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AND 

MODERN    PHYSICS 


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GLAZEBROOK 


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THE    CENTURY    SCIENCE   SERIES 
Edited    by    SIR    HENRY    E.    ROSCOE,    D.C.L.,    LL.D.,    F.R.S. 


JAMES      OLERK      MAXWELL 
AND    MODERN   PHYSIOS 


The  Century  Science  Series. 

EDITED    BY 

SIR  HENRY   E.   ROSCOE,   D.C.L.,  F.R.S.,  M.P. 


John  Dalton  and  the  Rise  of  Modern  Chemistry. 

By  Sir  Henry  E.  Roscoe,   F.R.S. 
Major  Rennell,  F.R.S. ,  and  the  Rise  of  English 
Geography. 

By   Clements   R.    Markham,  C.  B.,   F.R.S.,   President 
of  the  Royal  Geographical  Society. 

Justus  von  Liebig:  his  Life  and  Work  (1803-1873). 

By  W.  A.  Shenstone,  F.I.C.,  Lecturer  on  Chemistry  in 
Clifton  College. 

The  Herschels  and  Modern  Astronomy. 

By  Agnes  M.  Clerke,  Author  of  "A  Popular  History 
of  Astronomy  during  the  19th  Century,"  &c. 

Charles  Lyell  and  Modern  Geology. 

By  Rev.  Professor  T.  G.  Bonney,   F.R.S. 

James  Clerk  Maxwell  and  Modern  Physics. 

B>  R.  T.  Glazebrook,  F.R.S.,  Fellow  of  Trinity  College, 
Cambridge. 

In  Preparation. 

Michael  Faraday:  his  Life  and  Work. 

By  Professor  Silvanus  P.   Thompson,  F.R.S. 

Humphry  Davy. 

By   T.   E.  Thorpe,    F.R.S.,   Principal   Chemist    ol    the 
Government  Laboratories. 

Pasteur  :  his  Life  and  'Work. 

By  M.  Armand  Ruffer,  M.D.,  Director  of  the  British 
Institute  of  Preventive  Medicine. 

Charles  Darwin  and  the  Origin  of  Species. 

By  Edward  B.  Poulton,  M.A.,  F.R.S.,  Hope  Professor 
of  Zoology  in  the  University  of  Oxford. 

Hermann  von  Helmholtz. 

By  A.  W.  Rucker,   F.R.S.,  Professor  of  Physics  in  the 
Royal  College  of  Science,  London. 

MACMILLAN  &  CO.,  New  York. 


J.  ^l^L  rk^ui^pi 


(From  a  Photograph  of  the  Picture,  by  G.  Lowes  Dickinson,  Esq.,  in  the  Hall  of 
Trinity  College,  Cambridge.) 


THE    CENTURY   SCIENCE    SERIES 

James  Clerk  Maxwell 

AND  MODERN   PHYSICS 


BY 


E.   T.   GLAZEBEOOK,   F.E.S. 

Fellow  of  Trinity  College,  Cambridge 

University  Lecturer  in  Mathematics,  and  Assistant  Director  of  the 

Cavendish  Laboratory 


liefo  fork 
MACMILLAN     &     CO. 

1896 


20 


37 


QC 

Ik 


PREFACE. 


The  task  of  giving  some  account  of  Maxwell's  work 
— of  describing  the  share  that  he  has  taken  in  the 
advance  of  Physical  Science  during  the  latter  hall 
of  this  nineteenth  century — has  proved  no  light 
labour.  The  problems  which  he  attacked  are  of 
such  magnitude  and  complexity,  that  the  attempt 
to  explain  them  and  their  importance,  satisfactorily, 
without  the  aid  of  symbols,  is  almost  foredoomed 
to  failure.  However,  the  attempt  has  been  made, 
in  the  belief  that  there  are  many  who,  though  they 
cannot  follow  the  mathematical  analysis  of  Maxwell's 
work,  have  sufficient  general  knowledge  of  physical 
ideas  and  principles  to  make  an  account  of  Maxwell 
and  of  the  development  of  the  truths  that  he  dis- 
covered, subjects  of  intelligent  interest. 

Maxwell's  life  was  written  in  1882  by  two  of  those 
who  were  most  intimately  connected  with  him,  Pro- 
fessor Lewis  Campbell  and  Dr.  Garnett.  Many  of  the 
biographical  details  of  the  earlier  part  of  this  book 
are  taken  from  their  work.     My  thanks  are  due  to 


VI  PREFACE. 

them  and  to  their  publishers,  Messrs.  Macmillan,  for 
permission  to  use  any  of  the  letters  which  appear 
in  their  biography.  I  trust  that  my  brief  account 
may  be  sufficient  to  induce  many  to  read  Professor 
Campbell's  "  Life  and  Letters,"  with  a  view  of  learn- 
ing more  of  the  inner  thoughts  of  one  who  has 
left  so  strong  an  imprint  on  all  he  undertook,  and 

was  so  deeply  loved  by  all  who  knew  him. 

R.  T.  G. 

Cambridge, 

December,  1895. 


CONTENTS. 


PACK 

Chapter  I. — Early  Life .9 

,       II. — Undergraduate  Life  at  Cambridge  2S 

,     III. — Early  Researches-  Professor  at  Aberdeen     .       38 

,      IV. — Professor   at    King's   College,    London — Life 

at  Glexlaik  .        .         .         .         .         .        .54 

,        V. — Cambridge — Professor  of  Physics     ...       60 

,      VI. — Cambridge— The  Cavendish  Laboratory  .         .       73 

,    VII. — Scientific  Work — Colour  Vision       ...       93 

,  VIII. —Scientific  Work— Molecular  Theory      :         .     108 

,     IX.— Scientific  Work — Electrical  Theories    .         .148 

,       X.— Development  of  Maxwell's  Theory  .         .     202 


James   Clerk   Maxwell 

AND    MODERN    PHYSICS. 

— «3— 
CHAPTER     I. 

EARLY   LIFE. 

"  One  who  has  enriched  the  inheritance  left  by 
Newton  and  has  consolidated  the  work  of  Faraday 
— one  who  impelled  the  mind  of  Cambridge  to  a 
fresh  course  of  real  investigation — has  clearly  earned 
his  place  in  human  memory."  It  was  thus  that 
Professor  Lewis  Campbell  and  Mr.  Garnett  began  in 
1882  their  life  of  James  Clerk  Maxwell.  The  years 
which  have  passed,  since  that  date,  have  all  tended  to 
strengthen  the  belief  in  the  greatness  of  Maxwell's 
work  and  in  the  fertility  of  his  genius,  which  has 
inspired  the  labours  of  those  who,  not  in  Cambridge 
only,  but  throughout  the  world,  have  aided  in  de- 
veloping the  seeds  sown  by  him.  My  object  in  the 
following  pages  will  be  to  give  some  very  brief 
account  of  his  life  and  writings,  in  a  form  which  may, 
I  hope,  enable  many  to  realise  what  Physical  Science 
owes  to  one  who  was  to  me  a  most  kind  friend  as  well 
as  a  revered  master. 

The  Clerks  of  Penicuik,  from  whom  Clerk  Maxwell 
was  descended,  were  a  distinguished  family.  Sir  John 
Clerk,  the  great-great-grandfather  of  Clerk  Maxwell, 


10  JAMES   CLERK    MAXWELL 

was  a  Baron  of  the  Exchequer  in  Scotland  from  1707 
to  1755  ;  he  was  also  one  of  the  Commissioners  of 
the  Union,  and  was  in  many  ways  an  accomplished 
scholar.  His  second  son  George  married  a  first  cousin, 
Dorothea  Maxwell,  the  heiress  of  Middlebie  in  Dum- 
friesshire, and  took  the  name  of  Maxwell.  By  the 
death  of  his  elder  brother  James  in  1782  George 
Clerk  Maxwell  succeeded  to  the  baronetcy  and  the 
property  of  Penicuik.  Before  this  time  he  had 
become  involved  in  mining  and  manufacturing  specu- 
lations, and  most  of  the  Middlebie  property  had  been 
sold  to  pay  his  debts. 

