was  cotemporary  with 
Bacon.  The  use  of  oil  in  painting  is  commonly  supposed  to  have  been  in- 
troduced by  Van  Eyck,  but  there  are  traces,  in  the  records  of  this  country,  of 
its  employment  as  early  as  the  year  1235. 

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  sup- 
posed to  have  been  invented  in  the  year  1423.  Some  attribute  the  art  of 
printing  with  types,  to  Laurentius  Coster  of  Haerleni,  who,  as  they  say,  in 
1430,  employed  for  the  purpose  separate  blocks  of  wood,  tied  together  with 
thread.  Gensfleich,  one  of  his  workmen,  went  to  Mentz,  and  was  there  as- 
sisted by  Gutenberg,  who  invented  types  of  metal.  But  the  best  authors  ap- 
pear to  disbelieve  this  story ;  and  Gutenberg,  in  partnership  with  Fust  antl 


ojc  THE  HisToar  OF  iiEcnAjfics.  S-J-T 

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  cKcelled  not  only  in  painting  and  poetry,  but  also  in  ar- 
chitecture, mathematics,  and  mechanics.  The  state  of  practical  mechanics 
in  this  and  the  subsequent  centuries  may  be  estimated  from  Ramelli's  collec- 
tion 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  philosophical  ar- 
gument and  inquiry.  Guido  Ubaldi  published,  in  1577,  a  treatise  on  me- 
chanics, 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  founda- 
tions of  the  discoveries,  which  have  succeeded  each  other  with  increasing  ra- 
pidity 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  timekeepers.  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. 

The  application  of  the  more  intricate  parts  of  the  mathematics,  to  practical 
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:    and  they  were  reduced  to 


24S  LECTURE    XX. 

a  still  more  useful  form  by  the  labours  of  Briggs  and  of  Gunter,  Descartes, 
about  the  same  time,  was  makiug  considerable  additions  to  the  science  of 
algebra,  and  the  mathematics  were  soon  after  enriched  by  Cavalleri's  inven- 
tion of  the  method  of  indivisibles.  This  method  was  founded  on  the  prin- 
ciples 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  Iluygens.  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  sci- 
ence. 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  pen- 
dulums in  clocks;  the  quadrant,  the  telescope,  and  the  microscope,  were  ma- 
terially indebted  to  him ;  he  had  the  earliest  suspicions  of  the  true  nature  of 
the  cause  that  retains  the  planets  in  their  orbits ;  and  the  multitude  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  sub- 
jects, are  elegantly  treated  in  the  lectures  published  by  the  learned  Dr.  Bar- 
row. He  was  professor  of  mathematics  at  Cambridge,  and  voluntarily  re- 
signed his  chair  to  make  way  for  his  successor,  the  pride  of  his  country,  and 
the  ornament  of  mankind.  Sir  Isaac  Newton  was  born  at  Woolsthorpe  in 
Lincolnshire,  on  Christmas  day  in  l642,  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  immediately  publishing  any  work  on 
these  subjects.  His  first  optical  experiments  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  mecha- 


ON    THE   HISTORY    OF    MECHANICS,  249 

nics  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  parlia*ment,  and  in  I6g6",  he 
was  placed,  upon  the  recommendation  of  the  Earl  of  Halifax,  in  a  lucrative  situa- 
tion 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^  Fon- 
tenelle,  ' '  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  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 
iuall  the  excellent  productions  of  the  members  of  that  Society,  with  as  much 
confidence,  as  if  it  had  been  consecrated  by  the  respect  of  a  long  course  of 
ages."  A  remarkable  instance  of  the  extent  and  refinement  of  Newton's  ma- 
thematical 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  ac- 
quainted with  those  methods  of  algebraical  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 
fiuxions,  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  law* 
of  mechanics  were  very  elegantly  investigated,  and  successfully  applied  by 
these  three  contemporary  philosophers  on  the  continent,  while  Machin,  Gotes, 
Halley,  and  Demoivre,  were  applying  themselves  to  similar  pursuits  in  this 
country.     Perrault,  Lahire,  Amontons,  and  Parent,  members  of  the  Parisian; 

VOL.    I.  •  Kk 


I 


250  LECTURE    XX, 

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  tlieir  inventions  made  their  appearance  much  later^  in  the  va- 
luable collection  of  machines  approved  by  the  academy,  and  some  of  them 
liave  been  inserted  in  the  useful  work  published  by  Leupold,  at  Leipzig,  under 
the  title  of  a  Theatrum  Machinaruni.  Throughout  the  last  century,  the 
transactions  of  various  societies,  established  for  the  promotion  of  science,  be- 
came 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  facihtating  the  dissemination  of  all  new  discoveries. 

The  philosophy  of  Newton  assumed  also  a  more  popular  and  attractive  form 
in  the  writings  of  Clarke,  Pemberton,  Maclaurin,  and  Musschenbroek,  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  Mac- 
laurin 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  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  profound  mathematician,  and  Bernoulli  the  more  ac- 
curate philosopher. 

The  latter  half  of  the  eighteenth  century  was  in  many  respects  extremely 
auspicious  to  the  progress  of  the  sciences;  the  names  of  Dalembert,  Lan- 
den,  Waring,  Frisi,  Robisoa,  Lagrange,  and  Laplace,  deserve  to  be  enume- 
rated 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  magnificent 
.scale,  in  the  Encyclopedic,  a  work  which  does  as  much  honour  to  the  lai^our  and 
genius  of  some  of  its  authors,  as  it  reflects  disgrace  on  the  principles  and  poli- 
tics of  others.  The  Society  for  the  encouragement  of  arts,  manufactures,  and 
commerce,  was  established  in  London  about  the  same  time  that  the  Ency- 


»  ON    THE    HISTORY    OF    MECHANICS.  HSl 

clopedie  began  to  appear  at  Paris,  and  its  premiums  and  publications  have, 
witliout  doubt,  excited  a  degree  of  attention  to  the  subjects  of  practical  me- 
chanics, 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  17<52,  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  afford- 
ing very  essential  service  to  navigation,  especially  since  the  astronomical 
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,  suffici- 
ently 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  often  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  uni- 
versally disseminated,  as  within  the  last  forty  years.  This  advancement  has 
partly  been  the  cause,  and  partly  the  effect,  of  the  great  multiplication  of  scien- 
tific journals,  cyclopaedias,  and  encyclopaedias,  which  have  been  annually  in- 
creasing 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  amus- 
ing discoveries  and  improvements,  which  have  been  made  in  chemistry  and  na- 
tural history:  some  of  the  most  copious  of  these  works  have  had  a  sale,  un- 
precedented even  for  books  of  more  moderate  extent. 

The  charter  of  the  Royal  Institution  is  dated  in  1799;  its  foundation  Avill 
not  perhaps  make  an  era  in  the  history  of  the  refinements  of  science;  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., 


252  LECTURE    XX. 

After  all  that  lias  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  opportunity 
for  the  employment  of  genius  and  industry  in  following  their  steps.  To  sup- 
pose that  little  or  nothing  remains  to  be  done,  betrays  a  want  either  of  know- 
ledge, or  of  courage.  The  experimental  researches  of  some  of  the  greatest  philo- 
sophers 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  com- 
binations, \ve  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  ex- 
tended, and  the  miscellaneous  nature  of  the  works  in  which  many  of  the  most  va- 
hiable  disquisitions  have  been  communicated  to  the  public,  together  with  the 
natural  disposition  to  indolence,  which  a  high  degree  of  civilisation  too  fre- 
quently 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  continued  experience,with  the  truth  of  this  observa- 
tion, 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,  everyone  who  is  de- 
sirous of  enlarging  the  sphere  of  our  knowledge,  with  respect  to  any  branch 
of  science,  connected  with  the  subject  of  these  Lectures,  will  find  it  easy,  by 
consulting  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 
syoiid  at  large  to  participate  in  his  improvements  and  discoveries. 


ON    THE    HISTORY    OF    MECHANMCS. 


259     ~ 


CHRONOLOGY    OV    MATHEMATICIANS    AND    MECHANICS. 


roo  B.  c.                        6 

i    ....    1    ...    . 

00                                                          5  00 

•     ■     ■     .     1 

4 
.      .      .      1       .... 

00                                                          3 
....      1      ...      . 

00                                                     200 

.PITTA 

C    U    S. 

.E     U     D 

O     X     U    S.                  P  H 

I     L     O 

.T    H    A 

L      E      S. 

A    R    ClHYTAS 

APOLLONIUS    P. 

C    T 

E  S  I  P  H  O 

PII  ER  EC  YD  E  S. 

.  ARISTOTLE. 

.E  P  1  C  U 

ARCHIMEDES. 
R   U   S.  A  T  H  E  N  A  E  U  S 

.PYTHAGORAS 

. 

.D    E    M    O    C    R 

I   T   U   S.               DINOC 

RATES 

k . . 

1 

E  U  C 

L    I    D 

•iOO  B.  C.                                  I 

00                          BIRTH  Ot 
....     1    ...     . 

CHRIST                                   1 
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00 

.     ...     1     ...     . 

JO                                                     300 
....      1      ...      . 

CTES IB  I   U  S 

.LUCRETIUS. 

APOLLOD 

ORUS 

HERO 

VITRUVIUS 

DIOPHANTUS 

P  H  I  L  O 

.S  E 

N    E    C    A. 

B      I      T 

O 

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00                                                          5 
....      1       ...      . 

00 

6 
.     .      .      I      .      .      .      . 

00                                                          7 

....  1  ...  . 

JO                                                 800 
....      1      ...      . 

PA   P  P  US 

.P    R    O    C    L    U    S. 

L 

WILFRID 

800                                                       9 

00                                                       10 

00 

11 
.     .      .      1      .      .      .      . 

00                                                        12 
....      I      ...      . 

00                                               1300 
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WALTt 

H     C     .C    I    M    A    B    U    E 
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1300                                                  14 
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00                                                        15 

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00 

10 
.     .     .     1      .     .     .     . 

00                                          17 
....     1     ...     . 

00                                                  1800 
....      1      ...      . 

WALLING-                      VAN 

E    Y     C     K. 

.H     O     O     K     E 

.L    A    N     D     E     N. 

FORD                               FU 

SO  RI US 

.L    A     H     I     R 

E.     .S  M   E  A  T  O  N. 

G 

UTEMBERG 
FUST 
SCHAEFFER 
.C     A     X     T     O     N. 

.NEWT 
.L  E  I  B  N  I  T 
.J  A.    BERN 
.H     A     L 

O  N. 

Z.        WEDGWOOD. 
WARING. 
LEY. 

.L.    D  A  V  I  N 

C  1. 

.AM  ON  7 

.R  O   B    I    SON. 

TA 

RTAL  E  A. 

.PARE 

N  T. 

PAL  L  A  D  I  O 

.JO.     BE 

R  N  O  U  L  L  I. 

.N    A    P    I    E 

R.                      .D    E     M 

O    I    V  -R    E. 

.F.     B    A    C 

ON.                   LEU 

P  O   L  D. 

.B       R       I 

G    G    S.                .0    L    A 

R     K     E. 

S       T       E 

V     1     N.                 .HER 

MANN. 

.G     A     L     1 

LEO.                  .DES 

AGULIERS. 

.K      E      P 

L     E     R.                        .COT 

E  S. 

S  A  N  C 

T  O  R  I  U  S                       .GR 

AVESAND. 

.GUN 

T  E  R.                               .M 

USSCHENBR. 

V 

A  L  ERIO 

VOLTAIRE. 

.M 
C 

ERSENNE. 
AVALLERI. 
DESCARTES. 

.P  E  R   R   A    U   L  T,   . 

.W   I    L   K    I   N   S. 

.W      A      L      L      I      S. 

HARRISON. 

P  EMBERTON. 

MACLAUR. 

.D.    BERNOULLI. 

L.      E     U     L    E     R. 

.SIMPSON. 

.H    U  Y  G   E  N  S. 
.BARROW. 

.CLAIRAUT. 

.D  ALEMBERT. 

The  points  show  the  time  of  the  birth  and  death  of  each 

(lerson,  where  they  have  been  ascertained. 

.W          R          E 

N. 

COURSE  OF  LECTURES 


ON 


NATURAL    PHILOSOPHY 


AND    THE 


MECHANICAL    ARTS. 


PART    IT. 


HYDRODYNAMICS. 


COURSE  OF  LECTURES 


ON 


NATURAL    PHILOSOPHY 


AND    THE 


MECHANICAL  ARTS. 


LECTURE  XXI. 

ON     HYDROSTATICS. 


I  HE  mechanical  properties  and  affections  of  fluids,  and  the  laws  and  pheno- 
mena 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  fre- 
quently under  the  necessity  of  calling  in  the  assistance  of  experimental  deter- 
minations; and  for  this  reason,  as  well  as  others,  the  science  of  hydrod3'na- 
mics  may  with  propriety  hold  a  middle  rank,  between  mathematical  mechanics 
and  descriptive  physics.  In  treating  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  combi- 
nation of  circumstances  in  which  we  have  occasion  to  exarnine  their  conse- 
<|uences;  and  it  requires  only  a  certain  degree  of  attention  and  of  mathema' 
vol..   I.  L  1 


258  LECTUBE    XXI. 

tical  knowledge,  to  be  perfectly  convinced  of  the  justice  of  all  our  conclusions, 
without  any  reference  to  experimental  proof.  But  here  our  abstract  reason- 
ings begin  to  fail;  and  whether  from  the  imperfection  of  our  modes  of  consi- 
dering 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  unsuc- 
cessful. At  the  same  time  it  will  appear,  that  by  a  proper  mixture  of  calcu- 
lation with  experiment,  we  may  obtain  sufficient  foundations  for  all  such  de- 
terminations 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, 
Acustics,  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 
first  subdivision  which  we  shall  consider,  will  relate  to  the  laws  of  the 
eqivilibrium  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  maritime  nation,  as  any  de- 
partment 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  con- 
veyance 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  convinced  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  pro- 


ON    HYDROSTATICS.  Q^g 

^erties  of  fluids.  la  these  departments,  although  we  eftn  by  no  means  ex- 
plain 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  unin- 
telligible 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  inextricably  obscure.  Whether  this  ex- 
planation 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  phenomena  of  light  depend  on  causes  wholly 
deducible  from  the  mechanics  of  solid  bodies. 

We  must  commence  the  subject  of  hydfostaties,  or  the  doctrine  of  the  equili- 
brium of  liquids,  With  a  definition  of  the  essential  characteristics  of  a  fiui^i 
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,  witliout  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  mathematically,  in  a  manner  strictly 
demonstrative,  yet  we  may  obtain  from  mathematical  considerations  a  suffi- 
cient conviction  of  its  truth,  without  assuming  it  as  a  fundamental  or 
axiomatic  character.  A  fluid  which  has  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. 

W6  shall  for  the  present  consider  a  liquid  as  without  either  compressibility 
or  expansibility:  and  we  must  neglect  some  other  physical  properties  essen- 
tial to  liquids,  such  as  cohesion  and  capillary  attraction;  although, in  reality 
the  particles  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, 


260  lECTURE    XKI. 

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  con- 
cerned 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  simi- 
lar to  those  which  will  hereafter  be  examined,  when  we  investigate  the  subject 
of  pneumatic  equilibrium. 

The  first  law  of  hydrostatics  which  arrests  our  attention,  is  this,  that  the  sur- 
face of  every  homogeneous  gravitating  fluid,  when  at  rest,  is  horizontal.  If  any 
part  of  the  surface  were  inclined  to  the  horizon,  the  superficial  particles  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,  how- 
ever 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  re- 
servoir: and  it  is  obvious  that  the  tube  has  acquired  no  new  power  of  sup- 
porting it  from  being  tliawed:  consequently,  the  water  would  have  remained 
in  equilibrium  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  magni- 
tudes, it  is  necessary,  if  the  tubes  are  small,  to  apply  a  slight  correction  on 
account  of  the  actions  of  the  tubes  on  the  fluids  which  they  contain, 
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  Q,39-) 

If  several  separate  fluids  of  different  kinds  be  contained  in  the  same  vessel^ 
they  'vill  never  remain  at  rest  unless   all   the  surfaces   intervening  between 


ON    HTDROSTATICS.  fS.6l 

them  be  horizontal;  and  this  is  in  fact  the  state  of  the  surface  of  common  li- 
quids, which  is  exposed  to  the  pressure  of  the  atmosphere. 

The  power  of  gravitation,  strictly  speaking,  does  not  act  precisely  in  paral- 
lel 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  surface 
of  a  fluid  must  always  be  perpendicular  to  the  direction  of  the  joint  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  ob- 
served 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,  iu  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  surface  will  be  of  more  diffi- 
cult determination.     (Plate  XX.  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  equili^ 
brium  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  imaginaryf 
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  sur- 
foce  of  the  fluid.  Thus,  if  we  have  a  vessel  of  water  one  foot  deep,  each 
•quare  foot  of  the  bottom  will  sustain  the  pressure  of  a  cubic  foot  of  water, 


2(53  tECTUBE    XXT. 

or  nearly  1000  ounces;  if  we  have  a  vessel  of  mercury  an  inch  in  depth,  each 
square  foot  will  sustain  a  pressure  of  one  twelfth  part  of  a  cubic  foot  of  mer- 
cury, or  11 30  ounces;  the  atmosphere  presses  on  each  square  foot  of  the  earth's 
surface  with  a  force  of  about  34000  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  portion  of  the  bottom;  but  we  cannot  esti- 
mate the  force  sustained  by  any  large  portion  of  the  side,  without  considering 
the  difl'erent  depths  below  the  surface,  at  which  its  difierent  parts  are  si- 
tuated. 

It  is  obvious  that  if  wc  conceive  a  fluid  to  be  divided  by  an  imaginary 
sorface  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  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  increasing  or 
diminishing  any  of  the  pressures  concerned :  and  we  should  thus  obtain  a 
vessel  similar  to  that  which  was  the  subject  of  our  investigation,  the  pres- 
sure 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 


ON    HYDROSTATICS.  v         263 

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  surface  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  subjected  to  its  action. 
And  if  the  effect  of  the  column  be  increased  by  any  additional  pressure,  in- 
dependent of  its  weight,  that  pressure  may  be  represented  by  supposing  the 
height  of  the  column  to  be  augmented  ;  and  the  effect  of  the  additional  pres- 
sure 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  mechanical  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  com- 
mon 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  pro- 
portion 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 


264  LECTURE    XXI. 

unequal  diameter,  a  fluid  must  stand  at  tlie  same  height  in  both  of  them,  ia 
order  to  remain  in  equiUbrium :  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  belo%T 
remaining  unaltered :  consequently  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  sec- 
tion 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  respira- 
tion, 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,  w^hile  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  de- 
scending 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.  I'hus,  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  su])port  the  side  of  the  cube  externally  by  a 
force  applied  at  a  single  point*  that  point  must  be  at  tl\e  distance  of  one 


ON    HYDaOSTATlCS.  265 

third  of  the  height  only  from  the  bottom.  For  the  pressure  at  each  point 
may  be  represented  by  a  line  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  cerftre  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  pro- 
portional 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  de- 
termination is  of  no  practical  utility,  since  the  portions  of  the  forces,  which 
act  in  different  directions,  must  always  destroy  each  other.  Thus,  the  per- 
pendicular pressure  on  the  whole  internal  surface  of  a  sphere  filled  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  spe- 
cific gravities;  for  it  is  obvious  that  the  greater  density  of  the  one  will  pre- 
cisely 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  con- 
siderations are  necessary  for  the  determination  of  the  equilibrium  of  fluids  and 
solids  with  each  other;  and  in  the  first  place  the  properties  of  floating  bodies 
require  to  be  investigated, 

VOL.  I.  M  m  - 


255  LECTURE    XXI. 

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  dimi- 
nished, 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  will  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  continue  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  interstices  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  immers- 
ed 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  equi- 
librium, with  respect  to  stability,  is  determined  by  the  position  of  the  meta- 
centre,  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  inallcircum- 
:4tances,  and  the  nature  of  the  equilibrium  will  depend  on  the  distance  of  the 


ON    HYDROSTATICS.  267 

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  tlie  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  -rW  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  com- 
bined with  others  which  take  place  in  a  transverse  direction:  a  ship,  for  ex- 
ample, may  roll  on  an  axis  in  the  direction  of  her  length,  and  may  heel,  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  equivalent 
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  esti- 
mated by  the  weight  of  a  portion  of  the  fluid   equal  in  bulk  to  the  solid. 


268  LECTURE    XXI. 

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 
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  he- 
misphere, being  partly  supported  on  an  axis,  which  is  in  the  plane  of  the  sur- 
face 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  surface 
will  also  be  such  that  the  common  centre  of  gravity  of  the  fluid^and  the  ves- 
sel 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  calcula- 
tion :  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  ves- 
sel 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  ia 


ON    HYDROSTATICS.  Q69 

contact  with  upright  walls,  without  allowing  the  water  to  run  out,  the  na- 
ture 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,  supposing  the 
fixed  points  at  the  distance  of  its  diameter;  but  if  the  weight  of  the  bottom 
be  neglected,  the  curvature  will  be  every  where  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  adapt- 
ed to  the  equilibrium  of  arches,  intended  for  supporting  the  weight  of  superin- 
cumbent fluids,  or  of  such  soft  materials  as  approach  nearly  in  their  operation 
to  more  perfect  fluids.     (Plate  XIX.  Fig.  250.) 


\ 


sro 


LECTURE  XXII. 


ON    PNEUMATIC    EQUILIBRIUM. 


J.  HE  laws  of  the  pressure  and  equilibrium  of  liquids,  which  are  the  peculiar 
subjects  of  hydrostatics,  are  also  appHcable  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- 
niatostatics,  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  transfer- 
ring airs  and  gases  from  vessel  to  vessel,  in  the  pneumatic  apparatus_xused  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  expansive  force  of  the  aif.  (Plate  XIX.  Fig. 
S51.) 

If  the  diameter  of  the  tube,  in  an  apparatus  of  this  kind,  were  very  small  in 
comparison  with  tlie  bulk  of  the  air  confined,   the  column  of  mercury  would 


ON    PNEUMATIC    ZQUHIBRIUM,  S,7l 

be  raised,  in  the  ordinary  circumstances  of  the  atmosphere,  to  tlie  lieight  of 
nearly  30  inches.  But  supposing  the  magnitude  of  the  tube  such,  that  the 
portion  of  air  must  expand  to  twice  its  natural  bulk,  before  the  mercury  ac- 
quired 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  pres- 
sure 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  atmosphere,  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  dej)th  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. 

Not  only  the  common  air  of  the  atmosphere,  and  other  permanently  elastic 
gases,  but  also  steams  and  vapoMs  of  all  kinds,  appear  to  be  equally  subject 
to  thisuniversallaw:  they  must,  however,  be  examined  at  temperatures  suffici- 
ent to  preserve  them  in  a  state  of  elasticity ;  for  example,  if  we  wished  to  deter- 
mine the  force  of  steam  twice  as  dense  as  that  which  is  usually  produced,  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  confin- 
ed 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  gra- 
vitation, 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 


273  LECTURE   xxir, 

specific  gravity  of  the  air,  even  if  the  exhaustion  is  only  partial,  provided 
that  we  know  the  pvoportion  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  afire;  and  the  effect  is 
made  more  conspicuous,  when  either  the  hydrogen  gas,  or  the  heated 
air,  is  confined  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 
destruction  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  the  air 
by  a  much  smaller  weight  of  brass,  with  an  index,  which  shows,  on  a  graduated 
scale,  the  degree  in  which  the  large  ball  is  made  to  preponderate  in  the  re- 
ceiver of  the  air  pump,  by  the  rarefaction  of  the  air,  lessening  the  buoyant 
power  which  helps  to  support  its  weight.     (Plate  XIX.  Fig.  252.) 

From  this  combination  of  weight  and  elasticity  in  the  atmosphere,  it 
follows,  that  its  upper  parts  must  be  much  more  rare  than  those  which  are 
nearer  to  the  earth,  since  the  density  is  every  where  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;  consequently 
that  pressure  is  increased  one  twenty  eight  thousandth  by  the  addition  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  in- 
creased 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  10000, 
is  3010,  the  logarithm  of  4,  6030,  and  that  of  8,  9031;  the  logarithms  of 
numbers  always  increasing  in  continual  proportion,  when  the  numbers  are 
taken  larger  and  larger  by  equal  steps.     (Plate  XIX.  Fig.  253.) 


ON    PNEUMATJC    EQUILIBRIUM,  5173 

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,  rf  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  appears  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  28000  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  pre- 
vious knowledge  of  the  eifects  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  10000, 
is  2040;  and  this  is  the  number  of  fathoms  contained  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  distance  of  the  earth's  semi- 
diameter,  or  nearly  4000  miles,  above  its  surface,  the  air,  if  it  existed,  would 
become  sff-  rare,  that  a  cubic  inch  would  occupy  a  space  equal  to  the  sphere 
of  Satura'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,  28000  feet 
high,  supposing  its  density  every  where  equal  to  that  which  it  possesses  at  the 

VOL.    I.  N  n 


*274  lECTURE  xxir. 

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,  tlie  pressure  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  hemis- 
pheres, of  sufficient  magnitude  to  withstand  the  draught  of  the  emperor's  six 
coach  horses,  pulling  with  all  their  force  to  separate  them.  By  a  similar  pres- 
sure,athin  square  bottle  may  be  crushed  when  it  is  sufficiently  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  surface, 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;  and  his  pupil  Torricelli  confirmed  his 
doctrines  by  employing  a  column  of  mercury,  of  sufficient  height  to  overcome 
£he  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  sueking  up  a 
fluid  through  a  pipe,  with  the  mouth  or  otherwise,  the  pressure  of  the  air  is 
but  partially  removed  from  the  upper  surface  of  the  fluid,  and  it  becomes  ca- 
pable 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  ex- 
haustion of  one  fourth  of  the  air  of  the  cavity  would  enable  us  to  raise  water 
to  the  height  of  84-  feet,  and  mercury  to  7i  inches,  above  the  level  of  the  re- 


ON    PNEUMATIC    EQUILIBRIUM.  275 

servoir  from  which  it  rises.  \Ye  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  fiiiference  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  hy- 
drostatic or  pneumatic  pressure. 

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  sur- 
face 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  tlie  tube. 
If  such  a  tube  be  placed  under  the  receiver  of  an  air  punip,  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  tl>e  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  Ti  and  3 1  inches.  This  well  known  instrument,  from  its  use  in  mea- 
suring the  weight  of  the  air,  is  called  a  barometer.  In  the  same  manner  a  co- 
lumn of  water  from  30  to  35  feet  in  height  may  be  sustained  in  the  pipe  of  a 
pump;  but  if  the  pipe  Avere  longer  than  this,  a  vacuum  would  be  produced  in 
the  upper  part  of  it,  aiul  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  posi- 
tion, 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  sur- 
face 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  fulty  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 


276  LECTURE    XXII. 

shaken  in  it  for  a  considerable  time,  the  tube  being  held  in  an  inverted  posi- 
tion; and  where  great  accuracy  is  required,  the  mercury  must  be  boiled  in 
the  tube.  The  reservoir  most  commonly  employed  is  a  flat  wooden  boxy 
with  a  bottom  of  leather ;  the  cover,  which  is  unscrewed  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  brought  to  a  certain  level, 
indicated  by  a  float,  whatever  portion  of  it  may  be  contained  in  the  tube; 
but  the  necessity  of  this  adjustuicnt  may  be  easily  avoided,  by  allowing  the 
mercury  to  play  freely  between  two  horizontal  surfaces  of  wood,  of  moderate 
extent,aii  I  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  between 
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,  wi^'hout  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  sui)posing  the 
law  of  compression  to  resemble  that  of  the  air,  it  may  be  inferred  that  at  the 
depth  of  100  miles,  its  detisity  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. 


err 


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  dithculties  attending  the  mathematical  theory  of  hy- 
draulics, so  much  has  already  been  done,  by  the  assistance  of  practical  inves- 
tigations, that  we  may  in  general,  by  comparing  the  results  of  former  experi- 
ments 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  begin- 
ning of  thfl  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  application  of  the  theory  of  hy- 
draulics to  practical  cases,  and  to  affect  the  modes  of  calculation  so  materially, 
that  it  will  require  to  be  discussed,  hereafter,  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  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  as- 
cending 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  froitt  a  height  of  1  foot,be  caused  to  act  in  any  maanc*- 


273  LECTURE    XXIII. 

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  de- 
termination of  the  motions  of  fluids,  and  that  in  many  cases  it  becomes  necessary 
to  suppose  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  pro- 
per 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  assum- 
ed by  Bernoulli,  without  either  demonstration,  or  even  the  appearance  of 
perfect  accuracy,  is  this,  that  all  the  particles  of  a  fluid  in  motion,  contained  in 
anyone  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  irregular,  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  near- 
est 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 
ai-e  in  rapid  motion;  but  still  the  calculations  founded  on  the  hj'pothesis 
agree  tolerably  well  with  experiments.  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  ascend- 
ing force  required  for  the  escape  af  the  small  portion  which  is  flowing  through- 
the  orifice,  and  the  whole  ascending  force  may,  therefore,  be  supposed  t& 
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. 


OK  THE  THEORY  OF  HYDRAULICS.  279 

'  -  Tlus  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  30  feet  in  a 
second,  and  a  circular  orifice  an  inch  in  diameter  would  discharge  exactlv  an 
ale  gallon  in  a  second.  In  the  same  manner,  the  pressure  of  the  atmosphere 
being  equal  to  that  which  would  be  producetl  by  a  column  of  air  of  uniform 
density  28000  feet  high,  tlie  air  would  rush  into  a  vacuum  with  a  velocity 
of  more  than  1300  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  mo- 
tion 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  determined 
in  a  similar  manner.  Thus,  the  pressure  of  a  column  of  water,  1  foot  in  heio-ht, 
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  mercury  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  escape  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  as- 
sumes when  it  runs  through  an  orifice  in  a  thin  plate :    for  in  such  cases  the 


) 


280  LECTURE    XXIII. 

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  j  and  the  quantity  discharged  is  only  five  eighths  as 
great  as  that  which  the  whole  orifice  would  furnish,  according  to  the  preced- 
ing 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  dis- 
charged in  a  direction  nearly  perpendicular,  it  rises  almost  as  high  as  the  sur- 
face 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  eifect  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  calculation  of  the 
magnitude  of  this  contraction,  from  the  equilibrium  which  must  subsist  be- 
tween the  centrifugal  forces  of  the  particles,  as  they  pass  out  of  the  orifice, 
describing  various  curves,  according  to  their  various  situations,  and  the  pres- 
sure 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  contraction:  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,  281 

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  tlie  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  Bernoulli'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,   suppos- 
ing 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  experiments  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;  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  eff'ects  of  this  kind,   and  both' 
Venturi  and   Dr.  Matthew  Young  have   observed,  that  a  short  pipe  has  no 
effect,  ill  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  ah-- 
sence  of  atmospherical  pressure,  it  might  be  produced  by  an   accidental  co- 
hesion, like  that  which  sometimes  causes  a  column  of  mercury  to  remain  sus<-- 
pended  in  similar  circumstances.     (Plate  XX.  Fig.  25?.) 
VOi.   J.  oo 


i-r^ 


gSa  l,KGTUBK    XXIII. 

Tlie  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  samt  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  vreve  employed,  some  time  would 
be  required  before  the  velocity  became  uniform  ;but  in  such  cases  the  retardation, 
arising  from  friction  is  so  considerable,  as  to  cause  a  still  greater  deviatioa  tiom 
the  quantity  which  would  be  discharged  by  a  shorter  pipe  in  the  same  time. 

When  the  aperture,  through  which  a  tluid  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  fir^d  the 
quantity  of  the  discharge,  by  supposing  the  whole  velocity  equal  to  two 
thirds  of  the  velocity  at  the  lowest  point.  And  we  ma)  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  con- 
tinued, 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  consi- 
dering 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  la\v  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  uni- 
formly continued;  and  in  the  time  that  such  a  vessel  occupies,  in  emptying 
itgelf,  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. 


ON    THE   THEORY   OF  HYDRAULICS.  tlS 

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  im- 
mersion of  the  orifice  in  a  large  reservoir  has  been  found  to  make  no  differ, 
ence  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  orifices  of  any  dimen- 
sions, 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  deter- 
mining the  velocity  of  a  fluid,  forced  through  a  vessel  divided  by  several  par- 
titions, with  an  orifice  in  each;  if  the  orifices  are  small  in  proportion  to  their 
distance  from  each  other,  and  if  they  are  turned  in  different  directions,  each 
orifice  will  require  an  additional  pressure,  equivalent  to  the  whole  velocity 
produced  in  it:  but  if  the  partitions  occupy  a  small  part  only  of  the  vessel, 
and  are  placed  near  to  each  other,  the  retardation  will  be  much  less  con- 
siderable. 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  expansions,  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  at- 
mosphere forces  up  the  fluid  from  the  higher  vessel,  until  the  equilibrium  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  coiilck 
no  longer  continue  to  run.     (JPlate  XX.  Eig.  258.), 


<2f84  LECTURE    XXIII. 

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  cor- 
responding 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  si- 
phon, 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,  descending  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  descending  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  gravi- 
tation in  a  pipe  16  feet  long,  for  half  a  second  only,  should  acquire  the  velo- 
city of  32  feet  in  a  second,  which  woukl  require,  in  common  circumstance.% 
the  action  of  the  same  force  of  gravitation  for  a  whole  second,  and  this  fact 
may  be  considered  as  favourable  to  the  opinion  of  those,  who  wish  to  esti- 
mate the  magnitude  of  a  force,  rather  by  the  space  through  which  it  is  con- 
tinued, 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  produce,  or  to  develope,  a  portion  of  accelerating  force 
M'hich  is  actually  greater  than  the  weight  of  the  particles  immediately  con- 
cerned. 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,  niust  acquire,  either  for  itself  or  for  some  other 
particles,  a  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,  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  sta- 
tionary, will  be  very  nearly  equal  to  the  height  of  the  funnel  above  its  sur- 
face, so  that  the  same  height  produces  the  same  velocity  in  both  cases. 
^Plate  XX.  Fig.  259-) 


ON    THE    THEOUY    OF    HVDUAULICS.  285 

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  at- 
mosphere. The  water  entering  the  orifice  must  immediately  acquire  a  velo- 
city etjual  to  that  of  the  whole  water  in  the  pipe,  otherwise  there  would  be 
a  vacuum  in  the  upper  part  of  the  \npc,  which  the  pressure  of  the  atmo- 
sphere 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  counterprcssure  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  gravi- 
tation is  expended  in  producing  pressure  only;  so  that  the  pressure  of  the 
atmosphere  on  the  water  in  the  funnel  becomes  completely  analogous  to  the 
pressure  of  a  reservoir  of  water,  of  the  same  height  with  the  pipe.  The  cir- 
cumstance, 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  ori- 
fice; 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  derived  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  tlie  sup- 
ply of  the  fluid  be  scanty,  and  especially  if  it  approach  the  orifice  obliquely, 
the  pressure  of  the  atmosphere,    and  the  centrifugal  force  of  the  particles 


S8(5  tzcTvnx  xxiii. 

which  must  necessarily  revolve  round  tile  orifice,  will  unite  in  producing  a 
vacuity  in  the  centre;  and  when  this  happens, the  discharge  is  considerably  di- 
minished. 

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  is  ex- 
hausted, as  far  as  the  level  of  its  upper  orifice.  And  from  this  circumstance, 
the  phenomena  of  some  intermitting  springs  have  been  explained,  which 
only  begin  to  run,  when  the  resei-voirs  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  re- 
servoirs, 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  velocity  with  which  the 
particles  must  escape  laterally,  before  they  begin  to  descend.  The  truth  of 
this  conclusion  is  easily  confinned  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  horizontal  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  pimple  projectiles :  but  the  experiment 
is  most  conveniently  exhibited  in  the  motion  of  a  jet.     (Plate  XX.  Fig.  262.) 


ON    THE    THEORY    OF    HYDRAULICS.  2^7 

We  have  hitherto  considered  the  motions  of  fluids  as  continued  pvirtcipally 
in  the  same  direction ;  but  they  are  frequently  subjected  to  alternations  of 
motion,  which  bear  a  considerable  analogy  to  the  vibrations  of  pendulums; 
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  downwards  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  will  be  continued  by  the  inertia  of  the  particles  of  the  fluidi 
until  it  be  destroyed  by  the  difl^erence  of  pressures,  which  now  tends  to  retard' 
it;  and  this  alternation  will  continue,  until  the  motion  be  destroyed  by  fi-ic- 
tion  and  by  otlier  resistances.  It  is  also  obvious,  that  since  any  two  vibra- 
tions, in  which  the  forces  are  proportional  to  the  spaces  to  be  described,  arc 
performed  in  equal  times,  these  alternations  will  require  exactly  the  sam^' 
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  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  obHque  di- 
rection, provided  that  the  whole  length  remained  unaltered.  In  such  a  tube 
also,  all  vibrations,  even  if  of  considerable  extent,  would  be  performed  in  the 
same  time,  and  would  long  remain  nearly  of  the  same  magnitude;  but  in  ai 
single  tube,  open  below,  the  vibrations  would  continually  become  less  ex-" 
tensive,  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  sup- 
posed 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  demon- 
stration on  it.  The  motions  of  waves  have  been  investigated  in  a  new  and 
improved  manner  by  Mr.  Lagrange;  and  Ihave  given  a  concise  demonstra^ 


288  LECTURE    XXIII. 

tion  of  a  theorem  similar  to  his, but  perhaps  still  more  general  and  explicit.  It 
appears  from  these  determinations,  that  sui)posing  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  th.ough  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  considerably  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;  iu 
other  cases,  where  a  number  of  small  waves  follow  each  other  at  intervals- 
considerably  less  than  the  deptli,  I  have  endeavoured  to  calculate  the  retar- 
dation 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  detenninations  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  elevationsand  depressions,extending  their  in- 
fluence in  both  directions,  will  produce  efi'ects  only  half  as'great  on  each  side, 
and  those  effects  will  then  be  continued  until  they  are  destroyed  by  resist- 
ances 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 
scries,  in  the  same  manner  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  diflterence  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  up- 
right 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  constitutes  the 


ON    THE    THEORY    OP    HYDRAULICS.        .  289 

reflection  of  a  series  of  waves,which  is  easily  observed, wlien  they  strike  against  a 
steep  wall  or  bank  ;  and  when  this  reflection  is  sufficiently  reg-ular,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.  §63.) 

But  those  series  of  waves  which  are  usually  observable  in  any  broad  sur- 
face, and  which  constitute  a  number  of  concentric  circles,  are  usually  re- 
flected 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  produce  precisely  the 
same  eflfect  as  a  fixed  obstacle;  consequently  the  law  of  reflection  at  equal 
angles  is  a  very  simple  inference  from  this  mode  of  reasoning.  (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  thelawof  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  m  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,     Tha- 

VOL.    I.  J.  p 


&90  LECTURE    XXIII. 

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  may  fall  on  a  white 
surface,  extended  in  an  inchned  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  pro- 
portion to  its  own  breadth,  into  the  surface  of  a  part  of  the  water  which  is 
at  rest,  it  diverges  from  the  aperture  as  from  anew  centre;  but  when  the 
aperture  is  considerably  wider  than  the  wave,  the  wave  confipes  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  waves,  proceeding  from  centres  near 
each  other,  begin  their  motions  at  the  same  time,  they  must  so  cross,  each 
othei',  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  ob- 
served, 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  ap- 
plication 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  evi- 
dence of  the  truth  of  some  facts,  which  are  capable  of  being  applied  to  the  ex- 
planation of  some  of  the  most  interesting  phenomena  of  acustics  and  optics. 


ON    THI   THEORY    OP   HYDRAULICS.  2pi 

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 
clastic  pipe,  and  which  receives  an  impulse  at  any  part  of  the  pipe,  will 
transmit  its  effects,  with  the  same  velocity,  as  a  Avave  would  have  in  a  reser- 
voir, 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  bloodvessels; 
the  pulse  moves  on  with  great  rapidity,  the  elastic  force  of  the  vessels  being 
considerably  assisted  by  the  temporary  actions  of  the  muscular  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 
it5  own. 


!■;>■ 


293 


LECTURE  XXIV 


ON    THE    FRICTION    OF    FLUIDS. 


\V^E  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  Avith  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  laboriously 
and  judiciously  investigated  by  the  Chevalier  de  Buat,  it  was  almost  impossi- 
ble to  apply  any  part  of  our  theoretical  knowledge  of  hydraulics  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  in- 
clined 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  gravita- 
tion, and  the  motion  is  always  accelerated.  But  the  resistance  to  the  mo- 
tions of  fluids  arises  princij^lly  from  different  causes;  not  from  the  tenacity  of 


ON    THE    FRICTION    OF    FLU"lDS.  293 

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  curvature  assumed  by  the  outline  of  a 
stream  of  water  issuing  from  a  simple  orifice,  which  constitutes  the  contrac- 
tion already  described,   is  very  nearly  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  w^as  in  a  horizontal  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  inde- 
pendent of  it. 

It  is  obvious  that  wherever  the  friction  varies  as  the  square  of  the  velocity, 
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  be- 
come 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  speed- 
ily 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  ac- 
quired a  stationary  velocity,  is  wholly  employed  in  overcoming  the  friction 
produced  by  the  bottom  and  the  banks.  -       . 


394  lECTURE   XXIV. 

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  ho- 
rizon, we  may  determine,  by  following  the  methods  adopted  by  Mr.  Buat, 
the  velocity  of  any  river  of  which  we  know  the  dimensions  and  the  inclinar 
tion.  Supposing  the  whole  quantity  of  water  to  be  spread  on  a  horizontal 
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  proportional  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  se- 
cond will  be  nearly  equal  to  the  product  of  this  fall  multiplied  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  £800  yards  will  be  about  6~  inches,  which,  multiplied  by  360  inches, 
gives  2340  inches  for  the  square  of  the  mean  velocity,  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  determination,  some  fur- 
ther corrections  would  be  necessary,  on  account  of  the  deviation  of  the  resist- 
ance 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. 

It  is  obvious  that  the  friction  of  a  fluid,  moving  on  the  surface  of  a  solid 
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  immediate 
contact  with  the  solid,  might  remain  at  rest,  and  the  remaining  mass  of  the 
fluid  might  slide  over  this  portion  without  any  retardation.  It  appears,  how- 
ever, that  the  water  in  contact  with  the  bottom  of  a  river  moves  with  a  very 
considerable  velocity,  and  the  v/ater  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  sur- 
face of  a  solid.     This  internal  friction  operates  gradually   throughout  the 


ON    THE    I'-RICTIOV    OF    FLUIDS.  295 

water;  the  surface  being  retarded  by  the  particles  immediately  below  it, 
those  particles  i)y  the  next  inferior  stratum,  and  each  stratum  being  actuated, 
besides  its  OM'n  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,  isi 
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  ve- 
locity at  the  bottom, by  subtracting  from  it  the  same  number:  thus  the  square 
root  of  48^- being  nearly  T,  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-}. 
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  tliem,  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  ele- 
vated in  the  middle. 

The  course  of  a  river  is  sometimes  interrupted  by  a  were  or  a  fall,  natural 
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  consi- 
derable height;  supposing  the  whole  section  of  the  were  to  be  such  an  aper- 
ture, 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  velo- 
city of  the  river.  The  extent  of  the  swell  caused  by  a  were,  or  by  any  par- 
tial elevation  thrown  acj-oss  the  bed  of  a  river,  may  also  be  found  by  first 


fi^5  LECTURE    XXIV. 

determining  the  height  at  which  the  surface  must  stand  immediately  above 
the  were,  and  then  calculating  the  inclination  of  the  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  dimen- 
sions of  rivers,  as  well  as  from  immediate  observation,  that  a  considerable 
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  sometime* 
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  ve- 
locity, 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  curva- 
ture. This  effect  is  probably  occasioned  by  the  centrifugal  force,  which  ac- 
cumulates the  water  on  that  side;  so  that  the  banks  are  undermined,  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  efJect  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  pf  the  river's  motion, 
and  the  more  as  they  are  more  abrupt. 

It  has  sometimes  been  imagined,  that  because  the  pressure  of  fluids  is  pro- 
pagated equally  in  all  directions,  their  motions  ought  also  to  diverge  in  a  si- 
milar manner;  but  this  opinion  is  by  no  means  well  founded,  even  with 
respect  to  those  particles  which  receive  their  motions  in  an  unlimited  reser- 
voir from  the  impulse  of  a  stream  which  enters  it.  An  experiment,  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 


ON    THE    FRICTION    OF    FLUIDS.  297 

four  times  as  much  air  as  it  naturally  contained  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  iu 
the  air  of  the  box.     ( Plate  XXI.  Fig  268.) 

Professor  Venturi  has  also  made  several  experiments  of  a  similarnature  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  sur- 
face 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  the  water  of  the  vessel,  until  its  surface  be- 
comes 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  equilibrimn, 
theadhesionof  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  Philo- 
sophical Transactions.  Thus,  if  we  bend  a  long  plate  of  metal  into  the  form 
of  the  letter  S,  and  suspend  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  at- 
mosphere  being  diminished  by  the  centrifugal  force  of  the  current,  which 

VOL.  I.  Q  q 


glides  along  the  convex  surface,  because  it  finds  a  readier  .passage  in  the  neigh- 
bourhood of  the  solid,  towards  which  it  is  urged  by  the:  impulse. of  the  parti- 
cles 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.  2/0,    ^71.) 

From  considerations  similar  to  those  by  whichithe.V'clocity  of  a  river  tis  de- 
termined, 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  dia- 
meter: but  a  part  only  of  the  force  of  gravity  is  now  expended  in  overcoming 
the  friction,  the  rest  being  employed  in  producing  the  momentum  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  in- 
creased 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,  discharge  about  five  times  as  much 
water  as  the  former,  although  of  only  twice  the  diameter;  and  this  circum- 
stance 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 
Avater,  which  may  be  calculated,  if  it  be  required;  hut  if  a  pipe  be  fixed  into 
another  through  which  the  water  is  moving  very  rapidly,  in  a  direction  con- 
trary 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  dis- 


ON    THE    FRICTION    OF    FLUIDS.  299 

charge  nothing  at  all ;  on  the  contrary,  like  the  air  in  Hauksbee'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  si- 
milar nature  sometimes  happens  in  the  animal  economy.  When  an  artery  is 
dilated  so  as  to  fsjrm  an  aneurism,  it  has  been  observed  that  the  artery  is 
visually  distended  above  the  cavity;  and  this  effect  is  easily  understood  from 
the  actual  increase  of  resistance  which  the  aneurism  produces,  united  perhaps 
with  the  previous  debility  of  the  artery...       ,'U 

Mr.  Gerstner,  has  found  by  some  very  accurate  observations  on  the  motion 
of  water  in  v6ry  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  ca- 
pillary 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. 


/  -•    1  .  t  (J 


300 
LECTURE    XXV.. 

■  ON    HYDRAULIC    PRESST^rW. 

The  mutual  eflfects  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  hy- 
draulics  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  con- 
tinued 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   inten- 
sity may,  however,  be   easily  diminished  by  means  of  an  air  vessel  com- 
municating  with   the  pipe,   which  will  allow  the  motion  to  be  changed  in  a 
less  abrupt  manner.     But  in  the  principal  cases  Avhich  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. 


ON    HYDRAULIC    PRESSURE.  301 

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  tlie  same  time  be  causing  pressure;  and  when  the  motion  produced  is  in 
any  other  direction  than  a  vertical  one,  its  obliquity  must  be  immediately  de- 
rived from  the  reaction  of  the  vessel,  or  of  some  fixed  obstacle;  for  it  is  ob- 
vious that  a  vertical  force,  like  that  of  gravity,  cannot  of  itself  produce  an 
oblique  or  a  horizontal  motion. 

If  a  small  stream  descends  from  the  bottom  of  a  vessel,  the  weight  expend- 
ed 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  connected 
by  means  of  a  thread  passing  over  a  pulley,  and  one  of  them  begins  to  des- 
cend, 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  diminution  of  the 
pressure  in  that  direction  will  be  nearly  the  same  as  if  the  vessel  were  sub- 
jected to  an  equal  pressure  of  any  other  kind  in  a  contrary  direction;  andif 
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  pror 


302  LECTURE    XXV. 

ducing  the  v'elocity.  And  this  result  is  confirmed  by  experiments:  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  pre- 
vent 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  pressure  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  proportional  to 
its  square.  This  inference  was  first  made  in  a  more  simple  manner,  from  com- 
paring 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 
tifect  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  mo- 
tion, 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  dimen- 
sions of  the  reservoir,  containing  the  fluid,  might  produce  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,  strik- 
ing on  the  surface  exposed  to  it  with  a  certain  velocity:  and  in  this  case  the 
force  must  be  considered  as  simply  proportional  to  the  relative  velocity,  and 
not  to  its  square.  For  want  of  this  consideration,  the  effects  of  water  wheels 
have  frequently  been  very  erroneously  stated. 

When    a  jet  .strikes  a    plane  surface  obliquely,  its  force,   in  impelling 


ON    HYDRAULIC    PRESSURE.  303 

the  body  forwards,  in  its  own  direction,  is  found  to  be  very  nearly  pro- 
portional to  the  height  to  which  the  jet  would  rise,  if  it  were  similarly  in- 
clined 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  somewhat  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,  ac- 
cording to  the  simplest  theory  of  the  resolution  offerees,  might  be  found  bv 
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  mea- 
sure of  the  resistance,  tlie  whole  side  representing  the  resistance  to  the  sanie 
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  de- 
grees 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  lube,  the  fluid 
within  it  will  rise  half  as  high  again  as  if  the  whole  mouth  were  open.  It  h 
also  observable,  that  two  bodies,  equal  and  similar  in  the  form  of  the  part 
meeting  the  fluid,  undergo  very  <lifferent  degrees  of  resistance  according  to 
the  forms  of  their  posterior  terminations,  and  that  a  thin  circular  plate  is 
much  more  retarded  than  a  long  cyHnder  of  the  same  diameter.  These  cir- 
cumstances are  utterly  inexplicable  upon  the  vague  approximation  of  sup- 
posing the  resistance  produced  by  the  immediate  impidse  of  separate  particles 
of  the  fluid  on  the  solid ;  but  they  are  no  longer  surprising,  when  we  consider 
the  true  mode  of  action  of  continuous  fluids,  since  all  the  motion  which  is  j)ro- 
duced  by  the  fluid  in  the  solid  or  by  the  solid  in  the  fluid  is  communicated 
much  more  by  means  of  pressure  than  by  innnediate  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  mo- 
tion, the  pressure  is  increased  before  the  moving  substance,  and  diminished  be- 
hind it;  so  that  the  surface  is  elevated  at  the  one  part,  and  depressed  at  the  other, 


304  LECTURE  xxr. 

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  witliin  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,  there- 
fore,  expect  an  elevation  of  about  a  foot  before  the  body,  and  an    equal  de- 
pression  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  tlie  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  negative  pressure  will  be  considerably  diminished.     For  this 
reason,  the  bottoms  of  ships  are  made   to  terminate  behind  in  a  shape  some- 
what resembling  a  wedge ;  and  the  same  economy  may  be  observed  in  the 
forms  of  fishes,  calculated  by  nature  for  following  their  prey  with  t.he  great- 
est 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  ma- 
terial 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  indi- 
cate 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  substituting  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 


ON    HYDRAULIC    PRESSURil.  S05 

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  sepa- 
rately. Accordingly  it  is  found  that  no  calculation, deduced  from  experiments 
on  the  resistance  opposed  to  oblique  plane  surfaces,  will  determine  with  ac- 
curacy 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  re- 
sistance to  a  flat  circular  substance  ©f  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  vi^hich  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  small- 
er 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  resist- 
ance 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 

VOL.    T.  B  r 


30&  LECTURE    XXV. 

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  re- 
sistance 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 
160000,  and  the  velocity  itself  400  feet  in  a  second;  if  a  stone  of  such  di- 
mensions 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.  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,  therefore,  have  been  about  1 25,  and  the  velocity  1 1  feet  in  a 
second,  which  is  no  greater  than  that  with  which  a  person  would  descend,  in  leap- 
ing from  a  height  of  two  feet,  without  stooping.  Mr.  Garnerin  found  the  velo- 
city even  less  than  this,  and  it  is  not  improbable  that^the  concave  form  of  the 
parachute  might  considerably  increase  the  resistance.  Thus,  Mr.  Edgeworth 
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.  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  por- 
tion, 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 


ON    HYDRAULIC    PRESSURE,  307 

ball  moves  slowly,  its  effect  at  any  instant  is  in  some  degree  divided  through- 
out 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  11 30  feet  in 
a  second,  and  a  cannon  ball  may  be  discharged  with  a  velocity  of  aOOO;  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  have  attained  by  the  mere  hy- 
drostatic pressure  of  the  water  at  a  depth  so  inconsiderable.  But  a  more 
powerful  cause  than  this  appears  to  be  the  continual  succession  of  new  sur- 
faces 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  obliqvie  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. 


308 


LECTURE  XXVI. 

ON    HYDROSTATIC    INSTRUMENTS,    AND    HYDRAULIC 

ARCHITECTURE. 


At  E  have  now  examined  the  fundamental  laws  of  the  principal  departments 
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,  con- 
taining 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  rais- 
ing and  removing  weights,  in  which  the  principal  hydraulic  and  pneumatic 
machines  will  be  respectively  explained,  and,as  a  part  of  this  subject,  the  appli- 
cation of  pneumatic  force  will  also  be  examined. 

The  principles  of  hydrostatics  are  very  frequently  applied  to  the  determi- 
nation  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,  affbrds  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  plunging  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  pro- 
portion as  the  specific  gravities  of  the  two  fluids.  A  balance  adapted  for  such 
-examinations  is  called  a  hydrostatic  balance;  on  one  sidfi  it  has  a  scale  as 


ON    HTDROSTATIC    INSTRUMENTS,    AND    HYDRAULIC    ARCHITECTURE.  309 

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. 

For  the  speedy  examination  of  a  variety  of  fluids,  differing  but  little  in 
specific  gravity  from  some  known  standard,  a  hydrometer  may  be  very  con- 
veniently employed.  This  instrument  is  said  to  have  been  invented  by  Ar- 
chimedes: 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 
decree  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  ob- 
served ;  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  XXJ, 
Fig.  278.) 

Another  mode  of  ascertaining  the  specific  gravities  of  fluids  differing  bu<. 
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 
vising  to  the  surface  or  sinking.  This  method,  though  not  expeditious,  ap- 
pears to  be  very  secure  from  error:  the  globules  are  sold  by  patent,  adapted 
for  the  measurement  of  the  strength  of  spirituous  liquors. 


kV 


310  LECTURE    xxvr. 

In  whatevei'  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  different  tempera- 
tures. Platina,  the  densest  known  substance,  is  S3  times  as  heavy  as  dis- 
tilled water,  gold  194-,  mercury  134-,  lead  1]^,  silver  11,  copper  9,  iron  and 
steel  7-|.,  stony  substances  usually  about  24-,  rectified  spirits  1^,  naphtha,  the 
lightest  liquid-i^,  cork  about^-,  conjmon  air .g4^,  steam -^sW,  and  pure  hydrogen 
gas  ,  ,,000.  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  com- 
mon 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  hydro- 
meters 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  mixture:  and  that  in  ge- 
neral their  dimensions  are  considerably  contracted.  Thus,  1 8  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  contracted  by  the  addition  of  another  sub- 
stance: thus  iron,  by  the  addition  of  one  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  preserve 
a  horizontal  surface,  and  the  freedom,  with  which  the  particles  qf  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 


•ON    HYDROSTATIC    INSTRUMENTS,    AND    HYDRAULIC    ARCHITECTURE.   311 

proper  place,  unless  the  instrument  be  very  accurately  horizontal,  or  in  tlie 
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  hori- 
zontal, 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  sup- 
plying lamps  with  oil.  It  is  found  that  a  lamp  will  burn,  without  consuming 
any  considerable  portion  of  its  wick,  as  long  as  it  is  amply  supplied  with  oil ; 
hence  it  becomes  desirable  that  it  should  always  Ijife  level  with  the  surface  of  the  re- 
servoir, and  this  may  be  effected  sufficiently  well  by  placing  the  wick  at  the  ■ 
edge  of  a  very  large  vessel,or  atthe  end  of  a  tube  projecting  from  such  avessel,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  em- 
ployed 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  * 
vessel  under  the  lamp;  but  this  refinement  is  too  complicated  to  be  practi- 
cally 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,  a  little  modified,  the  height  of  this 
fluid  may  be  so  regulated,  that  the  surface  of  the  oil  may  remain  almost  in- 
variable, 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  bi- 
sects 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  hea- 
vier 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.) 


312  LECTURE    XXVI. 

The  art  of  embankment  is  a  branch  of  architecture  entirely  dependent  on 
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,ithas  been  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  im- 
portant subjects  have  been  discussed  by  various  writers,  in  many  copious 
treatises,   expressly  devoted  to  hydraulic  architecture. 

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  overturn 
them;  by  their  laterval  adhesion,  the  force  tending  to  thrust  them  aside  hori- 
zontally; 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  substance,  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  l^ss  than  a  right  angle.  The  pressure  acting  on  a  bank  thus 
inclined  will  also  tend  to  condense  the  materials,  and  to  increase  their  la- 
teral adhesion,  and  the  particles  will  become  less  liable  to  crumble  away  by 
their  weight,  than  if  the  surface  were  more  nearly  vertical.  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  brick- 
work,, 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  reservoir.     (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 


ON    HYDROSTATIC    INSTRUMENTS,    AND   HYDRAULIC    ARCHITECTURE;  313- 

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  iu  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.  aas.) 

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  practice  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  unifonn  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  me- 
chanical ;  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  cur- 
vatures 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  addi- 
tional strength,  obtained  from  the  lateral  supports,  may  very  properly  be  neg- 

VOL.    I.  s  s 


314  LECTURE    XXVI. 

Iccted,  as  only  assisting  in  affording  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  sup- 
ported on  both  sides  ;  l)iit  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  horizontal  direc- 
tions, 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  diminished  than 
that  of  a  roof  similarly  elevated,  since  the  hydrostatic  pressure  acts  always 
with  full  force  in  a  perpendicular  direction.  The  thickness  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  pres- 
sure of  the  water,  and  may  be  found,  with  suthcient  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  SO  pounds  for  each 
foot  of  the  breadth. 


ox    HTDROSTATIC    INSTRUMENTS,    AND    HYDRAULIC    ARCHITECTURE.   31J 

If  the  side  of  a  canal  gives  way,  it  is  sometimes  of  consequence  to  prevent, 
as  much  as  possible,  theescape  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  dra\r  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  tliese  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  larg-e  excavation, 
which  is  furnished  with  flood  gates,  and  is  constantly  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. 


•    316 


LECTURE  XXVn. 
I 

ON     THE    REGULATION    OF    HYDRAULIC    FORCES. 


.L  HOSIi  motlificatioHs  of  the  motions  of  fluids  which  are  employed  either  for 
conducting  them  from  place  to  place,  or  for  applying  their  powers  to  the  pro- 
duction of  mechanical  eft"ects,may  be  considered  as  constituting  a  separate  di- 
vision of  practical  hydrauHcs,  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  w^anted,  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  up- 
wards 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  tlie  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  purpose  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.  288.) 

Ifthejiipe  were  formed  into  a  syjhon,  having  its  flexure  above  both  orifices, 


ON    THE    REGULATION    OF    HlTDRAULIC    Ft>IlC"E!S.  31/ 

it  would  be  necessary  to  bend  it  upwards  at  the  extremities,  in  order  to  kee{» 
it  always  full :  but  in  this  case  the  accumulation  of  the  air  would  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  pressure,  and  neither  of 
the  methods  which  have  been  mentioned  would  be  of  any  use  in  extricatin(» 
it.  It  has  been  usual  in  such  cases  to  force  a  quantity  of  water  vioientlv 
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  Ire  necessary,  the 
momentum  of  the  water  in  the  pipe  would  ptobably  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  beea, 
employed  with  considerable  advantage.  A  pipe  of  lead  will  bear  the  pressure 
of  a  column  of  water  100  feet  high,  if  its  thickness  be  one  hundredth  of  its 
diameter,  or  even  less  than  this;  but  when  any  alternation  of  motion  is  pro- 
duced, a  much  stronger  pipe  is  required,  and  it  is  usual  to  make  leaden  pipes" 
of  all  kinds  far  thicker  than  in  this  proportion. 

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 
©f  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  Avatcr,  those  valves 
arc  the  best  which  interrupt  the  passage  least;    and  none  appears  to  fulfil 


318.  LECTURE  xxvrr. 

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  forma  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  unequally  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- 
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.  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  purpose,  require  some 
previous  experiments  for  determining  the  degree  in  which  they  are' affected  by 
different  velocities  ;  in  this  manner  the  hydrometrical  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.  Instamients  similar  to 
these  have  also  sometimes  been  employed,  for  measuring  the  relative  velocity, 
with  which  a  ship  under  way  passes  through  the  water  ;  and  an  apparatus,  re- 
sembling 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  M'hole 
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 


ox    THE    ItlGUtATION    OF    HYDKAULIC    rORCES.  319 

water,  since  the  discharge  is  considerably  retarded  by  any  considerable  degree  of 
cold.    But  when  the  aperture,  which  determines  the  magnitude  of  the  discharge, 
^s  .wholly  under  water,  as  Captain  Hamilton  has  placed  it,  this  source  of  error 
is  probably  much  diminished.     (Plate  XXII.  Fig.  1288,   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  arc   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  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 
"w^ater  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  M-hecl ;  its  impulse  may  be  di- 
rected either  perpendicularly  or  obliquely  against  a  moveable  surface  ;  and  its 
pressure  may  be  obtained,  without  any  immediate  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  me- 
chanical considerations  only ;  and  it  is  obvious  that  if  we  are  desirous  of  pre- 
serving 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, 


320  LECTURE   XXVII. 

or  empty  itself  into  the  first  when  it  has  ascended  again  to  its  original  situa- 
tion. The  action  of  a  column  of  water,  inclosed  in  a  pipe,  is  of  a  nature- 
nearly  similai-  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  commonly  employed  for  rais- 
ing welter  by  means  of  pumps.  But  both  these  methods  of  employing  the 
weight  of  water,  are  in  great  measure  confined  to  those  eases  in  which  it  is 
to  be  procured  in  a  small  quantity,  and  may  be  allowed  to  descend  through  a 
considerable  height,  and  when  the  circumstanceis  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  rnujs^t  estimate  the  ul- 
timate 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  eifect  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, 
we  shall  find  that  the  velocity  of  the  wheel, and  consequently  its  breadth,  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  A'ary.  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 


ON    THE    REGULATION    OF    HYDRAVLIC    FORCES.  ~  3ii  1 

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.  For  the  whole  quantity 
of  water  impelling  the  floatboards  is  nearly  the  same,  whatever  may  be  the  ve- 
locity, especially  if  the  wheel  is  properly  inclosed  in  a  narrow  channel,  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  seeri,  the  measure  of  the  hydraulic  pressure,  this 
force  Avill  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  thu.s 
retarded  will  not  retain  the  other  half  of  its  mechanical  power;  since  its 
greatest  effect  will  be  in  the  same  proportion  to  that  of  an  equal  stream  acting 
on  an  overshot  wheel  with  one  fourth  of  the  fall  of  the  former  :  and  the  re- 
maining fourth  of  the  power  is  lost  in  producing  the  change  of  form  of  the 
water  and  in  overcoming  its  friction.  In  whatever  way  we  apply  the 
4brce  of  water,  we  shall  find  that  the  mechanical  power  which.it  possesses 

VOL.    I.  T  t 


522  LECTURE    XXVII. 

must  be  measured  by  the  product  of  the  quantity  multiplied  by  the  height 
from  which  it  descends:  for  example,  a  hogsiiead  of  water  capable  of  descend- 
ing from  a  height  of  10  feet,  possesses  the  same  power  as  10  hogsheads  des- 
cending 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  pre- 
ferable 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  partakes  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  fol- 
lows 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  contented  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  mag- 
nitude 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  boat  has  only  six  floatboards  in  its  whole  circumference. 
(Plate  XXII.  Fig.  291,    292.) 

V 

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  l:>e  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  oblioue  surfaces  :  they  h^^ve  generally  arisen  from  inattention  to  the  distinc- 


ON    THE    REGULATION    OF    HYDRAULIC    FORCES.  323 

tiou  between    pressure  and  mechanical  power.     It  may  be  demonstrated  that 
the  greatest  possible  pressure  of  the   wind  or  water,  on  a  given  oblique  sur- 
face 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  in- 
creased without  limit  by  increasing  the  angle  of  inclination,  atid  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  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  as  great  as  that  of  the  wind.     It  appears,   there- 
fore, 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  revo- 
lution, 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  per- 
form 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;  ithe  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  frorn  too  great 
a  rapidity  in  the  motion,  or  any  other  accidents  which  might  happen  in  a  mill 


324  LECTURE    XXVII. 

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  cifect  in  China  and  in  the  south  of  France  :  for  tide  wheels,  such  float- 
boards  have  the  advantage  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.  '2.93.) 

A  smoke  jack  is  a  windmill  in  miniature ;  a  kite  affords  a  very  familiar  ex- 
ample 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.) 

The  counterpressure  of  the  water,  occasioned  by  the  escape  of  a  stream  from 
a  moveable  reservoir,  was  applied  by  Parent  to  the  purpose  of  turning  a  mill- 
stone, 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  should  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  ascertain- 
ed, we  might  calculate  not  only  what  the  motions  of  a  ship  would  be  under 
any  imaginable  circumstances,  but  we  might  also  determine  precisely  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 
m  setting  her  sails,  and  her  velocity  is  only  limited  by  that  of  the  wind,  and 


ON    THE    REGULATION    OF    HYDRAULIC    FORCES.  3SS 

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  considerably  mo- 
dified. 

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  con- 
fined to  its  proper  place  :  and  this  might  be  done  more  effectually  by  chang- 
ing 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  re- 
sistance 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  proportions  of  the  resistances  opposed  to  the  ship's 
motion  in  different  directions,  we  may  calculate  from  these  resistances  the 
magnitude  of  the  angular  deviation  or  lee  way  :  but  hitherto  such  calcula- 
tions have  generally  indicated  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  confin- 
ing 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  prin- 
cipal force  of  the  wind  is  applied  to  the  anterior  part  of  the  ship,  her  head 
would  be  naturally  turned  from  the  wind  if  the  rudder  were  not  made  to  pro- 
ject 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 


326  LECTURE    XXVIT. 

the  ship,  the  curvature  of  the  sails,  or  some  other  cause,  throws  the  pressure 
further  backwards,  and  the  action  of  the  rudder  is  necessary  to  prevent  the 
ship's  head  turning  towards  the  wind.     (Plate  XXII.  Pig  2,95.) 

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  in- 
crease 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  navigator, 
iii  enabling  him  to  derive  from  his  own  experience  all  the  benefits,  which  a 
correct  mode  of  reasoning  is  capable  of  procuring  him. 


32; 


LECTURE  XXVIII. 


ON     HYDRAULIC    MACHINES. 


VV  E  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  waterwheel, 
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  M'^hole  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  verti- 
cal or  in  an  inclined  position.  Such  M'heels  are  frequently  used  for  draining 
fens,  and  are  turned  by  windmills  ;  the  floatboards  are  not  placed  in  the  di- 
rection which  would  be  best  for  an  undershot  wheel,  but  on  the  same  princi- 
ple, so  as  to  be  perpendicular  to  the  surface  when  they  rise  out  of  it,  in  order 
that  the  water  may  the  more  easily  flow  off  them.  (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 


J28  LECTURE    XXVIII. 

feet  in  a  second,  and  drawing  a  certain  quantity  of  water  up  by  its  friction. 
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  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  friction  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  propor- 
tion to  its  bulk,  A  single  pipe  wound  spirally  round  a  cylinder  which  re- 
volves on  an  axis  in  an  oblique  situation,  has  been  denominated  the 
screw  of  Archimedes,  and  is  called  in  Germany  the  water  snail.  Its  opera- 
tion, 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  gra- 
dually elevated,  so  that  the  fluid  in  the  angje  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 


ON    HYDRAULIC    MACHINES.  329 

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  diminished.  It  is  gene- 
rally inclined  to  the  horizon  in  an  angle  of  hetwcen  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  im- 
properly be  considered  as  a  pump,  but  its  operation  is  precisely  similar  to  that 
of  the  screw  of  Archimedes.  It  is  evident  that  some  loss  must  here  be  oc- 
casioned by  the  want  of  perfect  contact  between  the  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  con- 
siderable depth  ;  so  that  if  the  height  of  the  surface  of  the  water  to  be  raised 
were  liable  to  any  great  variations,  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  conmiunicates  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  becomes  equivalent  to  that  of  the  co- 

VOL    I.  ~  ,    u  u 


imp  LECTURE    XXVIII. 

lumn  of  water,  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  consider;  ble,  it  be- 
comes 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.  1  he  loss  of  power,  suppobmg 
the  machine  well  constructed,  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,  tl*e 
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  tliat  the  wheel  required  above  100  feet  of  a  pipe  which  was  three 
quarters  of  an  inch  in  diameter ;  and  more  than  one  half  of  ihe  pipe  being 
always  fiiU  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  pro- 
duce 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  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  ofWirtz's 
machines,  has  sometimes  been  employed,  together  wirh  the  pressure  of  the  at- 
mosphere, 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  enxis,  the  whole  being  furnished  with  proper  valves  to    prevent  the 


ON    HYDRAULIC    MACHINES.  331 

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  horizon- 
tal pipe  causes  it  to  be  discharged  at  the  end,  its  place  being  supplied  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  deno- 
mination has  not  uncommonly  been  extended  to  hydraulic  machines  of  all 
kinds  ;  but  the  term,  in  its  strictest  sense,  is  to  be  understood  of  those  ma- 
chines, 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  consti- 
tute 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,  wheti  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  un- 
necessarily 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  apparatus  of  this  kind,  describ- 
ed by  Professor  Robison,an  active  man, loaded  with  a  weight  of  thirty  pounds, 
has  been  able  to  raise  580  pounds  of  water  every  minute,  to  a  height  of  1  In- 
fect, 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  equi- 


532  LECTURE   xxviir. 

valent  to  somewhat  more  than  11  pounds  raised  through  lOfcet  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  tlie  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  somewhat  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  apparatus  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  structure : 
the  pressure  of  the  water  on  the  inside  of  the  leather  makes  it  sufficiently 
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  propor- 
tion as  the  motion  of  the  piston  is  more  rapid.     (Plate  XXIII.  Fig.  307.) 

Mr.  Bramah  has  very  ingeniously  applied  a  forcing  puYnp,  by  means  of  the 
well  known  properties  of  hydrostatic  pressure,  to  the  construction  ot  a  con- 
venient 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 


ON    HYDRAULIC    SrACHINES.  333 

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  diameter  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 
pump  witli  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,  throvigh  which  the  water  is  to  be  raised,  is  considerable, 
some  inconvenience  might  arise  from  the  length  of  the  barrel  through  which 
the  piston  lod  of  a  sucking  pump  would  have  to  descend,  in  order  that  the 
piston  might  remain  within  the  hmits  of  atmospheric  pressure.  This  may  be 
avoided  by  placing  the  moveable  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  pumj)s,  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  througli  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  conr 
siderable.  The  condensed  air,  reacting  on  the  water,  expels  it  more  gra- 
dually, and  in  a  continual  stream,  so  that  the  air  vessel  has  un  effect  analo^ 
gous  to  that  of  a  fly  wheel  in  mechanics.     (Plate  XXIII.  Fig.  312.) 


334  LECTURE    XJtVIII. 

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  ajutage,  or  orifice  of  the  pipe,  is  by  no  means  in- 
different to  the  eff^ect  of  the  machine,  since  the  height  of  the  jet  may  be 
much  increased  by  making  it  moderately  contracted,  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  atmo- 
sphere. Sometimes  a  double  forcing  pump,  or  fire  engine,  is  formed  b}^  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  mechani- 
cal advantage  of  this  machine  is  nearly  the  same  as  that  of  the  n)ore  usual 
constructions,  but  it  appears  to  be  somewhat  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  com- 
municate with  each  other,  and  thus  both  sides  of  the  piston  may  be  employed 
at  once.     (Plate  XXIII.  Fig.  313.) 

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  reinvented,  by  Ramelli,  Cavalleri,  Amontons, 
Prince  Rupert,  Dr.  Hooke,  Mr.  Braniah,  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 


ON    HYDRAUtlC    MACHINES.  356 

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,  iu 
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  resemblance 
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  posi- 
tion, 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  banel,  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  con- 
siderable velocity  in  order  to  produce  any  effect  at  all.  Mr.  Cole  has  im- 
proved 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  wheelwork,  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  sufiiciently  long,  very  little  will  be  lost  by  the  obliquity  of  its  situatioji,  and 

■      -    ■  ( 


'336  LECTURE    XXVI  r  I. 

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  th.at  of  the  water  in  the  pipe,  or  when  the  force  em- 
ployed 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  w^eight-  of  water 
acting  within  a  barrel,  which  resembles  a  second  pump  placed  in  an  inverted 
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,  but  it  is  best  known  in  Germany 
under  the  name  of  HoU's  machine,  and  it  has  been  introduced  into  this 
country  by  Mr.  Westgarth  and  Mr.  Trevithick.  A  cliain  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  Schemnitz.  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  of  the  reservoir  or 
air  vessel,  on  the  water  in  a  second  reservoir,  at  any  distance  either  below  or 


ON    HTDRAULIC    MACHINES.  33T 

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  operation  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,  intend- 
ed 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  applied, 
by  means  of  a  series  of  reservoirs,  furnished  with  proper  valves,  to  tiie  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  re- 
servoir of  more  than  a  few  inches,  or  at  mpst  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. 

VOL.    I.  >  XX 


*338 


LECTURE    XXVIII. 


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  character- 
istic 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,  more  or  less  rapidly, 
to  the  degree  that  may  be  required,  for  raising  a  portion  of  the  water 
contained  in  it,  to  any  given  height.  Mr.  Whitehurst  appears  to  have 
been  the  first  that  employed  this  method:  it  was  afterwards  improved  by 
Mr.  Boulton ;  and  the  same  machine  has  lately  attracted  much  attention  in 
France  under  the  denomination  of  the  hydraulic  ram  of  Mr.  Montgolfier. 
(Plate  XXIII.  Fig.  323.) 


339 


LECTURE  XXIX. 


ON    PNEUMATIC    MACHINES. 


Pneumatic  machines  are  such  as  are  principally  dependent,  in  theij 
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  bellows,  ventilators, 
steam  engines,  and  guns. 

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 
exhausted  a  vessel  imperfectly  by  the  repeated  action  of  the  mouth,  and 
preserved  the  rarefaction  by  the  assistance  of  a  stopcock.  The  Torri- 
cellian vacuum,  obtained  by  inverting  a  receiver  filled  with  mercury,  and 
furnished  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  di- 
minished by  agitation,  but  can  only  be  completely  expelled  by  boiling  the 
mercury  for  some  time  in  the  vessel  and  its  tube,  previously  to  their  inver- 
sion.    (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 


340  LECTURE    XXIX. 

length  of  time,  the  limit  of  its  perfection  will  be  a  rarefaclion  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,  there- 
fore, 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  stojicock  may  be  occa- 
sionally 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  diiferently  rare- 
fied, 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  remainder,  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  possible  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  method  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  single  barrel  has 
nearly  the  same  advantage,  the  rod  of  the  piston  working  in  a  collar  of 
leathers  with  oil,  and  the  air  being  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.  3'^25.) 

That  the  air  is  really  removed  by  the  operation  of  the  air  pump,  may  be 
demonstrated  by  various  experiments,  which  show  the  absenceof  its  resist- 

2 


ox    PNEUMATIC    MACHINES,  341 

ance,  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  preponder- 
ance of  the  largx-r  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  ebul- 
lition of  etlier,  or  of  water  moderately  warm.  (Plate  XXIV.  Fig.  32.6, 
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  instead  .of 
the  short  gage,  the  difference  of  the  height  in  its  two  branches  indicating, 
the  pressure ;  and  this  instrument  has  the  advantage  of  requiring  no  cor- 
rection on  account  of  capillary  attraction,  since  the  depressions  of  the  two  co- 
lumns 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. 


342  LECTURE    XXIX. 

and  many  other  liquids,  have  the  property  of  emitting  a  vapour  which  pos- 
sesses 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  pro- 
cure a  total  absence  of  pressure,  the  short  mercurial  gage  commonly  stand- 
ing 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  re- 
ceiver,   whether  mixed    with  vapour  or  alone,    is  measured   by   means   of 
Smeaton's  pear  gage,   which  is  left  open  under  the  receiver  during  the  ex- 
haustion, 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  a'lr  may  be 
estimated.    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,   that  is,  it  was  expanded  to  nearly  3000  times  its  ori- 
ginal bulk.     The  pear  gage  often  indicates  a  much  more  complete  exhaus- 
tion, but  this  measurement  relates  only  to  the  quantity  of  dry  air  presenti 
(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  measuring  the 
degree  of  condensation  is  a  small  portion  of  air  contained  in  a  graduated 
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 


ON    PNEUMATIC    MACHINES.  3i3 

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  be  inter- 
mitted while  the  cavity  is  replenished ;  and  in  order  to  avoid  this  inconveni- 
ence, 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  not- 
withstanding 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  em- 
ployed may  be  much  diminished,  and  the  operation  expedited,  by  introduc- 
ing, 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  sup- 
ported by  a  counterpoise,  which,  in  the  best  kind,  acts  on  a  spiral  fusee, 


VT^TP 


LECTURE    XXIX. 


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  in- 
verted vessel  which  surrounds  the  pipe,  whence  it  may  be  conveyed  through 
another  pipe,  in  a  rapid  stream,  for  any  required  purpose;  and  the  water  es- 
capes at  the  bottom  of  the  air  vessel  into  the  general  reservou-,  from  the 
surface  of  which  it  runs  off.  The  quantity  of  air  supplied  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  4  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  cor- 
responds to  the  height;  that  is,  in  the  example  here  given,  £85  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  9  feet  of  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. 


ON    PNEUMATIC    MACHINES.  iJI'i 

A  corn  fan  is  turned  by  the  hand,  or  by  machinery ;  its  simplest  operation 
is  to  cause  a  portion  of  air  to  revolve  with  it,  and  to  create  a  wind  in  the  di- 
rection 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  common  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  di- 
rections, 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.  334.) 

The  operation  of  heat  affords  us  also  a  very  effectual  mode  of  ventilation. 
Its  action  upon  air  at  common  tempeiatures  occasions  an  expansion  of 
about -j^TT  for  every  degree  that  Fahrenheit's  thermometer  is  raised;  the  air 
becomes  in  the  same  proportion  lighter,  and  the  fluid  below  it  is  consequently 
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  amine  communicates  with  the  external  air  at  two  different  heights, 
there  is  generally  a  sufficient  ventilation  from  the  difference  of  the  tempera- 
tures 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  sum- 
mer; so  that  there  is  a  current  upwards  in  winter,  and  downwards  in  sum- 
mer; 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  summer ;  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  fif- 
tieth, and  the  pressure  of  the  whole  column  being  diminished  one  fif- 
tieth, the  difference  would   be  equivalent  to  a  column  of  one  foot  in  height, 

VOL,  I.  "        y  y 


\ 


346  LECTURE    XXIX. 

and  such  a  column  would  represent  the  pressure  causing  the  draught,  which 
might,  therefore,  be  expected  to  have  a  velocity  of  6  feet  in  a  second.  If 
the  room  were  perfectly  closed,  the  air  contained  in  it  would  by  degrees 
become  so  much  lighter  than  the  «xternal  air,  as  would  be  equivalent  to  one 
foot  of  the  height  of  the  column  causing  the  pressure,  and  the  current 
would  then  stop;  if  fresh  air  were  gradually  admitted  by  a  small  ori- 
fice, the  current  would  again  go  on,  but  the  air  in  the  room  would  always 
remain  somewhat  rarer  than  the  external  atmosphere,  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  Avas  first  applied  by  the  Marquis  of  Worcester,  and  after- 
wards by  Savery,  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 
tnade  capable  of  supporting,  in  addition  to  the  atmospherical  pressure,  a 
column  of  34  feet  of  water,  its  temperature  must  be  raised  to  248"  of  Fahieu'- 

4 


ON    PNEUMATIC    MACHINES.  '  347 

* 

heit,  and  for  a  column  of  68  feet,  to  i271°;  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  necessarily 
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  twentieth  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  great  measure  avoided 
in  Newcomen's  engine,  where  the  steam  was  gradually  introduced  into  a 
cylinder,  and  suddenly  condensed  by  a  jet  of  water,  so  that  the  piston  was 
forced  down  with  great  violence  by  the  pressure  of  the  atmosphere,  which  pro- 
duced the  effective  stroke:  this  effect  was,  iiowever,  partly  employed  in  rais- 
ing a  counterpoise,  which  descended  upon  the  readmission  of  the  steam,  and 
worked  a  forcing  pump  in  its  return,  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  afterwards  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.) 