The  property  of  Sir  George  Clerk  Maxwell  de- 
scended in  1798  to  his  two  grandsons,  Sir  George 
Clerk  and  Mr.  John  Clerk  Maxwell.  It  had  been 
arranged  that  the  younger  of  the  two  was  to  take 
the  remains  of  the  Middlebie  property  and  to  assume 
with  it  the  name  of  Maxwell.  Sir  George  Clerk  was 
member  for  Midlothian,  and  held  office  under  Sir 
Robert  Peel.  John  Clerk  Maxwell  Avas  the  father  of 
James  Clerk   Maxwell,  the   subject  of  this  sketch.* 

John  Clerk  Maxwell  lived  with  his  widowed  mother 
in  Edinburgh  until  her  death  in  1824.  He  was  a 
lawyer,  and  from  time  to  time  did  some  little 
business  in  the  courts.  At  the  same  time  he  main- 
tained an  interest  in  scientific  pursuits,  especially 
those  of  a  practical  nature.  Professor  Campbell 
tells  us  of  an  endeavour  to  devise  a  bellows  which 
would  give  a  continuous  draught  of  air.     In  1831  he 

*  A  full  biographical  account  of  the  Clerk  and  Maxwell  families 
is  given  in  a  note  by  Miss  Isabella  Clerk  in  the  "  Life  of  James  Clerk 
Maxwell,"  and  from  this  the  above  brief  statement  has  been  taken. 


AND   MODERN   PHYSICS.  11 

contributed  to  the  Edinburgh  Medical  and  Philosoph- 
ical Journal  a  paper  entitled  "Outlines  of  a  Plan 
for  combining  Machinery  with  the  Manual  Printing 
Press." 

In  1826  John  Clerk  Maxwell  married  Miss  Frances 
Cay,  of  North  Charlton,  Northumberland.  For  the 
first  few  years  of  their  married  life  their  home  was  in 
Edinburgh.  The  old  estate  of  Middlebie  had  been 
greatly  reduced  in  extent,  and  there  was  not  a  house 
on  it  in  which  the  laird  could  live.  However,  soon 
after  his  marriage,  John  Clerk  Maxwell  purchased  the 
adjoining  property  of  Glenlair  and  built  a  mansion- 
house  for  himself  and  his  wife.  Mr.  Maxwell  super- 
intended the  building  work.  The  actual  working 
plans  for  some  further  additions  made  in  1843  were 
his  handiwork.  A  garden  was  laid  out  and  planted, 
and  a  dreary  stony  waste  was  converted  into  a 
pleasant  home.  For  some  years  after  he  settled  at 
Glenlair  the  house  in  Edinburgh  was  retained  by  Mr. 
Maxwell,  and  here,  on  June  13,  1831,  was  born  his 
only  son,  James  Clerk  Maxwell.  A  daughter,  born 
earlier,  died  in  infancy.  Glenlair,  however,  was  his 
parents'  home,  and  nearly  all  the  reminiscences  we 
have  of  his  childhood  are  connected  with  it.  The 
laird  devoted  himself  to  his  estates  and  to  the  educa- 
tion of  his  son,  taking,  however,  from  time  to  time 
his  full  share  in  such  county  business  as  fell  to  him. 
Glenlair  in  1830  was  very  much  in  the  wilds  ;  the  jour- 
ney from  Edinburgh  occupied  two  days.  "  Carriages 
in  the  modern  sense  were  hardly  known  to  the  Vale  of 
Urr.  A  sort  of  double  gig  with  a  hood  was  the  best 
apology  for  a  travelling  coach,  and  the  most  active 


12  JAMES   CLERK   MAXWELL 

mode  of  locomotion  was  in  a  kind  of  rough  dog-cart 
known  in  the  family  speech  as  a  hurly."  * 

Mrs.  Maxwell  writes  thusf,  when  the  boy  was 
nearly  three  years  old,  to  her  sister,  Miss  Jane  Cay  : — 

"  He  is  a  very  happy  man,  and  has  improved  much  since 
the  weather  got  moderate.  He  has  great  work  with  doors, 
locks,  keys,  etc.,  and  'Show  me  how  it  doos'  is  never  out  of 
his  mouth.  He  also  investigates  the  hidden  course  of  streams 
and  bell-wires— the  way  the  water  gets  from  the  pond  through 
the  wall  and  a  pencl  or  small  bridge  and  down  a  drain  into 
Water  Orr,  then  past  the  smiddy  and  down  to  the  sea,  where 
Maggy's  ships  sail.  As  to  the  bells,  they  will  not  rust;  he 
stands  sentry  in  the  kitchen  and  Mag  runs  through  the  house 
ringing  them  all  by  turns,  or  he  rings  and  sends  Bessy  to  see 
and  shout  to  let  him  know  ;  and  he  drags  papa  all  over  to 
show  him  the  holes  where  the  wires  go  through." 

To  discover  "  how  it  doos  "  was  thus  early  his  aim. 
His  cousin,  Mrs.  Blackburn,  tells  us  that  throughout 
his  childhood  his  constant  question  was,  "  What's  the 
go  of  that  ?  What  does  it  do  ?  "  And  if  the  answer 
were  too  vague  or  inconclusive,  he  would  add,  "  But 
what's  the  particular  go  of  that  ?  " 

Professor  Campbell's  most  interesting  account  of 
these  early  years  is  illustrated  by  a  number  of 
sketches  of  episodes  in  his  life.  In  one  Maxwell  is 
absorbed  in  watching  the  fiddler  at  a  country  dance ; 
in  another  he  is  teaching  his  dog  some  tricks ;  in 
a  third  he  is  helping  a  smaller  boy  in  his  efforts 
to  build  a  castle.  Together  with  his  cousin,  Miss 
Wedderburn,  he  devised  a  number  of  figures  for  a 

*  "  Life  of  J.  C.  Maxwell,"  p.  26. 
f  "  Life  of  J.  C.  Maxwell,"  p.  27. 


AND    MODERN    PHYSICS.  13 

toy  known  as  a  magic  disc,  which  afterwards  de- 
veloped into  the  zoetrope  or  wheel  of  life,  and  in 
which,  by  means  of  an  ingenious  contrivance  of 
mirrors,  the  impression  of  a  continuous  movement 
was  produced. 

This  happy  life  went  on  until  his  mother's  death 
in  December,  1839  ;  she  died,  at  the  age  of  forty-eight, 
of  the  painful  disease  to  which  her  son  afterwards 
succumbed.  When  James,  being  then  eight  years  old, 
was  told  that  she  was  now  in  heaven,  he  said  :  "  Oh, 
I'm  so  glad  !     Now  she'll  have  no  more  pain." 

After  this  his  aunt,  Miss  Jane  Cay,  took  a  mother's 
place.  The  problem  of  his  education  had  to  be  faced, 
and  the  first  attempts  were  not  successful.  A  tutor 
had  been  engaged  during  Mrs.  Maxwell's  last  illness, 
and  he,  it  seems,  tried  to  coerce  Clerk  Maxwell  into 
learning ;  but  such  treatment  failed,  and  in  1841, 
when  ten  years  old,  he  began  his  school-life  at  the 
Edinburgh  Academy. 

School-life  at  first  had  its  hardships.  Maxwell's 
appearance,  his  first  day  at  school,  in  Galloway  home- 
spun and  square-toed  shoes  with  buckles,  was  more 
than  his  fellows  could  stand.  "  Who  made  those 
shoes  ?  "  they  asked  * :  and  the  reply  they  received 
was — 

"  Div  ye  ken  'twas  a  man, 
And  he  lived  in  a  house, 
In  whilk  was  a  mouse." 

He  returned  to  Heriot  Row  that  afternoon,  says 
Professor   Campbell,   "  with   his    tunic    in    rags   and 

*  "Life  of  J.  C.  Maxwell,"  p.  49. 


14  JAMES   CLERK    MAXWELL 

wanting  the  skirt,  his  neat  frill  rumpled  and  torn— 
himself  excessively  amused  by  his  experiences  and 
showing  not  the  slightest  sign  of  irritation." 

No.  31,  Heriot  Row,  was  the  house  of  his  widowed 
aunt,  Mrs.  Wedderburn,  Mr.  Maxwell's  sister;  and 
this,  with  occasional  intervals  when  he  was  with  Miss 
Cay,  was  his  home  for  the  next  eight  or  nine  years. 
Mr.  Maxwell  himself,  during  this  period,  spent  much 
of  his  time  in  Edinburgh,  living  with  his  sister  during 
most  of  the  winter  and  returning  to  Glenlair  for  the 
spring  and  summer. 

Much  of  what  we  know  of  Clerk  Maxwell's  life 
during  this  period  comes  from  the  letters  which 
passed  between  him  and  his  father.  They  tell  us  of 
the  close  intimacy  and  affection  which  existed  be- 
tween the  two,  of  the  boy's  eager  desire  to  please  and 
amuse  his  father  in  the  dull  solitude  of  Glenlair,  and 
his  father's  anxiety  for  his  welfare  and  progress. 

Professor  Campbell  was  his  schoolfellow,  and 
records  events  of  those  years  in  which  he  shared, 
which  bring  clearly  before  us  what  Clerk  Maxwell 
was  like.     Thus  he  writes  *  : — 

"  He  came  to  know  Swift  and  Dryden,  and  after  a  while 
Hobbes,  and  Butler's  '  Hudibras.'  Then,  if  his  father  was  in 
Edinburgh,  they  walked  together,  especially  on  the  Saturday 
half -holiday,  and  '  viewed  '  Leith  Fort,  or  the  preparations  for 
the  Granton  railway,  or  the  stratification  of  Salisbury  Crags 
—always  learning  something  new,  and  winning  ideas  for  im- 
agination to  feed  upon.  One  Saturday,  February  12,  1842,  he 
had  a  special  treat,  being  taken  'to  see  electro-magnetic 
machines.' " 


*  <( 


Life  of  J.  C.  Maxwell,"  p.  52. 


AND   MODERN    PHYSICS.  15 

And  again,  speaking  of  his  school-life  : — 

"  But  at  school  also  he  gradually  made  his  way.  He  soon 
discovered  that  Latin  was  worth  learning,  and  the  Greek 
Delectus  interested  him  when  we  got  so  far.  And  there  were 
two  subjects  in  which  he  at  once  took  the  foremost  place, 
when  he  had  a  fair  chance  of  doing  so  ;  these  were  Scripture 
Biography  and  English.  In  arithmetic  as  well  as  in  Latin  his 
comparative  want  of  readiness  kept  him  down. 

"  On  the  whole  he  attained  a  measure  of  success  which 
helped  to  secure  for  him  a  certain  respect ;  and,  however 
strange  he  sometimes  seemed  to  his  companions,  he  had  three 
qualities  which  they  could  not  fail  to  understand — agile 
strength  of  limb,  imperturbable  courage,  and  profound  good- 
nature. Professor  James  Muirhead  remembers  him  as  '  a 
friendly  boy,  though  never  quite  amalgamating  with  the  rest.' 
And  another  old  class-fellow,  the  Rev.  W.  Macfarlane  of 
Lenzie,  records  the  following  as  his  impression  : — '  Clerk 
Maxwell,  when  he  entered  the  Academy,  was  somewhat  rustic 
and  somewhat  eccentric.  Boys  called  him  "  Dafty,"  and  used 
to  try  to  make  fun  of  him.  On  one  occasion  I  remember  he 
turned  with  tremendous  vigour,  with  a  kind  of  demonic  force, 
on  his  tormentors.  I  think  he  was  let  alone  after  that,  and 
gradually  won  the  respect  even  of  the  most  thoughtless  of  his 
schoolfellows/'' 

The  first  reference  to  mathematical  studies  occurs, 
says  Professor  Campbell,  in  a  letter  to  his  father 
written  soon  after  his  thirteenth  birthday.* 

"After  describing  the  Virginian  Minstrels,  and  betwixt 
inquiries  after  various  pets  at  Glenlair,  he  remarks,  as  if  it 
were  an  ordinary  piece  of  news,  '  I  have  made  a  tetrahedron, 
a  dodecahedron,  and  two  other  hedrons,  whose  names  I  don't 
know.'  We  had  not  yet  begun  geometry,  and  he  had  certainly 
not  at  this  time  learnt  the  definitions  in  Euclid  ;  yet  he  had 

*  "Life  of  J.  C.  Maxwell,"  p  56. 


16  JAMES    CLERK    MAXWELL 

not  merely  realised  the  nature  of  the  five  regular  solids 
sufficiently  to  construct  them  out  of  pasteboard  with  ap- 
proximate accuracy,  but  had  further  contrived  other  sym- 
metrical polyhedra  derived  from  them,  specimens  of  which 
(as  improved  in  1848)  may  be  still  seen  at  the  Cavendish 
Laboratory. 

"Who  first  called  his  attention  to  the  pyramid,  cube,  etc.,  I 
do  not  know.  He  may  have  seen  an  account  of  them  by 
chance  in  a  book.  But  the  fact  remains  that  at  this  early  time 
his  fancy,  like  that  of  the  old  Greek  geometers,  was  arrested 
by  these  types  of  complete  symmetry  ;  and  his  imagination  so 
thoroughly  mastered  them  that  he  proceeded  to  make  them 
Avith  his  own  hand.  That  he  himself  attached  more  importance 
to  this  moment  than  the  letter  indicates  is  proved  by  the  care 
with  which  he  has  preserved  these  perishable  things,  so  that 
they  (or  those  which  replaced  them  in  1848)  are  still  in 
existence  after  thirty-  seven  years." 

The  summer  holidays  were  spent  at  Glenlair. 
His  cousin,  Miss  Jemima  Wedderburn,  was  with  him, 
and  shared  his  play.  Her  skilled  pencil  has  left  us 
many  amusing  pictures  of  the  time,  some  of  which 
are  reproduced  by  Professor  Campbell.  There  were 
expeditions  and  picnics  of  all  sorts,  and  a  new  toy 
known  as  "  the  devil  on  two  sticks  "  afforded  infinite 
amusement,  The  winter  holidays  usually  found  him 
at  Penicuik,  or  occasionally  at  Glasgow,  with  Professor 
Blackburno  or  Professor  W.  Thomson  (now  Lord 
Kelvin).  In  October,  1844,  Maxwell  was  promoted 
to  the  rector's  class-room.  John  Williams,  afterwards 
Archdeacon  of  Cardigan,  a  distinguished  Baliol  man, 
was  rector,  and  the  change  was  in  many  ways  an 
important  one  for  Maxwell.     He  writes  to  his  father  : 

"  I  like  P better  than  B .     We  have  lots  of 

jokes,  and  he  speaks  a  great  deal,  and  we  have  not 


AND    MODERN    PHYSICS.  17 

so  much  monotonous  parsing.  In  the  English  Milton 
is  better  than  the  History  of  Greece.     .     .     ." 

P was   the   boys'  nickname   for  the   rector  ; 

B for  Mr.  Carmichael,  the  second  master.     This* 

is  the  account  of  Maxwell's  first  interview  with  the 
rector : — 

Rector :  "  What  part  of  Galloway  do  you  come 
from  ? " 

./.  G.  M. :  "  From  the  Vale  of  Urr.  Ye  spell  it 
o,  err,  err,  or  oo,  err,  err." 

The  study  of  geometry  was  begun,  and  in  the 
mathematical  master,  Mr.  Gloag,  Maxwell  found  a 
teacher  with  a  real  gift  for  his  task.  It  was  here 
that  Maxwell's  vast  superiority  to  many  who  were 
his  companions  at  once  showed  itself.  "  He  seemed," 
says  Professor  Campbell,  "  to  be  in  the  heart  of  the 
subject  when  they  were  only  at  the  boundary ;  but  the 
boyish  game  of  contesting  point  by  point  with  such 
a  mind  was  a  most  wholesome  stimulus,  so  that  the 
mere  exercise  of  faculty  was  a  pure  joy.  With 
Maxwell  the  first  lessons  of  geometry  branched  out 
at  once  into  inquiries  which  became  fruitful." 

In  July,  1845,  he  writes  : — 

"I  have  got  the  11th  prize  for  Scholarship,  the  1st  for 
English,  the  prize  for  English  verses,  and  the  Mathematical 
Medal.  I  tried  for  Scripture  knowledge,  and  Hamilton  in  the 
7th  has  got  it,  "We  tried  for  the  Medal  on  Thursday.  I  had 
done  them  all,  and  got  home  at  half-past  two  ;  but  Campbell 
stayed  till  four.  I  was  rather  tired  with  writing  exercises 
from  nine  till  half-past  two. 

"Campbell   and   I   went  'once   more  unto  the   b(r)each 

*  "  Life  of  J.  C.  Maxwell,"  p.  67. 
B 


18  JAMES   CLERK    MAXWELL 

to-day  at  Portobello.  I  can  swim  a  little  now.  Campbell  lias 
got  6  prizes.  He  got  a  letter  written  too  soon,  congratulating 
him  upon  my  medal;  but  there  is  no  rivalry  betwixt  us,  as 
B Carmichael  says." 