348  LECTURE    XXIX. 

The  cylinder  of  Beighton's  machine  is  ne_cessarily  much  cooled  by  the  ad- 
mission of  the  jet,  and  by  exposure  to  the  air.  Mr.  Watt  has  avoided  this  in- 
convenience 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  excluded  ; 
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  man- 
ner with  a  smaller  quantity  of  steam;  but  there  would  be  some  difficulty  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  pressure;  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  cy- 
linder for  some  time  after  its  admission,  and  in  this  manner  it  appears  from 
calculation  that  much  more  force  might  be  obtained  from  it  than  if  it  were 
condensed  in  the  usual  manner  as  soon  as  its  admission  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  extricated 
from  the  water  during  the  process  of  boiling.  If  the  water  employed  has 
been  obtained  from  deep  wells  or  mines,  it  contains  more  air  than  usual,  and 
ought  to  be  exposed  for  some  time  in  an  open  reservoir  before  it  is  used ;  for  it  ap- 
vpears  that  the  quantity  of  air,  which  can  be  contained  in  water,  is  nearly  in  propor- 
■*^ion  to  the  pressure  to  which  it  is  subjected.     The  admission  of  the  steam  into 


ON    PNEUMATIC    MACHINES.  349 

the  cylinder  is  regulated  by  the  action  of  a  double  revolving  pendulum. 
The  piston  is  preserved  in  a  situation  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  Avas'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  flywheel;  this  machinery  is  generally 
applied  to  the  opposite  end  of  the  beam;  but  it  is  sometimes  immediately  con- 
nected 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  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  i;i  this  construction,  and  for  a  small  machine,  it  may 
perhaps  succeed  tolerably  well.  But  there  must  always  be  a  very  consi- 
derable 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  differ, 
ence  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  appear- 
ance of  novelty.     (Plate  XXIV.  Fig.  338.) 

The  force  of  steam,  or  of  heated  vapour,  is  probably  also  the  immediate 
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- 


350  LECTURE    XXIX. 

pears,  from  Bernoulli's  calculation,  to  be  at  least  equal  to  ten  thousand  times 
the  pressure  of  the  atmosphere,  and  upon  the  most  moderate  computation, 
from  Count  Rumford's  experiments,  to  be  more  than  three  times  as  great  as 
this.  The  quantity  of  moisture,  or  of  water  of  crystallization,  contained  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  fivehundreth 
for  each  degree  of  Fahrenheit  that  its  temperature  is  elevated ;  and  if  wt 
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  density  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  quantity  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  di- 
rectly as  the  quantity  of  powder,  and  inversely  as  the  weight  of  the  ball. 
Count  Rumford,  however,  found  that  the  same  quantity  of  powder  exerted 
somewhat  more  force  on  z  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  di- 
rection 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 


ON    PNEUMATIC    MACHINES.  351 

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. 

r 
Bullets  of  all  kinds  are  usually  cast  in  separate  moulds:  shot  are  granu- 
lated by  allowing  the  lead,  melted  wilh  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  round- 
est 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  of 
an  air  gun,  an  instrument  of  considerable  antiquity,  but  of  little  utihty.  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  consi- 
dered that  by  far  the  greatest  part  of  such  a  velocity  as  this  is  uselessly  em- 
ployed, 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.) 


352 


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  penetra- 
tion. His  treatise  on  floating  bodies,  although  the  theorems  which  it  con- 
tains are  not  so  general  as  they  have  been  rendered  since  the  late  improse- 
ments  in  the  methods  of  calculation,  still  affords  us  instances  of  very  in- 
genious determinations  of  the  equilibrium  of  floating  bodies  of  different 
forms,  grounded  on  the  true  principles  of  the  opposition  of  the  general  direc- 
tions of  the  weight  of  the  body  and  of  the  pressure  of  the  fluid  ;  and  in  this  man- 
ner he  has  shown  in  what  cases  the  equilibrium  of  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  been  little  difficulty  in  the  discovery,  but  the 
ancients  thought  otherwise.  Vitruvius  observes  that  this  invention  indicates 
a  degree  of  ingenuity  almost  incredible.  The  philosopher  himself  is  said  to 
have  valued  it  is  so  highly,  that  when  it  first  occurred  to  him,  in  a  public 
bath,  he  hastened  home  in  an  ecstasy,  without  recollecting  to  clothe  him- 
self, 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  re- 
turned 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,  Avhich  rendered  it  almost  impossible  to  determine  its  bulk 
by  calculation,  he  must  infallibly  escape  conviction.  The  hydrometer, 
which  has  sometimes  been  attributed  to  Hypatia,  a  learned  Greek  lady  of 


ON    THE    HISTORY    OF    HYDEAULICS    AND    PNEUMATICS.  353 

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  Ctesibiusof 
Alexandria,  the  greatest  mechanic  of  antiquity  after  Archimedes.  He  is 
also  said  to  have  invented  the  clepsydra,  for  the  hydraulic  measurement  of 
time,  and  Philo  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  im- 
pelled 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  at- 
tention 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 
Avindow. 

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,  ob- 
serving 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, 
Avhich  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 
little  further  progress,  until  the  revival  of  lette;rs.  The  Romans  had  water 
mills  in  the  time  of  Juhus  Caesar,  which  are  described  by  Vitruvius;  and 
it  appears  that  their  ac[ueducts  were  well  built,  and  their  waterpipes    well 

VOL.    I.  z  z 


354  LECTURE    XXX. 

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  re- 
ferred to  the  year  1299.  The  invention  of  gunpowder  possesses  perhaps  an 
equal  claim  with  theartof  printing,  to  the  honour  of  being  considered  as  consti- 
tuting 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  improvements,  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  employed  in  Europe  or  in  its  neighbour, 
hood  till  about  the  year  1 330 ;  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  eflPects  of 
the  weight  and  pressure  of  the  atmosphere,  in  the  operation  of  suction,  and  in 
various  other  phenomena.     Before  his  time,   it  was  generally  supposed  that 
water  was  raised  by  a  sucking  pump,  on  account  of  the  impossibility  of  the 
existence  of  a  vacuum :  if,  however,   a  vacuum  had  been  impossible  in'na- 
ture,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  con- 
cluded that  the  weight  of  a  column  of  this  height  was  the  measure  of  the  magni- 
tude of  the  atmospherical  pressure.     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  respecting  the  quantities  of  water  discharged  by  equal  orifices,  at 


OK   THE    HISTORY    Of    HYDRAULICS    AND    PNEUMATICS.  535 

difterent  distances  below  the  surface  of  the  water  in  the  reservoir.  Castelli's 
experiments,  made  about  \6iO,  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  quadruple  height  was  required  in  order  to  produce  a  double 
velocity;  and  his  assertions  were  afterwards  fully  confirmed  by  Mariotteand 
by  Gughelmini. 

A  little  before  the  year  l65i,  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  M'ater  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  intervening  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, 
when  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  experiments  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  imper- 
fection in  the  vacuum.  An  account  of  his  experiments  was  first  published 
in  different  works,  by  Caspar  Schott,  and  afterwards  by  himself,  in  his 
book  intitled  Experimenta  nova  Magdeburgica,  printed  in  1672  at  Am- 
sterdam. 

In  the  year   1658,  Hooke  finished  an  air  pump  for  Boyle,  in  whose  la- 


356  lECTURK    XXX. 

boratory  he  was  an  assistant:  it  was  more  convenient  than  Guericke's,  but 
the  vacuum  was  not  so  perfect;  yet  Boyle's  numerous  and  judicious  experi- 
ments gave,  to  the  exhausted  receiver  of  the  air  pump,  the  name  of  the  Boy- 
lean  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  Hauks- 
bee,  it  remained  in  common  use,  until  the  introductiian  of  Smeaton's  pump, 
which,  however,  has  not  wholly  superseded  it.  The  theory  of  pneumatics 
was  also  considerably  indebted  to  Hooke's  important  experiments  on  the 
elasticity  of  the  air,  which  were  afterwards  confirmed  and  extended  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 
intitled  Sarepta,  and  at  a  subsequent  period  by  Brunau  ;  but  the  Marquis  of 
Worcester  professes  to  have  carried  the  project  into  full  effect,  as  we  are  inform*- 
ed  by  his  account  of  what  he  called  a  fire  water  work,  which  is  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  nin  like  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  likewise  abundantly  perform  in  the  interim 
between  the  necessity  of  turning  the  said  cocks."  The  machine  was,  how- 
ever, not  at  that  time  practically  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  1/10,  the  piston 
4 


ox    THE    HISTORT    OF    HYDRAULICS    A^'D    PNEUMATICJ.  ~  S57 

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  resist- 
ance opposed  by  fluids  at  rest  to  the  motion  of  solid  bodies,  were  experi- 
mentally 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;  their  im- 
perfections 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  sub- 
mit 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  Avhich  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  contrac- 
tion of  a  stream  passing  through  a  simple  orifice,  which  was  then  ngw, 
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,  ai-e  tolerably 
accurate;  and  his  determination  of  the  oscillations  of  fluids,  in  bent  tubes, 
was  a  good  beginning  of  the  investigation  of  their  alternate  motions  in 
general.  .  , 


o 


The  accurate  experiments  of  Poleni  were  published  in  1718:  he  has  the 
merit  of  having  first  distinctly  observed  that  the  quantity  of  water,  discharg- 
"ed  by  a  short  pipe,  is  greater  tliau  by  a  simple  orifice  of  the  same  diameter; 


/ 


358  LECTunE  XXX. 

although  there  is  some  reason  to  suppose  that  Newtow  was  before  acquainted 
with  the  circumstance. 

In  1727,  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  con- 
tinue his  application  to  similar  studies,  and  about  twenty  years  afterwards 
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  mo- 
tions of  fluids,  bear  also  the  date  of  1727.  This  justly  celebrated  man  was  as 
happy  in  his  application  of  mathematies  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  elasti. 
city  of  the  bodies  concerned ;  for  it  is  only  with  this  limitation,  that  the  mo- 
tions 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  des- 
cended, 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  es- 
timated 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  gunpow- 
der, as  equivalent  to  the  daily  labour  of  100  men,  vvhile  in  fact  the  effect 
which  is  actually  obtained  from  two  tons  of  powder  is  no  greater  than  that 


ON    THE    HISTORY    OF    HYDRAULICS    AND    PNEUMATICS.  359 

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  Avind  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  pro- 
duces absolutely  no  effect  at  all. 

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  complicated  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,  Bernoulli  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  sup- 
posed to  act,  remains  also  wholly  undetermined;  and  it  was  principally  for 
this  reason,  that  John  Bernoulli  attempted  to  substitute,  for  his  son's  calcula- 
tions, a  method  of  deducing  the  motions  of  fluids  more  immediately  from  the 
gravitation  of  their  different  parts.  The  peculiarity  of- John  Bernoulli's 
mode  of  investigation  consists  in  his  imagining  the  weight  of  each  indi- 
vidual 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  re- 
quired for  the  motion  of  fluids,  in  vessels  of  all  imaginable  forms. 

Maclaurin,  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  peculiarly  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 


$60  LECTDRE    XXX. 

experiments  to  be  capable  of  affording  determinations  of  all  questions  which 
are  of  very  frequent  occurrence  in  practice.  AnappHcation  was  made  to  Mac- 
laurin,  and  at  the  same  time  to  Desaguhers,  a  man  of  considerable  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  cal- 
culation, 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  com- 
mendation on  account  of  their  practical  utility ;  but  he  appears  to  have  been 
less  successful  in  his  theoretical  mvestigations  than  Daniel  Bernoulli  had 
been  a  few  years  before. 

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  Bernoulli'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  calcu- 
lation, he  inserts  along  string  of  logarithms  for  performing  a  simple  multi- 
plication; and  in  a  work  which  comprehends  the  whole  range  of  the  mathe- 
matical sciences,  he  does  not  venture  to  determine  the  square  root  of  10  with- 
out quoting  an  authority. 


ON    THE    HISTORV    OF    HrDRAULrCS    AND    PNEUMATICS.  361 

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  raathe- 
inatical  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  Trans- 
actions 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  il- 
lustrate their  connexion  with  the  general  principles  of  mechanics.  It  was 
JVIr,  Borda  that  first  derived  from  a  just  theory,  about  10  years  after,  the 
same  results,  respecting  the  effects  of  undershot  water  wheels,  as  Smeatoil 
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  calcula- 
tions 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  17^9,  a  patent  for  his  improre- 
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  admiraWc 
application  of  the  sciences,  to  practical  purposes,  most  justly  entitles  him  to 
a  rank  among  philosophical  mechanics,  not  inferior  to  that  of  Ctesibius  a!i»d 
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,  "  con- 
sists 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  steam  that 

VOL  I.  3  a 


362  LECTURE    XXX. 

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,  of  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  cy- 
linders, 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  neighbourhood  of  the  en- 
gines, 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,  .1  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  Avhich  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  per- 
formed 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  considera- 
bly, so  that  the  engines  may  be  worked  by  the  alternate  expansion  and  con- 


ON    THE    HISTORY    OF    HYDRAULICS    AKD    PNEUMATICS.  363 

traction  of  the  steam.  Lastly,  instead  of  using  water  to  render  the  piston  or 
other  parts  of  the  engines  air  and  steam  tiglit,  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  diflficulty  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  of 
parliament  until  the  year  1799  ;  but  although  the  legal  privilege  of  the  ori- 
ginal manufacturers  is  expired,  yet  the  superiority  of  their  workmanship  still 
gives  thfeir  engines  a  decided  preference. 

Much  of  the  labour  of  the  later  writers  on  hydraulics  has  been  employed 
en  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  ex- 
tensive 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  Maritime,  which  appears  to  be  the  most  ingenious 
and  useful  treatise  on  the  theory  and  practice  of  seamanship  that  has  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  proposition 
on  the  subject,  that  a  double  force,  acting  in  a  given  small  space,  will  pro- 
duce a  double  velocity;  while  it  is  well  known  that  in  such  clrcuinstances 
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  acci- 
dental 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  magnitude  of  tlve  resistance  at  different 


3^4  LECTURE    XXX. 

^pths>  that  of  the  atmosphere  ought  by  no  means  to  be  omitted  in  the  cal- 
culation. But  if  a  more  correct  mathematician  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  ac- 
curate 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  in- 
stance rigidly  conformable  to  observation  and  experience,  but  it  is  probable 
that  where  such  a  coincidence  really  exists,  it  must  i)e  owing  to  some  com- 
bination 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  computations  respecting  the  descent  of  falling  bodies 
^nd  the  impulse  of  water. 

The  works  of  Chapman  and  of  Romme,  upon  various  departments  of  sea- 
manship, 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  lias  done. 

The  accurate  experiments  of  Dr.  Hutton  and  of  ('ount  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  after  main- 
tained a  contrary  opinion  in  the  commentaries  of  Bologna,  and  Count  Rum- 
ford  has  very  satisfactorily  shown  the  insufficiency  of  the  agents  considered 
by  Robins,  although  he  has  been  unsuccessful  in  attempting  ta  deduce  th» 
■whole  force  from  the  elasticity  of  aqueous  vapour  alone. 

The  theory  of  practical  hydraulics,  as  affected  by  friction,  may  be  consir 
dered  as  having  been  began  and  completed  by  the  highly  meritorious  labours 
of  the  Chevalier  du  Buat.  He  had  some  assistance  in  expressing  the  results 
of  hh  experiments  by  meana  of  general  rules  or  formulae^,  aad.  these,  air 


ON    THE    HISTORY    OF    HTDRAUIICS   AND    PNEUMATICS.  365 

though  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  Robi- 
son  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  of  cases,  which  occur  in  hydraulic  architec- 
ture. 

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,  of  Albertus,  and  of  Wilkins,  respecting  the 
various  modes  of  passing  through  the  air,  had  long  remained  disregarded  as 
idle  speculations;  and  Rosnier,  who,  in  the  l/th  century,  descended  ob- 
liquely over  some  houses,  by  means  of  wings,  was  wholly  unable  to  employ 
them  in  ascending.  Dr.  Black  had  exhibited  in  his  lectures  a  bladder  fdled 
with  hydrogen  gas,  and  floating  in  the  air  by  means  of  its  smaller  specific 
gravity,  many  years  before  Montgolfier  conceived  the  idea  of  applying  a  si- 
milar 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  ima- 
gination were  disposed  to  believe  that  the  discovery  would  be  of  great  import- 
ance to  the  convenience  of  mankind.  But  if  we  coolly  consider  the  magni- 
tude of  the  force  with  which  the  wind  unavoidably  impels  a  surface  so  large 
as  that  of  a  balloon,  we  shall  be  convinced  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  re- 
garding 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.  Blot  and  Mr. 
Gay  Lussac  having  ascended  to  a  height  of  above  four  miles,  for  the  laudable 
purpose  of  ascertaining  some  facts  relating  to  the  constitution  of  tlie  atmosphere, 
and  to  the  magnetic  properties  of  the  earth. 


366 


LECTURE    XXX. 


CHRONOLOGY    OF    AUTHORS    ON    HYDRODYNAMICS. 


700  B.  c.                         a 
1 

00                                                          5 

00                                     4 

00                                           3 

00                                       200 
....     1     ...     . 

.A  R  I  S  T  0  T  L  E. 

ARCHIMEDES. 

200  B.  C.                               1 

00                                  BIRTH   OF 
....      1      ...      . 

CHRIST.                                  1 

00                                                          i  00                                                     300 

•  •  •  •  1 1  .  .  .  . 

C  T  E  S  I  B  I  U  S 
HERO 

VITRUVIUS 

300                                                       4 

00                                              5 
....     1     ...     . 

00                                                          6,00                                                          7 
....       1      ....      1      ....      1       ...      . 

uo                                          boo 

800                                                       9 

00                                          10 

00                                                        IJ 

00                                                       12  00                                                  1300 
.•     .      .      .      1 1      .      .      .      . 

.R.       BACON. 

1300                                                  14 

00                                                       15 

00                                                       16 

00                                                        17 

....  1  ...  . 

00                                                  1 800 

• 

S      T      E 
.G  A   L   1 

CAS 

V  I  N.                      .J  0.    B  E 

LEO.                SAVE 

T    E    L   L   L                .P  0 

.G    U    E    R    I    C    K    E.    . 

.TORRICEL.LI 

WORCESTER. 

.BOYLE. 
.H  U  Y  G  E  N  S. 
M  A  R  I  0  T  T  E. 
.H    0    0    K    E 
PARDIES. 
.N    E    WT 
.R  E  IN  A  U 
.JA.  BERNO. 
.GUGLIEL 
.A  M  ON 

RNOULLI. 
RY 

L       E       N       I. 
B  0  U  G  U  E  R. 
MACLAUR.IN 
.D.     BERNOULLI. 
.L.        E    U    L    ER. 
.ROBINS. 
.DALEMBERT. 
.S  M  E  A  T   0  N. 
JUAN. 
0      N.       .B   0    R    D   A. 
D. 

U  L  L  I 
M.I  N  I 
.TONS 

... 

367 


LECTURE  XXXI. 


ON    THE    PROPAGATION    OF    SOUND. 

-L  HE  theory  of  sound,  which  constitutes  the  science  of  acustics,  is  on  many 
accounts  deserving  of  particular  attention,  for  it  not  only  involves  many  in- 
teresting 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  considered  as  ex- 
ceedingly abstruse  and  intricate,  but  the  difficulty  has  in  some  measure  ori- 
ginated from  the  errors  which  were  committed  in  the  first  inquiries  respect- 
ing 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  enter- 
tainment that  they  afford.  We  shall  consider  first  the  nature  and  propaga- 
tion of  sound  in  general,  secondly,  the  origin  of  particular  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  concern- 
ed, 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  distin- 
guished, they  constitute  a  continued  sound,  like  that  of  the  voice  in  speak- 


368  LECTURE    XXXI. 

ing;  and  if  they  are  equal  among  themselves  in  duration,  they  produce  a 
musical  or  equable  sound,  as  that  of  a  vibrating  chord  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  wlieel  are  at  equal  distances,  and  the  ve- 
locity 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  perceptible. 
The  experiment  is  most  conveniently  performed  in  a  moveable  receiver  or 
transferrer,  which  may  be  shaken  at  pleasure,  the  frame  which  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  communi- 
cation from  air  to  glass,  and  again  from  glass  to  air,  occasions  a  great  di- 
minution 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  con- 
veyed through  any  homogeneous  elastic  medium,  whether  solid  or  fluid, with  a 
uniform  velocity,  which  is  always  equal  to  that  which  a  heavy  body  would 
acquire  by  falling  througli  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  atmo- 
sphere 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  for- 


ON    THE    PROPAGATION    OF    SOUND.  3t)9 

wards,  and  then  either  remains  stationary,  or  returns  back  to  its  original 
situation ;  but  in  the  case  of  a  musical  sound,  is  continually  moved  back- 
wards and  forwards,  with  a  velocity  always  varying,  and  varying  by  differ, 
ent  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  lirst  suppose  for 
the  sake  of  simplicity,  a  single  scries  of  particles  to  be  placed  only  in  the  same 
line  with  the  direction  of  the  motion.  It  is  obvious  that  if  these  particles  were 
absolutely  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  particles  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  unduktion, 
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  anytime  maybe  representedby  supposing  it  to 
mark  its  path,  on  a  surface  sliding  uniformly  along  in  a  transverse  direction. 
Thus,if  wefix  asmall  pencil  in  a  vibrating  rod,  and  draw  a  sheet  of  paper  along, 
against  the  point  of  the  pencil, an  undulated  line  will  be  marked  on  the  paper, 
and  will  correctly  represent  the  progress  of  the  vibration.  Whatever  the  na- 
ture 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  opposite  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  forwards, 
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 

VOL.    I.  3  b 


370  ^  LECTURE    XXXI. 

well  as  the  g]:eatest  rarefaction  and  retrograde  velocity,  happening  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  pro- 
trusion 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  discoverable 
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  ho-  ' 
■?■  njogencous,   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  comparison  of  the  accurate  ex- 
periments of  Derham,  made  in  the  day  time,  with  those  of  the  French  Aca- 
demicians, made  chiefly  at  night,  it  appears  that  the  true  velocity  of  sound 
is  about  1 130  feet  in  a  second,  which  agrees  very  nearly  with  some  observa- 
tions made  with  great  care  by  Professor  Pictet.  This  difference  between 
calculation  and  experiment  has  long  occupied  the  attention  of  natural  phi- 
losophers, but  the  difficulty  appears  to  have  been  in  great  measure  removed 
by  the  happy  suggestion  of  Laplace,  who  has  attributed  the  cff'ect  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  experi- 
ments on  the  compression  of  air  appear  to  indicate;  but  those  experiments 
do  not  perfectly  agree  among  themselves;  and  the  observation  which  has- 
been  made  in  France,  that  a  heat,  sufficient  to  set  tow  on  fire,  may  be  pror 
duced  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 

5 


ticj/l*-*^   K  U 


ON  THE  PROPAGATION  OF  SOUND.  371 

may  be  completely  reconciled  with  experiments;   we  may  estimate  the  mo- 
dulus 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 
ZQ  800  feet,   instead  of  27  800,  which  is   the  supposed  height  of  the   atmo- 
sphere.    This  velocity  remains  unchanged  by  any  alternation  of  pressure  in-, 
dicated  by  the  barometer,  but  it  may  be  aftected  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  homogeneous  atmosphere  equiva- 
lent to  the  pressure,   remains  the  same,  consequently  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,  however,   be  satisfactorily   shown,   by 
means  of  experiments  on  the  sounds  of  organ  pipes,  whicli  are  intimately 
connected  with  the  velocitv  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.       Papin    screwed  a  whistle  on  the  orifice 
winch  admits  the  air  into  the  receiver  of  the  air  pump,  and  1  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  elas- 
ticity remains  unaltered,  which  happens  when  it  is  expanded  by  heat,  or  con- 
densed by  cold,   the  height  of  the  column,   and  consequently  the  velocity, 
will  also  be  altered;  so  that  for  each  degree  of  l-'ahrenheit's  thermometer  the 
velocity  will  vary  about  one  part  in  a  thousand.      Bianconi  has  actually  ob- 
served this  difference  of  velocity  according  to  the  different  heights  of  the 
thermometer,   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  correc- 
tion on  account  of  the  effect  of  compression  in  causing  heat,   remains  unal- 
tered,  although  Bianconi's  experiments  agree  very  well  with  the  supposition 
tliat  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 


372  LECTURE  xxxr. 

states  are  probably  often  produced  in  succession  in  wind  instruments  blown 
by  the  mouth,  the  air  within  them  being  at  first  cold  and  damp,  and  after- 
wards warm  and  moist. 

In  pure  hydrogen  gas,   the  velocity  of  sound  ought,  from  calculation,  to  be 
""  more  than  threje  times  as  great  as  in  common  air,   but  the  difference  does  not 

appear  to  have  been  so  great  in  any  experiment  hitherto  made  on, the  sounds 
of  pipes  in  gases  of  different  kinds.  For  such  experiments,  the  comparative 
specific  gravity  of  the  gas  may  be  most  conveniently  ascertained  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;  ac- 
cording 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  pro^ 
duced  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  thaa 
in  air. 

It  does  not  appear  tlmt  any  direct  experiments  have  been  made  on  the 
velocity  with  wliich  an  impulse  is  transmitted  through  a  liquid,  although 
it  is  well  known  that  liqaids  are  capable  of  conveying  sound  without  dififi- 
culty ;  Professor  Robison  informs  us,  for  example,  that  he  heard  the  sound 
of  a  bell  transmitted  by  water  at  the  distance  of  ]20{)feet.  It  is,  however, 
^  pasy   to   calculate  the  velocity  with  which  sound  must  be  propagated  in  any 

^.•^,yft**         liquid  of  which  the  compressibility   has  been  measured.     Mr.    Canton  has 
„^   _.  J  ascertained  that  the  elasticity  of  water  is  about  22  000  times  as  great  as  that 

of  air;  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  tlie  velocity  cor- 
responding to  half  this  height  is  4900  feet  in  a  second.  In  mercury,  also, 
it  appears  from  Mr.  Canton's  experiments,  that  the  velocity  must  be  nearly 
the  same  as  in  water,  in  spirit  of  wine  a  little  smaller.  These  ex])eriments 
were  made  by  filling  the  bulb  of  a  thermometer  with  water,  and  observing 
the  effects  of  placing  it  in  an  exhausted  receiver,  and  in  condensed  air; 
taking  care  to  avoid  changes  of  tcn>perature,  and  other  sources  of  error: 


OK   THE   PROPAGATION    OF    SOUND.  373 

the  fluid  rose  in  the  tube  when  the  pressure  was  removed,  and  subsided 
when  it  was  increased.  A  shght  correction  is,  however,  required  on  ac- 
count 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 
of  cavalry  is  said  to  be  perceived  at  a  greater  distance  by  listening  with  the 
head  in  contact  with  the  ground,  than  by  attending  to  the  sound  conveyed 
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  ap- 
peared to  transmit  a  sound  instantaneously,  while  a  sensible  interval  was  re- 
quired 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  tlie 
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  elasti- 
city of  fir  M'ood,  is  found,  by  means  of  such  experiments,  to  be  about 
9  500  000  feet,  whence  the  velocity  of  an  impulse  co-nveyed  through  it  must  be 
17  4-00  feet,  or  more  than  three  miles,  in  a  secoml.  It  is  obvious,  therefore, 
that  in  all  common  experiments  such  a  transmission  must  appear  perfectly 
instantaneous.  There  are  various  methods  of  ascertaining  tliis  velocity  from 
the  sounds  produced  under  different  circumstances  by  the  substances  to  be 
examined,  and  Professor  C-hladni  has  in  this  manner  compared  the  proper- 
ties 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  th?  impulse  spreads  ia  every  direction,  so- 


97*  LECTURE    XXXI. 

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  man- 
ner by  any  sound,  originating  from  a  vibration  confined  to  a  certain  direc- 
tion, 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  nega- 
tive, while  in  the  other  they  are  direct  or  positive;  consequently  at  the  sides, 
where  these  portions  join,  the  motions  can  be  neither  positive  nor  negative, 
and  the  particles  must  remain  at  rest;  the  motions  must  also  become  gra- 
dually less  and  less  sensible  as  they  approach  to  the  limit  between  the  two 
hemispheres.  And  this  statement  may  be  confirmed  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  per^ 
pendicular  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  hemispherical 
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  dis- 
tance 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  reflect- 
ing object  be  at  a  distance  moderately  great,  otherwise  the  returnii^-  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. 

B       (xmam^  h4^^'  If  ^  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  tliat 


ON    THE    PROPAGATION    OF    SOUND.  ,         37o 

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  ecjual  angles  with  the  curve  on 
each  side.  The  truth  of  this  proposition  may  be  easily  shown  by  means  of  the  ap- 
paratus 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  curva- 
ture 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  soond  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  car  in  directions  confined  within  certain  limits: 
the  voice  proceeds  also  from  the  mouth  without  any  very  considerable  diverg- 
ence, 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 
apart  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  speaking  trumpet 
has  any  immediate  effect  in  strengthening  the  voice,  independently  of  the 
reflection  of  sound.     (Plate  XXV.  Fig.  342.) 

An  umbrella,  held  in  a  proper  position  over  the  head,  may  serve  to  collect 


t/ferrt^ 


S76  LECTURE    XXXI. 

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  whisperino-  o-al- 
lery  at  St.  Paul's  produces  an  effect  nearly  similar,  by  a  continued  repetition 
of  reflections.  Mr.  Charles's  paradoxical  exhibition  of  the  Invisible  Girl  has 
also  been  said  to  depend  on  the  reflection  of  sound;  but  the  deception  is 
really  perfonned  by  conveying  the  sound  through  pipes,  artfully  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  proceeds 
through  a  wide  space,  without  being  supported  on  either  side,  there  is  a  cer- 
tain 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  reservoir,  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  towards  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  additional  strength  at  the  ex- 
pense 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  <?entre  increases;  consequently  their  energy,  which  is  to 


ON    THE    PROPAGATION    OF    SOUND.  377 

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. 


V.OL.    I,  3  c 


378 


LECTURE  XXXII. 


ON    THE    SOURCES    AND    EFFECTS    OF    SOUND. 


J.  HE  examination  of  the  origin  of  sound  might  naturally  be  deemed  anterior 
to  the  inquiry  respecting  its  propagation ;  but  it  will  appear,  that  the  pro- 
perties 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  hundredth  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  impulses 
independent  of  each  other,  as  when  a  wheel  strikes  in  rapid  succession  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  is  placed  at  equal  distances  in  a  line  nearly  per- 
pendicular to  them,  and  a  noise  of  any  kind  is  reflected  from  each  of  them 
in  succession;  a  circumstance  which  may  often  be  observed  when  we  are 
walking  near  an  iron  railing,  an  acute  sound  being  heard,  which  is  com- 
posed of  such  reflections  from  the  surfaces  of  the  palisades. 


ON    THE    SOURCES    AND    EFFECTS    OF   SOUND.  379 

Musical  sounds  are,  however,  most  frequently  produced  by  the  alternate    ^^.at-^*^-h^^ 
motions  of  substances  naturally  capable  of  isochronous  vibrations,  and  these 
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  one  of   UMin^^^^'^      / 
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  eflfect,  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    lyJtf^  t^^-Ci-'-i 
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    aft^brd  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  reenter  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 


380  LECTURE    XXXII. 

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  fifth,  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. 

J  .  _  It  is  obvious  from  this  statement  of  the  analogy  between  the  velocity  of 

/  U^.^lt^'^-^  sound  and  the  vibrations  of  the  air  in  pipes,  that  they  must  be  affected  in 

a  similar  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 


f^^^-f 


of  the  air  in  an  organ  pipe,  having  also  their  secondary  or  harmonic  notes 
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  \6  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  accurate  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  witli  a.  small  hammer^ 
in  the  direction  of  its  length.  , 

The  vibrations  by  which  solid   bodies   most   usually  produee  sound  are» 
however,  not  longitudinal,  but  lateral,  and  they  are  governed  either  by  a 


ON    THE    SOURCES    AND    EFFECTS    OF    SOUND.  381 

tension,  derived  from  the  operation  of  a  weight,  or  of  some  other  external 
force,  or  by  tlie  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  mo&t 
natural. 

Vibrations  derived  from  tension   are    either  those  of  chords  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  diifer  materially  in  their  properties  from  the  vibra- 
tions of  strings.      A  musical  string  or   chord  is  supposed  to  be  perfectly 
flexible,  and  of  uniform  thickness,   to  be  stretched  between  two  fixed  point^ 
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 
chord  to  a  portion  of  an  elastic  medium  of  the  same  length,  contained  be- 
tween 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  chord  will  be  performed  in  the  same  time,  suppos- 
ing the  height  or  depth  of  the  medium  equal  to  the  length  of  a  portion  of 
the  chord,  of  which  the  weight  is  equivalent  to  the  force  applied  to  stretch 
it,  and  which  may  be  called  with  propriety  the  modulus  of  the  tension.     If 
the  chord  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  chord  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  chord  will  assume  a  similar 
figure  on  the  opposite  side  of  its  natural  place,  but  iu  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 


^SiJ  I.ECTUIIE    XXXIl. 

inflecting  any  long   chord  near  one  of  its  ends,  having  first  drawn  a  line 
under  its  natural  position,  and  it  will  then  be  evident  that  the  chord  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  frequency  of  vibration  agrees  also  perfectly 
with  experiment,   nor  is   the  coincidence  materially  affected  by  the  inflexi- 
bility 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  corres- 
ponding to  half  this  height  would  be  80  feet  in  a  second;  and  every  impulse 
would  be  conveyed  with  th's   velocity  from  one  end  of  the  string  to  the 
other,   so  that  if  the  string  were  1  foot  long,   it  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  chord  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 
chord  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  chord  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 
lias  already  been  laid  down,  that  every  chord  vibrates  in  the  same  manner 
us  if  it  were  a  part  of  a  longer  chord,  composed  of  any  number  of  such 
chords,  continually  repeated  in  positions  alternately  inverted;  consequently 
if  a  long  chord  be  initially  divided  into  any  number  of  such  equal  portions, 
its  parts  will  continue  to  vibrate  in  the  same  manner  as  if  they  Avere  sepa- 
rate chords;  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  small 


ON    THE    SOURCES    AXD    EFFECTS    OF    SOUND.  383 

feathers  or  pieces  of  paper  on  the  string,  that  the  remaining  points  of  divi- 
sion are  also  quiescent,  while  the  intervening  portions  are  in  motion.  (Plate 
X^V.  Fig.  343.) 

These  harmonic  sounds  are  also  generally  heard  together  with  the  funda- 
mental sound  of  the  chord,  and  it  is,  therefore,  necessary,  in  such  cases,  tQ^ 
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  chord  is  susceptible;  for  I 
have  found  that  by  inflecting  the  chord  exactly  at  any  point  in  which  the 
cliord  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  reasonof  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  chord,  which  is  just  sufficient  to  derange  the  perfect  coinci- 
dence of  the  actual  motions  with  those  which  the  theory  indicates,  without 
producing  a  discordance  capable  of  offending  the  ear.  That  a  chord  ir- 
regularly 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  afi'ecting  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  chord  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  chord  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 


384 


LECTURE    XXXII. 


intermediate  direction,  or  a  revolution,  in  a  circle  or  in  an  ellipsis.  But 
besides  these  compound  vibrations  of  the  whole  chord,  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  sur- 
face of  the  chord,  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  chordjbutthey  often  pass  through 
an  amusing  variety  of  forms  during  the  progress  of  the  vibration;  they 
also  vary  considerably  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, 
plates,  rings,and  vessels.  These  admit  of  much  greater  variety,  and  are  of  more 
difficult  investigation  than  the  vibrations  of  chords.     A  rod  may  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  ex- 
tended by  Euler,   some  of  whose  conclusions  have  been  corrected  by  Riccati; 
and  Chladni  has  compared  them  all  with  experiment.     The  sounds  produced 
by  the  same  rod,  either  under  different  circumstances,  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  frequen- 
cy of  the  vibrations  of  the  subordinate  notes  is  expressed  by  the  series  of  the 
squares  of  the  natural  numbers,as  l,4,9,and  l6.    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 


ON    THE    SOURCES    AND    EFFECTS    OF    SOUND.  385 

vibrations  of  rods  of  different  kinds  as  in  those  of  chords ;  it  can  only  hap- 
pen 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  diifer  from  those  of  rods  in  the  same  manner  as 
the  vibrations  of  membranes  differ  from  those  of  chords,  the  vibrations  which 
cause  the  plate  to  bend  in  different  directions  being  combined  with  each  other, 
and  sometimes  occasioning  singular  modifications.  These  vibrations  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  military  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  sufficiently 
investigated.  A  glass,  or  a  bell,  divides  in  general  into  four  portions 
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  denominated 
reed  pipes,  the  length  of  a  tongue  of  metal  is  so  adjusted,  as  to  be  capable  of 
vibrating  in  tiie  same  time  with  the  air  contained  in  the  pipe.  Sometimes, 
however,  the  air  only  serves  to  excite  the  motion  of  the  solid,  as  jn  some 
other  organ  pipes,  which  are  usually  much  shorter  than  Avould  be  required 
for  producing  the  proper  note  alone,  and. pvobably  in  the  glottis,  or  organ 
of  the  voice,  of  animals.    On  the  other  hand,  the  alternate  opening  and  shut- 

VOL.    1.  So 


386  LECTURE    XXXII. 

ting  of  the  lips,  in  blowing  the  trumpet  or  French  horn,  can  scarcely  be 
called  a  vibration,  and  the  pitch  of  the  sound  is  here  determined  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  chord,  capable  of  vibrating,  either  accurately,  or  very  nearly,  with 
the  same  frequency,  it  causes  a  sympathetic  tone,  resembling  that  from 
which  it  originated ;  and  the  chord  may  produce  such  a  sound  either  by 
vibrating  as  a  whole,  or  by  dividing  itself  into  any  number  of  equal  parts. 
Thus,  if  the  daniper  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  chords  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  chords  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 
lliTOugh  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 
motion?,  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  accu- 
rately of  the  termination  of  a  sound.  Besides,  a  sympathetic  vibration  may 
be  excited  not  only  by  a  sound  producing  vibrations  of  equal  frequency, 
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  listen- 
ing 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  is,  however,  no  doubt  that  the  muscles^ 
with  which  the  different  parts  of  the  ear  are  furnished,are  concerned  in  accom- 
modating the  tension  of  some  of  them  to  the  better-transmission  of  sound; 


ON    THE    SOURCES    AND    EFFECTS    OF    SOUND.  3S7 

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 
soiinds  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  often  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  tlie  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  terminations  ' 
of  the  nerves,  which  form  a  loose  membranous  tissue,  almost  floating  in  it, 
Avhile  another  portion  of  them  is  distributed  on  the  surface  of  three  semi- 
circular tubes  or  canals,  opening  at  both  ends  into  the  cavity,  and  a  third 
portion  supplies  the  cochlea,  a  detached  channel,  which  appears  to  be  ar- 
ranged 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  atfecting  the  fluid  at  the 
base  of  the  cone  must  be  extremely  increased  at  its  vertex,  while  the  flexi- 
bility 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  scries 
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  respect- 


.')88  "  LECTURE    XXXII. 

ing  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  arrangement  for  the  perfection  of  the  sense. 
And  even  in  the  case  of  the  human  ear,  many  of  these  parts  may  be  spared 
withoyt  great  inconvenience  ;  thus,  we  hear  very  perfectly,  by  means  of  im- 
pressions communicated  to  the  teeth,  and  through  them  to  the  large  bones, 
of  the  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  the  organ  in  the  usual  manner..  (Plate 
XXV.  Fig.  349.  .  351.) 

Such  is  t^e  delicacy  of  the  organs  of  hearing  in  their  perfect  state,  that 
we  readily  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  vi- 
bration, and  which  constitutes  the  difference  between  instruments  of  differ- 
ent kinds,  or  different  instruments  of  the  same  kind,  or  even  the  same  instrument 
differently  employed.  Thus,  we  can  distinguish  very  accurately  the  voices  of 
our  friends,  even  Avhen  they  whisper,  and  those  modifications  of  the  same  voice 
which  constitute  the  various  vowels  and  semivowels,  and  which,  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 
Vhich  the  ear  is  enabled  to  make  this  discrimination,  we  cannot  reason  upon 
any  satisfactory  grounds. 


389 


LECTURE  XXXIir. 


ON    HARMONICS. 


The  philosopliical  theory  of  harmonics,  or  of  the  combinations  of  sounds, 
was  considered  by  the  ancients  as  affording  one  of  the  most  refined  em- 
ployments 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  entirely  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  motions 
produced  by  one  series  of  undulations  being  wholly  indiffisrent  with  respect  ^ 
to  the  effect  of  another  series,   and  each  particle  of  the  medium  being  neces- 
sarily 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  composi- 
tion  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  determin- 
ing 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 


390  LECTURE    XXXIII. 

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 
the  joint  effect  is  doubled,   or  perhaps  quadrupled,   since  it  appears  that  the 
strength  of  sound   ought    to  be  estimated  from  the  squares  of  the  veloci- 
ties of  the  particles:  but  when  the  particular  motions  of  the  two  sounds 
counteract  each  other,    both  their  effects  are  wholly  destroyed.     These  com- 
binations 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  combination. 
OWe  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.  359,.) 

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  quadru- 
ple force,  and  the  sound  gradually  increases  and  diminishes  in  continued  suc- 
cession 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  proportion  is  known; 
since  the  beats  are  usually  slow  enough  to  be  reckoned,  although  the  vibra- 
tions themselves  can  never  be  distinguished.  Thus,  if  one  sound  consisted 
of  100  vibrations  in  a  second,  and  produced  with  another  acuter  sound  a  single 


ON    HARMONICS.  391 

beat  in  ei'ery  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 
chord  equally  stretched,  or  two  simple  pipes,  of  whicli  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  numbei'  of  beats  in  15  seconds,  we  shall  find 
the  number  of  vibrations  in  a  single  setond.  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  4-  and  -J  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 
augmentations  of  their  force,  they  have  the  same  effect  as  any  other  impulses 
which  recur  in  regular  succession,  and  produce  a  musical  note,  which  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  succes- 
sion 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,  constitute 
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  tlms  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  predilec 
tion  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  Ave  cannot  im- 
mediately estimate  the  magnitude  of  the  vibrations,  yet  the  general  effect  of 


39S  .  LECTURE   xxxtir. 

a  regular  or  irregular  succession  necessarily  produces  the  impression  of  sweet-, 
ness  or  harshness.  The  same  sounds,  as  form  the  best  accompaniment  for  each 
other,  are  also  in  general  the  most  agreeable  for  melodies,  consisting  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  arc  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  kiud,  bears  a  considerable  resemblance  to  the  same  prin- 
ciple. 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  tlie 
rhythm  is  indeed  occasionally  introduced,  but  merely  for  the  sake  of  con- 
trast; 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  on  a 
bugle  horn, must  consist  of  the  harmonics  of  a  single  sound  only :  andwhen  an 
accompaniment  is  performed  by  a  French  horn,  the  length  of  the  instrument  is 
fust  adjusted  to  the  principal  note,  and  all  the  sounds  which  it  is  to  produce 
are  selected  from  this  natural  series.  But  the  notes  constituting  the  most 
natural  scale  are  not,  without  exception,  comprehended  among  the  har- 
monics; 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 


ON    HARMONICS.  SgS 

which  are  commonly  considered  as  filling  up  the  scale ;  and  on  account  of 
its  great  resemblance  to  the  fundamemtal  note,  it  is  described  by  the  same 
letter  of  the  alphabet,  or  by  the  same  syllable;  so  that  all  audible  sounds  are 
considered  as  repetitions  of  a  scries  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  harmonic  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  Sand  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  to  make  up  another 
perfect  triad  with  the  octave;  the  respective  notes  consisting  of  4  and  5 
vibrations,  while  the  fundamental  note  makes  3,  and  being  no  where  found 
among  the  natural  harmonics.  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  natuial  arrange- 
ment, and  it  appears  to  be  found  with  little  variation  in  barbarous  as  well  as 
in  civilised  countries.     (Plate  XXV.  Fig.  354.) 

A  long  piece  would,  however,  be  too  monotonous,  unless  the  fundamental 
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  succession  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  num- 
ber usually  employed  in  music  The  interval  between  any  two  adjoin- 
ing sounds  of  tlie  twelve  is  called  a  semitone  or  half  note,  two  semitones 

VOL.    I.  3  E 


3g4  ii;cTt;Ri:  xxxnr. 

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  the  neigh- 
bouring notes  on  either  side,  Avith  the  addition  of  the  term  sharp  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  cbange  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  regu- 
lar 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  dis- 
cords are  also  sometimes  introduced,  but  they  are  in  general  either  partial 
continuations  of  a  preceding,  or  anticipations  of  a  following  accord.  Two 
difi'erent  parts  of  a  harmony  are  never  allowed,  in  regular  and  serious  com- 
positions, 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  continue  for  some  time,  so  as  to  be  con- 
sidered as  a  repetition  of  the  same  part. 

These  are  almost  the  only  principles,  upon  which  the  art  of  accompaniment, 


/ 

/ 

ON    HARMONICS.  595 

as  well  as  the  general  theoryof  practical  music, is  founded.  Many  prolrx  treatises 
Jiave  been  written  on  the  subject,  but  they  only  contain  particular  illustra- 
tions 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  in- 
structing us  in  the  mode  of  attaining  what  is  beautiful  or  sublime. 

It  is  impossible  to  assign  any  such  proportions  foi  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  those  by  which  we  had  left  it.  The  simplest  mode  of  arranging  the 
twelve  sounds,  is  to  divide  the  octave  into  twelve  equal  intervals, 
all  the  notes  being  in  the  same  proportion  to  those  which  immedi- 
ately follow  them:  this  is  called  the  equal  temperament,  because  the  imper- 
fection is  equal  in  all  keys.  In  this  system  of  temperament,  the  fifths,  which 
consist  of  seven  semitones,  are  a  littfe  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  rnore  free  from  error;  partly  for  variety,  and  partly  because  some 
are  more  frequently  used  than  others  :  this  cannot,  however,  be  done  with- 
out 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  de- 
scending 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.  Anoth*er  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  tempered,  and  to  de- 


Sg6  ,  LECTUEE.XXXIir. 

scend  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  fre- 
quency 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  gene- 
rally disposed  on  five  or  more  lines,  with  their  intervening  spaces,  each  im- 
plying 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  im- 
plying 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  vibration  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,  consisting  of  256  vibrations  in  a 
second.  The  fifth,  consisting  of  sixteen  vibrations,  Avill  be  nearly  the  low- 
est 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.) 


397 


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  chords,  of  membranes,  of  elastic  plates,  or  of  the  air;  or  by  the 
joint  effects  of  the  air  and  a  solid  body  vibrating  together.  The  es- 
sential varieties  of  stringed  instruments  are  found  in  the  harp,  the 
harpsichord,  the  pianoforte,  the  clavichord,  the  guitar,  the  violin,  the 
vielle  or  monochord,  and  the  aeolian  harp.  In  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  per- 
former 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  a  separate  string;  and  in  the  Welch  harp  there  are  two  strings  to 
each  note  of  the  principal  scale,  with  an  intermediate  row  for  the  ficm'tones; 
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  pxoduce  the  semitones  by  changing  the 


398  LECTURE    XXXIV. 

tension  of  the  strings,    which  is  said  to  have  succeeded  tolerably  well 
although  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  tliis  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  indifferent  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  ham- 
mers,  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  l:)ridge,  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  ke}',  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  Avith  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 


ON    MUSICAL    INSTRUMENTS.  359 

pianoforte  guitar,  hammers  are  interposed  between  the  fingers  and  the  strings, 
acting  like  those  of  tlie  pianoforte.  The  mandoline  and  lute  are  species  of 
the  guitar:  and  the  arch  lute  was  a  very  powerful  instrument  of  the  same  kind, 
formerly  much  ulsed  in  full  pieces. 

In'  the  violin,  and  in  other  instruments  resembling  it,  all  the  strings  arc 
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  oppo- 
sition to  the  friction ;  for  the  friction  of  bodies  in  motion  is  generally  less 
than  their  adhesion  when  they  are  at  rest  with  respect  to  each  otlier,  besides 
that  the  contact  of  the  string  with  the  bow  is  usually  in  great  measure  in- 
terrupted 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  instrument  appears  to 
have  been  the  viola  or  tenor,  its  diminutive  the  violino,  its  intensitive,  ex- 
pressing 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  accom- 
paniment. 

The  vielle,  or  raonochorcl,  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  continually  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,  frecpiently  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.)  ' 


400 

*""  L?:CTURE    XXXIV. 

The  human  voice  depends  principally  on  the  vibrations  of  the  membranes 
of  the  glottis,  excited  by  a  current  of  air,  which  they  alternately  intercept 
and  suffer  to  pass;  the  sounds  being  also  modified  in  their  subsequent 
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  concerned  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   thyreoid  car- 
tilage,   and  behind,  the  two  arytaenoid  cartilages,   composing  together  the 
cavity  of  the  glottis,    over  which  the  epiglottis  inclines  backwards,  as  it 
ascends  from  its  origin  at  the  upper  part  of  the  thyreoid  cartilage.     Within 
the  glottis   arc  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  frequency,   and 
as  they  vibrate,  produce  a  continuous  sound.     Properly  speaking,   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  pro- 
cress  by  the  various  arrangements  of  the  different  parts  of  the  mouth.  Of 
simple  vowels  sixteen  or  eighteen  may  be  enumerated  in  different  languages: 
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  semiuasal  semi- 


ON    MUSICAL    INSTRUMENTS.  401 

vowels.  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  experi- 
ments on  the  effects  of  pipes  of  different  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.     (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  chord.  But  in  the  case  of  a  tambourine  and 
a  drum,  the  membrane  is  stretched  in  every  direction,  and  the  force  of 
tension  consequently  acts  in  a  different  manner.  The  principal  character 
of  such  instruments  is  their  loudness,  derived  from  the  magnitude  of  the  sur- 
face 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  sotinds,  by  means  of  vibrations  depend- 
ing on   the  elasticity  of   solid   bodies,    are  less   frequently  employed   than 
others;   they  have    a  peculiar   character   of   tone,  which    is   by   no    means 
unpleasant,  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  imme- 
diately with  hammers,   or  by  means  of  keys ;  the  tuning  fork,  the  gong,  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  some- 
times by  that  of  rubbers  of  cork.     The  vibrations  of  an  elastic  plate,  agi- 
tated by  a  current  of  air,    which  it  continually   admits  and  excludes,    con- 
stitute 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  de- 
pend.    (Plate  XXVI.  Fig  360  .  .  36i.)  '     . 

VOL    I.  3  I' 


402  LECTURE    XXXIV. 

Of  Simple  Avlnd  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  efl^ective  length  of  the  flute  and  flageolet  is  altered 
.  at  pleasure  by  opening  or  shutting  the  holes  made  at  proper  distances  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  tonebeing  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,  however,  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  whist- 
ling, by  a  current  of  air  which  is  forced  through  it.  (Plate  XXVI.  Fig. 
563  .  .  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  bonis  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.  Tlie  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,  so 

2 


ON    MUSICAL    INSTRUMENTS.  .       403 

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 
a  valve  is  opened,  when  the  proper  key  is  touched^  which  causes  all  the  pipes 
belonging  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  dis- 
cord, instead  of  the  grand  and  sublime  effect  which  this  instrument  is  capa- 
ble 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  tradi- 
tion 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,  about  700 
years  before  our  era,  and  two  centuries  afterwards,  either  P)  thagoras,  or  Si- 
monides,  completed  the  octave,  which  consisted  of  intervals  differing  verv 
little  from  the  modern  scale,  the  key  note  being  nearly  in  the  middle  of  the 
series.  In  subsequent  times  the  number  of  the  stiings  was  much  increased ;  the 
modulations,  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  man}  pleasini;'  combinations,  as  our  more  modern  systems.  Although 
it  is  certain  that  the  ancients  had  frequent  accompaniments  in  perfect  harmony 


404  LECTURE    XXXIV. 

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  clari- 
net, for  it  had  a  reed  mouth  piece,  about  three  inches  long;  the  same  per- 
former 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 
very  correct  idea  of  the  true  nature  of  the  motions  of  the  air  constituting 
sound.  He  knew  that  a  pipe  or  a  chord  of  a  double  length  produced  a 
sound  of  which  the  vibrations  occupied  a  double  time;  and  that  the  properties 
of  concords  depended  on  the  proportions  of  the  times  occupied  by  the  vibra- 
tions of  the  separate  sounds.  It  is  not  indeed  improbable  that  at  least  as  much  as 
this  was  known  to  Pythagoras,  since  he  established  correctly  the  numerical 
ratios  between  various  sounds;  but  so  little  justice  has  been  done  to  his  dis- 
coveries 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. 

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  Avere  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 
Galled,  which  owe  their  improvement  to  the  middle  ages.  The  old  ecclesi- 
astical 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  man- 
ner they  obtained  a  variety  much  resembhng  that  of  the  modes  or  kinds  of  music 
in  use  among  the  ancients.     Pope  Gregory,  about  the  year  600,  distinguished 


ON    MUSICAL    INSTRUMENTS.  405 

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  aeustics,  and  some  of  them  are 
not  perfectly  accurate,  Galileo  rediscovered  what  was  well  known  to  Aris- 
totle, respecting  the  nature  of  sound;  for  the  words  of  Aristotle  had  been 
so  much  misunderstood  and  misinterpreted,  that  he  could  have  profited  but 
little  by  them.  His  cotemporaries  Mersenne  and  Kircher  made  a  variety  of 
very  ingenious  experiments  and  observations,  on  sound  and  on  soundin<i- 
bodies,  many  of  them  unknown  to  authors  of  later  date.  The  theory  of 
the  ancient  music  was  very  accurately  investigated,  in  the  middle  of  the 
17th  century,  by  Meibomius  :  our  countryman  Wallis,  also,  besides  employ- 
ing much  learning  and  penetration  in  the  illustration  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  propagation 
of  sound  were  the  beginning  of  all  the  more  accurate  investigations  relating 
to  aeustics.  It  must  not  be  denied  that  these  propositions  contain  some  very 
inconclusive  reasoning  respecting  the  nature  of  the  motions  constituting 
sound,  by  which  the  determination  of  a  particular  case  is  erroneously  extended 
into  a  general  solution  of  the  problem.  The  velocity  is,  however,  truly  cal- 
culated, because  it  is  in  fact  independent  of  the  particular  nature  of  the  vibra- 
tion, 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  investigated  the  time  occupied  by  the  vibration  of  a  string  or 
chord  upon  a  particular  supposition,  which  he  co:>sidered  as  a  necessary 
condition,  but  which  in  fact  confined  the  inquiry  to  a  limited  case.  It 
happensjhowever,  that  the  same  determination  of  the  frequency  of  vibration  is 
equally  true  in  all  possible  cases.     Sauveur  obtained,  about  the  same  time 


4.06  tECTURE    XXXIV. 

a  similar  conclusion  from  reasoning  still  less  accurate:  his  merits  with  respect 
to  the  theory  of  acustics  in  general  are,  however,  by  no  means  contemptible. 
Lagrange  and  Euier  have  corrected  and  much  extended  the  investigations 
of  Newton,  and  of  Taylor;  and  Bernoulli  and  Daleinbert  have  also  materi- 
ally contributed  to  the  coijiplete  examination  and  discussion  of  the 
subject. 

About  the  year  1750,  Daniel  Bernoulli  succeeded  in  obtaining  a  solution 
of  a  problem  still  more  diificult  than  those  which  relate  to  the  motions  of 
chords:  he  determined  the  frequency  of  the  vibrations  of  an  elastic  rod 
fixed  at  one  end,  as  well  as  the  relations  of  its  subordinate  sounds.  Thesolution 
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  extending  and  facilitating  the 
mathematical  part  of  this  investigation,  although  he  has  committed  several 
mistakes  respecting  the  meclianical  application  of  it,  some  of  which  he 
has  himself  corrected,  and  others  have  been  noticed  by  Riccatiand  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 
computations  have,  however,  been  amply  confirmed  by  the  experiments  of 
Lambert  on  the  sounds  of  flutes. 

Dr.  Chladni's  method  of  examining  the  sounds  of  plates  has  affbrded  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  tlie  subject  of  acustics 
in  general.     Some  remarks  which  I  have  made  in  the  Philosophical  Trans- 


ON    MUSICAL    INSTRUMENTS. 


407 


actions  may  perhaps  also  be  considered  as  tending  to  illustrate  the  vi- 
brations of  chords.  The  latest  improvement  which  deserves  to  be  mention- 
ed, 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. 


CHRONOLOGY    OF    ACUSTICS. 


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40S 


LECTURE  XXXV. 


ON    THE    THEORY    OV    OPTICS. 


J.  HE  science  of  optics  is  one  of  the  most  elegant,  and  the  most  important 
branches  of  natural  and  mechanical  philosophy.  It  presents  us  with  experi- 
ments attractive  by  their  beauty  and  variety,  with  investigations  affording 
an  ample  scope  for  mathematical  refinementSj  and  with  instruments  of  exten- 
sive utility  both  in  the  pursuit  of  other  sciences,  and  in  the  common  em- 
ployments 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  conclusions 
immediately  deducible  from  those  properties;  and  next,  the  application  of 
these  laws  to  practical  purposes,  in  the  construction  of  optical  instruments. 
We  shall  afterwards  proceed  to  examine  the  more  complicated  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  explanation  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  pf  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  de- 
fine light  from  its  sensible  qualities.  The  sensation  of  light  is  sometimes  pro- 
duced by  external  pressure  on  the  eye;  we  mu>>t  exclude  this  sensation  from  the 
definitionof  light,  and  must  therefore  call  light  an  influence  capable  of  entering 

5 


ON    THE    THEORV    OF    OPTICS.  409 

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  <lo  not 
include  i  n  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  sometimes  conceiv- 
ed 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  exhi- 
bit to  the  senses  a  single  mathematical  line,  except  as  the  bountlary  of  two 
surfaces;  in  the  same  manner,  Ave  cannot  exhibit  a  single  ray  of  light,  except 
as  the  confine  between  light  and  darkness,  or  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  transparent 
mediums.  Perhaps  no  medium  is,  strictly  speaking,  absolutely  transparent; 
for  even  in  the  air,  a  considerable  portion  of  light  is  intercepted.  Ithas 
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  homo- 
geneous 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 

VOL.    I.  ^  3  G 


410  ^  LECTURE    XXXV. 

nature  of  the  medium  is  changed,  the  path  of  Ijght  dcA'iates  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  con- 
sequence of  the  action  of  heat. 

"When  rays  of  light  arrive  at  a  surface,  which  is  the  boundary  of  two  me- 
diums 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  re- 
fraction 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  black  as  to  reflect  no  light  at  all,  and  to  be  perfectly  invisible 
in  a  strong  light;  although  at  the  surface  separating  two  very  rare  bodies, 
as  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  reflecting 
surface;  and  these  angles  are  always  equal  to  each  other;  consequently 
the  inclination  of  the  rays  to  the  surface  remains  also  the  same.  The 
quantity  of  light  reflected,  when  other  circumstances  are  equal,  appears  to 


ON    THE    THEORY    OF    OPTICS.  411 

be  always  greatest  when  the  difFereace  of  the  optica)  or  refractive  density  of 
the  two  substances  is  greatest.  Thus  the  reflection  from  the  common  sur- 
face of  glass  and  water'  is  much  weaker,  than  from  a  surface  of  glass  ex- 
posed 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  den- 
sity of  the  metals  must  be  exceedingly  great. 

It  appears  also  that  a  portion  of  the  light  falling  on  a  reflecting  surfiice 
is  always  transmitted,  at  least  to  a  certain  depth,  notwithstanding  the  appa- 
rent 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  thick- 
ness, 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  ail  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  sur-r 
ffice.  Thus,  if  the  refractive  properties  of  the  substance  were  such,  tliat  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  "re- 
fracted, without  sensible  error,  into  an  angle  of  one  degree.  IJut  Avhen  the 
angles  are  larger,  they  vary  from  this  ratio,  their  sines  only  preserving  the 
proportion  with  accuracy:  for  example,  if  the  angle  of  incidence  at  the  sup- 
posed 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,  Avhich  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.) 


41<i  LKCTURTE  XXXV. 

In  order  to  obtain  the  eifects  of  regular  reflection  and  transmission,  wc 
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  realit}',  as 
many  separate  surfaces,  disposed  in  all  imaginable  directions,  so  that  from 
the  e(|uality  of  the  angles  of  incidence  and  reflection,  with  respect  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  continuing  the  mechanical 
operation  of  polishing,  we  only  render  these  surfaces  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  re- 
turned 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  wliich  the  rays  of  light  are  caused  to  approach  nearest  to 
the  line  perpendicular  to  its  surface,  is  said  to  have  the  greatest  refractive 
density.  In  general  there  is  a  considerable  analogy  between  this  re&active 
density  and  the  specific  gravity  of  the  substance:  thus  water  is  more  refrac- 
tive than  air,  and  glass  than  water.  But  inflammable  bodies  are  usually 
more  refractive  than  bodies  of  the  same  specific  gravity,  which  are  not  in- 
flammable;  and  it  is  well  known  that  from  the  high  refractive  power  of  the 
diamond,  in  proportion  to  its  actual  density,Sir  Isaac  Newton  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  combination  of  oily  or  inflammable 
particles,   with  others  earthy  or  not  inflammable.     In  the  order  of  refractive 


ON    THE    THEORY    OF    OPTICS.        '  413 

density,  beginning  from  the  lowest,  or  a  vacuum,  we  liave  airs  and  gases 
of  different  rarities,  water,  which  is  the  least  refractive  of  allliquids,  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-t, 
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  1^; 
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  sur- 
faces, must  transmit  a  ray  of  light,  after  a  second  refraction  at  its  posterior 
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  difi'erent  kinds,  produces  no  alteration  in  the  whole  an- 
gular 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  surface  of  any 
two  mediums  is  the  quotient  of  their  respective  indices.  For  instance,,  a 
plate  of  c  rown  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  surface  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  whenthe  angle  of  incidence  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. 


414  LECTURE    XXXV. 

Thus,  if  the  law  of  refraction  required  the  sine  of  the  angle  of  refraction  to 
be   twice  as  great  as  that  of  incidence,  this  condition  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  reflection  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  reflection  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  tw^o  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 
'mage  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  exa" 
.niine  the  general  theory  of  refraction  and  reflection,  at  surfaces  of  different 
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 
Ihey  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,  may  re- 
present the  actual  focus  of  converging  rays.     It  was  to  such  an  image  of  the 


ON    THE    THEORY    OF    OPTICS. 


415 


8un  that  the  term  focus,  meaning  a  fireplace,  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  re- 
fracted or  reflected  rays  are  called  conjugate  to  each  other:  the  new  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  object;  a  pror 
perty  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  experi- 
mental 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  the}'  are 
made  to  divei-ge,  is  called  the  principal  focus  of  a  surface  or  substance.  The 
sun  is  so  distant,  that  the  rays,  proceeding  from  any  point  of  his  surface, 
aifect  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  refrac- 


416  LECTURE    XXXV. 

tion.  A  small  portion,  however,  of  any  of  these  curves,  differs  very 
little  from  a  circle;  and  a  spherical  surface  is  ahuost  universally  substituted 
in  practice  for  all  of  them,  except  that  the  mirrors  of  large  reflecting  tele- 
scopes 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  observed :  and  the  same  is  true 
of  the  foci  produced  by  refracting  surfaces.  (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  diff'erent  direction.     (Plate  XX VII.  Fig.  379,  380.)  ' 

A  lens  is  a  detached  portion  of  a  transparent  substance,  of  which  the  op- 
posite 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  sufficiently  described  by  their  names, 
except  that  the  term  meniscus,  which  properly  implies  a  little  m  oon  or 
crescent,  is  applied  in  general  to  all  lenses  which  are  convex  on  the  one  side, 


ON    THE    THEORY    OF    OPTICS.  4J7 

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  cal- 
culations,  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  surface 
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  cither  causes  them  to  diverge,  or  lessens  their  convergence.  (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  dif- 
ference. 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  substance, 
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-i,  we  must  divide  the  radius  by  ^,  or  increase  it  one  half,  for 
the  principal  focal  distance  of  a  double  convex  or  double  concave  lens  of 
water. 

When  a  radiant  point  is  at  twice  the  distance  of  the  principal  fOcus  from 
a  convex  lens,  the  image  is  at  an  equal  distance  on  the  other  side;  when  the 

VOL.    I.  3  H 


4.18  LECTURE    XXXV. 

radiant  point  is  nearer  than  this,  the  image  is  more  remote,  tlie  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  neces- 
sary 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  col- 
lected into  as  many  distinct  points  of  the  image.     Some  of  the  rays  proceed- 
ing from  every  radiant  point  must  be  considerably   bent,    in  order  to  be  col- 
lected into  a,  common  focus;  others  remain  nearly  straight;  and  if  Ave  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  direction  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   irnage  of  any  radiant  point  must 
consequently  be  found  somewhere  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  ob- 
servable  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 


ON    THE    THEORY    OF   OPTICS.  419 

part  of  a  flat  image,  of  which  the  magnitude  is  determined  by  straight  lines 
drawn  from  the.  extremities  of  the  object  through  the  centre  of  the 
lens.  This  is,  however,  an  approximation  which  is  only  admitted  for 
the  greater  convenience  of  computation  and  representation,  the  image 
being  almost  always  in  reality  considerably  curved.  (Plate  XXVII.  Fig. 
386.) 


420 


LECTURE  XXXVI. 


ON    OPTICAL    INSTRUMENTS. 


Among  the  great  variety  of  instruments  depending  on  optical  principles, 
it  is  more  consistent  with  our  plan  to  attend  first  to  those  which  may  be 
denominated  optical  measures,  which  are  calculated  either  for  the  determina- 
tion of  the  quantity  or  intensity  of  light  itself,  or  for  the  examination  of  the 
properties  of  various  material  substances  with  respect  to  light.  Reflecting 
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  pr.operly  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,     tliat   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  inch  of  any  sur- 
face, 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  conclude  that  their  original 


OK    OPTICAL    INSTRUMENTS.  421 

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.  Dr.  Wol- 
laston's  apparatus  is  far  preferable  to  both  these  methods:  it  is  arranged  for 
ascertaining  the  angle   at  which  light,  moving  within  a  certain  dense  trans- 
parent 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  iixed  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  oft^   by  a 
vernier,  without  any  calculation,   the   index    of   the  refractive    power   of 
any  substance  less  dense  than  glass.      (Plate  XXVII.  Fig.  3S9.) 

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  continu- 


422  LECTURE    XXXVI. 

ally;  and  these  are  cither  microscopes  or  telescopes,  which  present  us  with 
great  diversity  in  their  arrangements,  and  in  the  appurtenances  subservient  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.  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  or  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  sub- 
tends at  the  centre  of  the  lens:  and  since  this  angle  ma/y  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  microscope;  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  distance  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  magnitude  may  be  increas- 
ed 17  times  instead  of  l6,  and  9  times  instead  of  8.  (Plate  XXVII. 
rig.  395,  596.) 

Since  the  magnifying  power  of  a  lens  is  the  greater,  the  smaller  its  focus, 


ON     OPTICAL    INSTRUMENTS.  423 

it  is  usual  ot  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  pro- 
posed to  substitute  for  water  a  transparent  varnish,  which  is  less  liable  t^ 
evaporate.  • 

Supposing  the  whole  light  that  proceeds  from  a  distant  object,  and  falls  on  g, 
lens  or  speculum,  to  be  collected  in  the  image,  its  intensity  must  be  increased 
in  the  ratio  of  the  surfaceof  the  lens  or  speculum  to  that  of  tile  image.  The  image 
is  greater  in  proportion  as  the  object  is  greater;   consecpiently  the  deoree  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   illumination  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  li<>-ht.      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  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  proposed 
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  anil' 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  reflection ;  but  thev 


424  LECTURE    XXXVI. 

are  more  .expensive,  and  are  liable  to  tarnish.     Where  a  large  mirror  is  re- 
quired,   with   a  weak  reflection   only,   we     may  employ  a  single  surface  of 
glass,   the  back   of  the  piece    being  covered  with  a  black  coating  of  some 
substance  diftering  little  from   glass  in  its  refractive  density,   by  means  of 
which  the  second  reflection  is  avoided. 

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  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 
an  an  inverted  position,  in  the  parts  of  the  room  diametrically  opposite  to 
them,  which  are  illuminated  in  dift^erent  degrees,  according  to  the  quantity 
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  defined,  unless  the 
objects  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  re- 
mote 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  obliquely, 
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  impression  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  the  speculum  above  it,  which  throws  the  image 
through  the  lens,  upon  a  flat  surfiice  placed  below,  on  which  the  objects 
may  be  delineated  in  their  natural  position,  but  not  without  some  impedi- 
ment from  the  interception  of  the  light  by  the  hand  and  the  instrument 
employed.  Such  a  surface,  however,  ought  not  to  be  perfectly  flat,  in 
order  to  aiford  the  most  distinct  image,  although  by  means  of  a  meniscus 


ox  OPTICAL  insthumexts.  425 

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  distant 
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  ex- 
tremely erroneous,  for  the  eflectof  the  obrujuity  of  the  different  pencils  of  rayg 
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  required  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  XXV^II.  Fig, 
397  .  .  399. ) 

In  the  solar  microscope,  an  image  is  formed  on  a  wall  or  screen,  by  mean* 
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  burn 
ing  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  adjust 
the  instrument  in  the  most  convenient  manner,  the  distances  of  all  the 
lenses  ought  to  be  moveable  at  pleasure:  the  want  of  this  precaution  is  a 
material  defect  in  the  usual  construction  of  the  instrument.  The  speculum 
which  first  receives  the  light  must  be  capable  of  motion  in  all  angular  direc- 
tions, in  order  to  allow  us  to  accommodate  its  position  to  the  changeable 
place  of  the  sun;  and  the  adjustment  has  sometimes  been  performed  by 
means  of  a  heliostate,  an  instrument  calculated  for  turning  the  speculuaj 

VOL   I.  3  I 


426  LECTURE    XXXVI. 

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  speculums, 
the  one  moveable  round  an  axis  parallel  to  that  of  the  earth,  and  reflecting 
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  amusement  of 
children,  is  called  a  magic  lantern:  and  this,  exhibited  on  a  larger  scale,  and 
projecting  an  image  on  a  semitransparent  screen  of  taifetas,  instead  of  a  wall,  has 
of  late  been  the  source  of  much  entertainment  under  the  name  of  the  phan- 
tasmagoria, 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  afterwards  varnished.  By  removing 
the  lantern  to  difl'erent  distances,  and  altering  at  the  same  time  more  or  less 
the  position  of  the  lens,  the  image  may  be  made  to  increase  or  di- 
minish, and  to  become  more  or  less  distinct  at  pleasure,  so  that  to  a  person 
unaccustomed  to  the  effects  of  optical  instruments,  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  thein  to  appear  fainter  when  they  are  remote 
than  when  they  are  near:  this  imperfection  might  be  easily  remedied  by  the 
interposition  of  some  seraiopaque  substance,  which  might  gradually  be 
caused  to  admit  more  light  as  the  figure  became  larger,  or  by  uncovering  a 
larger  6r  a  smaller  portion  of  the  lamp,  or  of  its  lens.     Sometimes,  by  throw- 


ON    OPTICAL    INSTRUMENTS.  427 

mg  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  sufticiently  distinct  at  once,  there- 
fraction  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  an  inverted  image  to  be  formed  between  them,  and 
to  throw  a  second  picture  of  tliis  image  on  the  screen,  in  its  natural  erect 
position,  unless  the  object  be  of  such  a  nature  that  it  can  be  inverted  with- 
out inconvenience.  This  effect  was  very  well  exhibited  at  Paris  by  Robert- 
son; he  also  combined  with  his  pictures  the  shadows  of  living  objects, 
which  imitate  tolerably  well  tlie  appearance  of  such  objects  in  a  dark  night,  or 
by  moonshine:  and  while  the  room  was  in  complete  darkness,  concealed 
screens  were  probably  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.) 

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  sub- 
sequent image.  The  simplest  of  such  instruments  is  the  astronomical  tele- 
scope. 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  (juotient  is  conse- 
quently 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  as- 


428  LECTURE    XXXVI. 

tronomical  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, 
Avhich  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  ad- 
vantage 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 
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  smce  the  speculum,  if  it  received  the 
principal  rays  perpendicularly,  would  send  them  back  in  the  same  direction, 
it  is  necessary,  in  this  construction,  to  have  them  reflected  somewhat  ob- 
licjuely,  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 
Avas  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  instruments  allow 
liim  to  extend  the  linear  dimensions  of  his  objects  several  thousand  times : 

5 


OK    OPTICAL    INSTRUMENTS.  429 

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  diminisJied  by  wholly  omit 
ting  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 
Avas  invented,  that  the  best  part  of  the  speculum  is  sacrificed  by  the  perfora- 
tion. 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.  Cassegrain  substituted 
a  convex  one,  placing  it  within  the  focal  distance  of  the  large  speculum,  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  inter- 
cepted 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 


4^0  LECTURE    XXXVI. 

considerably  less  curved  than  that  which  is  depicted  by  a  lens  of  equal  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  represented, 
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,  provided 
that  none  of  the  light  has  been  intercepted  in  its  passage  through  the  tele- 
scope: for  the  object  will  be  viewed  through  the  telescope  in  an  angle  as 
much  greater  tlian  that  which  it  naturally  subtends,  as  the  diameter  of  the 
object  glass  is  greater  than  that  of  this  contracted  pencil,  which  may  be  con- 
sidered as  an  image  of  the  object  glass.  But  in  the  Galilean  telescope,  this 
method  cannot  be  employed,  since  no  such  image  is  formed.  Th?  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  magnitude 
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  gLs« 
is,  therefore,  usually  placed,  both  in  telescopes,  and  in  the  common  com- 
pound 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  ad- 
justed by  experiment,  for  several  circumstances  are  concerned  in  the  perform- 


ON    OPTICAL    INSTRUMENTS.  431 

ance  of  a  telescope,  which  are  ahnost  too  intricate  for  practical  calculation, 
although  some  assistance  may  certainly  be  obtained  fi'om  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  planoconvex  lens  a  little  beyond  the 
image,  with  its, flat  side  turned  towards  it.  !Mr.  Ramsden  also  employs 
an  eye  piece  constructed  on  this  principle  instead  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  corresponding  point  of  the 
image,  requires  also  to  be  considered  in  the  construction  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  cir- 
cumference 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  focal  length,  this 
aberration  would  be  only  i-V  ^s  great;  it  may,  however,  be  slmost  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  edges: 
this  imperfection,  however,  Mr.  DoUond  has  in  great  measure  obviated, 
by  his  achromatic  object  glasses:  the  construction  of  which  depends  on 
the  important  discovery,  that  some  kinds  of  glass  separate  the  rays  of  differ- 
ent 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  power- 
ful 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 


433  LECTURJR    XXXVI. 

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  re- 
frangibilities  of  the  different  rays,  is  partially  corrected  in  an  eye  piece,  by 
placing  a  field  glass  in  such  a  manner,  as  considerably  to  contract  the  di- 
mensions 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  afliected  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  tbe  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 
ns  at  once  to  read  ofi^'  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, 
cither  a  scale,  or  any  other  object  of  known  dimensions,  placed  at  a  given  dis- 
tance: the  lucid  disc  micrometer  of  Dr.  Herschel  is  employed  in  this  man- 
ner 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  dis- 
placement 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 


ON    OPTICAL    INSTRUMENTS.      ♦  435 

principle,  and  which  seems  to  be  somewhat  less  liable  to  error.  In  a  reflect- 
ing telescope  of  Cassegrain's  construction,  Mr.  Ramsden  has  also  pro- 
duced the  same  effect  by  dividing  the  convex  speculum,  and  causing  a 
part  of  it  to  turn  round  an  axis.  All  these  arrangements  particularly 
deserve  the  attention  of  those  who  are  employed  "n  practical  astro- 
norriy  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.) 


VOL.    1.  ^K 


434 


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    affectiots 
of  Hght,  which  rather  belong  to  its  natural  history,   than  to  its  mechanical 
effects;  to  trace  its  relations  to  the  particular  phenomena  of  nature;  to  in- 
vestigate 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  density  of  the  at- 
mosphere, 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  consti- 
tute 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  combus- 
tion. 

Light  is  also  afforded,  without  any  sensible  heat,  by  a  number  of  vegetable 


ON    PHYSICAL  OPTICS.  '  4,35 

and  animal  substances,  which  appear  to  be  undergoing  a  slow  decomposition,, 
not  wholly  unlike  combustion.  Thus  decayed  wood,  and  animal  substance* 
slightly  salted,  often  afford  spontaneously  a  faint  light,  without  any  elevation 
ef  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  electrical 
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  diificult  to  ascertain  whether  friction  may  not  be  partly  concerned  in 
the  luminous  phenomena  attributedto  electricity,  or  electricity  in  the  apparent 
eflf'ects  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  accom- 
panied by  combustion,  the  heat  produced  by  the  union  of  these  causes  may  be 
very  moderate :  thus  it  is  usual  in^some  coalmines,  to  obtain  a  train  of  light  by 
the  continual  collision  of  flint  and  steel,  eflfected  by  the  machine  called  a 
fire  wheel,  in  order  to  avoid  setting  fire  to  the  inflammable  gas  emitted  by  the 
coal,  which  would  be  made  to  explode  if  it  came  near  the  flanie  of  a  candle. 

There  is  a  remarkable  property,  which  some  substances  possess  in  arv 
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  emission  is  in- 
terrupted by  cold.  The  Bolagnan  phosphorus  was  one  of  the  first  of  these 
substances  that  attracted  notice  ;  it  is  a  sulfate  of  bary  tes,  found  in  the  st.ate 
of  a  stone;  it  is  prepared  by  exposuri  to  heat,  and  is  afterwards  made  up  into 
cakes:  these,  when  first  placed  in  abeam  of  the  sun's  light,  and  viewed  after- 
wards in  a  dark  room,  have  nearly  the  appearance  of  a  burning  coal,or  a  red  hot 
iron.  Burnt  oyster  shells,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  experiments  apparently  accurate,  made  by  difterent 
persons,  there  is  reason  to  conclude  that  some  of  these  phosphori  emit  only 
the  same  kind  of  light  as  they  have  received,  while  others  exliibit  the  same  ap- 
pearances, 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  effita- 


% 


435  '^tECTURE    XXXVII. 

cious  in  exciting  in  a  diamond  the  appearance  of  another  kind  of  light,  which 
it  was  naturally  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  sub- 
stances, which  are  not  remarkable  for  their  power  of  imbibing  light,  a  tem- 
porary scintillation,  or  flashing,  at  a  heat  much  below  ignition:  the  most  re- 
markable of  these  are  fluor  spar  in  _po\\^der,  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  ob- 
servations 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  confirmed  it  by  his  discovery  of  the  cause  of  the  apparent  aber- 
ration of  the  fixed  stars. 

This  aberration  is  produced  by  the  eflfect  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  undisturbed,  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  manned" 
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  reseuibling  such  a  tube,  the  passage 
of  the  light  through  tlie  refracting  substances  not  altering  the  necessary  in- 
clination of  the  axis.     In  various  parts  of  the  earth's  orbit,  the  aberration 


ON    PHYSICAL    OPTICS.  437 

of  any  one  star  must  be  different  in  quantity  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  ob- 
liquity 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  quicksilver 
more  than  two  thirds:  but  when  the  obliquity  was  as  great  as  possible,  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  com- 
pound 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 
proc'eeds  by  gradual  changes  from  red  to  violet,  and  that  those  substances 
whifch  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.  Herschel  has  added  to  this  series 
rays  of  heat  less  refrangible  than  the  red,  and  Hitter  and  Dr.  Wollaston  have 
discovered,  beyond  the  violet,  other  still  more  refrangible  rays, which  blacken 
the  salts  of  silver. 

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 
refraction,     they    exhibit    seven    varieties    of    colour,     related  ■  to    each 


T. 


43S  LECTURE   XXXVIl. 

Other  with    respect  to  the  extent  that  they   occupy,   in  ratios  nearly  analo- 
ffous  to  those  of  the   ascendino;   scale   of  the  minor  mode  in   music.     The 
ohservations  were,   however,   imperfect,  and  the  analogy  was  wholly  imagin- 
ary.    Dr.  Wollaston  has  determined  the    division  of  the   coloured  image  or 
spectrum,  in  a  much  more  accurate  manner  than  had  been    done   hefore:   by 
looking  through  a  prism,  at  a  narrow  line  of  light,   he  produces  a  more  effec- 
tual 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 
tonsists  of  four  colours  only,   red,  green,   blue,   and  violet,  which  occupy 
spaces  in  the  proportion  of  \6,  23,   36,  and  25,  respectively,  making  together 
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  breadth  scarcely 
pxceeds  that  of  the  aperture  by  which  the  light  is  admitted,  and  Dr.  Wollaston 
attributes  it  to  the  mixture  of  the  red  with  the  green   light.     There  are  also 
several  dark   lines  crossing  the  spectrum  within  the  blue  portion  and  in  its 
neighbourhood,  in  which  the  continuity  of  the  light  seems  to  be  ii\terrupted. 
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  variations  of  the  obliquity  of  the  rays.     The  angu- 
lar 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  spectrum 
is  sometimes  still  more  interrupted  ;  thus,  the  bluish  light  of  the  lower  part 
of  the  flame  of  a  candle  is  separated  by  refraction  into  five  parcels  of  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  spai  k  furnishes  also  a  light  which  is  differently 
divided  in  different  circumstances.     (Plate. XXIX.  Fig.  420.) 


ON    PHYSICAL    OPTICS.  439 

If  the  breadth  of  the  aperture  viewed  through  a  prism  is  somewhat  in- 
creased, the  space  occupied  by  each  variety  of  hght  in  tiie  spectrum  is  aug- 
mented in  the  same  proportion,  and  each  portion  encroaches  on  the  neigh-, 
bouring  colours,  and  is  mixed  with  them:  so  that  the  red  is  succeeded  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  mag 
nitude  of  the  spectrum,  it  retains  its  whiteness  in  the  centre,  and  is  term i-" 
nated  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  pf 
the  violet  being  scarcely  distinguishable  from  the  neighbouring  white  light:- 
on  the  other  hand,  the  space  belonging  to  the  red,  green,  and  blue,  of  thft 
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  pos- 
terior surface  of  a  prism.     (Plate  XXIX.  Fig.  422.) 

Sir  Isaac  Newton  observed  that  the  effect  of  white  light  on  the  senso 
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  naturallyl 
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  respec- 
tively, 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 
aensations  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  w^  may  consider. white  light  gis  composed  of 


440  LECTURE  xxxvri, 

a  mixture  of  red,  green,  and  violet,  only,  in  the  proportion  of  about  two 
parts  red,  four  green,  and  one  violet,  with  respect  to  the  quantity  or  intens- 
ity of  the  sensations  produced. 