After  a  summer  spent  chiefly  at  Glenlair,  he 
returned  with  his  father  to  Edinburgh  for  the  winter, 
and  began,  at  the  age  of  fourteen,  to  go  to  the 
meetings  of  the  Royal  Society  of  Edinburgh.  At 
the  Society  of  Arts  he  met  Mr.  R.  D.  Hay,  the 
decorative  painter,  who  had  interested  himself  in  the 
attempt  to  reduce  beauty  in  form  and  colour  to 
mathematical  principles.  Clerk  Maxwell  was  in- 
terested in  the  question  how  to  draw  a  perfect  oval, 
and  devised  a  method  of  drawing  oval  curves  which 
was  referred  by  his  father  to  Professor  Forbes  for 
his  criticism  and  suggestions.  After  discussing  the 
matter  with  Professor  Kelland,  Professor  Forbes 
wrote  as  follows  *  : — 

"  My  Dear  Sir,— I  am  glad  to  find  to-day,  from  Professor 
Kelland,  that  his  opinion  of  your  son's  paper  agrees  with  mine, 
namely,  that  it  is  most  ingenious,  most  creditable  to  him,  and, 
we  believe,  a  newr  way  of  considering  higher  curves  with 
reference  to  foci.  Unfortunately,  these  ovals  appear  to  be 
curves  of  a  very  high  and  intractable  order,  so  that  possibly 
the  elegant  method  of  description  may  not  lead  to  a  corre- 
sponding simplicity  in  investigating  their  properties.  But  that 
is  not  the  present  point.  If  you  wish  it,  I  think  that  the 
simplicity  and  elegance  of  the  method  would  entitle  it  to  be 
brought  before  the  Royal  Society. — Believe  me,  my  dear  sir, 
yours  truly,  «  James  d  Foebes. 

In    consequence    of    this,   Clerk    Maxwell's    first 
*  "Life  of  J.  C.  Maxwell,"  p.  75. 


5 


AND   MODERN    PHYSICS.  19 

published  paper  was  communicated  to  the  Royal 
Society  of  Edinburgh  on  April  6th,  1846,  when  its 
author  was  barely  fifteen.  Its  title  is  as  follows : 
"  On  the  Description  of  Oval  Curves  and  those  having 
a  Plurality  of  Foci.  By  Mr.  Clerk  Maxwell,  Junior. 
With  Remarks  by  Professor  Forbes.  Communicated 
by  Professor  Forbes." 

The  notice  in  his  father's  diary  runs :  "  M.  6  [Ap., 
1846.]  Royal  Society  with  Jas.  Professor  Forbes 
gave  acct.  of  James's  Ovals.  Met  with  very  great 
attention  and  approbation  generally." 

This  was  the  beginning  of  the  lifelong  friendship 
between  Maxwell  and  Forbes. 

The  curves  investigated  by  Maxwell  have  the 
property  that  the  sum  found  by  adding  to  the 
distance  of  any  point  on  the  curve  from  one  focus 
a  constant  multiple  of  the  distance  of  the  same  point 
from  a  second  focus  is  always  constant. 

The  curves  are  of  great  importance  in  the 
theory  of  light,  for  if  this  constant  factor  ex- 
presses the  refractive  index  of  any  medium,  then 
lio'ht  divenrinu-  from  one  focus  without  the  medium 
and  refracted  at  a  surface  bounding  the  medium,  and 
having  the  form  of  one  of  Maxwell's  ovals,  will  be 
refracted  so  as  to  converge  to  the  second  focus. 

About  the  same  time  he  was  busy  with  some 
investigations  on  the  properties  of  jelly  and  gutta- 
percha, which  seem  to  have  been  suggested  by  Forbes' 
"  Theory  of  Glaciers." 

He  failed  to  obtain  the  Mathematical  Medal  in 
1846 — possibly  on  account  of  these  researches — but 
he  continued  at  school  till  1847,  when  he  left,  being 
b  2 


20  JAMES   CLERK    MAXWELL 

then  first  in  mathematics  and  in  English,  and  nearly 
first  in  Latin. 

In  1847  he  was  working  at  magnetism  and  the 
polarisation  of  light.  Some  time  in  that  year  he  was 
taken  by  his  uncle,  Mr.  John  Cay,  to  see  William 
Nicol,  the  inventor  of  the  polarising  prism,  who 
showed  him  the  colours  exhibited  by  polarised  light 
after  passing  through  unannealed  glass.  On  his 
return,  he  made  a  polariscope  with  a  glass  reflector. 
The  framework  of  the  first  instrument  was  of  card- 
board, but  a  superior  article  was  afterwards  constructed 
of  wood.  Small  lenses  mounted  on  cardboard  were 
employed  when  a  conical  pencil  was  needed.  By 
means  of  this  instrument  he  examined  the  figures 
exhibited  by  pieces  of  unannealed  glass,  which  he 
prepared  himself ;  and,  with  a  camera  lucida  and  box 
of  colours,  he  reproduced  these  figures  on  paper, 
taking  care  to  sketch  no  outlines,  but  to  shade  each 
coloured  band  imperceptibly  into  the  next.  Some  of 
these  coloured  drawings  he  forwarded  to  Nicol,  and 
was  more  than  repaid  by  the  receipt  shortly  after- 
wards of  a  pair  of  prisms  prepared  by  Nicol  himself. 
These  prisms  were  always  very  highly  prized  by 
Maxwell.  Once,  when  at  Trinity,  the  little  box 
containing  them  was  carried  off  by  his  bed-maker 
during  a  vacation,  and  destined  for  destruction.  The 
bed-maker  died  before  term  commenced,  and  it  was 
only  by  diligent  search  among  her  effects  that  the 
prisms  were  recovered.*  After  this  they  were  more 
carefully  guarded,  and  they  are  now,  together  with 
the  wooden  polariscope,  the  bits  of  unannealed  glass, 

*  Professor  Garnctt  in  Nature,  November  13th,  1879. 


AX  I)    MODERN    PHYSICS.  21 

and  the  water-colour  drawings,  in  one  of  the  show- 
cases at  the  Cavendish  Laboratory. 

About  this  time,  Professor  P.  G.  Tait  and  he  were 
schoolfellows  at  the  Academy,  acknowledged  as  the 
two  best  mathematicians  in  the  school.  It  was 
thought  desirable,  says  Professor  Campbell,  that  "  we 
should  have  lessons  in  physical  science,  so  one  of  the 
classical  masters  gave  them  out  of  a  text-book.  .  .  . 
The  only  thing  I  distinctly  remember  about  these 
hours  is  that  Maxwell  and  P.  G.  Tait  seemed  to  know 
much  more  about  the  subject  than  our  teacher  did." 

An  interesting  account  of  these  days  is  given  by 
Professor  Tait  in  an  obituary  notice  on  Maxwell 
printed  in  the  "  Proceedings  of  the  Royal  Society  of 
Edinburgh,  1879-80,"  from  which  the  following  is 
taken : — 

"When  i  first  made  Clerk  Maxwell's  acquaintance,  about 
thirty-five  years  ago,  at  the  Edinburgh  Academy,  he  was  a 
year  before  me,  being  in  the  fifth  class,  while  I  was  in  the 
fourth. 

"At  school  he  was  at  first  regarded  as  shy  and  rather  dull. 
He  made  no  friendships,  and  he  spent  his  occasional  holidays 
in  reading  old  ballads,  drawing  curious  diagrams,  and  making 
rude  mechanical  models.  This  absorption  in  such  pursuits, 
totally  unintelligible  to  his  schoolfellows  (who  were  then  quite 
innocent  of  mathematics),  of  course  procured  him  a  not  very 
complimentary  nickname,  which  I  know  is  still  remembered 
by  many  Fellows  of  this  Society.  About  the  middle  of  his 
school  career,  however,  he  surprised  his  companions  by 
suddenly  becoming  one  of  the  most  brilliant  among  them, 
gaining  high,  and  sometimes  the  highest,  prizes  for  scholar- 
ships, mathematics,  and  English  verse  composition.  From 
this  time  forward  I  became  very  intimate  with  him,  and  we 
discussed    together,   with    schoolboy    enthusiasm,    numerous 


22  JAMES   CLERK   MAXWELL 

curious  problems,  among  which  I  remember  particularly  the 
various  plane  sections  of  a  ring  or  tore,  and  the  form  of  a 
cylindrical  mirror  which  should  show  one  his  own  image 
unperverted.  I  still  possess  some  of  the  MSS.  we  exchanged 
in  1846  and  early  in  1847.  Those  by  Maxwell  are  on  '  The 
Conical  Pendulum,'  '  Descartes'  Ovals,'  '  Meloid  and  Apioid,' 
and  '  Trifocal  Curves.'  All  are  drawn  up  in  strict  geometrical 
form  and  divided  into  consecutive  propositions.  The  three 
latter  are  connected  with  his  first  published  paper,  communi- 
cated by  Forbes  to  this  society  and  printed  in  our  '  Proceed- 
ings,' vol.  ii.,  under  the  title,  'On  the  Description  of  Oval 
Curves  and  those  having  a  Plurality  of  Foci'  (1846).  At  the 
time  when  these  papers  Avere  written  he  had  received  no 
instruction  in  mathematics  beyond  a  few  books  of  Euclid  and 
the  merest  elements  of  algebra." 

In  November,  1847,  Clerk  Maxwell  entered  the 
University  of  Edinburgh,  learning  mathematics  from 
Kelland,  natural  philosophy  from  J.  D.  Forbes,  and 
logic  from  Sir  W.  R.  Hamilton.  At  this  time,  accord- 
ing to  Professor  Campbell  *  — 

"he  still  occasioned  some  concern  to  the  more  conven- 
tional amongst  his  friends  by  the  originality  and  simplicity  of 
his  ways.  His  replies  in  ordinary  conversation  were  indirect 
and  enigmatical,  often  uttered  with  hesitation  and  in  a 
monotonous  key.  While  extremely  neat  in  his  person,  he  had 
a  rooted  objection  to  the  vanities  of  starch  and  gloves.  He 
had  a  pious  horror  of  destroying  anything,  even  a  scrap  of 
writing-paper.  He  preferred  travelling  by  the  third  class  in 
railway  journeys,  saying  he  liked  a  hard  seat.  When  at  table 
he  often  seemed  abstracted  from  what  was  going  on,  being- 
absorbed  in  observing  the  effects  of  refracted  light  in  the 
finger-glasses,  or  in  trying  some  experiment  with  his  eyes — 
seeing  round  a  corner,  making  invisible  stereoscopes,  and  the 
like.  Miss  Cay  used  to  call  his  attention  by  crying,  '  Jamsie, 
you're  in  a  prop.'     He  never  tasted  wine ;    and  he  spoke  to 

*  "Life  of  J.  0.  Maxwell,"  p.  105. 


AND   MODERN   PHYSICS.  23 

gentle  and  simple  in  exactly  the  same  tone.  On  the  other 
hand,  his  teachers— Forbes  above  all — had  formed  the  highest 
opinion  of  his  intellectual  originality  and  force  ;  and  a  few- 
experienced  observers,  in  watching  his  devotion  to  his  father, 
began  to  have  some  inkling  of  his  hei'oic  singleness  of  heart. 
To  his  college  companions,  whom  he  could  now  select  at  will, 
his  quaint  humour  was  an  endless  delight.  His  chief  associates, 
after  I  went  to  the  University  of  Glasgow,  were  my  brother, 
Robert  Campbell  (still  at  the  Academy),  P.  G.  Tait,  and  Allan 
Stewart.  Tait  went  to  Peterhouse,  Cambridge,  in  1848,  after 
one  session  of  the  University  of  Edinburgh  ;  Stewart  to  the 
same  college  in  1849  ;  Maxwell  did  not  go  up  until  1850." 

During  this  period  he  wrote  two  important  papers. 
The  one,  on  "  Rolling  Curves,"  w^as  read  to  the 
Royal  Society  of  Edinburgh  by  Professor  Kelland 
— ("  it  was  not  thought  proper  for  a  boy  in  a  round 
jacket  to  mount  the  rostrum  ") — in  February,  1849  ; 
the  other,  on  "The  Equilibrium  of  Elastic  Solids," 
appeared  in  the  spring  of  1850. 

The  vacations  were  spent  at  Glenlair,  and  we  learn 
from  letters  to  Professor  Campbell  and  others  how 
the  time  was  passed. 

"  On  Saturday,"  he  writes*—  April  26th,  1848,  just, 
after  his  arrival  home — "  the  natural  philosophers 
ran  up  Arthur's  Seat  with  the  barometer.  The 
Professor  set  it  down  at  the  top.  .  .  .  He  did  not 
set  it  straight,  and  made  the  hill  grow  fifty  feet ;  but 
we  got  it  down  aoain." 

In  a  letter  of  July  in  the  same  year  he  describes 
his  laboratory : — 

"I  have  regularly  set  up  shop  now  above  the  wash-house 
at  the  gate,  in  a  garret.    I  have  an  old  door  set  on  two  barrels, 

*  "  Life  of  J.  C.  Maxwell,"  p.  11G. 


24  JAMES   CLERK   MAXWELL 

and  two  chairs,  of  which  one  is  safe,  and  a  skylight  above 
which  will  slide  up  and  down. 

"  On  the  door  (or  table)  there  is  a  lot  of  bowls,  jugs, 
plates,  jam  pigs,  etc.,  containing  water,  salt,  soda,  sulphuric 
acid,  blue  vitriol,  plumbago  ore  ;  also  broken  glass,  iron,  and 
copper  wire,  copper  and  zinc  plate,  bees'  wax,  sealing  wax, 
clay,  rosin,  charcoal,  a  lens,  a  Smee's  galvanic  apparatus,  and 
a  countless  variety  of  little  beetles,  spiders,  and  wood  lice, 
which  fall  into  the  different  liquids  and  poison  themselves.  I 
intend  to  get  up  some  more  galvanism  in  jam  pigs ;  but  I 
must  first  copper  the  interiors  of  the  pigs,  so  I  am  experiment- 
ing on  the  best  methods  of  electrotyping.  80  I  am  making 
copper  seals  with  the  device  of  a  beetle.  First,  I  thought  a 
beetle  was  a  good  conductor,  so  I  embedded  one  in  wax  (not 
at  all  cruel,  because  I  slew  him  in  boiling  water,  in  which  he 
never  kicked),  leaving  his  back  out ;  but  he  would  not  do. 
Then  I  took  a  cast  of  him  in  sealing  wax,  and  pressed  wax 
into  the  hollow,  and  blackleaded  it  with  a  brush  ;  but  neither 
would  that  do.  So  at  last  I  took  my  fingers  and  rubbed  it, 
which  I  find  the  best  way  to  use  the  blacklead.  Then  it 
coppered  famously.  I  melt  out  the  wax  with  the  lens,  that 
being  the  cleanest  way  of  getting  a  strong  heat,  so  I  do  most 
things  with  it  that  need  heat.  To-day  I  astonished  the 
natives  as  follows.  I  took  a  crystal  of  blue  vitriol  and  put 
the  lens  to  it,  and  so  drove  off  the  water,  leaving  a  white 
powder.  Then  1  did  the  same  to  some  washing  soda,  and 
mixed  the  two  white  powders  together,  and  made  a  small 
native  spit  on  them,  which  turned  them  green  by  a  mutual 
exchange,  thus  : — 1.  Sulphate  of  copper  and  carbonate  of  soda. 
2.  Sulphate  of  soda  and  carbonate  of  copper  (blue  or  green)." 

Of  his  reading  lie  says  : — "  I  am  reading  Herodotus' 
Euterpe,'  having  taken  the  turn — that  is  to  say  that 
sometimes  I  can  do  props.,  read  Diff.  and  Int.  Gala, 
Poisson,  Hamilton's  dissertation,  etc." 

In  September  he  was  busy  with  polarised  light. 
"We   were   at    Castle   Douglas    yesterday,   and    got 


AND   MODERN   PHYSICS.  25 

crystals  of  saltpetre,  which  I  have  been  cutting  up 
into  plates  to-day  in  hopes  to  see  rings." 
In  July,  1849,  he  writes  *  :  — 

"I  have  set  up  the  machine  for  showing  the  rings  in 
crystals,  which  I  planned  during  your  visit  last  year.  It 
answers  very  well.  I  also  made  some  experiments  on  com- 
pressed jellies  in  illustration  of  my  props,  on  that  subject. 
The  principal  one  was  this  : — The  jelly  is  poured  while  hot 
into  the  annular  space  contained  between  a  paper  cylinder  and 
a  cork ;  then,  when  cold,  the  cork  is  twisted  round  and  the 
jelly  exposed  to  polarised  light,  when  a  transverse  cross,  x, 
not  +,  appears,  with  rings  as  the  inverse  square  of  the  radius, 
all  which  is  fully  verified.    Hip  !  etc.     Q.E.D." 

And  again  on  March  22nd,  1850  : — 

"At  Practical  Mechanics  I  have  been  turning  Devils  of 
sorts.  For  private  studies  I  have  been  reading  Young's 
'  Lectures,'  Willis's  '  Principles  of  Mechanism,'  Moseley's 
'  Engineering  and  Mechanics,'  Dixon  on  '  Heat,'  and  Moigno's 
'  Repertoire  d'Optique.'  This  last  is  a  very  complete  analysis 
of  all  that  has  I  teen  done  in  the  optical  way  from  Fresnel  to 
the  end  of  1849,  and  there  is  another  volume  a- coming  which 
will  complete  the  work.  There  is  in  it,  besides  common  optics, 
all  about  the  other  things  which  accompany  light,  as  heat, 
chemical  action,  photographic  rays,  action  on  vegetables,  etc. 