If  \vc  mix  together,  in  proper  proportions,  any  substances  exhibiting  these 
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  combination  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  substances  mixed  to- 
gether usually  make  rather  a  brown  than  a  yellow  colour,  and  many  yel- 
low colours, when  laid  on  very  thickly,  or  mixed  with  black,  become  brown.  The 
sensations  of  various  kinds  of  light  may  also  be  combined  in  a  still  more  satisfac- 
tory manner  by  painting  the  surface  of  a  circle  with  different  colours,in  any  way 
that  may  be  de,sired,  and  causing  it  to  revolve  with  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  combina- 
tions 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,  composecl 
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  pre- 
dominance 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  directions, 
and  the  third  on  projections  perpendicular  to  the  surface,  which, 
while  the  eye  remained  at  rest  in  any  one  point,  obliquely  situated,   would 


ON    PHYSICAL    OPTICS."  .441 

exhibit    more  or  less  of  their  painted  sides,  as  they  passed  through  their  dif- 
ferent   angular  positions:  and  the  only  further  alteration,  that  could  be  pro- 
duced 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  differ-    - 
ent  proportions,    by  means  of  the  pencil,   beginning  from  three  equidistant 
points  as  the  centres  of  the  respective  colonrs,     (Plate  XXIX.  Fig.  427.)  ..j*. 

The  ordinary  atmospherical  refraction  cannot  be  determined  in  the  usual 
manner  from  the  knowledge  of  its  density,  and  of  the  angular  direction  of.  the 
incident  or  refracted  light,  since  the  constitution  of  the  atmosphere  is  such, 
that  its  density  varies  every  where  Avith  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  temperature  at  different 
elevations  increases  also  the  difficulty  of  an  exact  calculation,  and  it  is  only 
very  lately  that  Mr.  Laplace,  by  a  comparison  of  astronomical  with  meteorologi- 
cal observationSjhas  given  a  satisfactory  solution  of  the  problem  in  all  its  extent. 
But  for  practical  uses,  the  refraction  may  be  determined  with  sufficient 
accuracy  by  an  approximation  which  is  easily  remembered;  the  deviation 
being  at  a^^l  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  tlie  refraction  amounts  to  33  minutes, 
when  the  barometer  stands  at  29-^  inches,  and  Fahrenheit's  thermometer 
at  50'.  '         *  ■ 

The  accidental  variations  of  the  temperature  of  the  air,  at  different  paits. 
produce,  however,  great  irregularities  in  its  refraction,  especially  near  thfe 
horizon.  The  most  remarkable  of  these  is  occasioned  by  the  rarefac- 
tion of  the  air  in  the  neighbourhood  of  the  surface  of  wrater,'  of  a  building* 
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  de- 
pressed and  elevated,  so  as  to  appear  double,  one  of  the  images  being  gene- 
rally in  an  inverted  position,  as  if  the  surface  possessed  a  reflective  powei ;  ~ 
and  there  seems  indeed  to  be  a  considerable  analogy  between  this  kind  of  refrac- 
tion and  the  total  reflection  which  happens  within  a  denser  medium.  These 
effects  arc  known  by  the  appellations   looming,  mirage,  and  Fata  Morgana: 

VOL.    I.  ,  3  L 


442  LECTURE    XXXVII. 

they  may  be  very  completely  imitated,  as  Dr.  Wollaston  has  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  ex- 
amples 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  for- 
mation 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,  scat- 
tered 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  refraction^ 
and  reflections;  and  the  drops  so  situated  must  necessarily  be  found  some- 
Avhere  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  sur- 
face of  a  sphere,  is  scattered  almost  equally  in  all  directions,  setting  aside  the  dif- 
ference 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, 
therefore,  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- 
nous arch  is  produced  by  the  rays  of  each  colour  at  its  appropriate  distance. 
The  rays  which  never  enter  the  drops  produce  soother  effect,  than  to  cause  a 
bright  ness,  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  op- 
posite 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  Mould  appear  at  the  distance  of  ab<mt  42  degrees 
trom  the  sun.     The  colours  of  both  rainbows  encroach  considerably  on  each 


/  ON    PHYSICAL    OPTICS.  '      445 

Other  ;  for  each  point  of  the  sun  may  be  considered  as  affording  a  distinct 
arch  of  each  colour,  and  the  whole  disc  as  producing  an  arch  about  half  a 
degree  in  breadth  for  each  kind  of  light;  so  that  the  arrangement  nearly  re- 
sembles that  of  the  common  mixed  spectrum.  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  con- 
taining about  five  times  as  much  light  as  a  minute  at  the  distance  of  a  quarter 
of  a  degree:  the  abrupt  termination  is  on  thesideof  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  com- 
monly 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,  espe^ 
cially  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  supposi- 
tions, which  were  imagined  by  Huyg^ris,  are  in  themselves  extremely  com- 
plicated and  improbable,  and  are  wholly  unauthorised  by  observation.  A 
much  simpler,  and  more  natural,  as  well  as  more  accurate  explanation,  which 
was  suggested  at  an  earlier  period  by  Mariotte,  had  long  been  wholly  for- 
gotten, until  the  same  idea  occurred  to  me,  without  any  previous  knowledge 
of  what  Mariotte  had  done.     The  natural  tendency  of  water  to  crystallize,  in 


444  '    LECTURE    xxxvir. 

fi-eezing,  at  an  angle  of  60  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 
the  obliquity  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  afterwards 
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  con^ 
sidered  as  the  least  refractiv'e  of  any  known  substances  not  aeriform. 

Sometimes  the  figures  of  halos  and  parhelia  are  so  extremely  complicated, 
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.) 


ON    PHYSICAL    OPTICS.  445 

-  The  most  singular  of  all  the  phenomena  of  refraction  is  perhaps  tlie  property 
of  some  natural  substances,  which  have  a  double  eftect  on  the  light  transmitted 
tlirough  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  remain- 
ing portion.     These  substances  are  usually  crystallized  stones,  and  their  refrac- 
tions have  sometimes  no  further  peculiarity;   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  the  greater  angle  of  the  crystal.     It  appears 
from  the  experiments  of  Huygens,   confirmed  and  extended   by  Dr.  Wollas- 
ton,  that  the  medium,   which  causes  the  unusual  refraction,  has  a  different 
refraqtive  power,  according  to  tlae  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  princi- 
pal 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  equal 
to   that  of  the  medium   wliich  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  spheroid,  will 
meet  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  tbe  two  portions  of  light,  thus  separated,  will  not 
be  further  subdivided  by  a  transmission  through  a  second  piece,  provided 
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  Avhieh  appears  to  be  the  most  unintelligible 
of  any  that  has  been  discovered  respecting  the  phenomena  of  double  re- 
fraction. 

The  appearances  of  colours,  which  are  protluced  by  transparent  plates  of 


446  LECTURE   xxxvir. 

different  thicknesses,  and  of  those  which  are  seen  in  light  variously  diffracted  or 
inflected,  will  be  more  conveniently  examined,  when  we  investigate  the  inti- 
mate 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. 


447 


LECTURE  XXXVIIL 


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  substances,  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,  tlut  we  have  only  been  able  to  un- 
derstand, by  means  of  a  laborious  investigation,  the  nature  and  operations 
of  this  wonderful  structure,  while  its  whole  mechanism  still  remains  far  be- 
yond 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  de.- 
termined  by  the  angular  place  of  the  object.     (Plate  XXX.  Fig.  436.), 

The  first  refraction  happens  at  the  surface  of  the  cornea,  or  that  transparent 
eoat  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  humour,  which 
fills  its  concavity,  and  distends  it.  This  humour  is  partially  divided  by  the 
uvea  or  iris,  which  is  of  different  colours  in  different  persons,  having  a  perfora- 
tion 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,. 


448  •  LKCTURE  XXXVIII. 

like  a  short  fringe,  before  the  crystalline  lens,  a  substance  much  more  re- 
fractive than  the  aqueous  humour,  and  increasing  in  density  towards  its 
centre.  The  remaining  cavity  is  fdled  by  an  aqueous  fluid,  lodged  in  a  eel" 
lular  texture  of  extremely  fine  membrane,  and  called  the  vitreous  humour. 
The  retina  lines  the  whole  posterior  part  of  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  imme- 
diately where  the  retina  is  connected  with  the  optic  nerve,  thechoroid  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  cor- 
nea, 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  col- 
lected 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  pen- 
cil 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  completely,  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  equivalent  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 


ON  VISION.  449 

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  the  ground ;  and  the  image  of  the  trunk  of  a 
tree  being  in  contact  with  the  image  of  the  ground  on   the  retina,   we  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  acci- 
dentally near,   and  with  which  indeed  it  would  perhaps  be  impossible  to  com-   , 
pare  it,  as  far  as  we  judge  by  the  immediate  sensations  only. 

We  might  indeed  call  in  experience  to  our  assistance,  ahdhabitually  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  re- 
corded by  Galen,  on  the  instincts  of  a  kid,  which  is  sufficiently  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 

VOL.    I.  3  M 


ioO  LECTURE    XXXVIII. 

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  maile  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  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  sensibility  is  deficient. 

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.  Tims,  if  we  open  our 
eyelids  suddenly,  without  particular  preparation,  we  find  that  distant  objects 
onlv  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  perception  of  nearer 
objects,  yet  not  of  objects  within  certain  limits.  Between  the  ages  of  40 
and  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  con- 
tinues 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,  and 
sometimes  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  opti- 
cians and  physiologists,  but  I  apprehend  that  at  present  there  is  little  further 
loom  for  doubting,  that  the  change  is  produced  by  an  increase  of  the  con^ 


ov  VISION.  451 

vexity  of  the  crystalline  ]e"s,  arising  from  an  internal  cause.  The  argu- 
ments in  favour  of  this  conclusion  are  of  two  kinds;  some  of  them  are  nega- 
tive, derived  from  the  impossibility  of  imagining  any  other  mode  of  perform- 
ing the  accommodation,  without  exceeding  the  limits  of  the  actual  dimen- 
sions 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  co!r.r)lctely  re- 
moves the  effect  of  its  convexity,  without  impairing  the  power  of  altering  the 
focuSj'wand  by  holding  the  whole  eye,  when  turned  inwards,  in  sucl^  a 
manner  as  to  render  any  material  alteration  of  its  length  utterly  impossible. 
Other  arguments  arc  deduced  from  positive  evidence  of  the  change  of  form 
of  the  crystalline,  furnislied  by  the  particular  effects  of  refraction  and  aber- 
ration 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  pro^ved  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. 

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  in- 
tercepts 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  eves  as  cannot  accommodate  them- 

7.4/ 

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  the  pupil  within  the 


452  LECTURE  xxxvrir. 

limits  of  perfect  vision,  unless  we  allowed  the  irregularity  of  the  form  as- 
sumed by  the  marginal  parts  of  the  crystalline  lens.  The  iris  is  also  pecu- 
liarly 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.  Porterfield. 
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  perforations,  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  aline  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  measurement  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  con- 
fusion 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  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  object;  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. 


ON  VISION.  453 

When  the  imao-es  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;  and  in  general, 
all  objects  at  the  same  distance,  in  any  one  position  of  the  eyes,  appear  alike 
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  adjust- 
ment is  imperfect:  but  the  eyes  seem  to  be  in  most  persons  inseparably  con- 
nected together  with  respect  to  the  changes  that  their  refractive  powers 
undergo,  although  it  sometimes  happens  that  those  powers  are  originally  very 
different  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  distinct- 
ness or  confusion  of  the  image  still  continues  to  assist  the  judgment.  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  knowledge  of  the  real  magni- 
tude 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  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  similar  reason,  the  apparent  distance  of  an  object  seen 


454  LECTURE    XXXVIII. 

at  sea,  is  smaller  than  its  true  distance.  Tiie  city  of  Lo  rid  on  is  unquestion- 
ably larger  than  Paris;  but  the  ditTerence  appears  at  first  sight  much  greater 
than  it  really  is;  and  the  smoke, produced  by  the  coal  fires  of  London, is  proba- 
bly the  principal  cause  of  the  deception. 

The  sun,  moon,  and  stars,  are  much  less  luminous  when  they  are  near 
the  horizon,  than  wdien  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  sub- 
tend 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  impediment 
to  the  deception,  which  it  is  partly  the  business  of  a  painter  to  produce.  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  accompany  the  images  of  the 
objects  themselves  on  the  retina:  and  this  indistinctness  is  so  generally 
necessary,  that  its  absence  has  the  disao:reeable  efltcct  called  hardness.  The 
apparent  magnitude  of  the  suSjects  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  im- 
prove the  representation  of  distance  hy  attending  to  the  art  of  aerial  perspec- 
tive, which  consists  in  a  due  observation  of  the  loss  of  light,  and  the  bluish 
tinge,  occasioned  by  the  interposition  of  a  greater  or  less  depth  of  air  between 
us  and  the  ditfcrent  parts  of  the  scenery. 

We  cannot  indeed  so  arrange  the  picture,  that  either  tlie  focal  length  of 
the  eye,-  or  the  position  of  the  optical  axes,  may  be  such  as  would  be  required 


ON  visiox,  455 

I- 

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  Tallacy ; 
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  requir- 
ed 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  detects  of  the  repre- 
sentation, and  for  which  the  eye  is  usually  prepared,  by  being  long  detained 
in  the  dark  winding  passages,  which  lead  to  the  place  of  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  impres- 
sion 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  rinff;  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,  without 
much  regularity,  and  gradually  vanishes:  this  may,  however,  be  considered 
as  a  morbid  efl'ect. 

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  oppo- 
site to  the  first,  that  is,  of  such  a  colour  as  would  be  produced  by  with- 
drawing 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  pro- 
bably 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 


456  '  LECTURE    XXXVIII. 

I 

are  most  conveniently  exhibited  by  means  of  the  shadows  of  objects  placed 
in  coloured  ligh't:  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  consider- 
able 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  sub- 
stituted the  indico  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.) 


457 


LECTURE  XXXIX. 


ON    THE    NATURE    OF    LIGHT    AND    COLOURS. 


X  HE  nature  of  light  is  a  subject  of  no  material  importance  to  the  concerns  of 
life  or  to  the  practice  of  the  arts,  but  it  is  in  many  other  respects  extremely  in- 
teresting, especially  as  it  tends  to  assist  our  views  both  of  the  nature  of  our  sen- 
sations, and  of  the  constitution  of  the  universe  at  large.  The  examination  of 
the  production  of  colours,  in  a  variety  of  circumstances,  is  intimately  con- 
nected with  the  theory  of  their  essential  properties,  and  their  causes  ;  and  we 
shall  find  that  many  of  tliese  phenomena  will  afford  us  considerable  assistance 
in  forming  our  opinion  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  pro- 
jected, and  continue  to  move,  with  the  velocity  commonly  attribut- 
ed to  light,  or  in  the  excitation  of  an  undulatory  motion,  analogous  to 
that  which  constitutes  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  opi- 
nions. There  are  also  some  circumstances  which  induce  those,  who  entertain 
the  first  hypothesis,  either  to  believe,  with  Newton,  that  the  emanation  of 
tlie  particles  of  light  is  always  attended  by  the  undulations  of  an  etherial 
medium,  accompanying  it  in  its  passage,  or  to  suppose,  with  Boscovich, 
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,  how- 
ever necessary  they  may  have  been  thought  for  explaining  some  particular 
phenomena,  have  never  been  very  generally  understood  or  admitted,  although 
no  attempt  has  been  made  to  accommodate  the  theory  in  any  other  manner  to 
tiiose  phenomena. 

VOL.    I.  3  N 


458  LECTURE    XXXIX. 

We  shall  proceed  to  examine  in  detail  the  manner  in  which  the  two  principal 
hypotheses  respecting  light  may  be  applied  to  its  various  properties  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  portion 
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  capable  of  in- 
flecting 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  effects;  and  there 
is  reason  to 'conclude  from  experiments,  that  such  a  force,  if  it  existed,  must 
extend  to  a  very  considerable  distance  from  the  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  Iluygenian  system  of  undulation, 
this  divergence  or  diffraction  is  illustrated  by  a  comparison  with  the  motions 
of  waves  of  water  and  of  sound,  both  of  which  diverge  when  they  are  ad- 
mitted into  a  wide  space  through  an  aperture,  so  much  indeed  that  it  has 
usually  been  considered  as  an  objection  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  in- 
ferred, that  in  a  still  more  highly  elastic  medium,  the  undulations,  constituting 
light,  must  diverge  much  less  considerably  than  either.   (Plate»XX.  Fig.  266.) 

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  ligh 
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  suppo- 
sitions as  Boscovich"s,  that  matter  itself  is  penetrable,  that  is,  immaterial,  it  h 
almost  useless  to  argue  the  question  further.  It  is  certain  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  therefore  suppose  the  distances 


ON    THE    NATURE    OF    LIGHT    AND    COLOURS.  459 

of  the  atoms  of  matter  in  general  to  be  so  great  as  the  hundred  milllonjth  of 
an  inch.  Now  if  ten  feet  of  the  most  transparent  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  dia- 
meter of  each  atom  must  be  less  than  the  hundred  and  forty  thousandth  part 
of  its  distance  from  the  neighbouring  particles:  so  that  the  whole  space  oc- 
cupied by  the  substance  must  be  as  little  filled,  as  the  whole  of  England 
would  be  filled  l^y  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  state- 
ment to  agree  in  some  measure  with  the  actual  constitution  of  material  sub- 
stances; but  the  Huygenian  hypothesis  does  not  require  the  disproportion  to 
be  by  any  means  so  great,  siuce  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  inadmissible. 

A  very  striking  circumstance,  respecting  the  propagation  of  light,  is  the 
uniformity  of  its  velocity  in  the  same  medium.  According  to  the  projectile 
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,  whatever  may  be  its  cause,  and  it  is  extremely  difficult  to  imagine 
that  so  immense  a  force  of  repulsion  can  reside  in  all   substances  capable  of 


460  •  LECTURE    XXXIX. 

becoming  luminous,  so  that  the  light  of  decaying  wood,  or  of  two  pebbles 
rubbed  together,  may  be  projected  precisely  M'ith  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  interfere  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  thg  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  unneces- 
sary 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  Huy- 
genian  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  unaltered. 

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  incidence  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  cases  of  the  production  of  colours,  which  lead  us  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  existence  of  such  an  attractive 
force  could  no  longer  be  allowed,  nor  could  the  system  of  emanation  be 
maintained  by  any  one. 

The  partial  reflection  from  all  refracting  surfaces  is  supposed  by  Newton 
to  arise  from  certain  periodical  retardations  of  the  particles  of  liglit,  caused 


ON    THE    NATURE    OF    LIGHT    AND    COLOURS.  46l 

by  undulations,  propagated  in  all  cases  through  an  ethereal  medium.  Tlie 
mechanism  of  thesf  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,  therefore,  safely  be  asserted,  that 
in  the  projectile  hypothesis  this  separation  of  tlie  rays  of  light  of  the  same 
kind  by  a  partial  reflection  at  every  refracting  surface,  remains  wholly  unex- 
plained. In  the  undulatory  system,  on  the  contrary,  this  separation  follows 
as  a  necessary  consecjuence.  It  is  simplest  to  consider  the  ethereal  medium 
Avhich  pervades  any  transparent  substance,  together  with  the  material  atoms 
of  the  substance,  as  constitutmg  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  conunon  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  circum- 
stances. Thus,  if  one  of  two  equal  bodies  strikes  the  other,  it  communi- 
cates to  it  its  whole  motion  without  any  reflection;  but  a  smaller  body 
striking  a  larger  one  is  reflected,  Avitlr  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  scries 
of  motions  which  necessarily  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  tlie 
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  ap- 
proach 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  tlie  same  effects  may  be  expected  at  the 
surface  of  two  mediums  separated  by  an  abrupt  termination. 


462  tECTURE  XXXIX. 

The  chemical  process  of  combustion  may  easily  be  imagined  either  to  dis- 
engage the  particles  of  light  from  their  various  combinations,  or  to  agitate 
the  elastic  medium  by  the  intestine  motions  attending  it:  but  the  operation 
of  friction  upon  substances  incapable  of  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  seems  to  be  no  easy  way 
of  supposing  a  decomposition  of  any  kind.  The  phenomena  of  solar  phos- 
phori  appear  to  resemble  greatly  the  s^'mpathctic  sounds  of  musical  instru- 
ments, which  are  agitated  by  other  sounds  conveyed  to  them  tbrough  the 
air:  it  is  difficult  to  understand  in  wliat  state  the  corpuscles  of  light  could 
be  retained  by  these  substances  so  as  to  be  reemittcd  after  a  short  space  or 
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. 

The  phenomena  of  the  aberration  of  light  agree  perfectly  well  with  the 
system  of  emanation ;  and  if  the  ethereal  medium,  supposed  to  pervade  the 
earth  and  its  atmosphere,  were  carried  along  befoie  it,  and  partook  materia^y 
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  supposi- 
tion: 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  hypothesis. 

The  unusual  refraction  of  the  Iceland  spar  has  been  most  accurately  and 
satisfactorily  explained  by  Iluygens,  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  constilutintr 
light  must  assume  a  spheroidical  instead  of  a  spherical  form,  and  lays  down  such 
laws  for  the  direction  of  its  motion,  as  are  incomparably  more  consistent 
with  experiment  than  any  attempts  which  have  been  made  to  accoiiimndate 
the  phenomena  to  other  principles.  It  is  true  that  nothing  has  yet  been 
done  to  assist  us  in  understanding  the  effects  of  a  subsco"  nt  refraction  by 
a  second  crystal,  unless  any  person  can  be  satisfied  with  the  name  of  polarity 


ON    THE    NATURE    OF    LIGHT    AND    COLOUKS.  463 

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  \vc  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  un- 
derstand how  thes^  dispositions  are  continued  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  medmnis  have  an  elective  attraction,  acting  mOre  powerfully  pn  the 
violet  rays,  in  proportion  to  their  mass,  than  on  the  red.  But  an  elective  at- 
traction of  this  kind  is  a  property  foreign  to  mechanical  pliilosophy,  and  when 
we  use  the  term  in  chemistry,  we  only  confess  our  incapacity  to  assign  a  mechani- 
cal cause  for  the  effect,  and  refer  to  an  analogy  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  effects  of  waves  of  different  breadths.  The  simple  calculation  of  the 
velocity  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  existing 
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  consider- 
able depth,  that  the  wider  waves  proceed  much  more  rapidly  than  the  nar- 
rower. We  may,  therefore,  consider  the  pure  ethereal  medium  as  analogous 
to  an  infinitely  elastic  fluid,  in  which  undulations  of  all  kinds  move  wi-th 
equal  velocity,  and  material  transparent  substances,  on  the  contrary,  as 
resembling  those  fluids,  in  which  we  see  the  large  waves  advance  beyond  the 
smaller;  and  by  supposing  the  red  light  to  consist  of  larger  or  wider  undu- 
lations 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 


454  LECTURE  xxxrx. 

more  directly  to  the  same  conclusion  ;  they  consist  chiefly  of  the  production 
of  colours  by  means  of  transparent  plates,  and  by  diflraction  or  inflection, 
none  of  which  have  been  explained,  upon  the  supposition  of  emanation,  in 
a  manner  suiliciently  minute  or  comprehensive  to  satisfy  the  most  candid 
even  of  the  advocates  for  the  projectile  system;  while  on  the  other  liand  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,  arc 
lieard  to  vibrate  together. 

Supposing  the  light  of  any  given  colour  to  consist  of  undulations,  of  » 
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  tiie  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  other  points  at  to  re- 
double 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  deviating 
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  light  is  diffract- 
ed 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  divult'd  by 
dark  stripes  into  portions  nearly  equal,  but  becoming  wider  as  the  surface  is 
more  remote  ftom  the  a])ertures,  so  as  to  subten  :  very  nearly  c^ual  angles 
from  the  apertures  at  all  distances,  and  wider  also  in  the  same  proportion  as 
the  apertures  art  closer  to  each  other.  Tlie  middle  of  the  two  portions  is 
always  light,  and  the  bright  stripes  on  each  side  arc  at  such  distances,  that  the 
light,  coming  to  them  from  one  of  the  ai^rtuies,  must  have  passed  through  a 


ON    THE    NATURE    OF    LIGHT    AND    COLOURS.  A6S 

longer  space  than  that  which  conies  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  sup- 
posed undulation,  of  one  and  a  half,  of  two  and  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  dimen- 
sions 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,  cor- 
responding to  this  interval ;  although,  upon  closer  inspection,  the  distinct 
effects  of  an  infinite  number  of  stripes  of  different  breadths  appear  to  be  com- 
pounded together,  so  as  to  produce  a  beautiful  diversity  of  tints,  passing  by 
degrees  into  each  other.  The  central  whiteness  is  first  changed  to  a  yellow- 
ish, 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  Avith  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  sub- 
stance to  cast  its  shadow,  the  divergence  from  its  opposite  margins  still  con- 
VOL.   I.  3  o 


466  LECTURE    XXXIX. 

tinues  to  produce  the  same  fringes  as  before,  but  they  arc  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  its  neighbourhood,  the  stripes  will  still 
appear;  and  in  this  manner  the  colours  of  small  fibres  are  probably  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  belono-ino- 
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  distances  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,  maybe  exhibited. 
(Plate  XXX.  Fig.  444.) 

4 

If,  on  the  other  hand,  we  remove  the  portion  of  the  screen  which  separates 
the  parallel  slits  from  each  other,  their  external  margins  will  still  continue  to  ex- 
hibit the  effects  of  di.ffracted  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  con- 
cerned in  the  appearance  of  fringes,  wherever  their  Avhole  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  obli- 
quity, 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  appearance  of 

2 

\ 


ON    THE    NATURE    OF    LIGHT    AND    COLOURS.  467 

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  reflection,  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  become  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  abeam 
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  curv- 
ed fringes  within  the  shadow,  situated  on  each  side  of  the  diagonal,  which 
were  first  observed  by  Grimaldi,  and  which  are  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  easily  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  nar- 
row that  margin  may  be;  the  fringes  are,  however,  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  calculation,  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  degre^  with  that  of  the  fringes :  the 


4fi8  LECTURE    XXXIX. 

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  suc- 
cessive 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  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  iron,  affords  us  an  example  of  such  a  series  formed  in  reflect- 
ed 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,    Avhich 
changes  to  red,  and  then  to  crimson  and  blue,  after  which  the  effect  is  de- 
stroyed by  the  opacity  which  the  oxid  acquires.     Usually,    however,   the 
series  of  colours  produced  in  reflected  light  follows  an  order  somewhat  dif- 
ferent: 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  undu- 
lations, 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 


ON    THE    NATURE    OF    LIGHT    AND    COLOURS.  469 

wineglass,  and  placed  in  a  vertical  position,  its  upper  edge  becomes  ex- 
tremely 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  crimson 
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  circum- 
stance which  necessarily  follows  from  the  proportion  of  the  velocities  with 
which  light  must,  upon  the  lluygenian  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  magnitude 
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  remark- 
able of  them  is  that  of  blue  glass,  probably  coloured  with  cobalt,  which 
becomes  divided  into  seven  distinct  portions.  It  seems,  however,  im- 
possible 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^ 


470  LECTUUE    XXXIX. 

but  difficult  to  believe  with  respect  to  any  of  their  arrangements  constituting 
the  diversities  of  material  substances. 

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  num- 
ber 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  at  much  greater  thick- 
nesses, depending  on  the  difference  of  the  refractive  densities  of  the  sub- 
stances employed.  The  effect  is  observed  by  holding  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  surfaces  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  reflec-  ■ 
tions  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  magnitude,  the  effects  of  these 
fringes  must  be  confounded  and  destroyed:  in  general,  howeyer,  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  rain- 
bows as  are  usually  observed,-  is  between  the  50th  and  the  100th  of  an  inch: 
they  become  gradually  narrower  as  they   are  more  remote  from  the  common 


ON    THE    NATUEE    OF    LIGHT    AND    COLOURS.  471 

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  necessary 
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  the  circumferenceof  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  diffraction.  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  considerable  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  inter- 
ference of  light  has  been  shown  to  be  applicable  to  so  great  a  variety  of  foots, 
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. 


472 


LECTURE  XL 


ON    THE    HISTORY     OF    OPTICS. 


A  HE  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  occurrence  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  ea5ily 
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,  partial- 
ly 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  personages,    introduced    by   Aristophanes, 
proposes  to  destroy  the  papers  of  his  adversary  by  the  assistance  of  this  in- 
strument.    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 
substances,  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  systematically 
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 


ON    THE    HISTORY    OF    OPTICS.  4:7'^ 

itself.  Both  of  these  doctrines  were  combated  by  Aristotle,  who  thought  it  ab- 
surd to  suppose  that  a  visual  influence  §hould  be  emitted  by  the  eye,  and  that 
it  should  not  enable  us  to  see  in  the  dark;  and  who  considered  it  as  more  pro- 
bable that  light  consisted  in  an  impulse,  propagated  through  a  continuous 
medium,  than  in  an  emanation  of  distinct  particles.  Light,  he  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  wc  should  see  it. 

It  is  said  that  Archimedes  made  a  compound  burning  mirror,  of  sufficient 
power  to  set  on  fire  the  Roman  ships:  in  this  form  the  story  is  scarcely  pro- 
bable, 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,  and  that  he  confirmed  his  theories 
by  some  experimental  investigations.  The  work  on  catoptrics,  attributed 
to  Euclid,  contains  the  determination  of  the  eflfects  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  manu- 
script. 

The  mathematical  theory  of  optics,  or  the  science  of  dioptrics  and  cat- 
optrics, made  some  advances  in  the  middle  ages  from  the  labours  of  Alhazen 
and  Vitellio.  Alhazen  was  mistaken  in  some  of  his  propositions  respecting 
refraction ;  Vitellio,  a  native  of  Poland,  gave  a  more  correct  theory  of  this 
subject,  and  constructed  a  table  of  refractive  densities,  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  defective 
sight.  It  has  been  much  disputed  whether  or  no  Bacon  was  acquainted  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 

VOL.    I.  3  p 


474  LECTURE    XL. 

actually  invented  a  telescope,  but  that  Recorde  .himself  knew  something  of 
its  construction.  Digges  also,  in  a  work  published  in  1571,  has  a  passage 
of  a  similar  nature,  and  from  Bacon's  own  words  it  has  been  conjectured  that 
an  instrument  resembling  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  magnitude  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  family  discovered  a  satellite  of  Jupiter  with  them.  Galileo 
had  heard  of  the  instrument,  but  had  not  been  informed  of  the  particulars  of 
its  construction,  he  reinvented  it  in  I6O9,  and  the  following  year  redis- 
covered 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  fur  finding  the  focal 
lengths  of  simple  lenses  of  glass;  he  showed  how  to  determine  the  magnify- 
ing 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  observa- 
tions were  thirty  or  forty  years  later. 

The  next  great  step  in  optics  was  made  by  De  Dominis,  who  in  16II  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  refrac- 
tion, first  made  by  Snellius,  who  ascertained,  about  I62I,  that  the  sines  of 
the  angles  of  incidence  and  refraction  are  always  in  the  same  proportion  to 
each  other  at  the  same  surface;  he  died,  however,  in  16^6,  without  having 
made    his    discovery    public.      Descartes,    is  generally   supposed   to     have 


ON    THE    HISTORY    OF    OPTICS.  '        475" 

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,   and  truly  determined  the  angular 
magnitude  of  both  the  bows  from  mathematical  principles;  he  did  not,  how- 
ever, give  a  sufficient  reason  for  the  production  of  colours  in  either  case. 
Descartes  imagined  light  to  consist  in  motion,   or  rather  pressure,   transmit- 
ted instantaneously  through  a  medium  infinitely  elastic,  and  colours  he  at- 
tribsted  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,   with- 
out deciding  with  respect  to  any  general  theory  of  light :  thus  Fermat  and 
Leibnitz  deduced,  on  tliis  supposition,  the  path  of  refracted    light  from  the 
natural  tendency  of  every  body  to  attain  its  end  by  the  shortest  possible  way; 
and  Barrow  derived  the  same  law,  in  a  more  geometrical  manner,  from  a  simi- 
lar 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  mathematician  for  the   first  accurate  inves- 
tigation of  the  properties  of  refracting  and  reflecting  surfaces,  and  for  the 
most  general  determination  of  the  situations  of  focal  points. 

The  industrious  Mr.  Boyle  had  noticed  with  attention  the  phosphorescence  of 
diamonds,  the  colours  produced  by  the  eflfect  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,  investigated  these  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  pro- 
duced by  the  readier  transmission  of  light  through  the  denser  medium,  and 
that  difference  of  colour  consists  in  the  different  law  of  the  particular  im- 
pulse 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 


476  LECTURE    XL.  ' 

inadequate,  nor  were  the  phenomena  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  ca- 
pable 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  inte- 
resting 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  ac- 
company 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 
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  Ds.  Hooke,  and  disliked  the  dispute  so  much,  that  he 
deferred  the  publication  of  his  treatise  on  optics  till  after  Hooke's  death 
in  1703.  Very  soon  after  his  first  communication  to  the  Royal  Society,  in 
1672,  he  had  sent  them  a  description  of  his  reflecting  telescope,  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  l6l5.  The  principal  parts  of  the 
treatise  on  optics  had  been  communicated  at  diflf'erent  times  to  the  Royal 
Society;  besides  the  experiments  on  refraction  and  the  theory  of  the  rain- 
bow,  they  consist  of  an  elegant  analysis  of  the  colours  of  thin    transparent 


Oisr    THE    HISTORY    OF    OPTICS.  ,  477 

substances,  in  which  the  phenomena  are  reduced  to  their  simplest  forms, 
and  of  a  collection  of  miscellaneous  experiments  on  the  colours  produced  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  prv)jection  of  minute 
particles  of  matter  from  the  luminous  body,  and  maintained  that  this  pro- 
jection was  only  accompanied  by  the  vibration  of  a  medium  as  an  accidental 
circumstance,  which  was  also  renewed  at  the  surface  of  every  refractive  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  re- 
fraction is  a  happy  combination  of  accurate  experiment  with  elegant  theory; 
it  was  published  in  I690,  making  apart  of  his  treatise  on  light,  the  funda- 
mental doctrines  of  which  he  had  communicated  to  the  Academy  of  Paris  in 
1678.  They  scarcely  differ  in  their  essential  parts  from  those  of  our  country- 
man Dr.  Hookc,  but  the  subject  of  colours  Huygens  has  left  wholly  un- 
touched. Roemer  had  then  lately  made  the  discovery  of  the  immense  velo- 
city 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;  althougli  Hooke,  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  of  Huygens  in  the 
mathematical  theory  of  optics  were  no  less  considerable  than  in  the  investi- 
gation of  the  nature  of  light;  his  determinations  of  the  aberrations  of  lenses 
were  the  first  refinement  on  the  construction  of  telescopes. 

In  the  year  1720  Dr.   Bradley  had  the  good  fortune  to  discover  both  the 


478  LECrUKE    XL. 

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  direction 
of  the  wind  on  board  of  a  boat  which  was  moving  in  a  transverse  direction. 
He  also  determined  with  accuracy  the  magnitude  of  the  atmospherical  refrac- 
tion, which  had  been  theoretically  investigated  by  Newton  and  by  Taylor, 
but  never  before  practically  ascertained  with  sufficient  precision.  The  for- 
mula, which  Bradley  appears  to  have  deduced  from  observation  only,  agrees 
precisely  with  an  approximation  which  was  obtained  by  Simpson  from  calcu- 
lation; 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  exmai- 
nation  of  the  properties  of  a  variety  of  substances,  with  respect  to  the  trans- 
mission and  reflection  of  light  in  different  circumstances,  and  in  the  comparison 
of  lights  of  different  kinds,  require  to  be  mentioned  with  the  highest  commen- 
dation. Dr.  Porterfield's  investigations  of  the  functions  of  the  eye  tended 
greatly  to  illustrate  the  economy  of  this  admirable  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  mathematical  part  of  the  science. 

The  invention  of  achromatic  telescopes  is  with  justice  universally  attri- 
buted to  our  countryman  Mr.  DoUond,  but  there  is  reason  to  believe  that  he 
was  not  absolutely  the  first  author  of  the  improvement.  Mr.  Hall,  a  gen- 
tleman of  Worcestershire,  is  said  to  have  discovered,  about  the  year  1729,  Sir 
Isaac  Newton's  mistake,  in  supposing  that  the  rays  of  different  colours  must 
of  necessity  be  equally  separated  by  all  surfaces  which  produce  an  equal 
mean  refraction ;  and  by  combining  the  different  dispersive  properties  of 
different  kinds  of  glass,  he  constructed,  in  1733,  several  compound  object 
glasses,  which  were  calculated  not  only  for  avoiding  all  appearance  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 

2 


ON    THE    HISTORY    OF    OPTICS.  479 

consequence  of  a  discussion  with  Euler,  Klingenstierna,  and  some  other 
mathematicians,  that  Mr.  DoUond  was  led  to  make  experiments  on  the  re- 
fraction 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  Klingenstierna  had  shown  the  possibility 
of  producing  a  deviation  by  refraction,  without  a  separation  of  colour,  ac- 
cording to  the  laws  of  refraction  laid  down  by  Newton  himself.  When 
Dollond  had  once  discovered  the  material  difference  which  exists  between 
the  dispersive  properties  of  flint  glass  and  of  crown  glass,  it  was  easy  to 
produce  the  combination  recjuired;  but  this  ingenious  artist  was  not  satis- 
fied with  the  advantage  of  freedom  from  colours  only;  he  adjusted  the 
forms  and  apertures  of  his  lenses  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  mathema- 
tician was  less  fortunate  in  his  optical  theories  than  in  many  other  depart- 
ments 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  co- 
lours, 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  direction;  he  also  conceived  that  the  undu- 
lations of  light  are  simply  propagated  through  the  solid  substances  of  trans- 
parent mediums,  in  the  same  manner  as  sound  travels  through  the  air.  But 
on  these  suppositions,  all  bodies  would  have  the  properties  of  solar  phos- 


480  LECTURE    XL. 

phori,  and  the  refraction  of  the  rarest  of  natural  bodies  would  be  incompa- 
rably 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  certain  degree  of  authorit}'  to  all  his  opinions,  so  that 
in  this  instance  the  name  of  Iluygens  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  may  be  considered  as  a  continuation  of  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  eqvial  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  ac- 
cording to  the  obliquity  of  that  direction.  The  mathematical  theory  of 
optics  is  considerably  indebted  to  the  labours  of  Clairaut,  Dalembert,  and 
Boscovich  ;  Jeaurat,  Beguelin,  Redern,  and  Kliigel  have  also  continued  the 
investigation;  their  calculations  may  be  of  considerable  utility  to  the  prac- 
tical optician,  but  it  requires  the  ingenuity  of  a  Dollond  or  a  Ilamsden  to 
apply  the  whole  of  the  results  to  any  useful  purposes. 

The  experiments  of  Maz6as  on  the  colours  of  thin  plates  are  mere  repeti- 
tions of  those  of  Newton  under  disadvantageous  circumstances;  Mr.  Dutour 
has,  however,  considerably  diversified  and  extended  these  experiments,  as 
well  as  those  on  the  colours  which  are  produced  in  diffracted  light, yet  without 
obtaining  any  general  results  of  importance.  Comparetti's  experiments  on 
inflection  have  every  appearance  of  accuracy,  but  they  are  much  to^o  in- 
tricate 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  defi- 


ON    THE    HISTORY    OF    OPTICS.  481 

cient  in  mathematical  accuracy,   and  the  author  was  not  sufficientlj'  master  of 
the  science  to  distinguish  the  good  from  the  indift'erent. 

Mr.  Delaval's  experiments  on  colours  appear  to  show  very  satisfactorily, 
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.  Dr.  Robert  Darwin's 
investigation  of  the  eti'ects  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,  Mr.  Vince,and  Dr.  Wollaston, 
so  that  at  present  there  appears  to  be  little  doubt  remaining  with  respect  to 
their  origin.  Dr.  WoUaston's  instrument,  for  the  measurement  of  refractive 
densities,  very  much  facilitates  the  examination  of  the  optical  properties  of  sub- 
stances of  various  kinds :  he  has  applied  it  very  successfully  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  Hitter,  the  dark  rays  which 
blacken  the  salts  of  silver  ;  and  he  has  remarked  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  indebted. 
He  has  carried  the  construction  of  the  reflecting  telescope  to  a  degree  of  per- 
fection, far  exceeding  all  that  had  been  before  attempted,  and  the  well  known 
improvements,  which  astronomy  has  derived  from  his  observations,  are  nume- 
rous 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. 

VOL.    I.  Sq 


482  LECTURE    XX. 

The  investigations  of  ^Ir.  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 

liglit  similar  to  that  of  Ilooke  and  Hiiygens,   with  an  improvement  originally 

suggested  by  Newton,  respecting  the  nature  of  colours,   I  have  endeavoured 

to  obtain  a  satisfactory  explanation  of  many  circumstances,  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  excited,   I  trust  that  the  science  of  optics  will  be 

essentially  benefited,  even  if  the  theory  should  be  ultimately  confuted. 


ON    THE    HISTORY    OF    OPTICS. 


CHRONOLOGY     OF    OPTICAL    AUTHORS. 


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AYLOR.      RAMSDEN 

.S  C    H 

E    I    N    E   R. 

S      M     I     T     H. 

.K     E 
R   H 
.S 

P  LER. 
EITA 
NELLIUS. 
DESCARTES. 
GRIMALDI. 
.BARTHOLIN. 

.H  U  Y  G  E  N  S. 
.BAKROW. 
^MARIOTTE. 
.BOYLE. 
.H     0     0     K,     E 
NEWT 

HALL 
B   R  A  D  L  E  Y. 
BOUGUER. 
PORTERFIELD. 
.J     E     A      U      R     .4    T. 
.DOLLOND. 
.L.       E    U     L    E     R. 
.S  ITVI  P  S   0  N. 
.CLAIR  A  UT. 

.DALEMBERT. 

KLINGENSTIERNA 

ON.    .LAMBERT. 

D    U    T    0    U    R 

COURSE  OF  LECTURES 


ON 


NATURAL  PHILOSOPHY 


AND  THE 


MECHANICAL  ARTS. 


PART  III. 


PHYSICS. 


I    ui 


COURSE  OF  LECTURES 


OI7 


NATURAL  PHILOSOPHY 


AND  THE 


MECHANICAL  APiTS. 


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  in- 
tricacy 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  absolutely  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 


488  LECTURE    XLI. 

to  enter  completely  into  a  mathematical  examination  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  some- 
times denominated  plain  astronomy,  in  contradistinction  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  de- 
scriptive, and  what  is  usually  called  physical,  must  be  denominated  mathe- 
matical astronomy.  We  shall,  therefore,  confine  ourselves  in  great  measure 
to  descriptive, astronomy,  and  shall  take  only  a  general  view  of  the  laws  of 
gravjitation,  as  an  illustration  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  terraqueous  globe,  and  to  the  tides,  produced  by  the  influence  of  the 
celestial  bodies  on  the  ocean:  and  then,  quitting  the  aft'ections  of  the  larger 
features  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 
dependent  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  properties  of 
matteu  in  general;  but  this  science  is  of  too  great  extent  and  importance  to 
occupy  a  subordinate  place  in  a  system  of  natural  philosophy,  and  must, 
therefore,  be  considered  as  requiring  a  separate  course  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  na- 
turally arranged.  The  stars  and  sun,  the  planets  and  their  satellites,  and 
lastly  the  comets,  will  be  severally  described;  the  causes  of  the  motions  of 


ON    THE    FIXED    STAIIS.  '"  485 

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  explained. 

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  disproportion 
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  with- 
out 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 
iare  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  corpuscles,  or  to  be  an  affection  of  a  highly 
clastic  ether,  pervading  the  universe  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  per- 
fect freedom;  and  if  we  follow  Newton's  opinion  of  the  nature  of  light,  wc 
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  phi- 
losophy, that  would  aspire  to  comprehend,  within  its  own  contracted  sphere, 
the  whole  extent  of  the  mighty  work  of  the  creation. 

The  expanse  of  the  universe  is  strewed,  at  immense  distances,  with  detached 
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  probability,  have 
many  other  properties  in  common.     Such  of  these,  as  emit  their  own  light,  are 

VOL..  I,  3  R  , 


4gO  LECTURE    XLI. 

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  it  be  possible,  on  account  of  their  immense  distance  from  us,  to  distin- 
guish two  such  bodies  from  each  other.  It  follows  also,  on  the  same  sup- 
position 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  con- 
centrated 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  probability,  to  changes 
which  are  perpetually  taking  place  in  the  atmosphere,  and  which  aflfect  its 
refractive  density.  It  is  said  that  in  some  climates,  where  the  'air  is  re- 
markably 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 
than  the  imperfection  of  the  instrument.  Dr.  Herschel  has  observed  in  the 
milky  way  above  ten  thousand  stars  in  the  space  of  a  square  degree.  Lucre- 
tius and  Dr.  Halley  have  argued  that  their  number  must  be  absolutely  infi- 
nite, in  order  that  all  of  them  may  remain  at  rest  by  the  opposition  of  attrac- 
tions 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 
quantity  of  light  emitted  by  the  brightest  stars,  that  some  of  them  are  much 


ON    THE    FIXED    STARS.  4£)l 

larger  than  the  sun.  Those  stars  which  are  below  the  sixth  magnitude  arc 
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  im- 
mediately compared  with  their  diameters;  for  no  star  subtends  an  angle  large 
enough  to  be  ascertained  by  direct  observation.  The  more  perfect  the  instru- 
ments that  we  employ,  the  smaller  are  the  apparent  diameters  of  the  fixed 
stars.  Dr.  Herschel  found  that  one  oi'  the  stars  of  the  first  magnitude,  when 
viewed  in  his  best  telescopes,  appeared  to  be  about  one  third  of  a  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  perhaps  be  for  ever  im- 
possible 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  consequence  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.  Herschel 
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  bright- 
est 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  inequality  in  their  dimensions.  At 
any  rate  there  is  little  doubt,  that  the  diversity  of  their  apparent  magnitudes 
is  principally   owing   to  their  different  distances ;  perhaps  none  of  them  are 


49l8  LECTURE  XLI. 

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  Irom  the 
centre;  in  a  sphere  of  twice  tlie  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  tlie  stars  of  the  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  ditierent  stars,  we 
may  infer,  that  if  their  real  magnitudes  are  nearly  equal  tlieir  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 
object.  The  light  of  stars  of  different  magnitudes,  situated  near  each  other, 
may  be  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  sup- 
position 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  ancients  had  notic- 
ed some  of  the  most  conspicuous  nebulae,  but  Huygens  first  directed  the  atten- 
tion 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 
•everal  itars  to  which  ihey  seem  to  belong.     (Plate  XXI.  I'ig.  45o  .  .  46"3.) 

3 


ON    THE    TIXED    STAR8.  4S>5 

It  has  been  conjectured  that  all  stars  are  disposed  in  nebulae,  and  that 
those,  which  apj)ear  to  us  to  be  more  widely  separated,  are  individual  s  ars  of 
that  particular  nebula  in  which  we  are  placed,  and  of  which  the  marginal 
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 
thfe  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  constituting  a 
distinct  nebula  placed  among  a  multitude  of  others,  which  together  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 
pnjected  into  the  form  of  the  milky  way.  We  must  not,  however,  suppose 
that  each  of  Dr.  Herschel's  2500  nebulae  can  be  at  all  comparable  in  mag- 
nitude to  this  supposed  nebula,  since  many  of  them  are  almost  as  much  re- 
solved by  the  telescope  into  single  stars  as  the  milky  way  itself;  which 
would  be  utterly  impossible,  if  the  stars  which  they  contain  were  equally 
numerous  with  those  of  the  nebula  to  which  the  milky  way  belongs.  Sup- 
posing all  the  stars  of  this  nebula  to  be  as  remote  from  each  other  as  the 
nearest  of  them  are  from  the  sun,  it  may  be  calculated  that  the  most  distant 
are  abuut  500  times  as  far  from  us  as  the  nearest,  aud  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  ifears  to  reach  us.      (Plate  XXXI.    Fig.  464.) 

The  stars  are  not,  properly  speaking,  absolutely  fixed  with  respect  to  each 
other,  for  several  of  t:,em  have  particular  motions,  which  have  been  dis- 
covered by  a  comparison  of  accurate  observations,  made  at  very  <listant  times. 
Arcturus,  for  instance,  has  a  progressive  motion,  amounting  to  more  than 
two  seconds  annually.  Dr.  Maskelyne  found,  that  out  of  S6  stars,  of  which 
he  ascertained  the  places  with  great  precision,  35  had  a  proper  motion.  Mr. 
Michell  and  Dr.  llerschcl  have  conjectured,  that  some  of  the  stars  revolve  round 
others  which  are  apparently  situat<>d  very  near  them;  and  perhaps  even  all 
the  stars  may  in  reality  change  their  places  more  or  less,  although  their  re- 


494  LECTURE    XLI. 

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  gravitation,  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  about  a  centre  of  attraction;  and  clusters  by 
a  still  greater  central  compression.  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  de- 
scription resemble  stars  surrounded  by  a  bur,  or  a  faint  disc  of  light:  a  diffused 
milky  nebulosity,  apparently  produced  by  some  cause  distinct  from  the 
mmediate  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  nebulae, 
with  and  without  bright  central  points.  Many  of  these  distinctions  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  liave  periodical 


ON    THE    FIXED    STARS.  495 

changes  of  brightness,  which  are  suppnsed  to  arise  either  from  the  temporary 
interpositioa  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  ^  days 
and  21  hours  each,  of  the  fourth  only,   and  occupies  7  hours  in  the  gradual 
diminution  and  recovery  of  its  light.     A  less  probable  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  produc- 
ed by  the  attraction  of  planets  revolving  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  disap- 
peared, and  sometimes  have  been  again  recovered ;  others  have  made  their  ap- 
pearance 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  circum- 
stance 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  sixteen 
months.     Kepler,   in  1604,  observed  a  new  star  in   Serpen tarius,  more  bril- 
liant than  any  other  star  or  planet,    and  changing  per{>etually  into  all  the 
colours  of  the  rainbow,  except  when  it  was  near  the  horizon ;  it  remained 
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  situa- 
tions, 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 
sometimes  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 


496  LECTURK    XLI. 

usual  to  describe  particular  stars  by  their  situation  with  respect  to  the  imagi- 
nary figure  to  which  they  belong,  or,  more  commonly,  at  present,  by  the 
letters  of  the  Greek  alphabet,  which  were  first  applied  by  Bayer  in  \60S,  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.  Sometimes  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  situations  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  Cas- 
siopoia,  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 
iittle  out  of  the  milky  way,  is  the  bright  star  Lyra.     The  dragon  consists  of 


OM    THE    FIXED    STARS.  497 

a  chain  of  stars  partly  surrounding  the  little  bear;  and  between  Cassiopeia 
and  the  swan  is  the  constellation  Cepheus. 

Near  Algenib,  and  pointing  directly  towards  it,  are  two  stars  of  Andro- 
meda, and  a  third  is  a  little  beyond  them.  A  line  drawn  through  the 
great  bear  and  Capclla  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 
points  of  a  W.  In  Aries  we  observe  two  principal  stars,  one  of  them  with  a 
smaller  attendant. 

A  line  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  fust  horse  nearly  to  Arcturus, 
in  the  waggoner,  or  Bootes.  Much  further  southwards,  and  near  the  milky 
way,  is  Antares,  in  the  scorpion,  forming,  Avith  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  drawti 
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  An- 
dromeda makes,  with  three  of  Pegasus,  a  square,  of  which  one  of  the  sides 
points  to  Fomalhaut,  situated  at  a  considerable  distance  in  the  southern  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 
VOL.    I.  3  s 


498  LECTURK    XU. 

in  Britain  may  be  easily  recognised.  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  according  to  Humboldt's 
observations,  perhaps  some  others  may  require  to  be  admitted  into  the 
same  class.     (Plate  XXXVI,  XXXVII.) 


499 


LECTURE  XLll.  sEmT^^ 


j(lUN 


ON    THE    SOLAR    SYSTEM. 


JL  HE  most  conspicuous  of  all  the  celestial  bodies,  which  we  have  becH 
examining,  is  the  sun,  that  magnificent  luminary  which  occupies  the  ceiitrc 
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  comparatively 
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,  there-' 
fore,  in  itself  highly  probable  that  the  sun  may  have  such  a  motion.  But 
Dr.  Herschel  has  confirmed  this  conjecture  by  arguments  ahnost  demon- 
strative. 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 


500  LECTURE    XLII. 

greatest  apparent  motions.  Besides,  the  star  Castor  appears,  Avhen  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  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  change 
of  place,  dependent  on  the  situations  of  the  planetary  bodies,  which  was 
lono-  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  from  his  centre: 
and  since  the  centre  of  inertia  of  the  whole  system  must  ,be  undisturbed  by 
any  reciprocal  actions  or  revolutions  of  the  bodies  composing  it,  the  sun 
must  describe  an  irregular  orbit  round  this  centre,  his  greatest  distance  from 
it  being  equal  to  his  own  diameter.  Wc  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  presupposed  know- 
ledge 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  to- 
wards the  centre,  our  right  hands  will  be  eastwards,  and  our  left  westwards. 
All  the  rotations  of  the  diflferent  bodies  which  compose  the  solar  system,  as 
far  as  they  have  been  ascertained,  are  in  the  same  direction,  and  all  their 
3 


ON    THE    SOLAR    SYSTEM.  501 

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  stm'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  variations, 
but  they  arc  generally  found  about  the  same  points  of  the  sun's  surface. 
Lalande  imagines  that  they  are  parts  of  the  solid  body  of  the  sun,  which, 
by  some  agitations  of  the  luminous  ocean,  with  which  he  conceives  the  sun 
to  be  surrounded,  are  left  nearly  or  entirely  bare.  Ur.  Wilson  and  Dr. 
Herschel  are  disposed  to  consider  this  ocean  as  consisting  rather  of  a  flame 
than  of  a  liquid  substance,  and  Dr.  Herschel  attributes  the  spots  to  the 
Anission  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  appearance  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  appearance  somewhat  mottled, 
some  parts  of  it,  appearing  brighter  than  others,  have  generally  been  called 
faculae;  but  Dr.  Herschel  distinguishes  them  by  the  names  of  ridges  and 
nodules.  The  spots  are  usually  surrounded  by  margins  less  dark,  than  them- 
selves, which  Dr.  Herschel  calls  shallows,  and  which  he  considers  as  parts 
of  an  inferior  stratum  consisting  of  opaque  clouds,  capable  of  protecting  tlie 
immediate  surface  of  the  sun  from  the  excessive  heat  produced  by  combus- 
tion in  the  superior  stratum,  and  perhaps  of  rendering  it  habitable  to  ani- 
mated 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  bd  conviucecJ 
that  no  clouds,  however  dense,  could  impede  its  rapid  transmission  to  the 


\. 


502  LECTURE    XLII. 

parts  below.  Besides,  the  diameter  of  the  sun  is  1 1 1  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  imaained 
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  at- 
mosphere, imperfectly  transparent;  conceiving  that,without  such  an  atmosphere' 
the  marginal  parts,  which  are  seen  most  obliquely,  must  appear  consider- 
ably the  brightest ;  but  this  opinion  is  wholly  erroneous,  and  the  inferences 
which  have  been  drawn  from  it," respecting  the  sun's  atmosphere,  are  con- 
sequently 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  Mer- 
cury. It  is  said  to  have  been  first  distinctly  described  in  Childrey's  Bri- 
tannia Baconica,  a  work  published  in  l66l,  and  it  was  afterwards  more  par- 
ticularly observed  by  Cassini,  Mairan,  and  others.  In  the  torrid  zone  it  is 
almost  constantly  visible;  and  in  these  climates,  it  may  often  be  distin- 
guished in  the  beginning  of  March,  after  the  termination  of  twilight,  ex- 
hibiting the  appearance  of  a  narrow  triangle,  somewhat  rounded  off,  of  a 
whiteness  resembling  the  milky  way,  ascending  from  the  sun  as  a  base,  likjC 
the  projection  or  section  of  a  very  flat  spheroid,  and  extending  to  a  distance 
of  more  than  50°  from  the  sun.  The  whole  orbit  of  Venus  never  subtend* 
80  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  be  a 
continuous  fluid  atmosphere,  revolving  with  the  same  velocity  as  the  sun; 
for  the  gravitation  of  such  an  atmosphere  would  cause  it  to  assume  a  form 
more  nearly  spherical;  and  the  only  probable  manner  in  Avhich  it'  can  be 
4 


ON    TH£    SOLAR    SYSTEM.  503 

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  coincide 
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  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,  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  complete  agreement  with 
the  visible  phenomena  of  the  heavens,  and  with  the  laws  of  gravitation,  will 
hereafter  appear  to  afi^brd  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  aberration  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  hghc 
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  represented  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;  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. 


504  LECTURE    XLII. 

Tlie  ecliptic  passes  through  the  constellations  denomiuated  the  signs  of 
the  zodiac,  between  Aries,  the  Pleiades,  the  twins,  and  Ilegulus,  to  the  north, 
and  Aldebaran,  Spica,  and  Antares,  to  the  south.  Its  position  has  varied 
slowly  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  »tar  than  it  was  in 
the  time  of  Eratosthenes,  who  observed  its  place  230  years  before  the  birth  of 
Christ.  It  appears  from  Lagrange's  calculations,  that  the  limit  of  its  great- 
est possible  variation  is  about  10  or  11  degrees.  The  ecliptic  is  supposed 
to  be  divided  into  twelve  angular  parts,  or  signs,  each  containing  thirty 
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,  Arcitcnens,   Caper,   Amphora,  Pisces. 

The  planes  of  the  orbits  of  the  other  primary  planets,  excepting  the  three 
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 


ON    THE    SOLAR    SYSTEM.  505 

he  found  that  a  right  line,  joining  the  sun  and  any  planet,  describes  always 
equal  areas  in  ecjual  ^imes.  1  he  ohsi-rvations,  on  which  Ktpler  founded  these 
important  laws,  were  made  pnntipally  on  the  phmet  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  situati;)n  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  having 
done  this,  the  velocity  of  the  motion  in  different  parts  of  the  orbit  was  easily 
determined  from  the  apparent  change  of  place  in  a  given  time.  (Plate 
XXXII.  Fig.  471.) 

The  same  as''  ronomer  also  ascertained,  that  the  squares  of  the  times  of  re- 
volution of  the  different  planets  are  in  proportion  to  the  cubes  of  their  mean 
distances  from  the  sun.  For  example,  if  oneplann  were  four  times  as  distant 
as  aiother,  it  wjuld  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  Jupifer, 
and  their  periods  are  nearly  eight  times  as  long  respectively. 

It  is  probable  that  all  the  planets  have  a  rotatory  motion  from  west  to  east, 
cither  perfectly  or  very  nearly  equable.  This  motion  has  been  observed  in 
Venus,  the  Earth,  Mars,  Jupirer,  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  rotatory  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  in- 
tersections of  the  apparent  ecliptic,  or  the  path  of  the  sun  in  the  heavens, 

VOL.    I  3  T 


506  LECTURE    XLII. 

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  2(5^°.  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,  al- 
though he  failed  in  the  attempt  to  ascertain  its  quantity  with  accuracy  ;  it 
was  first  actually  observed  by  Dr.  Bradley,  about  the  year  1747.  The  abso- 
lute 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  dis- 
tinguished from  the  change  of  the  position  of  the  ecliptic.  The  inclination 
ot*  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  small  planets,  Juno,  Pallas,  and  Ceres;  twice  24  or  48,  making  52,  for 
Jupiter;  twice  48  or  96  for  Saturn,  making  100  ;  and  twice  96  or  162, 
making  I96,  for  the  Georgian  planet;  and  these  sums  will  represent 
the  distances,  without  any  material  exception,  in  the  nearest  integer  num- 
bers. \ 

The  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, 
at  about  two  fifths  of  the  distance  of  the  earth.  His  orbit  is  more  eccentric, 
and   more  inclined  to  the  ecliptic,   than  those   of  any    of  the  planets  ex- 


V 


ON    THE    SOLAR    SYSTEM.  507 

cept  the  three  small  ones  lately  discovered;  the  eccentricity  being  one  fifth 
of  the  mean  distance,  and  the  inclination  7°.  Of  his  density  and  his  rota; 
tion  we  know  nothing  but  from  conjecture. 

Venus  is  very  nearly  as. large  as  the  earth;  Dr.  Herschel  thinks  her  even 
ahtcle  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  cir- 
cular, inclined  in  an  angle  of  3°  24'  to  the  ecliptic  .  Mr.  Schroeter  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  ttie  motions 
of  the  other  planets,  and  it  has  been  supposed  to  be  a  little  less  thjin  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  tliat  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  comparison,  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  36"5days,6  hours,9minutes,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  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 


508  LECTURE  xnr. 

is  ^lyth  shorter  than  his  equatorial  diameter.  From  this  form,  compared  with 
the  time  of  his  rotation,  it  may  be  inferred  that  his  density  must  be  very 
unequal  in  different  parts:  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  distance 
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  pri- 
mary planet,  the  observations  of  Mr.  Piazzi,  Dr.  Olbers,  and  Mr.  Harding 
have  placed  three  very  small  bodies,  differing  but  little  in  their  mean  distance 
and  their  periodical  time.  They  have  named  them  Ceres,  Pallas,  and  Juno: 
none  of  them  subtends  an  angle  large  enough  to  be  measured  by  our  best 
instruments;  and  all  the  circumstances  of  their  motions  are  yet  but  imper- 
fectly established.  Juno,  however,  appears  to  be  somewhat  less  remote  tlian 
the  other  tMo;  all  their  orbits  are  considerably  inclined  to  the  ecliptic,  espe- 
cially 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  1 1  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°  ly'  with  ours.  His  belts  are  supposed 
by  many  to  be  clouds  in  his  atmosphere ;  they  seem  to  have  a  rotation  some- 
what 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  incHned  24-°  to  the  ecliptic,  at  the  distance 
4)f  94:  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  greSt  as 


ON    THE    SOLAR    SYSTEM.  --^y 

that  of  the  planet,  F^is  figu"-  appears  also,  according  to  Dr.  Hcrschel's 
observations,  to  be  extremely  singular;  deviating  very  considerably  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. 

The  Georgian  planet,  discovered  by  Dr.  Herschel  in  1780,  sometimes  also' 
called  Herschel,  and  sometimes  Uranus,  revolves  in  83:1  years,  at  a  distance 
from  the  sun  equal  to  19  times  that  of  the  earth.  Its  diameter  is  a  little 
more  than  4  times  that  of  the  earth,  and  the  weight  of  bodies  at  its  surface  a 
little  less  than  here.  Notwithstanding  its  dimensions  are  by«no  means  compara- 
tively 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  re- 
volve with  considerable  rapidity. 

These  ten  planetary  bodies  are  the  only  ones  hitherto  discovered  which 
have  any  title  to  be  considered  as  primary  planets,  that  is,  as  bodies  revolving 
round  the  sun,  in  orbits  so  nearly  circular,  as  to  remain  always  within  the 
reach  of  bur  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  appropriation  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  attend- 
ant 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 


5lU  tECTURE    XLII. 

Older  of  the  signs,  and  in  planes  not  very  remuu  from  the  ecliptic,  except, 
ing  those  of  the  Georgian  planet,  which  revolve  in  planes  nearly  perpendi- 
cular to  the  ecliptic.  Each  of  these  planets  thus  becomes  the  central  lumi- 
nary of  a  little  system  of  its  oAV'n,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.  llerschel  for  the 
knowledge  of  9;  the  Georgian  planet,  with  its  six  satellites,  and  the  two 
'  innermost  moons  of  Saturn. 

The  motions  of  some  of  these  satellites,  in  particular  of  those  of  Jupiter> 
and  of  the  niQon,  are  of  considerable  importance  for  the  assistance  they  aftbrd 
us  in  determinations  of  time,  and  of  the  relative  situations  of  places.  They 
are  subjected  to  considerable  irregularities,  but  the  united  labours  of  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, 
and  a  synodical  revolution,  during  which  she  returns  to  the  same  position 
with  respect  to  the  earth  and  sun,  in  29  days  IQ^  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,  but  this  inclination  is 
liable  to  great  variations:  the  place  of  its  nodes  is  also  continually  changing, 
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  times;  the  ap- 
sides, or  the  extremities  of  the  greater  axis  of  the  ellipsis,  which  are  called 
the  apogee  and  perigee,  have  on  the  whole  aidirect  motion.  From  a  com-  - 
parison  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  periodof  her  revolution 
round  tbe  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  I''  A'3'  to  the         ^ 


ON    THE    SOLAR   SYSTEM.  511 

ecliptic,  and  sometimes  as  much  as  7°  to  her  own  orbit.  Her  distance  from 
the  earth  is  about  240 000  miles;  her  diameter -,?-  of  that  of  the  earth,  or 
2160  miles;  and  the  weight  of  bodies  at  her  surface  is  supposed  to  be  about 
one  fifth  of  their  weiglit  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   satisfactory  evi- 
dence of  the  truth  of  the  conjecture.  The  appearance  of  a  perforation,  which 
UUoa  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.  Weidler  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  commonly  supposed  to  exceed  very  consider- 
ably that  of  the  mountains  of  the  earth;    but  Dr.   Herschel  is  of  opinion 
that  none  of  them  are  so  much  as  two  miles  high.     The  names,  which  hare 
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  Sf  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  under- 
go, 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;  but  the  plane  of 
the  seventh  or  outermost  satellite  is  but  half  as  much  inclined  to  the  ecliptic. 
The  ring  has  been  observed  by  Dr.  Herschel  to  revolve  in  104-  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  satellites  of  the 


5ig      '  LECTURE    XLir. 

Georgian  pknet  are  nearly  perpendicular  to  the  ecliptic;    and  some  of  tlieir 
re/olutions  are  supposed  to  be  rather  retrograde  than  direct. 

Besides  the  bodies  which  revolve  completely  round  the  sun,  within  the  li- 
mits 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  sometimes 
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  ]6'80,  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  ligbt,   directed  always  towards  a  point 
nearly  opposite  to  the  sun:  it  is  quite  uncertain  of  what  substance  they  con- 
sist; and  it  is  difficult  to  determine  which  of  the  conjectures  respecting  them 
can  be  considered  as  the  least  improbable;  it  is  possible  that,  on  account  of 
the  intense  cold,  to  which  the  comets  are  subjected  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,  perhaps,  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  at- 
traction for  the  tail  consequently  weak,    so  that  it  has  little  tendency  to  re- 
duce 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 
4 


ON    THE    SOLAR    SYSTEM.  513 

suffered  by  the  inhabitants  of  the  planet  might  be  merely  temporary  and  lo- 
cal: the  chances  are,  however,  much  greater,  that  a  comet  might  interfere  in 
such  a  manner  with  a  planet,  as  to  deflect  it  a  little  from  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  ue  have 
no  opportunity  of  observing  a  sufficient  portion  of  the  orbit  of  any  comet,  to 
determine  with  accuracy  the  whole  of  its  form  as  an  ellipsis,  since  the  part 
which  is  within  the  limits  of  our  observation  does  not  sensibly  differ  from  the 
parabola,  which  would  be  the  result  of  an  ellipsis  prolonged  without  end. 

Two  comets  at  least,  or  perhaps  three,  have  been  recognised  in  their  re- 
turn. A  comet  appeared  in  1770,  which  Prosperin  suspected  to  move  in  an 
orbit  materially  different  from  a  parabola:  Mr.  Lexell  determined  its  period 
to  be  5  years  and  7  months,  and  its  extreme  distances  to  be  between  the 
orbits  of  Jupiter  and  of  Mercury;  but  it  does  not  appear  that  any  sub- 
sequent observations  have  confirmed  his  theory.  It  has,  however,  been  cal- 
culated, that  supposing  the  theory  correct,  it  must  afterwards  have  approach- 
ed so  near  to  Jupiter  as  to  have  the  form  of  its  orbit  entirely  changed. 

Dr.  Halley  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  con- 
vert 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  1 106,  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  1 848.  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 

VOL.   I.  3  u 


514  lECTURE    XLII. 

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  coincidenc«  of  the  calculation  of  Hal  ley  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.) 


515 


LECTURE  XLIII. 


ON    THE    LAWS    OF    GRAVITATION. 


At  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  eflfects  of  the  same  force  of  gravitation  which  causes  a  heavy  body 
to  fall  to  the  earth ;  he  has  shown  that  in  consequence  of  this  universal 
property  of  matter,  all  bodies  attract  each  other  with  forces  decreasing  as  the 
squares  of  the  distances  increase;  and  of  later  years  the  same  theory  has  been 
still  more  accurately  applied  to  the  most  complicated  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  mathematically  the  effects  of  gravity  in  each 
particular  motion,  but  we  may  in  some  measure  illustrate  the  subject,  by 
considering  in  what  manner  astronomers  have  proceeded  in  their  explanations 
and  calculations,  and  we  may  enter  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;  and 
in  order  to  determine  the  effects  of  their  attraction,  we  must  suppose  the  ac- 
tions of  an  infinite  number  of  such  points  to  be  combined.  It  was  shown  by 
Newton,  that  all  the  matter  of  a  spherical  body,  or  of  a  spherical  surface, 
may  be  considered,  in  estimating  its  attractive  force  on  other  matter,  as' 
collected  in  the  centre  of  the  sphere.  Tlie  steps  of  the  demonstration  arc 
these:  a  particle  of  matter,  placed  at  the  summi^t  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,  whateve  r  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  ot  the  opposite  and 


516  LECTURE    XLIir. 

equal  actions  of  the  infinite  number  of  minute  surfaces,  terminating  the  oppo- 
site 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  iii  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  in- 
finite 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  propo- 
sition tends  very  much  to  facilitate  all  calculations  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  gra- 
vity 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  in- 
considerable to  be  perceived  by  us.  It  may  possibly  influence  the  progres- 
sive motions  of  some  of  the  stars;  and  if,  as  Dr.  Herschel  supposes,  there 
ave  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  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  esti- 
mate, but  about  40  feet  in  the  first  year,  and  in  1000  years  only  8000  miles. 
It  has  been  conjectured  that  the  mutual  gravitation  of  the  stars  of  a  nebula 
is  sometimes  the  cause  of  the  peculiar  form  of  the  aggregate,  which  some- 
what resembles  that  of  a  drop  of  a  liquid,  held  together  by  its  cohesion:  hut 


ON    THE    LAWS    OF    GRAVITATION.  517 

unless  the  form  of  the  nebula  was  originally  spherical,  it  could  scarcely  have 
acquired  that  form  from  the  operation  of  gravity,  since  the  spherical  form  of 
a  drop  is  owing  as  much  to  the  elasticity  as  to  the  attractive  force  of  the  par- 
ticles 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  pla- 
nets, is  so  inconsiderable,  that  it  escaped  observation  until  its  existence  had 
been  deduced  from  theory.  Not  but  that  this  change  would  be  suihciently 
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  dis- 
tance of  the  moon  from  the  earth  ;  and  this  change  is  readily  deducible  from 
the  general  and  unquestionable  law  of  mechanics,  tliat  the  place  of  the  cen- 
tre of  inertia  of  a  system  cannot  be  changed  by  any  reciprocal  or  mutual  ac- 
tion of  the  bodies  composing  it,  the  action  of  gravity  being  found  to  be  per- 
fectly reciprocal.  But  the  earth  accompanies  the  sun  in  great  measure  in  this 
aberration,  and  the  other  planets  are  also  more  or  less  aff'ected  by  similar 
motions ;  so  that  the  relative  situations  are  much  less  disturbed  than  if  the 
sun  described  this  irregular  orbit  by  the  operation  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  ma- 
thematically pfoved  that  the  force  directed  to  the  sun  must  increase  in  pro- 
portion as  the  square  of  the  distance  decreases. 

The  times  of  the  revolutions  of  the  planets  are  also  in  perfect  conformity 
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 ; 


518  LECTURE    XLIII. 

but  Newton  first  demonstrated  the  same  proportion  with  respect  to  elliptic 
orWts,  and  showed  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,  shows  also  that  the  matter,  of  which  they  are  composed,  is  equally 
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  the 
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  the 
other  planetary  bodies;  but  the  calculations  of  the  exact  quantities  of  these 
perturbations  are  extremely  intricate.  In  general,  each  of  the  disturbing 
forces  causes  the  nodes  to  have  a  slight  degree  of  retrograde  motion ;  but  on 
account  of  the  peculiar  situation  of  the  orbits  of  Jupiter  and  Saturn,  it  hap- 
pens 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  retrograde 
motion  of  Jupiter's  nodes  on  the  ecliptic. 

The  secular  diminution  of  the  obliquity  of  the  ecliptic,  or  that  slow  vari- 
ation of  its  position,  which  is  only  discovered  by  a  comparison  of  very  dis- 
t^mt  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 


ON    THE    LAWS    OF    GRAVITATION.  519 

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  Adhere 
equal,  the  equatorial  parts  would  necessarily  recede  from  the  axis,  until  the 
greater  number  pf  particles,  acting  in  the  same  column,  compensated  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  surface  of  a  fluid, 
cither  wholly  or  partially  covering  a  solid  body,  must  assume  the  same 
figure,  in  order  that  it  may  remain  at  rest.  The  surface  of  the  sea  is  there- 
fore spheroidical,  and  that  of  the  earth  deviates  so  far  only  from  a  spheroi- 
dical figure,  as  it  is  above  or  below  the  general  level  of  the  sea.  (Plate 
XXXI V.  Fig.  436.) 

The  actions  of  the  sun  and  moon,  on  the  prominent  parts  about  tlie  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  re- 
trograde 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  notles;  in  conse- 
quence 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  precession  of  the  equi- 
noxes. On  account  of  the  different  quantity  of  the  precession  at  different 
times,  the  actual  length  of  the  tropical  year  is  subjected  to  a  slight  varia- 
tion; it  is  now  4  or  5  seconds  shorter  than  it  was  in  the  time  of  Hipparchus. 
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 
Hrell  as  the  most  important  problems  in  astronomy;  but  it  is  easy  to  under- 
stand, in  general,  how  the  dilierence  in  the  quantity  and  direction  of  the 
sun's  actions  ofi  the  moon  and  earth,  may  cause  such  a  derangement  of  the 


SQO  LECTURE    XLIII. 

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  simple  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  difference  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  together;  but  this  force  is,  on  the 

,  whole,  much  smaller  than  the  former;  and  the  result  of  both  these  disturbing 
forces  is  alwaj's  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  inclination  of  the  orbit,  since  it  acts  wholly  in 
the  plane  of  that  orbit;  but  when  they  are  in  any  other  situation,  the  dis- 
turbing 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  a])pear  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  de- 
crease more  rapidly  than  the  square  of  the  distance  increases;  and  the  re- 
verse happens  when  the  disturbing  force  tends  to  bring  the  earth  and  moon 
nearer  together ;  but  the  former  effect  is  considerably  greater  than  the  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  revolving  rJdius,  until,  at 


Oy    THE    LAWS    OF    GRAVITATIOX.  521 

a  certain  point,  which  is  called  the  lovver  apsis,  it  becomes  per])endicular  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  the  contrary,  tlie  force  varies 
more  slowly,  the  apsis  has  a  retrograde  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.  And  a  similar  theory  is  applicable  to  the  mutual 
perturbations  of  the  primary  planets.     (Plate  XXXlV.   Fig.  488.) 

The  secular  acceleration  of  the  moon's  mean  motion,  which  had  long  pre- 
sented a  difficulty  amounting  almost  to  an  exception,  against  the  sufficiency 
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  explanation.  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  sug- 
gested 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  revolution  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  applica- 
tion of  the  laws  of  gravity,   excepting  the  modifications  whicli    depend  on 
VOL.    I.  5  X 


522  LECTUHK    XLIll. 

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  rhe  comet  of  1759  about  618  days;  and  the  prediction  was  ac- 
complished within  the  probable  limits  that  they  had  assigned  for  the  error  of 
the  calculation.  The  labours  of  Clairaut  have  indeed  in  many  respects  im- 
proved the  science  of  mathematical  astronomy ;  he  was  the  first  that  ob- 
tained a  complete  determination  of  the  effects  of  the  mutual  actions  of  three 
gravitating  bodies,  disturbing  each  other's  motions;  and  his  investigations, 
which  were  founded  on  those  of  Newton,  led  the  way  to  still  further  improve- 
ments and  refinements,  which  have  been  since  made  in  succession  by  Euler, 
Lagrange,  and  Laplace. 


523 


LECTURE  XLIV. 


ON    THE    APPEARANCES    OF    THE    CELESTIAL    BODIES. 


tVe  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  developement  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  appearances  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  connexion  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. 

The  proper  motions  of  the  fixed  stars,  as  they  are  subjected  to  our  obser- 
vation, undergo  two  modifications;  the  one  from  the  relative  direction  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  attending  him. 
This  motion  has  indeed  only  been  inferred  from  the  apparent  motions  of  a 
great  number  of  stars,  which  are  either  partly  or  ro  Uy  referable  to  it,  and 
which  could  scarcely  i'ave  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  of  the  fixed  stars  are 
not  sensibly  affected  by  the  earth's  annual  revolution:  if  any  of  them  had  been 
considerably  less  remote  tlian  they  are,  it  is  probable  that  this  motion  would 


SQi  IKCTURE  XLty. 

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  diiferent 
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  aberration,  in  consetjuence  of  the 
progressive  motion  of  the  earth  in  its  orbit,  combined  with  the  limited 
velocity  of  light;  and  the  standard  of  comparison  being  the  earth's  axis,  its 
nutation  must  also  in  some  degree  affect  the  apparent  places  of  the  stars.  It 
Avas  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  ap- 
parent 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  heavenly  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:  con- 
sequently, 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  distances  from  him,  and  thus  we  obtain  a  correct 
knowledge  of  his  path. 


ON    THE    APPEARANCES    OF    THE    CELESTIAL    BODIES.  525 

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  surt  in  winter  than  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  srui  passes  through  the  vviaiter  half 
of  the  ecliptic  in  a  time  7  or  8  days  shorter  than  the  summer  half.  Accord- 
ing 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  straigiit, 
but  in  all  other  situations,   elliptical. 

The  rotation  of  the  earth  on  its  axis  produces  the  still  more  obvious  vicis- 
situdes of  day  and  night;  and,  in  combination  with  its  annual  motion,  oc- 
casions 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  66^°, 
the  plane  of  the  equator,  which  is  perpendicular  to  the  axis>  must  pass  twice 
in  the  year  through  the  sun.  VVhen  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  ecjuator,  which  are  conse- 
quently nearer  to  the  unenlightened  pole,  have  their  day  sliorter.  Tlie  parts 
nearest  to  the  poles  have  also  one  of  their  days  and  one  of  their  nights  pro- 
tracted 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  £34°;  so  that  by  determining  the 


5^6  LECTUUK    XLIV. 

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  -i^T  of  the  force  of  gravity  ;  tut  the  diminution  of  the  force  of  gravi- 
tation appears,  by  experiments  on  pendulums,  to  be  T-'-g-;  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  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  observations 
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  which  this 
may  happen,  has  been  variously  estimated,  and  it  is  perhaps  actually  dif- 
ferent in  different  climates,  being  a  little  greater  in  countries  near  the  poles 
than  in  those  which  are  nearer  the  equator:  there  is  also  sometimes  a  second- 
ary 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,  allow- 
ing 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 


ON    THE    APPEARANCES    OF    THE    CELESTIAL    BODIES.  527 

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  opposi- 
tion 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  stationary,  accord- 
ing to  the  directions  and  the  comparative  velocities  of  the  real  motions.  If 
the  earth  were  at  rest,  the  inferior  planets  would  appear  to  be  station;uy  when 
they  are  at  the  greatest  elongation  or  angular  distance  from  the  sun;  but, 
on  account  of  the  effect  of  the  earth's  motion,  Venus  is  stationary  at  an 
elonga*^ion  of  about  29°,  while  her  greatest  elongation  is  between  45°  and 
48°.  The  greatest  elongation  of  Mercury,  in  each  revolution,  is  from  28-j° 
to  17t°>  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,  re- 
presents correctly  the  true  positions  of  the  planets  with  respect  to  tiie  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  inferior 
planets,  and  the  transits  of  these  planets  over  the  sun,  depend  on  their 
positions  in  their  orbits,  and  on  the  places  of  the  nodes,  with  respect  to  tlie 
earth.  Jupiter,  Saturn,  and  the  Georgian  planet,  are  so  remote  in  com- 
parison of  the  earth's  distance  from  the  sun,  that  they  appear  always  fully 
illuminated.  Venus  is  brightest  at  an  elongation  of  about  40°  fron)  the  sun, 
in  that  part  of  her  orbit  which  is  nearest  to  the  earth;  she  then  appears  like 
tlie  moon  when  5  days  old,  one  fourth  of  her  disc  being  illuminated;  slie 
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  15^°  of  Jier  node  at  the  time  of  conjunction, 


528  LF.CTUHE    XLIV. 

Otherwise  she  wijl  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;  that  part  of  the  nroon  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  m  )on  is  illuminated.  The  parts  of  the  moon 
which  are  immeaditely  op|)osed  to  the  earth,  appear  to  undergo  a  libration, 
or  chang-e  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  XXX IV.  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  circum- 
stances, she  herself  enters  the  earth's  shadow.  1  he  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  34 
limes  the  mean  distance  of  tiie  moon;  the  penumbra,  on  the  contrary,  consti- 
tutes, together  with  the  shadow,  a  portion  of  a  cone  diverging  from  the  earth 
without  limit;  but  the  only  effect  of  this  imperfect  shadow^  is,  that  it  causes 
the  beginning  of  a  lunar  eclipse  to  be  incapable  of  very  precise  determina- 
tion; 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  atmo- 
spheric refraction  inflects  the  light  passing  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  of  which  the  moon  remains  still  visible  to  us,  the 


ON    THE    APPEARANCES    OF    THE    CELESTIAL    BODIES.  53,9 

cone  of  total  darkness  extending  to  somewhat  less  than  two  thirds  of  the 
m/)on'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  diameters  arc 
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  appar- 
ent diarmeter  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  attri- 
buted to  the  effect  of  the  sun's  atmosphere,  since  that  of  the  moon  is  pro- 
bably too  inconsiderable  to  produce  the  appearance:  a  red  streak  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  observation 
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  spectator  on  the  moon, 
an  eclipse  of  the  earth,  or  a  transit  of  the  moon's  shadow  over  the  earth'* 
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  eartb  after  2^3  lunations,  or  revolutions  of  the  moon,  which  are  per- 
formed in  18  years  of  365  days  each,  15  days,7  hours,  and  43|:  minutes ;  so  that 
after  a  period  of  about  18  years,  the  series  of  eclipses  reeommences  nearly  in 
the, same  order.     This  circumstance  was  observed  by  the  ancients,  and  i& 

VOL.  I.  3y 


530  Lt;CTUUE    XLIV. 

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  conj  unction  with  the  sun,  at  any  dis- 
tance within  1  r-j°  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  into 
12  parts,  called  digits,  each  of  which  contains  30  minutes:  thus  if  o  n 
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  time  sof  the  moon's  rising  on  two  successive  days,  is,  in  London, 
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 :  t\^e  great- 
est possible  difference  is  1  hour  17miivute3.  But  it  happens  every  month  that 
the  difference  becomes  greater  and  less  by  turns,  and  when  the  least  differ- 
ence is  at  the  time  of  the  fuU  moon,  it  is  usually  called  the  harvest  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  fii-st  three  never  pass  the  shadow  without  being  plunged 
into  it,  and  the  fourth  but  seldom;  while  those  of  Saturn  are  much  less  fre- 
quently liable  to  be  eclipsed,  on  account  of  their  greater  deviation  from  the 
plane  of  his  ecliptic.  These  satellites  are  also  frequently  hidden  behind  the 
body  of  the  planet,  and  this  circumstance  constitutes  an  occultation:  hence 
it  happens  that  we  can  never  see  both  the  immersion  of  the  first  satellite  into 
the  shadoM'  of  Jupiter,  and  its  emersion  from  it;  but  both  the  immersion  and 
emersion  of  the  three  outer  satellites  are  sometimes  observable.     The  ring  of 


ON    THE    APPEARANCES    OF    THE    CELESTIAL    BODIES.  531 

Saturn  exhibits  a  variety  of  forms  according  to  its  angular  position:  it  dis- 
appears to  common  observation  when  either  its  edge  or  its  dark  side  is  pre- 
sented 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.  Bou- 
guer.  He  states  the  intensity  of  the  moon's  light  as  only  one  three  hundred 
thousandth  of  that  of  the  sun.  These  calculations  have  been  extended  by  Euler 
and  by  Lambert;  Euler  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  effect  of  1  candle,  at  the  distance 
of  7-i  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  thousand  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  conterri- 
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  coa- 


^32  LECTUHE    XLIV. 

jecture  and  imagination ;  and  thus,  from  natural  philosophy,  our  imaginations 
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  diver- 
sify ;  he  dwells  on  a  favourite  idea,  and  repeats  it  in  a  thousand  emblemati- 
cal forms ;  his  object  is,  to  say  a  little,  very  elegantly,  in  very  circuitous,  and 
somewhat  obscure  terms.  But  the  information,  which  the  natural  philoso- 
pher has  to  impart,  is  too  copious  to  allow  of  prolixity  in  its  detail ;  his  sub- 
jects 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  ornamented  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  Fontenelle'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  quick- 
silver; 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  circum- 
polar  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  seasons,  and 
her  day  and  night,  must  greatly  resemble  oui-s.  The  earth,  when  in  oppo- 
sition 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  frequently,  and 
perhaps  generally,  visible  in  tlie  day ;  and  together  with  the  moon,  must  eK» 


ON    THE    APrEARA'NCES    OF    THE    CELKSTIAL    BODIES.  533 

hibit  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  at- 
mosphere 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  ap- 
pearance 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  aiford,  especially  when  viewed  with  a  telescope,  an  ex- 
cellent timepiece;  the  continents  and  seas  coming  gradually  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  afJbrd  us  an  easy  me- 
thod of  discovering  the  longitude  of  a  place,  by  comparing  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  na- 
vigation, 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  de- 
serted, 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  dis- 
turbances 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 


534  LICTURE    XLir. 

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  me- 
teors, 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.  Russels 
lunar  globe,  which  is  also  capable  of  exhibiting,  with  great  accuracy,  the 
changes  produced  by  its  librations. 

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  inclina- 
tion of  his  axis  to  his  echptic  being  nearly  the  same  as  that  of  the  earth's 
axis,  the  changes  of  seasons  must  be  nearly  like  our  own.  Dr.  Herschel  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  surrounding 
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  tne  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  tp 
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,  perhaps,  fiom  copious 
atmospheres;  and  in  this  respect,  as  Avell  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  contem- 
plated from  Jupiter,  would  be  the  diversified  positions  and  combinations  of 
his  satellites;  their  light  must  be  faint,  but  yet  of  service;  and  to  a  traveller 


ON    THE    APTEARANCES    OF    THE    CELESTIAL    BODIES.  555 

on  the  surface  of  this  vast  globe  they  must  aflord  useful  information,  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  proxi- 
mity to  the  sun,  in  the  same  manner  as  a  planet  at  half  the  distance  of  Mer- 
cury 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  aftbrd,  in  different  parts  of  his  surface,  very  diversified  appear- 
ances of  magnificent  luminous  arches,  stretched  across  the  heavens,  especi- 
ally 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  ap- 
proach to  the  equator,  so  that  almost  every  place  on  his  surface  must  some- 
times remain,for  a  great  number  of  diurnal  revolutions,  in  light  and  in  dark- 
ness; 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. 
rig.  501.) 

On  the  whole,'we  are  tempted,  from  an  almost  irresistible  analogy,  to  con- 
clude that  the  planets  are  all  in  some  manner  or  other  inhabited  ;  but  at  the 
same  time  we  can  scarcely  suppose  that  a  single  ecipses  of  terrestrial  animals  or 
even  vegetables  could  exist  in  any  of  them;  their  minerals  may,  perhaps,  re- 
semble ours,  and  if  the  stones  which  Mr.  Howard  has  analysed  are  realiy  lu- 
nar productions,  we  ha/e  proofs  that  the  moon  at  least  contains  some  sub- 
stances resembling  those  which  compose  the  eartli;  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. 


536 


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  S-i 
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  e(juator,  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  declination  and  right  ascension  are  most 
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 


ON    PRACTICAL   ASTBONOMY.  537 

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  be  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 
referable  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  time- 
keepers afe  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,  witli  almost  equal 
accuracy,  in  any  other  situation,  and  sometimes  with  greater  convenience. 
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  necessary.  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,  ex- 
pressed 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  tliemselves ;  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  difl^'erence  between  his  path  in  every  sidereal  day,  and 

VOL.    I.  3  z 


5S8  lECTURE    XLV. 

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 
chano-e  of  right  ascension  is  liable  to  adouble  inequahty.  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  quantity,  which  is  to  be  added  to,  or  subtracted  from,  another, 
quantity;  thus  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  cor- 
rections 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  sometimes 
embarrassed  with  a  complicated  apparatus, calculated  forimitating  the  inequali- 
ties 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  becon- 
structed,  with  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  equinoctial,  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  calcula- 
tion or  by  construction.  A  point  may  also  be  used  as  a  gnomon,  as  well  as 
aline;  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.  60i  .  .  506.) 

The  changes  of  the  seasons  depend  on  the  return  of  the  sun  to  the  same 
position  Avith  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 


ON    PRACTICAL    ASTRONOMT.  539 

very  little  change  of  declination ;  whence  the  time  when  tlie  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 
dav  and  the  tropical  year;  and  since  the  tropical  year  exceeds  the  time  of 
365  days,  by  5  hours,  48  nnnu*-es  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  with- 
out 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- 
commonly  called  by  astronomers  the  year  0,  but  by  chronologists  the  year 
before  Christ.  The  correction  introduced  by  Caesar  was,  however,  t 
great,  the  error  being  exactly  7  days  in  900 years;  so  that  in  1582  it  amount-  ■ 
ed  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  cen- 
tury. 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  bissextiles  are  omitted  in  3600  years,, 
while  the  true  length  of  the  year  would  require  tlie  omission  of  28;  but  so» 


540  LECTURE    XLIV. 

small  a  difference  can  be  of  no  material  consequence.  The  Persians  had  in- 
troduced into  their  calendar,  in  the  1 1th  century,  an  intercalation  still  more 
accurate;  they  make  8  bissextiles  only  every  33  years,  reckoning  four  common 
years  together  instead  of  three,  at  the  end  of  this  period,  so  that  in  13'i  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  accu- 
rate as  it  is  possible  for  our  calculations  to  render  it.  The  adoption  bf  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  uncorrected ;  but  better  arguments  at  last  overcame  these 
difficulties,  and  the  new  stile  was  introduced  on  the  14  September  1754, 
"which  would  have  been  called,  according  to  the  old  stile,   the  third. 

Any  tolerable  approximation  of  this  kind,  when  once  generally  established, 
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  judiciously 
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  calculation  to 
determine  on  what  day  the  republican  year  ought  to  begin;  and  perhaps 
these  arguments  have  cooperated  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  j'ears  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  celebration  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. 


ON    IPRAcrlCAh   ASTRONOJir.  541 

If  we  subtract  1  from  the  golden  number,  then  multiply  by  11,  and 
divide  by  30,  the  remainder Avill  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  no'on  on  the  31st  of  December,  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  as- 
tronomical 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  qua- 
drants, 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  estimate,  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 
Avithin  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. 


542  LECTURE    XLV. 

the  precession  of  the  equinoxes,  which  produces  a  slight  change  in  the  places 
of  the  stars,  has  made  it  necessary  to  wait  1  minute  134- 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.) 

The  quadrant  in  most  common  use,  especially  for  nautical  observations,' 
was  first  proposed  by  Newton,  but  improved,  or  perhaps  reinvented,  by 
Hadley.  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  per- 
formed serves  to  determine  the  angle.  The  ray  proceeding  from  one  of  the 
objects  is  made  to  coincide,  after  two  reflections,  with  the  ray  coming  immedi- 
ately from  the  other,  and  since  the  inclination  of  the  reflecting  surfaces  is  then 
half  the  angular  distance  of  the  objects,  this  inclinatoin  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  kcond  fixed  speculum,  placed  a 
right  angles  to  the  moveable  one,  when  in  its  remotest  situation,  which  then 
produces  a  deviation  of  two  right  angles  in  the  appareut  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  spe- 
culum for  it  with  accuracy.  The  reflecting  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  equi- 
noctial point,  allowing  15  degrees  for  each  sidereal  hour.  (Plate  XXXV. 
Fig.  512.) 

In  all  astronomical  observations  it  is  necessary  to  make  proper  corrections, 
according  to  the  rules  of  optics,  for  the  effects  of  atmospherical  refrac- 
tion; and  also,  in  observations  on  the  moon  more  especially,  for  those  of 
parallax,   or   the    difference  of  the    apparent   place  of  the  luminary   with 


ON    PRACTICAL    ASTRONOMr,  545, 

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  seniidia- 
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  decli- 
nation 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 
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  insure  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  as- 
certain the  time  that  elapses  between  the  passages  of  a  given  point  in  the 
heavens  over  its  meridian  and  some  other  meridian  wliich  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  maybe  certain  that  we  are  in  some  part  of  a  meridian  45°  west 
i)i'  that  of  Greenwich.  Had  we  perfect  timekeepers,  we  might  easily  adjust  them 


544  LECTURE    XLV. 

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  sufficiently  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  calcu- 
lation. Sometimes  the  transits  of  Mercury  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  aboutone  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  ease  of  the  sun.  the 
simple  comparison  of  his  calculated  with  his  apparent  altitude  is  insufficient  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  ascertaining  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 
Avith  the  motion  of  Venus  iu  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.) 

Our  countryman  Horrox  was  the  first  that  particularly  attended  to  the  phe- 
nomena of  a  transit  of  Venus  over  the  sun's  disc:  Dr.  Halley,  when  be 


ON"    PnACTICAL   ASTRONOMY.  566 

observed  a  transit  of  Mercury  at  St.  Helena,  thought  that  he  could  ascertain 
the  times  of  immersion  and  emersion  Avithout  an  error  of  a  single  second; 
and  hence  he  concluded,  that  by  means  of  a  transit  of  Venus,  the  sun's  dis- 
tance might  be  determined  within  a  five  hundredth  part.  The  most  advan- 
tageous places  for  the  experiment  being  such  as  diifer  most  in  longitude, 
and  are  most  remote  from  each  other.  Captain  Cook  was  se^nt  by  the  British 
government  to  the  South  Seas,  in  tne  years  I76I  and  1/69,  in  order  to  ob- 
serve the  transits  of  Venus  in  the  island  of  Otaheite.  These  observations 
were  compared  with  those  which  were  made  at  Wardhuys,iu  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  num- 
"ber  of  collateral  observations,  the  sun's  mean  parallax  was  found  to  be  8  se- 
conds and  two  thirds,  or  perhaps  85;  for  it  does  not  appear  that  we  are 
sure  of  having  avoided  even  an  error  of  one  fortieth  part  of  the  whole;  al- 
though Mr.  Laplace's  determination  of  the  sun's  distance,  from  the  lunar  mo- 
tions, agrees  very  well  with  that  which  is  usually  considered  as  the  result  of 
the  observations  of  the  transit  of  Venus. 

The  comparative  densities  of  the  sun,  and  of  such  planets  as  have  satellites, 
may  be  calculated  from  the  periods  and  distances  of  the  bodies  revolving 
round  them;  the  densities  of  the  other  planets  have  sometimes  been  assigned 
from  conjecture  only,  but  of  late  years  the  mathematical  theory  of  the  planet- 
ary 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  re- 
gularly 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  par- 
ticular times;  their  places  being  first  ascertained  from  tables,  or,  in  the  caSe 
of  the  sun,  m.erely  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, 

VOL.    I.  4  a 


^66  LECTURE    XLV. 


yr 


that  its  axis  may  form  the  same  angle  with  its  horizon  as  the  axis  of  the  eartU 
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  shown  by  the  index  of  the  globe;  thus  we  may  find  the  length  of  the 
day  and  night,  and  the  time  and  place  of  rising  and  setting;  and  by  means  of 
a  graduated  circle,  perpendicular  to  tlfS  horizon,  we  may  measure  the  al- 
titude of  the  sun  or  planet  at  any  other  time,  and  also  itsazimuthi  or  th« 
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  horizon,  allowing  for  the  effects  of  re- 
fraction; 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  duration  of 
twilight,  on  any  supposition  that  might  be  formed  respecting  the  depression 
of  the  sun  required  for  producing  total  darkness.  By  means  of  the  celestial 
globe,  the  apparent  motions  of  the  fixed  stars  may  be  represented  in  a  man- 
ner nearly  similar,  proper  attention  being  paid  to  the  situation  of  the  sun  ia 
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  Bodc's  planisphere  comprehends  in  one  view  all  tlie 
stars  that  are  ever  visible  at  Berlin :  he  has  added  to  it  a  moveable  circle,  re- 
presenting the  horizon  of  that  place,  carrying  with  it  the  circles  of  altitude 
and  azimuth,  delineated  on  a  transparent  paper,  which  is  adjusted,  by  gradu- 
ations 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  projected,  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 


OJf    PRACTICAL   ASTRONOMY.  SSj 

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  era- 
ployed,  in  which  the  comparative  periods  of  the  revolutions  have  been  cx^ 
pressed  by  various  combinations  of  wheelwork.  Of  these  instruments  Ar- 
chimedes was  the  original  inventor,  and  Iluygens  revived  them,  with  many 
improvements,  in  modern  times.  The  construction  of  the  large  planetarium, 
which  has  been  made  in  the  house  of  the  Royal  Institution,  was  principally 
directed  by  Mr.  Pearson.  I  suggested  to  him,  that  the  instrument  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  instru- 
ment. 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. 


sns 


LECTURE  XLVI. 


ON    GEOGRAPHV. 


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  dis- 
appearance 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.rig- 
ging  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  frequent  inequalities 
of  the  soird  parts  of  the  earth  usually  cause  the  prospect  to  be  bounded  by 
some  irregular  prominence,  as  a  hill,  a  tree,  or  a  building'  so  that  the 
general  curvature  is  the  less  observable. 


to 


The  surface  of  a  lake  or  sea  must  be  always  perpendicular  to  the  direction 
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  as- 
certain 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  difference  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  circumference  may  be 
determined;    and  on  these  principles  the  earliest  measurements  of  the  earth 


ON    GEOGRAPHT.  S69 

were  conducted.     The  first  of  these,  which  can  be  considered  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  truths  it  was  cal- 
culated by  Newton,  and  ascertained  experimentally  by  the  French  Acade- 
micians, 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  prominent  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 
ecjuator,  than  nearer  the  poles.  If  the  density  of  the  earth  were  uniform 
throughout,  its  ellipticity,  or  the  difterence  of  the  length  of  its  diameters, 
would  be  ^li  of  the  whole;  on  the  other  hand,  if  it  consisted  of  matter  of 
inconsiderable  density,  attracted  by  an  infinite  force  in  the  centre,  the  el- 
lipticity would  be  only  ^^5  ^^^^  whatever  may  be  the  internal  structure  of 
the  earth,  its  form  must  be  between  these  limits,  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  thousand  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  superficial.  Whatever  this  difterence  may  be,  it  has  been  de- 
monstrated by  Clairaut,  that  the  fractious  expressing  the  ellipticity  and  the 
ap|)arent  diniinntion  of  gravity  at  the  equator  must  always  make  together -j-fg-, 
and  it  has  been  found,  by  the  most  accurate  observatioiis  on  the  lengths  of 
])endulums  in  difterent  latitudes,  that  the  force  of  gravity  is  less  powerful  by 
vf^  at  the  equator  than  at  the  pole,  whence  the  ellipticity  is  found  to  be  -j-^-g- 
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  lesa 
liable  to  error  and  irregularity,  than  the  measurement  of  the  lengths  of  de- 
grees in  various  parts,  since  the  accidental  variations  of  curvature  produced 
by  local  diftcrences  of  density,  and  even  by  superficial  elevations,  may  oftea 


o70  LECTURE    XLVl. 

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  Nortli  America, 
and  in  Eugland,  have  all  exhibited  signs  of  similar  irregularities.  There  ap- 
pears also  to  be  some  difference  in  the  length  of  degrees  under  the  same  la- 
titude, and  in  different  longitudes.  We  maj-,  however,  imagine  a  regular 
elliptic  spheroid  to  coincide  very  neariy  with  any  small  portion  of  the  earth's 
surface,  although  its  form  must  be  somevvhat  different  for  different  parts  : 
thus,  for  tiie  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  txs-- 

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  and  the  tropics, 
he  is  vertical  twice  in  the  year,  when  his  declination  is  equal  to  the  latitude 
qf  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  Sep- 
tember. At  the  polar  circles,  the  sun  describes  on  midsummer  day  a  com- 
plete circle,  touching  the  north  or  south  point  of  the  horizon ;  and  in  mid- 
winter 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 


ON    GEOSBAPHT.  571 

describe  a  spiral,  of  which  each  coil  is  nearly  horizontal,  half  of  the  spiral 
being  abo\'e  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  probably  no 
Avhere  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  collec- 
tions of  water,  at  various  heights,  and,  in  a  few  instances,  somewhat  lower 
than  the  general  surface  of  the  main  ocean.  Thus  the  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,-bave  some  slight  resemblance  in  their  forms,  and  that  each  of  them 
is  terminated  to  the  eastward  by  a  collection  of  numerous  islands.  The  large 
cap^s  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  IMadagascar,  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  sixteenth, 
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  2S  to  the  land.  These  proportions  nid.y 
be  ascertained  with  tolerable  accuracy  by  weighing  the  paper  made  for  cover- 


57^2, 


LECTURE    XLVl. 


ino-  a  globe,  first  entire,  and  then  cnt  out  according  to  the  terminations  of 
the  ditterent  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  portions  only  weighed. 

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  Iloangho,  the  River  La- 
plata,  the  Jenisei,  the  Mississippi,  the  Volga,  the  Oby,  the  Amur,  tlie  Oro- 
nooko,  the  Ganges,  the  Euphrates,  the  Danube,  the  Don,  the  Indus,  the 
Dnieper,  and  the  D\yina;  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  calculation,  be 
somewhat  different:  taking  the  length  of  the  Thames  for  unity,  he  estimates 
that  of  the  River  of  Amazons  at  15^,  the  Kian  Kew,  in  China,  1.54:,  the 
Iloangho  134,  the  Nile  12-^,  the  Lena  II4.,  the  Amur  11,  the  Oby  104,  the 
Jenisei  10,  the  Ganges,  its  companion  the  Burrampooter,  the  rive^  of  Ava, 
and  the  Volga,  each  94-,  the  Euphrates  84,  the  Mississippi  8,  the  Danube  7, 
the  Indus  54,   and  the  Rhine  5^. 

We  may  form  a  tolerably  accurate  idea  of  the  levels-of  the  ancient  continent, 
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,  keep-- 
ing  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  ap- 
proach 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  north- 
wards through  Lithuania,  leaving  the  Don  wholly  to  the  right ;  and  the  Volga, 
/to  pass  still  further  north,  between  Petersburg  and  Moscow,  a  little  above  Bjele- 
sero.  We  may  then  go  eastwards  to  the  boundary  of  Asia,  and  thence  northwards 
to  Nova  Zembla.     Hence  we  descend  to  the  west  of  the  Oby,  and  then  to  the 


OJf    GEOGRAPHY.  573 

fast  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  ex- 
tended elevation  of  India,  in  the  neighbourhood  of  the  sources  of  the  Indus: 
and,  lastly,  in  our  way  from  hence  towards  Kanischatka,  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  dif- 
ferent 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  Mace- 
donia; it  is  found  again  beyond  the  Euxine,  under  tlie  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  be- 
tween the  Nile  and  tlie  Red  Sea.  In  the  new  world,  the  neighbourhood  of 
the  western  coast  is  in  general  the  most  elevated ;  in  North  America  the 
Blue  mountains,  or  Stony  mountains,  are  the  most  considerable ;  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  difterent  seas ;  such  are  Swisserland,  Bjelosero 
Tartary,  Little  Tibet,  Nigritia  or  Guinea,  and  Quito.  The  highest  moun- 
tains are  Chimborapao  and  some  others  of  the  Cordeliers  in  Peru,  or  perhaps 
Descabesado  in  Chili,  Mont  Blanc,  and  the  Peak  of  Tenerifte.  Chimborafao 
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  thousandtli  part  of  the  earth's  semi- 

VOL.   I.  4  b 


57*  tECTORE    XLVI. 

diameter,  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  eleva- 
tions in  the  island  Owhyhee.  Ben  Nevis,  in  Scotland,  is  the  loftiest  of  the 
British  hills,  but  its  height  is  consideraljly  less  than  a  mils.  (Plate 
XXXVIII.  Fig.  5iy.) 

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  ge- 
nerally 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  vegetable  re- 
mains, in  an  obscure  form,  together  with  salt,  coals,  and  sulphur.  The  ter- 
tiary, 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  se- 
condary and  tertiary  mountains  are  intersected  by  vallies,  the  opposite  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  inter- 
mixed with  veins  of  metal,  running  in  all  possible  directions,  and  occupying, 
vacuities  which  appear  to  be  of  somewhat  later  date  than  the  original  forma- 
tion of  the  mountains.  The  volcanic  mountains  interrupt  those  of  every 
other  description  without  any  regularity,  as  if  their  origin  were  totally  in- 
dependent of  that  of  all  the  rest. 

The  internal  constitution  of  the  earth  is  little  known  from  actual  observa- 
tion, for  the  deptlis  to  which  we  "have  penetrated  are  comparatively  very  in- 
considerable, the  deepest  mine  scarcely  descending  half  a  mile  perpendicularUv 


/  OV    GEOGRAPHY.  575 

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  44-  to  1,  judging  from  the  probable  density  of  the  internal  substance 
of  the  mountain,  which  he  supposed  to  be  a  solid  rock.  Mr.  Cavendish  haS' 
concluded  more  directly,  from  experiments  on  a  mass  of  lead,  that  the  mean 
density  of  the  earth  is  to  that  of  water  as  54-  to  1.  Mr.  Cavendish's  experi- 
ments, which  were  performed  with  the  apparatus  invented  and  procured  by 
the  late  Mr.  Michell,  appear  to  hare  been  conducted  wi^th  all  f)ossible  ac- 
curacy, 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  calculations  free  from  error,  it  will  only  follow 
that  the  internal  parts  of  Shehallion  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  conjecture  affords  us  a  new  proof,  in  addition  to  many  others,  of 
the  accuracy  and  penetration  of  that  illustrious  philosopher. 


570 


LECTURE  XLVir. 


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  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, 

Tliere  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  become* 
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  284-  lunar  days 
are  nearly  equal  to  S9i  solar  ones. 
4 


ON    THE    TtDES,  ^  577 

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  moou 
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  abso- 
lutely perfect,  to  the  solution  of  every  difficulty  that  might  occur.  A  very  in- 
judicious 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  Avhich  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  gra- 
vitation, 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  distance  of  794-°  froii^ 


578  LECTURE    XLYII. 

the  line  passing  througli  the  attracting  body,  either  in  the  nearer,  or  in  the  re- 
moter hemisphere;  but  to  urge  them  towards  the  centre, although  with  a  smaller 
force,  in  the  remaining  part.  Hence,  in  order  that  there  may  be  an  equi- 
librium, the  depth  of  the  fluid  must  be  greatest  where  its  gravitation,  thu» 
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  immediately 
under  the  moon,  the  lunar  tide  would  remain  stationary,  the  greatest  eleva- 
tion 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  eleva- 
tion 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  rota- 
tion. 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  equili- 
brium. The  force  employed  in  producing  this  accommodation  may  be  esti- 
mated 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  consi- 
dering the  subject,  a  theory  of  the  tides  which  appears  to  be  more  simple  and 
satisfactory  than  any  which  has  yet  been  published:  and  by  comparing  the 
tides  oi'  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  pen- 
dulum itself,  when  they  have  arrived  at  a  state  of  permanence,  will  be  perform- 
ed 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  sliortcf!- 


ox     THE    TIDES,  57!) 

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,  Avhich 
woukl  be  produced  if  the  waters  always  assumed  the  form  of  the  spheroid  of 
equilibrium,  according  to  tlie  depth  of  the  ocean,  and  to  the  breadth  as  well 
as  tlie  depth  of  the  lai<e.  In  the  case  of  a  direct  tide,  the  time  of  the  passage 
of  the  luminary  over  the  meridian  must  coincide  with  that  of  high  w  ater,  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  be, 
and  in  all  cases  they  would  be  greater  than  the  primitive  tides.  But  in  fact  the 
height  of  the  tides  in  the  open  ocean  is  always  far  short  of  that  which  would 
be  produced  in  this  maii|ier;  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,  tlie  depth  of  the  open  sea  must 
be  64-  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 


580  LKCTURE    XLVII. 

deep,  in  Older  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  resist- 
ance ;  but  M'here  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  accele- 
rated ;  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  particular  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  cfl^'ect  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  ISladeiras,  and  the  Azores,  which  constitute  such  a  suc- 
cession as  might  be  expected  to  have  indicated  the  progress  of  the  principal 
tide,  if  it  had  been  such  as  My.  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  ori- 
ginal tide,  which  happens  in  this  widely  extended  ocean,  where  its  depth  is  suffi- 
ciently uniform,  must  take  place,  according  to  the  theory  which  has  been  ad- 
vanced, at  some  time  before  the  sixth  lunar  hour.  It  sends  a  wave  into  the  At- 
lantic, which  is  perhaps  12  or  13  hours  in  its  passage  to  the  coast  of  France,  but 
certainly  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  tjie  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  which  favours  the 


Oy    THE    TIDES.  581 


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;  rliis  part  of 
Africa  being  not  very  remote  from  thc'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  eifects  with  those  of  other 
tides  at  various  parts  of  the  coast  of  Europe. 

Wc  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  5  hours 
after  the  moon's  southing,  and  on  the  coast  of  America,  a  little  more  than 
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,  arid  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  com- 
bined more  or  less  both  with  the  general  southern  tide,  and  with  the  par- 
tial 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  tlie 
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  11th  hours,  apparently  because  they  receive 
them  principally  from  distant  parts  of  the  ocean,  which  are  nearer  to  the 
equator. 

4  c  # 


58f  LECTURE    XLVri. 

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  arc 
perhaps  too  near  the  middle  of  the  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  Almirantes,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  2S  fathoms,  in- 
dependently of  the  magnitude  of  the  resistances  of  various  kinds  to  be  over- 
come, which  require  us  to  suppose  the  depth  from  30  to  40  fathoms.  In 
the  great  river  of  Amazons,  the  eifects  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  contrary  direction^ 
(Plate  XXXVIIL  Fig.  521.) 


OK    THE    TIDES.  583 

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.  Hence  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  de- 
rived 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  lati- 
tude 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  differ- 
ence in  the  tides,  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  magnitude 
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  I'i  parts,  the  point  will 
pass  over  each  of  these  parts  in  a  lunar  hour.  It  sometimes  happens,  how- 
ever, in  confined  situations,  that  the  rise  and  fall  of  the  water  deviates  con- 
siderably from  this  law,  and  the  tide  rises  somewhat  more  rapidly  than  it 
falls;  and  in  rivers,  for  example  in  the  Severn,  the  tide  frequently  advances 


584  -  LECTURE    XLVII. 

suddenly  with  a  head  of  several  feet  in  height.  These  deviations  probably 
depend  on  the  magnitude  of  the  actual  displacement  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  con- 
veniently observed,  by  means  of  a  pipe  descending  to  some  distance  below  the 
surface,  so  as  to  be  beyond  the  reach  of  supe'rficial  agitations,  and  having 
Avithin  it  afloat,  carrying  a  wire,  and  indicating  the  height  of  the  Avater  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  thej' actually  exist,  depend  also  ort 
the  action  of  the  sun,  which  produces  a  serves  of  effects  precisely  similar  ta 
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  whiclt 
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  ojjposition, 
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  produced  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  de- 
termine the  time  of  high  and  law  water,  which,  in  the  spring  and  neap  tides, 
remains  unaltered  by  the  efTcct  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  inter- 
inctliate  times,  the  lunar  high  water  is  more  or  less  accelerated  or  retarded. 
The  progress  of  this  alteration  may  easily  be  traced  by  means  of  a  simple 


ON    THE    TIDES.  585 

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  precisely  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  aj)pears  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  lu- 
minaries 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  ac- 
cordingly.     In  some  ports, from  a  combination  of  circumstances  in  the  chan- 
nel,  by  which  the  tides  reach  them,  or  in  the  seas,   in  which  they  originate, 
the  influence  of  the  sun   and  moon  may  acquire  a  propartion  somewhat  dif- 
ferent from  that  which  naturally  belongs  to  them:    thus  at   Brest,   the  in- 
fluence 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    XXXVIIL 
Fig.  5^22.) 

The  greatest  and  least  tides  do  not  happen  immediately  at  the  tinres  of  the 
new  and  full  moon,  but  at  least  two,  and  commonly  three  tides  after,  evert 
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  mucli 
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 
title  may  be  tju-ee  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^  wilt 
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. 


586  ^  LECTURK  XLVII. 

The  particular  forms  of  the  channels,  through  which  the  tides  arrive  at  dif- 
ferent 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  chan- 
nels, 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  ^0;  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  immediate  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  distinctly  observ- 
able, 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  communicate 

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  coincide, 

and  the  effects  will  be  doubled;    and  the  same  will  liappen  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  ti^e  coincides  with  the  low  water  of  another.     The 

tides  at  the  port  of  Batslia  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  xmequal  tides  which  happen  in 

succession  every  day,  by  combining  with  two  equal  tides  another  tide,  in- 


ox    THE    TIDE3.  557 

dependent  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  greati^r  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  shat  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,  o24.) 

Besides  the  variations  in  the  height  of  the  sea,  which  constitute  the  tides, 
the  attractions  of  the  sun  and  moon  are  also  supposed  to  occasion  a  retardation 
in  its  rotatory  motion,  in  consequence  of  which  it  is  left  a  little  behind  the 
solid  parts  of  the  earth  ;  and  a  current  is  produced,  of  which  the  general 
direction  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  to- 
wards the  Brazils,  and  northwards  into  the  Gulf  stream,  which  ti'avels  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  Pted  Sea  is  found  to  be  about  25  feet  higher  than  tlte  Mediterranean: 
their  direction  may  possibly  have  been  somewhat  changed  in  the  course  of 
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  tlie  weather;    but  their  influence  must  be  very  incousider- 


588  LECTURE    XLVir. 

able,  since  the  addition  of  two  or  three  feet  to  the  height  of  the  atmosphere 
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  -ri-^  •jf  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,  on  account  of  the  actions 
of  his  satellites,  which  must  be  considerably  more  powerful  thau  that  of  the 
mooa. 


589 


LECTURE  XLVIII. 


ON    THE    HISTORY    OF    ASTRONOMY. 


V\' E  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  pecu- 
liarities 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  con- 
clude 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  ob-- 
servations  of  the  obvious  motions  and  eclipses  of  the  sun  and  moon,  the 
rising,  setting,  and  occultations  of  the  principal  stars,  and  the  apparent  mo- 
tions 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 
diflferent  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,  denoting  his  retrograde  motion 
after  the  time  of  the  solstice,    and  the   balance  the  equality   of  day   and 

VOL.   r.  4  p 


jgO  LECTURE    XLVIIT. 

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  precisely  with  the  constellations  of  the 
zodiac  from  which  they  derive  their  names. 

The  most  ancient  observations  of  which  we  are  in  possession,   that  are  suffi- 
ciently accurate  to  be  employed  in  astronomical  calculations,   are  those  made 
at  Babylon  in  the  years  719  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  Chaldeans, 
however,   must  have  made  a  long  series  of  observations  before  they  could 
discover  their  Saros  or  lunar  period   of  65854-  <J^ys,    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  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  36.5  days  each.  The  accurate  corres- 
pondence of  the  faces  of  their  pyramids  with  the  points  of  the  compass  is  con- 
sidered as  a  proof  of  the  precision  of  their  observations:  but  their  greatest 
merit  was  the  discovery  that  Mercury  and  A'^enus  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.  5^5,  62,6.} 

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 
C)nfjrmed  by  an  incontestable  series  of  historical  monuments.  The  regula- 
tion of  the  calendar,  and  the  prediction  of  eclipses,  were  regarded  in  this 
country  as  important  objects,  for  which  a  mathematical  tribunal  was  esta* 
blished  at  a  very  early  period.    But  the  scrupulous  attachment  of  the  Chinese 


OV    THE    HISTORT    OF    ASTRONOMV^  5,91 

to  their  ancient  customs,  extending  itself  even  to  their  astronomy,  has  im- 
peded its  progress,  and  retained  it  in  a  state  of  infancy.  The  Indian  tables 
indicate  a  much  higher  degree  of  perfection  in  tlie  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,  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  philosopher,  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  ty- 
ranny 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  celebrated  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  ascend- 
ing 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  magnitude,  as  deduced  from  eclipses,  must  have  been 
affected  by  a  contrary  error  with  respect  to  the  moon's  place:  and  the  de- 
termination 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  correspond  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  respect- 
ing it.  It  is  singular  that  amidst  the  confusion  of  systems  heaped  up  on  each 
other,  without  aftbrding  the  least  information  to  the  mind,  it  should  never  have 


592  '  LECTUnE    XLVIII. 

occurred  to  men  of  so  great  talents,  that  the  only  way  to  become  accurately  ac- 
quainted with  nature,  is  to  institute  experimental  inquiries  throughout  her  works. 

Thales  of  Miletus,  who  was  born  in  the  year  640  before  Christ,  having 
travelled  and  studied  in  Egypt,  founded,  on  his  return,  the  Ionian  school  of 
philosophy,  in  which  he  taught  the  sphericity  of  the  earth,  and  the  obliquity 
of  the  ecliptic  with  respect  to  the  equator.  He  also  explained  the  true  causes 
of  eclipses,  which  he  was  even  able  to  foretel,  unquestionably  by  means  of 
the  information  that  he  had  obtained  from  the  Egyptian  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,  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  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  astronomy 
is  the  foundation  of  the  school  of  Alexandria,  which  was  the  first  source  of 
accurate  and  continued  observations.  Upon  the  death  of  Alexander,  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  Philadelphus,  continued  and  in- 
creased 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.  The  first  astronomers,  who  were  appointed  to  occupy  this 
building,  Avere  Aristyllus  and  Timocharis;  they  flourished  about  300  years 
before  Christ,  and  observed  with  accuracy  the  places  of  the  principal  stars  of 


ON    THE    HISTORY    OF    ASTRONOMY.  $93 

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  estimation 
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.  Pto- 
lemy, 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. 

Hipparchsu  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  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  equa- 
tion 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 


594  LECTURE    XLVIII. 

astronomical  observations   for  determining  the  latitudes  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,  occasion- 
ed 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  revolution  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  circle.  This  mode  of  approxima- 
tion is  exceedingly  ingenious;  it  is  said  to  have  been  the  invention  of  Apol- 
lonius  of  Perga,  the  mathematician,  and  although  it  sometimes  becomes  com- 
plicated, yet  it  is  very  convenient  for  calculation ;  and  it  may  be  employed 
with  advantage  in  the  representation  of  the  planetary  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  at- 
tributed to  the  earth  a  diurnal  motion  only;  but  the  doctrine  of  the  Pytha- 
goreans appears  to  have  been  wholly  exploded  or  forgotten.  Ptolemy  deter- 
mined the  quantity  of  the  precession  of  the  equinoxes  from  a  comparison  of 
his  own  observations  with  those  of  Hipparchus;  but  he  made  it  sHialler  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 


ON    THE    HISTORY    OF    ASTRONOMT.  59S 

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  tiie  equinoctial  points.  Ptolemy's  principal  work  is 
his  mathematical  system  of  astronomy,  M-hich  was  afterwards  called  the  great 
syntax  or  body  of  astronomy,  and  is  at  present  frequently  quoted  by  the 
Arabic  name  Almagest.  He  also  wrote  a  treatise  on  optics,  in  which  the 
phenomena  of  atmospherical  refraction  are  described,  and  which  is  extant 
in  manuscript  in  the  National  library  at  Paris.  (Plate  XXXVIII.  Fig. 
528.; 

Ptolemy  was  the  last  as  well  as  the  greatest  of  the  Alexandrian  astronomers* 
and  the  science  made  no  further  progress  till  the  time  of  the  xArabians.  The 
first  of  these  was  Almamoun,  was  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  transla- 
tion. 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,  Al- 
bategni  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  liabit  of  em- 
ploying, 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  bissextiles- 
in  33  years,  which  was  afterwards  proposed  by  Dominic  Cassini  as  an  im- 
provement of  the  Gregorian  calendar.  The  most  illustrious  of  this  nation- 
was  Ulugh  IJeigh,  who  observed  in  his  capital  Samarcand,  about  the  year 
1437|  with  very  elaborate  iostrumeuts.     In  the  mean  time  Cocheouking.  had 


S96  LECTURE    XLVIII. 

made  in  China,  some  very  accurate  observations,  which  are  valuable  for  the 
precision  Avith  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,  inquest  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  dili- 
gence 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  the  sun;  and  from 
a  minute  examination  of  these  circumstances  he  calculated  the  relative  dis- 
tances 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 
56  years  of  retirement  and  meditation,  he  completed  his  work  on.the  celes- 
tial 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  obser- 
vations. After  the  death  of  his  patron,  his  progress  was  impeded,  and  he 
sought  an  establishment  at  Prague,  under  the  emperor  Rudolph.     Here  he 


ON    THE    HISTORY    OF   ASTRONOMY.  5^7 

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  misinterpre- 
tation of  the  scriptures,  he  imagined  a  new  theory,  which,  although  mechani- 
cally 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 
sj'stem;  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  standstill.  But  in  the  Copernican 
system,  there  was  an  evident  regularity  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  tlie  earth,  this  analogy  was  entirely  lost.  Tycho 
Brahe  was  the  discoverer  of  the  variation  and  of  the  annual  equation  of  the 
moon,  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  per- 
turbations 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  appointments  at 
Prague,  and  enjoyed  the  title  of  Imperial  Mathematician.  Adopting  the 
Copernican  system,  which  was  then  becoming  popular,  he  proceeded  to 
examine  the  distances  of  the  celestial  bodies  from  each  other  at  various  time?}; 
and  after  many  fruitless  attempts  to  reconcile  the  places  of  the  planets  with 
the  supposition  of  revolutions  in  eccentric  circles,  at  last  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,  tliat  the  squares  of  the  times  of  revolution 
are  always  proportional  to  the  cubes  of  the  mean  distances  from  the  sun. 

VOL.    I.  4  E 


59$  tSXTUftE    XLVIII. 

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  Coperaican 
system,  was  born  at  Pisa  in  J 564,  and  lived  to  the  age  of  7«,  fuli  of  that 
enthusiasm  which  made  him  despise  the  threats  of  the  Inquisition,  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  observatiions  of 
Hevelius  deserve  also  to  be  mentioned  with  commendation.  The  discoveries 
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,  ia 
tlie  preface  of  his  Astronomy,  has  endeavoured  to  prove  that  Pythagoras  must 
have  been  acquainted  even  with  the  law  of  the  decrease  of  gravitation;  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 
chords, which  we  have  no  reason  to  suppose  that  he  even  completely  understood : 
and  this  merely  because  he  fancifully  imagined,  that  there  was  a  correspon- 
dence between  the  planets  and  the  strings  of  a  lyre.  But  the  nature  of  gra- 
vitation 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  tkscent  of  heavy  bodies  the  motion 


©N    THE   BTSTORT    OF   ASTRONOMY.  599 

of  ''  general  congregation",  and  attributes  the  tiJcs  to  the  attraction  of  the 
moon.  Kepler  mentions  also  the  perfect  reciprocality  of  the  action  of  gravita- 
tion, 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  pro- 
jectile motion  with  a  centripetal  force  ;  he  expresses  his  sentiments  on  thd 
subject  very  clearly  in  his  Attempt  to  prove  the  motion  of  the  earth,  pub- 
lished in  J  674,  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  Cott- 
fined  his  genius  to  speculations  purely  mathematical;  had  he  beeii  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  I676,  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  respect- 
ing the  periods  of  the  different  planets,  some  time  before  1(571,  as  he  asserts  to 
Dr.  Halley,  and,  to  the  best  of  his  recollection,  about  1668,  although  in  his 
Principiahe  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  Principia, 
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  gra- 
vity: 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  ? 


600  LECTURE    XLVIII. 

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  Ave  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.     Tliis  he  concluded   by  supposing  them  to  move 
in  perfect  circles  concentrical  to  the  sun,  from  which  the  orbits  of  the  great- 

•  est  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  geographers  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  about  69^  of  our  miles,  his  computation  did  not 
answer  expectation;  whence  he  concluded  tliat  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  I'ound  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,  iu  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 
tarth,  in  the  manner  our  author  had  formerly  conjectured.  Upon  this  prin- 
ciple he  found  the  line  described  by  a  falling  body  to  be  an  ellipsis,  the  centre 


ON    THE    HISTORY    OF    ASTRONOMY.  "  601 

of  the  earth  being  one  focus.  And  tlie  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  mentioned,  in  the  space  of 
one  year  and  a  half." 

The  astronomers  of  Great  Britain  have  not  been  less  diligent  in  the  practi- 
cal, than  successful  in  the  theoretical  part  of  the  science.  The  foundation  of 
the  observatory  at  Greenwich  was  laid  in  1675,  some  years  before  the  com- 
pletion 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  determin- 
ing the  longitude  of  a  ship  at  sea;  and  the  states  of  Holland  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  proposq.ls.  Mr.  Flamsteed  was  con- 
sulted by  the  commissioners,  and  was  added  to  their  number:  he  showed  the 
disadvantages  of  the  method  proposed  by  I\Ir.  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  determine  the  longitudes  of  places  with  suiScient  ac- 
curacy by  lunar  observations.  The  king,  being  informed  of  Flamsteed 's  repre« 


6&S  ttcfttRt  «inii. 

scntations,  is  said  to  have  replkd  with  earnestness,  that  he  "  ftiust  have  the 
places  of  the  stars  anew  observed,  examined,  and  corrected,  for  the  use  of  his  sea- 
men"; 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  01)0  for  a  determina- 
tion 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  Longitmle  for  the  examination  of  the  methods  which  might  be  proposed. 
Under  this  act  several  rewards  were  assigned,  and  in  ]  77^^,  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  1  degree, 
and  cflOOOO  if  within  30  miles  ;  and  a  reward  of  .=£'5000  to  the  author  of  any 
lunar  tables,  which  should  be  found  within  15  seeonds  of  the  truth;  allowing 
the  Board  also  the  power  of  granting  smaller  sums  at  their  discretion.  Time- 
keepers are  at  present  very  commonly  employed  in  the  British  navy,  atid  some 
of  them  have  been  capable  of  determining  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  mo-re  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,  Dol- 
lond,  Harrison,  and  Ramsden  have  long  been  celebrated  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 


ON  THX  HMTORT    OF    ASTnONOMT.  €03 

their  share  of  the  labour.     The  observations  of  the  transit  of  Venus  were 
twice  made  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  mounfeiins,  which  -wete  instituted  jifter  their  return.     In 
this  country  also.  Dr.  Herschel,  besides  many  other  important  additions  to 
our  astronomical    knowledge,   has   discovered   a  primary  planet,  and  eight 
secondary  ones,  unknown  before.     The  astronomers  of  Sicily  and  Germany 
h&ve,   however,   the  honaur  of  the  first  discovery  of  tlie  three  humbler  mem- 
bers of  the  solar  system  which  have  been  last  introduced  to  our  acquaintance, 
Ceres  by  Piazzi,   Pallas  by  Gibers,   and   Juno  by   Harding:  and  the  mathe- 
maticians of  France  have  excelled  all  their  predecessors  in  the  elaborate  and 
refined  application  of  the  theory  of  gravitation,  to  the  investigation  of  the 
Djost  minute  and  intricate  details  of  the  celestial  motions. 


604 


ON    THE   HISTORY    OF   ASTRONOMT. 


CHRONOLOGY    OF    ASTRONOMERS. 


HERMES  1450.  B.  C.         CHIRON     050.         BABYLONIAN  OBSERVATIONS   719. 

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R   A   M   S   D   E   N 

605 


LECTURE  XLIX. 


ON    THE    ESSENTIAL    PROPERTIES    OF    MATTER. 

JL.UE  objects,  which  have  lately  occcupied  6ur  inquiries,  are  the  most 
sublime  and  magnificent  tliat  nature  any  where  exhibits  to  us,  and  the  con- 
templation of  them  naturally  excites,  even  in  an  uncultivated  mind,  an 
admiration  of  their  dignity  and  grandeur.  But  all  magnitude  is  relativCj 
and  if  we  examine  Avith  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  aftbrd,  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  luminaries,  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  soundi  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 

VOL.    I.  4    J" 


606  ^  LECTURE    XI.IX. 

thickness,  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  fonn  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  supposes  the  subject  of  our  definition 
already  known;  besides  that  tiie  property  of  attraction  may  also  possibly 
belong  to  substances  not  simply  material ;  for  the  electrical  fluid,  if  such  a 
fluid  exists,  is  probably  attracted  by  matter,  and  yet  it  seems  to  be  different 
in  most  respects  from  any  modification  of  common  matter.  A  similar  diffi- 
culty would  occur  if  we  attempted  to  define  matter  by  its  impenetrability  or 
mutual  repulsion,  or  if  we  considered  every  thing  as  material  that  is  capable 
of  aftecting  the  senses.  We  must,  therefore,  take  it  for  granted  that  matter 
is  known  without  a  definition,  and  we  may  describe  it  as  a  substance  occupy- 
ing 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  general  laws,  as 
the  more  mathematical  doctrines  of  space  and  motion  ;  and  since  our  know- 
ledge 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  doctrine  of  matter  as  apart  of 
the  subject  of  mechanics  ;  although,  in  treating  of  the  streugth  of  materials, 
as  subservient  to  practical  mechanics,  it  was  necessary  to  consider  the  effit^cts 
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 

'2 


ON    THE    ESSENTIAL    PROPERTIES    OF    MATTER.  60/ 

supposing  a  previous  knowledge  of  many  other  departments  of  natural  phi- 
losophy. 

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  separate 
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  hav^e  imagined  that  the  minute  particles  which 
they  suppose  to  constitute  light,  may  penetrate  the  ultimate  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  6f  matter  is  great  beyond  the  power  of  imagination,  bat 
wc  have  no  reason  for  asserting  that  it  is  infinite;  for  the  demonstrations, 
which  have  sometimes  been  adduced  in  favour  of  this  opinion,  are  obviously 
applicable  to  space  only.  The  infinite  divisibility  of  space  seems  to  be  essen- 
tial to  the  conception  that  we  have  of  its  natur^;  and  it  may  be  strictly  de- 
monstrated, that  it  is  mathematically  possible,  to  draw  an  infinite  number  of 
circles  between  any  given  circle  and  its  tangent,  none  of  which  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  meridian, for  example,  sailing 
north  eastwards,  would  continue  perpetually  to  approach  the  pole  without 
ever  completely  reaching  it.  But  when  Ave  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.  Newton  observes,  that  it  is  doubtful 
whether  any  human  means  may  be  sufficient  to  separate  the  particles  of  mat- 
ter beyond  a  certain  limit;  and  it  is  not  impossible  that  there  may  be  some. 


608  LECTURE    XLIX. 

constitution  of  atoms,  or  single  corpuscles,  on  which  tbeir  properties,  as 
matter,  depend,  and  which  would  be  destroyed  if  the  units  were  further 
divided;  but  it  appears  to  be  niOre  probable  that  there  are  no  such  atoms; 
and  even  if  there  are,  it  is  ahnost  certain  that  matter  is  never  thus  annilii- 
lated  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 vo'oo-  of  an  inch  in  diameter;  by  the  assistance  of  a  microscope,  we  may 
perhaps  distinguish  a  body  one  hundredth  part  as  large,  or^-^^'-o-^-o  of  aninch 
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 -^-^^ 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.  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  remarkable,  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  sinlplc  as  they  deviate  more  from  the  form  of  quadrupeds, 
and  from  that  of  the  human  sjjecies ;  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  amofig  the  microscopic  insects  in  par- 
ticular, 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  ap- 
pears 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 
III  general,  were  suificieutly  established,  it  would  afford  us  a  limit  to  the  dl- 


ON    Tin    ESSENTIAL    PROPERTIES    OT    MATTER.  609 

visibility  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  -ro-s-'o^-s-  of  an  inch.  But  we  have  positive  evi- 
dence 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  milliontli  of  an  inch,  or  one  sixtieth  part  of  the  limit  deduced 
from  the  supposition  of  Newton ;  and  it  is  tlierefore  scarcely  possible  that  the 
colours  of  such  substances  can  precisely  resemble  those  of  thin  plates,  although 
they  may  perhaps  still  be  in  some  measure  analogous  to  them. 

Impenetrability  is  usually  attributed  to  matter,  from  the  common  observa- 
tion 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  in- 
verted 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  mercury  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  di- 
minution 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  thickness  may  be,  as 
if  a  vacuum  only  intervened.  It  may,  however,  be  inquired  if  the  gold  or 
the  glass  has  riot  certain  passages  or  pores,  through  which  the  influence  may 
be  transmitted  :  and  it  may  be  shown,  in  many  instances,  that  substances, ap- 
parently 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  foxce :  and,  how- 
ever great  we  may  suppose  the  proportion  of  the  pores  to  the  solid  matter,  it 


I 
did  tECtURE   XLfX.  *  -  . 

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  continuous;  and  there  may  possibly  be  other  substances  in  na- 
ture that  contain  in  a  given  space  'iOO  thousand  times  as  many  atoms  as  pla- 
tina; 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  arc 
fully  acquainted,  and  the  earth  is  only  one  fourth  as  dense  as  if  it  were  com- 
posed entirely  of  platina ;  so  that  we  have  no  reason  to  believe  that  there 
exists  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  any 
thing  in  the  unprejudiced  study  of  physical  philosophy  that  can  induce  us  to 
doubt  the  existence  of  immaterial  substances;  on  the  contrary  we  see  ana- 
logies that  lead  us  almost  directly  to  such  an  opinion.  The  electrical  fluid 
is  supposed  to  be  essentially  different  from  common  matter;  the  general  me- 
dium of  light  and  heat,  according  to  some,  or  the  principle  of  caloric,  ac- 
cording to  others,  is  equally  distinct  from  it.  We  see  forms  of  matter  dif- 
fering in  subtility  and  mobility,  under  the  names  of  solids,  liquids,  and 
gases;  above  these  are  the  semimal:erial  existences  which  produce  the  pheno- 
mena of  electricity  and  magnetism,  and  either  caloric  or  a  universal  ether; 
higher  still  perhaps  are  the  causes  af  gravitation,  and  the  immediate  agents 
in  attractions  of  all  kinds,  which  exhibit  some  phenomena  apparently  still 
more  remote  from  all  that  is  compatible  with  material  bodies ;  and  of  these 
diiferent  orders  of  beings,  the  more  refined  and  immaterial  appear  to  pervade 
freely  the  grosser.  It  seems  therefore  natiKal  to  believe  that  the  analogy 
may  be  continued  still  further,  until  it  rises  into  existences  absolutely  im- 
material 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  sup- 
pose that  even  the  presence  of  matter,  in  a  given  spot,*  necessarily  excludes 
these  existences  from  it.  Those  who  maintain  tlmt  nature  always  teems  with 


ON    THE    ESSENTIAL    PROPERTIES    OF    MATTER.  6ll 

life,  wherever  living  beings  can  be  placed,  may  therefore  speculate  with  free- 
dom on  the  possibility  of  independent  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  impene- 
trability of  matter  inthis  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  na- 
ture, those  of  the  gas  cannot  be  in  perfect  contact;  and  when  water  is  con- 
tracted by  the  effect  of  cold,  or  when  two  flukls  have  their  joint  bulk  di- 
minished by  mixture,  as  in  the  case  of  alcohol,  or  sulfuric  aciti,  and  water, 
the  particles  cannot  have  been  in  absolute  contact  before,  although  they 
would  have  resisted  with  great  force  any  attempt  to  compress  them.  JNIetals 
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*  Th^  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  himself,  that  when  two  plates  of  glass  are  within 
about  this  distance  of  each  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  th^;  contact  is  ever  perfect,  other- 
wise 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  obvioua  that  in  all  common  cases  of  the  contact  of  two  distinct 
bodies,  it  n)ust  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  inde- 
pendent of  the  presence  of  air;  but  under  water,  it  disappears.. 


612  tECTUBE   XLIX. 

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  pro- 
ducing 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  conse(iuently  that  matter  is  not  abso- 
lutely impenetrable;  such  a  supposition  appears  however  to  lead  to  the  ne- 
cessity of  believing  that  the  particles  of  matter  must  sometimes  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  d^mpression,  increases  nearly  in  proportion  to  the 
degree  of  compression,  or  to  the  decrease  of  the  distances  between  the  part- 
icles. 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  di- 
minished, the  effect  of  a  double  change  of  dimensions  would  ahvaj's  be 
nearly  a  double  chaage  of  the  repulsive  force;  that  is,  if  an  elastic  substance 
were  compressed  one  thousandth  part  of  its  bulk,  it  would  in  either  case  re- 
sist 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  Avith  the  increase  of  distance, 
they  can  never  remain  at  rest  without  the  operation  of  some  external  pres- 
sure, 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  compress- 
ing force,  whence  it  may  be  demonstrated,  that  the  primary  repulsive  force 
of  the  particles  must  increase  in  the  same  proportion  as  the  distance  de- 
-  creases.  It  follows  also  that  this  force  can  only  be  exerted  between  such 
particles  as  are  cither  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 
of  half  a  pint;  which  could  not  be,  if  the  particles  exercised  a  mutual  re- 
pulsion at  all  possible  distances. 


ON    THE    ESSENTIAL    PROPERTIES    OF    MATTER.  6l$ 

Mr.  Dalton  has  proposed  a  singular  theory  respecting  the  constitution  artd 
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  connecting  some  facts 
together,  or  in  leading  to  some  other  less  improbable  suppositions;  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  ffortion  of  common  air  with 
which  it  is  in  contact;  nor  is  there  any  circumstance,  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  m  solids,  this  repulsive  force  appears  at  first  sight  to  be  want- 
ing; 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,  actino- 
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.  Thusj  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. 

VOL.    I.  4g 


6*14  LECTURE    XLIX. 

xinertia  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. 

Another  universal  property  of  matter  is   reciprocal  gravitation,  of  which 
the  force  is  directly  in  the  joint  proportion  of  the  quantities  of  matter  attract- 
ing 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  substances,  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  rario  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  propor- 
tional 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  principles; 
and  if  it  were  possible  to  refer  either  all  attraction  to  a  modification  of  re- 


OK    THE    ESSENTIAL    PROPERTIES    OF    MATTER.  6l5 

pulsion,  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  gravitat  ion. 
only.  We  have,  however,  at  present,  little  prospect  of  such  a  simplifij 
tion. 


It  has  been  of  late  very  customary  to  consider  all  the  phenomena  of  nature  lp^^,,  '' 
as  derived  from  the  motions  of  the  co  rpuscles  of  matter,  agitated  by  forces 
varying  according  to  certain  intricate  laws,  which  are  supposed  to  be  pri- 
mary qualities,  and  for  which  it  is  a  kind  of  sacrilege  to  attempt  to  assign 
any  ulterior  cause.  This  theory  was  chiefly  introduced  by  Boscovich,  and  it  has 
prevailed  very  widely  among  algebraical  philcsoj.hers,  who  have  been  in  the 
habit  of  deducing  all  their  quantities  from  each  other  by  mathematical  rela- 
tions, making,  for  example,  the  force  a  certain  function  or  power  of  the  dis. 
tance,  and  then  imagining  that  its  origin  is  sufficiently  explained;  and  when 
a  geometrician  has  translated  this  language  into  his  own,  and  converted  th^ 
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  pro- 
cedure of  nature.  Such  methods  may  often  be  of  temporary  advantage,  as  long 
as  we  are  contented  to  consider  them  as  approximations,  or  as  classifica- 
tions of  phenomena  only;  but  the  grand  scheme  of  the  universe  must  surely* 
amidst  all  the  stupendous  diversity  of  parts,  preserve  a  more  dignified  sim- 
plicity of  plan  and  of  principles,  than  is  compatible  with  these  complicated 
Suppositious. 

"  To  show",  says  Newton,  in  the  preface  to  the  second  edition  of 
his  Optics,  "  that  1  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  experiments."  In  the  query  here  mentioned,  he  pro- 
ceeds 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  arguments,  deduced  as  well  from  the  phe- 
nomena of  light  and  heat,  as  from  the  analogy  of  the  electrical  and  mag- 
netic 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. 


6\6  ~  LECTUIiE  XLIX. 

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  constituted, 
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  tlie  appearance  of  an  attraction  vary- 
ing like  that  of  gravitation.  Such  an  ethereal  medium  would  therefore  have 
the  advantage  of  simplicity,  in  the  original  law  of  its  action,  since  the  re- 
pulsive force  which  is  known  to  belong  to  all  matter,  would  be  sufficient, 
when  thus  modified,   to  account  for  the  principal  phenomena  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  modifi- 
cations 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,  there- 
fore, be  no  occasion  to  apprehend  any  difficulty  from  a  retardation  of  the 
celestial  motions  ;  the  ultimate  impenetrable  particles  of  matter  being  perhaps 
scattered  a?  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  con- 
tinuous 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  remembered  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  Avhich  that  planet  is 
the  centre;  and  we  may  then  deduce  the  force  of  gravitation  from  a  medium 
of  no  very  enormous  elasticity. 

We  shall  hereafter  find  that  a  similar  (pombination  of  a  simple  pressure  with 
a  variable  repulsion  is  also  observable  in  the  force  of  cohesion ;  and  suppos- 
ing two  particles  of  matter,  floating  in  such  an  elastic  medium,  capable  of  pro- 
ducing 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. 


Ojr   THE     ESSENTIAL    PROPERTIES    OF    MATTER.  61/ 

however,  directly  opposite  to  that  which  assigns  to  the  elastic  medium  the 
power  of  passing  freely  through  all  the  interstices  of  the  ultimate  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  considered  merely  as  specula- 
tive amusements,  which  are  of  no  further  utility  than  as  they  make  ovir  views- 
more  general,  and  assist  our  experimental  investigations. 


618 


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  experiments.  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. 

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  hghter  than  this,  but  they  appear  to  be  extremely  porous;  and  perhaps 
the  solid  substances  of  some  of  the  celestial  bodies  may  also   be  a  Httle  more 
rare.     It  frequently  happens,  that  the  compression  of  an  elastic  fluid  alone  is 
suflicient  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,   pro- 
vided 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,  not- 
withstanding 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 


OV    COHESION.  '  619 

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  supposition  agrees  also  with  the  eicperiments  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  l)e  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  heat- 
ing it,  that  the  repulsive  force  of  the  particles  of  bodies  at  very  small  dis- 
tances is  even  diminished  by  heat,  unless  the  force  be  again  supposed  to 
decrease  much  more  rapidly  than  the  distance  diminishes:  thus  the  diminu- 
tion 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 
probably  be  somewhat  diminished,  although  less  tlian  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  tem- 
perature 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 
direction:  thus,  two  pieces  of  glass  require  to  be  brought  together  with  con- 
siderable 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  sufhciently  detached  from  other  subr- 


620  recTURE  l. 

stances,  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  consti- 
tutes fluidity.  The  apparent  weakness  of  the  cohesion  of  liquids  is  entirely 
owing  to  tliis  mobility,  since  their  form  may  be  clianged  in  any  degree  with- 
out 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 
Avill  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  prin- 
ciple 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  withstand 


ON    COHESION.  ^21 

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  perhaps  impracticable. 
A  drop  descending  in  a  vacuum  would  be  perfectly  spherical;  and  if  its  mag- 
nitude were  inconsiderable,  it  would  be  of  the  same  form  when  descending 
through  the  air;  a  small  bubble  rising  in  a  hquid  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  con- 
tractile 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  aflfected  by  the  action  of 
other  liquids,  and  of  solids  of  different  descriptions.  Supposing  the  horizontal  sur- 
face 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  at- 
tractions;  for  the  particles  situated  exactly  at  the  junction  of  the  surfaces  may  be 
considered  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  itmaybe  shown  that  the  combination  of  thesethree  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  per- 
pendicular to  it,  must  be  more  elevated  at  the  side  of  the  vessel  than  else- 

VOL.    I.  4  H 


62f  lECTURE    L. 

where,  and  therefore  concave;  consequently  the  fluid,, mu,st  ascend  until, a[^ 
arrives  at  a  position  capabb  v4  aftording  an  equilibrium  i,u  this  manner:  if^ 
on  the  contrary,  the  attractu-e  power  of  the  solid  be  wealter,  the- liquid  will 
descend,  and  its  surface  will  be  convex.     (Plate;XX^IX.  Fig.  S32.) 

■  if .  -■'■. 
It  may  also  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 
in  other  cases  the  angle  of  contact  will  be  greater  in  proportion  as  the  solid 
is  less  attractive.  These  conclusions  are  obtained  by  comparing  the  jconunon 
surface  of  the  liquid  and  solid  with  the  surface  of  a  single  liquid,  of  which 
the  attractive  power  is  equal  only  to  the  difference  of  th^,  respective  powers  of 
the  substances  concerned;  and  the  comparison  is  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  equi- 
valent to  17  grains,  which  is  the  weight  of  -^-^  of  a  cubic,  inch  of.  mer- 
cury. 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  containing  it,  the  fluid  will  be  elevated  around  it  to  such  a 
height,  that  24:  or  17  grains,  for  each  inch  of  the  circumference  of  the  solid,, 
will  retnain  above  the  general  level  of  the  reservoir,  the  surface  assuming 
nearly  the  same  form  as  a  very  long  and  slender  elastic  rod,  fixed  horizontally 
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  water,  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  contact  may 
support  its  proper  weight :  thus,  if  the  distance  were  one  fiftieth  of  an  inch, 


O.N   <:OHESI0N-.  6io 

the  elevatioi^  woukl  he  a  whole  inch;  and  if  the  distance  were  smaller  than 
this,  ,tl>e.  eleMatioQ  would  he  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  S'upportcd  by  the  cohesion  of  the  water  in  a  tube  may  be  de- 
termin-e<l.,in  a  similar  manner,  from  the  extent  of  the  circumference ;  the  height 
being  an  inch  in  a,  tul>e,  one  twenty  fifth  of  an  inch  in  diameter,  or  as  much 
greater  as  the  diameter  of  the  tube  is  smaller:  and  iii  a  tube  wetted  with 
mercmy  the  height  would  be  half  as  ;great.  It  is  obvious  that  if  the  Ipwer 
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  isthe  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  misjcury  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  their  distance 
is  ..j4t»  and  in  a  tube,  when  its  diameter  is-g^  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  overpower  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 


624  LECTURE  X. 

'^^  raised  from  water  will  elevate  it  to  the  height  of  one  fifth  of  an  inch,  and 
will  require  a  force  of  504-  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.  5S9,  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  considerable,  its  height 
must  always  be  less  than  that  at  which  the  liquid  would  separate  from  a  hori- 
zontal 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  ^^  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  suffi- 
cient 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  Iwo 
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 


ON    COHESION.  '  625 

force  of  a  similar  nature,  the  pressure  of  the  atmosphere  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  atmo- 
sphere 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  advantage,  like  a  tube 
of  smaller  diameter,  and  will  tend  to  draw  the  drop  towards  it;  and  the  ap- 
parent attraction  towards  the  line  of  contact  of  the  glasses  will  increase  in 
proportion  as  the  square  of  the  distance  decreases.  This  result  was  experi- 
mentally observed  almost  a  century  ago,  but  it  has  been  usually  explained 
on  mistaken  grounds.     CPlate  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  airy  want  of 
chemical  affinity,  between  the  substances  concerned,  diminishes  their  cohe- 
sive power;  water  readily  adheres  to  tallow  when  solid,  and  probably  essen- 
tial 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  some- 
times remain  for  a  few  seconds  beyond  it. 

A  sponge  affords  us  a  familiar  instance  of  the  application  of  capillary  at- 


#25  ]l:cctu!RE  t,. 

traction  to  usefiU  puifroses:  it  is  well  known,  that  in  order  to  its  speetlj. 
operatian,  it  Tequires  to  be  previously  moistened,  by  the  .assistauce  of  a  little 
pressure,  otherwirse  it  exhibits  the  same  appearance  of  repulsion  that  is  ob- 
servable in  many  other  cases  where  the  contact  is  imperfect.  The  absorp- 
tion of  moisture  hy  sugar  depends  on  the  same  principle,  and  .here  the  tuibes 
are  so  minute,  that  the  height  of  ascent  appears  to  be  almost  unlimited. 

The  magiritude  of  the  cohesion  between  flnids  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 
l)arometer,  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  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 
both  these  cases  it  is  obvious  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  be  exerted  by  solid  substances  on  other 
solids,  either  of  the  same  kind,  or  of  diiferent  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  remaining 
attached  to  iron  or  steel,  with  which  they  have  been  made  to  cohei'e  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 


ON    COHESION.  627 

que  mass  ;  the  unlou,  however,  appears  to  be  nearly  of  the  same  kind  as  the 
camniou  cohesion  of  aggregation ;  and  if  the  lead  were  softened  into  an 
amalgam  by  the  addition  of  aiercury,  the  cohesion  of  the  two  masses  would 
liecome  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  eacli  pthex  as  to  touch 
throughout.  The  interposition  of  a  fluid  usually  increases  the  apparent  at- 
traction of  such  substances,  but  this  circumstance  has  already  been  explained 
from  the  eifect  of  the  capillary  contraction  of  its  surface;  and  when  the 
substances  are  wholly  immersed  in  a  fluid,  the  cohesion  is  little  if  at  all  in- 
creased. 

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  ajjproach  directly, 
to  each   other,   or  be  withdrawn  further  from  each    other,    and  the  resist- 
ance is  nearly  the  same,as  if  the  same  substancc,in  a  fluid  state,  were  inclosed 
in  an  unalterable  vessel,  and  forcibly  compressed  or  dilated,-    Thus  the  resist- 
ance of  ice  to   extension  or  compression  is  found  by  experiment  to  diifer 
very,  little  from  that  of  water  contained  in  a  vessel ;  and  the  same  effect  may 
be  produced  e\'en  when  the  solidity  is  not  the  most  perfect  which  the  sub- 
stance 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  iiingnitude  of  the  lateral  adhesion  is  so  much  limited  as  to  allow  a  greater 
facility  of  extension  or  compression,  and  it  may  yet  retain  a  pow  er  of  restor- 
ing the  bodies  to  their  original  form  by  its  reaction.     This  force  may  even  be 
the  pitncipal  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  greate*" 


628  LECTURE    L. 

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:  i^'is  certain  that 
almost  all  bodies  are  disposed,  in  becoming  solid,  to^sume  the  form  of 
crystals,  which  evidently  indicates  the  existence  of  pitch  an  arrangement ; 
and  all  the  hardest  bodies  in  nature  are  of  a  crys^fline  form.  It  appeaffe, 
therefore,  consistent  both  with  reason  and  with  Experience  to  supposS-ttfkf  k 
crystallization  more  or  less  perfect  is  the  universal  cause  of  soli{fftj|^,j„ 
may  imagine  that  when  the  particles  of  matter  ai^disposed  without  am 
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  rankat  once;  and  hence  they  may  be  enabled  to  coope- 
rate 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  particles  which  must  be  dis- 
placed by  a  cliange  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  follow?  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  leduce  the  force  of  cohe- 
sion to  one  halfjand  extend  the  substance  to  twice  its  dimensions.     But,  if,  as 


OV    COHESlO'V.  '  ^2^ 

there  i*,softie  reason  to  suppose,  the  mutual  repulsion  of  the  particles  of 
solids  varies  a  little  more  vapidly  than  their  distance,  the  modulus  of  elas- 
ticity will  be  a  little  greater  than  the  true  measure  of  the  whole  cohesive  and 
repulsive  force:  this  difference  will  not,  however,  affect  the  truth  of  our 
calculations  respecting  the  properties  of  elastic  bodies,  founded  on  the  mag- 
nitude 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  fonnerly  called  detrusion,  the  primitive  elasticity  and  rigid- 
ity 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  in\ersely  as  its  length;  for  the  same  force  will  com- 
press 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  com- 
pressed, 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  stiffness,  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;  sometimes, 
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  considerable  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  gol<[  and 
of  the  gilding  of  silver  wire  has  already  been  mentioned;  and  it  is  said  that 

VOL.    I.  4  J 


630  LECTURE    L. 

a  single  grain  of  gold  has  been  drawn  into  a  wire  500  yai'ds  in  length,  and 
consequently  little  more  than-j-^Wof  an  inch  in  diameter.  The  ductility 
or  tenacity  of  a  spider's  web  is  of  a  different  kind,  it  is  particularly  shown 
by  its  capability  of  being  twisted,  almost  without  limit,  and  of  accommodat- 
ing itself  to  its  new  position  without  any  effort  to  untwist. 

With  respect  to  the  ultimate  agent  by  which  the  effects  of  cohesion  arc 
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,  Avhich  are 
unquestionably  produced  by  the  pressure  of  the  atmosphere,  that  one  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  materially 
concerned.  The  well  known  experiment,  of  the  two  exhausted  hemispheres 
of  Magdeburg,  affords  a  still  more  striking  instance  of  apparent  cohesion 
derived  from  atmospherical  pressure;  and  if  wq  place  betweea  them  ift. 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  hemis|»heres  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  knowledge  of  every  thing 
which  relates  to  the  intimate  constitution  of  matter,  partly  from  the  in- 
tricacy 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. 


631 


LECTURE  LL 

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  per- 
suaded that  what  we  call  heat  is,  in  its  intimate  nature,  rather  a  mecha- 
nical 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  per- 
manent: 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 
pecvdiar  sensation  which  bears  its  name,  and  of  which  the  diminution  produces 
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 
posiilve  cold.  Both  these  ideas  are  simple,  and  each  of  them  might  be  de- 
rived either  from  an  increase  or  from  a  diminution  of  a  positive  quality:  bdt 
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  expe- 
rience 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  pro- 
duced in  those  bodies  to  which  heat  is  attached  in  an  increased  quantity,  and 
the  contraction  of  those  from  which  it  is  subtracted. 


632  LECTURE   LI. 

The  simplest  modes  of  exciting  heat  appear  to  be.  the  compression  of  elas- 
tic 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  influence  of  the  solar  rays, 
which  are  probably  emitted  in  consequence  of  the  chemical  processes  that 
continually  take  place  at  the  surface  of  the  sun.  '«-    :!.If  J' 

The  effects  of  the  condensation  and  rarefaction  of  elastic  fluids  are  shown 
by  the  cendenser  and  the  air  pump;  Avhcn  an  exhaustion  is  made  with  rapid- 
ity, 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  va- 
cuum, the  sudden  condensation  of  the  rarefied  air  raises  the  mercury:  and  a 
similar  elevation  of  temperature  is  produced  by  the  operation  of  the  con- 
denser. Much  of  this  heat  is  soon  dissipated,  but  by  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  Fah- 
renheit; 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 
calculation,  is  wholly  derived  from  the  heat  and  cold  produced  by  condensa- 
tion and  expansion,  that  a  condensation  amounting  to  ^rs-  ^f  fhe  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 
sometimes  so  much  heated  as  actually  to  set  on  fire  a  small  portion  of  tow, 
placed  near  the  end  of  the  barrel. 

The  production  of  heat  by  friction  is  too  well  known  to  require  an  experi- 
mental 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  de- 


t  ON    THE    SOURCES    AND    EFFECTS    OF    HEAT.  633 

serve  to  be  briefly  related.  He  took  a  cannon,  not  yet  bored,  having  a  pro- 
jection of  two  feet  beyond  its  muzzle,  a  part  M-^hich  is  usMally  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  cylin- 
der, 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  hol- 
low cylinder,  by  a  force  equal  to  about  10  000  pounds  avoirdupois;  the  sur- 
face 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  i)()0  turns,  the 
horses  being  stopped,  a  mercurial  thermometer  was  introduced  into  a  perfora- 
tion 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  -§4^  of  the  whole  weight  of  ihe  cy- 
linder. In  another  experiment,  the  cylinder  was  surrounded  by  a  tight  deal  box, 
fitted  with  collars  of  leather,  so  as  to  allow  it  to  revolve  freely,  and  the  in- 
terval 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  produced  in  this  man- 
ner, 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  rela^ 
tive  velocity  of  the  bodies  is  more  cotisiderable,  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 ;  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. 


634  LECTURE    LI. 

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  pf 
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  sub- 
jected to  the  friction  of  various  substances  as  it  revolved  ;  and  he  found  that 
the  soft  filaments  of  the  cotton  excited  much  mpre  heat,  than  any  other  of  tlie 
substances  employed. 

The  chemical  productioii  of  heat  is  of  greater  practical  importance^fhan  its 
mechanical  excitation  ;  but  by  what  means  chemical  changes  operate  in  excit- 
ing 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  aeriform  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  uncon- 
cerned. It  appears  on  the  whole,  that  however  heat  may  be  excited,  the  corpus- 
cular poAvers  of  cohesion  and  repulsion  are  always  disturbed  and  called  into 
action,  their  equilibrium  being  destroyed  and  again  restored,  whether  by  me- 
chanical or  by  chemical  means.  A  wax  candle,  ^  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  experi- 
ments of  Mr.  Lavoisier  and  Mr.  Laplace,  the  combustion  of  ten  grains  of 
phosphorus  requires  the  consumption  of  15  grains  of  oxygen,  the  combustion 
of  ten  grains  of  charcoal  2C,  and  of  hydrogen  gas  56;  and  by  the  heat  pro- 
duced during  the  combustion  of  a  pound  of  phosphorus,  100  pounds  of  ice 
may  be  melted,  during  that  of  a  pound  of  charcoal  96i,  of  hydrogen  gas 
^95^  of  wax  133,  and  of  olive  oil  149;  and  during  the  deflagration  of  a 
pound  of  nitre  with  about  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  exa- 


OS    THE    SOURCES    AND    EFEECTS    OF    HEAT.  635 

mined.  We  shall  find  that  this  communication  happens  in  one  of  both  of  two 
Avays,  by  contact,  or  by  radiation;  and  that  it  may  also  differ  both  with  re- 
spect to  the  quantity  of  heat  concerned,  and  to  the  time  occupied  by  the  pro- 
cess. Whatever  heat  may  be,  we  may  safely  conclude  that  in  substances  of 
the  same  kind,  at  the  sailie  temperature  or  apparent  degree  of  warmth  or 
coldness,  its  quantity  must  be  proportional  to  tlae  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  imme- 
diately an  intermediate  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  mo- 
derate time,  too  small  to  be  perceptible.  The  nature  of  the  substances  con- 
cerned has  also  a  material  effect  on  the  velocity  with  which  heat  is  commu- 
nicated 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  de- 
scends; but  the  effect  of  the  air  remaining  in  the  imperfect  vacuum  of  the 
air  pump  may  be  sufficient  to  explain  his  experiments;  the  difference  of  terrt- 
perature  producing  an  ascending  current  in  the  neighbourhood  of  the  heated 
body,  by  means  of  which  the  cold  air  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  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 


636  '  LECTUBE    LI. 

between  cliiFerent  portions  of  the  same  fluid,  almost  entirely  by  the  mixture 
of  their  particles:  hence  a  fluid  heated  on  its  surface  transmits  the  lieat  very 
slowly  downwards,  since  the  parts  which  are  first  lieated,  being  rendered  spe- 
cifically 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,  sus- 
pended by  a  fine  thread  under  the  receiver  of  an  air  pump,  or  in  the  Torricel- 
lian vacuum,  will  continue  to  vary  its  temperature  with  that  of  the  surround- 
ing 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  -r^,  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  papers,  or  a  glossy  surface  of  any 
kind,  produces  an  eft'ect  nearly  approaching  to  that  of  black  paint.  This  radia- 
tion 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  sur- 


ON    THE    S0URCE3    AND    EFFECTS    OF    HEAT.  637 

face  is  only  one  sixth  of  that  which  the  air  receives.  Mr.  Leshe  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. 

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  transpa- 
rent mediums  but  little.  But  the  heat  of  a  fire  warms  a  piece  of  common 
glass  very  rapidly,  and  its  further  progress  is  almost  entirely  interrupted  by 
the  glass,  although  probably  a  certain  portion  still  continues  to  accompany 
the  light  in  all  cases.  Hence  a  sci-een  of  glass  is  sometimes  practically  con- 
venient 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  lit- 
tle diff'erence  was  observable  in  the  quantity  of  light,  and  he  very  justly  at- 
tributed 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.  Opacjue  substances  in  general  appear  to  be 
wholly  impervious  to  radiating  heat  of  all  kinds;  but  Dr.  Herschel  has  found 
that  dark  red  glass,  which  transmits  a  very  small  portion  of  light  only,  suffers 
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.  Buff'on,  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  Hoff^mann,  em- 
ployed two  mirrors  facing  each  other;  and  by  means  of  this  arrangement  the 
experiment  may  be  performed  when  the  thermometer  is  placed  at  a  considera- 
ble 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  iir  this  manner;  and  as  the 
raj's  of  light  cross  each  other  freely  in  all  possible  directions,  so  it  appears 

VOL.  I.  4  k 


638  LECTURE    LT. 

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  anotlier  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  t  ohave  been  first  suggested  by 
Mr  Provost,  as  an  explanation  of  an  experiment  on  the  reflection  of  cold,  re- 
vived by  Mr.  Pictet,  but  originally  made  some  centuries  before,  by  Plempius, 
and  by  the  Academicians  del  Cimento.  A  thermometer,  for  example,  must  be 
supposed  to  retain  its  temperature  by  means  of  the  continual  accession  of  ra- 
diant heat  from  the  surrounding  bodies,  supplying  the  place  of  that  which  is 
continually  thrown  off  in  all  directions  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,  notwithstanding,  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  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  be- 
fore 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  in- 
stantly show  its  effect  in  depressing  the  temperature ;  as  if  the  cold  were  ab- 
solutely 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,  invisible  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  properties  of  various  kinds  of  co- 
loured 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 


ON     THE    SOURCES    AND    EFFECTS    OF    HEAT.  '  639 

which  of  the  rays  would  furnish  the  greatest  quantity  of  light,  without  sub- 
jecting the  eye  to  the  inconvenience  of  unnecessary  heat.  He  first  observed 
that  the  heat  became  more  and  more  considerable  as  the  thermometer  ap- 
proached 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  Englefield  has  repeated  these  experiments  with  many  additional 
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  considerably,  than  would  be  required 
in  order  to  affect  any  thermometer  in  the  same  degree. 