"  My  notions  are  rather  few,  as  I  do  not  entertain  them 
just  now.  I  have  a  notion  for  the  torsion  of  wires  and  rods, 
not  to  be  made  till  the  vacation  ;  of  experiments  on  the  action 
of  compression  on  glass,  jelly,  etc.,  numerically  done  up;  of 
papers  for  the  Physico-Mathematical  Society  (which  is  to 
revive  in  earnest  next  session  !) ;  on  the  relations  of  optical 
and  mechanical  constants,  their  desirableness,  etc. ;  and  sus- 
pension bridges,  and  catenaries,  and  elastic  curves.  Alex. 
Campbell,  Agnew,  and  I  are  appointed  to  read  up  the  subject 
of  periodical  shooting  stars,  and  to  prepare  a  list  of  the 
phenomena   to   be    observed    on    the   9th   August  and    13th 

*  "Life  of  J.  C.  Maxwell,"  pp.  123-129. 


26  JAMES    CLERK   MAXWELL 

November.  The  society's  barometer  is  to  be  taken  up  Arthur's 
Seat  at  the  end  of  the  session,  when  Forbes  goes  up,  and  All 
students  are  invited  to  attend,  so  that  the  existence  of  the 
society  may  be  recognised." 

It  was  at  last  settled  that  he  was  to  go  up  to 
Cambridge.  Tait  had  been  at  Peterhouse  for  two 
3'ears,  while  Allan  Stewart  had  joined  him  there  in 

1849,  and  after  much  discussion  it  was  arranged  that 
Maxwell  should  enter  at  the  same  college. 

Of  this  period  of  his  life  Tait  writes  as  follows  : — 

"The  winter  of  1847  found  us  together  in  the  classes  of 
Forbes  and  Kelland,  where  he  highly  distinguished  himself. 
With  the  former  he  was  a  ]  (articular  favourite,  being  admitted 
to  the  free  use  of  the  class  apparatus  for  original  experiments. 
He  lingered  here  behind  most  of  his  former  associates,  having 
spent  three  years  at  the  University  of  Edinburgh,  working 
(without  any  assistance  or  supervision)  with  physical  and 
chemical  apparatus,  and  devouring  all  sorts  of  scientific  works 
in  the  library.  During  this  period  he  Wrote  two  valuable 
papers,  which  are  published  in  our  'Transactions,'  on  'The 
Theory  of  Rolling  Curves '  and  on  '  The  Equilibrium  of  Elastic 
Solids.'     Thus  he  brought  to  Cambridge,  in  the  autumn  of 

1850,  a  mass  of  knowledge  which  was  really  immense  for  so 
young  a  man,  but  in  a  state  of  disorder  appalling  to  his 
methodical  private  tutor.  Though  that  tutor  was  William 
Hopkins,  the  pupil  to  a  great  extent  took  his  own  way,  and  it 
may  safely  be  said  that  no  high  wrangler  of  recent  years  ever 
entered  the  Senate  House  more  imperfectly  trained  to  produce 
'paying'  work  than  did  Clerk  Maxwell.  But  by  sheer  strength 
of  intellect,  though  with  the  very  minimum  of  knowledge  how 
to  use  it  to  advantage  under  the  conditions  of  the  examina- 
tion, he  obtained  the  position  of  Second  Wrangler,  and  Avas 
bracketed  equal  with  the  Senior  Wrangler  in  the  higher  ordeal 
of  the  Smith's  Prizes.  His  name  appears  in  the  Cambridge 
'Calendar'  as  Maxwell  of  Trinity,  but  he  was  originally 
entered  at  Peterhouse,  and  kept  his  first  term  there,  in  that 


AND   MODERN   PHYSICS.  27 

small  but  most  ancient  foundation  which  has  of  late  furnished 
Scotland  with  the  majority  of  the  professors  of  mathematics 
and  natural  philosophy  in  her  four  universities." 

While  W.  I).  Niven,  in  his  preface  to  Maxwell's 
collected  works  (p.  xii.),  says  :— 

"  It  may  readily  be  supposed  that  his  preparatory  training 
for  the  Cambridge  course  was  far  removed  from  the  ordinary 
type.  There  had  indeed  for  some  time  been  practically  no 
restraint  upon  his  plan  of  study,  and  his  mind  had  been 
allowed  to  follow  its  natural  bent  towards  science,  though  not 
to  an  extent  so  absorbing  as  to  withdraw  him  from  other 
pursuits.  Though  he  was  not  a  sportsman— indeed,  sport  so- 
called  was  always  repugnant  to  him — he  was  yet  exceedingly 
£ond  of  a  country  life.  He  was  a  good  horseman  and  a  good 
swimmer.  Whence,  however,  he  derived  his  chief  enjoyment 
may  be  gathered  from  the  account  which  Mr.  Campbell  gives 
of  the  zest  with  which  he  quoted  on  one  occasion  the  lines  of 
Burns  which  describe  the  poet  finding  inspiration  while 
wandering  along  the  banks  of  a  stream  in  the  free  indulgence 
of  his  fancies.  Maxwell  was  not  only  a  lover  of  poetry,  but 
himself  a  poet,  as  the  fine  pieces  gathered  together  by  Mr. 
Campbell  abundantly  testify.  He  saw,  however,  that  his  true 
calling  was  science,  and  never  regarded  these  poetical  efforts 
as  other  than  mere  pastime.  Devotion  to  science,  already 
stimulated  by  successful  endeavour ;  a  tendency  to  ponder 
over  philosophical  problems  ;  and  an  attachment  to  English 
literature,  particularly  to  English  poetry — these  tastes,  im- 
planted in  a  mind  of  singular  strength  and  purity,  may  be  said 
to  have  been  the  endowments  with  which  young  Maxwell 
began  his  Cambridge  career.  Besides  this,  his  scientific 
reading,  as  we  may  gather  from  his  papers  to  the  Royal 
Society  of  Edinburgh  referred  to  above,  was  already  extensive 
and  varied.  He  brought  with  him,  says  Professor  Tait,  a  mass 
of  knowledge  which  was  really  immense  for  so  young  a  man, 
but  in  a  state  of  disorder  appalling  to  his  methodical  private 
tutor." 


28  JAMES   CLERK    MAXWELL 


CHAPTER    II. 

UNDERGRADUATE    LIFE    AT   CAMBRIDGE. 

Maxwell  did  not  remain  long  at  Peterhonse  ;  before 
the  end  of  his  first  term  he  migrated  to  Trinity,  and 
was  entered  under  Dr.  Thompson  December  14th, 
1850.  He  appeared  to  the  tutor  a  shy  and  diffident 
3Touth,  but  presently  surprised  Dr.  Thompson  by 
producing  a  bundle  of  papers — copies,  probably,  of 
those  he  had  already  published  —  and  remarking, 
"  Perhaps  these  may  show  that  I  am  not  unfit  to 
enter  at  your  College." 

The  change  was  pressed  upon  him  by  many 
friends,  the  grounds  of  the  advice  being  that,  from 
the  large  number  of  high  wranglers  recently  at 
Peterhouse  and  the  smallness  of  the  foundation,  the 
chances  of  a  Fellowship  there  for  a  mathematical 
man  were  less  than  at  Trinity.  It  was  a  step  he 
never  regretted  ;  the  prospect  of  a  Fellowship  had 
but  little  influence  on  his  mind.  He  found,  however, 
at  the  larger  college  ampler  opportunities  for  self- 
improvement,  and  it  was  possible  for  him  to  select  his 
friends  from  among  men  whom  he  otherwise  would 
never  have  known. 

The  record  of  his  undergraduate  life  is  not  very 
full ;  his  letters  to  his  father  have,  unfortunately, 
been  lost,  but  we  have  enough  in  the  recollections  of 
friends  still  living  to  picture  what  it  was  like.  At 
first  he  lodged  in  King's  Parade  with  an  old  Edin- 
burgh schoolfellow,  C.  H.  Robertson.     He  attended  the 


AND   MODERN   PHYSICS.  29 

College  lectures  on  mathematics,  though  they  were 
somewhat  elementary,  and  worked  as  a  private  pupil 
with  Porter,  of  Peterhouse.  His  father  writes  to  him, 
November,  1850 :  "  Have  you  called  on  Professors 
Sedgwick,  at  Trin,  and  Stokes,  at  Pembroke  ?  If 
not,  you  should  do  both.  Stokes  will  be  most  in  your 
line,  if  he  takes  you  in  hand  at  all.  Sedgwick  is  also 
a  great  Don  in  his  line,  and,  if  you  were  entered  in 
geology,  would  be  a  most  valuable  acquaintance." 

In  his  second  year  he  became  a  pupil  of  Hopkins, 
the  great  coach  ;  he  also  attended  Stokes'  lectures, 
and  the  friendship  which  lasted  till  his  death  was 
thus  begun.  In  April,  1852,  he  was  elected  a  scholar, 
and  obtained  rooms  in  College  (G,  Old  Court).  In 
June,  1852,  he  came  of  age.  "  I  trust  you  will  be  as 
discreet  when  major  as  you  have  been  while  minor," 
writes  his  father  the  day  before.  The  next  academic 
year,  October,  1852,  to  June,  1853,  was  a  very  busy 
one ;  hard  grind  for  the  Tripos  occupied  his  time,  and 
he  seems  to  have  been  thoroughly  overstrained.  He 
was  taken  ill  while  staying  near  Lowestoft  with  the 
Rev.  C.  B.  Tayler,  the  uncle  of  a  College  friend.  His 
own  account  of  the  illness  is  given  in  a  letter  to 
Professor  Campbell*,  dated  July  14th,  1853. 