It  was  first  observed  in  Germany  by  Ritter,  and  soon  afterwards  in 
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  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  permanent. 
The  permanent  effects  are  principally  confined  to  solids,  but  the  temporary 
eitects  are  different  with  respect  to  substances  in  different  states  of  aggrega- 
tion, 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  aug- 


(5^40  tECTURE   hi. 

iTientation  of  the  elastirfty  when  the  fluid  is  confined  to  a  certain  space.  This 
expansion  is  very  nearly  the  same  for  all  gases  and  vapours,  amounting  to 
^l^  for  each  degree,  at  the  common  temperature  of  50°  of  Fahrenheit,  but 
at  higher  temperatures  it  is  less  than  -j-^-o-  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,  determined 
by  the  degree  of  pressure  to  M'hich  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  would 
be  condensed  at  a  temperature  36°  higher,  and  with  the  pressure  of  half  our 
atmosphere  only,  it  might  be  cooled  without  condensation  33°  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  pro- 
ducing, 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  Fahrenheit.  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  10£°, 
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  sufticiently  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  eflfect  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  thousandth  for  each 


ON    THE    SOUnCJES    AND    EFPJECTS    OF    HEAT.  641 

degree:  that  of  water  is  equal  to  this  at  the  temperature  6i°,  and  is  greater 
or  less  nearly  in  proportion  to  the  distance  from  39°,  where  it  hegins,  hut 
in  high  temperatures  it  varies  less,  since  it  is  not  quite  four  times  as  great  at 
the  heat  of  boiling  water.  The  expansion  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  capil- 
lary tube  is  diminished  somewhat  less  than  -^o-  for  each  degree  of  Fahren- 
heit 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  atmospherical  pres- 
sure, or  any  other  pressure  which  may  be  substituted  for  it,  a  certain  por- 
tion 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  opera- 
tion may  be  continued. 

It  is  not,  however,  only  at  the  boiling  point  that  a  fluid  begins  to  be  con- 
verted 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  thet^uantity,  which  is  thus  suspended,  bears 
very  nearly  some  constant  proportion  to  the  density  of  which  the  steam  is 
capable  at  the  given  temperature  in  a  separate  state,  the  interposition  of  the 
air  either  not  affecting  the  distance  at  which  the  cohesion  would  take  place, 


642  LECTURE    Lr. 

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 
independently  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  tempera- 
ture evaporation  takes  place  it  is  always  accompanied  by  the  production  of 
cold ;  hence  it  is  usual  in  warm  climates,  to  em])loy  various  methods  of  pro- 
moting 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 
freezing  point:  they  then  expand  agam  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  extri- 
cated in  the  act  of  freezing.  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  l6th  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  atmosphere,  when  the 
pressure  of  the  air  is  excluded,  and  may  be  made  to  crystallize  by  admitting 
it  suddenly,  the  liquor  becoming  at  the  same  tiir^e  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  substances,  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 

2 


ON  THE  SOURCES  AND  EFFECTS  OF  HEAT.  643 

that  "the  substance  has  become  heated,  and  that  a  blow,  or  the  agitation 
produced  vvhen  they  are  made  to  sound  by  the  friction  of  the  bow  of  a  vioHn, 
may  sometimes  be  observed  to  cause  them  to  assume  the  state  of  equilibrium 
with  greater  rapidity.  Brass  expands  about  one  hundred  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 -j-bW  of  the  whole  for  each  degree:  but 
probably  various  substances  are  variously  aiFected  in  this  respect. 

/ 
The  liquefaction  of  solids,  and  their  conversion  into  fluids  by  the  operation 
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  retard- 
ed 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  ccnverted  into  vapour,  either  mixed  with  air,  or  in  a  separate 
state:  thus  ice  loses  weiglit  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  e>ist  as  liquids  in  elevated  temperatures.  In  all  changes  from  solidity  to 
liquidity  or  to  elastic  fluidity,  a  certain  quantity  of  heat  disappears,  except 
some  cases  in  which  a  chemical  decomposition  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  pro- 
duced. 

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  consequently 
expanded,  while  the  other  remains  much  colder,  and  if  the  vessel  canno>t 
readily  accommodate  its  form  to  this  change  of  proportions,  it  will  most  com- 
monly crack,  the  colder  parts  dividing,  in  consequence  of  their  being  too 
much  stretched  by  the  adjoining  hotter  parts.     Hence  the  thinner  the  ^lass  is, 


fl44  LECTURE    LI. 

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  externul 
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,  some- 
times 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  iu 
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  destroying  them,  so  that  the  concussion  produced  by 
breaking  the  drop  seems  to  be  concerned  in  the  destruction  of  the  equili» 
brium. 

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  wliich  accompanies  it  would  be  inconvenient 
for  others.  By  heatmg  them  again  to  a  more  moderate  temperature,  and 
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  considerable. 

3 


/ 


ON    THE    SOURCES    A^D    EFFECTS    OF    HEAT.  645 

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  yellowish  colour  which  it  assume^ 
indicating   the  first  stage  of  tampering,-  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.     Th  e  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  measure  explanatory  of  the  fact^;'i)iit  it  is  safer, 
in  the  present  state  of  our  knowledge,  to  be  contented  \vitli  tracing  the 
analogy  between  these  effects  in  substances  of  different  kinclg,  and  under 
different  circumstances,   without  attempting  to  understand   completely  the 
immediate  operation  of  the  forces  which  are  concerned. 


VOL.    I.  4  L 


646 


LECTURE  LII. 


ON  THE  MEASURES  AND  THE  NATURE  OF  HEAT. 

XhE  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  imme- 
diate operation. 

The  expansion  of  solids  is  measured  by  a  pyrometer,  which  is  calculated 
for  rendering  the  smallest  change  of  dimensions  perceptible  either  by  me- 
chanical or  by  optical  means.  The  first  of  these  methods  was  adopted  by 
those  who  first  investigated  these  ejects;  a  bar  of  metal  being  placed  in  a 
vessel  of  water,  or  of  oil,  which  was  heated  by  lamps,  while  the  extremities 
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  themselves,  must  very 
much  interfere  with  the  accuracy  of  such  an  instrument.  A  much  more  cor- 
rect mode  of  determination  is  to  employ  two  microscopes,  fixed  to  an  appara- 
tus, 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  betM'een  these  points,,  other 
means  must  be  employed.  The  most  natural  mode  o^determining  the  inter- 
mediate degrees  of  heat,  which  must  be  considered  as  the  standard  for  the 


ON    THE    MEASURES    AND    THE    NATURE   OF    HEAT.  647 

-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  tem- 
peratures, 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  exist- 
ence of  which  might  be  detected  by  a  comparison  of  experiments  on  various 
liquids  at  the  same  temperatures.  13y  repeating  the  operation,  we  may  subdi- 
vide the  interval*  as  often  as  we  please,  or  we  may  mix  the  liquids  in  any 
other  proportion,  so  as  to  obtain  at  once  any  otheripoint  of  the  scale,  which 
may  afterwards  be  identified  by  a  thermometer  of  any  description. 

There  is  also  another  method  of  comparing  thcdivisions  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  lieat  falling  on  it  must  be  nearly 
in  the  inverse  proportion  of  the  square  of  its  distance  from  the  focus  j  and 
the  elevation  of  a  common  thermometer  appears  to  be  nearly  proportional  to 
the  lieat  which  is  throwft_ott  It  ia .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  Jess  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  mostaccuratc,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  indi- 
cate, 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  measurement  of  very  low  tem- 
peratures, 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  ebul- 
lition.    For  higher  temperatures  than  this,  a  thermometer  has  been  made  of 

1 


648  LECTURE    Lir. 

semitransparent  porcelain,  containing  a  fusible  metal,  which  may  he  com- 
pared with  the  upper  part  of  the  mercurial  scale,  and  then  continued  further; 
and  the  expansion  of  such  of  the  metals,  as  are  difficult  of  fusion,  affords  an- 
other mode  of  determining  the  highest  degrees  of  heat.  Mr.  Wedgwood's 
thermometer  derives  its  properties  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  farnaces,  of  any  kind,  can  produce  a  heat  of  so  many 
thousand  degrees  of  a  natural  scale,  as  Mr,  Wedgwood's  experiments  have  led 
liim  to  suppose;  nor  is  the  i^upposition  consisteiat  with  the.  observations  of 
other  philosophers.  '     )/i  ■'[.':  ■-.[,■••   [-   .,;, 

Mercurial  thermometers  are  in  general  hermetically  sealed,  the  tube  being 
perfectly  closed  attheend,  inordertoexcludedust,  andtopreventthedissipation 
of  the  mercury.  When  a  standard  therm  ometer  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  precautions  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  30  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  difference 
of  nine  tenths  of  an  inch  either  way  requiring  an  alteration  amounting  to  -,4^ 
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  occupied  by  a  detached  portion  cxf 
mercury,  and  to  allow  for  any  irregularities  which  may  have  been  thus  de- 
tected. 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 


ON  THE  MEASURES  AND  THK  NATURE  OF  HEAT.         649 

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  cir- 
cumstance produces  no  difference  in  the  accuracy  of  the  results.  The 
separate  effects  of  the  expansion  of  glass  are,  however,  sometimes  perceptible; 
tlms,  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  tlie  temperature  of  the  sur- 
rounding: medium  than  a  mercurial  thermometer. 


'o 


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  quantity  of 
heat  is  sufficient  to  raise  their  temperature  very  considerably.  The  thermo- 
meter first  invented  by  Drebel  was  an  air  thermometer;  but  instruments  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  thermo- 
meters, 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  experi- 
ments of  short  duration,  since  the  changes  of  th«  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  consists  in-  closing 
the  bulb  of  a  common  barometer, so  as  to  leave  the  column  of  mercury  in  equili- 
brium 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  subse- 
quent changes  in  the  temperature  of  the  air,  which  must  afl'ect  both  its  bulk 
and  its  elasticity.  Mr.  Leslie's  photometer,  or  differential  thermometer,  has 
some  advantagesover  this  instrument,  but  it  can  only  be  employed  where  the 
changes  of  temperature  can  be  confined  to  a  part  only  of  the  instrument.  The 
elasticity  of  the  air  contained  in  the  bulb  is  here  counteracted,  not  by  the  pres- 
sure of  a  column  of  mercury,  but  by  the  elasticity  of  another  portion  of  ak 


(SiSO  iECTURE    LH. 

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 
M-hich  joins  them.    (Plate  XXXIX.  Fig.  548  .  .  550.) 

The  degree  of  heat,  as  ascertained  by  a  thermometer,  is  only  to  be  considered 
as  a  relation  to  the  surrounding  bodies,  iu  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,  wc  may  infer  that  the  water  and  the 
mercury  may  be  mixed  without  an}'  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  tlie  temperature  of  a  pound  of  water  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  tem- 
perature 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  ascertained,  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  becomehotterorcoldtr,  according 
to  the  nature  of  the  change,  adiminution  of  the  capacity  producing  beat, and  an 
augmentation  cold.  Such  a  change  of  capacity  is  often  a  convenient  mode  of  re- 
presentation for  some  of  the  sources  of  heat  and  cold :  thus,  when  heat  is  produc- 
ed by  the  condensation  ofa  vapour,  or  by  the  congelation  of  a  liquid,  we  may  ima- 
gine that  the  capacity  of  the  substance  isdimiuished;  and  that  it  overflows,  as  a 
vessel  would  doif  its  dimensions  were  contracted.  It  appears  also  from  directex- 


ON    THE    MEASUREir  AWD    THE   NATURE    OF    HEAT.  651 

perimcnts,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  cither; 
and  both  Dr.  Irvine  and  Dr.  Crawford  have  attempted  to  deduce,  from  a 
comparison  of  the  proportional  capacities  of  water  and  ice,  with  the  quantity 
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  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 
temi)€rature  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  tem- 
perature of  a  pound  of  water  140°,  or  that  of  140  pounds  a  single  degree. 
Pr.  Crawford  found,  by  means  of  other  experiments,  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  capacity  of  ice  wasT?,-  as  great  as  that  of 
water,  and  that  if  this  capacity,  instead  of  being  reduced  to  -^,  had  been 
Avholly  destroyed,  the  quantity  of  heat  extricated  would  have  been  10  times, 
as  great,  or  about  1400°,  which  has,  therefore,  been  considered  as  tl>e  whole 
quantity  of  heat  contained  in  a  pound  of  water  at  32°,  and  the  beginning  of 
the,  natural  scale  has  been  placed  about  13^8°  below  the  zero  of  Fahren- 
lielt.  ;  Dr.  Irvine  makes  tl>e  capacity  of  ice  still  less  considerable,  and  places- 
the  natural  zero  about  900-  degrees  below  tliat  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,  maimer  with  the  emission  or  absorption  of  heat  which  takfes 
place  while  those  changes  are  performed,  agreed  with  similai-  experiment* 
made  on  different  substances,  there  could  be  no  objection  to  the  mode  of 
representation.  But  if  it  should  appear  that  such  compaiTsous  frequently 
present  us  with  contradictory  results,  we  could  no  longer  consider  the  theory 
of  capacities  for  heat  as  sufficient  to  explain  the  phenomena.  With  respect  to  the 
simple  changes  constituting  congelation  and  liquefaction,  comlensationandeva- 
poration,  and  compression  and  rarefaction,  there  appears  to  be  at  present  noevi- 
dcnce  of  the  insufficiency  of  this  theory ;  it  has  not  perhaps  yet  been  shown  that  the 
heat  absorbed  in  any  one  cliange  is  always  precisely  equalto  that  which  is  emitted 


55-2  LECTURE    LII. 

ill  the  return  of  the  substance  to  its  former  state,  but  nothing  has  yet  been 
advanced  which  renders  this  opinion  improbable;  and  tlie  estimation  of  the 
natural  zero,  which  is  deduced  from  this  doctrine,  may  at  least  be  considered 
as  a  tolerable  approximation. 

if,  how-ever,  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  difference 
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  tlie  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.  A  pound  of  nitre  contains 
about  half  its  weight  of  dry  acid, and  the  capacity  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:  but 
Lavoisier  and  Laplace  have  found,  that  the  deflagration  of  a  pound  of  nitre 
produces  a  quantity  of  heat  sufficient  to  melt  twelve  pounds  of  ice,  conse- 
quently 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  char- 
coal contained,  which  is  for  several  reasons  higlijy  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  Fahren- 
heit. 

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  might 
he  thought  applicable,    the  heat  being  supposed  to    be  contained  in   the 


OV    THE    MEASURKS    AKD    THE    NATURE    OF    HEAT.  653 

SuTfstance,  withovit  being  comprehended  in  the  quantity  required  for  main- 
taining its  actual  temperaturCi  But  even  this  hypothesis  is  wholly  inap- 
plicable 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  tempera- 
ture 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  diminution  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  appropriate  name, 
and  a  place  in  the  order  of  the  simplest  elements  has  been  bestowed  on  it, 
appears  to  have  caused  the  most  eminent  chemical  philosophers  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  quantities,  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  equilibrium  of  temperature:  it  has  also  beert 
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  continued  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  «tated,  respecting  the  produc- 
tion of  heat  by  friction,  a^ipear  to  afford  an  unanswerable  confutation  of  the 
VOL.    I.  4  m 


^'54  tECTURE  Lll, 

whole  of  this  doctnne.  If  the  heat  is  neither  received  from  the  suirouiuHng 
bodies,  which  it  cannot  be  without  a  depression  of  their  temperature,  nor 
derived  from  the  quantity  aheady  accumulated  in  the  bodies  themselves, 
which  it  could  not  be,  even  if  their  capacities  were  diminished  in  any  imagin- 
able degree,  there  is  no  alternative  but  to  allow  that  heat  must  be  actually 
generated  by  friction;  and  if  it  is  generated  out  of  nothing,  it  cannot  b^ 
matter,  nor  even  an  immaterial  or  semimaterial  substance.  The  collateral 
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  respect- 
'  ing  heat,  and  it  will  only  be  necessary  to  suppose  the  vibrations  and  undula- 
tions, 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 
raySjderived  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  invisible,  are  a  little  more  perceptible 
in  the  violet,  which  still  possess  but  a  faint  power  of  illumination;  the 
yellow  green  afibrd  the  most  light;  the  red  give  less  light,  but  much  more 
heat,  while  the  still  larger  and  less  frequent  vibrations,  which  have  no  effect 
on  the  sense  of  sight,  may  be  supposed  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 


ON    THE    MEASUllEi:    AND    THE    IfATURE    OF    HEAT.  65S 

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  ori 
which  it  may  be  restored,  in  consequeiice  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  communicatii>g  heat  to  each  other  by  their  imme- 
diate 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 
sometimes  been  referred  to  the  centrifugal  forces  and  mutual  collisions  of  the 
revolving  and  vibrating  particles  ;  and  the  increase  of  the  elasticity  of  aeri- 
form 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  imme- 
diate 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  resem- 
ble tloose  of  sound,  since  every  sounding  body  is  in  a  state  of  vibration^  and 


656  LECTURE   txr. 

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  prin- 
cipal 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  com- 
municated by  contact,  when  the  end  of  a  tuning  fork  is  placed  on  a  table,  or 
on  the  sounding  board  of  an  instrument,   which  receives  from  the  fork  an 
impression    that    is  afterwards  propagated   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  convert- 
ed 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  chord  which  is  slowly  vibrating,  or  revolving  in  such  a  manner  as  to 
emit  little  or  no  audible  sound;   while  the  diminution  of  heat  by  expansion, 
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  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  ta 
the  dogmas  of  the  modern  schools  of  chemistry,  will  probably  long  retain  % 


ON    THE   MEASUnES   AND    THE   NATURE   OP   HEAT.  657 

partiality  for  the  convenient,  but  superficial  and  inaccurate,  modes  of  reason^ 
jng,  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  impression  on  the  minds 
of  the  cultivators  of  chemistry,  to  induce  them  to  listen  to  a  less  objection- 
able theory. 


658 


LECTURE  LIII. 


ON    ELECTRICITY    IN    EQUILIBRIUM. 

JL  HE  phenomena  of  electricity  are  as  amusing  and  popular  in  their  external  form 
as  they  are  intricate  and  abstruse  in  their  intimate  nature.  In.examiiiing  these 
phenomena,  a  philosophical  observer  will  not  be  content  with  such  exhibitions  as 
dazzle  the  eye  for  a  moment,  without  leaving  any  impression  that  can  be  instruct- 
ive to  the  mind,  but  he  will  be  anxious  to  trace  the  connexion  of  the  facts  with 
their  general  causes, and  to  compare  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  satisfactory  manner,  and  which  are  extremely  useful  in  connect- 
ing a  multitude  of  detached  facts  into  an  intelligible  system.  These  hypo- 
theses, 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  experimentally  observable.  The  motions  of  the 
electric  fluid  will  next  be  noticed,  as  far  as  we.  can  form  any  general  con- 
clusions respecting  them;  and  the  manner  in  which  the  equilibrium  of  elec- 
tricity is  disturbed,  or  the  excitation  of  electricity,  will  also  be  considered ; 
and,  in  the  last  place,  it  will  be  necessary  to  take  a  view  of  the  mechanism  or  the 

3 


Oy    ELECTRICITY    IN    EQUILIBRIUM.  659 

practical  part  of  electricity,  and  to  examine  the  natural  and  artificial  appara- 
tus concerned  in  electrical  phenomena,  as  well  as  in  those  effects,  which 
have  been  denominated  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 
thfm  with  more  or  less  facilit}',  according  to  their  different  powders  of  conduct- 
ing it:  that  the  particles  o:  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  substances 
by  an,attractive  or  repulsive  quality,  which  it  appears  to  communicate  ta 
different  bodies,  and  which  differs  in  general  from  other  attractions  and 
repu  sions,  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  pame  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  aflections.  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  consider- 
ed, is  much  greater  than  that  of  gravitation,  and  they  might  be  supposed 


^60  LECTURE    LIII. 

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  electrical  attractions  and  repulsions. 

The  attraction  of  the  electric  fluid  to  common  matter  is  shown  by  its  com- 
munication, from  one  body  to,  another,  which  is  less  copiously  supplied 
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  secon<l, 
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  remain* 
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  uncompensated.  We  are, 
however,  scarcely  justified  in  classing  this  mutual  repulsion  among  the 
fundamental  properties  of  matter;  for  useful  as  these  laws  are  rn  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  modifica- 
tions 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  ac- 
cumulation 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 


ON    ELECTRICITY    IN    EQUILIBRIUM.  66'l 

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  ac- 
cumulated, 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  difterent  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  may  be  communicated  in  any  part  of 
its  surface,  by  the  contact  of  an  electrified  body;  and  the  parts  thus  electri- 
fied may  afterwards  be  distinguished  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  some- 
what 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  di- 
minishing till  it  becomes  imperceptible. 

These  are  the  fundamental  properties  of  the  electric  fluid,  and  of  the  dif-^ 
ferent  kinds  of  matter  as  connected  with  that  fluid.     We  are  next  to  examia<i: 

VOL.     I.  4iX 


^6j[  LECTURE    LIII. 

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  etlJect  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  gravita- 
tion, 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  neu- 
trality: and  since  the  quantity  of  electric  fluid  taken  away  from  a  body,  in 
any  common  experiment,  bears  but  a  very  small  proportion  to  the  whole 
.that  it  contains,  thedeflciency  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  afrerwards  more  fully  shown,  by  Dr.  Gray's  experi- 
ments, 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  di- 
mensions, there  will  be  an  equilibuum,  when  the  actions  of  the  redundant 
fluid  in  the  spheres,on  the  whole  fluid  in  the  cyliuderjare  equal;  that  is,  uhtn 
both  the  spheres  have  their  surfaces  electrified  in  an  equal  degree:  but  if  the 
length  of 'the  cylinder  is  consid&iable,  the  fluid  within  it.caa  only  remain  at 


ON    ELECTRICITY    IN    EQUILIBRIUM,  665 

rest  when  the  quantities  of  redundant  fluid  are  nearly  equal  ii^  both  spheres, 
and  consequently  when  the  density  is  greater  in  the  smaller.  And  for  a  simi- 
lar 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.   Tig.  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  pres- 
sure 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  over- 
come, as  the  electrified  substance  is  more  pointed,  and  as  the  point  is  more 
prominent;  and  even  the  presence  of  dust  is  often  unfavourable  to  the  suc- 
cess of  electrical  experiments,  on  account  of  the  great  number  of  pointed  ter- 
.  minations  which  it  affords. 

The  general  effect  of  electrified  bodies  on  each  other,  if  their  bujk  is  sniall 
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  nratter  or  of  fluid,  and  it  may  also  easily  be  con- 
firmed by  experimental  proof.  A  neutral  body,  if  it  were  a  perfect  noncon- 
ductor, would  not  be  affected  either  way  by  the  neighbourhood  of.an  electri- 
fied body  :  for  while  the  whole  matter  contained  in  it  remains  barely  saturated 
with  the  electric  fluid,  the  attractions  and  repulsions  balance  each  other,  Eut 
in  general,  a  neutral  body  appears  to  be  attracted  by  an  electrified  body,   on 


664  lECTURE    LIII. 

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  elec- 
trical 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  re- 
dundancy of  the  fluid  expels  a  portion  of  the  natural  quantity  from  the  near- 
est parts  of  the  neutral  body,  so  that  it  is  accumulated  at  the  opposite  extre- 
mity; while  the  matter,  which  is  left  deficient,  attracts  the  redundant  fluid 
of  the  first  body,  in  such  a  manner  as  to  cause  it  to  be  more  condensed  in  the 
neighbourhood  of  the  second  than  elsewhere;  and  hence  the  fluid  of  this  body 
is  driven  still  further  ofi",  and  all  the  cff'ects  are  redoubled.  The  attraction  of 
the  redundant  fluid  of  the  electrified  body, for  the  redundant  matter  of  the  neu- 
tral 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  distance  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  con- 
ductor 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  acertain  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  substances, 
is  strong  enough,  if  they  are  suflSciently  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 
4 


©N    ELECTRICITY    IN    EQUILIBRIUM.  665 

usually  in  a  contrary  state,  and  therefore  renders  them  still  more  capable  of 
returning,  when  they  have  touched  it,  to  the  first  substance,  in  conseciuence 
of  an  increased  attraction,  assisted  also  by  a  new  repulsion.  This  alternation- 
has  been  applied  to  the  construction  of  severalelectrical  toys  ;  a  little  hammeiv 
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  supposed 
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  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  attrac- 
tion 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  thiti, 
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  temporary  vacuum  which  is  formed. 


666  LECTURE   LIII. 

When  a  comnninication  is  made  in  any  manner  by  a  conducting  substance 
between  the  two  coatings  of  a  charged  plate  or  vessel,  the  equilibrium  is  re- 
stored, and  the  effect  is  called  a  shock.  If  the  coatings  be  removed,  the 
plate  will  still  remain  charged,  and  it  may  be  gradually  discharged  by  mak- 
ing a  communication  between  its  several  parts  in  succession,  but  it  cannot  be 
discharged  at  once,  for  want  of  a  common  connexion;  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  ajar.  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  coaling  is  allowed  to  communicate  with  the  ground.  A  collect- 
ion 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 
effiects  by  the  motion  of  the  electric  fluid,  in  its  passage  from  one  to  the 
other  of  the  surfaces. 

The  conducting  powers  of  diff"erent  substances  are  concerned,  oiot  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  particularly 
in  the  properties  of  charged  substances,  which  depend  on  the  resistance  op- 
posed by  nonconductors  to  the  ready  transmission  of  the  fluid.  These  pow- 
ers may  be  compared,  by  ascertaining  the  greatest  length  of  each  of  the  sub- 
stances to  be  examined,  through  which  a  spark  or  a  shock  will  take  it  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;  ajar  of 


ON    ELECTRICITY    IN    EQUILIBRIUM.  667 

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  ajar  may  be  discharged  by  miuute  agitation,  when  it  is 
caused  to  ring  by  the  friction  of  the  finger,  Ic  has  oeen  observed  that,  in  a 
great  variety  of  cases,  those  substances,  which  are  the  best  conductors  of  heat, 
attbrd  also  the  readiest  passage  to  electricity;  thus,  copper  conducts  heat 
more  rapidly,  and  electricity  more  readily,  than  iron,  aijd  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  re- 
spects imperfect,  and  it  affords  us  but  little  light,  with  regard  either  to  the 
natore  of  heat,  or  to  that  of  the  electric  fluid. 


668 


LECTURE  LIV. 


ON    ELECTRICITY    IN    MOTION. 


XHE  manner  in  which  the  electric  fluid  is  transferred  from  one  body  to  an- 
other, the  immediate  effects  of  such  a  transfer,  the  causes  which  originally 
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  ex- 
citation by  which  the  equilibrium  is  originally  disturbed, one  of  the  most  inter- 
esting 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  che- 
mical than  to  the  mechanical  doctrine  of  electricity. 

The  progressive  motion  of  the  electric  fluid  through  conducting  substances 
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  pas« 
to  a  very  great  distance,  a  perceptible  portion  of  time  is  actually  occupied  ia 
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  sub- 
stance, 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 


ON    ELECTRICITY    IN    MOTION.  669 

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  heen  supposed,  although  perhaps  somewhat  hastily,  that  the  actual  ve- 
locity 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  sub_ 
stance,  while  the  part  presented  to  the  electrified  body  is  most  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  com- 
munication of  electricity  has  rendered  the  substance  more  capable  of  conduct- 
ing 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  contained  in  the  glass,  while 
the  plate  of  air  is  perhaps  little  concerned  in  the  distribution  of  the  elec- 
tricity. 

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 

VOL.    I.  4  o 


G/O  LECTURE    LIV. 

between  them,  is  found  to  heat  the  negative  ball  much  more  than  the  posi- 
tive. 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  de- 
composition 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  ad- 
vancement of  the  growth  of  plants,  which  have  been  sometimes  attributed 
to  it,  have  not  been  confirmed  by  the  most  accurate  experiments.  An  un- 
interrupted 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  our  hand  on  the  conductor  of 
an  electrical  machine,  the  electricity  will  pass  oft'  continually  through  the 
body,  without  exciting  any  sensation.  A  constant  stream  of  galvanic  elec- 
tricity, 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  in- 
terruption of  the  current  is  necessary  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  production 
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 

a 


ON    ELECTRICITY   IN"    MOTION.  67I 

overflows  a  little  into  the  neiglibouring  space.  There  is  always  an  appearance 
of  light  whenever  the  path  of  the  fluid  is  interrupted  by  an  imperfect  con- 
ductor; nor  is  the  apparent  contact  of  conducting  substances  sufficient  to 
prevent  it,  unless  they  are  held  together  by  a  considerable  force;  tluis,  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  thnes  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,  represents  at  once  a  brilliant  delinea- 
tion 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  phosphor),  retain  for 
some  seconds  the  luminous  appearance  thus  acquired  Even  water  is  so  im- 
perfect 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  con- 
ductor, 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  accotnpanies  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  lengthened,  accordingly 
as  it  is  loose  or  stretched  during  the  experiment.  The  more  readily  a  metal  con- 
ducts, 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  oFthe  same  kind. 

The  mechanical  effects  of  electricity  are  probably  in  many  cases  the  consc- 


572  LECTURE    LIV.  ,  ' 

quences  of  the  rarefaction  produced  by  the  heat  which  is  excited;  thus,  the 
explosion,  attending  the  transmission  of  a  shock  or  sparii  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, 
Avhen  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  jac 
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 
dischar<i-e,  when  the  glass  is  in  contact  with  oil  or  with  sealing  wax;  and  no 
sufHcicnt  explanation  of  this  circumstance  has  yet  been  given. 

A  stron""  current  of  electricity,  or  a  succession  of  shocks  or  sparks,  trans- 
mitted 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  diiFer- 
ent.  Of  these  the  most  remarkable  is  the  production  of  oxygen  and  hy- 
drogen gas  from  common  water,  which  are  usually  extricated  at  once,  in 
such  quantities,  as,  when  again  combined,  will  reproduce  the  water  which 
has  disappeared ;  but  in  some  eases  the  oxygen  appears  to  be  disengaged 
most  copiously  at  the  positive  wire,  and  the  hydrogen  at  the  negative. 

When  the  spark  is  received  by  the  tongue,  it  has  generally  a- subacid  taste; 
anil  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  6f  the  muscles  through  wh.ich  it 
passes;  although  in  some  cases  it  produces  pain  cf  a  different  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  diiliculty 
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  immediate  exhaustion  of  the  whole  energy  of  the 
nervous  system.  It  is  remarkable  th!i,t  a  very  minute  tremor,  communicated  to 
the  most  elastic  partsof  the  body,in  particular  to  the  chest,  produces  an  agita- 
tion of  the  nerves,  whicli  is  not  wholly  unlike  the  effect  of  a  weak  eltjctricity. 


ON    ELECTRICITY    IN    MOTIOW^  673* 

The  principal  modes,  in  which  the  electric  equiUbrium  is  primarily  de- 
stroyed, are  simple  contact,  friction,  a  change  of  the  fofm  of  aggregation,, 
and  chemical  combinations  and  decompositions.  The  electricity  produced 
by  the  simple  contact  of  any  two  substances  is  extremely  weak,  and  can  only 
be  detected  by  very  delicate  experiments  :  in  general  it  appears  tlvit  the  substance,, 
which  conducts  the  more  readily,  acquires  a  slight  degree  of  negative  elec- 
tricity, 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  sutxstance  always  losing  as  much  as  the  other  gains ^  and  commonly 
although  not  always,  the  worst  conductor  becomes  positive.  At  thq  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  cliange,  this  re- 
dundancy or  deficiency  is  rendered  sensible.  When  two  substances  of  the 
same  kind  are  rubbed  together,  the  smaller  or  the  rougher  becomes  nega- 
tively electrified;  perhaps  because  the  smaller  surface  is  more  heated,  in  con- 
se(|uence  of  its  undergoing  more  friction  than  an  equal  portion  of  the  larger^ 
and  bence  becomes  a  better  conductor;  and  because  the  rougher  is  in  itself 
a  better  conductor  than  the  smoother,  ana  may  possibly  have  its  conducting 
powers  increased  by  the  greater  agitation  of  its  parts  which  the  friction  pro- 
duces. The  back  of  a  live  cat  becomes  positiveh'  electrified,  with  whatever 
substance  it  is  rubbed;  glass  is  positive  in  most  cases,  but  not  when  rubbed 
with  mercurj'  in  a  vacuum,  although  sealing  wax,  which  is  generally  nega- 
tive, 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  blacL 
dye  renders  tlie  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  surf^ices,  where  it  remains 
accumulated,  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  iniperfect  conductor :; 


574  -  lECTORE   X.IV. 

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.  Sul- 
fur becomes  electrical  in  cooling,  and  wax  candles  are  said  to  be  sometimes  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  electrical  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  transmits  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  elec- 
tricity by  chemical  changes,  are  those  which  have  lately  received  the  appella- 
tion of  galvanic.  Some  of  the  effects  which  have  been  considered  as  belong- 
ing 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  philo- 
sophers on  the  continent,  to  the  mere  mechanical  actions  of  bodies  possessed 
of  diflferent  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 
certainly  is  not. 

The  phenomena  of  galvanism  appear  to  be  principally  derived  from  an  in- 
equality 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 


aN    ELECTRICITY    IN    MOTION.  675 

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  consequence  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  considering  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,  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 
hy  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  obtained  by 
their  union;  thus  it  usually  happens  that  both  the  metals  employed  are  oxid- 
able  in  some  degree,  and  the  oxidation,  which  takes  place  at  the  surface  of  the 
better   conductor,  tends  to  impede  the  Avhole  effect,  perhaps  by  impeding 
the  passage  of  the  fluid  through  the  surface.     The  most  oxidable  of  the 


676  LECTURE    LIV. 

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  thesiipply  of  electricity  through  the  more  con- 
ducting metal  promotes  the  oxidation  of  the  zinc  of  a  galvanic  battery  ;  and 
the  eftect  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  isloos^,  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  cfl^iect  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  eftect,  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  extrication  of.  hydrogen,  the  same 
causes  will  sometimes  occasion  a  deposition  of  a  metal  which  has  been  dis- 
solved, 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 
knowledge.  The  intensity  of  the  electrical  charge,  and  the  chemical  and 
physiological  eft'ects  of  a  pile  or  battery,  seem  to  depend  principally  on  the 
number  of  alternations  of  substances;  the  light  and  heat  more  on  the  joint  mag- 
nitude of  the  surfaces  employed.     In  common  electricity,  the  greatest  heat 


©N    ELECTRICITT    IN    MOTION.  '  677 

appears  to  be  occasioned  by  a  long  continuation  of  a  slow  motion  of  the  fluid; 
and  this  is  perhaps  best  furnislied  in  galvanism  by  a  surface  of  large  extent^ 
while  some  other  effects  may  very  naturally  be  expected  to  depend  on  the  in- 
tensity of  the  charge,  independently  of  the  quantity  of  charged  surface.  It 
may  easily  be  imagined,  that  the  tension  of  the  fluid  must  be  nearly  propor- 
tional to  the  number  of  surfaces,  imperfectly  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  un- 
derstood, that  any  point  of  the  pile  may  be  rendered  neutral,  by  a  connexion 
with  the  earth,  while  those  parts,  whichareaboveitorbelow  it,  will  still  preserve 
their  relations  unaltered  with  respect  to  each  other:  the  opposite  extremi- 
ties 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  con- 
ducting substance.  The  various  forms,  in  which  the  piles  or  troughs  are  con- 
structed, are  of  little  consequence  to  the  theory  of  their  operation  :  the  most 
convenient  are  the  varnished  troughs,  in  which  plates  of  silvered  zinc  are  ar- 
ranged side  by  side,  with  intervening  spaces  for  the  reception  of  water,  or  of 
an  acid.     (Plate  XL.  Fig.  55?.) 

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  comnmnicating  this  electricity  at  pleasure  to  conduct- 
ing 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  de- 
rived; but  the  effect  of  the  shock,  which  they  produce,  resembles  in  all  re- 
spects that  of  the  weak  charge  of  a  very  large  battery.  It  has  also  been  shown 
by  the  experiments  of  Galvani,  Volta,  and  Aldini,  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  in- 
clined 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 

4  p 


678  LECTURE    LIV. 

which  the  subject  of  galvanism  afforded  before  Mr.  Davy's  late  ingenious  and 
interesting  researches,  which  have  thrown  much  light,  not  only  on  the  foun- 
dation 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  com- 
binations, depend  on  the  opposite  natural  electricities  of  the  bodies  concerned; 
since  such  bodies  are  always  found,  by  delicate  tests,  to  exhibit,  when  in  con- 
tact, marks  of  different  species  of  electricity;  and  their  mutual  actions  may 
be  either  augmented  or  destroyed,  by  increasing  their  natural  charges  of  elec- 
tricity, or  by  electrifying  them  in  a  contrary  Avay.    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  decom- 
posed 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  attrac- 
tions for  them.  Alkali,  sulfur,  and  alkaline  sulfurcts,  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  considered  as  belonging  to  the  same  class  with  the 
alkalis. 

Supposing  now  a  plate  of  zinc  to  decompose  a  portion  of  water:  the  oxy- 
gen, 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  elec- 
tricity; 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:  audit  re- 
ceives 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  ne- 
gatively. Mr.  Davy  therefore  considers  this  chemical  action  as  destroying,  or 


ON    ELECTRICITY    IST    MOTION. 


679 


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,   sulfurct,  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,  accord- 
ing to  its  natural  tendency,  from  the  copper  to  the  iron,  and  from  the  iroa  "REEsfT^ 
to  the  sulfuret.     In  a  third  case,    when  copper,   an  acid,  and  water,    forra 
a  circle,  the  natural  tendency  is  from  the  acid  to  the  copper  on  one  side,  s^.'*'<j//.'.     '' 
and  from  the  acid  to  the  water,  and  from  the  water  to  the  copper  on  the  other;       ^"<<^  ' 
here  we  must  suppose  the  first  force  to  be  only  a  little  weakened  by  the  che- 
mical action,   while  the  third  is  destroyed,   so  that  the  first  overcomes  the  sc 
cond,  and  the  circulation  is  determined,  although  very  feebly,  in  such  a  direc- 
tion,  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  copperi 
and  secondly,  from  the  water  to  the  sulfuret :  in  this  instance  a  chemical  ac- 
tion 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  tlie  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 
cither  their  conducting  power,  or  their  simple  action  on  the  other  elements  of  the 
series:  thus,  the  sulfuric  acid,  which  conducts  electricity  better,  and  dissolves 
the  metals  more  readily,  than  a  neutral  solution,  is,  notwithstanding,  less 
active  in  the  batt-ery,  because  it  is  not  easily  decomposed.  Mr.  Davy  lias  also 


680  LECTURE    LIV. 

extended  his  researches,  and  the  application  of  his  discoveries,  to  a  vari- 
ety 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  hi  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  negatively  electrified;  and  either 
conductor  may  contain  within  it  ajar,  which  may  be  charged  at  once  by  the 
operation  of  the  machine,  when  its  internal  surface  is  connected  cither  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  electri- 
city 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  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  4800  feet  of  wire. 

The  electrophorus  derives  its  operation  from  the  properties  of  induced  elec- 
tricity.    A  cake  of  a  nonconducting  substance,  commonly  of  resin  or  of 


ON    ELECTRICITY    IN    MOTION.  681 

sulfur,  is  first  excited  by  friction,  and  becomes  negatively  electric:  an  in- 
sulated 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  sub- 
stance 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  ajar;  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,  re- 
ceived 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  neighbour- 
hood 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  re- 
ceived is  sufficient,  when  the  capacity  of  the  plate  is  again  diminished,  to  pro- 
duce 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  elec- 
trophorus,  both  instruments  deriving  their  properties  from  the  effects  of  induc- 
tion. 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  gene- 
ral a  thin  stratum  of  air  only  is  interposed ;  but  sometimes  a  nonconducting 
varnish  is  employed ;  this  method  is,  however,  liable  to  some  uncertaiqty, 
from  the  permanent  electricity  which  the  varnish  sometimes  contracts  by  fric- 
tion. The  electricity  is  accumulated  by  the  attraction  of  the  plate  communi- 
cating 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  substance,  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  fa- 
ciUtated  by  several  subordinate  arrangements.    (Plate  XL.  Fig.  561.)' 


682  LECTORE    LIV. 

JNfr.  Cavallo's  multiplier  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  ex- 
amined, to  the  first  or  insulated  plate  of  the  second  condenser,  which  receives 
it  repeatedly,  until  it  has  acquired  an  equal  degree  of  tension;  and  when  the 
two  plates  of  this  condenser  are  separated,  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,  although  it  has  been  supposed  that  these  instruments  are  more 
liable  to  inconvenience  from  the  attachment  of  a  greater  portion  of  electri- 
city 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.  Ben- 
net  employs  three  varnished  plates  laid  on  each  other,  but  Mr.  Nicholson  has 
substituted  simple  metallic  plates,  approachingonly  very  near  together,  so  that 
there  can  be  no  error  from  any  accidental  friction.  In  both  of  these  instru- 
ments, 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.  56<2,  563.) 

The  immediate  intensity  of  the  electricity  may  be  measured,  and  its  cha- 
racter distinguished,  by  electrical  balances,  and  by  electrometers  of  difierent 
constructions.  The  electrical  balance  measures  the  attraction  or  repulsion 
exerted  by  two  balls  at  a  given  distance,  by  tlie  magnitude  of  the  force  re- 
quired to  counteract  it;  and  the  most  convenient  manner  of  applying  this 
force  is  by  the  torsion  of  a  wire,  which  has  been  employed  for  the  purpose  by 
Mr.  Coulomb.  The  quadrant  electrometer  of  Henley  expresses  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  propor- 
tional 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 


ON    ELECTRICITV    IN    MOTION.  683 

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,   Avhich  are  made  to  diverge  by  a  smaller  degree  of 
electricity.     Mr,  Eennet's  electrometer  is  still  more  delicate;   it  consists  of 
two  small  portions  of  gold  leaf,   suspended  from  a  plate,  to  whicli  the  electri- 
city of  any  substance  is  communicated  by  contact:  a  very  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  glass 
which  covers  the  electrometer,   opposite  to  the  extremities  of  the  leaves,   pre- 
vents 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  m  hen  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  pleasure;  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  re- 
quired 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   -^.     Mr.    Volta   says,     that   the  indications  of  Lane's  and 
Henley's  electrometer  agree  immediately  with  each  other;  but  it  seems  diffi- 
cult 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 


684  LECTURE    IIV. 

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  igno- 
rant of  the  constitution  of  bodies,  by  Avhich  they  become  possessed  of  differ- 
ent conducting  powers;  and  we  have  only  been  able  to  draw  some  general 
conclusions  respecting  the  distribution  and  equilibrium  of  the  supposed  electric 
fhiid,  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  ori- 
gin 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  prin- 
cipal phenomena  of  galvanism  are  universally  considered  as  depending  on  che- 
mical changes;  perhaps,  also,  time  may  show,  that  electricity  is  very  materi- 
ally concerned  in  the  essential  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. 


68i 


LECTURE  LV. 


ON    MAGNETISM. 

.llIE  theory  of  magnetism  bears  a  very  strong  resemblance  to  that  of  elec- 
tricity, and  it  must  therefore  be  placed  near  it  in  a  system  of  natural  philoso- 
phy. We  have  seen  the  electric  fluid  not  only  exerting  attractions  and  re- 
pulsions, and  causing  a  peculiar  distribution  of  neighbouring  portions  of  a  fluid 
similar  to  itself,  but  also  excited  in  one  body,  and  transferred  to  another,  in 
such  a  manner  as  to  be  perceptible  to  the  senses,  or  at  least  to  cause  sensible 
eft'ects,  in  its  passage.  The  attraction  and  repulsion,  and  the  peculiar  distri- 
bution of  the  neighbouring  fluid,  are  found  in  tlie  phenomena  of  magnetism; 
but  we  do  not  perceive  that  there  is  ever  any  actual  excitation,  or  any  per- 
ceptible 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  increasqs;  and 
the  particles  of  such  iron  must  also  be  imagined  to  repel  each  other,  in  a  si- 
milar manner.  Iron  and  steel,  when  soft,  are  conductors  of  the  magnetic 
fluid,  and  become  less  and  less  pervious  to  it  as  their  hardness  increases. 
The  ground  work  of  this  theory  is  due  to  Mr,  Aepinus,  but  the  forces  have 
been  more  particularly  investigated  by  Coulomb  and  others.  There  are  the 
same  objections  to  these  hypotheses  as  to  those  which  constitute  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  pe- 
culiar force,  which  happens  to  be  precisely  a  balance  to  the  attraction  of  the 
magnetic  fluid  for  iron.     This  is  obviously  improbable;  but  tlie  hypotlieses 

VOL.    I.  4  Q 


686  lectuhe  lv. 

are  still  of  great  utility  in  assisting  us  to  generalise,  and  to  retain  in  memory, 
a  number  of  particular  facts  wliicli  would  otherwise  be  insulated.  The  doc- 
trine 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,  appear  to  be  too  compli- 
cated, 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  soft- 
ening iron,  must  consequently  render  it  a  conductor;  even  the  heat  of  boil- 
ing water  affects  it  in  a  certain  degree,  although  it  can  scarcely  be  supposed 
to  alter  its  temper;  but  the  effect  of  a  moderate  heat  is  not  so  considerable  in 
magnetism  as  in  electricity.  A  strong  degree  of  heat  appears,  from  the  expe- 
riments of  Gilbert,  and  of  Mr.  Cavallo,  to  destroy  completely  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  has  observed  that  there  are  scarcely  any  bodies  in  nature 
which  do  not  exhibit  some  marks  of  being  subjected  to  the  influence  of  mag- 
netism, although  its  force  is  always  proportional  to  the  quantity  of  iron  which 
they  contain,  as  far  as  that  quantity  can  be  ascertained;  a  single  grain  being 
sufficient  to  make  20  pounds  of  another  metal  sensibly  magnetic.  A  combi- 
nation with  a  large  proportion  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  de- 
gree; it  is  also  said  that  antimony  renders  iron  incapable  of  being  attracted 
by  the  magnet.  Nickel,  when  freed  from  arsenic  and  from  cobalt,  is  decid- 
edly magnetic,  and  the  more  so  as  it  contains  less  iron.  Some  of  the  older 
chemists  supposed  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;  had  nickel 

4 


ON    MAGNETISM.  687 

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 
raagnetical  phenomenon,  and  if  iron  were  the  only  substance  capaple  of 
exhibiting  magnetic  effects,  it  would  follow  that  some  ferruginous  particles 
must  exist  in  the  upper  regions  of  the  atmosphere.  The  light  usually  attend- 
ing this  maguetical  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  ia 
the  air. 

We  arc  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  considered 
as  the  part  in  which  the  magnetic  fluid  is  either  redundant  or  deficient,  pro- 
vided 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 
temporary  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  apiece  of  soft  iron,  the  north  pole 


688  LECTURE  LV. 

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  direction, 
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  oval  figure,  pass- 
ino-  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  represent  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  magnetism, 
the  north  pole  of  each  particle  being  attached  to  the  south  pole  of  the  par- 
ticle 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 


ON    MAGNETISM,  GSQ 

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  out- 
wards, as  if  they  were  repelled  by  it.     (Plate  XLI.  Fig.  571.) 

The  magnets,  which  we  have  hitherto  considered,  are  such  as  have  a  simple 
and  well  determined  form;  but  the  great  compound  magnet,  which  directs 
the  mariner's  compass,  and  which  appears  to  consist  principally  of  the  me" 
tallic  and  sfightly  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  considerably 
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  survey- 
ing: a  needle,  whichis  poised  with  a  liberty  of  horizontal  motion,  assuming  \ 
the  direction  of  the  magnetic  meridian,  which  for  a  certain  tiaie  remains 
almost  invariable  for  the  same  place;  and  a  similar  property  is  also  observa- 
ble in  the  dipping  needle,  whichis  moveable  only  in  a  vertical  plane;  for 
when  this  plane  is  placed  in  the  magnetic  meridian,  the  needle  acquires 
an  inclination  to  the  horizon,  which  varies  according  to  the  situation  of  the 
place  with  respect  to  the  magnetic  poles.     (Plate  XLI.  Fig.  57'2,  57'o.) 

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  \yith  much 
more  regularity.     In  either  case  the  whole  needle  is  scarcely  more  or  less 


ggO  '  LECTURE    LV. 

atttacted  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  substances,  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  iuduction,  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  i)olarity  from  the  great  primitive  mag- 
net. 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,  according 
to  a  law  which  has  never  yet  been  generally  determined,  although  the  varia- 
tion which  has  been  observed,  at  any  one  place,  since  the  discovery  of  the 
compass,  may  perhaps  be  comprehended  in  some  very  intricate  expressions; 
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  attributeil  the  efliect  to  the  motions  of 
the  celestial  bodies:  but  in  either  case  the  changes  produced  would  have 
been  much  more  regular  and  universal  than  those  which  have  been  actually 
observed.  Temporary  changes  of  the  terrestrial  magnetism  have  certainly 
been  sometimes  occasioned  by  other  causes ;  such  causes  are,  therefore, 
most  likely  to  be  concerned  in  the  more  permanent  effects.  Thus,  the  erup- 
tion of  Mount  Hecla  was  found  to  derange  the  position  of  the  needle  consi- 
derably; the  aurora  borealis  has  been  observed  to  cause  its  north  pole  to  move 


ON    MAGNETISM.  69I 

6  or  7  degrees  to  the  westward  of  its  usual  position;  and  a  still  more  remark- 
able change  occurs  continually  in  the  diurnal  variation.  In  these  climates 
the  north  pole  of  the  needle  moves  slowly  westwards  from  about  8  in  the  morn- 
ing till  2,  and  in  tiie  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  mag- 
netic 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  constant  for 
the  same  place,  or  even  if  it  varied  according  to  any  discoverable  law;  since 
it  would  alford  a  ready  mode  of  deternrniing  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  castor  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  liave  moved  more  uniformly  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  6"  near  the  island  of  Barbadoes,  from.  1700  to  17^6.  (Plate 
XLI.   Fig.  574  .  .  576.     Plate  XLIL  XLIII.) 


692  LECTUllE    LV. 

Tlie  dip  of  the  nortli  pole  of  the  needle  in  the  neighbourhood  of  London 
is  72°.  Hence  the  lower  entl  of  a  bar  standing  upright,  as  a  poker,  or  a  lamp 
iron,  becomes  always  a  north  pole,  and  the  temporary  south  pole  of  apiece 
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  tlie  fluid  in  the  magnet  itself  being  also  a  little  more  favourable  to  the  at- 
traction, while  its  north  pole  is  downwards.  It  is  obvious  that  the  magnetism 
of  the  nortliern  magnetic  pole  of  the  earth  must  resemble  that  of  the  south 
pole  of  a  magnet,  since  it  attracts  the  north  pole ;  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  po- 
sition of  this  supposed  magnet  would  probably  be  sufficient  to  produce  it; 
but  the  operation  of  such  a  magnet,  according  to  the  general  laws  of  the  forces 
concerned,  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  I)y  no  means  sufficiently  accurate  to  allow  us  to  place  any  de- 
pendence on  it.     (Plate  XLL  Fig.  577,  578) 

The  art  of  making  magnets  consists  in  a  proper  application  of  the  attractions 
and  repulsions  of  the  magnetic  fluid,  by  means  of  the  ditferent  conducting 
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  ex- 
hibition of  its  peculiar  properties. 

We  may  begin  with  any  bar  of  iron  that  has  long  stood  in  a  vertical  posi- 
tion; 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 


ON    MAGNETISM.  GQS 

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  operation  is  re- 
peated, 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  distri- 
bution of  the  fluid ;  but  the  fact  is  certain,  and  the  strength  of  the  new  mag- 
net 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  tlie  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  magnetic  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  with- 
drawn in  the  middle;  in  order  to  keep  the  poles  at  equal  distances. 

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  col- 
lectively magnetic.  A  bar  of  steel,  placed  red  hot  between  two  magnets,  and 
suddenly  quenched  by  cold  water,  becomes  in  some  degree  magnetic,  but  no4: 
so  powerfully  as  it  may  be  rendered  by  other  means.  For  preserving  mag- 
nets, 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  in- 
duced magnetism,  tend  to  favour  the  accumulation  of  the  magnetic  power  in 
a  greater  quantity  than  the  nietal  can  retain  after  they  are  removed.  Hence 
the  ancients  imagined  that  the  magnet  fed  on  u"on. 

A  single  magnet  may  be  made  of  two  bars  of  steel,  with  their  ends  pressed 
VOL.  I.  •  4  R 


69^  LECTURE    LV. 

into  close  contact;  and  it  might  be  expected  that  when  these  bars  are  sepa- 
rated, or  when  a  common  magnet  has  been  divided  in  the  middle,  the  por- 
tions 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.  lii 
this  case  we  must  suppose,  contrarily  to  the  general  principles  of  the  theory, 
that  the  magnetic  fluid  has  actually  escaped  by  degrees  from  otie  of  the 
])ieces,  and  has  been  received  from  the  atmosphere  by  the  other. 

There  is  no  reason  to  imagine  any  immediate  connexion  between  magnet- 
ism 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  slwck  of  electricity,  may  expe- 
dite 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  exer- 
tion of  the  cohesive  and  repulsive  powers  appears  to  favour  the  transmission 
of  the  magnetic  as  well  as  of  the  electric  fluid.  The  internal  agitation,  pro- 
duced 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  beiri'g  attracted  when  it  has 
been  hammered,  even  between  two  flints;  and  that  this  property  is  again  di- 
minished by  fire:  in  this  case  it  may  be  conjectured  that  hammering  increases 
the  conducting  power  of  the  iron  contained  in  the  brass,  and  thus  renders  it 
more  susceptible  of  magnetic  action.  I\Ir.  Cavallo  also  observed  that  a  mag- 
netic needle  was  more  powerfully  attracted  by  iron  filings  during  their  solu- 
tion in  acids,  especially  in  the  sulfuric  acid,  than  either  before  or  after  the 
operation:  others  have  not  always  succeeded  in  the  experiment;  but  there  is 
nothing  improbable  in  the  circumstance,  and  there  may  have  been  some  actual 
difference  in  the  results,  dependent  on  causes  too  minute  for  observation.  In 
subjects  so  little  understood  as  the  theory  of  magnetism,  we  are  obliged  to  ad- 


ON    MAGNETISM.  695 

mit  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  amus- 
ing as  well  as  interesting  phenomena;  and  the  principles  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. 


696 


LECTURE  LVL 


ON    CLIMATES    AND    WINDS. 


TL  HE  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  con)plicated  and  intricate  na- 
ture; it  comprehends  many  effects  derived  from  such  causes,  as  belong  sepa- 
rately to  every  department  of  physics  which  we  have  hitherto  examined;  and 
although  it  has  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  agriculture,  or  to  medicine,  is  at  present  uncertain;  al- 
though some  advantage  has  already  been  derived  from  the  indications  of  me- 
teorological instruments;  and  the  philosophy  of  the  science  is  in  many  re- 
spects much  more  advanced  than  has  commonly  been  supposed.  We  shall  di- 
vide this  extensive  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,  re- 
quire to  be  examined  in  the  first  place;  since  they  are  not  only  of  considera- 
ble 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 


ON    CLIMATES    AND    WINTJS,  657 

is  usuall)'  filled  with  spirit  of  wine,  which  is  in  contact  with  a  portion  of  mer- 
cury 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  conse- 
quently 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  arrangement  of  a  pair 
of  thermometers,  one  with  mercury,  the  other  with  spirit  of  wine,  placed  in  a 
horizontal  position;  one  index  being  without  the  surface  of  the  mercury,  the 
other  within  that  of  the  spirit:  the  thermometers  being  in  contrary  direc- 
tions, 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  varia- 
tions 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  tlie  earth's  surface  are  unquestionably 
owing  in  great  measure  to  their  position  with  respect  to  the  sun.  At  the  equa- 
tor, where  the  sun  is  always  nearly  vertical,  any  given  part  of  the  surface  re- 
ceives a  much  greater  (juantity  of  light  and  heat,  than  an  equal  portion  near 
the  poles;  and  it  is  also  still  more  affected  by  the  sun's  vertical  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  tlie 
same  as  that  of  the  meridian  heat  of  a  vertical  sun,  to  the  heat  derived,  at  the 
altitude  234^°,  in  the  middle  of  the  long  annual  day  at  the  poles.  Hut  the 
difference  is  rendered  still  greater,  by  the  effect  of  the  atmosphere,  which  in- 
terrupts a  greater  portion  of  the  heat  at  the  poles  than  elsewhere.  IJouguer 
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 


(t(9"8  lecture  xv«. 

neighbonring  places.  It  is  obvious  that,  at  any  individual  j)lace,  tlie  climate  ia 
summer  must  approach  in  some  degree  to  the  equatorial  climate,  the  sun's  al- 
titude 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.  Pr6vost  has  very  ingeniously  deduced  the  proportion  of  the  sun's 
beat  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 
verj-^  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  di- 
urnal variation  of  temperature  is  6°,  in  March  £0°,  in  July  10°,  and  in  Sep- 
tember, 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  probably  have  attained  its  maxir 
mum.  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 


ON    CLIMATES    AND    WINDS.  '  699 

onfirmed,  it  will  introduce  a  great  uncertainty  into  all  theories  upon  the 
subject:  since  in  these  calculations  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  tem- 
perature 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  freezing 
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  freezing  than  it  is 
absorbed  in  thawing;  that  the  heat,  thus  extricated,  being  disposed  to  fl}'  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; 


700  LECTUKE    LVI. 

and  for  this  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  pro- 
portion 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  com- 
pensates 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.  Provost  has  shown,  that  in  all  probability  the  same  quantity 
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  tempera- 
ture 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  somewhat  warmer  than  the 
northern:  but  in  fact  they  are  colder,  partly  perhaps  from  the  much  greater 
proportion  of  sea,  which  in  some  degree  equalises  the  temperature,  and 
partly  for  other  reasons.  The  comparative  intensity  of  tlie  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  IB"  or 
S0° ;  in  some  parts  even  30°;  and  floating  ice  has  occasionally  teen  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  6o°  south  latitude,  the 
snow  lies  on  the  ground,  at  the  sea  side,  throughout  the  summer.  The  line  of 
perpetual  congelation  is  three  miles  above  the  surface  at  the  equator,  where  the 
mean  heat  is  84°;  at  Teneriffe,  in  latitude  fe8°,  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  com- 
parison of  various  observations,  the  mean  temperature  should  be  31°.  In 
London  the  mean  temperature  is  50"* ;  at  Rome  and  at  iNlontpelier,  a  little 
more  than  60° ;  in  the  island  of  Madeira,   70°;  and  in  Jamaica,  80°. 

There  are  frequently  some  local  causes  of  heat  and  coldM'hich  are  independ- 


ON    CLIMATES    AND    WINDS,  701 

cnt  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  observation,  the 
thermometer  frequently  rises  a  degree  or  two  almost  instantaneously.  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  ahigher  temperature  than  the  earth.  Mr,  Six  has  observed  that  in 
clear  weather,  the  air  is  usually  some  degrees  colder  at  night,  and  warmer  by  day, 
close  to  the  ground,  than  a  few  feet  above  it;  but  that  in  cloudy  weather  there 
is  less  difference:  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  atmosphere. 

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  re- 
gularity can  be  observed  in  their  recurrence,  it  may  in  most  cases  be  suffi- 
ciently 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  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 

VOL.    I.  4s 


^<S|^  I.KCTOllE  XVI. 

greatest  at  the  equator,  and   is  directed  eastwards,  the  air  coming- 'from  thfc 
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  -eaist  to  north  west.     Dr.  Hjrlley  sup- 
posed that  the  air  was  made  in  some  measure  tofoilowthe  son  roimd  rhecartA, 
simply  by  means  of  the  expansion  of  the   atmosphere,   which  takes  place  im- 
mediately  under  him,  and  accompanies  him  round  the  globe  ;  but  it  does 
rot  seem  evident  that  the  air  could  have  any  greater  tendency  to  follow  the 
sun  than  to  meet  him.     Astronomers  have,  however,   deduced  an   additional 
cause  for  an  easterly  wind  from  the  attractions  of  the  moon  and  of  tlie  sun, 
■which -appeair,  from    the  laws  of  gravitation,  to   liave  a  slight  tendency  to 
retard  the  rotatory  motion  of  the  atmosphere:  and  a  similar  instance  has 
been  observed  in   the  motions  of  the  atmosphere  of  the  planet  Jupiter,   by 
means  of  the  appearances  of  spots  of  different  kinds  on  his   disc,  some  of 
which   seem  to  revolve  less  rapidly  than    the  body  of  the  planet.     At  so 
great  a  distance,  the  influence  of  the  sun's  heat  must  be  comparatively  incon- 
siderable, and  the  want  of  a  tendency  in  the  spots  towards  the  equator  appears 
to  show,  that  the  atmosphere,  iii  which  they  float,  is  not  put  in  motion  by  tlie 
same  causes,  which  we  have  supposed  to  be  most  concerned  in  the  production 
of  our  own  trade  winds.     It  has  been  remarked  that  the  friction  of  the  atmo- 
sphere, thus  retarded  by  the  attraction  of  the  sun  and   moon,   must  in  the 
course  of  ages  have   impaired   the  uniformity  of  the  earth's  diurnal  motion  ; 
and  it  has  been  observed,  on  the  other  hand,   that  even  this  effect  would  be 
partially  counteracted  by  the  gradual  filling  up  of  valleys,   by  means  of  the 
descent  of  the  superficial  parts  of  mountains,   which,  at  a  greater  distance 
from  the  centre,   were  revolving  with  a  rapidity  somewhat  |>reater  than  the 
valleys  in  which   they  are  deposited;  but  probably  neither  of  these  changes 
would  become  sensible  in  millions  of  years. 

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  nor.h  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  declination,  accordingly  as  different  parallels  of  latitude  become  in 
succession  somewhat    hotter    than    the    neighbouring    parts.     Where  the 


ON    CLIMATES    AND    VtKDS.  70f 

northern  and  southern  currents  meet,  their  joint  effect  mu«t  naturally  be  to 
produce  a  due  east  wind;  but  in  some  parts  of  the  ocean,  temporary  calms 
and  irregular  squalls  have  been  observed  to  take  place  of  this  easterly  wind, 
■which  generally  prevails  in  the  neutral  parts  near  the  equator. 

The  tliird  fact,  that  is,  the  frequency  of  westerly  winds  between  the  ^-^'^ESg  ^ 
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  ^*^/:/>r, 
we  have  liitherto  neglected,  and  which  passes,  in  the  upper  parts  of  the 
atmosphere,  from  the  equator  each  way  towards  the  poles,  and  whiJi,  being 
the  converse  of  the  trade  wind,  must  be  a  south  west  and  north  west  \viud> 
in  the  different  hemispheres,  becomes  here  sufficiently  cool  to  descend  and  mix 
with  tke  lower  parts  of  the  atmosphere,  or  to  carry  them  along  by  itslateral  fric- 
tion; and  while  it  descends  to  complete  the  circle,  necessary  for  supplying  the 
current  to  tlie equator, its  motion  with  respect  to  tlie  horizon  nuist  btcomeat  a 
certain  time  due  M-est,  since  the  cause  which  stops  its  progress  n.rthwdnis,  has 
no  tendency  to  impede  its  motion  eastwards.  The  outN\ard  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  southwest  winds  are 
more  common  in  our  latitudes  than  south  east,  and  north  east  than  northwest. 

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  circumstancey  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  declination,  the  heat  on  this 
continent,  a  little  north  of  the  tropic,  is  very  intense,  and  the  general 
current  is  consequently  towards  the  north.  The  air,  therefore,  coming 
from  douth  latitudes  towards  the  equator,  becomes,  on  account  of  tlje  defi- 


704  •    LECTURE    LVI. 

ciency  of  rotatory  motion,  a  south  east  wind,  as  usual,  which  is  found  to 
prevail  between  Madagascar  and  New  Holland,  as  far  as  the  equator.  In 
consequence  perhaps  of  friction  in  its  passage,  it  gradually  loses  its  impetus 
towards  the  west,  and  at  the  equator  is  nearly  a  south  wind  :  but  in  proceed- 
ing 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  particular  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  o»her  side  of  the  equator.    (Plate  XLII.  XLIII. ) 

The  last  fact  is  the  simplest  of  all.  The  land  and  sea  breezes  are  produced 
by  the  ascent  of  the  air  over  the  land  in  the  day  time,  while  the  land  is 
hotter  than  the  sea;  and  jits  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 
generally  opposite  to  that  of  the  trade  winds  ;  but  tornados,  which  are  less 
regular  hurricanes,   originate  indift'erently  from  every  quarter. 

The  variations  of  the  weight  of  the  air,  which  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 
neighbourhood  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  sometimes  as  low  as  28  inches,  but  never  higher  than  31.  We  have 
already  seen  that  the  elevation  of  any  place  above  the  lea  reduces  the  height 
^f  the   barometer  according  to  a  law  which  is  determined  by  the  general 


ON    CLIMATES    AND   WINDS.  705 

properties  of  elastic  fluids :  thus,  at  an  elevation  of  1  mile  above  the  sea,  the 
mean  height  of  the  barometer  is  244-  inches,  and  at  £  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,  con- 
clusions may  be  drawn  from  it,  which  may  in  many  cases  be  of  considerable 
utility:  and  it  has  even  been  applied  with  success,  by  some  late  navigators,  to 
the  prediction  of  changes  of  wind,  sit  times  when  they  could  not  have  been 
suspected  from  any  other  circumstances. 


yotf 


LECTURE  LVII. 


ON    AQtrEOFS    AND    IGNEOUS    METEORS. 

J- HE  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  un- 
concerned 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  va- 
pour, 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  tempe- 
rature, 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.  Sometimes  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  un- 
connected 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,  and  Dalton,  to  be  wliolly  inde- 
pendent of  the  nature,  the  density,  or  even  the  presence  of  the  air  or  gas 


ON    AQUEOUS    AKD    IGNEOUS    METEORS,  707 

Av^lch  that  ■space  contains:  and  we  may  easily  imagine  that  the  smallest  dis- 
taitce,  at  which  the  particles  of  water,  constituting  vapour,  can  exist,  with- 
ou't  coming  within  the  reach  oftiieir  mutual  coliesion,  is  the  same,  whatever 
Ocher  ^particles  .«ia\  be  scattered  through  the  intervening  space.  It  appears, 
howciver,  more  consistcnit  with  sofiie  cx;perimcnts, to  suppose, that  the  presence 
of  air  of  the  usual  density. allows  the  particles  of  water  to  approach  a  little 
nearer  together  without  coliering,  so  that  the  utmost  quantity  of  moisture, 
that  can  be  contained  iu  a  cubic  foot  of  air  at  a  given  temperature,  is  not  ex- 
actly the  same  as  would  make  a  cubic  foot  of  pure  vapour,  but  always  in  a 
certain  proportion  to  it;  and  it  seems  to  follow,  from  the  experiments  of 
Saussure,  compared  with  those  of  Pictet,  ihat  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,  iu  the  neighbourhood  of  the  surface  of  the  water,has  become 
thus  saturated  with  moisture,  the  evaporation  proceeds  very  slowly,  the  va- 
pour being  precipitated  as  soon  as  it  rises;  but  if  the  air  be  continually 
changed,  so  that  the  moistened  portion  may  be  removed,  and  dry  air  substi- 
tuted for  it,  the  process  will  be  greatly  expedited ;  and  such  a  change  may  bp 
effected  cither  by  wind, or  by  the  natural  circulation, occasioned  by  any  eleva- 
tion of  temperature  crmmunieated  by  the  water  to  the  neighbouring  air;  but 
when  this  circulation  is  jjievented,  the  evaporation  is  much  diminished,  al- 
though the  temperature  may  be  considerably  elevated.  Iu  moderate  exposures, 
theVlepth  of  the  quantity  of  water,  evaporating  in  24  hours  from  any  surface,  is 
'ex pressed, ^according  to  Mr.  Dalton's  experiments,  by  the  height  of  the  column 
of  mercury  ccjuivalent  to  the  force  of  steam  at  the  given  temperature,  deduct- 
ing, however,  theeffect  of  the  elasticity  of  the  moisture  already  existing  in  the 
air. 

*Since  the  quantity  of  moisture,  which  the  air  is  capable  of  receiving,  is 
■grta.tev  ns  iis  .teiinperature  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  r'epositfd.  Thus,  if  we  take  a  glass  of  cold  water,  and 
add  to  it  some  common  salt,  or  some  muriate  of  lijrie,  we  may  cool  the  air 
near  it  so  TnnciJ,  as  to  cause  it  to  deposit  a  pait  of  its  moisture  on  the  glass: 
and  by  measuiing  the  temperature  uf  the  water  when  the  precipitation  begins. 


703  LECTURE    LVir. 

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. 
tlie  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  corre- 
sponding 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 
nioister  than  this,  and  the  mean  evaporation  of  all  England  is,  according  to 
Air.  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  over  it  are  drier;  con- 
sequently its  evaporation  is  greater  than  that  of  the  Atlantic,  and  its  specific 
gravity  is  increased  by  the  increased  proportion  of  salt;  so  that  at  the  straights 
of  Gibraltar,  a  current  runs  inwards  at  the  surface  and  outwards  near  the  bot- 
tom, 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  con- 
tinual 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  remarka- 
ble 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. 

f» 

Experiments  on  the  deposition  of  moisture,  like  those  of  Mr.  Dalton,  arc 
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  re- 
mains 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  construc- 
tion of  hygrometers  depends;  and  it  is  probably  by  a  property  somewhat  si- 


ON    AQUEOUS    AND    IGNEOUS    METEORS.  70^ 

inilar,  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  substance  whicli  has  a  very  weak  attrac- 
tion 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  protects 
also  the  opposite  side  of  the  glass  from  the  deposition  of  dew;  and  Mr.  Bene^ 
diet  Provost  has  shown,  that  in  general,  whenever  the  metal  is  placed  on  the 
M'armer  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  re- 
ceives the  humidity,  nor  permits  its  deposition  on  the  glass;  but  that  the  ad- 
dition of  a  second  piece  of  glass,  over  the  metal,  destroys  the  effect,  and  a  se- 
cond piece  of  metal  restores  it.  It  appears  that,  from  its  properties  with 
respect  to  radiant  heat,  the  metallic  surface  produces  "these  effects,  by  pre- 
venting 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  instruments 
'have  hitherto  remained  in  a  state  of  great  imperfection.     A  sponge,'  a  quan- 
tity 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,   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  in- 
dex. Buttheextensionofahair,orofaslipof  whalebone,  which  have  been  employ- 
ed by  Saussure  and  Deluc,  appear  to  be  more  certain  and  accurate  in  their  indi- 
cations.    The  hair  hygrometer  acquires  more  speedily  the  degree  correspond- 
ing 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  hygrome- 
ter appears  to  express  a  greater  change  upon  immersion  in  water  than  from  the 
effect  of  the  moistest  transparent  air,  which  has  also  been  considered  by  some 
as  an  imperfection.     Both  these  instruments  are  impaired  by  time,  and  ac- 
(juire  contrary  errors,    so  that  a  mean  between  both  is  more  likely  to  be  cor- 
rect 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 

VOL.    I.  4t 


710  lECTUBE    LVII. 

scale  than  eitlier  of  them.    Mr.  Leslie  employs  a  very  delicate  thermometer,  of 
which  the  bulb  is  moistened,  for  measuring  the  dryness  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  consider- 
able 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  deposition  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  hygro- 
meter 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,  saturated 
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  mois- 
ture by  means  of  the  presence  of  water.  It  follows  from  the  properties  of  mois- 
ture thus  determined,  that  if  any  two  portions  of  perfectly  humid  air,  at  differ- 
ent 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  tempera- 
ture must  be  46°;  if  they  are  saturated  with  moisture,  they  must  contain  8 
grains  of  water  when  separate;  but  when  mixed  they  will  be  too  cold  by  2°  to 
contain  the  same  quantity;  since  air  at  48°  can  only  contain  4  grains  for  each 
foot;  and  it  has  been  supposed  that  such  mixtures  frequently  occasion  a  pre- 
cipitation in  nature.  Thus,  it  often  happens  that  the  breath  of  an  animal, 
which  is  in  itself  transparent,  becomes  visible  when  mixed  with  a  cold  atmo- 


ON    AQUEOUS    AND    IGNEOUS    METEOKS,  711 

Sphere;  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  suspended,  in 
the  form  of  a  mist  or  of  a  cloud :  sometimes,  however,  it  appears  to  be  at  once 
deposited  on  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  g 
distinct  aggregates. 


The  dew,  which  is  commonly  deposited  on  vegetables,  is  paitly  derived,  TiL.^/f^nr;.^i^  -^ ■  i}' 
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  morning,  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  Avithin,  but  sometimes  without,  they  call  givre. 

Mists  are  said  to  consist  sometimes  of  other  particles  than  pure  water: 
these  are  called  dry  mists,  and  they  have  been  swpposed  to  blight  vegetables. 
Such  mists  are  sometimes  attended  by  a  smell,  resembling  that  which  is  occa- 
sioned 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  4:he  atmosphere.  There  must  indeed  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  velocity;  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  iii visible  as  separate  drops:  the  least  particle, that  could 


712  LKCTURE    rVII. 

be  discovered  by  the  naked  eye,  being  such  as  would  fall  with  a  velocity  of  about 
a  foot  in  asecond,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  experiments 
made  on  a  much  larger  scale,  and  their  descent  consequently  much  slower. 

When  the  particles  of  a  mist  are  united  into  drops  capable  of  descendino- 
■with  a  considerable  velocity,  they  constitute  rain ;  if  they  are  frozen  durino- 
their  deposition,  they  exhibit  the  appearance  of  a  perfect  crystallization,  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  de- 
scent through  very  dry  air,  they  acquire  the  character  of  hail,  which  is 
often  observed  in  weather  much  too  hot  for  the  formation  of  snow. 

It  cannot  be  doubled  but  that  there  is  a  connexion  between  the  descent  of 
the  barometer  and  the  fall  of  rain;  but  no  satisfactory  reason  has  yet  been  as- 
signed 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  ob- 
served. The  immediate  dependence  of  rain,  or  of  any  other  atmospherical 
phenomena,  on  the  influence  of  the  moon,  appears  to  be  rendered  highly  im- 
,  probable,  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  suf- 
ficiently 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  up- 
per regions  of  the  atmosphere,  and  may  be  redissolved  by  the  warmer  air  be- 
low; but  when  they  descend  in  an  equal  degree  among  mountains,  they  fall 
on  the  earth;  and  besides  the  quantity  of  water  which  they  furnish  for  vege- 
tation, and  that  which  is  carried  off  by  evaporation,  they  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  na 
means  the  principal  sources  of  rain  in  ordinary  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 


ON    AQUEOUS    AND    IGNEOUS    METEOKS.  713 

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  arethecausesoftheinundationoftheNIle;  theylastfrom 
April  to  September ;  but  for  the  fiist  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  pf  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.  Vicissitudes 
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  com- 
municating with  the  earth,  in  the  same  manner  as  bodies  which  have  been 
electrified  by  artificial  means;  they  also  sometimes  produce,  in  the  neighbour- 
ing 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  t& 
the  more  remote,  may  be  fatal,  without  any  appearance  of  an  immediate 
discharge,  at  the  place  where  the  animal  stands. 


Tl^  lECTUnjf     LVII. 

We  can,  however,  by  no  means  precisely  ascertain  in  what  manner  all  tlie 
electrical  phenomena  of  the  atmosphere  are  produced.  It  appears  from  the 
experiments  of  Beccaria  and  Cavallo  that  the  air  is  in  general  positively 
electrical,  and  most  so  in  cold  and  clear  weather;  in  cloudy  weather  more  slight- 
ly: and  that  during  rain,  the  air  is  generally  in  a  negative  state.  Mr.  Read 
has  found  that  air  charged  with  putrid  vapours  of  any  kind,  and  in  particular 
the  air  of  close  rooms,  is  almost  always  negatively  electrified.  The  electri- 
city 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  con- 
tinued along  the  string,  we  may  frequently  obtain  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,  insertf^d  in  the  Philosophical 
Transactions.  The  circumstance  happened  in  September  1780,  at  East 
liourn,  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  succes- 
sively into  the  sea,  and  one  in  particular,  appearing  like  an  immense  sky 
rocket,  broke  against  the  front  of  the  house  in  diiferent  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:  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  fur- 
niture 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  wnndows,  were  struck  dead  :  both  the  bodies  were 
turned  black;  one  of  them  had  a  wound  near  the  heart;  and  neither  of  theih 
became  stilf  after  death;   a  third  servant,  who  was  a  little  behind  one  of  them, 

4 


ON    AQUEOUS    AND    IGNEOUS    METEORS.  715 

escaped  with  the  loss  of  a  telescope,  which  he  held  in  his  hand,  and  M'ith 
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  eflects  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  pro- 
perly fixed,  they  afford  a  degree  of  security  which  leaves  very  little  room  for 
apprehension.    A  conductor  ought  to  be  continued  deep  into  the  earth,  or  con- 
nected 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  been  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,  on  the  contrary,   showed  that  a  ball  is  often  struck  in  preference 
to  a  point.   But  it  has  been  observed,  that  if  a  poiat  attracts  the  lightning  from 
a  greater  distance,   it  must  protect  a  grea/ter  extent  of  building.      It  is  easy 
to  show,   by  hanging  cotton  or  wool  on  a  conductor,  that  a  point  repels  light 
electrical  bodies,  and  that  a  pointed   conductor  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  efiect  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  conductors.     The  neighbourhood  of  windows, look, 
ing  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. 


716  LECTURE    LVII. 

The  phenomena  of  waterspouts,  if  not  of  electrical  origin,  appear  to  have 
some  connexion  with  electrical  causes.  A  waterspout  generally  consists  of  laro-e 
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  horizon- 
tally, accompanied  in  general  hy  a  sound  like  that  of  the  dashing  of  waves. 
Spouts  are  sometimes,  although  rarely,  ohserved  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  perhaps  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  elec- 
trical nature:  the  phenomenon  is  certainly  connected  with  the  general  cause 
pf  magnetisrn  ;  the  primitive  beams  of  light  are  supposed  to  be  at  an  eleva- 
tion of  at  least  50  or  100  miles  above  the  earth,  and  every  where  in  a  direc- 
tion parallel  to  that  of  the  dipping  needle ;  but  perhaps,  although  the  sub- 
stance 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  transmitted  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  sur- 
face. There  are  however  some  circumstances,  which  indicate  such  a  con- 
nexion between  the  state  of  the  atmosphere  and  the  approach  of  an  earthquake, 
as  cannot  easily  be  explained  by  any  hypothesis. 


ON    AQUEOUS    AND    IGNEOUS    METEORS.  7J7 

Tlife  shocks  of  earthquakes,  and  the  eruptions  of  volcanos,  are  in  all  pro- 
bability modifications  of  the  effects  of  one  common  cause;  the  same  coutitrie* 
are  liable  to  both  of  them;  and  where  the  agitation  produced  by  an  earth* 
quake  extends  further  than  there  is  any  reason  tosuspectasubterraneousconimo* 
tion,  it  is  probably  propagated  through  the  earth  nearly  in  the  same  manner  a*  A 
noise  is  conveyed  through  the  air.  Vokanos  are  found  in  almost  all  parts  of 
the  world,  *  but  most  commonly  in  the  neighbourhood  of  the  sea;  and  espe- 
cially 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  Coto- 
paxi.  The  subterraneous  fires,  which  are  continually  kept  up  in  an  open 
volcano,  depend  perhaps  in  general  on  suU'ureous  combinations  and  decom- 
positions, like  the  heating  of  aheap  of  wet  pyrites,  or  the  union  of  sul- 
fur 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.  Tlie  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  i» 
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  ignited  materials,  may  in  some  measure  be  under- 
stood, from  the  accidents  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  40000 
persons,  continuing  its  ravages  for  more  than  three  months ;  it  destroyed 
the  towns  and  villages  occupying  a  circle  of  nearly  50  miles  in  diame- 
ter, lying  between  33  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  Imve  been  either  immediately  under  the  towa 

VOL.  I.  4  u 


718  LECTURE    LVII. 

of  Oppido,  in  the  centre  of  this  circle ;  or  under  some  part  of  the  sea,  be- 
tween 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  propagated  somewhat  like  a  wave,  from 
■west  to  east:  besides  this,  the  ground  had  also  a  horizontal  motion  backwards 
and  forwards,  and  in  some  measure  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;  andin  many  cases  large  portions  of  them  were  separated, 
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"  was  thrown  into 
the  sea,  that  it  raised  an  immense  wave,  which  carried  off  more  than  2000 
inhabitants  who  were  collected  on  the  beach,  and  even  extended  its  formi- 
dable 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  Jeas  violent.     Open  volcanos  continually 

4 


ON    AQUEOUS    AND    IGNEOUS    METEORS,  7I9 

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  jNIarch,  I767,  Vesuvius  began  to  throw  out  a  considerable  quantity  of  ashes 
and  stones,  which  raised  its  summit  in  the  course  of  theyearnoless  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  tlirough  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  volcano,  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  accompanied  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  mountain,  and  remained  hot 
for  several  weeks.  In  1794  a  still  more  violent  eruption  occurred:  it  was 
expected  by  the  inhabitants  of  the  neighbourhood,  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  co- 
piously, 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  vine- 
yards 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 


720  LECTUUE    LVII. 

into  the  sea;  yet  notwithstanding  the  frequency  of  such  accidents,  the  in- 
habitants had  so  strong  a  predilection  for  their  native  spot,  that  they  refused 
the  offer  of  a  safer  situation  for  rebuilding  their  houses. 