"You  wrote  just  in  time  for  your  letter  to  reach  me  as  I 
reached  Cambridge.  After  examination,  I  went  to  visit  the 
Rev.  C.  B.  Tayler  (uncle  to  a  Tayler  whom  I  think  you  have 
seen  under  the  name  of  Freshman,  etc.,  and  author  of  many 
tracts  and  other  didactic  Avorks).  We  had  little  expedites  and 
walks,  and  things  parochial  and  educational,  and  domesticity. 
1  intended  to  return  on  the  18th  June,  but  on  the  17th  I  felt 

*  "Life  of  J.  C.  Maxwell,"  p.  190. 


30  JAMES   CLERK   MAXWELL 

unwell,  and  took  measures  accordingly  to  be  well  again — i.e. 
Avent  to  bed,  and  made  up  my  mind  to  recover.  But  it  lasted 
more  than  a  fortnight,  during  which  time  I  was  taken  care  of 
beyond  expectation  (not  that  I  did  not  expect  much  before). 
When  I  was  perfectly  useless  and  could  not  sit  up  without 
fainting,  Mr.  Tayler  did  everything  for  me  in  such  a  way  that 
I  had  no  fear  of  giving  trouble.  So  did  Mrs.  Tayler  ;  and  the 
two  nephews  did  all  they  could.  So  they  kept  me  in  great 
happiness  all  the  time,  and  detained  me  till  I  was  able  to  walk 
about  and  got  back  strength.     I  returned  on  the  4th  July. 

"  The  consequence  of  all  this  is  that  I  correspond  Avith  Mr. 
Tayler,  and  have  entered  into  bonds  Avith  the  nephews,  of 
all  of  whom  more  hereafter.  Since  I  came  here  I  have  been 
attending  Hop.,  but,  Avith  his  approval,  did  not  begin  full 
SAving.  I  am  getting  on,  though,  and  the  work  is  not  grinding 
on  the  prepared  brain." 

During  this  period  he  Avrote  some  papers  for  the 
Cambridge  and  Dublin  Mathematical  Journal  which 
will  be  referred  to  again  later.  He  was  also  a  member 
of  a  discussion  society  known  as  the  "  Apostles,"  and 
some  of  the  essays  contributed  by  him  are  preserved 
by  Professor  Campbell.  Mr.  Niven,  in  his  preface  to 
the  collected  edition  of  Maxwell's  works,  suggests 
that  the  composition  of  these  essays  laid  the  founda- 
tion of  that  literary  finish  which  is  one  of  the 
characteristics  of  Maxwell's  scientific  Avritings. 

Among  his  friends  at  the  time  Avere  Tait,  Charles 
Mackenzie  of  Caius,  the  missionary  bishop  of  Central 
Africa,  Henry  and  Frank  Mackenzie  of  Trinity, 
Droop,  third  Wrangler  in  1854  ;  Gedge,  Isaac  Taylor, 
Blakiston,  F.  W.  Farrar  *  H.  M.  Butler,f  Hort,  V. 
Lushington,  Cecil  Munro,  G.  W.  H.  Tayler,  and  W.  N. 
Lawson.      Some   of    these   Avho   survived   him    have 

*  Dean  of  Canterbury.  f  Master  of  Trinity. 


AND   MODERN   PHYSICS.  31 

given    to    Professor   Campbell    their   recollections   of 
these  undergraduate  days,  which  are  full  of  interest. 
Thus  Mr.  Lawson  writes  * : — 

"  There  must  be  many  of  his  quaint  verses  about,  if  one 
could  lay  hands  on  them,  for  Maxwell  was  constantly  producing 
something  of  the  sort  and  bringing  it  round  to  his  friends, 
with  a  sly  chuckle  at  the  humour,  which,  though  his  own,  no 
one  enjoyed  more  than  himself. 

"I  remember  Maxwell  coming  to  me  one  morning  with  a 
copy  of  verses  beginning,  '(Jin  a  body  meet  a  body  going 
through  the  air,'  in  which  he  had  twisted  the  well-known  song 
into  a  description  of  the  laws  of  impact  of  solid  bodies. 

"There  was  also  a  description  which  Maxwell  wrote  of 
some  University  ceremony — I  forget  what — in  which  somebody 
'  went  before '  and  somebody  '  followed  after,'  and  '  in  the 
midst  were  the  wranglers,  playing  with  the  symbols.' 

"These  last  words,  however  meant,  were,  in  fact,  a  descrip- 
tion of  his  own  wonderful  power.  I  remember,  one  day  in 
lecture,  our  lecturer  had  filled  the  black-board  three  times 
with  the  investigation  of  some  hard  problem  in  Geometry  of 
Three  Dimensions,  and  was  not  at  the  end  of  it,  when  Maxwell 
came  up  with  a  question  whether  it  would  not  come  out 
geometrically,  and  showed  how,  with  a  figure,  and  in  a  few 
lines,  there  was  the  solution  at  once. 

"Maxwell  was,  I  daresay  you  remember,  very  fond  of  a 
talk  upon  almost  anything.  He  and  I  were  pupils  (at  an 
enormous  distance  apart)  of  Hopkins,  and  I  well  recollect  how, 
when  I  had  been  working  the  night  before  and  all  the  morning 
at  Hopkins's  problems,  with  little  or  no  result,  Maxwell  would 
come  in  for  a  gossip,  and  talk  on  while  I  was  wishing  him  far 
away,  till  at  last,  about  half  an  hour  or  so  before  our  meeting 
at  Hopkins's,  he  would  say,  'Well,  I  must  go  to  old  Hop.'s 
problems ' ;  and,  by  the  time  we  met  there,  they  were  all  done. 

"  I  remember  Hopkins  telling  me,  when  speaking  of 
Maxwell,  either  just  before  or  just  after  his  degree,  '  It  is  not 

*  "  Life  of  J.  C.  Maxwell,"  p.  174. 


32  JAMES   CLERK   MAXWELL 

possible  for  that  man  to  think  incorrectly  on  physical  subjects ' ; 
and  Hopkins,  as  you  know,  had  had,  perhaps,  more  experience 
of  mathematical  minds  than  any  man  of  his  time." 

The  last  clause  is  part  of  a  quotation  from  a  diary 
kept  by  Mr.  Lawson  at  Cambridge,  in  which,  under 
the  date  July  15th,  1853,  he  writes  : — 

"  He  (Hopkins)  was  talking  to  me  this  evening  about 
Maxwell.  He  says  he  is  unquestionably  the  most  extra- 
ordinary man  he  has  met  with  in  the  whole  range  of  his 
experience  ;  he  says  it  appears  impossible  for  Maxwell  to 
think  incorrectly  on  physical  subjects  ;  that  in  his  analysis, 
however,  he  is  far  more  deficient.  He  looks  upon  him  as  a 
great  genius  with  all  its  eccentricities,  and  prophesies  that 
one  day  he  will  shine  as  a  light  in  physical  science — a  prophecy 
in  which  all  his  fellow-students  strenuously  unite." 

How  many  who  have  struggled  through  the 
"  Electricity  and  Magnetism "  have  realised  the 
truth  of  the  remark  about  the  correctness  of  his 
physical  intuitions  and  the  deficiency  at  times  of 
his  analysis ! 