Convulsions  of  these  kinds  must  have  very  materially  influenced  the  dis" 
position  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  maintaining  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  materi- 
ally concerned  in  producing  the  changes  which  have  happened  to  the  solid 
parts;  but  it  may  be  difficult  for  them  to  confute  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  concerned,  in  giving  to  minerals  of  dif- 
ferent kinds  tlieir  actual  form;  although  on  the  whole  it  seems  probable  that 
the  operation  of  heat  has  been  much  more  limited  than  that  of  aqueous  solu- 
tions and  precipitations.  Mr.  Davy  has  also  very  justly  inferred,  from  his 
experiments  with  the  battery  of  Volta,  that  the  effects  of  the  electricity  ex- 
cited 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  convul 
sions  have  actually  happened  to  the  earth,  are  too  well  known  to  require 
minute  examination :  the  variety  of  fossil  substances,  many  of  them  ma- 
rine productions,  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;  al- 
though some  philosophers  are  of  opinion,  that  such  of  the  primary  mountains  as 
are  above  6  or  7OO  feet  high,  have  never  been  wholly  covered  by  the  sea.  It 
is  not  at  ail  easy  to  explain  the  change  of  climate,  which  some  of  these  cir- 
1 


ON    AQUEOUS    AND    IGNEOUS    METEOltS.  731. 

r  *  ■  ■ 

cumstaiices  appear  to  indicate;  the  remains  of  animals  inhaijiting  hot  countries, 
and  the  marine  productions  of  hot  climates,  which  are  frequently  found  in  - 
high  northern  latitudes,  would  induce  us  to  suspect,  that  the  position  of  the  ' 
earth's  axis  was  at  a  former  time  very   different  from  its  present  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  apprehensive  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  attracted  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  has  in- 
croached  in  particular  parts,  and  retired  from  others;  and  the  mouths  of 
large  rivers,  running  through  low  countries,  have  often  been  variously  modi- 
fied, 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  consider- 
ably 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  Missis- 
sippi 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  direc- 
tions, 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 
nmch  as  100  or  200,  but  usually  about  50;  their  velocity  is  commonly 
about  20  miles  in  a  second,  wliich  differs  very  little  from  that  of  the  earth 


72S  lECTORE    LVII. 

in  its  orbit.  The  rapidity  of  their  motion,  as  well  as  its  occasional  deviation 
from  a  right  line,  has  generally  been  considered  as  a  reason  for  supposing 
that  they  depend  on  electricity;  but  the  opinion  is  by  no  means  fully  esta- 
blished. 

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.  Mr.  Howard  has  ascer- 
tained 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  continent,  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  im- 
mediately before  them,  and  even  their  friction  might  easily  produce  enough 
of  electric  light,  to  render  them  visible  in  the  dark.  Among  many  such  sub- 
stances projected  from  the  moon,  it  is  probable  that  a  few  only  would  be  di- 
rected towards  the  earth,  and  many  more  would  be  made  to  revolve  in  ellipses 
round  it,  and  become  little  satellites,  too  small  for  human  observation,  ex- 
cept when  they  enter  far  enough  into  the  atmosphere  to  produce  an  appear- 
ance of  light,  resembling  that  of  a  shooting  star ;  but  it  is  scarcely  probable 
that  their  velocity  could  ever  be  at  all  comparable  with  that  which  has  been 
attributed  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  de- 
scription 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. 


72S 


LECTURE   LVIII. 


ON    VEGETATION. 


It  may  appear  idle  to  some  persons,  to  attempt  to  reduce  the  outlines  of  na- 
tural history  into  so  small  a  compass,  as  is  required  for  their  becoming  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  sci- 
ence, even  in  a  much  longer  time  than  we  shall  bestow  on  it.  But  many  na- 
turalists 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  sci- 
ence, than  might  have  been  told  them  in  a  few  hours,  by  persons  who  had  ob- 
served 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  systematical  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  ac- 
cretion or  external  growth  only.  When  mineral  substances  crystallize,  they 
often  imitate  the  form, and  almost  assumetheexternalappearanceof  vegetables: 
but  their  particles  are  never  extended  to  admit  others  between  them,  and  to 
be  thus  enlarged  in  all  their  dimensions  ;  their  growth  is  only  performed  by 
the  addition  of  similar  particles,  upon  the  surface  of  those  t' at  have  been  al- 
ready deposited. 

Vegetables  derive  their  existence,  by  seeds,  or  otherwise,  from  a  parent 


724  LECTURE    LVni. 

stock,  their  parts  arc  extended  and  evolved  from  within,  and  they  imbibe  their 
nutriment  by  superficial  absorption  only.  There  is  indeed  in  the  crystalliza- 
_tion  of  minerals  a  slight  resemblance  to  a  reproduction  or  generation,  wlien  a 
small  portion  of  the  substance  serves  as  a  basis  for  the  formation  of  subse- 
quent 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  containing  within  it- 
self the  simplest  rudiments  of  a  new  individual,  which  is  afterwards  evolved 
and  enlarged.  Sometimes,  however,  vegetables  are  propagated  by  means  of 
bulbs,  or  by  spreading  roots,  by  slips,  or  by  ingrafted  scions,  Avithout  a  seed  de- 
tached 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  sometimes,  where  they  are  without  roots,  their  nu- 
triment 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  vegetables,  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  imaaine  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  distinction  would  supersede  every  other: 
but  in  many  cases  it  is  extremely  difficult  to  say  where  sensation  is  present, 
and  where  irritation  only  produces  the  same  apparent  effects.  We  cannot  be 
sure  that  the  hydra,  or  fresh  water  polypus,  or  the  trichurus  sol,  an  animal- 
cule described  by  Dr.  Shaw,  suffers  any  sensation  of  pain  when  it  is  diviiled 
into  two  parts;  at  least  the  pain  seems  to  agree  remarkably  well  with  its  con- 
stitution, 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 
sensitive  plants  close  or  depress  their  leaves,  in  consequence  of  agitation  or  of 


ox    VEGETATION.  79,5 

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  supported  by  the 
wall  only,  has  concentrated  all  its  force  in  tbe  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  far  as  wc  know,  the 
same  explanations  might  be  applied  to  some  animal  motions:  and  although  it 
is  very  possible  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  vege- 
tables; animal  substances  commonly  containing  greater  proportions  of  azote 
or  nitrogen,  and  of  phosphoric  acid;  but  there  are  some  exceptions  to  this  ob- 
servation; thus  the  carica  papaya,  or  papaw,  contains  nearly  the  same  prin- 
ciples 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,  W£ 
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. 

VOL.  I.  4  X 


72^  LECTURE    LVIII. 

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  lit- 
tle diversified,  although  little  understood.  With  respect  to  the  apparent  per- 
fection 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  resemblance  to  the  flowers  of 
other  vegetables,  but  on  the  whole,  the  class  appears  to  form  one  of  the  con- 
necting links  between  the  three  kingdoms  of  nature;  its  physiology  is  proba- 
bly 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  dispositions  of  the  organs  of  fructifica- 
tion, while  they  have  all  a  general  resemblance  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  subjected 
to  peculiar  chemical  and  vital  actions,  and  exposed  in  the  leaves  to  the  in- 
fluence 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,  and 
undergoing  a  chemical  fermentation,  in  which  oxygen  is  ab*orbed,  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  some- 
times 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  be- 

3 


OK    VEGETATION.  727 

ing  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   sur- 
rounded by  the  woody  part,   composed  of  fibres   more  or  less  strongly  com- 
pacted together,  but  not  actually  ramifying  into  each  other  in   any  great 
degree,  although  there  is  reason  to  suspect  some  lateral  communications  bcf 
tween  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  vege-- 
table;  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.     Th« 
wood  consists  of  a  number  of  concentric  layers  or  strata,   formed  in  succes- 
sive 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  ia- 
as  many  difterent  years  ;  the  external  parts  usually  cracking,  and  allowing  us 
at  their  divisions   to  observe  their  number,   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  ofiice 
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.  Desfontaines  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  vegeta- 
bles: 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  arc  composed  of  single  threads  wound  into  a 


728  iECTUKE    LVIII. 

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  containing,  during 
the  life  of  the  plant,  an  aqueous  fluid:  and  they  are  probably  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  generally  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  difterent 
kinds  of  plants;  for  the  sap  is  nearly  the  same  in  all,  at  least  it  is  independ- 
ent of  the, gums  and  resin,  which  often  distinguish  particular  plants;  it  con- 
tains a  certain  portion  of  mucilage,  and  probably  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  dif- 
ferent kinds  of  vessels.  The  circulation  of  the  sap  is  not  completely  under- 
stood; 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  sup- 
ported 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  contact  with 
them.  The  growth  of  every  tree  takes  place  at  the  internal  surface  of  the 
bark,  not  only  the  bark  itself  being  formed  there,  but  the  wood  also  being 
deposited  by  the  bark;  for  Pr.  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  experiment  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 


ON    VEGETATION.  729 

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  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  some- 
what analogous  to  lungs,  or  rather  to  the  gills  of  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 i'resh   wood  or  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  secrcj- 
tion  of  the  alburnum,   and  of  the  internal  la\ers  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  in- 
ternal parts  of  the  wood,   having  served  the  purposes  of  vegetation,  are  hard- 
ened,  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  gra- 
vity 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  dia- 
meter 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,  however, 
that  the  nature  of  the  plants  be  not  too  diiTerent.     Something  of  the  same 


73b  LECTURE  i.viir. 

kind  occurs  in  animal  life,  Avliere  a  tooth  has  been  transplanted  intb  tht 
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  mois- 
ture, or  nipped  by  frost,  their  leaves  and  branches  often  die^  and  if  the 
plants  recover  their  vigour,  a  separation  is  affected  by  a  natural  process,  re- 
sembling 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 
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  ex- 
cluding 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  in- 
creases its  fertihty ;  its  force  being  more  concentrated,  by  lopping  off  its  use- 
less branches  and  leaves,  it  produces  a  larger  quantity  of  fruit,  with  the  juices 
which  would  have  been  expended  in  their  nourishment. 

The  Linnean  system  of  vegetables  is  confessedly  rather  an  artificial  than  a 
natural  one;  but  it  is  extremely  well  adapted  for  practice,  and  its  universal 
adoption  has  been  productive  of  the  most  important  improvements  in  the  sci- 
ence of  botany.  Of  the  24  classes  into  which  Linn^>  has  divided  the  vegeta- 
ble 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  niimber  of  the  stamina,  or  filaments, 
surrounding  the  seed  vessel;  and  the  orders  are  deduced  in  a  similar  manner 


ON    VFGETATIOV.  731 

from  the  number  of  pistils,  or  little  columns  immediatefy  connected  Math  the 
seed  vessel;  and  denominated  nionogyaia,  digynia,  and  so  foith,  as  far  as  po- 
lygynia.  These  classes  dift'er  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  M'ith  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  tvv^o  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,  tetradynaniia,  is  a  class 
of  plants  strongly  characterized  even  by  chemical  properties;  two  of  the  fila- 
ments 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,  somewhat  resembling  a 
butterfly  in  their  form,  like  the  pea,  and  other  leguminous  plants,  the  broom, 
the  furze,  and  the  acacia.  The  18th  class,  polyadelphia,  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  syngenesiai 
sunflowers,  daisies,  and  artichokes,  are  familiar  examples  of  the  plants  of  this 
class.  The  20th  class,  gynandria,  though  it  contains  the  natural  family  pf 
the  orchides,  has  been  omitted  by  some  late  botanists;  here  the  filaments  arc 
fixed  on  the  pistil ;  or  more  properly,  in  the  arums,  within  the  pistils.  The 
three  following  classes,  monoecia,  dioecia,  and  polygamia,  difter  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  mare  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  exceeilingly 
numerous;  the  families  of  ferns,  mosses,  algae,  or  membranous  weeds,  and 


732  IICTURE    LVIII. 

fungi  or  mushrooms,  fill  up  its  extensive  departments;  some  have  also  sepa-  * 
rated  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;  Avhile  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  cryptogamic  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  dis- 
tinct classes.  The  plants  which  have  two  cotyledons  follow,  and  are  divided 
into  apetalous,  monopetalous,  and  polypetalous,  from  distinctions  respect- 
ing the  corolla  or  flower  leaves,  which  are  somewhat  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  natu- 
ral orders  of  plants;  such  vegetables  as  nearly  agree  in  their  habits  and  ap- 
pearances 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  advan- 
tage: 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  defini- 
tions. 


753 


LECTURE  LIX. 


ON    ANIMAL    LIFE. 

The  functions  of  animal  life  are  not  only  more  complicated  in  the  sanu' 
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  Linnd  for  the  first  enlargement  of 
our  views  of  the  different  classes  of  animals,  and  perhaps  for  the  most  conve- 
nient arrangement,  of  the  animal  kingdom ;  although  his  method  has  never 
been  universally  adopted  by  our  neighbours  on  the  continent. 

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  transpar- 
ent fluid,  or  a  red  blood,  into  the  extremities  of  the  veins  ;  through  which  it 
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 ;  but  insects  have  legs  furnished  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  cavities,  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  Linn6  into  different 
VOL.  I.  4y 


734  LECTUBfe    LIX. 

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  cetaceous 
fishes,  which  is  known  by  the  fins  that  are  found  in  the  place  of  feet.  The 
distinctions  of  the  teeth  are  somewliat  minute,  but  they  appear  to  be  con- 
nected 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  elejihant,  the  rhinoceros,  the  ant  cater,  and  the 
ornithorhynchus,  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  kan- 
garoo also  belong  to  this  order,  and  the  kangaroo  feeds  on  vegetables, 
although  its  teeth  are  like  those  of  carnivorous  animals.  The  fourth  order, 
glires,  comprehends  beavers,  mice,  s({uirrels,  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  up- 
permost, 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  (juadruped, 
and  like  the  cotyledons  of  young  plants,   until  the   system   is   become  sulfi- 


ON    ANIMAL    LIFE.  735 

ckntly  strong  for  extracting  its  own  foot!  oat  of  the  ordinary  nutriment  of 
the  species. 

Birds  are  divided,  according  to  the  form  of  their  bills,  into  six  orders: 
accipitres,  as  eagles,  vultures,  and  hawks;  picae,  as  crows,  jackdaws,  hum- 
ming 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  circulation 
may  continue  without  interruption  in  other  parts,  although  it  may  be  im- 
peded 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  ev-en  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 
tlieir  parts  are  not  yet  developed,  as  we  observe  in  the  tadpole;  and  in  this 
respect  they  resemble  the  class  of  insects.  They  are  now  universally  consider- 
ed 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  serpen tes  are  without  feet.  Most  of  the  serpentes 
are  perfectly  innocent,  but  others  have  fangs,by  which  they  instila  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  stiipe  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  indiiferently 


736  LECTURE    LIX. 

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;  jugularis,  as  the  cod;  thoracici,  as  the 
sole  and  perch,  and  abdominales,  as  the  salmon  and  pjke :  distinctions 
which  appear  to  be  perfectly  artificial,  although  useful  in  a  systematic 
'  arrangement.  Tiie  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  ofvthe  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  ramified  tracheae; 
and  if  these  are  stopped  with  oil,  they  are  suflfocated.  Instead  of  bones,  they 
have  a  hard  integument  or  shell.  Their  mouths  are  formed  on  constructions 
extremel)-  various,  but  generally  very  complicated  :  Fabriciushas  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  Avhich  such  characters  can  be  rendered  really  useful,  is  when  they  are 
employed  in  the  subdivision  of  the  genera,  as  determined  from  more  con- 
spicuous distinctions.  Insects  have  most  frequently  jaws,  and  often 
several  pairs,  but  they  are  always  so  placed  as  to  open  laterally  or  horizon- 
tally. 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  tlieir 

2  .   ' 


ON    ANIMAL    LIFE. 


IZ'T 


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,  scor- 
pions, millepeds,  centipeds,  mites,  and  monoculi.  The  monoculus  is  a  genus 
including  the  little  active  insects  found  in  pond  water,  w'hich  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  tbetti-^,^^>i^r,  '^^■^ 
are  not  deficient  either  in  magnitude  or  in  beauty.     The  most  natural   divi-- 


■'?^w 


sion  of  vermes  is  into  five  orders;  the  intestina,  as  earthworms  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  com- 
pound animals,  united  by  a  common  habitation,  which  has  the  general  ap- 
pearance of  a  vegetable,  although  of  animal  origin;  each  of  the  little  inhabit- 
ants, resembling  a  hydra,  or  polype,  imitating  by  its  extended  arms  the  appear- 
ance 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  can  discover  no  traces  of  the  man- 
ner in  which  they  are  produced.  The  process,  by  which  their  numbers  are 
sometimes  increased,  is  no  less  astonishing  than  their  first  production ;  for 
several  of  the  genera  often  appear  to  divide  spontaneously,,  into  two  or  more 


738  LECTURE    LIX. 

parts,  which  become  new  and  distinct  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  strain- 
ing 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  informed 
of  the  qualities  of  external  objects  by  the  senses  of  touch,  taste,  smell,  hear- 
ing, 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  completely  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,  denominated  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  mastication  of  the 
food,  which  has  been  received  by  the  mouth-  The  food  thus  prepared  is  con- 
veyed into  the  stomach  by  the  operation  of  swallowing;  but  in  ruminating 
cattle,  it  is  first  lodged  in  a  temporary  receptacle,  and  more  completely  mas- 
ticated at  leisure.  In  the  stomach,  it  undergoes  digestion,  and  being  af- 
terwards 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  absorbents  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  circulation,  before  they  can  arrive  at  the  kidneys,  by 
which  the  superfluous  parts  are  rejected.     The  chyle  passes  unaltered,  with 


ON    ANIMAL    LIFE.  739 

the  blood,  through  the  right  auricle  and  ventricle  of  the  heart,  and  enters  the 
lungs,  to  be  tliei  e  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  superflu- 
ous carbonic  matter,  in  the  form  of  carbonic  acid.  The  blood,  thus  rendered 
arterial,  returuing  to  the  left  side  of  the  heart,  is  distributed  thence  to  every 
part  of  the  system,  supplying  nutriment  throughout,  while  the  glands  and  ar- 
teries secrete  from  it  such  tluids,as  are  become  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  blood,  returning  from  the  lungs,  is  not  warmer  than  be- 
fore its  entrance  into  them  :  we  must  therefore  suppose,  that  when  the  tlorid 
arterial  blood  is,  by  some  unknown  means,  converted,  in  the  extreme  ramifica- 
tions 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  ex- 
trication 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  con- 
verted 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  docs  its  power  of  coagulation  to  a  glutinous  lymph,  mixed  with 
a  less  coagulable  scrum.  The  red  particles  in  the  human  blood  are  about 
•a-oW  of  an  inch  in  diameter,  somewhat. oblong,  and  flattened;  they  have 
usually  the  appearance  of  a  dark  point  in  the  centre;  but  there  is  tome 
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  with- 
drawn from  the  vessels,  these  globules  tend  to  subside,  and  to  leave  it  semi- 
transparent:  hence  arises  the  appearance  of  a  buff  coat  on  blood  left  to  co- 
agulate, whicli  is  thinner  or  thicker,  accordingly  as  the  globules  are  sooner  or 
later  arrested  in  their  descent. 

Themusclesareprobably  furnished  by  the  blood  with  a  store  of  that  unknown 
principle,  by  which  they  are  rendered  ca])able  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  arc 
also  sustained,  by  means  of  the  vascular  circulation,  in  a  fit  state  for  trans- 
mitting the  impressions,  made  by  external  objects  on  the  senses,   to  the  im- 


740  LECTURE    LTX. 

mediate  seat  of  thought  and  memory,  in  the  sensorlum ;  and  for  conveying 
the  dictates  of  the  will,  and  the  habitual  impulses  almost  independent  of  vo- 
lition, 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  conjectured,  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  gal- 
vanic experiments,  have  added  very  materially  to  the  probability  of  the  opi- 
nion. An  extremely  slender  fibre, of  a  substance  capable  of  conducting  elec- 
tricity with  perfect  freedom,  enveloped  in  a  sheath  of  a  perfect  nonconductor, 
would  perhaps  serve  to  communicate  an  impulse,  very  nearly  in  the  same  man- 
ner, as  the  nerves  appear  to  do.  Indeed  nothing  can  be  more  fit  to  constitute 
a  connecting  link  between  material  and  immaterial  beings,  than  some  modi- 
ficatiori  of  a  fluid,  which  appears  to  difter  very  considerably,  in  its  essential 
properties,  from  the  common  gross  matter  of  the  universe,  and  to  possess  a 
subtility  and  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  disturbed, 
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  sys- 
tematical order.  Dr.  Cullen  has  divided  them  into  four  classes.  Febrile  dis- 
eases, which  constitute  the  first  class,  consist  principally  in  an  increase  of 
the  frequency  of  the  pulsations  of  the  heart  and  arteries,  together  with  an 
elevation  of  the  temperature,  the  whole  animal  economy  being  at  the  same 
time  in  some  measure  impaired:  they  are  often  accompanied  by  unnatural  or 
irregular  actions  of  the  vessels  of  particular  parts,  constituting  local  inflamma- 
tions, 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 


ON    ANIMAL   LIFI.  741 

system  are  peculiarly  in^paired,  form  the  class  of  neuroses,  including  spasmo- 
dic affections,  madness,  melancholy,  and  epilepsy,  A  general  derangement 
of  the  system,  without  fever,  or  any  peculiar  debility  of  the  nerves,  consti- 
tutes the  class  of  cachectic  diseases,  such  as  atrophy,  consumption,  scrofula, 
and  dropsy.  Besides  these  diseases,  we  have  a  fourth  class,  consisting  of  lo- 
cal affections  only,  such  as  blindness,  deafness,  tumors,  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  dis- 
eases is  still  in  a  state  of  great  imperfection.  Happily,  however,  for  man- 
kind, we  may  observe  in  almost  all  cases,  where  the  offending  cause  is  disco- 
verable, and  where  the  system  is  not  at  once  overwhelmed  by  its  magnitudcr  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  employed  agents 
equally  well  adapted  for  counteracting  it,  although  their  operations  are  ut- 
terly beyond  the  reach  of  human  penetration. 


VOL." I.  4  z 


LECTURE   LX. 


ON    THE    HrSTORY     OF    TERllESTRIAL    PHYSICS. 


jLhROUGHOUT  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  innumerable  lumina- 
ries which  enliven  the  widely  expanded  regions  of  immeasurable  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  distances  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  pro- 
perties 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  after- 
wards examined  the  combinations  of  all  these,  in  the  great  atmospherical 
apparatus  of  nature,  which  serves  for  the  exhibition  of  meteorological  phe - 
nomena.  The  forms  and  the  laws  of  animal  and  vegetable  life  have  been  tlie 
last  objects  of  our  inquiries;  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 


ON    THE    HISTORY    OF    TERRESTRIAL    PHYSICS.  743 

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  wvU 
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  compass 
above  3000  years  ago;  but  in  such  accounts,  it  is  impossible  to  ascertain  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  Pro- 
fessor llichniaun,  ,was  occasioned  by  some  unguarded  experiments  on  the 
electricity  of  the  atmosphere,  which  drew  on  him  the  effects  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  exciting  the  elec- 
tricity 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. 


744  LECTUUE    LX. 

.  Pythagoras,  great  as  he  was  in  some  other  departments  of  science,  reasoned 
r:speccing  physical  effects  in  a  manner  too  mathematical  and  visionary,  to 
allow  him  much  claim  to  he  ranked  among  those,  who  have  studied  to  inves- 
tigate 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  antiquity, 
that  he  imagined  the  number  of  elements  nearly  if  not  absolutely  infinite. 
He  conceived  that  the  ultimate  atoms,  composing  every  substance,  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.  Dcmocritus,  adopting  the  sentimentsofLeucippus,  proposed 
a  still  more  correct  theory  of  the  constitution  of  matter,  supposing  it  to  be 
ultimatel}'  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  primi- 
tive difference  of  form,   they  were  also  susceptible  of  a  variety  in  the  mode 

lof  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  observation. 

Plato  introduced  into  philosophy  a  variety  of  imaginations,  which  re- 
sembled 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  philosophers, 
Empedocles,  Anaxagoras,  Anaximenes,  Heraclitus,  and  Democritus,  sub- 
mitted their  minds  to  things  as  they  found  them  ;  but  that  Plato  made  the 
world  subject  to  ideas,  and  Ajystotle  made  even  ideas,  as  well  as  all  other 
things,  subservient  to  words ;  the  minds  of  men  beginning  to  be  occupied,  in 


Oy    THE    HISTORY    OF    TERRESTRIAL    PHYSICS.  745 

those  times,  with  idle  discussions  and  verbal  disputations,  and  the  correct 
investigation  of  nature  being  wholly  neglected.  Plato  entertained,  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  collection  of  real  information 
contained  in  his  works  on  natural  history.  Aristotle  attributed  absolute 
levity  to  fire,  and  gravity  to  the  earth,  considering  air  and  water  as  of  an 
intermediate  nature.  By  gravity  the  ancients  appear  in  general  to  have  un- 
derstood 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  Plu- 
tarch. 

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  measure  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  arrangements,  all  the 
varieties  of  natural  bodies.  He  considered  both  heat  and  cold  as  material; 
the  heat  emitted  by  the  sun  he  thought  not  absolutely  identical  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 
v^ision.  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  observa- 
tions 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 


746  ■      tF.CTURE    LX. 

in  Theophrastus,  Dioscorides,  andPlmy,.as  wellas  in  some  of  the  historical  writ- 
ers of  aatiquity.  Protagorides  of  Cyziciim,  who  is  quoted  by  Athenaeus,  rehites 
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  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  phi- 
losophy, 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  Amalfi,  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  familv  of  France, 
then  reigning  at  Naples.  The  declination  of  the  needle  from  the  true  meri- 
dian is  mentioned  by  Petei*  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  Gesncr  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 


ON    THE    HISTORV    OiF    TERRESTRfAL    PHYSICS.  747 

natuial  bodies  excite  our  attention,  by  their  novelty  and  importance,  is  Dr. 
Gilbert,  of  Colchester:  his  work  on  magnetism,  published  in  1590,  contains 
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  preceding  century, 
that  sulfur,  as  vvell  as  amber,  was  capable  of  electric  excitation,  and  Gilbert 
made  many  further  experiments  on  the  natui*e  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  \6Q5;  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  considerably  less  than  Burrows  had 
found  it  in  I08O. 

In  the  beginning  of  the  seventeenth  century.  Lord  Bacon  acquired,  by  hH 
laudable  efforts  to  explode  the  incorrect  modes  of  reasoning,  which  had  oc- 
cupied the  schools,  the  just  character  of  a  reformer  of  philosophy:  but  his 
immediate  discoveries  were  neither  striking  nor  numerous.  In  1620,  he 
j)roposed,  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  expan- 
sive 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  suggested,  about  the  same 
time,  by  David  Gorlaeus,  and  it  was  afterwards  adopted  by  Descartes,  as  a 
part  of  his  hypothesis  respecting  the  constitution  of  matter;  which  he  ima- 
gined 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  concern- 
ing 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  instrument  remained, 
however,  much  limited,  for  want  of  an  accurate  method  of  adjusting  its  scale. 


748  LECTURE    LX. 

and  it  was  not  till  the  close  of  the  century,  that  Dr.  Ilooke's  discovery,  of  the 
permanency  of  the  temperature  of  boiling  water,  afftnded  a  correct  and  con- 
venient limit  to  the  scale  on  one  side,  M'hile  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  sufficiently  natural,  from  the  proportion 
of  the  expansion  of  the  fluid  contained  in  the  thrrnomeeter  to  its  whole 
bulk.  ' 

It  was  about  the  year  1628,  that  Dr.  Harvey  succeeded  in  demonstrating, 
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  re- 
volution, 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  the  distinctions  and  properties  of  plants,  have  not  yet  been 
superseded  by  the  latest  publications.  Our  countrymen,  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 
Reaumur,  are  of  the  more  value,  as  they  were  far  more  studious  than  their 
predecessors  to  discriminate  truth  from  fiction. 


ON   THE    HISTORY    OF    TERRESTRIAL    PHYSICS.  74*) 

The  foundation  of  the  most  celebrated  of  the  philosophical  societies  of  Eu- 
rope renders  the  latter  half  of  the  seventeenth  century  a  very  interesting  pe- 
riod in  the  history  of  natural  knowledge.  The  Royal  Society  of  London,  and 
the  Academy  of  Sciences  of  Paris,  have  always  been  the  most  distinguished 
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  in- 
teresting collection  of  experiments,  relating  to  various  subjects  of  physical  re- 
search. In  the  Royal  Society,  Boyle,  Hooke,  and  Newton  were  the  most  industri- 
ous, as  well  as  the  most  successful  investigators  of  natural  phenomena :  the  ele- 
mentary doctrines  of  chemistry,  the  nature  of  combustion,  the  effects  of  heatand 
cold,  and  the  laws  of  attraction,  repulsion,  and  cohesion  were  attentively  examin- 
ed and  discussed.  The  expansion  ol  water,  by  a  reduction  of  its  temperature,  near 
the  freezing  point,  was  first  observed  by  Dr.  Croune  ;  although  his  experi- 
ments 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  Hauksbee; 
this  accurate  observer  investigated  also  the  nature  of  capillary  attraction 
with  considerable  success.  Early  in  the  succeeding  century,  many  of  the 
members  of  the  Academy  of  Petersburg  followed  the  example  of  other  so- 
cieties 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  in- 
formation respecting  the  variation  of  the  compass;  he  undertook  a  voyage 
round  the  world,  for  the  express  purpose  of  making  raagnetical  observations ;  and 
he  published  a  chart  of  variation, adapted  to  the  year  1700.  He  also  collected 
many  particulars  respecting  the  trade  winds  and  monsoons,  and  he  endea- 
voured to  explain  them  by  a  theory  which  has  been  adopted  by  some  of  the 
latest  authors,  but  which  is  in  reality  nmch  less  satisfactory  than  the  hy- 
pothesis proposed  some  time  afterwards  by  Hadley.  His  magnetical  investi- 
gations were  continued  with  great  diligence  by  Mountaine  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 

VOL.  I.  5  a 


750  LECTURE    LX. 

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,  and 
.Franklin.  As  early  as  1735  it  was  remarked  by  Gray,  that  "the  electric  fire 
seemed  to  be  of  the  sanie  nature  as  lightning,"  and  their  identity  was  after- 
wards more  strongly  asserted  by  Winkler,  and  experimentally  demonstrated  by 
Franklin.  The  shock  of  a  charged  jar  was  first  discovered  by  Kleist,  in  1745; 
and  the  experiment  was  repeated  by  Lallamand  and  Musschenbroek,  who  de- 
scribed its  disagreeable  effects  on  the  sensations  with  an  exaggeration  not  the 
most  philosophical.  The  theory  of  the  nature  of  the  charge  was  the  second 
gceat  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  natu- 
ral history;  nor  has  its  celebrated  author  wholly  neglected  the  philosophy  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  different  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,  Spal- 
lanzani,  Daubenton,  Degeer,  Geoffrey,  Pennant,  the  Jussieus,  Lacepede  and 
Haiiy,  have  particularly  distinguished  themselves  by  the  importance  of  theit 
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  doctrine  of  la- 
tent heat,  supposed  to  'be  retained  in  chemical  combination  by  the  particles 
of  fluids.  Dr.  Irvine  and  Dr.  Crawford  explained  the  circumstances  some- 
what, differently,  by  the  theory  of  a  change  of  capacity  for  heat  only.  Berg- 
njann,  Lavoisier,  Laplace,  Eifwan,  Seguin,  and  many  other  philosophers  have 

2 


ON    THK    BISTORT   OF   TERRESTRIAL    PHYSICS.  jT'SI 

illustrated,  by  experiments  and  calculations,  the  various  opinions  which  have 
been  entertained  on  this  subject;  and  few  chemists,  from  the  times  of  Boer- 
haave,  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  electficitj-, 
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  conse- 
quences, without  being  acquainted  with  Aepinus's  work  ;  although  the  publi- 
cation 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  cul- 
tivation of  a  rational  system  of  electricity,  and  Mr.  Cavendish's  investigation 
of  the  properties  of  the  torpedo  may  sei-ve  as  a  model  of  accuracy  and  |)reci- 
sion  in  tlie  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  consequently 
be  both  inaccurate  and  superfluous. 

The  attention  of  several  experienced  philosophers,  who  are  now  living,  has 
been  devoted,  with  much  perseverance,  to  the  ditficult  subject  of  hygrome- 
try.  Deluc's  experiments  have  offered  us  a  very  useful  comparison  of  the 
feygrometrical  qualities  of  various  substances:  Saussure  has  investigated,  with 
great  labour,  the  indications  of  the  hjgrometer  and  the  thermometer,  a^ 
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  unmixed  with  any  air.  The  hy- 
potheses, which  have  usually  accompanied  the  relation  of  most  of  these  cxpe- 


752  LECTURE    tX. 

riments,  have  however  been  in  general  too  little  supported  by  facts  to  be  en- 
titled 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  Galvani,  Volta, 
and  others,  respecting  the  operations  of  the  electric  fluid.  The  first  circum- 
stance, 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  co- 
vered 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  tliis  effect:  it  proved,  however,  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  sufiScient  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  electricity,  and 
that  the  communication  produced  a  discharge  between  them.  He  observed, 
however,  a  considerable  difference  in  the  effects,  when  different  metals  were 
employed  far  forming  the  circuit;  and  this  circumstance  led  to  the  discovery 
of  the  excitation  of  electricity  by  means  of  a  combination  of  different  inani- 
mate substances  only,  which  Mr.  Davy  attributes  to  Fabroni,  Creve,  and  Dr. 
Ash.  It  was,  however,  stilt  more  satisfactorily  demonstrated  by  Volta; 
and  he  at  first  supposed  that  all  the  phenomeaa  observed  by  Galvani  were  de- 
rived from  effects  of  this  kind,  but  on  further  examination  he  was  obliged  to 
allow  the  independent  existence  of  animal  electricity.  This  industrious  and 
ingenious  philosopher  has  the  sole  merit  of  the  invention  of  the  pile  or  battery, 
which  has  rendered  every  other  mode  of  exciting  the  galvanic  action  compa- 
ratively insignificant. 

No  sooner  was  VoUa's  essay  communicated  to  the  Royal  Society,  than  a 

4 


ON    THE    HISTOUY    OF    TEIlRESTItf A t    PHVSICS.  753 

■pile  was  constructed  by  j\fr.  Carlisle,  and  its  singular  effects  in  tlie  decompo- 
^sition  of  water  were  jointly  observed  by  himself  and  Mr.  Nicholson.  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  ten- 
dencies 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  investigations.  I  hope  that  I  shall  be  par- 
doned 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  nuist  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  subjects, 
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  hy- 
potheses are  very  arbitrarily  assumed;  some  of  them  are  manifestly  contrary 
to  experiment,  and  others  to  analogy  and  probability;  at  the  same  time  his 
remarks  appear  in  some  cases  to  be  either  perfectly  correct,  or  to  lead  to  de- 
terminations which  are  sufficiently  accurate  for  every  practical  purpose.  I  have, 
attempted  to  borrow  from  Mr.  Dalton's  ideas  some  hints,  which  I  have  incor- 
porated with  a  less  exceptionable  system;  and  by  a  comparison  of  his  experi- 
ments with  those  of  many  other  philosophers,  I  have  deduced  some  methods 
of  calculation  which  may  perhaps  be  practically  useful;  in  particular  a  sim- 
ple 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 


754  LECTURE    LX. 

years  by  the  Royal  Society  to  the  author  6f  the  most  valuable  discovery  re- 
specting heat  or  light,  forms  an  era  less  remarkable,  than  the  first  adjudication 
of  the  medal  to  himself,  and  the  second  to  Mr.  Leslie.  Count  Rumford's  nu- 
merous experiments,  on  the  production  and  communication  of  heat  are  highly 
important,  both  for  the  utility  which  may  be  derived  from  their  economical 
application,  and  for  the  assistance  which  they  afford  us  in  the  investigation 
of  the  intimate  nature  of  heat.  Mr.  Leslie's  discovery  of  the  different  pro- 
perties possessed  by  surfaces  of  different  kinds,  with  regard  to  emitting  and 
receiving  radiant  heat,  is  in  every  respect  highly  interesting;  and  the  multi- 
plicity and  diversity  of  his  experiments  would  have  entitled  him  to  still 
higher  commendation  than  he  has  obtained,  if  they  had  been  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  refraction.  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  ex- 
periments of  Hauksbee,  Juvin,  and  Musschenbroek;  many  other  circum- 
stances, depending  on  the  same  principles,  had  been  examined  by  Taylor, 
Achard,  and  Guyton ;  and  some  advances  towards  a  theory  of  the  forms  as- 
sumed 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  opera- 
tion of  a  cohesive  and  repulsive  force,  which  balance  each  other;  assuming 
only  that  the  repulsion  is  move  augmented  by  the  approach  of  the  particles  to 
(?ach  other  than  the  cohesion ;  and  I  have  had  the  satisfaction  of  discovering 
i^  this  manner  a  perfect  correspondence  between  many  facts,  which  had  not 
l?een  supposed  to  have  the  slightest  coanexion  with  each  other.  Alinost  a 
year  after  the  publication  of  this  paper,  Mr.  Laplace  Fcad  to  the  National  In- 
stitute a  memoir  on  capillary  tubes,  in  which,  as  far  as  he  has  pursued  the 
subject,   he  has  precisely  confirm«d  the  most  obvious  of  my  concLusicns; 


ON    THE   HISTORY    OF    TEItltfeSf RIAL    PHYSICS.  755 

although  his  mode  of  calculation  appears  to  be  by  no  means  unexcep- 
tionable, as  it  does  not  include  the  consideration  of  the  effects  of  repul- 
sion. Had  my  paper  been  so  fortunate  as  to  attract  Mr.  Laplace's  attention 
before  his  memoir  was  presented  to  the  Institute,  he  would  perhaps  have 
extended  the  results  of  my  theory  with  the  same  success,  which  has  uni- 
formly distinguished  his  labours  in  every  other  department  of  natural  philo- 
sophy. 

When  we  reflect  on  the  state  of  the  sciences  in  general,  at  the  beginning 
cf  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  advancement,  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  in- 
creases, new  facts  will  be  continually  discovered,  and  those,which  are  already 
known,  will  be  better  uliderstood,^and  more  beneficially  applied.  The  Royal  In- 
stitution, with  other  societies  of  a  similar  nature,  will  have  tlie  merit  of  assist- 
ing in  the  dissemination  of  knowledge,  and  in  the  cultivation  of  a  taste  for 
its  pursuit ;  and  the  advantages  arising  from  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  ac- 
tive in  the  establishment  and  support  of  associations  so  truly  laudable. 


rss 


LECTURE   IX. 


CHRONOLOGY    OF    PHYSICAL    AUTHORS. 


700  B.  C.                           e  00                                      i 
....    1    ....    1    ....    1    ...    . 

00                                                        4  00                                                        3 
....      1 1       .      .      .      . 

00                                                   200 
....      1      ...      . 

V 

.r  H  A 

.AN 

L        E       S.                      A 
AXIMANDE.R 

AN  AXI  MEN  ES. 
.VYTHAGORAS 
H  E  R  A  C 

NAXAGORAS. 

.D    E    M    O    C    R 
.  P      L 

LITUS 

.TH  EOPHRASl 
I    T    U    S.            .EPIC 
A       T       O. 
.ARISTOTLE. 

US. 

U  RUS. 

200  B.  C.                                 I'OO                            BIRTH  OF 
....     I     ....     1     ....     1     ...     . 

CHRIST.                                  1 
....     1     ...     . 

00                                                        -J 

00                                                   300 

....     1     ...    . 

;                ~    DIOSCORIDES 

.PLINY. 

300                                                      4 
....      1       ...      . 

00                                                s 

....  1  ...  . 

00                                                6 
....     1     ...     . 

op                                              7 

00                                                    800 

800                                        g 

00                                                      10 

....  1  ...  . 

00                                                      11 

00                                    la 
....    1    ...    . 

00           .                                      1300 

....  1  ...  . 

.R.       BACON. 
G  I  O  J  A 

ADSIGE  R 

D  A  N 

1300                                                  14 
....      1      ...      . 

00                                                      15 
....      1      ...      . 

00                                                      16 

00                                         i; 
....     1     ...     . 

00                                                 1800 
....      1      ...      . 

T     E. 

.G  E  S  N  E  R. 

.ALDROVANDUS 

.GILBERT 

.J.    B  A  U  H  I 

G  0  R  L  A 

.B     A      C 

.C.    B  A  L 

.G   A    L  I 

.D  R  E 

.R          A          y 

.WILLU  G.HBY 
.H     O     O     K     E 
N.                .NEWT 
EUS.                 C     R     O     U 
ON.                 .TOUR 
H  I  N.                    .HAL 
LEO.               .S  T  A 
BEL                      .BOER 
DESCARTES.             .J     U 
GELLIBR.AND                  S. 
.G  U  E  R    I    C   K   E.      H 
•.TORRIC.  ELLI          .R 
PASCAL                R 
B     O     Y     L     E.. 

.PRIESTLEY 

.BERGMANN 

I   R  V  I  N  E. 

O       N.   .G  A  L  V  A  N  I 

N  E          .R  O  B  I  S  O  N. 

N.EFORT  .SCHEELE. 

L     E    Y     .S  A  U  S  S  U  R  E 

H      L.         .LAVOISIER. 

HAAVE.        CRAWFORD. 

R      I      N, 
GRAY. 
AUKSBEE 
E  A  U  M  U  R. 
1  C  H  MA  N  N. 
MUSSCHENBR.OEK 
D  U  F  A  Y. 

J      U     S     S     I     E     U. 
N     O     L     L     E     T. 
.FRANKLIN. 
-E        U        L       E        R. 
.L     I       N       N       E. 
.B  O  S  C  OV  I  C  H. 
.K  L  E    I   S    T. 
.D  A   U  B   E  N  T  O  N. 
■D    E    G    E  E    R 
.MAYER. 
.P    E  N  N  A    NT. 
•B      L       A      C      K. 
W    I     L     K    E 
A  E  P  I    N  U  S 
.LAMB   E  Rt 
.SPALLANZANI. 

EXPLANATION  OF  THE  PLATES. 


5b 


758 


PLATE  I. 


Fig. 'I.  The  point  A  being  supposed  to  move  in  a 
right  line  to  B,  AB  is  the  direction  of  its  motion.  P. 
SI. 

Fig.  9.  The  lines  A  B,  B  C,  C  D,  are  the  successive 
directions  of  the  point  A,  moving  from  A  to  D  in  the 
figure  A  BCD.     P.  21. 

Fig  3.  The  tangent  A  B  is  the  direction  of  the  mo- 
tion of  the  point  C,  moving  in  the  curve  C  D,  when  it 
arrives  at  E.    P.  21. 

Fig.  4.  The  square  AB,  moving  on  the  hoard C  D, 
so  that  the  points  E,  F,  describe  the  parallel  lines  E  G, 
J  E  H,  with  eqOal  velocities,  the  plane  A  E  F  B  is  in  rec- 
tilinear motion  with  respect  to  the  surface  C  D.  P.  24. 
Fig.  5.  The  cycloid  A  B  C,  and  the  trochoid  D  E  F 
are  the  resuits  of  the  rotatory  motion  of  the  points  B 
and  E  round  the  centre  of  the  wheel,  combined  with 
^he  progressive  motion  of  the  wheel  along  the  base 
AC.     P.  24,  44. 

Fig.  6.  A  B  is  a  fixed  bar,  C  D  an  arm  which  slides 
on  it,  ECF  a  thread  passing  round  the  pulley  at  C, 
and  either  fixed  to  the  pin  on  the  slider  F,  or  passed 
over  the  pulley  G,  and  fixed  again  at  II.  The  arm 
turns  round  the  same  axis  that  carries  the  pulley  at 
C,  and  may  be  fixed  by  means  of  the  screw  which  is 
cut  on  the  axis,  while  two  other  screws  keep  it  steady 
,  by  pressing  on  the  slider  below  it.  The  point  I  de- 
scribes, by  its  compound  motion,  the  oblique  line  KI. 
P.  24. 

Fig.  7.  The  diagonal  A  B  of  the  parallelogram  C  D 
is  the  joint  result  of  the  motions,  represented  by  its 
sides  AC,  AD.     P,  2a. 

Fig.  8.  The  line  A  B  may  be  either  simply  drawn 
in  the  direction  A  B,  or  it  may  be  traced  by  the  equal 
motions  AC  and  AD  of  the  arm  and  its  slider,  or  by 
the  unequal  motions  A  E  and  A  F.     P.  25. 

Fig.  9.  The  body  A,  moving  uniformly  along  the 
line  AB,  first  approaches  to  the  point  C,  and  then 
recedes  from  it,  as  if  repelled.     P.  27. 

Fig.  10.  When  A  Band  AC  approach  each  other, 
and  coincide,  the  diagonal  AD  becomes  equal  to  their 
snm.    P.  30. 


Fig.  11.  Atwood's  machine.  The  boxes  A,  B,  con- 
taining equal  weights,  are  connected  by  the  thread 
A  C  B,  passing  over  the  puUey  C,  which  is  supported  ei- 
ther on  friction  wheels,  or  by  the  points  of  screws,  one 
of  which  is  seen  at  D.  The  box  A  is  made  to  descend 
either  by  a  flat  weight  placed  on  it,  or  by  the  bar  E, 
which  is  intercepted  by  the  ring  F,  and  the  box  conti- 
nues to  descend  till  it  strikes  die  stage  G;  the  space 
being  measured  on  the  scale  H  I,  and  the  time  by  the 
pendulum  K,  which  may  be  kept  in  motion  by  a  clock 
scaperoent  with  a  weight.  The  machine  is  levelled 
by  the  screws  L,  M.     P.  31. 

Fig.  12.  The  time  of  the  descent  of  a  falling  bodjr 
being  represented  by  any  portion  A  B  of  the  base  of  a 
triangle,  the  velocity  will  be  proportional  to  B  C,  which 
is  equal  to  A  B,  and  the  space  described  during  the 
time  D  E,  supposed  infinitely  short,  will  be  propor- 
tional to  the  area  D  E  F  G,  which  is  expressed  by  the 
product  of  BC  and  D  E;  consequently  the  whole  area 
A  E  F  will  represent  the  space  described  in  the  time 
AE,  and  A  HI  the  space  described  in  the  time  AH; 
but  A II I  is  half  of  the  square  H  K,  and  A  E  F  of 
E  L :  the  space  is  therefore  always  as  the  square  of  tlie 
time,  and  is  equal  to  half  the  space  which  would  be  de- 
scribed in  the  same  time  with  the  final  velocity.   P.  32. 

Fig.  13.  The  whirling  table.  The  arms  A  B,  C  D, 
are  made  to  revolve  on  the  axes  E  F,  G  II  by  the 
string  passing  over  the  wheel  I,  the  upper  or  under 
pulley  of  either  axis  being  employed  at  pleasure:  the 
stages  K,L,  with  their  weights,  are  placed  at  certain  * 
distances  from  the  centre,  by  means  of  the  racks  or 
teeth  belovi  them;  they  move  along  the  arms  by  means 
of  friction  wheels  resting  on  wires,  and  they  raise  the 
weights  M,N,  by  rrieans  of  threads  passing  each  over 
two  puUies.     P.  35. 

Fig.  14.  If  a  body  revolving  in  a  curve  ABC,  by 
means  of  a  force  directed  to  D,  describe  the  portions 
A  E,  B  F,  C  G  in  equal  times,  the  areas  A  D  E,  B  D  F, 
CDG,  will  be  equal,  and  the  velocities  in  A,B,  and 
G,  will  be  inversely  as  the  perpendiculars  D  H,  D  I, 
andDK.    P.  36. 


PLATE  1 . 


Tie-.  5. 


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Tig.  4-. 

C   


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■■■■■l»iiilllfflliiillllliiiiiili|||^^    -  l||||l«lllllii 


C—  G 


2'u/f . by  J.  Johnson, London. i  July  1 8o6 . 


Jos.  Skeitem    srtdp . 


Plate  H. 


Piff.  16  . 


P%.2+. 


t^  Pip-  in. 


Pig;.  25. 


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B 


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Ttih.by  J.Johnson.ZonloTi  xJiiiy26o&. 


JojepTv  ShfUon    sci±> 


759 


PLATi;  II. 

■  1  i    JL  I.  I 


Fig.  15.  The  ball  A,  revolving  round  the  point  B, 
and  being  drawn  towards  it  by  means  of  the  thread 
BC,  with  a  force  variable  at  pleasure,  its  veldcity  may 
be  observed  to  vary,  abcording  to  itrdistancfe  from  the 
point  B.    P.  ST. 

Fig.  16.  The  curve  A  B  C  D  E  is  an  ellipsis;  E  and 
G  are  its  f6ci,  A  D  its  greater  axis,  and  C  E  ite  lesser 
axis.    P.  ST. 

Fig.  17.  The  hol-izontal  range,  A  B,  Of  a  body  pro- 
jected at  an  elevation  of  45",  is  greater  than  A  C  or 
A  D,  the  ranges  of  bodies  projected  with  the  same  ve- 
locity at  a  greater  or  less  elevation.  If  the  parallel 
lines  EF,  G  H,  be  always  as  the  squares  of  A  E,  AG, 
the  curve  A  F  H  will  be  a  parabola ;  and  such  is  the 
path  of  a  projectile.     P.  39,  4o. 

Fig.  18.  The  path  of  a  ball  moviilg  swiftly  through 
the  atmosphere  nearly  resembles  the  curve  A  B.  P. 
89. 

Fig.  IP.  TheballA,having  descended  along  the  groove 
A  B,  describes  the  parabola  B  C,  passing  through  the 
rings  D,  E.     P.  40. 

Fig.  20.  The  cylinder  A,  loaded  at  the  axis,  de- 
scends along  an  inclined  plane  more  rapidly  than  the 
cylinder  B,  loaded  with  an  equal  weight  at  the  circum- 
ference.    P.  42. 

Fig.  21.  The  balls  A,  B,C  descend  along  the  planes 
A  D,  B  E,  CF,  of  equal  height,  in  times  proportional 


and  the  balls  B,  E,  deicendiug  from  any  two  points  of 
the  curve,  will  meet  at  E,  in  the  same  time  that  the' 
Ijall  G  falls  from  a  point  nearly  j  of  A  E  above  A.  The 
space  described  by  the  pendulum  in  descending  is  al- 
ways proportional  to  the  height  H  I,  to  which  a  body 
setting  out  fiom  E,  and  revolving  uniformly  in  a  circle, 
will  rise  in  the  same  time.  The  circle  E I  lies  without 
the  cycloid  C  E  D,  and  is  somewhat  less  incUncd  to 
the  horizon  at  equal  distances  from  E.     P.  44,  45. 

Fig.  25.  The  ball  A,  descending  from  B  in  the 
curve  B  A,  arrives  at  C  before  the  ball  D  moving  in  a 
right  line  on  the  plane  B  C.     P.  46. 

Fig.  26.  The  balls  A,  B,  C,  being  made  to  revolve 
by  means  of  the  whirling  table,  they  are  always  found 
in  the  same  horizontal  plane.  The  joint  connecting 
them  with  the  axis  is  represented  at  D,  as  seen  from 
above,     r.  47. 

Fig.  27.  The  equal  vibrations,  represented  by  A  B, 
C  D,  compose,  when  united,  the  circular  revolution 
AEB:  the  unequal  vibrations  AB,  FG,  compose  the 
ellipsis  AIIB;  the  place  of  the  body  being  always  as- 
certained by  combining  the  versed  sines  of  two  circu- 
lar arcs  increasing  uniformly.     P.  47. 

Fig.  28.  The  biUls  A,  B,  as  their  revolution  be- 
comes more  rapid,  fly  out,  and  the  point  C  is  depressed. 
P.  48. 

Fig.  29.    The  mass  of  the  body  A  being  1  and  that 


to  their  lengths.    The  upper  surfaces  of  the  slips  AD,      of  B  2,  and  AC  being  twice  BC,  C  is  the  centre  of  iu- 


B  E,  C  F,  are  slightly  grooved.     P.  43. 

Fig.  22.  The  balls  A,B,C,  descend  in  equal  times 
along  the  chords  A  D,  B  D,  C  D.     P.  43. 

Fig.  23.  The  same  ball,  descending  from  equal 
heights,  at  A,  B,  or  C,  by  different  paths,  will  rise  to 
the  same  height  at  D  on  the  opposite  side  of  E.  P. 
43. 

Fig.  24.  Tlic  thread  A  B,  playing  between  the  cy- 
cloidal  checks  AC,  AD,  desciibes  the  cycloid  C  ED, 


ertia.     P.  51. 

Fig.  30.  The  balls  A  and  B  are  suspended  by  long 
threads,  which  allow  them  to  move  in  tlie  arcs  AC, 
B  D ;  the  ball  A  is  perforated  in  a  horizontal  direc- 
tion, and  contains  aspiral  spring,  which  is  confined  by 
the  thread  E,  and  being  set  at ,  liberty  by  burning 
this  thread,  strikes  the  ball  B,  so  as  to  cause  each  of  the 
balls  to  move  through  an  arc,  of  which  the  chord  is  pro- 
portional to  the  weight  of  the  other  ball,    P.  52. 


760 


PLATE  III. 


Fig.  SI.  The  centre  of  inertia  of  the  bodies  A,B, 
C,D,  may  be  determinet)  either  by  finding  E  the  cen- 
tre of  inertia  of  A  and  B,  and  supposing  a  body  equal 
to  their  sura  to  be  placed  in  it,  then  determining  F 
from  E  and  C ;  and  G,  the  point  required,  from  F  and 
D;  or  by  finding  first  H  and  I  from  A,  C,  B,  D,  taken 
in  pairs,  and  dividing  HI  in  due  proportion  in  th? 
same  point  G.     P.  54. 

Fig.  32.  The  point  A  being  the  centre  of  inertia  of 
the  bodies  B,  C,  D,  E,  the  products  obtained  by  multi- 
plying B  by  B  F,  C  by  C  G,  D  by  D  H,  and  E  by  E  I, 
»re  equal,  when  added  together,  to  the  product  of  the 
masses  of  all  the  bodies  by  the  distance  A  K;  all  ihe 
lines  drawn  to  the  plane  F I  being  parallel.     P.  55. 

Fig.  33.  The  weights  ABC  will  remain  at  rest 
when  they  are  in  the  same  proportion  to  each  other 
as  the  respective  sides  of  the  triangle  D  EF;  D  Fbeing 
parallel  to  EG.     P.  61. 

Fig.  34.  The  bodies  A,  B,  remain  in  equilibrium 
when  their  centre  of  inertia  C  is  immediately  below  the 
point  of  suspension  D.     P.  61. 

Fig.  35.  The  system  of  bodies  A,  B,  C,  is  at  rest 
,  when  the  centre  of  inertia  D  is  immediately  below  the 
point  of  suspension  E.     P.  61. 

Fig.  36.  The  bodies  A,B,  remain  at  rest  when  the 
centre  of  inertia  C  is  immediately  above  tlie  point  of 
support  D.    P.  61. 

Fig.  37.  The  bodies  A,  B,  remain  at  rest  when  the 
centre  of  inertia  C  coincides  with  the  fulcrum  or  point 
of  support.     P.  61. 

Fig.  38.  The  irregular  body  A  B,  remains  at  rest 
when  the  centre  of  inertia  C  is  immediately  below  the 
point  of  suspension  D.     P.  61. 

Fig.  39.  A  being  the  centre  of  gravity  of  the  board 
B,C,  the  point  ofsuspension  being  D,E,  or  F,  the  posi- 
tion of  the  vertical  line  will  be  D  A,  E  A,  or  F  A.  P.  62. 

Fig.  iO.    The  equilibrium  of  the  vessel  A  is  stable  j 


tiiat  of  the  vessel  B  tottering,  the  path  of  the  centre  of 
gravity  having  its  concavity,  upwards  in  the  first,  and 
downwards  in  the  second.     P.  62. 

Fig.  41.  Paths  of  the  centre  of  gravity  of  an  oval. 
P.  62. 

Fig.  42.  Paths  of  the  centre  of  gravity  of  a  body 
resting  on  a  sphere.     P.  62. 

Fig  4S.  A,  the  path  of  the  centre  of  gravity  of  k 
body  standing  on  a  flat  basis;  B,  the  tottering  equili- 
brium of  the  same  body  inclined.     P.  63. 

Fig.  44.  The  effects  of  a  certa'm  inclination  of  a 
waggon,  loaded  with  light  and  heavy  materials,  are  re- 
presented at  A  and  B  respectively.     P.  63. 

Fig.  45.  The  suspension  of  a  weight^om-aTp^  pro- 
jecting over  a  table.     P.  64.  >'  ,•,,,,  ,,:  p   ,pf   , : 

Fig.  46.  A  shows  the  path  of  the  centre  of  gravity 
of  a  loaded  cylinder  on  an  inclined  plaije,  B  that  of 
the  centre  of  gravity  of  a  double  cone  moving  towards 
the  more  elevated  end  of  a  triangular  surface.  C  is  an 
elevation  of  the  double  tone.     P.  64. 

Fig.  47.  A  B  is  a  lever  of  the  first  kind,  tlie  forces 
acting  on  different  sides  of  the  fulcrum  C;  D  E  of  tlie 
second  kind,  the  forces  being  applied  at  D  and  F,  on 
the  same  side  of  E.     P.  65. 

Fig.  48.  A  force  applied  at  A  may  be  held  in  equi- 
librium by  a  triple  force,  applied  in  die  direction  B  C 
either  at  B  or  at  C,  or  in  a  direction  perpendicular  to 
the  arm  C  D  at  E,  D  E  and  D  B  being  each  one  third 
of  A  D.     P.  67. 

Fig.  49.  A  force,  acting  at  A  on  the  lever  A  B,  h^i 
a  great  mechanical  advantage  in  turning  the  lever  C  D ; 
but  when  the  levers  are  in  the  position  B  E,  D  F,  the 
force. acts  witli  a  similar  disadvantage.     P.  67. 

Fig.  50.  The  diameter  of  the  cylinder  A  being  three 
times  as  great  as  that  of  B,  the  weight  C,  or  an 
equivalent  force  applied  to  the  winch  D,  will  support 
a  triple  weight  at  £.    P.  6T. 


plaib  m. 


Fie-.3x. 


E  B 


Kg". 3 


rxg;.33. 


Fig^.34 


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Fig;.  37 


Fig;.  38 


Tig-. 46. 

imigiiiiiiiiiiii iiiiiiiiiiiii 


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Fig-.  5o.  A 


FiJy.'hy  J.  Johnson.  .London  i  July  2S06. 


Joj^K  Skeltan   . 


Pub.  by  J.  Johnson ,  London,  i  July  iSoS. 


JotspK  Sl<dtm  Jcitlp- 


761 


PLATE  IV. 


Ti-;.  51.  The  weiglit  A,  acting  on  the  double  cylin- 
der H,  supports  the  weight  C  by  the  pulley  running  in 
the  angle  of  the  rope  D  C  E,  which  is  wound  on  the 
larger  cylinder  nt  D,  while  it  is  uncoiled  from  the 
smaller  at  E,  and  the  force  is  the  same  as  if  the  weight 
C  were  attached  to  the  lineC  F,  acting  on  the  axis  F, 
of  which  the  diameter  is  equal  to  the  difference  of  the 
radii  of  the  double  cylinder.     P.  63,  206. 

Fig.  52.  A  single  fixed  pulley,  supporting  two  equal 
weights.     P.  68. 

Fig.  53.  A  single  moveable  pulley,  by  means  of 
whicfi  a  weight  supports  another  twice  as  great.  P. 
68. 

Fig.  51.  The  arrangement  ofpuUies  in  ships' tackles, 
with  a  force  of  six  to  one.     P.  69. 

Fig.  55.  An  arrangement  of  puUies  in  a  vertical 
line,  with  a  force  of  six  to  one.     P.  69. 

Fig.  56.  Mr.  Smcaton's  blocks,  giving  a  force  of 
twenty  to  one,  the  rope  being  applied  in  the  middle 
of  the  outer  series,  and  following  the  order  of  the  fi- 
gures from  1  to  21.     P.  69,  207. 

Fig.  5l.  A  system  of  puUies  fixed  on  one  axis  in 
each  block;  having  a  power  of  8  to  1.     P.  69. 

Fig.  58.  A  system  of  pullies,  each  of  which  doubles 
tlie  effect;  having  a  power  of  8  to  1.     P.  69. 

Fjg.  59.  A  system  of  pullies  with  each  rope  fixed  to 
the  weight,  having  a  force  of  7  to  1.     P.  69. 

Fig.  60.    Two  systems  of  pullies,  of  the  kind  dcuomi- 


natcd  Spanish  bartons,  in  which  two  of  the  pullies  arc 
suspended  by  the  same  rope:  the  one  has  a  power  of 
4,  tlieother  of5.     P.  69. 

Fig.  61.  A.  The  depression  of  the  middle  weight  be- 
ing one  third  of  its  distance  from  tlie  pullies,  it  sustains 
two  equal  weiglits,"  which  are  together  three  times  as 
great  as  itself.  B.  The  depression  of  the  smaller 
weight  being  one  fourth  of  its  distance  from  the  pulley, 
it  supports  a  weight  twice  as  great  as  itself.     P.  70. 

Fig.  63.  A  joiner's  saw,  stretched  by  twisting  a 
double  cord,  by  means  of  a  lever  passing  through  it. 

Fig;  63.  The  weight  A,  resting  on  an  inclined  plane 
of  which  the  height  is  to  the  oblique  length  as  3  to  5> 
is  sustained  by  a  weight  B  three  fifths  as  great  as  itself; 
and  if  for  the  resistance  of  the  plane  we  substitute  the 
action  of  the  weight C,  reduced  to  the  direction  AT) 
perpendieular  to  the  plane,  this  weight  must  be  four 
fifths  of  the  weight  A,  the-  horizontal  length  of  the 
wedge  being  four  fifths  of  its  oblique  length.     P.  70. 

Fig.  64.  The  weights  A,  B,  and  C,  acting,  by  means 
of  threads  passing  over  pullies,  wliich  are  fixed  to  any 
required  part  of  a  horizontal  table,  on  the  rollers 
which  press  against  the  sides  of  a  wedge,  proportional 
in  length  to  the  respective  weights,  retain  each  other 
in  equilibrium,  when  their  directions  meet  in  one  point. 
In  order  that  the  threads  may  pass  on  each  side  of  the 
wedge,  it  may  be  supported  by  three  or  more  balls.. 
P.  71. 


7S2 


PLATE  V. 


Fig.  65.  Bjr  means  of  the  moveable  inclined  plane 
AB,  of  which  the  height  AC  is  one  third  of  the  hori- 
zontal length  BC,  the  weight  D,  acting  horizontally, 
sustains  a  triple  weight  E,  acting  iu  a  vertical  direc- 
tion.   P.  n. 

Fig.  66.  A  B  being  one  fourth  of  B  C,  the  rope 
A  B  must  exert  a  force  of  tension  equal  to  one  fourth 
of  the  weight  C,  in  orderto  support  it,  supposing  the 
»urfacesj  to  be  without  friction.  But  if  the  friction  of 
the  end  of  the  beam  A  C  were  equal  to  one  fourth 
of  the  pressure,  it  would  support  the  weight  C  with- 
out any  other  force,  whatever  might  be  its  magnitude" 
P.  T2. 

Fig.  67.  AB  being  half  of  BC,  or  one  fourth  of 
C  D,  the  force  extending  the  rope  C  D  each  way  is 
equal  to  the  weight  E.     P.  72. 

Fig.  68.  The  thin  wedge  AB,  of  which  the  height 
is  one  fifth  of  the  length,  being  rolled  round  the  cy- 
linder C,  makes  the  screw  D,  by  means  of  which  the 
weight  E  is  capable  of  supporting  a  weight  five  times 
as  great  as  F.     P.  72. 

Fig.  69.  A  is  a  screw,  and  B  the  nut  belonging  to 
it.     P.  72. 

Fig.  70.  Tlie  endless  screw  A  B  acts  on  the  teeth 
of  the  wheel  CO.    P.  72. 

Fig.  71.  The  listance  of  the  threads  of  the  inte- 
rior screw  is  four  fifths  of  that  of  the  exterior  or  per- 
forated screw,  and  this  distance  is  one  thirtieth  of  the 
circumference.  Hence  the  weight  A  is  capable  of 
sustaining  a  %veight  B  150  times  as  great  as  itsell". 
P.  73. 

Fig.  72.  The  apparatus  for  experiments  on  collision. 
Those  balls  which  are  not  employed  may  be  left  be- 
hind the  graduated  arc,  as  at  A  and  B;  some  of  tlie 
strings  have  balls  of  half  the  weight  of  the  rest,  others 
have  a  small  dish  C,  on  which  balls  of  clay,  or  of  wax 
softened  with  one  fourth  its  weight  of  oil,  may  he  sup- 
ported.    P.  76. 

Fi;;.  73.  If  the  ball  A  strike  the  ball  B  iu  the 
oblique  direction  A  C,  the  ball  B  will  be  impelled  iu 
the  direction  C  D  perpendicular  to  the  surface  of  con- 
tact; and  the  velocity  EC  being  resolved  into  EF 
and  FC,  t!io  part  FC  will  continue  unaltered;  and  if 
the  bulls  are  equal,  the  part  EF  will  be  destroyed,  so 
that  the  ball  A  will  move  after  the  stroke  in  the  direc- 
tion C  G,  excepting  the  effect  of  any  accidental  dis- 

4 


turbance  which  may  be  derived  from  the  resistance  ot 
the  surrounding  bodies.  If  we  imagine  a  ball  at  C  in 
contact  with  B,  in  the  direction  D  B,  we  may  aim  a 
blow  at  the  centre  of  this  ball,  in  order  to  drive  the 
ball  B  toD  ;  and  if  B  happen  to  be  situated  any  where 
in  the  semicircle  D  C  G,  the  motion  of  A  after  the 
impulse  will  be  in  the  direction  B  G  or  G  B,  if  there 
be  no  resistance.  When  the  ball  H  is  reflected  by  a 
fixed  obstacle,  as  by  the  cushion  of  a  billiard  table,  at 
I,  its  velocity  K I  may  be  resolved  into  the  parts  K  L, 
LI;  the  partKLcontinues,and  may  be  represented  by 
L  M  equal  to  K  L,  the  part  L I  is  converted  into  I L  iu 
a  contrary  direction,  which  when  combined  with  LM 
makes  I M,  the  angle  LI  M  being  equal  to  LI  K.  We 
may  find  the  proper  direction  for  striking  any  ball  by 
reflection  if  we  suppose  a  ball  N  in  contact  with  the  near- 
est point  of  the  eushion,  and  making  NO  equal  toMN, 
aim  at  a  ball  supposed  to  be  at  O.  In  the  same  man- 
ner if  we  wish  to  impel  the  ball  P  in  the  direction  P  Q 
by  a  stroke  of  the  ball  11  after  reflection  at  S,  we  first 
place  a  ball  at  T  behind  P,  and  determine  the  direc- 
tion RS  by  aiming  at  a  ball  U,  as  if  we  wished  to  strike 
a  ball  at  T  with  a  direct  impulse.  But  in  the  case  of  a 
billiard  ball,  the  rotation  of  the  ball  round  its  axis,  which 
is  not  destroyed  by  the  collision,  will  cause  the  ball  to 
move,  on  account  of  the  friction  of  the  table,  in  a  direc- 
tion difterent  from  its  first  direction:  thus  the  ball  C 
will  not  go  on  to  G,  but  will  strike  the  cushion  be- 
tween C  and  D ;  and  the  ball  H,  after  reflection  at  I, 
will  proceed  in  a  direction  a  little  nearer  to  N  than 
IM;  so  that  the  imaginary  ball  O  ought  perhaps  to  be 
placed  as  far  from  the  cushion  itself  as  M,  in  order  that 
the  ball  may  be  struck  after  reflection.     P.  82. 

Fig.  74.  Mr.  Stneaton's  apparatusfor  experiments  on 
rotatory  motion.     P.  84. 

Fig.  75.  The  moveable  centre  of  suspension  being 
fixed  at  the  distance  of  5  inches  from  one  of  the  balls, 
and  7  from  the  otlier,  the  vibration  is  performed  at  the 
same  time  as  that  of  a  pendulum  37  inches  long.  P. 
85. 

Fig.  76.  The  three  weights,  supported  on  wheels, 
being  drawn  up  the  three  inclined  planes  at  the  same 
time,  by  the  action  of  three  other  equal  weights,  the 
middle  weight  arrives  first  at  the  top,  the  length  of  its 
plane  being  twice  the  height.     P.  88. 


Plate  t  . 


Pig-.S5 


Fig-.  69  . 


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Fig-.  75 


A^.  ^  .7;  John^fon  .Londcn.iJidy  1806 : 


Joseph,  Slcelton 


Plate  "vi. 


Fig-.  77. 


Fig;-  .78. 


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Fig.  85. 


I^ub.hy  J  .Johnson  .Zojldon  2  J'ldy  %6o6 , 


Jiyfijrh  Skeiten  J<  iJr 


763 


PLATE  VI. 


Fig.  7T.  The  proportions  of  the  diameters  of  the 
different  parts  of  the  double  pullies  being  3  to  2,  5  to 
2,  and  8  to  2,  the  middle  weight  may  be  observed  to 
rise  the  most  rapidly.     P.  88. 

Fig.  78.  A  wheel  supposed  to  be  capable  of  pro- 
ducing a  perpetual  motion;  the  descending  balls,  act- 
ing at  a  greater  distance  from  the  centre,  but  being 
fewer  in  number,  than  the  ascending.  In  the  model, 
the  balls  may  be  kept  in  their  places  by  a  plate  of 
glass  covering  the  wheel.     P.  92. 

Fig.  7^.  A,  the  inclination  of  cross  lines  generally 
most  convenient  for  producing  the  effect  of  a  tint,  in 
drawing,  B  shows  the  effect  of  lines  crossing  each 
other  perpendicularly,  and  C  that  of  lines  crossing  too 
obliquely.  Where  the  surface  to  be  shaded  is  large, 
the  separate  lines  or  hatches  should  begin  and  end  w  ith 
a  point,  in  order  that  the  junction  of  the  different  por- 
tions may  escape  observation.    P.  95. 


Fig.  80.  Dr.  Hooke's  telegraph,  in  which  the  cha- 
racters are  arranged  behind  a  screen,  and  drawn  out 
as  they  are  required.     P.  100. 

Fig.  81.    Dr.  Ilooke's  alphabet,  with  some  other 
arbitrary  characters  for  his  telegraph.     P.  100. 

Fig.  82.    A  beam  compass,  witli  a  scale.    P.  102. 

Fig.  83  .  .  85.    Instruments   for   drawing  arcs    of 
large  circles.    P.  102. 

Fig.  86.    A  pair  of  triangular  compasses.    P.  102. 

Fig,  87.  Marquois's  scales,  for  drawing  parallel  lines. 
P.  103. 

Fig.  88.    A  pen  for  ruling  musical  lines.    P.  103. 

Fig.  89.  A  pantograph.  A  being  the  centre  of  motion, 
B  the  tracing  point,  and  C  the  describing  point,  AB 
is  always  to  AC  as  A  D  to  A E,  and  the  copy  F  is  si- 
milar to  tlie  original  G.     P.  103. 

Fig.  90.    A  pair  of  proportioaal  compasses.  P.  104. 


r64 


PLATE  VII. 


Fig.  91.  A  sector.  The  scale  of  equal  parts  is 
marked  L.  As  A  B  is  to  AC,  so  is  B  D  to  C  E ;  and 
if  any  line  R  D  be  placed  with  its  extremities  in  the 
third  division  of  the  scale  on  each  leg,  tfie  distance 
C  E  between  the  seventh  divisions  will  contain  7  equal 
parts,  of  which  B  D  contains  3 ;  and  the  sam«  is  true 
of  any  other  numbers.     P.  104. 

Fig.  92.  A  vernier,  indicating  38ot  of  the  divisions 
of  its  scale.     P.  105. 

Fig.  93.  A  sliding  rule.  The  slider  being  drawn 
out,  so  that  the  division  marked  1  is  opposite  to  3  on 
the  rule  ;  all  the  other  figures  on  the  rule  are  triple  of 
tliose  which  stand  opposite  to  them.     P.  107. 

Fij^.  9t.  A  circular  logarithmic  instrument.  The 
inner  circle  slides  within  the  outer,  and  as  it  is  represent- 
ed in  the  figure,  each  number  stands  opposite  to  an- 
other which  is  twice  as  great.     P.  107. 

Fig.  95.  A  steel  chain,  made  by  llarasden.  A,«the 
•crew  for  bringing  the  mark  B  precisely  to  the  point 
required;  C  a  joint  between  the  adjoining  links;  D, 
a  cross  joint  at  every  tenth  link;  E,  a  pulley  and 
weight  for  stretching  the  chain.     P.  11?. 

Fig.  9(5.  A  micronietrical  scale  made  by  Troughton. 
The  compound  microscopes  A  and  B  are  fixed  nearly 
»t  the  required  distance  on  the  scale  C :  A  is  the;i  made 
to  point  exactly  to  a  division  of  the  standard  scale  D 
by  means  of  the  screw  E,  and  B  to  another  division, 
at  the  required  distance,  by  means  of  the  screw  F,  the 
fractiona  parts  being  added  by  the  turns  of  the  screw 
G.  The  scale  D  is  then  removed,  and  the  object  to 
be  compared  with  it  is  put  in  its  place.     P.  112. 

Fig.  97.  A  diagonal  scale.  The  line  A  B  contains 
S74  parts,  of  which  the  units  of  the  scale  contain  100. 
P.  112. 

Fig.  98.  The  statuary's  compass,  seen  sideways. 
The  pin  .IB  is  forced  down,  till  it  is  stopped  by  th« 


moveable  stud  C  ;  the  screw  D  fixes  it  in  its  angular 
position.  It  is  also  capable  of  motion  round  the  axis 
E  F,  which  is  fixed  by  the  screw  G.     P.  113. 

Fig.  99.  An  instrument  for  making  drawings  in 
perspective;  the  perforated  sight  may  be  drawn  out  to 
any  required  distance.  The  dotted  lines  show  how  a 
cecond  frame  may  be  applied  instead  of  the  sight,  so 
as  to  answer  the  same  purpose.     P.  115. 

Fig.  100.  Illustration  of  the  princij;les  of  pcrspec 
vc.  A  being  the  place  of  the  eye,  and  BC  the  plane 
of  proj  ection,  if  A  D  be  parallel  to  E  F,  G 11,  and  I K,  D 
will  be  their  vanishing  point,  and  E  D,  G  1),  and  I D, 
thtir  whole  images  :  AL  being  parallel  to  EM  and  IN, 
L  will  be  their  vanishing  point,  and  EL,IL,  their 
whole  images  :  and  A  O  being  parallel  to  P  Q,  O  will 
be  its  vanishing  point.     P.  115. 

Fig.  101.  A  being  the  centre  of  the  picture,  A  D  the 
horizontal  vanishing  line,  AC  the  vertical  line,  and  D  the 
point  of  distance,  if  a  ground  plan  EFGHofany  figure 
on  the  horizontal  plane  be  placed  in  its  true  position  with 
respect  to  I  K,  the  bottom  of  the  picture,  the  vanish- 
ing points  of  all  its  lines  will  be  found  by  drawing  DL, 
D  M,  D  N,  and  D  O,  parallel  to  those  lines  respect- 
ively;  and  the  whole  images  of  the  lines  will  be  PL, 
QM,  KN,  and  10,  determining,  by  their  intersec- 
tions, the  figure  IISTU,  which  will  be  the  projec- 
tion ofEFGH.  The  plan  may  also  be  drawn,  in  an 
inverted  position,  below  the  line  I  K,  and  the  point  of 
distance  taken  above  A  instead  of  below  it.     P.  115. 

Fig.  102.  A  B  being  the  whole  image  of  the  line  re- 
presented by  A  C  as  a  ground  plan,  and  D  the  point' 
of  distance,  we  may  find  E,  the  image  of  the  point  C, 
by  drawing  CD;  or  we  may  make  BF^rRD  and 
AG=AC,  FG  will  then  also  cut  AB  in  the  point  E. 
P.  116. 


Plate  VK. 


Tig. 91. 


Tig-.  9 


I'ig-S^ 


Of    tfl 


Fub.  by  J.  Johnjori,.  London,  1  July  iSa6 


Jufcph  Skciii'i 


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PXAXB  Tin. 


Ti^.104 


Tig-.  106 . 


Pig-.  108 


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Fig".  107 . 


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Fig:.  110. 


A  D 


Jhih.by  J.  Johns  art,  London  iLJuly  ido6 . 


Jojcfli,  JlcehtoTv  jculp. 


765 


PLATE  Vlir. 


Fig.  103.  Tlie  heights  of  the  housp5, -windows,  doors, 
»nd  figures  are  determined  by  lines  directed  to  the 
centre  of  the  picture ;  tlio  true  height  being  measured 
on  the  lines  A  B,  C  D,  where  the  objects  are  supposed 
to  touch  the  plane  of  prnjection.  The  distance  EF> 
■and  all  other  parts  of  lines  perpendicular  to  the  pic- 
ture, are  measured  bj  laying  off  the  lengths  of  the 
originals,  as  Gil,  on  the  line  AC,  and  drawing  I  EG 
I  EH,  from  I,  the  point  of  distance;  which,  inmost 
cases,  will  be  mbrc  remote  fi-om  the  centre  of  the  pic- 
ture than  it  is  here  made.  The  line  K  L,  and  others 
parallel  to  A  C,  may  be  measured  by  the  assistance 
of  any  point  M  in  the  horizontal  line,  the  distances, 
NO,  O  P,  being  laid  off  on  AC,  or  simply  by  reduc- 
ing the  scale  in  the  proportion  of  M  P  to  M  L.  P- 
116. 

Fig.  104.  A  circle  thrown  into  perspective,  by 
means  of  the  ■  circuiffscribfed  square,  the  points  of  con- 
tact being  found  by  bisecting  the  sides.    P.  116. 

rig.  105,  Two  perspective  delineations,  and  two 
orthographical  projections  of  a  cube,  in  differen' 
positions.  For  the  orthograpliical  projection,  the 
ground  plan  being  A  BCD,  the  image  of  any  point 
A,B,  may  be  found  by  drawing  A  E,  B  F,  perpendicu- 
lar to  the  ground  line,  EG,  FII,  parallel  to  the  line 
assumed  for  the  direction  of  the  centre  of  the  picture, 
and  AG,  BlI  parallel  to  the  line  of  direction  of  the 
point  of  distance;  the  interjections  G  and  II  will  then 
be  the  points  corresponding  to  A  and  B.    P.  116. 

Fig.  IOC.  A  is  the  orthographical  projection  of  a 
sphere,  with  some  ofits  circles;  B  the  stcrcographical 
projection  of  the  same  circles.     P.  117. 

Fi"  107.     A  balance  made  by  Fidler  for  the  Royal 
Institution,  nearly  resembling  those  of  Ramsden  and 
Troughton.    The  middle  column  A  is  raised  at  plea- 
sure by  the  cock  B,  and  carries  the  round  ends  of  the 
VOL.  I. 


axis  in  the  forks  at  its  upper  part,  iu  order  to  rcmOTC 
the  pressure  ou  thfe  sharp  edges  of  the  axis  within  the 
forks.  The  scales  are  occasionally  supported  by  the 
pillars  C  and  D,  which  are  elevated  or  depressed  by 
turning  the  handle  E.  The  screw  F  serves  for  rais- 
ing or  lowering  a  weight  within  the  conical  beam,  by 
means  of  which  the  place  of  the  centre  of  gravity  is 
rculated.  The  extent  of  the  vibrations  is  measured 
on  the  graduated  arc  G.    P.  125. 

Fig.  108.  A  balance  for  the  illustration  of  the  dif- 
ferent kinds  of  equilibrium.  When  the  scales  are  hung 
on  the  middle  pins.  A,  B,  which  are  in  the  same  hori- 
zontal line  with  the  support  of  the  beam,  the  equili- 
brium is  neutral,  the  weights  acting  as  if  the  centre  of 
gravity  coincided  with  the  point  of  suspension.  If  the 
scales  be  hung  on  the  lowest  pins  C,  D,  the  centre  of 
gravity  will  be  nearly  in  the  line  C  D,  and  its  path  the 
curve  E,  which  has  its  concavity  upwards;  but  if  the 
scales  are  hung  on  the  pins  F,  G,  the  path  of  the 
centre  of  gravity  will  be  convex  upwards,  and  the  beam 
will  overset.  In  reality  the  true  paths  of  the  centre  of 
gravity  would  be  nearly  in  the  curves  II  and  I,  situated 
between  the  weights  in  the  scales:  but  these  are 
similar  to  the  other  curves.     P.  125. 

Fig.  109.  When  the  equilibrium  of  abalance  is  totter- 
ing, the  lower  weight  acts  with  the  greatest  advantage: 
thus  the  effect  of  the  weight  A  is  reduced  in  the  pro- 
portion of  BCtoDC,  by  the  obliquity  of  tlie  ann 
C  A,  while  the  weight  E  acts  on  the  whole  length  of 
its  arm  CF.     P.  125. 

Fig.  110.  If  A  BC  be  a  semicircle,  and  BD  repre- 
sent a  given  weight,  and  A  D  its  counterpoise  in  one 
of  the  scales  of  an  unequal  balance  D  C  will  be  the 
counterpoise  in  the  other  scale.  It  is  obvious  that 
AC  is  more   than  twice  as  great  as  BD.    P.  126. 

5  C 


766 


PLATE  IX. 


Fig.  111.  A  weighing  machi»c.  The  platform  sup. 
porting  the  weight  rests  on  the  pins  A,B,C,  D,  at 
equal  distances  from  the  fulcra  E,F,G,II;  so  that 
wherever  the  weight  may  be  placed,  it  presses  equally 
ou  the  lever  IK,  at  L,  and  is  counterpoised  by  a  much 
smaller  weight  placed  in  the  scale  M.    P.  126. 

Fig.  112.  A  steelyard  resembling  that  of  Mr.  Paul, 
in  which  different  weights  may  be  employed.  A,  a 
loop  to  check  the  vibrations;  B  a  scale  to  be  sus" 
pended  by  the  hook  C.  If  great  delicacy  be  required 
in  the  weiglits,  the  fractional  parts  may  be  expressed 
by  the  turns  of  a  micrometer  screw  D,  furnished  with 
an  index.     P,  126. 

Fig.  113.    A  bent  lever  balance.    P.  127. 

Fig.  1 14.  A  spring  steelyard :  half  the  case  being 
removed,  to  show  the  spring.     P.  127. 

Fig.  115.  A  B,  the  path  of  the  centre  of  gravity  of 
the  human  body,  such  as  it  would  be  described  in 
walking,  if  the  legs  were  inflexible.  C  D,  the  path  de- 
scribed in  running,  on  the  same  supposition.     P.  ISO. 

Fig.  lie.  The  actual  path  of  the  centre  of  gravity, 
•s  it  is  usually  described.    P.  130. 


Fig.  117.  An  elastic  column,  compressed  by  a  weight 
acting  at  the  distance  of  one  third  of  its  depth  from 
the  concave  surface;  the  compression  being  every 
where  as  the  distance  of  the  lines  A  B,  A  C.     P.  139. 

Fig.  118.  An  elastic  column,  extended  by  a  weight 
acting  at  the  distance  of  one  third  of  its  depth  from 
the  convex  surface,  the  extension  being  every  where 
as  the  distance  of  A  B,  A  C.    P.  139.    . 

Fig.  119.  An  elastic  column,  compressed  by  a  weight 
acting  immediately  on  the  concave  surface :  the  com- 
pression extends  only  to  the  line  A  B,  the  parts  beyond 
this  line  being  extended.    P.  139. 

Fig.  120.  A  column  bent,  by  a  weight  acting  lon- 
gitudinally, into  the  form  of  a  harmonic  cur\e:  the 
line  A  B  C  D  is  the  limit  between  the  parts  which  are 
compressed,  and  those  which  are  extended.     P.  139. 

Fig.  121.  An  elastic  plate  or  rod,  considerably  bent 
by  a  weight  acting  at  its  extremity.     P.  139. 

Fig.  122.  An  elastic  rod  fixed  at  one  end,  and  bent 
by  its  own  weight.    P.  139. 

Fig.  123.  An  elastic  rod  supported  at  each  end,  and 
bent  by  its  own  weight.    P.  139. 


Plate  IX. 


Tie-.m. 


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g-.lL2 


Tie- .  313 . 


^tvi.T^y  J.JoTtnsffn, ,ZonA0n  iJuZy iSo(}  . 


Jt^s,-ph   Skeh.'tt 


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PLATE  X. 


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Pig-. 126.  Pig'.ia']. 


Kg-.x36. 


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Fig.x32. 


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iii|ipiiipipi*'«t"i*ri 


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IjllllJjIlllllllilltllllillliillMmiiiiimmmJiaJuiiuumummm...., 


Fig'. 140. 


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«L   «t.  tJL -^  «A.  ^   U. 

T""  ,j;^|"fr'|nn|ini'|''in|  |  |n»ii  ji-j^ijiai  jiinM 


Fig;.  145. 


Fig".  146  . 


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"T"""II!JT 


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Fig. 1+4- 


Puh.bv  J.  John^oti., X-ondert  1  July  1806 . 


767 


PLATE  X. 


Fig.  121.  The  mannci-  in  which  a  prismatic  column 
h  crushed  by  pressure,  supposing  tlic  hiteral  adhesion 
to  be  simply  proportional  to  the  surface  concerned. 
P.  1-1(3. 

I'ig.  125.  The  manner  in  nhicli  a.  column  is  crush- 
ed, supposing  the  lateral  adhesion  to  be  increased  by 
pressure.     P.  llti. 

rig.  I'i6.  The  circle  is  as  strong  as  the  circumscrib- 
ing square,  supposing  the  adiiesion  proportional  to 
the  surface,  tlie  relative  force  of  all  its  chords  being 
equal.  P.  116. 

Fig.  127.  The  three  circles  are  as  strong  as  the  cir- 
cumscribing parallelogram.     P.  146. 

Fig.  128.  A,  the  strongest  form  for  a  beam,  cut  out 
ofa  plank  of  uniform  depth,  for  resisting  a  longitu- 
dinal force;  U,  the  form  mto  which  it  is  bent;  both 
curves  being  circular.     P.  150. 

Fig.  129.  A,  the  strongest  form  for  a  beam  cut  out 
of  a  plank  of  ecpiablo  breadth,  for  resisting  a  longitu- 
dinal force  which  beads  it  into  llie  cycloidal  cun'e 
seen  at  B.    P,  150. 

Fig.  130.  A,  the  strongest  form  for  a  square  or  turn- 
ed beam  or  column,  slightly  bent  by  a  longitudinal 
force:,  U,  the  form  into  which  it  is  bent  by  such  a 
force.     P.  150. 

Fig.  131.  The  strongest  form  of  a  beam  cut  out  of 
ft  horizontal  plank,  fixed  at  one  end,  and  supporting  a 
weight  at  die  other.   P.  1 50. 

Fig.  132.  The  strongest  form  of  a  beam  cut  out  of 
a  vertical  plank,  fixed  at  one  end,  and  supporting  a 
weight  at  the  other;  the  outline  being  parabolic.  In 
practice  the  best  method  in  such  a  case  would  be 
simply  to  reduce  the  depth  at  the  end  to  one  half  of 
the  whole,  keeping  the  outline  straight;  in  this 
manner  one  fourth  of  the  timber  would  he  saved.  P. 
150. 

Fig.  133.  Tlie  strongest  form  of  a  square  or  turned 
beam,  fixed  at  one  end,  and  supporting  a  weight  at 
the  other;  the  outline  being  a  cubic  parabola.  P. 
150. 

Fig.  134.  The  sU'ongest  form  for  the  outline  of  a 
compound  spring,  supporting  a  weight  at  the  end. 
P.  150. 

Fig.  135.  The  strongest  form  for  a  beam  cut  out  of 
a  horizontal  plank,  fixed  at  one  end,  and  supporting 
a  weight  equally  distributed  throughout  its  length ; 
the  outline  being  a  parabola.     P.  150. 

Fig.  136.  The  strongest  form  for  a  beam  cut  out  of 
*  ycrtical  plank,  fixed  at  one  end,  and  supporting  a 


weight  equally  distributed  throughout  its  length.     P. 
150. 

Fig.  137.  The  strongest  form  for  a  square  or  turned 
beam,  fixed  at  one  end,  and  supporting  a  weight  equally 
distributed  throughout  its  length;  the  outline  being 
a  seniicubic  parabola,  in  which  the  cube  of  the  thick- 
ness is  as  the  square  of  the  distance  from  the  end. 
P.  150. 

Fig.  133.  The  strongest  form  for  a  beam  cut  out 
of  a  vertical  plank,  for  supporting  its  own  weight;  the 
outline  being  a  parabola.     P.  150. 

Fig.  139.  The  strongest  form  for  a  turned  beam, 
for  supporting  its  own  weight;  the  outline  being  para- 
bolic.    P.  15<1. 

Fig.  140.  The  strongest  form  of  a  beam  calculated 
to  resist  the  pressure  of  its  own  weight  by  lateral  ad- 
hesion only.  The  outline  is  a  logarithmic  curve, 
which  iKjver  comes  into  contact  with  the  axis,  and  ia 
order  that  the  condition  of  equal  strength  may  be 
possible,  the  beam  must  be  loaded  with  a  weight,  at 
Its  extremity,  qqual  to  that  of  the  portion  which  is 
wanting  to  complete  the  figure.     P.  150. 

Fig.  141.  The  strongest  form  for  a  beam  cut  out  of 
a  horizontal  plank,  supported  at  both  ends,  and  bear- 
ing a  weight  at  the  middle.     P.  150. 

Fig.  142.  The  strongest  form  for  a  beam  cut  out  of 
a  horizontal  plank,  supported  at  both  ends,  and  bear- 
ing a  weight  equally  distributed  throughout  its  length; 
the  outhoe  being  p.vabolic.     P.  150. 

Fig.  143.  The  strongest  form  for  a  beam  cut  out 
of  a  vertical  plank,  supported  at  both  ends,  and  bear- 
ing a  weight  equally  distributed  throughout,  the  ouC- 
liiie  being  elliptic.     P.  150. 

Fig.  144.  The  strongest  form  for  a  beam  cut  out  of 
a  horizontal  plank,  firmly  fixed  at  both  ends,'and  sup- 
porting a  weight  at  the  middle.     P.  150. 

I'ig.  145.  ihc  strongest  form  for  a  beam  cut  out  of 
a  vertical  plank,  firmly  fixed  at  both  ends,  and  sup- 
porting a  weight  at  the  middle,  the  curves  being  pai- 
rabolic.     P.  l.iO. 

Fig.  146.  The  strongest  form  for  abeam  cutout  of 
a  vertical  plank,  and  supporting  every  where  a  weight 
proportional  to  tlie  distance  from  the  extremity :  the 
outline  being  a  cubic  parabola.     P.  150. 

Fig.  14T.  The  strongest  form  for  a  square  or  turned 
beam,  supporting  every  where  a  weight,  proportional 
to  the  distance  from  the  extremity,  and  represented 
by  the  section  of  the  same  figure,  which  is  a  pyramid 
or  a  cone.    P.  150. 


768 


PLATE  XI. 


Fig.,  148.  A  machine  Cor  examining  tlie  strength  of 
materials.  The  force  is  applied  by  means  of  the 
winch  A,  which  winds  up  the  rope  BC,  passing  over 
the  first  pulley,  and  under  the  second,  which  is  directly 
under  the  point  D,  at  which  the  force  acts  on  the  piece 
EFto  be  broken;  the  puUies  slide  on  two  parallel 
bars,  fixed  in  a  frame,  which  is  held  down  by  a  paint 
projecting  at  G,  from  the  lever  Gil,  which  is  gra- 
duated like  a  steelyard,  and  measures  the  force.  The 
piece  to  be  broken  is  held  by  a  double  vice,  I,K,  with 
four  screws,  two  of  them  hiding  the  other  two  in  the 
figure:  if  a  wive  is  to  be  torn,  it  may  be  fixed  to  be 
the  cross  bar  LM;  and  a  substance  to  be  crushed 
must  be  placed  under  the  lever  N  O,  the  end  N  re- 
ceiving the  rope,  and  the  end  O  being  held  down  by 
thejclick,  which  acts  on  the  double  ratchet  O  P.  The 
leve.r  is  double  from  O  to  Q,  and  acts  on  the  substance 
by  a  loop,  fixed  to  it  by  a  pin.    P.  151. 

Fig.  149.  The  outline  of  a  column  diminished  one 
^fth  of  its  diameter,  in  two  difierent  Avays :  the  side  A 
being  an  arc  of  an  ellipsis,  of  which  the  semidiameter 
AB  is  the  lesser  semiaxis,  joined  at  A  to  u  right  line 
AC, of  one  third  of  the  length  of  the  column,  the 
part  AD  being  cylindrical;  the  side  D  E  is  a  cubic 
pjiraboU,  and  may  be  drawn  mechanically  by  fixing  a 
straight  ruler  EFjinsuchaposition  that  DF  may  be  twice 
the  diminution  at  E,  and  then  bending  it  to  D  :  the  dinii- 
Qutiofi  being  every  where  as  the  cube  of  the  distance 
from  D.  These  two  methods  are  compared  in  a  con- 
tracted scale  at  G:  the  outer  line  represents  the  first 
method,  and  the  next  line  the  second ;  thq  third, 
which  is  nearest  to,  G  the  conclioid  of  Nicomedes,  re- 
commended by  Chambers,  said  to  be  found  in  the 
columns  of  the  Pantiicon;  the  curve  beginning  at  the 
base.  Palladio  fixes  the  ruler  at  A,  and  bends  it  to  H> 
which  makes  the  curvature  abruptly  greater  at  II.  P. 
158. 

Fig.  150.    A  section  of  Mr.  Smeaton's  liglit  house 
at  the  Eddystone.    P.  159. 


Fig.  151.  Mr.  Smeaton's  mode  of  uniting  tiers  o*^ 
stones  by  wooden  pins  and  wedges.    P.  160. 

Fig.  152.  A  string  of  beads,  suspended  in  equilibrium 
from  two  points,  and  remaining  in  equilibrium  in  an 
inverted  position.  The  ends  are  supported  by  two 
pieces,  which  slide  backwards  and  forwards,  and  are 
fixed  by  screws:  the  string  is  also  tightened  by  turn 
ing  a  pin.     P.  161. 

Fig.  153.  A  system  of  bars,  hanging  in  equilibrium, 
and  supporting  each  other  in  the  same  form  when  in- 
,,erted.     P.  161. 

Fig.  154.  A,  a  chain  loaded,  at  cqu^  distances, 
with  other  chains  of  such  a  length,  as  to  represent 
the  depth  of  the  materials  pressing  on  an  arch  of 
the  form  shown  by  the  first  chain,  and  holding  it  in 
equilibrium.  B,  an  arch  of  a  similar  form.     P.  161. 

Fig.  155.  A  comparison  of  the  curves  which  have 
various  advantages  for  the  construction  of  an  arch  sup- 
porting a  horizontal  road.  TVie  full  line  is  an  elliptic 
arc,  somewhat  less  than  half  the  ellipsis.  The  outside 
curve,  which  is  also  continued  furthest  down,  is  that 
which  iscalculated  for  resisting  tlie  pressure  of  materials 
acting  like  a  fluid,  or  in  the  manner  of  wedges :  the  second 
dotted  curve,  for  supporting  the  pressure  of  the  mate- 
rials above  each  part,  supposed  to  act  in  a  vertical  di- 
rection only:  the  third"  is  a  circular  arc,  making  one 
third  of  a  whole  circle :  the  fourth  is  part  of  a  logarith- 
mic curve,  whicli  is  nearly  of  equal  strength  with  re- 
spect to  the  tendency  of  the  materials  to  give  way  for 
want  of  lateral  adhesion,  and  the  fifth  is  composed 
of  parabolic  curves,  showing  the  outline  which  would 
be  strongest  for  supporting  any  additional  weight  placed 
on  the  middle  of  the  arch.  If  the  height  were  greater 
in  proportion  to  the  span,  as  usually  happens  in  prac- 
tice, there  would  be  less  difference  between  the  curves. 
The  radius  of  curvature  at  the  summit  being  AB,  the 
horizontal  thrust  is  e'qual  to  the  weight  of  the  por- 
tion A  B  C  D  of  the  materials. 


PLAa-E  XI . 


Tig,- •  148  ■ 


Kg.  149. 


Tig",  i5o. 


Piar.  i5 


rig.i55 . 


Tig-.  i5  4 . 


S^ 


IPiih.by  J.  Johnson., London  ^Jidy  t8o6 . 


Joseph  Skcltan  scuiv. 


PLATE  Xa. 


rig.i56. 


^ib .  by  y.  Johnson  .Zondon  i  Jufy  :i.8o6 . 


Ji'scph    SAeit,/-    .nt/) 


7^9 


PLATE  XII. 


Fig.  156,  The  middle  areh  of  Black  Friars  Bridge, 
P.  164. 

Fig.  157.  A  spherical  dome,  of  wliich  the  lower 
parts  are  made  thicker,  in  order  that  they  may  be  of 
equal  stability  throughout.  From  A  to  B  the  dome  is 
of  equable  thickness :  below  C  and  D  the  thickness  can-* 
not  be  increased  sufficiently  to  procure  an  equilibrium, 
without  the  application  of  a  chain  or  hoop,  of  which 
tlie  section  is  represented  at  C,  D.  If  the  thickness 
.were  not  at  all  increased,  a  hoop  would  be  required 
at  E,  F,  or  still  higher.     P.  165. 

Fig.  158.  A  section  of  the  roof  of  St.  Paul's  Cathe- 
dral. The  section  of  the  dome  consists  of  two  circu- 
lar arcs,  of  which  the  centres  are  a  little  beyond  the 
axis:  it  is  supported  by  carpentry,  resting  on  a  cone  of 
brickwork.  The  internal  dome  is  of  brickwork  only, 
■  and  is  open  at  the  summit.     P.  165. 

Fig.  159.  A  section  of  the  dome  of  the  Pantheon  at 
Kome,    P.  165. 


Fig.  160.    A  Tuscan  column,  with  its  pedestal,  capi- 
tal, and  entablature.     P.  165. 

Fig.  161.    A  Doric  column.    P.  165. 

Fig.  162.    An  Ionic  column.    P.  165. 

Fig.  163.    A  Corinthian  column.     P.  165, 

Fig.  164.    A  Composite  column.     P.  165. 

Fig.  163.  An  elevation  of  the  end  of  King's  College 
Chapel, Cambridge;  showing  on  one  side  the  buttresses, 
the  tower  being  supposed  to  be  removed,  and  on  the 
other  the  tower,  which  not  only  supplies  the  place  of  a 
buttress  at  the  end,  but  assists  also  in  supporting  a 
considerable  portion  of  the  thrust  in  the  direction  or 
the  length  of  the  chapel ;  the  roof,  which  is  of  stone, 
being  vaulted  in  this  direction  as  well  as  tranversely. 
There  is  also  a  roof  of  carpentry,  covered  with  lead 
above  the  stone  roof.    P.  166. 


770 


PLATE  XIII. 


Fig.  166.  Joints  for  a  tie  Insam.  The  joints  at  A  and 
n  cannot  be  more  than  half  as  strong  as  the  entire 
beam,  supposing  the  ^adhesion,  produced  by  the  pres- 
sure of  the  bolts,  as  strong  as  could  be  required.  The 
joint  at  C  is  calied  a  dovetail  joint;  its  strength  is  a 
little  less  than  chat  of  A  and  B,  but  the  adhesion  is 
nvorc  easily  secured,  since  a  force  tending  to  separate 
the  beams  must  tighten  the  joint.     P.  167. 

Fig.  167.  Joints  for  a  lie  beam.  The  joint  A,  if 
sufliciently  liglit,  may  possess  t  of  the  strength  of  tl)e 
beam.  The  joint  B  might  be  as  strong  as  the  beam,  if, 
the  adhesion  were  great  enough,  but  it  would  be  diffi- 
cult to  apply  sufficient  pressure  to  create  such  an  ad- 
hesion, and  if  the  beam  were  subject  to  be  much 
sliakcn,  the  joint  would  be  a  very  bad  one.     P.  167. 

Fig.  168.  A  good  joint  for  a  tic  beam;  the  adhe. 
•ion  being  secured  by  a  slight  diminution  of  the 
strength.     P.  167. 

Fig.  16?.  A,  a  simple  scarfed  joint,  which  may  be 
tightened  by  a  wedge  at  the  centre;  it  is  not  strong. 
B,  a  scarfed  joint  wliich  is  much  stronger.    P.  167. 

Fig.  170.  A  joint  for  a  beam  supporting  a  weight 
by  its  transverse  strength.  Thejunction  might  be  made, 
if  it  were  necessary,  by  means  of  a  third  piece,  of 
which  the  limits  are  marked  by  the  dotted  line.  The 
strength  is  but  little  diminished  by  the  joint,     P.  168. 

Fig.  171.  A  beam  supporting  a  weight  by  its  trans- 
verse strength,  joined  to  anotlier  by  means  of  a  third 
piece  of  half  the  depth,  spliced  or  fished  on,  below 
the  beam,  and  secured  by  pins,  and  by  blocks  or  jog- 
gles. The  strength  is  a  little  greater  than  that  of  the 
original  beam.  The  dotted  lines  show  the  proportion 
in  which  the  strata  ate  extended  or  compressed,  the 
lower  part  of  the  original  beam  remaining  in  its  natu- 
ral state,  without  sustaining  any  pressure,  as  far  as  one 
fourth  of  the  depth,  and  a  little  further.    P.  158. 


Fig.  172.  A  joint  for  a  beam  pressing  obliquely 
against  another.  The  dotted  lines  show  the  form  of 
the  tenon,  which  may  occupy  a  considerable  part  of 
the  breadth  of  the  beam.  The  uppers  trap,  A,  is  in  the 
most  usual  situatiou,  but  the  lower  one,  B,  appears 
to  afford  greater  strength,  as  it  presses  the  beams  more 
closely  together,  yet  without  any  danger  of  crippling 
them;  besides  the  advantage  of  having  a  firmer  hold 
of  the  lower  beam.     P.  169. 

Fig.  173.  A  joint  for  a  horizontal  beam  suspended 
from  a  vertical  one:  the  end  of  tlie  tenon  being  di- 
lated by  wedges,  and  the  whole  secured  by  a  strong 
strap.  The  tenon  ought  not  to  be  wide,  since  it  dimi- 
nishes the  strength  of  the  horizontal  beam.    P.  169. 

Fig.  174.  The  straps,  bent  so  as  to  deviate  from 
the  right  lines  joining  their  extremities  in  the  degree 
that  is  here  represented,  have  their  strength  reduced 
to  about  one  seventh  of  that  which  they  would  have 
if  straight.  Thus,  A  B  is  only  one  seventli  as  strong 
as  C  D,  supposing  the  substance  inflexible.  P.  169. 
Fig.  175.  The  simplest  form  of  a  roof  AB,  AC,  are 
the  rafters,  and  B  C  the  tie  beam;  the  weight  of  each 
half  being  i-eprcsented  by  AB,  or  A  C,  the  thrust  in  the 
direction  of  the  rafters  will  be  A  D,  and  the  horizontal 
thrust  each  way  BD  or  C  D.  It  is  obvious  that  A  D 
will  be  least  when  B  AC  is  a  right  angle.     P.  170. 

Fig.  176.  A  common  roof,  with  braces.  A  B  is  the 
king  post,  and  B  C,  B  D  the  braces.     P.  170. 

Fig.  177.  A  kirb  or  mansard  roof,  the  rafters  of 
which  hold  each  other  in  equilibrium.  A  B  and  C  D 
ai-e  queen  posts  helping  to  support  the  tie  beam.  The 
piece  A  C  acts  as  a  strut,  in  supporting  the  pressure 
occasioned  by  the  weight  of  the  tie  beam.  The  heads  of 
the  queen  posts  are  not  much  thickened,  in  order  to 
avoid  the  change  arising  from  the  unequal  contraction 
cf  the  wood.    P.  170. 


Fi^.x66. 


Plate  UK 


Fag.x6'5 


Fig.x68 


Fig,-.x69 


rigr-^72-  A 


J*uo.  hy  J.  Joluhs<m,,L{mdo7i  2  Ju]a' 1806. 


Joseph  SJcclti?n    sctiip . 


77'i 


PLATE  XV. 


Fig.  189.  The  form  of  «  wheel  or  pulley,  on  which  a 
'broad  strap  runs,  the  surface  being  convex :  the  wheel 
wliich  drives  it  is  of  a  similar  form,  but  its  upper 
part  only  is  shown  in  the  figure.    P.  175. 

Fig.  190.  The  teeth  of  two  wheels,  formed  into  epi- 
cycloidal  curves,  acting  on  planes :  the  dotted  lines 
show  the  effective  nnagnitude  of  the  wheels.    P.  176. 

Fig.  191.  The  teeth  of  two  wheels,  formed  into  in-. 
volutes  of  circles,  described  by  uncoiling  a  thread 
from  the  dotted  circles;  the  point  of  contact  of  the 
teeth  being  always  in  the  straight  line  which  touches 
both  circles.     P.  176. 

Fig.  192.  Two  surfaces  formed  into  involutes  of  cir- 
cles, revolving  in  contact  with  each  other,  the  equi- 
distant lines,  drawn  on  them,  continuing  to  meet  each 
other  throughout  the  revolution.     P.  176. 

Fig.  193.  The  pinion  A  is  of  the  kind  called  a  spur 
wheel ;  B  is  a  crown  wheel,  or  a  contrate  wheel.  P. 
177. 

Fig.  194.  The  wheel  apd  pinion  are  both  bevilled  : 
the  faces  of  the  teeth  being  directed  to  the  point  A. 
P.  177. 

Fig.  195.   Two  wheels  a  little  eccentric,  acting  on 
each  other.    P.  178. 
Fig.  196.    An  eccentric  contrate  wheel,  acting  on  a 


ong  pinion.    P.  178 


Fig.  197.  A  machine  for  cutting  the  teeth  of  wheels. 
A  is  the  wheel,  of  which  the  teeth  are  formed  by  the 
revolving  saw  B,  turned  by  the  wheel  and  pinion  C, 
D,  by  means  of  the  handle  E,  while  the  frame,  which 
holds  the  saw,  moving  on  hinges,  and  resting  on  a 
spring,  is  depressed  by  the  handle  F,  its  place  having 
been '  previously  adjusted  by  the  screw  G.  The  large 
plate  III  contains  a  number  of  concentric  circles,  va- 
riously divided  by  points,  into  which  the  end  of  the 
spring  I  sinks  at  each  step,  so  as  to  fix  the  apparatus 
in  the  required  position.    P.  178. 

Fig.  198.  A  chronometer  for  measuring  minute  por- 
tions of  time.  The  axis  A  B  being  turned,  either  by 
the  handle  A  or  by  the  weight  C,  the  balls'D,  E  fly  oat, 
and  carry  the  weights  F,  G  further  ftdm  the  'axis  ;  in 
consequence  of  which  the  increased  effect  of  friction 
retards  the  motion,  when  it  becomes  too  rapid.  The 
barrel  H  is  turned  in  the  mean  time,  with  the  axis,  and 
is  allowed  to  descend  as  the  thread  at  I  is  uncoiled,  so 
that  the  point  K,  which  is  pressed  against  it  by  a  spring, 
tiescribes  on  it  a  spiral,  which  is  interrupted  whenever 
the  pin  K  is  touched.    P.  191. 

Fig.  199.  The  fusee  of  a  watch  or  clock,  the  gene- 
ral outline  of  which  forms  part  of  the  hyperbola  A  B, 
in  which  the  distance  of  each  point  from  the  axis  C  D 
is  inversely  as  its  distance  from  the  line  D  E.   P.  192. 


PLA.TE  Vf. 


¥1^.189. 


E%.X90. 


i'isf.xgx. 


Fig-.  19 


¥1^.193. 


lig-.  195. 


''"^^^.: 


J^ii.by  jr..Jo7inso7v,Xond£fn  J.Jidy  ^So6 . 


Jpsqyh  Skeltan  saJp. 


PlATK  XVI. 


Fig'.  200. 


Yie-.  201 


R.g.202. 


<iniinill«l!A; 


\  i  ^  \ 


Jij^.hy  J.  Johnson, .London.  xJuly  x8o6 . 


Jasepk  SkdU'n  stM!^' 


773 


PLATE  XVI. 


Fiff.  200,  A  fusee  n  ith  an  auxiliary  spring,  for  con- 
tinuing the  motion  wlica  the  watcli  is  wound  up.  The 
action  of  the  main  sprii-g  turns  the  fusee  in  tlie  direc- 
tion A  B;  tlie  ftisee  nets  on  the  ratchet  wheel  ABC 
by  means  of  tlic  click  B,  and  this  wheel  impels  the 
toothed  wlieel  D  E  by  the  spring  C  B  A,  which  is  sup- 
posed to  be  seen  through  it.  When  tlie  watch  is 
■wound  up,  this  spring  forces  back  the  wheel  ABC 
against  the  click  F,  which  serves  as  a  fixed  point,  while 
the  other  end  continues  to  act  on  D  E,  and  to  main- 
tain the  motion.     P.  193. 

Fig.  201.    The  scape   wheel   A  B,  moving   in    the 

direction  AC  B,  impels  the  pallets  \),  E  of  llie  crutch 

or  anchor,  alternately  in  contrary  directions.    1'.  191. 

Fig.  202.    A  is  the  scape  wheel,  B  and  C  the  pallets 

of  the  common  watch  scapement.     P.  194. 

Fig.  203.  The  dead  beat  scapement.  'J'he  teelh 
are  first  received  on  the  flat  or  rather  cylindrical  sni-- 
faces  A,B,  on  which  they  rest  until  the  pendulum  ar- 
rives near  the  middle  of  its  vibration,  when  the  teeth 
begin  to  act  on  the  inclined  surfaces  terminating  the 
pallets.     P.  195. 

Fig.  201.  The  horizontal  scapement,  for  a  watch. 
The  tooth  A  rests  first  on  the  external  surface  of  the 
cylinder,  BC,  and  then  impels  it  by  its  inclined  face, 
in  the  direction  BC;  it  afterwards  falls  on  the  con- 
cave surface  D  K,  and  lastly  impels  the  cylinder  in  the 
contrary  direction.     P.  195. 

Fig.  205.  The  duplex  scapement.  A  B  is  the  pallet, 
through  which  the  cylinder,  and  the  tooth  which  rests 
ou  it,  arc  supposed  to  be  seen,  the  point  of  the  tooth 
being  about  to  escape  from  the  notch  towards  C.  The 
short  tooth  D  next  nnpels  the  point  of  the  pallet,  and 
the  long  tooth  E  falls  on  the  cylinder.  It  first  rests  on 
the  convex  surface,  and  then  drops  into  tlie  notch, 
which  causes  a  shght  recoil  in  the  wheel,  and  passes  by, 
the  tooth  F  being  beyond  the  reach  of  the  pallet;  but 
on  its  return,  the  tooth  falls  again  into  the  notch;  and 
when  it  escapes,  the  pallet  is  impelled  as  before.  P. 
196. 

Fig.  200.  Mr.  Mudge's  watch  srai)cmcnt.  A,  the 
scapewheel,  and  one  of  the  subsidiary  springs,  seciV 
from  above;  B  a  general  view  of  the  balance,  with 
both  the  subsidiary  springs,  seen  from  one  side.  The 
point  of  one  of  the  teeth  rests  at  C  on  the  end  of  the 
pallet,  which  is  bent  so  as  to  detain  it  until  the  pin  D, 
which  is  attached  to  the  balance,  sets  it  at  liberty,  bv 
striking  against  the  arm  E:  this  arm  is  then  carried 
on  by  the  balance,  to  the  end  of  its  vibration,  and  im- 
pels it  in  its  return,  until  the  pall«;t  meets  the  next 
tooth.  The  other  spring  acts  alternately  in  the  same 
tuunner,  but  in  a  couiriiry  diicctioa.    P.  19T, 


Fig.  207.  An  improvement  on  Mr.  Cumming's 
scapement  for  a  clock.  The  tooth  A  is  seen  resting 
on  a  Hat  surface  at  tlie  end  of  the  pallet  B ;  it  is  dis? 
engaged  by  the  descent  of  the  opposite  pallet  into  the 
position  in  which  it  is  represented,  tlie  pallet  B  being 
impelled  by  it  at  C.  This  pallet  continues  resting  on 
the  flat  end  of  the  tooth,  until  the  pin  U  of  the  pendu- 
lum strikes  against  the  arm  E,  which  is  carried  before 
it,  and  impels  the  pendulum  in  its  descent,  until  the 
pallet  B  acquires  the  situation  in  which  the  opposita 
pallet  is  represented,  and  sets  that  pallet  at  liberty 
from  the  tooth  E,  which  has  raised  it.  The  situation 
and  magnitude  of  the  weights  G,  II,  may  be  adjusted 
at  pleasure      P.  197. 

Fig.  208.  Mr.  Arnold's  watch  scapement.  The 
pill  A,  projecting  from  the  verge  or  axis  of  the  balance, 
moving  towards  B,  carries  beiore  it  the  spring  B,  and 
with  it  the  stifler  spring  C,  so  as  to  set  at  liberty  the 
tooth  D,  which  rests  on  n  pallet  projecting  frotri  the 
spring.  The  angle  E  of  tlie  principal  pallet  has  then 
just  passed  the  tooth  F,  and  is  impelleil  by  it  until  the 
tooth  G  arrives  at  the  detent.  In  the  return  of  the 
balance,  the  pin  A  passes  easily  by  the  detent,  by  forc- 
ing back  the  spring  B.  The  screw  II  serves  to  adjust 
the  position  of  the  detent,  which  presses  asjaiiist  it.  P. 
197." 

Fig.  209.  Mr.  Eariishaw's  scapement.  A  is  the 
unlocking  pallet,  B  the  spring  on  which  it  acts,  C  the 
detent,  holding  the  tooth  D  by  a  pin;  E  is  the  point 
of  the  principal  pallet  first  impelled  by  the  tooth  F, 
G  is  the  tooth  next  locked,  and  U  the  adjusting  screw. 
P.  197.  ■  ■'         ^ 

Fig.  210.  A  gridiron  pendulum,  consisting  of  three 
bars  of  iron,  and  two  ot  a  mixture  of  zinc  and  silver. 
P.  200. 

Fig.  211.  A  compensation  balance,  as  employed  ty 
Arnold.  The  outside  of  the  hoops  A,  B  is  of  Irass, 
the  inside  of  sleeh  the  weights  C,  D  are  screwed 
backwards  and  forwards,  in  order  to  obtain  the  reqiii- 
siie  degree  of  coiiipeiisutiun.  I'he  weights  E,  F,  arc  em- 
ployed to  regulate  the  mean  rate  of  the  watcli,  and 
G,  U,  and  I,  for  adjusting  it  to  all  positions  with  re- 
spect to  the  hori/on.     P.  201. 

Fig.  212.  The  compound  plate  A  B  rests  on  two 
supports,  which  are  adjusted  to  a  proper  distance  by 
luriihig  the  double  screw  C,  the  flexure  of  the  plate 
by  heat  raising  the  bar  D,  which  supports  the  pendu- 
lum, while  its  effective  length  is  determined  by  a 
fixed  clip,  whicfi  is  seen  below  the  plate.     P.  211. 


VOL.  r. 


0  D 


774 


PLATE  XVII. 


Fig.  213,  A  jack  for  laisiag  welglits  by  the  alter- 
nate motions  of  a  lever,  the  clicks  on  each  side  being 
detained  in  the  teeth  of  the  ratchets  by  the  assistance 
of  the  springs  in  which  they  terminate,  and  which  are 
coiinccied  together.     P.  204. 

Fig.  214.  The  mode  of  supporting  a  tackle  for 
raising  stones  in  building ;  the  summit  of  the  triangle, 
which  is  composed  of  three  poles,  being  raised  or 
lowered  by  means  of  a  rope  and  puUies.     P.  907. 

Fig.  ai5.  A  method  of  raising  weights  obliquely, 
by  means  of  a  rope,  passing  over  a  pulley,  which  is 
drawn  along  horizontally.     P.  207. 

Fig.  216.  AB,  a  section  of  an  inclined  plane,  belong- 
ing to  the  Duke  of  Bridgwater's  canal:  the  boats  are 
drawn  into  the  looks  at  A,  which  are  then  filled  with 
water ;  C  is  the  plan  of  the  windlass,  by  which  the  de- 
scending and  ascending  boats  are  connected  together, 
and  which  is  turned  by  a  winch ;  D  and  E  a"re  the 
locks.    P.  308. 

Fig.  217.  A  crane,  with  an  oblique  walking  wheel, 
for  oxen  or  horses.  The  wheel  is  taken  from  a  mill 
of  Leupold.     P.  209. 

Fig.  218.  A  crane  with  a  wheel  and  break  like  Mr. 
White's.  The  man  wdlks  at  any  required  distance 
from  the  axis  of  motion,  and  pushes  forwards  the  lever 


A,  which  moves  the  bar  B  C,  connected  to  the  same 
axis,  and  removes  the  break  CD  from  the  ciicuiiife- 
rence  of  the  wliccl.    P.  210. 

Fig.  219.    A  lewis,  for  raising  stones.     P.  210. 
Fig.  220.    When  the  centre  of  gravity  A  is  twice  as 
far  from  one  of  the  porters  B,  as  from  the  other  C,  the 
first  bears  one  third  of  the  weight,  the  other  two  thirds. 
P.  212. 

Fig.  221.  When  the  centre  of  gravity  A  is  above  the 
line  joining  the  points  of  support  B,  C,  the  load  is  di- 
vided in  the  ratio  of  the  segments  CD,  BD,  termi- 
nated by  the  vertical  line  AD;  but  it  may  be  sup- 
ported by  two  equal  forces  in  the  directions  BE,  C  F, 
found  by  makhig  G  H  equal  to  BG,  and  joining  C  H; 
the  angle  G  B E  being  equal  to  G U  F;  the  forces  and 
the  weight  may  then  be  rtpreseutcd  by  the  lines  C  I, 
IK,  andCK.     P.  212. 

Fig.  222.  A  roller  with  two  wheels  fixed  on  its  ends, 
by  means  of  which  tlie  slab  resting  on  it  may  be 
moved  to  a  considerable  distance  without  leaving  the 
roller  behind.    P.  213. 

Fig.  223.  Mr.  Garnet's  roIlers,for  diminishing  fric- 
tion :  their  axes  being  loosely  connected  by  a  ring,  in 
order  to  keep  tliem  in  their  places.    P.  213. 


Plate  xvn . 


Kg-.  219 


:"ig'.  222. 


Fig-.  220. 


Fig;.  223. 


Fi<"    .    1 


•■£       T       •' 


I'ub.by  ^T.Johnjron ,  Lcrufvrt  j  July  1806. 


Joseph  Skclton,  saJjp 


Plate  IVIIE. 


Fig".  224 . 


Fig".  22  5 


Fig-.  226. 


Fig:. 


g:.  227 


Fig-.  237.  ^ 


Fi^.238 


-^h.  ^  J'.  JoJmson , J. London,  x  July  J.S06 . 


Jo.fcph  SlfAton   .i3 


ns 


PLATE  XVIII. 


Fig.  224.  A  pair  of  friction  wheels,  supporting  one 
end  of  the  axis  of  a  wheel.    1'.  214. 

Fig.  225.  The  centre  of  tiie  wheel  A  B,  passing 
over  the  obstacle  C,  describes  the  path  DE;  that  of 
the  larger  wheel  F  G,  the  path  II  I,  which  i»  less 
»teep.     P.  2 14. 

Fig.  226,  The  centre  of  the  wheel  AB  describes 
the  curved  path  C  D,  in  passing  over  the  obstacle  E, 
while  that  of  the  larger  wheel  FG  has  an  angle  at 
H.     P.  214. 

Fig.  22T.  The  wheel  AB,  moving  on  a  soft  road 
towards  B,  has  to  overcome  the  resistance  of  the  ciirth 
atC.     P.  815. 

Fig.  228.  A  section  of  the  wheel  of  a  carriage,  a 
little  dished,  or  inclined  outwards.     P.  217. 

Fig.  229.  A  B  and  G  D  being  the  straps  or  braces  by 
which  a  coach  is  suspended,  if  the  centre  of  gravity  be 
at  E,  F,  or  G,  it  must  move,  when  the  carriage  swings, 
in  the  curve  passing  through  the  respective  point.  P. 
818. 

Fig.  230.  The  mode  of  harnessing  two  horses,  so  as 
to  make  them  draw  conveniently  together:  when  ei- 
tlier  horse  advance»-sO  far  that  the  bar  A  B  assumes 
the  position  C  D,  the  foremost  horse  has  the  disad- 
vantage of  acting  on  a  lever  equivalent  only  to  K  F, 
while  the  other  horse  acts  on  EC.     P.  218. 

Fig.  231.  A  sugar  mill.  The  axis  K  is  turned  cither 
by  animal  force  or  by  water:  the  liquor  is  collected  in 
the  trongh  B,  and  runs  oft"  in  the  channel  C.  Thex 
openings  D  are  for  the  purpose  of  adjusting  the  axes 
of  the  rollers.  The  canes  arc  supplied  by  the  liands 
of  the  workmen.     P.  221. 

Fig.  232.  A  glazier's  vice.  The  vacuity  in  the  mid- 
dle shows  the  form  of  the  section  of  the  lead  which  is 
drawn  through  it,    P.  223. 

Fig.  233.  A  forge  hammer,  clevnted  by  the  plugs, 
projecting  from  an  axis,  either  at  A,  or,  more  coiueni- 
cnriy,  at  B,  and  thrown  forcibly  against  the  woode6 
spring  C.     P.  224.  -  ■> 

Fig.  234.  An  engine  for  driving  piles,  on  Vauloue's 
construction.  -  The  horses,  drawing  at  A,  B,  raise  the 


weight  C,  held  by  the  tongs  D,  fixed  in  the  follower 
E,  which  are  opened,  when  thty  reach  the  summit,  by 
being  pressed  between  the  inclined  planes  F,  G,  so  as 
to  let  the  weight  fall.  At  the  same  tmie  the  lever  11 
is  raised  by  the  rope  I,  and  presses  on  the  pin  K  L,  so 
as  to  depress  the  lever  M  N,  and  draw  the  pin  O  out 
of  the  drum  PQ;  the  follower  then  descends,  and  un- 
coils the  rope,  its  too  rapid  motion  being  prevented 
by  the  counterpoise  R,  acting  on  the  spiral  barrel  Q. 
The  motion  is  regulated  by  the  fly  S,  ihe  pinion  of 
which  is  turned  by  the  great  wheel  T.     P.  23G. 

Fig.  235.    The  rollers  of  the  slitting  mill.    P.  228. 

I'ig.  23t3.  A  simple  plough.  A  is  the  coulter,  for 
dividing  the  ground;  B  the  share,  fixed  on  the  mould 
board  C,  for  turning  it  to  the  right  hand;  D  is  the  rest, 
and  E,F,' the  handles.    P.  229. 

Fig.  237.  Sectimi  of  a  threshing  mill.  The  corn  is 
drawn  in  by  the  rollers  or  feeders  A,  B:  it  is  beaten 
by  the  rc\  ol\  ing  beaters  C,  D,  and  the  straw  is  drawn 
out  by  the  rakeu  E  F,  which  discharge  it  at  G;  the 
grain  fulling  through  tho  arched  bottoms  II  I,  I G, 
which  are  formed  like  sieves.     P,  233. 

lig.  238.  A  corn  mill,  with  some  of  the  improve- 
ment* made  in  America,  by  Mr.  I'Uicott  and  Mr. 
Evans.  The  corn,  being  poured  into  ihc  funnel  A,  is 
conveyed,  by  the  revolutions  of  a  spiral  B  C,  to  C, 
whence  it  is  raised, by  the  chain  of  buckets  C  D,  to  be 
cleaned  by  the  revolving  sievo  E,  and  the  fan  F;  it  is 
then  deposited  in  the  granary  G,  which  supplies  the 
funnel  or  mill  hopper  11;  this  being  perpetually  agitated 
by  the  iron  axis  of  the  upper  mill  stone,  shakes  it  by 
degrees  into  the  perforation  of  the  stone;  it  escapes, 
when  ground,  at  I,  and  is  conveyed,  by  means  of  the 
carrier  K  I.,  RJid  the  elevator  L  M,  to  the  cooler  N, 
where  it  is  spread  on  a  large  surface  :,  it  passes  after- 
terwards  to  the  bolter  O,  and  is  received  in  tlie  binn 
P,  from  whence  it  is  taken  to  bp  packed  in  sacks  or 
barrels.  Q  represents  the  surface  of  a  mill  stone, 
cut  into  furrows,  in  order  to  make  it  act  more  readily 
on  the  corn.     P.  SS-i. 


776 


PLATE  XIX. 


Fig.  239.  The  surfaces  of  the  fluid  in  the  bent 
tube  A B  lemBin  on  the  same  level,  in  the  same  man- 
ner as  if  the  tube  were  absent,  and  the  fluid  made  a 
part  of  that  which  is  contained  in  the  reservoir  C  D, 
P.  260. 

Fig.  240.  The  bucket  A  being  suspended  by  the 
rope  B,  and  made  to  revolve  rapidly  round  its  axis,  the 
surface  of  the  water  assumes  a  panibolic  form.  P. 
261. 

Fig.  241.  A  heavier  fluid  being  contained  in  the 
upper  part  of  the  bent  tube  A  li,  which  is  immersed 
in  the  lighter  fluid  filling  the  vessel  CD,  the  fluid  in 
the  tube  remains  in  a  state  of  tottering  equilibiiura, 
when  its  surfaces  arc  in  the  same  level.    P.  261. 

Fig.  242.  The  fluid  ABC  presses  on  the  bottom  of 
the  vessel  BC  with  the  same  force  as  if  the  vessel  were 
of  the  form  B  C  D  E.     P.  261. 

Fig.  243.  The  portion  A  B  C  D  of  the  fluid  being 
supposed  to  be  congealed,  and  then  to  fonn  a  part  of 
the  vessel,  the  pressure  oji  the  bottom  would  remain 
unaltered.     P.  263. 

Fig.  244.  The  weight  A  may  be  supported  by  the 
pressure  of  a  small  quantity  of  fluid,  either  by  making 
the  surface  of  the  vessel  B  C  very  large,  and  the  height 
of  the  tube  D  E  moderate,  or,  while  the  vessel  F  re- 
mains of  a  moderate  size,  by  making  the  height  of  the 
tube  G  H  very  great.     P.  263. 

•  Fig.  245.  The  pressure  on  any  small  part  of  the  side 
of  the  vessel  A  B,  at  C  or  D  may  be  represented  by 
the  line  C  E,D  F,  and  the  whole  pressure  on  the  side 
by  the  triangle  BG,  of  which  the  centre  of  gravity  is 
at  II;  and  if  the  side  A  I  be  supported  by  a  single 
prop,  it  must  be  placed  at  the  point  K,  the  height  of 
*hich  is  equal  to  that  of  II.     P.  265. 

Fig.  246.  If  the  heiglit  of  the  surface  A  above  B  he. 
to  BC  as  tlie  specific  gravity  of  tiie  {iuid  in  BC  to  that 
of  the  fluid  in  A  B,  the  fluids  will  support  each  other. 
r.  265. 

Fig.  247.    Two  square  beams  floating  at  the  depths 


shown  at  A  and  B,  will  have  a  certain  degree  of  sta- 
bility, but  if  they  sink,  as  at  C,  they  will  overset.  But  a 
beam  of  the  breadth  shown  at  D  will  always  float 
securely.     P.  26r.  ^ 

Fig.  248.  A  jar  containing  images  of  fishes,  with 
bubbles  of  air  in  them,  which  sink  when  tlie  cover  of 
the  jar  is  pressed  with  the  hand.     P.  268. 

Fig.  249.  Dr.  Ilookc's  semicylindrical  counter- 
poise, by  means  of  which  a  vessel  is  kept  always  full. 
P.  268. 

Fig.  250.  The  form  into  which  the  flexible  bottom 
of  a  cistern  would  be  bent  by  the  jjressure  of  the  water: 
the  curve  is  the  same  as  that  into  which  an  elastic  rod 
would  be  bent  by  forces  acting  at  A  and  B.     P.  269. 

Fig.  251.  TTiebottle  A,  containing  air  and  mercury, 
has  the  tube  AB  fitted  into  it:  and  when  the  jar 
C  D,  in  which  it  is  enclosed,  is  exhausted  by  means  of 
the  air  pump,  the  elasticity  of  the  air  in  the  bottle 
forces  the  mercury  up  the  tube.     P.  270. 

Fig.  252.  An  instrument  for  showing  the  buovanS 
effect  of  the  iiir,  called  by  Boyle  a  statical  baroscope; 
the  index  A  shows,  on  the  scale  BC,  tlie  degree  in 
which  the  ball  D  is  obliged  to  descend,  by  the  di- 
minution of  the  weight  of  the  air.     P.  272. 

Fig.  253.  The  line  0  denoting  the  natural  density 
of  the  air,  the  line  1  A  next  above  it  shows  the  degree 
in  .which  the  air  is  expanded  at  the  height  of  a  mile, 
and  1  B  the  density  of  the  air  at  the  same  height:  in 
the  same  m.inncr  10  C  shows  the  expansion  of  the  air 
at  the  height  of  10  miles,  .ind  10  D  its  density;  and 
51'",  below  the  line,  the  density  which  it  would  acquire 
at  the  depth  of  5  miles  below  the  earth's  surface.  The 
lines  AC,DBE,  are  of  the  kind  called  logarithmic 
curves.     P;  272. 

Fig.  954.  The  box  or  bason,  in  which  the  mercury 
of  the  common  b:iromcter  is  contained :  A  is  a  float 
for  adjusting  the  luiglit,  by  means  of  the  screw  B, 
operating  on  th(:  leather  which  forms  the  bottom  of 
the  cavity.     P.  376. 


PLATE   XJX. 


Fig;.  239. 


ig.242. 


Fig-.  243. 


Ihih .by  J.  Johnson,  T.ondxin  j  July  J.806 . 


Josrph   Slcehon   sctdr . 


J 


V-;. 


El-ATE  XS . 


Fig.  2  55. 


Pig.  2  56. 

3  \W  1:1  I: J'?'//" 


HA.  by  J.  JdJmson  JLcnion  3.Ju2y  j.6oS . 


Joseph    Skeli 


777 


PLATE  XX. 


Fig.  255.  A  jet  or  vein  of  a  fluid,  passing  through  an 
orifice  in  a  tl)in  plate  in  any  direction,  and  contracted 
after  its  escape,  in  consequence  of  tlie  lateral  motions 
of  the  particles  which  flow  towards  the  stream,  nearly 
in  the  directions  of  the  lines  here  drawn.     P.  HBO. 

Fig.  256.  A  stream  flowing  through  a  short  cylin- 
drical pipe,  compared  with  another  flowing  through  a 
diverging  conical  pipe,  the  directions  of  the  motions 
of  the  particles  appearing  to  be  nearly  similar  in  both 
cases.     P.  281.  ,  ■  : 

Fig.  SST.  In  an  experiment  of  D,  Bernoulli,  the 
water  flowing  through  the  conical  pipe  A  drew  up 
water  through  the  tube  B  from  the  vessel  C ;  in  another 
of  Venturi,  the  water  flowing  through  the  cylindrical 
pipe  D  raised  water  througli  the  tube  E.  P.  281. 
,  Fig.  258.  A  siphon,  through  which  a  fluid  rnns 
from  the  higher  vessel  into  the  lower  one.     P.  283. 

Fig.  259.  A  fluid  flowing  through  a  vertical  pipe, 
and  filling  a  vessel  to  a  height  nearly  equal  to  the 
length  of  the  pipes,  while  it  is  discharged  through  a  si- 
milar horizontal  pipe.     P.  284. 

Fig.  260.  Subterraneous  cavities,  with  outlets  in 
tlie  form  of  siphons,  through  which  they  do  not  begin 
to  discharge  auy  waliT  till  they  are  nearly  full;  tlie 
lower  one  will  then  continue  to  nui  liU  it  be  empty. 
In  the  mean  time  either  of  them  may  keep  up  a  con- 
stant stream  by  other  passages.     P.  285- 

Fig.  261.  A  tube  turned  up  and  Contracted,  sn  as 
to  throw  out  the  fluid  contaiurd  in  it,  in  a  jet,  which 
rises  very  nearly  to  the  height  of  the  fluid  in  tlic  tube. 
P.  286. 


Fig.  262.  The  forms  of  jets  issuing  from  various 
parts  of  a  reservoir,  tlie  amplitude  A  B  being  twice 
C  D,  and  AE  four  times  F  G.     P.  280. 

Fig.  263.  A  series  of  waves,  moving  in  the  direc- 
tion A  B,  and  reflected  by  the  obstacle  B,  loses  the 
appearance  of  pi'ogrcssive  motion,  and  vibrates  up  and 
down  within  the  limits  of  the  curves  A  C  D  E  B,  and 
F  G II I  K ;  the  elevation  and  depression  become 
however  twice  as  gieat  as  before  reflection.     P.  289> 

Fig.  26-1.  A  series  of  waves  diverging  from  a  centre 
A,  and  striking  a  fixed  obstacle  B  C,  are  reflected  by  it 
into  the  same  form  as  if  they  proceeded  from  the  centre 
D,  at  an  equal  distance  on  the  opposite  side  of  the  sur- 
face BC.     P^2«9. 

Fig.  265.  An  apparatus  for  observing  the  motions 
of  waves  excited,  in  a  fluid  poured  into  the  trough 
A  B,  by  the  vibrations  of  the  elastic  wire  C,  loaded 
with  a  moveable  weight  D;  the  shadow  of  the  waves 
being  thrown  on  a  screen  E  by  the  lamp  F,  through 
the  bottom  of  the  trough,  which  is  of  glass.     P.  290; 

Fig.  2CC.  A  series  of  waves,  diverging  from  the 
centre  A,  and  passing  through  the  aperture  BC,  ex- 
tend themselves  on  each  side  so  as  to  fill  the  space 
BCDE,  while  they  alTect  the  parts  without  thi» 
space  much  less  sensibly.     P.  290,  458. 

Fig.  267.  Two  equal  series  of  waves,  diverging  from 
the  centres  A  and  B,  and  crossing  eaeh  other  in  sucii 
a  manner,  that  in  the  lines  tending  towards  C,D,E, 
and  F,  they  counteract  each  other's cflVcts,  and  tlie 
water  remains  nearly  smooth,  while  in  the  interme- 
diate spaces  it  is  agitated.     P.  290,  461. 


778 


PLATE  XXI. 


Fig.  2(53.  A  stream  of  air  being  forced  through  the 
pipes  A  tind  B,  the  mercury  in  the  barometer  C  D 
Calls  from  C  to  D.  P.  29r. 
-  Vig.  *ti9.  A  stream  entering  the  reservoir  A,  by  the 
pipe  B,carrics  with  it  all  the  vvaterC,vvhich  stands  above 
the  level  of  its  upper  surface.     P.  297. 

Fig.  270.  The  ball  A  is  permanently  supported  by 
tJie  jet  B,  because,  when  it  fulls  into  the  position  here 
represented,  the  centrifugal  force  of  the  water  at  A 
cairics  it  back  to  the  middle  of  the  jet.     P.  208. 

Fig.  271.  A  plate,  bent  into  the  form  A  BC,  turn- 
in:;  on  the  centre  B,  is  impelled  by  a  stream  of  air 
D  in  the  direction  C  D.  I'.  298. 
-  Fig.  272.  A  cylinder  moveable  on  an  axis,  with  two 
curved  pipes  inserted  in  its  lower  part,  seen  from 
above.  The  stream  A  enters  at  the  top  of  the  cy- 
linder, and  is  discharged  by  the  orifices  B,  C,  so  as  to 
turn  the  vessel  in  the  direction  B  D.     P.  301. 

Fig.  V3.  A  jet  of  a  Huid,  striking  on  an  obstacle 
of  equal  diameter,  and  separated  by  it  so  as  to  con- 
tinue its  motion  obliquely.     P.  302. 

Fig.  274.  The  whole  resistance  directly  opposed 
to  tlie  sutfacc  A'B  being  represented  by  BC,  the  por- 
tion which,  according  to  Uie  principles  of  the  reso- 
lution of  forces,  ought  to  at  t  on  the  wedge  A  B  U,  is  re- 
presented by  B  E;  and  in  the  same  manner  the  resist- 
ance on  AB  F  is  to  the  whoje  as  B  G  to  BC.   P.  303. 

Fig.  275.  The  form  of  the  dead  water  moving  before 
an  obtuse  body  is  nearly  like  that  of  ABC;  and  the 
form  adiiptcd  for  moving  through  the  water  with  the 
least  possible  resistance  like  A  BDC.     P.  804. 

Fig.  276.  The  direction  in  wliirh  the  particles  of  a 
fluid  arc  supposed  to  move  when  they  strike  against  a 
concave  surface.     P.  305. 

Fig.  277.    A  hydrostatic  balance.     P.  309. 

Fig.  278.  Mr.  Nicholson's  hydrometer,  to  be  em- 
ployed with  weights,  for  finding  the  specific  gravity  of 
Muids  or  solids.     P.  309. 

Fig.  279.    A  spirit  level.     P.  311. 

Fig.  20O.    An  overflowing  lamp.    The  hemispheri- 


cal counterpoise,  wliich  is  so  loaded,  that  its  centre  of 
gravity  is  at  A,  raises  the  surface  of  the  heavy  fluid  B 
tlte  higher  as  it  is  more  exhausted,  so  that  the  oil  C 
is  always  forced  up  nearly  to  the  level  of  the  wick  at  D. 
The  oil  is  poured  in  by  a  pipe,  in  the  middle  of  the 
cylindrical  column.  The  air  holes  may  bo  made 
wherever  it  is  most  convenient.    P.  311. 

Fig.  281.  A  section  of  an  embankment,  of  a  proper 
form  to  be  opposed  to  the  sea,  with  a  drain  passing 
through  it,  and  a  valre  at  its  opening.     P.  312. 

Fig.  282.  The  form  recommended  for  the  section 
of  a  river  or  canal.     P.  313. 

Fij.  283.  A  B  shows  the  strongest  form  for  a'vertical 
beam,  fixed  above  and  below,  and  calculated  to  resist 
the  pressure  of  a'fluid;  the  greatest  thickness  being  at 
C ;  and  D  E  is  the  outline  of  a  series  of  horizontal 
planks,  of  such  a  thickness  as  to  afford  equal  strength 
throughout  the  sluice  or  floodgate.     P.  314. 

F'ig.  281.  A  box,  with  a  valve  supported  by  a  hol- 
low ball,  for  letting  out  air  from  pipes,  when  it  is  be- 
low the  level  of  the  reservoir.     P.  310. 

Fig.  285.  Two  methods  of  letting  out  air  from  pipes, 
when  it  is  above  the  level  of  the  reservoir;  A  a  valve 
with  a  stopcock  near  it;  B  a  vessel  of  water,  screwed 
on  for  receiving  the  air ;  to  be  replenished  with  water 
as  it  becomes  empty.     P.  317. 

Fig.  286.  A  section  of  a  compound  stopcock,  which 
receives  a  fluid  from  either  of  the  pipes  A,  B,  or  C, 
into  a  cavity  which  descends  a  little  in  the  direction 
of  the  axis,  and  communicates  with  the  pipe  D,  by 
riicans  of  one  of  thfe 'bores  represented  by  dotted  lines, 
according  to  the  position  into  which  the  moveable  cy- 
linder is  turned.     P.  318. 

Fig.  287.  Valves  of  difterent  kinds;  A  the  commoA 
clack  valve;  B  a  double  clack  valve,  consisting  of  two 
semicircular  valves;  C  a  pyramidical  valve,  consisting 
of  four  triangular  pieces;  U  a  circular  valve  turning  on 
an  axis;  E,  a  stcain  valve  of  metal,  sometimes  called 
a  T  valve,  F,  a  valve  of  oiled  silk  or  bladder,  support- 
ed by  a  grating,  for  air.     P.  318. 


Plate  :kxl. 


Tig'.  268 


Tub. by  J.  Johnson .Zondon  2.  July  1806 . 


Joseph    Skehon   srulp 


Pr.ATE,  Txn 


-^uh .hy  J.  Johnson. JLenion  iJidy 280&.    . 


J^os^h  Skel: 


779 


PLATE  XXir. 


Fig.  288,  Mr.  Woltmann'g  liydrometrical  fly.  Tlie 
plates  A,B,  are  so  adjasted  by  experiment,  as  to  move 
exactly  or  very  nearly  with  the  velocity  of  the  wind,  a 
few  degrees  being  allow  ed  as  a  compensation  for  the 
retardation  of  friction.  The  cord  C  is  drawn  up,  and 
the  wheel  D  is  caused  to  revolve,  at  a  time  observed 
by  a  stop  watch;  and  its  surface  is  gnuluated  so  as  to 
number  the  revolutions  of  tlie  fly.     P.  319. 

Fig.  289.  An  apparatus  fur  measuring  a  ship's  way, 
resembling  Captain  Ilamilton't.  A  is  a  funnel  partly 
covered,  B  a  part  of  the  ship's  keel,  C  the  upper  part 
of  the  pipe  D,  in  which  the  smaller  pipe  El'  slides  in 
a  collar  of  leathers,  so  as  to  have  the  orifice  F  level 
with  the  surface  of  the  water.  This  pipe  has  a  small 
aperture  at  the  bottom,  wliich  limits  the  magnitude 
of  the  stream  discharged  into  the  vessel  G,  the  end 
F  being  considerably  larger.  The  tube  II  serves  as  a 
gage,  to  measure  the  velocity  at  any  given  time.  P. 
819. 

Fig.  290.  An  overshot  riheel,  on  which  the  water  is 
admitted  in  a  retrograde  direction,  so  as  to  run  ofl"  in 
a  continued  stream ;  at  the  lower  part  of  the  h  heel  it 
is  retained  in  the  buckets  partly  by  the  assistance  of  a 
sweep.     P.  321. 

Fig.  291.    A  breast  wheel,  witli  a  sweep.     P.  322. 

Fig.  292.    An  undershot  wheel.     P.  322. 

Fig.  293.  A  the  form  of  the  sail  of  a  windmill :  B 
the  best  inclination  for  each  part  of  the  sail  A,  accord- 
ing to  Smeaton's  experiments.    P.  32-1-. 

Fig.  294.  A  kite  supported  by  the  wind,  of  which 
the  force  acts  nearly  in  the  line  A  B,  perpendicular  to 


tlie  surface  of  the  kitQ;.and  this,  compounded  with  the 
force  of  the  cord  A  C,  produci^s  the  result  A  D,  which 
sustains  the  weight  of  the  kite.     P.  324. 

Fig.  295.  A  ship  working  against  a  wind;  the  force 
of  the  wMid  acting  nearly  in  the  direction  AB,  per- 
pendicular to  the  saijs,  the  sliip's  real  course  is  BC, 
the  angle  C  B  D  being  the  lee  way.     P.  320. 

Fig.  296.  The  auoria,  or  noria,  used  in  Spain,  for 
drawing, water,  by  a  series  of  earthen  pitchers,  con- 
nected by  ropes,  and  passing  over  a  sprocket  wheel. 
P.  327. 

Fig.  297.  An  undershot  waterwhecl,  carrying  fixed 
buckets,  which  raise  a  portion  of  water,  and  deliver  it 
into  a  trough,  furnished  w  ith  a  projection,  which  stands 
under  the  buckets,  at  the  upper  part  of  the  wheel. 
P.  327. 

I'ig.  298.  A  throwing  wheel,  for  draining  fens, 
worked  by  a  windmill  or  otlierwise,  and  cairying  the 
water  upon  a  sweep  from  a  lower  to  a  higher  level. 
P.  327. 

•Fig.  299.  The  rope  pump  of  Vera,  for  raising  water 
by  means  of  friction;  the  rope  is  kept  stretched  by  a 
pulley  under  the  water,  which  is  loaded  with  a  weight, 
and  slides  in  a  groove.     P.  328. 

Pig.  300.  The  screw  of  Archimedes,  nearly  as  de- 
scribed by  Vitruvius.     P.  399. 

Fig.  .001.  The  screw  of  Archimedes,  as  recom- 
mended by  I).  Bernoulli.     P.  329. 

Fig.  302.  A  waterscrew,  revolving  within  a  fixed 
cylinder.     P.  329. 

Fig.  303.    the  spiral  i>ump  of  Wirtz.    P.  330. 


780 


PLATE  XXIII. 


Fig.  SD4.  A  centrifugal  pump.  The  machine  is 
first  filled  through  tlie  fuiuiel  A,  and  when  it  is  made 
to  revolve,  the  water  is  discharged  into  a  circular 
trough,  of  which  a  section  is  seen  at  B  and  C.  The 
valve  at  U  remains  shut  while  the  pump  is  filling.  P. 
331. 

Fig.  303.  A  pump  consisting  of  two  plungers,  con- 
tinued nearly  to  the  height  at  which  the  water  is  de- 
livered.    P. 332. 

Fig.  306.  Lahire's  double  forcing  pump.  When 
the  piston  is  depressed,  the  water  enters  the  barrel  at 
the  valve  A,  and  goes  out  at  B;  when  it  is  elevated,  it 
enters  at  C  and  escapes  at  D.     P.  332. 

Fig.  307.  The  common  piston,  coated  with  leather. 
P.  332. 

Fig.  308.  Mr.  Bramah's  press.  The  pump  A  forces 
tlie  water  throngh  the  jiipe  B  into  the  barrel  C,  in 
which  it  acts  very  powerfully  on  the  large  piston  D, 
and  raises  tlie  bottom  of  the  press  E.     P.  332. 

Fig.  309.    Tlie  common  sucking  pum)).     P.  333. 

Fig.  310.  A  bag  pump,  the  bag  or  pufl"  A  being  ex- 
tended and  contracted  by  the  motion  of  the  piston. 
P.  333. 

Fig.  311.  A  lifting  pump,  the  piston  rod  A  B  being 
drawn  up  by  a  frame.     P.  333. 

Fig.  312.  A  sucking  pump,  converted,  by  the  addi- 
tion of  a  collar  of  leathers  at  A,  into  a  forcing  pump. 
P.  333. 

F'ig.  313.  A  fire  engine,  on  a  construction  similar  to 
some  machines  described  by  Raiuclli.  A  B  is  the  pis- 
ton, working  within  a  cylindrical  barrel,  and  moved 
by  the  handles  C  1).  When  the  end  C  is  depressed, 
the  water  enters  through  the  valves  E  and  F,  and  is 
discharged  at  O  and  II ;  when  D  is  depressed,  the  wa- 
ter enters  at  I  and  K,  and  is  discharged  at  L  and  M, 
into  the  air  vessel  N,  whence  it  is  expelled  by  the  pipe 
O.  The  pipes  P  and  Q  may  be  united,  if  it  be  re- 
quired.    P.  334. 

Fig.  314.  I'rom  Ramelli.  The  wheel  A  B,  revolving 
in  the  direction  B  A,  carries  a  portion  of  water  C  be- 
tween itself  and  the  sweep  D  F,,  which  ii  intercepted 
by  the  shder  F,  and  forced  up  the  pipe  FG.     P.  335. 

Fig.  815.  From  Ramelli.  The  roller  A,  revolving 
within  the  reservoir  B  C,  which  is  nearly  cylindrical, 
carries  with  it  the  slider  D  E,  which  is  wade  to  sweep 


the  internal  surface  of  the  cylinder  from  C  to  F,  by 
means  of  a  projecting  surface  acting  on  the  end  D,  so 
that  the  water  G  is  forced  through  the  pipe  F.   P.  335. 

Fig.  316.  From  the  cabinet  of  jMr.  Serviere.  The 
wheels  A  and  B  carry,  during  their  revolution,  a  quan- 
tity of  water  from  C  to  D,  or  from  D  to  C,  according 
to  the  direction  in  which  they  are  turned.     P.  335. 

Fig.  317.  Mr.  Gwynu's  patent  water  engine.  The 
valve  A  is  kept,  partly  by  means  of  the  spring  B,  bat 
still  more  by  the  pressure  of  the  water,  in  contact  with 
the  roller  or  piston  C,  which  revolves  within  the  box 
J)  E,  and  sweeps  it  from  E  to  F,  so  that  the  portion 
of  water  G  is  forced,  during  each  half  of  a  revolution, 
into  the  pipe  F;  or  is  drawn  from  F  to  E,  when  the 
roller  revolves  in  a  contrary  direction.     P.  335. 

F'ig.  318.    A  chain  pump.     P.  335. 

F'ig.  319.  The  mechanism  of  Hull's  acting  pump. 
In  the  position  of  the  stopcock  A  B,  here  represented, 
the  water  flows  out  of  the  barrel  C,  and  the  piston  1> 
is  allowed  to  descend.  The  rod  E  then  turns  the 
stopcock,  and  the  barrel  C  communicates  only  with 
the  pipe  F,  which  fills  it,  and  forces  up  the  piston, 
until  the  stopcock  is  turned  back  to  its  former  posi- 
tion.    P.  336.  * 

t  Fig.  320.  The  hydraulic  air  vessels  of  Schcranit2. 
The  reservoir  A  being  filled  with  water,  and  B  with 
.  air,  and  water  being  poured  into  the  funnel  C,  the  air 
in  B  acts  by  the  pipe  D  on  the  water  in  A,  and  forces 
it  up  the  pipe  E.     P.  337. 

Fig.  321.  A  being  the  high  water  mark,  and  B  the 
low  water  mark,  the  vessels  C  and  D  are  filled  at  high 
water  from  below,  the  air  being  suft'ercd  to  escape  by  a 
stopcock,  which  is  opened  by  the  fall  of  the  ball  F ;  at 
low  water  the  air  will  enter  the  vessel  D  at  B ;  and  be- 
fore the  next  high  water,  the  water  C  will  be  forced  up 
the  pipe  E.     P.  337. 

i'ig.  322.  The  fountain  of  Hero.  Its  operation  re- 
sembles that  of  the  hydraulic  air  vessels,  fig.  320;  but 
the  pipe  D  here  ascends.     P.  337. 

Fig.  323.  The  hydraulic  ram  of  Montgolfier.  When 
the  w  ater  in  the  pipe  A  B  has  acquired  a  sufficient  ve- 
locity, it  raises  the  valve  B,  which  stops  its  passage, 
so  that  a  part  of  it  is  forced  through  the  valve  C,  into 
the  air  vessel  D,  whence  it  rises  through  the  pipe  E, 
P.  338. 


Plate  xxm. 


Fig.  304. 


Fig.3o6 


Fig.  30/]. 


Fig-.3o8. 


i_l 


LB 


Fig.  309.  Fig.3io.  Fig.Sn.  Fig.Si 


C    J 


rig.3i3.  >^i3EL"-7.:^ 


Fuh.by  J.  Johnson, Lo?idi.'nt  July  1806. 


Joseph  Skrlton  Jrinf. 


Pig-.  33o 


Jii^ivX  Johnson..  Zcrtdon  j  July  1S06. 


JosepJv  Sheltot 


781 
PLATE  XXIV. 


Fig.  824,  Tlic  cupping  instrument  of  Hero.  The 
cavity  A  was  partly  exhausted  by  applying  the  mouth 
repeatedly  to  the  pipe  D,  the  stopcock  U  being  turned 
after  each  application.  When  the  stopcock  C  was 
opened,  the  air  at  D  in  contact  w  ith  the  skin  was  also 
rarefied,  and  the  effect  ot"  suction  was  produced.  P. 
539,053. 

Fig.  3H5.  Mr.  Cuthbertson's  air  pump.  When  the 
piston  rod  A  is  depressed,  it  leaves  the  piston  B  a 
little  behind  it,  so  as  to  make  an  opening  betwetn  two 
conical  parts  which  arc  ground  togetlier,  and  the  air 
escapes  from  the  lower  part  of  the  barrel  into  the 
Tipper  part;  when  it  is  elevated,  the  whole  piston  is 
raised,  and  a  wire,  which  slides  through  the  axis  of  the 
rod,  raises  a  small  valve  at  the  bottom  of  the  barrel, 
which  leads  to  the  receiver  C,  by  the  tube  DE:  the 
air  is  forced  from  the  upper  part  of  the  barrel  through 
a  valve  in  the  oil  vessel  F,  wlience  the  oil  runs  back, 
when  it  overflows,  by  a  tube  leading  to  the  mouth  of 
the  barrel;  and  if  this  tube  be  stopped  by  turning  its 
cock,  the  air  may  be  condensed  into  a  receiver  fixed 
at  G.  At  U  is  a  long  gage,  with  a  barometer  im- 
mersed in  the  same  bason  of  mercury.  The  piston  rod, 
which  is  hollow,  has  a  perforation  a  little  above  A,  to 
admit  the  oil,  in  order  that  the  wire  may  work  freely 
in  it.     P.  340. 

lig.  326.  Tlie  two  flics  A  and  B  being  caused  to 
revolve  with  equal  velocities  V)y  the  descent  of  the 
weight  C,  they  continue  to  move  for  an  equal  length 
of  time  in  the  vacuum  of  the  air  pump.     P.  341. 

I'ig.  327.  The  air  in  the  bottle  A  expands,  when  the 
receiver  B  is  exhausted,  and  causes  the  water  to  rise 
in  a  jet,     P.  341. 

Fig.  328.  A  pear  gage  ;  to  be  suspended  in  a  receiver 
by  a  book  like  that  which  is  shown  in  fig.  325.  P. 
342. 

Fig.  329.  A  condenser,  with  screws,  for  confining 
the  receiver.  A  is  a  gage  for  showing  the  degree  of  con- 
densation; B  the  piston  of  tlie  Syrinire,  with  a  valve 
of  the  best  kind,  which  is  conical,  and  is  coiyfined  by 
a  spiral  spring.  But  iu  common,  the  valves  are  made 
of  leather,  wjth  a  phite  of  metal  to  strengthen  it.  P. 
342. 

Fig.  SSO.  A  diving  bell.  A  is  the  forcing  pump, 
B  a  stopcock  for  letting  out  the  heated  air,  C  a  strong 
glass  for  giv  ing  light,  D  a  float  for  the  security  of  tlie 
diver.     P.  343. 

Fig.  331.  Laurie's  hydraulic  bellows.  When  the 
yessel  A  is  raised,  the  air  enters  at  the  valve  B;  when 
it  is  depressed,  the  valve  B  shuts,  and  the  air  is  forced 
through  the  pipeC  D,  which  conducts  it  to  the  reser- 
voir E,whei"e  it  is  confined  by  the  valve  F,  and  forced  by 
the  pressure  of  the  water  through  the  pipe  G.  P.  343. 

Fig.  332.  Mr.  Watt's  gasometer.  The  pressure  is 
regulated  by  the  magnitude  of  the  weights  A  and  B, 
which  act  by  the  spiral  fusees  C,  D,  so  as  to  guslain  a 
part  of  the  weight  of  the  inverted  vessel,  represented 
by  the  exterior  dotted  line.  The  gas  is  admitted  at  E 
or  F,  and  is  delivered  at  0.     G  H  is  a  gage  for  show- 


ing the  height  of  the  water  within  and  without  the 
moveable  vessel.  I  is  a  cock  for  lettii^  off  the  water 
P.  344. 

Fig.  333.  The  shower  bellows.  The  stream  A, 
passing  through  the  strainer  B,  carries  with  it  a  quantity 
of  air  through  the  pipe  C,  which  rises  to  the  upper 
pait  of  the  air  vessel  D,  and  is  discharged  by  the  piue 
E.     P.  344. 

Fig.  334.  The  centrifugal  bellows.  By  the  revolu- 
tion of  the  fly,  the  air  is  caused  to  enter  at  A,  and  is 
discharged  at  B.     P.  345. 

Fig.  335.  The  original  steam  engine  of  Savery.  Tlie 
vessel  A  being  filled  with  steam  from  the  boiler  B,  and 
the  stopcock  being  turned,  the  steam  cools  and  is  con- 
densed, and  water  is  forced  into  its  place  by  the 
pressure  of  the  atmosphere,  through  the  valve  C : 
the  steam  is  then  readmitted,  and  forces  the  water  to 
ascend  through  the  valve  D  and  the  pipe  U  E.  The 
vessel  F  acts  alternately  with  A.     P.  317. 

F'ig.  836.  The  common  steam  engine  of  Xcwcomen 
and  Beighton.  The  steam  being  admitted  into  the  cy- 
linder A  below  the  piston,  tlic  weight  B  is  allowed  to 
descend:  a  jet  of  water  is  then  admitted  by  the  pipe 
C,  which  condenses  the  steam,  and  the  pressure  qf 
the  atmosjihere  then  depresses  the  pi^ton:  a  part  of  this 
water  is  admitted  by  the  pipe  i)  into  the  boiler,  in 
order  to  keep  it  suliiciently  lull.     P.  347. 

Fig.  337.  Mr.  Watt's  steam  engine.  The  steam, 
which  is  below  the  piston,  is  suffered  to  escape  into 
the  condenser  A  by  the  cock  B,  which  is  opened  by 
tlie  rod  C,  and  at  the  same  time  the  steam  is  admit- 
ted by  the  cock  D  into  the  upper  part  of  the  cylinder; 
when  the  piston  has  descended,  the  cocks  11  and  F  act 
in  a  similar  manner  in  letting  out  the  steam  from  above 
and  admitting  it  below  the  piston.  Tlie  jet  is  suppli- 
ed by  the  water  of  the  cistern  G,  which  is  pumped 
uj)  at  H  from  a  reservoir :  it  is  drawn  out,  togetlier 
with  the  air  that  is  extricated  from  it,  by  the  air  pump 
I,  which  throws  it  into  the  cistern  K,  whence  the 
pump  L  raises  it  to  the  cistern  M;  and  it  enters  the 
boiler  through  a  valve,  which  opens  whenever  the 
float  Jvi  descends  below  its  proper  place.  The  pipes 
O  and  P  serve  also  to  ascertain  the  quantity  of  water 
in  the  boiler.  The  piston  rod  is  confined  to  a  motion" 
nearly  rectilinear  by  the  frame  Q;  tlie  fly  wheel  R  is 
turned  by  the  sun  and  planet  wheel  S,T;  and  the  strap 
U  turns  the  centrifugal  regulator  W,  which  governs 
the  supply  of  steam  by  the  valve  or  stopcock  X.  P. 
349.  ,, 

F'ig  338.  Mr.  Symington's  steam  boat.  A  is  the 
boiler,  B  the  cylinder,  C  the  piston,  D  the  conden- 
sation pipe,  E  the  air  pump,  F  stampers  for  break- 
ing ice.     V.  349. 

Fig.  339.  An  air  gun.  The  air  is  fiirced  by  the 
syringe  A  into  the  cavity  surrounding  the  barrel,  whence 
it  is  discharged  by  the  valve  B,  which  is  opened  either 
immediately  by  the  action  of  the  trigger  C,  or  by  a 
spring,  which  is  bent  by  cocking  the  gun,  and  set  at 
liberty  by  the  trigger.     P.  351. 


VOX.   I. 


5e 


782 


PLATE  XXV. 


rig.  340.  A  scries  of  waves  or  pulses  of  sound, 
diverging  frem  one  of  the  foci  of  an  ellipsis,  and  re- 
flected towards  the  other.     P.  375. 

rig.  341.  Waves  diverging  from  a  point  near  the 
centre  of  a  circle,  and  converging  after  reflection  to 
a  point  at  an  equal  distance  on  the  other  side  of  the 
centre.    P.  375. 

rig.  342.  A  section  of  a  speaking  trumpet  and  of  a 
hearing  trumpet:  the  lines  representing  the  direction 
of  tlie  sound  before  and  after  its  reflections.     P.  375. 

Fig.  343.  A  string  impelled  by  the  bow  of  a  violin, 
and  lightly  touched  at  tl>e  same  time  at  a  point  one 
third  of  its  length  from  the  end :  the  small  pieces  of 
paper  fly  ofl'  from  the  middle  of  tl>e  vibrating  portions, 
while  the  pi^ce  situated  at  the  remaining  point  of 
division  retains  its  situation.    P.  383. 

Fi".  344.  A  vibration  compounded  with  another 
smaller  vibration,  three  times  as  frequent,  in  a  trans- 
verse direction,  the  separate  vibrations  being  such 
that  tl'.e  points  may  be  always  opposite  to  a  point 
moving  uniformly  in  a  circle.  Thus  the  vibrations  in 
the  hnes  AB  and  AC  compose  the  complicated 
figure  D  E.     P.  384. 

Fi"  345.  A  specimen  of  the  manner  in  which  the 
-vibrations  of  a  string  are  usually  performed  when  it  is 
struck  with  a  bow.     P.  384. 

Fig.  346.  Specimens  of  the  simplest  manner  iij 
which  sand  is  collected  into  lines,  on  a  plate  of  glass 
or  metal,  which  is  made  to  sound  i)y  means  of  the  bow 
4)f  a  violin.     P.  385. 

Fig.  847.  A  round  plate,  performing  some  of  its 
most  complicated  vibrations,  the  lines  of  division 
being  indicated  by  the  place  of  the  sand.  From 
Chladni.     P.  385. 

Fig.  348.  A  square  plate  divided  into  a  diversity 
of  vibrating  portions.     From  Chladni.     P.  385. 

Fig.  34!>.  The  small  bones  of  the  left  ear,  nearly 
three  times  the  natural  size,  supposed  to  be  seen 
through  tUe  membrane  of  the  tympanum,  by  looking 
directly  into  ilie  auditory  canal.  A  B  is  the  membrane 
of  the  tympanum,  C  the  hammer,  D  the  anvil,  E  its 
attachment  to  the  surrounding  bone,  F  the  stirrup,  G 
the  round  aperture  in  the  bone  leading  to  the  cochlea. 
P.  388. 

Fig.  350.  A  view  of  the  vestibule  of  the  left  ear, 
with  the  semicircular  canals  and  the  cochlea,  seen 
with  the  eye  a  little  more  depressed  than  by  looking 
ktraight  tlirough  the  canal,  and  exactly  in  the  direc- 


tion of  the  stirrup.  ABC  is  the  vestibule,  imme< 
diately  behind  the  oval  aperture,  which  is  covered  by 
the  basis  of  the  stirrup,  D  are  the  canals,  E  the 
cochlea,  the  upper  spire  terminating  in  the  vestibule, 
the  lower  in  the  round  aperture  at  B.  The  projec- 
tion of  the  membrane  of  the  tympanum  is  marked  by 
an  oval  line.    P.  388. 

Fig.  351.  The  structure  of  the  left  ear,  seen  from 
above,  the  upper  part  of  the  canal  being  supposed  to 
be  removed.  A  is  the  auditory  canal,  B  the  membrane 
of  the  tympanum,  C  the  hammer,  D  the  anvil,  E  the 
stirrup;  F  the  place  of  the  canals,  which  are  higher 
than  the  parts  represented,  G  the  place  of  the  cochlea, 
H  the  round  aperture.     P.  388. 

Fig.  352.  A,B,  C,  a  representation  of  the  joint 
effect  of  two  equal  vibrations  variously  combined,  the 
middle  line  being  always  half  way  between  the  two 
outer  ones,  and  showing  the  compound  vibration  re- 
duced to  half  its  real  extent:  D  shows  the  mode  of 
finding  the  joint  efliect  of  vibrations,  by  cutting  a  sur- 
face into  sliders,  which  are  retained  in  their  places 
by  a  screw.     P.  390. 

Fig.  353.  The  uppermost  and  lowermost  curves  re- 
present a  series  of  vibrations,  of  which  12  occupy  any 
given  period  of  time :  the  third  and  sixth  lines  two 
series  of  which  15  and  16  occupy  respectively  the 
same  time: -the  joint  eflfcct  of  each  pair  is  shown  by 
the  dotted  curves  which  are  interposed  between  them, 
the  middle  one  representing  the  effect  denominated 
a  beat.     P.  391. 

Fi".  354.  The  proportional  lengths  of  a  chord  or 
pipe,  constituting  the  different  notes  of  the  simple  dia- 
tonic scale,  with  their  mutual  relations,  shown  by  their 
divisions  into  aliquot  parts.     P.  393. 

Fi".  355.  A  good  practical  mode  of  temperament; 
making  all  the  fifths  and  the  third  in  the  first  division 
perfect  concords;  the  three  remaining  fiULs  equally 
imperfect.     P.  396. 

Fig.  356.  Tlie  trumpet  Marigni,  with  its  bridge, 
which  is  suppoited  by  the  string  AB  nearly  in  contact 
with  the  sounding  board;  this  string  being  either 
stretched  by  a  pin  at  B,  or  by  a  cross  string  B C.  Jte 
places,  at  which  the  string  is  to  be  touched,  may  be 
marketl  by  frets  fixed  un<^erthc*h,  as  they  are  here 
shown  by  points.  At  D,  tlie  scale  of  this  instrument 
is  exhibitcrl,  resembling  that  of  the  trumpet  and  the 
French  horn.     P.  399. 


Kg" .  S40. 


jeiff.  34a, 


TLATT.  XXY. 

Pigr.  342. 


Kg-.  343 . 


*^"ljj  ^jf 


Pie-.  3 


^1=^ 


H^ 


^ 


Pig-.  345. 


Tig^.  346. 


Fig-.  347, 


ffl  ^ 


Kg-.  348. 


iX.Q? 

**^i#>^;^torr 

Pie*.  35?. 


Eg^.35i. 


X) 


iiiiliii 


Fig-.  353. 


/xrxru' 


-.y-  ^■-. 


AAA/\A) 


\ryrvi\r\K/\/'^'r\  r\>VA/v  AKaAA^ij;^  A  AAAV^b      |j 


r\r\f\!\f\j^f\j\f\S\f\p^ 

-    /■■■     ........ .^--.  r-.    ■..-.    /-"■. J/'i  /-...'^-./■"■■.  J'X  ■■'"■--■-■-/'vj^- 


Fig-.  35  +  . 
1, 


\f'---J~\/~-y---^-^ 


.A/i  r(/^J\r\^J\oJ\rvr<r\f\{iPJ''^  ^^ 


"vyA/VTv/ArUiz 


mmw 


iiiiiiiiiiiiiiH 


lillffi 


niffii 


Fig-.3i6. 


PEKTUCT 


0:sO'^t>oT;o' 


o*^ 


'';?bo  ■»'^^g'<-i'-o: 


IMP. 

r.00 


00'' 


Li 

3  6 


"19 


-I r     T- 

15" 


D 


^^" 


.^ 


o=f^ 


Fig*.  366 


.^2)  .1>Y  J.,T<>hf3,f{Tn  .XonBjjiiiJuJy  -r8o6 . 


Joseph    Sk-L-lten   .^cidp. 


PlAIEXXVI. 


Kg-.SS]. 


Rg:.3b9. 


Pig. 364. 


Fig. 367 . 


Tig. 366. 


Fig.  368.     B 
A. 


I 


Tig. 369. 


Tig. 3^0 


Fig.571 


Pig. 37 


Fig.  374- 


£ub  .l>y  J.  Jolinstm  .^imdxfTi  ijidy  J-80S . 


Joseph  Sh:/t 


783 


PLATE  XXVI. 


Fig.  357.  The  right  half  of  the  human  larynx. 
ABC  is  the  outline  of  the  cricoid  cartilage,  DEFGH 
of  the  thyreoid,  and  I K  L  of  the  arytaenoid  cartilage; 
M  is  the  epiglottis,NK  the  upper  ligament  ot  the  glot- 
tis, OP  the  lower  ligament,  and  Q,  the  trachea.  P.  400. 

Fig.  358.  A  view  of  the  ligaments  of  the  glottis, 
seen  from  above,  the  larynx  being  divided  by  a  hori- 
zontal section  a  little  above  them.    P.  400. 

Fig.  359.  Sections  of  the  pipes  employed  by  Kratz- 
ensteln  for  producing  the  sounds  of  the  different  vow- 
els ;  in  general  by  means  of  a  larynx  resembling  the 
moutli  piece  of  a  reed  organ  pipe,  but  in  the  case  of 
the  vowel  I  by  simple  inflation  through  the  tube  B. 
The  pipe  for  U  produces  the  sound  O,  except  when  it 
is  very  nearly  shut  up.     P.  401. 

Fig.  306.  Tiie  vox  humana  organ  pipe,  with  the 
mouth  piece  common  to  reed  pipes  in  general ;  the 
lower  part  in  contact  with  the  tongue  being  nearly  sc- 
micylindrical :  the  tongue  being  adjusted  to  the  pro- 
per pitch  by  means  of  a  sliding  wire,  which  regulates 
tlie  length  of  the  part  that  is  at  liberty  to  vibrate.  P. 
40i. 

Fig.  361.  The  mouth  piece  proposed  by  Kratzen- 
stein,  for  imitating  the  human  voice,  the  tongue  A 
passing  freely  in  and  out  of  the  tube,  which  is  more 
than  half  of  a  cylinder,  as  is  seen  at  B.     P.  401. 

Fig.  362.  The  form  of  the  regal  organ  pipe.  P. 
401. 

Fig.  363.  A  front  view  and  section  of  the  open 
diapason  organ  pipe  of  metal.  It  is  tuned  by  open- 
ing or  contracting  the  upper  orifice.     P.  402. 

Fig.  364.  A  a  front  vievr  of  the  flute  organ  pipe, 
of  wood,  which  is  tuned  by  a  plug.  B  a  section  of 
the  pipe.     P.  402. 

Fig.  365.  A  stopped  diapason  organ  pipe,  of  metal. 
It  is  tuned  by  altering  the  position  of  the  pieces  on 
each  side  of  the  mouth.     P.  402. 

Fig.  366.    A  chinmey  pipe.     P.  402. 

Fig.  367.  A  spindle  shaped  organ  pipe,  contracted 
above.    P.  402. 

Fig.  368.  A  the  form  of  a  cromorn  pipe,  B,  of  a 
trumpet  pipe,  both  having  reed  mouth  pieces.  P.  403. 


Fig.  369.  A  ray  or  pencil  of  light  A  B,  C  B,.falUnjr 
on  the  surface  D  E,  a  portion  of  tiie  light  in  reflected, 
and  another  portion  is  transmitted,  in  the  direction 
B  F,  B  G,  so  tliat  B  G  is  equal  to  B  C,  and  B  H  to  B  I, 
C I K  and  G  H  L  being  lines  perpendicular  to  D  E  at 
any  such  distances,  that  BK  may  be  to  B  L  in  a  cer- 
tain proportion,  which  is  that  of  the  sines  of  the  angles 
of  incidence  ABM,  C;B  M,  to  those  of  the  angles  of  re- 
fraction F  B  N,  G  B  N.  B  O  and  B  P  are  tlie  reflected 
portions  of  the  rays.     P.  411. 

Fig.  370.  A  mode  of  determining  the  position  of  a 
refracted  ray,  which  is  particularly  convenient  in  the 
case  of  refractions  at  spherical  surfaces.  ABC  being 
any  circle,  either  touching  the  refractive  surface  at  A, 
or  being  itself  a  section  of  Uie  refracting  substance,  if 
another  circle  D  E  F  be  drawn  on  the  same  centre, 
having  its  diameter  to  that  of  the  first  as  the  sine  of 
the  angle  of  incidence  to  that  of  refraction,  and  a  third 
circle  G  H  I,  which  is  less  than  the  first  in  the  same 
proportion  as  the  second  is  greater;  and  if  the  direction 
of  the  incident  ray  K  A  be  continued  to  D,  andLD  be 
drawn  from  the  centre,  cutting  G  H I  in  G,  A  G  will  be 
the  direction  of  the  refracted  ray:  and  if  this  ray 
pass  again  out  of  tlie  denser  medium  at  B,  its  direc- 
tion BM  may  be  found  by  drawing  LIF,  and  FBM 
will  be  thus  truly  determined.     P.  411. 

Fig.  371.  A  ray  or  pencil  A  B,  refracted  at  B  to  C, 
and  there  reflected  by  a  perpendicular  surface  into  an 
opposite  direction  C  B,  will  return  also  in  the  direction 
B  A,  a  portion  of  it  being  reflected,  in  the  first  place  to 
D,  and  in  the  second  to  E.     P.  412. 

Fig.  372.  A  pencil  A  B  passing  through  a  substance 
CD  contained  between  parallel  surfaces,  continues  its 
course  in  the  direction  E  F  parallel  to  A  B.     P.  413. 

Fig.  373,  The  ray  AB,  entering  the  medium  CD 
through  the  transparent  substance  E  F,  contained  be- 
tween parallel  surfaces,  acquires  the  direction  Gil,  pa- 
rallel to  IK,  into  which  LI  is  at  once  refracted.  P. 
413. 

Fig.  374.  The  appearance  of  a  prism,  of  which  the 
lower  surface  is  divided  into  a  bright  and  a  dark  por- 
tion, separated  by  a  coloured  arch  A  B  C.    P.  414. 


784 


•  PLATE  XXVII. 


Fig.  375.  A  is  an  Actual  focus  of  diverging  rays,  B 
M  actual  focus  both  of  couverging  and  of  diverging  rays, 
C  a  virtual  focus  of  converging  rays,  and  D  a  virtual 
focus  of  diverging  rays;  A  and  B,  B  and  C,  and  C  and 
D  are  foci  conjugate  to  each  other,  with  respect  to  the 
refractions  of  the  three  lenses.     P.  415. 

Fig.  376.  The  image  of  the  point  N,  formed  by  the 
plane  mirror  A  B,  is  at  an  equal  distance  behind  the 
mirror;  and  in  this  manner  the  whole  image  of  the 
word  is  formed  in  an  inverted  position.     P.  415. 

Fig.  S77.  ABCD  represents  a  pencil  of  parallfl 
rays  falling  on  the  concave  mirror  C  D,  and  collected 
into  the  principal  focus  at  E,  wWch  is  half  way  be- 
tween the  surface  and  its  centre.  F  is  tlie  principal 
focus  of  the  convex  mirror  G;  and  H  that  of  the  re- 
fracting surface  I.     P.  416. 

Fig.  378.  A  being  the  centre  of  the  concave  mirror 
B,  tlie  image  of  an  object  at  C  will  be  found  at  D,  and 
the  reverse.     P.  416. 

Fig.  379.  A  pencil  of  light,  deflected  from  its  path 
by  a  prism  of  a  denser  substaiicc,  in  different  posi- 
tions.    P.  416. 

Fig.  380.  A  pencil  of  light  scattered  into  various 
directions  by  a  multiplying  glass.     P.  416. 

Fig.  381.  A  is  a  section  of  a  double  con  vex  lens,  B  of 
a  double  conc«ve.  C  is  a  planoconvex,  D  a  planocon- 
cave; and  E  and  V  meniscus  lenses;  but  a  menis- 
cus ot  the  form  represented  by  F  is  sometimes  called 
a  concavoconvex  lens.     P.  417. 

Fig.  S8'.J.  The  pencils  of  light  A,  B  are  refracted  by 
the  convex  lens  tj  in  the  same  manner  as  lliey  would 
have  been  by  the  circumscribed  double  prism  DE; 
and  in  the  same  manner  the  concave  lens  F  resembles 
in  its  operation  the  prisms  G,  H.     P.  417. 

Fig.  S83.  A,  a  pencil  of  parallel  rays,  made  to  con- 
verge, by  a  double  convex  lens  of  crown  glass,  to  the 
centre  of  cui-vature  of  one  of  its  surfaces.  B  a  double 
concave  lens,  causing  the  rays  to  diverge  from  the 
centre  of  curvature.  C,  D  a  planoconvex  lens,  of 
which  the  principal  focus  is  at  the  distance  of  a  dia- 
meter.    P.  417. 

Fig.  384.  The  lenses  represented  by  the  shaded 
surfaces  are  equivalent  in  their  effects  to  those  of 
which  the  sections  are  shown  by  the  dotted  lines;  the 
figures  at  A  and  B  being  of  equal  thickness  in  the 
middle,  and  at  C  at  the  edges  also.     P.    417. 

Fig.  385.  At  A,  a  r.idiant  point  and  its  image  are 
both  situated  at  the  distance  of  twice  the  focal  length 
from  the  lens;  at  B,  the  one  is  more  remote,  tlie  other 
nearer;  and  CD  is  to  D E  as  EF  to  FG;  D  and  F 
being  the  principal  foci  of  the  lens.     P.  418. 

Fig.  386.    Thie  oblique  pencils  of  rays  A,  B,  and 


the  direct  pencil  C,  are  supposed  to  be  brought  to 
their  respective  foci  in  the  same  plane  D  E.     P.  419. 

Fig.  387.  The  square  A  intercepts  the  whole  light, 
proceeding  from  the  point  B,  which  would  fall  on  the 
surface  C  D,  four  times  as  great,  placed  at  a  double 
distance.     P.  421. 

Fig.  388.  The  box  of  Count  Rumford's  photome- 
ter. The  lights,  being  placed  at  proper  distances  on 
the  graduated  arms  or  tables  A,  B,  throw  equally  dark 
shadows  of  the  cylinders  C,  D  on  a  white  surface  at 
EF.  The  wings  of  the  cylinders  serve  to  make  the 
shadows  of  equal  breadth.  The  shadows  are  viewed 
through  the  aperture  at  G.     P.  421. 

F'ig.  389.  Dr.  Wollaston's  instrument  for  the  mea- 
surement of  refractive  densities.  A  is  a  rectangular 
prism  of  flint  glass,  under  which  the  substance  to  be 
examined  is  attached;  BC  is  a  rod,  or  ruler,  10 
inches  lone,  C  D  and  D  E  are  each  15  ,»jji.  Wlicn  the 
sights  at  B  and  C  are  so  placed  that  the  division  be- 
tween the  light  and  dark  portion  of  the  lower  surface 
of  the  prism  is  seen  through  them,  the  rod  F,  which 
carries  a  vernier,  shows  the  index  of  the  refractive 
density,  which,  in  the  situation  here  represented, 
would  be  1.43.     P.  421. 

Fig.  390.  A  is  the  actual  image  of  the  candle  B, 
formed  by  the  convex  lens  C.     P.  422. 

Fig.  391.  A  is  the  actual  image  of  the  candle  B, 
formed  by  the  concave  mirror  C.     P.  422. 

Fig.  392.  A  is  the  actual  image  of  the  candle  B, 
formed  by  the  convex  lens  C,  being  as  much  larger 
than  the  object  as  it  is  more  distant  nom  the  lens.  P. 
422. 

F'ig.  393.  A  is  the  virtual  image  of  the  Candle  B, 
placed  within  the  focal  distance  of  the  concave  mirror 
C,  the  image  remaining  erect.     P.  422. 

Fig.  394.  A  is  the  virtual  image  of  the  candle  B, 
formed  by  the  concave  lens  C,  and  less  than  the  ob* 
ject.     P.  422. 

Fig.  395.  When  the  object  A  is  placed  in  the  prin- 
cipal focus  of  the  convex  lens  B,  a  virtual  image  i% 
formed  at  an  infinite  distance,  which  subtends,  when 
viewed  from  C,  or  from  any  other  point,  the  same  an- 
gle as  the  object  subtends  at  the  centre  of  the  lens. 
P.  422. 

Fig.  396.  The  object  A  being  placed  a  little  within 
the  focus  of  the  lens  B,  a  virtual  image  C  is  fonned,  at 
such  a  distance  as  is  most  convenient  to  the  eye,  which 
subtends  the  same  angle  a>  the  object,  from  theceotrC 
of  the  lens,  and  therefore  appears  somewhat  more 
magnified  than  when  the  object  is  in  the  principal  fo- 
cus.    P.  422. 


Plate  XXVn. 


r.K.?,--. 


FtA.hy  J.  Johnson. London  i  July  1806 . 


Joseph.  Skrltan   sculp. 


Pi  ATE  XXVffl.. 


Tig-.  357 


Pub  hy  J.  Johjhson  .london  i  Juiy  1S06. 


Joseph  Skfhim   SI 


PLATE  XXVIII. 


Fig.  Z9T.  An  imperfect  image  of  an  externa!  object, 
painted  in  a  dark  room,  in  an  inverted  position,  by  the 
light  coming  in  right  lines  tlirough  a  small  aperture. 
P.  425. 

Fig.  398.  A  portable  camera  obscura.  A  is  a  lens, 
B  a  mirror  placed  obliqnely,  and  throwing  the  image 
on  a  plate  of  ground  glass,  CD.  E  is  a  moveable  cover, 
and  FO  a  screen  attached  to  it,  for  excluding  foreign 
light.     P.  425. 

Fig.  399.  A  camera  oljscura,  whicli  throws  down  an 
image,  by  means  of  the  mirror  A,  and  the  Ions  B,  on 
the  surface  C,  where  it  may  be  seen  through  the  aper- 
ture D.  The  surface  C  has  here  the  curvature  best 
adapted  to  receive  every  where  a  perfect  image  of  a 
distant  object.     P.  425. 

Fig.  4o6.  An  arrangement  proposed  for  a  solar  mi- 
croscope, adapted  to  a  window  facing  the  souUi.  I  he 
mirror  A  is  moved  by  a  hinge  into  the  position  required 
for  tlie  day,  and  during  the  emph)ymeut  of  the  instru- 
ment is  turned  only  round  the  axis  .\  B,  which  is  pa- 
rallel to  that  of  the  earth.  The  mirror  C  is  fixed:  it 
receives  the  beam  of  light  from  A,  and  throws  it  on  the 
object  through  the  lenses  D  and  E,  of  which  the  joint 
focus  is  near  the  magnifying  lens  F;  this  lens  paints 
an  image  of  the  object  in  an  inverted  position  on  a 
screen  at  G.  If  the  focus  of  the  condensing  lenses 
were  behind  the  object,  as  at  H,  the  light  would  be 
liable  to  be  condensed  into  a  spot  on  the  screen  at  I. 
P.  426. 

Fig.  401.  An  arrangement  proposed  for  a  phantas- 
magoria. The  light  of  the  lamp  A  is  thrown  by  the 
mirror  C  and  the  lenses  C  and  D  on  the  painted  slider 
at  E,  and  the  magnifier  F  forms  the  image  on  the 
screen  at  G.  This  lens  is  6xed  to  a  slider,  which  may 
be  drawn  out  of  the  general  support  or  box  H:  and 
when  the  box  is  drawn  back  on  its  wheels,  the  rod  I 
K  lowers  the  point  K,  and  by  means  of  the  rod  K  L 
adjusts  the  slider  in  «urh  a  manner,  tliat  the  image  is 
always  distinctly  painted  on  the  screen  G.  When  the 
box  advances  towards  the  screen,  in  order  that  the 
images  may  be  diminished  and  appear  to  vanish,  the 
support  of  the  lens  F  sutTers  the  screen  M  to  fall  and 
intercept  a  part  of  the  lijht.  The  rod  K  N  must  be 
equal  to  I  K,  and  the  point  I  must  be  twice  the  focal 
length  of  the  lens  F,  before  the  object,  L  being  iinmc- 
<liatc!y  under  the  focus  of  the  lens.  I'he  screen  M  may 
have  a  triangular  opening,  so  as  to  uncover  tlie  middle 
of  the  lens  only,  or  the  light  may  be  intercepted  in  any 
otlier  manner.    P.  427. 

Fig.  402.  The  construction  of  the  astronomical  te- 
lescope. ABC  and  D  EC  arc  the  central  parts  of  the 
pencils  of  rays,  coming,  from  the  c:i!tiemities  of  the  visi- 
ble field,  through  the  middle  of  the  object  glass.  P. 
427. 

Fig.  403.  The  extreme  pencils  of  rays  in  the  double 
or  compound  microscoj-e.     P..438. 

Fig.  404.  The  extreme  pencils  in  the  Galilean  tele- 
€cope,  or  opera  glass.     P.  423. 

Fig.  405.  A,  ilic  directions  of  the  extreme  pencils 
in  the  common  daj  telescope  of  lUicita.  If  only  two 
€ye  glasses  were  employed,  as  at  H,  the  field  would 
tibviously  be  more  ccnUactLd.     P.  428. 

Fig.  406.  Dr.  Ilerschers  forty  fet  t  telescope.  ABC 
the  path  of  a  ray  of  light,  reflected  by  the  mirror  at 
B  to  the  eye  glass  C.  I)  a  chair  in  which  the  observer 
sits.  E  a  moveable  gallery,  on  which  several  persons 
may  stand.  F  G  a  smooth  surface,  on  which  the  bottom 
of  the  telescope  is  made  to  roll  along,  while  its  opening 

2 


is  raised  or  depressed  by  the  pullies  at  II  and  I.  K  one 
of  two  rooms  or  huts  for  the  accommodation  of  the  ob- 
server's assistants.  The  wheels,  under  the  frame,  serve 
to  turn  the  whole  instrument  round  its  centre.    P.  429. 

Fig.  407.  The  Newtonian  telescope,  with  the  di- 
rection of  the  central  r.nys.  These  are  not  the  rays  by 
which  the  object  is  actually  seen,  because  they  are 
intercepted  by  the  small  .speculum,  but  they  afford  the 
simplest  determination  of^  the  magnitude  of  the  field 
of  view.     P.  429. 

Fig.  408.  The  supposed  path  of  the  central  rayl 
in  the  Gregorian  telescope.     P.  429. 

Fig.  409.  The  supposed  path  of  the  central  rays  in 
Cassegrain's  telescope.  Here  the  rays  actually  repre- 
sented would  not  only  be  intercepted  by  the  small 
mirror,  but  they  would  also  fall  on  the  perforation  of 
the  great  mirror.  They,  however,  serve  equally  well 
to  determine  the  magnitude  of  the  field.     P.  429.    ■ 

Fig.  410.  The  supposed  path  of  the  central  rays  ia 
Dr.  Smith's  microscope.  The  rays  running  directly  from 
the  object  are  intercepted  by  a  screen.     P.  429. 

Fig.  411.  A;  the  dotted  line  represents  the  curr* 
called  the  caustic  of  a  concave  mirror,  in  which  the 
rays  proceeding,  in  the  section  represented  by  the  fi- 
gure, from  a  distant  point,  would  be  collected.  B;  the 
dotted  line  is  the  caustic  of  a  convex  mirror.  The  eye 
being  supposed  to  be  at  a  great  distance  from  the  he- 
mispherical mirrors  C  and  13,  the  images  of  distant  ob- 
jects ill  all  directions  will  be  found  between  the  dotted 
curves,  the  distance  of  those  curves  sliowing  the  de- 
gree of  confusion.  The  images  of  distant  objects  ia 
all  directions  formed  by  the  small  concave  and  convex 
mirrors  E  and  F,  are  found  between  the  dotted  circle 
and  the  straight  line  touching  it.     P.  430. 

Fig.  412.  The  effect  of  a  field  glass  in  a  compound 
microscope;  the  inner  lines  showing  what  would  be 
the  magnitude  of  the  field  without  it.     P.  431. 

Fig.  413.  The  manner  in  which  Mr.  Ilamsden  em- 
ployed a  planoconvex  lens  in  the  eye  pieces  of  his  tele- 
scopes and  in  his  double  magnifiers.  The  curved  dot- 
ted line  shows  the  image  of  the  straight  line  divided 
into  equal  parts,  which  is  formed  by  the  larger  lens,  ia 
the  focus  of  the  smaller,  through  which  it  is  viewed. 
P.  431. 

Fig.  414.  An  achromatic  telescope,  with  a  triple 
object  glass,  and  with  Boscovich's  achromatic  eve 
piece,  consisting  of  two  similar  lenses,  one  of  which  is 
every  w.-iy  three  times  as  groat  as  the  other,  their  dis- 
tance being  twice  the  focal  length  of  the  smaller.  P. 
432. 

Fig.  415.  The  dotted  lines  AB  and  CD  represent 
two  images  of  the  same  object,  formed  by  rays  tliffer- 
ently  refrangible,  passing  through  a  simple  object  glass, 
which  are  brought,  Vjy  the  effect  of  the  Ions  or  field  glass 
E,  into  such  places  and  dimensions  aslo  subtend  nearly 
the  same  angle  from  the  eye  glass  F.     P-  432. 

Fig.  410.  A  represents  Mr.  Ilamsden's  divided  eye 
glass  micrometer,  the  two  portions  being  moved  at 
once  in  contrary  directions  by  turning  the  pinion  B, 
until  the  two  extremities  of  the  distance  to  be  mear- 
sured  appear  to  coincide.     P.  433. 

Fig.  417.  Dr.  Maskelyne's  micrometer,  made  by  a 
double  achromatic  prism  A,  exhibiting  two  images  B, 
C,  the  different  parts  of  which  are  made  to  coincide,  by 
moving  the  prism  backwards  and  forwards  in  the  direc- 
tion of  the  axis  of  the  telescope.  Mr.  Ramsden  thinks 
that  any  substance  thus  interposed  must  interfere 
greatly  with  the  perfection  of  the  telescope.    P.  4S3. 


786 


PLATE  XXIX. 


Fig.  418.  If  A  B  and  AC  represent  tlie  comparative 
velocity  of  light  and  of  the  eartli,  in  their  respective 
directions,  a  telescope  must  be  placed  in  the  direction 
BC,  in  order  to  see  the  star  D,  and  the  star  v^ill  ap- 
pear at  E.     P.  437. 

Fig.  419.  The  spectrum  produced  by  lookingthrough 
a  prism  at  a  narrow  line  of  light.     P.  438. 

Fig.  420.  The  appearance  of  a  portion  of  the  blue 
light  at  the  bottom  of  a  candle,  viewed  through  a 
prism.     P.  438. 

Fig.  421.  The  appearance  of  a  circular  aperture, 
moderately  large,  when  viewed  through  a  prism.  P. 
439. 

Fig.  422.  A  B  and  C  D  represent  the  appearance  of 
the  two  ends  of  a  broad  white  surface,  or  a  window, 
'when  viewed  through  a  prism.  The  oblique  stripes  of 
colour  show  the  degrees  by  which  the  lights  of  different 
kinds  enter  into  the  compound  light.  It  follows  from 
this  analysis,  that  the  colours,  horizontally  opposite 
each  other  in  A  B  and  C  D,  would  always  together 
make  up  white  light.     P.  439. 

Fig.  423.  The  colours  on  the  circle  A  exhibit,  when 
whirled  swiftly  round,  a  whitish  light  resembling  B. 
P.  440. 

Fig.  424 . .  426.  The  colours  of  the  circle  A  pro- 
duce, when  made  to  revolve  rapidly,  the  tints  shown 
atB.    P.  440. 

Fig.  427.  A  triangular  figure,  exhibiting  in  theory 
all  possible  shades  of  colours.  The  red,  the  green,  and 
the  violet,  are  single  at  their  respective  angles,  and  are 
gradually  shaded  off  towards  the  opposite  sides:  a 
little  yellow  and  blue  only  are  added  in  their  places, 
in  order  to  supply  the  want  of  brilliancy  in  the  colours 


which  ought  to  compose  them.  The  centre  is  grey,  atvd 
the  lights  of  any  two  colours,  which  are  found  at  equal 
distaiices  on  opposite  sides  of  it,  would  always  very 
nearly  make  up  together  white  light,  as  yellow  and 
violet,  greenish  blue  and  red,  or  blue  and  orange.  P. 
441. 

Fig.  428.  The  appearance  of  a  pin,  and  of  the  word 
POKER,  when  viewed  by  looking  along  the  surface  of  a 
red  hot  poker.     From  Dr.  WoUaston.    P.  442. 

Fig.  429.  The  appearance  of  an  oblique  line,  and  of 
the  word  spin  it,  viewed  simply  through  rectified  spi- 
rit of  wine,  and  through  a  portion  of  the  spirit  mixing 
by  degrees  with  the  water  on  which  it  floats.  From 
Dr.  WoUaston.     P.  442. 

Fig.  430.  The  colours  of  the  primary  and  secondary 
rainbow,  as  they  usually  appear.     P.  443.  ! 

Fig.  431.  The  most  common  form  of  halos  and 
parhelia.     P.  444. 

Fig.  432.  Magnified  figures  of  the  simplest  crystals 
of  snow,  which  are  sufficient  to  account  for  the  produc- 
tion of  halos.     From  Nettis.     P.  444. 

Fig.  433.  A  complicated  system  of  halos.  From 
Lowitz.  The  arcs  A,  B,  and  C,  were  coloured,  and, 
like  all  the  other  coloured  parts,  bad  the  red  towards 
the  sun.    D  and  E  are  two  anthelia.     P.  444. 

Fig.  434.  The  figures  of  two  complicated  flakes  of 
snow.    From  Nettis.    P.  444. 

Fig.  435.  The  ray  of  light  AB,  falling  perpendicu- 
larly on  the  surface  of  the  piece  of  calcarious  spar  C  D 
atB,  is  divided  into  the  portions  BE  and  BF:  the 
portion  B  E  passing  to  the  point  E,  where  the  surface 
of  the  spheroid  EGH,  inscribed  in  the  greater  angle 
of  the  crystal,  becomes  parallel  to  C  B.    P.  44d. 


Plate  txtx  . 


Tig-.  419 


Fig.  420.     Fig^.421. 


Fig-.  418 


Fig-.  428 . 


Fig-.  429 


Fig-.  4^0 . 


FuJb.by  J.  Johnjon  .ZonAonj.  Julyx8o6 . 


JosefJv  Skdtort  jc 


\ 


Plate  XXX 


Tig  438. 


Fig.  443 . 


Tig-.  .1,16 


illll   Bli 


^i?-447- 


I'ig'-  444- 


Pig.  440  ■ 


Eg-.  460 . 


Tub.hy  J.  Johnson. LonSyOrt  2  July  1.S06 . 


Joseph  SkeiUn  sadp . 


787 


PLATE  XXX. 


Fig.  436.  A  section  of  the  human  eye.  A  is  the 
cornea ;  B  the  aqueous  humour,  in  which  the  uvea 
hangs;  C  the  crystalline  lens;  the  ciliary  processes 
being  between  it  and  the  uvea;  D  the  vitreous  hu- 
mour ;  E  F  G  is  the  choroid  coat,  lined  by  the  retina; 
li  I  K  the  sclerotica,  and  L  the  optic  nerve.     P,  447. 

Fig.  43r.  A  picture  painted  on  the  retina  in  an 
inverted  position,  seen  by  dissecting  off  tlie  sclerotica 
and  choroid  behind  it.     P.  448. 

Fig.  438.  The  apparent  figure  of  the  heavens  being 
nearly  like  the  curve  ABC,  the  sun  or  moon  at  A 
or  C  appears  to  be  much  larger  than  at  B.     P.  454. 

Fig.  439.  The  red  square  A,  inclosing  a  green  square, 
produces,  if  viewed  attentively,  in  a  strong  light,  a 
spectrum  resembUng  B,  which  is  red  within  and  green 
without,  and  which  appears  when  we  look  soon  after 
cn  any  white  object.    P.  456. 

Fig.  440.  Tlie  spot,  wliich  is  tinted  with  blact  lines 
only,  appears,  upon  the  yellow  grouud,  of  a  purple 
hue.     P.  456. 

Fig.  441.  A  grey  spot  on  a  purple  ground  appears 
of  a  greenish  yellow  or  olive  hue.     V.  456. 

Fig.  442.  The  manner  in  which  two  portions  of 
coloured  liglit,  admitted  through  two  small  apertures, 
produce  light  and  dark  stripes  or  friivges  by  their  in- 
terference, proceeding  in  the  form  of  hyperbolas;  the 
middle  ones  are  however  usually  a  little  dilated,  as  at 
A.    P.  465. 

Fig.  443.  A  series  of  stripes  of  all  colours,  of  their 
appropriate  breadths,  placed  side  by  side  in  the  man- 
ner in  which  they  would  be  separated  by  refraction, 
and  combj^ncd  together  so  as  to  form  the  fringes  of 
xolourB  bcluw  them,  beginning  from  white.     P.  465. 


Fig  444.  A  series  «fcoronae,  seen  round  the  sun  sr 
moon.     P  466. 

Fig.  445.  The  internal  hyperbolic  fringes  of  a  rect- 
angular shadow.     P.  467. 

Fig.  446.  The  external  fringes  seen  on  each  side 
of  the  shadow  of  a  hair  or  wire,  which  is  also  divided 
by  its  internal  fringes.  The  dotted  lines  show  the 
natural  magnitude  of  the  shadow,  independently  of 
diffraction.     P.  468. 

Fig.  447.  Analysis  of  the  colours  of  thin  plates  seen 
by  reflection,  beginning  from  black.  A  line  drawn 
across  the  curved  fringes  would  show  the  portions  into 
which  the  light  of  any  part  is  divided  when  viewed 
through  a  prism.     P.  469. 

Fig.  448.  The  coloured  stripes  of  a  film  of  soapy 
water,  covering  a  wine  glass.     P.  469. 

Fig.  449.  The  colours  of  a  thin  plate  of  air  or  water, 
contained  between  a  convex  and  a  plane  glass,  as  seen 
by  reflection.    P.  469. 

Fig.  450.  The  colours  of  a  mixed  plate;  as  seen  by 
partially  greasing  a  lens  a  little  convex,  and  a  flat  glass, 
and  holding  them  together  between  the  eye  and  the 
edge  of  a  dark  object.  One  half  of  the  series  begins 
from  white,  the  other  from  black,  and  each  colouris  the 
contrast  to  that  of  the  opposite  half  of  the  ring.  P.  470. 

Fig.  451.  The  composition  of  the  colours  of  the 
primary  rainbow,  when  attended  by  supernumerary 
bows.     P.  471. 

Fig.  452.  The  colours  of  concave  mirrors.  The 
small  circles  in  the  middle  white  ring  represent  the 
aperture  by  which  the  light  is  adrnitted,  and  its  image ; 
the  coloured  rings  are  formed  by  the  light  irregularly 
dissipated,  before  and  after  reflection.    P.  471. 


788 


PLATE  XXXI. 


Fig.  453, 454.  The  appearance  of  the  star  Lyra, 
viewed  with  telescopes  magnifying  460  and  «J450 
times  respectively.     From  Dr.  Herschel.     P.  491. 

Fig.  455.  The  appearance  of  the  nebula  in  Orion, 
abont  lialf  a  degree  in  length.  From  Messier.    P.  492. 

Fig.  456  .  .  463.  The  appearances  of  different  nebu- 
lae.   From  Dr.  Ilerschcl.     P.  492. 

Fig.  464.  A  section  of  the  nebula  to  which  the  sun 
is  supposed  to  belong,  its  projection  forming  the  milky 
way ;  taken  in  a  plane  perpendicular  to  its  longest  dia- 
meter. From  Dr.  Herschel.  The  large  stai  in  the 
middle  represents  the  sun,  and  the  circle  drawn  round 
itis  at  forty  times  the  distance  of  the  nearest  fixed  stars, 
comprehending  probably  all  the  stars  which  are  visible 
to  the  naked  eye.    P.  493. 

Fig.  465.  A  large  spot,  traced  through  different 
forms  in  its  path  across  the  sun.  From  Dr.  Wilson. 
A  is  its  place  23  Nov.  1769;  B,  24  Nov.  C,  11  Dec. 
D,  12  Dec.  and  E,  U  Dec.    P.  501. 


Fig.  466.  A,  a  large  spot  on  the  snn;  B,  the  ar- 
rangement of  the  luminous  and  opatjue  strata  of  clouds 
by  which  Dr.  Herschel  explains  the  appearance  of  the 
spot.     P.  501. 

Fig.  467.  A,  a  spot  with  a  lighter  portion  in  the 
middle;  B,  the  arrangement  of  the  strata  correspond- 
ing to  it.     P.  501. 

Fig,  468.  The  position  assumed  by  the  strata  which 
had  formed  the  spot  shown  in  the  last  figure,  viewed 
about  an  hour  afterwards.     P.  501. 

Fig.  469.  A  and  B  are  the  forms  of  a  solar  spot, 
at  about  two  hours  distance  of  time;  C,  D,  and  E, 
are  the  successive  forms  of  another  spot.     P.  501. 

Fig.  470.  The  appearance  of  the  zodiacal  light,  or 
solar  atmosphere,  as  it  is  seen  in  these  climates,  in  the 
evening,  about  the  beginning  of  March ;  A  B  being  the 
horizon,  and  C  the  supposed  place  of  the  sou.  P. 
SOS. 


Plate  jxkl. 


Sg.453 


Tig.  464. 


Tig . 45  5 . 


Kg.  466 . 


Tab. by  J.  Johnson  .J.ondon  1  July  1806. 


Soscph  Skehorh  sa 


'^\t.  0Jflu  .  '  tt^ 


/ 


Plate  xxxn. 


OJTie  suTt.   '^Miercvry     ^  Venus. 

©  ITie  ear0v.       <S  2iars. 

^  Jiaio .     <^JPk3aj . 

O  Ceres.   %  Jupiter. 

%j  Satzcm . 

O  Geor^iaih 
planet. 


Fig.  475 


£uh.lfy  J.Johju<m,,X(mdorv  d.  JiJyx8o6 . 


Joseph.  Skeitmt  scuT^ 


789 


PLATE  XXXir. 


rig.  471.  A  representing  the  sun,  B  tlie  eartli,  and 
C  the  planet  Mars;  supposing  Mai's  and  the  earth  lo 
net  out  to;;et!ier  from  D  and  E,  the  angle  D  A  C  was 
letermined  by  Kepler  from  calculation,  and  the  angles 
BAD  and  ABC  hy  observation  ;  whence  it  was  easy 
to  construct  the  triangle  ABC,  and  to  find  the  pro- 
portion of  A  B  to  A  C.     P.  .505. 

Fig.  472.  The  solar  system,  representing  the  form 
and  proportions  of  the  orbits  of  all  the  primary  planets, 
and  of  three  of  the  comets.  The  parts  of  the  orbits 
represented  by  entire  lines  are  on  the  north  of  the 
ecliptic,  the  dotted  parts  on  the  south  :  the  letters  A 
nnd  P  denote  the  aphelion  and  perihelion.  The  point 
in  the  centre,  which  ought  to  be  only  7J5  of  an  inch  in 
diameter,  represents  the  sun.  The  figures  of  the  re- 
«pective  planets  show  their  comparative  magnitude, 
that  of  the  sun  being  represented  by  the  innermost  of 
the  graduated  circles  which  inclose  the  whole :  they 


are  placed  according  to  their  actual  situations  on  the 
14th  June,  1806.  The  letters  M  D  show  the  mean 
distance  of  the  comet  of  1759,  being  placed  at  the  ex- 
tremity of  the  lesser  axis  of  the  ellipsis  in  which  it 
must  be  supposed  to  revoWe.    P.  514. 

Fig.  473.  The  periodical  times  of  the  different  pla- 
nets, represented  by  lines  of  different  lengths.  P. 
514. 

Fig.  474.  The  comparative  velocities  of  the  dif- 
ferent planets,  represented  by  lines  which  show  the 
number  of  English  miles  described  in  a  second,  on  tht 
scale  marked  on  the  lowest  line.     P.  514. 

Fig.  475.  The  places  of  the  ascending  nodes  of  all 
the  planets,  marked  on  one  half  of  the  ecliptic,  sup- 
posed to  be  extended  in  a  straight  line ;  together  with 
the  inclinations  of  their  orbits.  The  line  marked 
F.  F.  £.  £,  shows  the  situatioQ  of  the  fixed  ecliptic.  P. 
514. 


VOL.   I. 


5  F 


790 


PLATE  XXXIII. 


Fig.  476.  A.  The  appearance  of  Venus,  from 
Dr.  Herschel:  B,C,  from  Mr.  Schroeter.     P  514. 

Fig.  47r.  A  .  .  D,  the  appearance  of  Mars,  from 
Dr.  Herschel.  The  figures  are  inverted,  as  they 
appear  in  the  astronpmical  telescope.     P.  514. 

Fig.  478.  A,B.  The  appearance  of  Jupiter,  witli 
his  belts,  from  Dr.  Herscliel.     P.  514. 

Fig.  479.  The  appearance  of  Saturn,  with  his  ring, 
from  Dr.  Herschel.     P.  514. 

Fig.  480.  The  appearance  of  tlie  moon,  in  an  in- 
verted position.  The  figure  is  copied  from  Mr. 
Nicholson's  plate,  the  references  from  Cassini  and 
Lalandc.  Eq.  is  the  place  of  the  moon's  equator.  P. 
514. 

Names  of  the  spots,  according  to 
Riccioli,  and  Hevelius. 


.  1  Grimaldus         or 
3  Galileus 

3  Aristarchus 

4  Keplerus 

5  Gassendus 

6  Schikardus 

7  Harpalus 

8  Hera  elides 
(J>)  Vulcanus 

9  Lansbergius 

10  Reinoldus 

11  Copernicus 

12  Helicon 

13  Capuanui 

14  Buliialdus 

15  Eratosthenes 

16  Timocharis 
IT  Plato 

18  Archimedes 
(«)  Aratus 

19  Insula  sinus  medii 
SO  Pitatus 

31  Tycho 


Palus  Mareotis 
Mens  Audus 
Mons  Porphyrites 
Loca  paludosa 
Mons  Cataractcs 
Mons  Troicus 
Insula  sinus  hyperborej, 
Caput  mulieris 

Insula  Malta 
Mons  Ncptunus 
Mons  Aetna 
Insula  erroris 
Itegio  Cassiotis 
Insula  Cueta 
Insula  Vulcania 
Insula  Corsica 
Locus  niger  major 


Mare  mortuum 
Mont  Sinai 


Mons  Carpathes 
Mons  .Serrorura 
Insula  Berbicus 
Byzantium 
Mons  Bodinus 


Promontorium  Acherusia 
Mons  Moschi 
Lacus  Thospitis 
Promontorium  acutum 

Promontorium  Somnii 
Mons  Corax 
Montes  Riphaei 
Mons  Paropamisus 
Petra  Sogiliana 
Insula  major 
Sinus  Phasianus 


22  Eudoxus 

23  Aristoteles 

24  Manilius 

25  Menelaus 

26  Hermes 

27  Dionysius 
(rf)  Albatcgnius 

29  Plinius 

30  S.  Thcophilu* 

31  Fracastorius 

32  Ccnsorinus 

33  Mesisala 
34 

35  Proclus 

36  Cleomedes 

37  Snellius 
83  Petavius 

39  Langrenus 

40  Taruntius 
A  Marc  Humorum 
B  Mare  Nubiura 
C  Mare  Imbrium 
D  Mare  Nectaris 

£  MareTranquilitatis 

F  Mare  Serenitatis 

G  Marc  Foecunditatis 

11  Mare  Crisium  » 

Fig.  481  .  .  483.  The  satellites  of  Jupiter,  Saturn, 
and  the  Geori;ian  planet,  at  their  proper  distances,  i" 
proportion  to  the  diameters  of  the  planets,  shown  on 
tiie  same  scale.     P.  514. 

Fig.  484.  The  figure  of  tlie  tail  of  the  comet  of  1680, 
represented  in  the  plane  of  its  orbit,  from  Newton. 
A  B  is  the  earth's  orbil,  C  and  D  arc  the  first  and  last 
appearances  of  the  tail,  and  E  F  is  the  line  of  tlie 
nodes.     P.  514,    ■ 

Fig.  485.  A,  B,  Two  successive  appearances  of  the 
comet  of  1723,  from  Lord  Paisley.    P.  314. 


Plate   XXXUL. 


Fig-.  476. 


Hg-.48i 


Tuh.hy  J.Jahruitn.  .London  1  July  1806. 


Joseph  Skelion  jctdp. 


PLATE  XXXIV  . 


Rg .  486 . 


Fig;.  488 


Figr-  499 


Hth.  by  J.  Johnson  .London  j  July  iSot*. 


Joseph  JX-cM'//    sai{ 


791 


PLATE  XXXIV. 


Fig.  486.  Tlic  gravitating  body  ABC,  being  sup- 
posed to  revolve  on  the  axis  A  C,  the  fluid  column 
B  D  must  be  longer  than  ED,  in  order  to  support  its 
pressure.     P.  510. 

Fig.  487.  If  A  represent  the  place  of  the  sun,  B 
that  of  the  earth,  and  C  that  of  the  moon,  taking  A 1) 
to  A  C  as  tlie  square  of  A  C  is  to  the  square  of  A  B, 
AD  will  represent  the  sunV  attraction  acting  on  the 
earth,  and  CD  the  disturbing  force,  wliich,  together 
with  AD,  makes  up  AC,  the  force  actin;;  on  the 
moon  ;  and  it  is  obvious  that,  when  the  nodes  are  in 
any  oblique  situation,  as  E  F,  the  force  being  directed 
to  some  point  D,  bclwcen  B  and  A,  while  t!ie  moon 
moves  from  G  to  H,  the  force  CD  will  tend  to  lesson 
the  inclination,  while  the  moon  is  ascending  from  E 
towards  C,  and  to  cause  the  node  E  to  move  back  to- 
wards G,  and,  when  it  is  again  de-cending  towards 
F,  the  inclination  will  he  increased,  and  the  node  F 
made  to  recede  towards  11,  until  the  nioon  arrives  at 
II,  and  the  force  becomes  directed  to  a  point  on  the 
other  side  of  B;  the  nodes  only  advancing  while  the 
moon  is  between  II  and  F,  or  between  G  and  E.  P. 
520. 

Fip:.  488.  A  body  attracted  towards  the  centre  A, 
and  descending  from  B  in  the  ellipsis  BCD,  has  the 
inclination  of  its  orbit  to  tlie  revolving  radius  A  B,  A  C, 
AD,  perpetually  changed,  until  at  D  it  becomes  per- 
pendicular to  it ;  but  when  the  force  increases  more 
rapidly,  the  radius  does  not  become  perpendicular  to 
the  orbit  till  it  arrives  at  E,  and  the  line  of  the  apsides 
AD  moves  forwards  to  E.     P.  521. 

Fig.  489.  A  represents  the  position  of  the  limit  of 
light  and  darkness  on  the  earth's  surface  at  the  vernal 
equinox,  B  at  the  summer  solstice,  and  C  at  the  win- 
ter solstice:  EQ  denotes  the  equator,  N  the  north 
pole,  and  S  the  south.     P.  525. 

Fig.  400.  NESW  being  the  horizon,  and  Z  the 
7cnith,  F' A  W  shows  the  sun's  apparent  path  in  Lon- 
don at  the  time  of  the  equinoxes,  BCD  at  midsummer, 
and  F  G II  at  midwinter,  projected  orthographically, 
as  if  the  circles  were  described  on  the  surface  of  a 
globe,  and  viewed  from  a  great  distance.  The  circle 
I  K  L  is  the  boundary  of  twilight,  supposing  it  18°  be- 
low the  horizon,  and  its  intersections  with  the  sun's 
path  show  the  beginning  and  end  of  twihght,  af  at  I 
andK.     P.  627. 

Fig.  491.  The  rays  of  light,  coming  in  the  direction 
AB,  arc  bent  V)y  the  atmosphere  so  as  to  arrive  at  C^ 
and  to  illuminate  a  part  of  the  atmosphere  there, 
which  is  visible,  by  mean.s  of  a  second  retraction,  to  a 
upectator  at  D,  and  occasions  the  first  and  last  twi- 
gbt.  •  P.  527. 


Fig.  492.  Venus  is  at  her  greatest  elongation  or 
angular  distance  from  the  sun  A,  when  situated  as  at 
B,  with  respei  t  to  the  earth  at  C ;  and  she  is  stationary 
at  D,  when  she  is  moving  with  the  same  velocity  as  the 
earth,  with  respect  to  the  dhection  of  the  earth's  mo- 
tion, the  line  E  D  being  then  more  oblique,  with  respect 
to  a  fixed  line,  than  either  before  or  after.     P.  627. 

J'ig.  493.    A  BCD  is  the  apparent  path  of  Venusfor 
the  year  1806,  supposing  the  sun  E  to  revolve  round 
the  earth  F.   "rhe  place  of  the  sun  and  planet  is  mark-  ' 
cd  for  every  four  weeks.     P.  527. 

Fig.  494.  The  apparent  path  of  Saturn  in  the  hea- 
vens for  the  year  1806,  referred  to  its  proper  place 
with  respect  to  tbe  eclijitic.  The  figures  denote  the 
places  at  the  beginning  of  eacii  month.     P.  527. 

Fig.  495.  I  he  small  figures  represent  the  phases  of 
the  moon  in  different  parts  of  her  orbit.  The  smaller 
detached  fii'inf  s  show  the  appearance  of  the  moon,  as 
seen  from  the  earth  ;  the  larger  ones,  those  of  the  earth 
at  the  same  times,  as  seen  from  the  moon,  which  are 
always  the  reverse  of  the  moon's  appearance.  At  A 
the  moon  is  new;  B  is  the  first  quarter,  C  the  full 
moon,  and  D  the  last  quarter.  A  and  C  are  some- 
times called  the  syzygies,  and  B  and  D  the  quadra- 
tures.    P.  528. 

Fig.  496.  A,  the  moon  passing  through  the  earth's 
sliadow ;  which  is  distinguished  into  three  parts,  the 
perfect  shadow,  the  true  shadow,  and  the  penumbra. 
At  B  and  C  the  moon  is  shown  passing  through  the 
section  of  the  shadow,     P.  529. 

F'ig.  497.  The  path  of  the  moon's  shadow  passing 
over  the  earth,  in  the  solar  eclipse  of  1764,  the  earth 
being  supposed  at  the  same  time  to  revolve  on  its 
axis.  The  line  A  B  is  the  part  in  which  ihe  eclipse  ap- 
peared annular,  CD  being  the  breadth  of  the  whole 
shadow  or  penumbra.     P.  529. 

Fig.  498.  The  shadow  of  the  moon  falling  on  the 
earth.  The  true  shadow  not  extending  here  ta  the 
earth,  the  cone  formed  by  tUe  continuation  of  its  out- 
lines marks  the  extent  of  the  parts  in  which  the  eclipse 
appears  annular.     P.  529. 

Fig.  499.  The  termination  of  the  moon's  disc  in  a 
solar  eclipse.     From  Dr.  Ilerschel.     P.  .')29. 

Fig.  500.  The  apparent  mag^iiludes  of  the  planets, 
that  of  the  sun  or  moon  being  supposed  equal  to  a 
circle  a  foot  in  diameter;  whtrr  there  are  two  figures, 
one  of  them  shows  the  mean  apparent  niagnilude,  and' 
the  other  the  greatest.     P.  531. 

F'ig.  501.  "Vhe  apparent  n  ngnitude  of  tlie  sun,  as 
seen  from  the  different  planets ;  for  Mercury,  the  mag- 
nitude is  shown  by  that  of  the  tarth  in  fig.  ')07.  P. 
535. 


792 


PLATE  XXXV. 


Fig.  50'.!.  AB  btin  s;  the  eRrth'3  axis,  ll>c  circle 
A  I'lj  is  tlie  moridian  o  I  tlu-  pWe  C,.aiid  C  E  repre- 
siiitii  the  [ilanc  of  its  hori/oii.     P.  537. 

rig.  60:5.  Tlie  (tVtet  ol  tlu-  obliqiiity  of  the  ecliptic 
ii.i  llie  equation  of  time  i.s  lovvii  by  tlie  tlitTeniicc  of 
tilt  unalch  ABC  and  D  BE,  ^ubiended  at  tiie.  jiole  B 
bj  equal  portions  of  the  oblique  circle  A  1'..  P.  5;5i>. 
riif.  .504.  A  Hbciiiii  paiaUfl  to  llie  earlii's  axis,  the 
12  pUiues  passiiijitbrnugli  it,  at  cqir.il  angular  distances, 
mark, on  the  circle  CD  perpendicular  to  it,  the  liour . 
lines  of  an  equatoiiai  dial,  and  on  the  liorizoiitid  .sur- 
face P.  V  those  of  a  tiori/outal  dial.     P.  o38. 

Pig.  605.  A  method  of  coiistnictiug  a  dial  on  any 
given  plane.  .'V  li  C  is  the  eleviaion  of  the  pole,  or 
more  generally,  the  angle  which  the  surface  makes 
with  tlie  i^nomon  A  B.  J'he  circles  are  divided  into 
equal  parts,  and  1,2,0,1,6,0  are  the  hour  lines,  B 
tieiiig  the  place  of  the  t;uonion.  The  reason  of  this 
construction  will  appear  by  comparing  the  circle  111 
the  last  figure  with  the  ellipsis  which  is  formed  on  the 
horizontal  surface.     P.  ^iliii. 

Pig.  50().  A  dial  for  a  pointed  gnomon,  or  obcliic, 
drawn  on  a  liorizontal  surface.     P.  538. 

Fig.  507.  A  mural  quadrant,  with  its  telescope; 
A  P>  is  the  plumb  line,  for  adjusting  the  instrument, 
and  C  the  counterpoise  for  the  telescope.     P.  542. 

I'ig.  503.  A  portable  transit  instrument.  A  and  B 
are  screws  for  adjusting  the  axis  by  a  vertical  and  a 
horizontal  motion ;  C  D  is  a  spirit  level,  w  hich  may 
occasionally  he  hung  on  the  telescope  by  the  pins  E 
and  F.  G  is  a  small  graduated  arch,  to  be  viewed 
through  the  microscope  H,  for  taking  elevations  of  a 
few  degrees.     P.  542. 

Fig.  509.  A  transit  circle,  resembling  Mr.  Wollas- 
ton's,  with  a  horizontal  circle,  by  means  of  which 
both  altitudes  and  azimuths  may  be  measured.  A  is 
a.  microscope  for  viewing  the  plumb  line,  B  anotlier 
for  reading  ojT  the  divisions  of  tl>e  horizonlid  circle; 
C  and  D  are  spirit  levels.     P.  642. 

Fig.  510.  A  zenith  sector,  with  its  telescope,  which 
has  usually  a  reflecting  prism,  like  that  of  the  Nev^- 
tonian  telescope,  for  its  eyeglass.     P.  542. 

Pig.  511.  The  marine  octant,  introduced  by  lladley. 
The  mode  of  taking  tlie  common  or  front  observation, 
is  shown  by  the  lines  drawn  to  the  sun  and  moon :  the 
fcack  observation  by  the  two  stars.     A  is  a  dark  glass 


to  be  used  in  observations  of  the  sun,  and.wluch  may 
be  fixed  at  B,  when  required.     P.  5 12. 

Fig.  512.  A  B  being  the  situation  of  the  earth's  ax- 
is, if  the  angle  C  B  U,  or  the  altitude  of  the  body  D,  be 
measured,  and  wt  subtract  from  it  tlie  elevation  of  the 
equinoctial  CHE,  the  remainder  will  be  the  decliua- 
tion  EBl).     I'.aU,  543. 

Fig.  513.  The  aiigle  ABC  is  the  moon's  horizon- 
tal parallax,  and  DBC  the  parallax  when  she  is  ele- 
vated above  the  horizon  D  E  in  the  angle  BDE.  P» 
61,"). 

Fi:;.  514.  The  situation  of  the  earth  at  the  transit  of 
Venus  in  June  17d9.  A  spectator  at  the  North  Cape 
was  carried  during  the  trimsit  from  A  to  B,and  the  tran- 
sit apjieared  to  liim  to  last  while  Venus  moved  from 
C  to  1) :  tlie  island  of  Otaheite,  on  the  contrary, 
wliidi  is  situated  on  the  lower  part  of  the  illuminated 
hemisphere,  was  carried  from  E  to  F,  and  the  duration 
of  the  transit  was  there  only  while  Venus  moved  from 
G  to  il.  Hence  tiie  rotatory  motion  of  the  earth  was 
compared  with  the  excess  of  the  motion  of  Venus  in 
its  orbit  above  that  of  the  earth.     P.  514.. 

I'ig.  515.  A  planisphere  ncaijly  resembling  tliat  of 
Professor  Bode.  The  outer  circle  i.s  fixed  to  the  chart, 
and  is  divided  either  according  to  tiie  degrees  of  the 
ecliptic,  or  the  dajs  of  the  month;  the  graduated  cir- 
cle immediately  within  it  is  divided  into  2  li  hours,  and 
is  fixed  to  a  circle  of  pasteboard,  out  of  which  the 
circle  NF^SW,  representing  the  horizon,  is  cut,  the 
place  being  filled  by  thin  varnished  paper,  with  circles 
of  azimuth  and  altitude  engraved  on  it,  which  is  car- 
ried round  with  the  hour  circle.     P.  "jtiT. 

Fig.  516.  A  diagram  showing  the  length  of  the  day, 
and  the  time  of  the  sun's  rising  and  setting  in  any  part 
of  the  globe,  within  a  few  minutes;  the  time  of  the 
yoar  being  found  in  the  graduated  circle  representing 
portions  of  the  ecliptic,  and  tlie  latitude,  on  tjip  mid- 
dle line,  by  following  the  concentric  circles  of  decli- 
nation till  they  meet  tiie  horizon  passing  through  the 
given  latitude,  the  line  drawn  from  the  pole  ttiniugh 
this  point  will  cut  the  equator  in  the  point  showing 
the  length  of  the  day  or  night.  Thus,  on  the  first  of 
March,  in  latitude  50"  north,  the  length  of  the  day 
appears  to  be  nearly  10  liours  andJ,  whence  tiie  sun 
must  rise  about  37  minutes  after  six  ;  but  in  latitude 
So'the  sun  never  se  ts  on  that  day.     P.  567.  ,^  | 


PLATES  XXXVr,  XXXVIL 


Plate  XXXVI.  Fig.  517.  Projection  of  the  con- 
stellations of  the  nortliern  hemisphere  ou  the  plane  of 
'fie  equator.     P.  498,  567. 


Plate  XXXVn.     Fi^-.  518.  Projection  of  the  south 
ern   hemisphere.  P.  498,  567. 


Plate  xxxv. 


Pig' .  5o  2  . 


A 

^_\ 

■■ 

Fig;.  5o3. 


Pig-.  504. 


Tig'.  5o5 . 


Pig-.  Sog 


Pub.  by  J.  JoJuLSon,  Londarv  2  July  tdo6. 


Joseph    Skelt*}n,  sculp- 


Plate  5XXVi.T"ig.  5i']. 


The  place  tt'dt^   hori- 
zon at  jmdni^ht  shows 
also  its  piacc  at  six  lire 
the  cre/ii/iif  ^e.  foOuwaifl 
quarter. 


^Fuh.hv  J.Jphnson.Lendtm   tJulv^So^.  ^ 


Joseph    Skriton    sculp. 


Plate  IIIVn.Fig.5i8. 


-ft/^.  ^v  ./;  Johnson  .Zcndon  x  July  ido!?. 


Jasfffh   S?arZtzm.  scttlp. 


PT.ATRTXXVm. 


Bo- .  Sag . 

^ISfiles 


oooTeet 


.Oamhora^ao 


o'ooo 


oooToisesI 


x8 


a6 


HI 


a5 


■4:: 


GftOp<LXi 


-  .  Ophir 


.0>rne  ^34idji 
'Tic  A  Ossmw 


n.  .Tike  of  Xmeriffe 
SEtna. 


,-Buet 
.  JMonte  Viso 
JioTW  CerUs 
:  z:  GoTuiar  ^byss- 


,  JMJmt  d,  or 
'a  000;  > 

-  -^^^^  Cenis,post  house 

^  JdffuiTt  Jvra, 
_  .1  Tuy  de  Dome 
5-  -^Tic  MuifoJiiad/ 


,VUi>Ti.  . 

-  ~Jrtgleborou^n, 

Vtyui'itLT 
^  ^Snowdorv 
z-zs:-Sh<JuiUion 

-  ^v-j^U  nwtmt 
'    \*'  Ouujwiuiy  i/tn 

Skiddmv 

,  Bert  Lomorid, 

Saddleback 


\Aosta> 

JjoIcc  of  Geneviv 

.^T'thurs  scat 
'Oiankhury  rb^  Suss 
vS^Teters  irvrwi/ic  t/rvu/ul/ 

SetL 


jjau-piart  SetL 


IlllPirilnillH       FTm\    .^^nr\       ifmifk      -^fmrn   l^      _Jiil!lli™Mnm.nn.r-,„„ 


Fig'.  522 


■^ 


Fig'.  62a. 


B        D 


Tiib.by  J.  Jofuison ..London  jJuJ^  1806 . 


Joseph  Skeltmi  sad  p. 


793 


PLATE.  XXXVIII. 


Fig.  510.  A  scale  of  tlic  heiglit  of  different  parts  of 
the  earth's  surface  above  tlie  level  of  the  sea,  in 
English  feet  and  miles,  and  in  French  toises.     P.  .574. 

Fig.  ."iSO.  A.  Tiie  dotted  ellipsis  shows  the  section 
of  a  spheroid,  which  would  be  the  form  of  the  earth 
and  sea  if  it  wcro  always  in  a  state  of  equilihriuni  with 
the  attraction  of  a  distant  body,  and  the  shaded  ellip- 
sis the  actual  form  assumed  in  consequence  of  its  ro- 
tation round  its  centre,  the  depth  of  tlie  sea  being  less 
than  l.*;  miles.  B.  The  surface  of  the  sphere  being 
supposed  to  be  flattened,  and  the  tides  spread  on  it, 
they  wo\rld  assume  the  form  of  the  waves  here  shown. 
The  dotted  straight  line  shows  the  mean  height, 
which  is  a  little  above  the  surface  in  the  principal 
sections  of  the  spheroid,  although  not  universally.  C. 
The  nature  of  the  tides  of  lakes,  the  surface  beiijg  re- 
gulated by  that  of  the  dotted  line  at  B,  nearly  agree- 
ing with  it  in  direction,  as  at  D,  when  the  lake  is  nar- 
row and  deep, but  differing  from  it,  as  at  E,  when  sha.- 
lower.     P.  579. 

Fig.  521.  The  progress  of  the  tides  from  the  At- 
lantic through  the  channels  surrounding  the  British 
islands,  the  lunar  tides  happening  in  any  part  of  the 
shaded  lines  nearly  at  the  hour,  after  the  moon's  south- 
ing, which  is  indicated  by  the  figure  annexed  to  it. 
P.  582. 

Fig.  522.  The  lines  AB  and,BC,  repreeentingithe 
heights  of  the  lunar  and  solar  tides,  find  the  angle 
ABC  twice  their  angular  distance,  or  A  DC  being 
simply  the  angular  distance,  the  line  A  ;C  shows,  the 


height  of  the  compsand  tide,  and  the  angles  B  A  C  and 
A  C  B  its  distance  from  the  lunar  and  solar  tides  re- 
spectively.    P.  585. 

F'ig.  523.  Tlie  two  unequal  tides  represented  by  the 
elevation  of  the  ellipsis  above  the  smaller  circle  may 
be  considered  as  composed  of  two  equal  tides  cut  off 
by  the  dotted  circle,  and  the  single  tide  between  the 
two  circles;  as  the  tides  B  and  C  make  the  unequal 
rides  at  D,     P.  587. 

Fig.  521.  The  first  and  second  curves  represeni 
two  equal  semidiurnal  and  one  diurnal  tide,  whicL 
would  make  together  two  unequal  tides :  the  third  and 
fourth  the  same  tides  six  hours  more  advanced  :  and 
when  these  are  combined,  the  first  and  third  destroy 
each  other,  hut  the  second  and  fourth  together  com- 
pose the  fifth,  or  a  large  diurnal  tide.     P.  587. 

Fig.  525.  A  tlie  ancient  system  of  the  world, 
adopted  by  Ptolemy.  B  th^  arrangement  supposed 
Lv  some  other  astronomers.     P.  590. 

Fig.  526.  The  Egyptian  system  of  the  world.  P. 
590. 

Fig.  527.  The  system  of  the  Pythagoreans,  and  of 
Copernicus.     P;  592. 

Fig.  528.  The  mode  of  representing  the  inequalities 
of  the  celestial  motions  employed  by  Ptolemy,  the 
small  circle  being  carried  round  the  circumference  of 
the  larger,  while  the  lumiuary  revolves  in  it,  so  as  to 
diescribe  the  dotted  curve.     P.  595. 

Fig.  529.  The  Tychonic  system  of  the  world.  P. 
597.  ■ 


794 


PLATE  XXXIX. 


fii;.  530.  '(lie  repulsive  force  of  two  piirtides  of 
maiif  !■,  situated  at  tlie  distance  A  H  or  AC,  is  rtpre- 
sriiled  liy  the  oidiirates  or  perpeiidicularfa  B  I),  C  E, 
i)i:uvn  to  tile  curve  T)  K,  supposiiic;  tlie  force  to  be 
inversely  as  the  distance;  but  the  law  of  the  force 
appears  to  be  uiure  nearly  represented  by  a  curve  like 
1'  K.  The  line  I)  I"  G  shows  the  maguitudc  of  the 
cohesive  force,  which  (ivercomc?  the  repiiUioii  at  the 
distance  A  G,  and  is  balanced  by  it  when  the  particles 
arrive  at  the  distance  A  U  or  A  11.  The  dotted  lines 
represent  the  nature  of  the  changes  made  in  the  lines 
V  v.,  I)  F  (i,  and  FH,  by  aii  elevation  of  temperature. 
P.  619. 

Fig.  531.  The  general  direction  of  the  cohesive  force 
acting  on  a  particle  of  a  liquid  at  A  being  represent- 
ed by  A  B  or  AC,  that  of  the  repulsive  force  will 
be  1)  A  or  E  A,  and  in  order  to  maintain  the  equili- 
brium, the  forces  B  F  and  C  G,  making  together  H  A, 
must  bo  supplied  by  the  pressure  or  reaction  of  the 
internal  parts.     P.  620. 

Fig.  532.  A.  The  trarsverse  section  of  a  drop,  sup- 
posed to  lie  of  considerable  length,  and  flatatthe  sides: 
the  curvature  of  the  outline  being  every  where  propor- 
tional to  its  distance  from  the  horizontal  line  A  B. 
B,  a  round  drop,  the  concavity  at  the  horizontal  line 
being  equal  to  the  convexity  which  would  be  found 
by  cutting  oft'  the  drop  horizontally;  the  sum  or  differ- 
ence of  the  curvatures  being  every  where  proportional 
to  the  distance  from  this  line.     P.  621. 

Fig.  533.  The  solid  AB  possessing  }ialf  the  attrac- 
tive power  of  the  liquid  CD,  the  surface  of  the  liquid 
will  remain  horizontal :  for  the  attractions  will  be  re 
presented  by  D  A,  DE,  and  D  C  ;  and  of  these  D  A 
and  D  E  make  D  B,  and  D  B  and  D  C  make  D  F,  which 
IS  in  a  vertical  direction.  If  the  solid  be  more  attract- 
ive, the  forces  will  be  combined  nearly  as  at  G,  and 
if  less  attractive,  as  at  H.     P.  622. 

Fig.  534.  The  form  of  the  surface  of  a  liquid  in 
contactwith  a  pl.ane  and  vertical  side  of  a  solid  which  is 
wetted  by  it.  The  height  of  the  ascent  of  water  is  about 
one  fourth  of  that  which  is  here  represented.  P.  622. 
Fig.  535.  The  form  of  the  surface  of  a  liquid  clerat- 
ed  between  two  plates  which  meet  at  A,  and  are  at  a 
little  distance  from  each  other  at  B  ;  about  one  third 
of  an  inch,  supposing  the  liquid  to  be  water.  P.  623. 
Fig.  536.  The  height  at  which  water  will  stand  in 
tubes  of  the  form  and  magnitude  which  arc  here  re- 
presented.    P.  623. 


Fig.  537.  The  depression  of  niorcury,  in  contact 
witli  a  large  or  Hat  glass  vessel,  is  one  fourth  as  great 
as  that  which  is  here  represented.     P.  623. 

F'ig.  533.  The  depresKion  of  mercury  within  a  small 
tube  of  glass.     P.  CV3. 

Fig.  530.  The  actual  elevation  of  a  portion  of  water 
In  contact  with  a  horizontal  surface  which  is  wetted 
by  it.     P.  624. 

Fig.  540.  The  elevation  of  mercury  in  contact  with 
a  horizontal  surface  of  glass.     P.  624. 

Fig.  541.  A,  a  wide  drop  of  water  standing  on  a  dry 
surface,  not  attracting  it.  B,  a  wide  drop  of  mercury, 
staiidhig  on  glass.     P.  624. 

Fig.  512.  A  magnified  representation  of  the  man- 
ner in  which  the  seeds  of  lycopodium  prevent  a  drop 
of  water  from  wetting  the  substance  od  which  it  stands. 
P.  624.  ; 

Fig.  543.  The  bodies  A  and  B,  and  the  bodies  C 
Snd  D,  appear  to  attract,  and  E  and  F  to  repel  each 
other.     P.  625. 

Fig.  544.  The  apparent  cohesion  of  two  plates,  be- 
tween which  a  fluid  is  interposed.     P.  625. 

Fig.  545.  The  apparent  attraction  of  adrop  between 
two  plates,  tending  to  draw  it  towards  the  line  of  their 
junction,  causes  the  drop  to  rest  in  an  inclined  posi- 
tion of  the  plates.     P.  625. 

Fig.  546.  Dr.  Ilerschel's  figure,  representing  by  tlie 
distance  of  the  curve  ABC  from  the  line  .\  C  the  heat 
thrown  on  different  parts  of  A  C  by  a  |irism,  while  DC 
ii  the  illuminated  part,  divided  according  to  Newton's 
experiments,  tbr  quantity  of  light  being  expressed  by 
the  distance  of  the  line  D  E  C.     P.  639. 

Fig.  547.  Dr.  Ilerschel's  figure  of  the  distribution 
of  heat  and  light  corrected  ac«ording  to  the  division 
of  the  coloured  spectrum,  as  ascertained  by  Dr.  Wol- 
laston.     P.  639. 

Fig.  548.    Bernoulli's  air  thermometer.     P.  C50. 
Fig.  549.  A  differential  air  thermometer,  or  tliermo- 
scope,  from  which  the  pressure  of  the  atmosphere  is 
excluded.     From  Kunze.     P.  650. 

Fig.  550.  A  differential  thermometer  on  Mr.,Leslie's 
construction.     P.  650. 

Fig.  551.The  distribution  of  the  electric  fluid  in  spheres 
of  different  sizes,  and  at  different  distances,  and  in  a 
conical  point.  The  density  is  represented  by  the  dis- 
tance of^the  dotted  line  from  the  surface.    P.  603. 


PLATE  XXXIX 


ng.s3i. 


Fig.,53c 


Fig.^Si. 


R  G  B  V  D 


Jos'.  S/ceUon  scu/p 


Tub.  by  J.  Johnson,  LonJori .  Julyj^/to6. 


PLATE   XL. 


Vig.  56! . 


Tig-.  553 


Tig-.  564. 


P<itlis?ud  h^  J .  Jrthrucn.  J.iindcn.1  JiJv  tfof 


Joseph    Skeitvn   sculp. 


795 


PLATE  XL. 


Fig.  552.  A.  A  spark  passiiij;  between  a  negti'ive 
Slid  a  neutral  h-M ;  B,  'ictween  a  neutral  and  a  positive 
ball;  C,  beHveen  a  negative  and  a  pobitive  ball.  D, 
two  spark*  between  a  negative  and  a  positive  cy- 
linder, each  of  tlie  same  form  as  if  it  were  passing 
sini:!^  frn:ii  the  end  of  ji  charged  to  the  side  of  a  neu- 
tral cylinder.     From  Mr.  Nicholson.     1'.  671. 

Fig.  553.  A  com|)Ound  galvanic  circuit,  formed  by 
portionsof  an  acid,  pieces  of  zinc,  and  wires  of  silver; 
the  arrows  show  the  directions  of  the  electric  current. 
P.  676. 

Fit'.  55*.  A  compound  galvanic  circuit,  formed  by 
•n  acid,  charcoal  and  watci ,  the  water  and  the  acid 
coniaiuiiicatini!;  by  a  small  siphon.     P.  676. 

Fig.  555.  A  compoinid  galvanic  circuit,  formed  by 
portioiis  of  an  alkaline  sulfurct,  and  water,  and 
{)ieces  of  c  )pper:  the  liquids  being  connected  by  a 
siphon,     p.  676. 

Fig.  556.  A  simple  galvanic  circuit,  formed  by  wires 
of  zinc  aijd  sjU  er,  or  platina,  the  lovwer  ends  being  im- 
mersed in  an  aci:i,  and  tlie  upper  being  brought  into 
contact  at  pH  asure.     P.  676. 

Fij.  557  A  galvanic  battery,  in  the  form  of  a 
trough,  composed  of  plates  of  zinc,  silvered  on  one 
side,  with  vax;ant  •ipaces  f  >r  rhe  reception  of  an  acid : 
the  letters  show  the  order  of  the  elements,  and  the 
arrows  the  dirt  clion  of  the  current,  from  Che  positive 
wire  +  to  the  negative  wire  — .     P.  677. 

Fig.  558.  An  electrical  machine,  on  Xairnc's  con- 
struction. A,  the  cylinder  of  glass;  B,  the  cushion, 
or'rubber;  C,  the  silk  flap;  D,  the  negative  conduc- 
tor; E,  the  i)ositive  conductor;  F,  a  ball  connected 
with  the  internal  coating  of  a  glass  jar,  contained  in 
the  conductor.  The  conductors  are  insulated  by  var- 
nished rods  of  glass.     P.  OiiO. 

Fig.  559.  A  plate  machine.  A  and  B,  the  rubbers, 
which  .ire  usually  doubU;  ;  C  I),  double  flaps  of  oiled 
silk,  for  confining  the  electricity  ;  K,  the  conductor.  P. 
680. 

Fig.  560.  An  rlcctrophorus.  A,  the  cake  of  resin; 
B,  the  plate  of  metal ;  C,  the  ball  for  taking  the  spark  : 
D,  the  ha  idle  of  glass.     P.  681. 

Fig.  561.  A  condenser,  as  arranged  by  Mr.  Cavallo, 
under  the  name  of  a  collector :  the  middle  plate  is  in- 
sulated :  the  two  outward  platcp  communicate  with 
the  earth ;  they  stand  near  the  first  plate  when  the 
electricity  is  imparted  to  it,  and  are  afterwards  re- 
moved by  means  of  their  hinges.     P.  681. 

F^  562.    Mr.  Cavallo's  multiplier.     The  electri- 


city being  first  communicated  to  the  insulated  piate  A, 
the  moveable  pLate  B  is  brought  near  it,  while  the  wire 
C  touches  the  pin  D  so  as  to  form  a  communicatioo 
with  the  earth;  the  plate  B  is  then  made  to  commu- 
nicate with  E,  which  is  insulated,  and  stands  near  the 
plate  F,  which  enables  it  to  receive  ahnosr  the  whole 
of  the  electricity  brought  at  eacii  alternation  by  B  ; 
and  when  the  plate  Fis  removed  from  tlie  neighbour- 
hood of  E,  this  plate  becomes  strongly  charged.  P. 
682. 

Fig.  563.  A  revolving  deubler,  on  the  principle  of 
Mr.  Bcnnet's  instrument.  The  fixed  and  insulated 
plate  A  first  receives  the  electricity,  and  "hen  the 
moveable  piate  B  stands  opposite  to  it,  it  receives  by 
a  wire  from  the  stand  of  the  instrument  C  the  opposite 
electricity;  wlien  it  is  brought  oppisitc  to  D,  this 
plate  is  made  to  communicate  witii  the  stand  by  the 
wire  E,  and  acquires  a  charge  similar  and  nearly  equal 
to^that  of  A.  M'hen  B  comes  again  to  A,  the  wire  F 
forming  a  communication  between  A,  and  D,  nearly 
the  wliole  charge  of  both  these  plates  is  brought  into 

A,  and  B  receives  a  charge  almost  twice  as  great  as  at 
first.     P.  682. 

Fig.  564.  Mr.  Coulomb's  electrical  balance.  The 
needle  A  is  made  of  silk,  covered  with  sealing  wax;  it, 
supports,  at  the  end  B,  a  ball  of  the  pith  of  elder' 
another  similar  ball  being  fixed  at  C;  the  force  of  at- 
traction or  repulsion  is. ascertained  by  the  torsion  of 
the  wire  AD,  which  is  measured  by  a  graduated 
circle  E.     P.  683. 

Fig.  565.  Mr.  Henley's  quadrant  electrometer;  it  is 
made  of  box  wood,  sui^i^orted  by  mttal;  tlie  ball  is  of 
cork,  the  graduated  arc  of  iviiry.     P.  683. 

Fig   566.    A,  Mr.  Beniiet's  gold  leaf  electrometer; 

B,  a  piece  of  excited  scaling  wax  held  over  it,  for  dis- 
tinguishing the  electricity.  Instead  of  the  pieces  of 
fiold  leaf  C,, we  may  substitute  Mr.  CavalloVpith  balls 
D,  or  the  straws  E,  employed  by  Volta,     r.  683.    i    ,: 

Fig.   5fi7.  ■  Mr.  Lane's    discharging   electrometer." 
The  djstaiice  ofthe  fcalls  A,JJ  is trtt'asUrid  by'thetufn^ 
of  the  screw  on  the  scale  C ;  and  the  parts  of  a  turn 
are  ascertainud  by  the  graduated  circle  D.     P.  683. 

Fig.  568.  A  discharger  for  a  battery.  When  the 
repulsion  of  the  balls  A,  B,  becomes  greater  th.an  the 
weight  (if  a  wire  which  passes  through  a  perforation  in 
the  ball-',  tliey  separate,  and  the  ball  C,  descending 
to  D,  forms  a  communication,  ^vbich  completes  the 
circn  t,  so  that  the  shock  passes  tbrough  any  luhitancc 
1  Uc€d  at  £,     P.  083. 


796 


PLATE   XLI. 


fig.  569.  The  form  of  the  curves  which  show  the 
jiirection  of  the  magnetic  needle,  in  cotisequence  of 
the  attraction  and  repulsion  of  two  poles,  situated  at 
A  and  B.  They  are  found  by  drawing  the  lines  A  C  D, 
BED,  so  that  the  sura  or  difterence  of  the  parts  AC' 
BE,  shall  be  always  equal,  ACEB  being  a  semi- 
circle :  and  the  direction  D  F  may  be  found  by  making 
AF  to  BF  as  the  cube  of  AD  to  that  of  DD.  P. 
688. 

Fig.  570.  The  arrangement  of  iron  filiogs  in  the 
neighbourhood  of  a  magnet.     P.  688. 

Fig.  571.  The  particle  of  iron  A  B,  lying  on  a  card 
nearly  over  the  magnet  C,  assumes,  when  the  card  in 
shaken,  first  the  position  D,  then,  falling  to  E  and  E, 
is  left  a  little  further  from  the  magnet  than  at  first. 
P.  689. 

Fig.  572.  An  azimuth  compass.  The  box  is  turned 
round,  until  the  shadow  of  the  thread  A  B  or  AC  falls 
on  the  .  line  C  D :  the  position  of  the  needle  is  then 
ascertained  by  that  of  the  card  E,  which  is  fixed  on  it. 
The  compass  is  kept  always  in  a  horizontal  position, 
by  means  of  a  double  suspension  On  the  gimbals  E  G. 
Instead  of  this  suspension,  Mr.  M'Cullbch  makes  the 
bottom  of  the  box  in  the  form  of  a  hollow  cone,  rest- 
ing on  a  point,  and  loaded  with  a  weight,  which  brings 


the  centre  of  gravity  below  the  point  of  support,  as  at 
H.     P.  689. 

Fig  573.  A  dipping  needle.  The  piece  A  B  is 
brought  into  such  a  situation,  that  the  line  drawn  on 
it  coincides  with  the  middle  of  the  vibrations  of  the 
needle.  The  position  of  the  needle  may  be  chajiged, 
either  by  turning  the  stand  half  round,  or  by  turning  the 
needle  within  the  stand.     P.  689. 

Fig.  574  . .  576.  The  situations  of  the  lines  of  equal 
declination  in  1700,  1744,  and  1794,  in  the  hemi- 
sphere, which  is  bisected  by  the  meridian  of  London. 
The  first  two  from  Mouiitaine's  Tables,  the  last  from 
Churchman's  Chart.     P.  691. 

Fig.  577.  The  actual  situations  of  the  lines  of  equal 
dip.     From  Churchman's  Chart.     P.  69?. 

Fig.  578.  The  lines  of  equal  dip,  calculated  from 
the  supposition  of  a  small  magnet,  situated  at  the 
centre  of  the  eartli,  directed  to  a  point  in  latitude 
75°  N.  and  longitude  70°  W.     P.  699. 

Fig.  579.  A,  Six's  thermometer;  B,  the  wire  with  a 
fine  spring,  which  serves  as  an  index.     P.  697. 

Fig.  580.    Rutherford's  double  thermometer.  P.  697. 

Fig.  581.  Deluc's  whalebone  hygrometer.  A,  the 
slip  of  whalebone;  B,  a  spiral  spring,  serving  to  kee{)  it 
stretched;  C,  the  index.     P.  710. 


PLATES  XLII,  XLIIL 

Fig.  582.    A  chart  of  the  world,  on  Mercator's  pro-      year  1794;  and  with  the  trade  winds  and  monsoons,    P, 
jection,  from  Arrowsmith  ;  with  the  dip  and  variation       £71,691. 
•f  the  coxapass,  priacipally  from  Cburchman,  for  the 


Plate  Xl.l 


Fig',  ofic) 


Fig'.  370 


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Pui.by  J.  Johnsttfv.Zorui^rh  i  Jiify  xSaff. 


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Plate  xlh  Tig-,  b  02 . 


Joseph    SkciUm   .cidf- 


Pui).  bif  J.  Jo/mson ,  Zondmv  l  July  iSoS. 


Toiir  hound  rwiN./  Plate  yTsTII  . 


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A  Chart.  ""--,. 

oil  ^ercaxors   Proiecrioii 
•'^J*  From  Arrcfw^smixh.,  """-^^ 

^        'Wath.  tlie  Dip    ajxtl.  Tju-iatiouof the  CampaTs; 

principally  irom  Clnirtliimm_;for  tlie  year  i*]  94.; 
and  Tvitli  the  Trade  Winds  and  Monaoons. 

/  Constaat  "Winds .      /   S-ummjer     and    Autnnm. 


./,..r,-;./,    SbH.m   .milp.^ 


Pub.  bv  J.  Johnson  Zondon  ijidj  iifo6. 


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