Dr.  Butler,  a  friend  of  these  early  days,  preached 
the  University  sermon  on  November  16th,  1879,  ten 
days  after  Maxwell's  death,  and  spoke  thus  : — ■ 

"  It  is  a  solemn  thing — even  the  least  thoughtful  is  touched 
by  it — when  a  great  intellect  passes  away  into  the  silence  and 
we  see  it  no  more.  Such  a  loss,  such  a  void,  is  present,  I  feel 
certain,  to  many  here  to-day.  It  is  not  often,  even  in  this 
great  home  of  thought  and  knowledge,  that  so  bright  a  light 
is  extinguished  as  that  which  is  now  mourned  by  many  illus- 
trious mourners,  here  chiefly,  but  also  far  beyond  this  place.  I 
shall  be  believed  when  I  say  in  all  simplicity  that  I  wish  it  had 
fallen  to  some  more  competent  tongue  to  put  into  words  those 
feelings  of  reverent  affection  which  are,  I  am  persuaded,  upper- 
most in  many  hearts  on  this  Sunday.     My  poor  words  shall  be 


AND   MODERN   PHYSICS.  33 

few,  but  believe  me  tbey  come  from  the  heart.  You  know, 
brethren,  with  what  an  eager  pride  we  follow  the  fortunes  of 
those  whom  we  have  loved  and  reverenced  in  our  under- 
graduate days.  We  may  see  them  but  seldom,  few  letters  may 
pass  between  us,  but  their  names  are  never  common  names. 
They  never  become  to  us  only  what  other  men  are.  When 
I  came  up  to  Trinity  twenty-eight  years  ago,  James  Clerk 
Maxwell  was  just  beginning  his  second  year.  His  position 
among  us— I  speak  in  the  presence  of  many  who  remember 
that  time— was  unique.  He  Avas  the  one  acknowledged  man 
of  genius  among  the  undergraduates.  We  understood  even 
then  that,  though  barely  of  age,  he  was  in  his  own  line  of 
inquiry  not  a  beginner  but  a  master.  His  name  was  already 
a  familiar  name  to  men  of  science.  If  he  lived,  it  was  certain 
that  he  was  one  of  that  small  but  sacred  band  to  whom  it 
would  be  given  to  enlarge  the  bounds  of  human  knowledge. 
It  was  a  position  which  might  have  turned  the  head  of  a 
smaller  man  ;  but  the  friend  of  whom  we  were  all  so  proud, 
and  who  seemed,  as  it  were,  to  link  us  thus  early  with  the 
great  outside  world  of  the  pioneers  of  knowledge,  had  one  of 
those  rich  and  lavish  natures  which  no  prosperity  can  im- 
poverish, and  which  make  faith  in  goodness  easy  for  others.  I 
have  often  thought  that  those  who  never  knew  the  grand  old 
Adam  Sedgwick  and  the  then  young  and  ever-youthful  Clerk 
Maxwell  had  yet  to  learn  the  largeness  and  fulness  of  the 
moulds  in  which  some  choice  natures  are  framed.  Of  the 
scientific  greatness  of  our  friend  we  were  most  of  us  unable  to 
judge ;  but  anyone  could  see  and  admire  the  boy-like  glee,  the 
joyous  invention,  the  wide  reading,  the  eager  thirst  for  truth, 
the  subtle  thought,  the  perfect  temper,  the  unfailing  reverence, 
the  singular  absence  of  any  taint  of  the  breath  of  worldliness 
in  any  of  its  thousand  forms. 

"  Brethren,  you  may  know  such  men  now  among  your  college 
friends,  though  there  can  be  but  few  in  any  year,  or  indeed  in 
any  century,  that  possess  the  rare  genius  of  the  man  whom  we 
deplore.  If  it  be  so,  then,  if  you  will  accept  the  counsel  of  a 
stranger,  thank  God  for  His  gift.  Believe  me  when  I  tell  you 
that  few  such  blessings  will  come  to  you  in  later  life.  There 
c 


34  JAMES   CLERK   MAXWELL 

are  blessings  that  come  once  in  a  lifetime.  One  of  these  is  the 
reverence  with  which  we  look  up  to  greatness  and  goodness  in 
a  college  friend — above  us,  beyond  us,  far  out  of  our  mental  or 
moral  grasp,  but  still  one  of  us,  near  to  us,  our  own.  You 
know,  in  part  at  least,  how  in  this  case  the  promise  of  youth 
was  more  than  fulfilled,  and  how  the  man  Avho,  but  a  fortnight 
ago,  was  the  ornament  of  the  University,  and — shall  I  be 
wrong  in  saying  it  'I — almost  the  discoverer  of  a  new  world  of 
knowledge,  was  even  more  loved  than  he  was  admired,  retain- 
ing after  twenty  years  of  fame  that  mirth,  that  simplicity,  that 
child-like  delight  in  all  that  is  fresh  and  wonderful  which  we 
rejoice  to  think  of  as  some  of  the  surest  accompaniment  of 
true  scientific  genius. 

"  You  know,  also,  that  he  was  a  devout  as  well  as  thought- 
ful Christian.  I  do  not  note  this  in  the  triumphant  spirit  of  a 
controversialist.  I  will  not  for  a  moment  assume  that  there  is 
any  natural  opposition  between  scientific  genius  and  simple 
Christian  faith.  I  will  not  compare  him  with  others  who  have 
had  the  genius  without  the  faith.  Christianity,  though  she 
thankfully  welcomes  and  deeply  prizes  them,  does  not  need 
now,  any  more  than  when  St.  Paul  first  preached  the  Cross  at 
Corinth,  the  speculations  of  the  subtle  or  the  wisdom  of  the 
wise.  If  I  wished  to  show  men,  especially  young  men,  the 
living  force  of  the  Gospel,  I  would  take  them  not  so  much  to 
a  learned  and  devout  Christian  man  to  whom  all  stores  of 
knowledge  were  familiar,  but  to  some  country  village  where 
for  fifty  years  there  had  been  devout  traditions  and  devout 
practice.  There  they  would  see  the  Gospel  lived  out ;  truths, 
which  other  men  spoke  of,  seen  and  known  ;  a  spirit  not  of 
this  world,  visibly,  hourly  present ;  citizenship  in  heaven  daily 
assumed  and  daily  realised.  Such  characters  I  believe  to  be 
the  most  convincing  preachers  to  those  who  ask  whether 
Revelation  is  a  fable  and  God  an  unknowable.  Yes,  in  most 
cases — not,  I  admit,  in  all— simple  faith,  even  peradventure 
more  than  devout  genius,  is  mighty  for  removing  doubts  and 
implanting  fresh  conviction.  But  having  said  this,  we  may 
well  give  thanks  to  God  that  our  friend  was  what  he  was,  a 
firm  Christian  believer,  and  that  his  powerful  mind,  after 


AND   MODERN   PHYSICS.  35 

ranging  at  will  through  the  illimitable  spaces  of  Creation  and 
almost  handling  what  he  called  '  the  foundation-stones  of  the 
material  universe,'  found  its  true  rest  and  happiness  in  the 
love  and  the  mercy  of  Him  whom  the  humblest  Christian  calls 
his  Father.  Of  such  a  man  it  may  be  truly  said  that  he  had 
his  citizenship  in  heaven,  and  that  he  looked  for,  as  a  Saviour, 
the  Lord  Jesus  Christ,  through  whom  the  unnumbered  worlds 
were  made,  and  in  the  likeness  of  whose  image  our  new  and 
spiritual  body  will  be  fashioned." 

The  Tripos  came  in  January,  1854.  "  You  will 
neod  to  get  muffetees  for  the  Senate  Room.  Take 
your  plaid  or  rug  to  wrap  round  your  feet  and  legs," 
was  his  father's  advice — advice  Avhich  will  appeal  to 
many  who  can  remember  the  Senate  House  as  it  felt 
on  a  cold  January  morning. 

Maxwell  had  been  preparing  carefully  for  this 
examination.  Thus  to  his  aunt,  Miss  Cay,  in  June, 
1853,  he  writes  : — "  If  anyone  asks  how  I  am  getting 
on  in  mathematics,  say  that  I  am  busy  arranging 
everything  so  as  to  be  able  to  express  all  distinctly, 
so  that  examiner  may  be  satisfied  now  and  pupils 
edified  hereafter.  It  is  pleasant  work  and  very 
strengthening,  but  not  nearly  finished." 

Still,  the  illness  of  July,  1853,  had  left  some  effect. 
Professor  Baynes  states  that  he  said  that  on  entering 
the  Senate  House  for  the  first  paper  he  felt  his  mind 
almost  a  blank,  but  by-and-by  his  mental  vision 
became  preternaturally  clear. 

The  moderators  were  Mackenzie  of  Caius,  whose 
advice  had  been  mainly  instrumental  in  leading  him 
to  migrate  to  Trinity,  Win.  Walton  of  Trinity, 
Wolstenholme  of  Christ's,  and  Percival  Frost  of  St. 
John's. 

c   2 


36  JAMES   CLERK   MAXWELL 

When  the  lists  were  published,  Routh  of  Peter- 
house  was  senior,  Maxwell  second.  The  examination 
for  the  Smith's  Prizes  followed  in  a  few  days,  and 
then  Routh  and  Maxwell  were  declared  equal. 

In  a  letter  to  Miss  Cay  *  of  January  13th,  while 
waiting  for  the  three  days'  list,  he  writes  : — 

"  All  my  correspondents  have  been  writing  to  me,  which  is 
kind,  and  have  not  been  writing  questions,  which  is  kinder. 
So  I  answer  you  now,  while  I  am  slacking  speed  to  get  up 
steam,  leaving  Lewis  and  Stewart,  etc.,  till  next  week,  when  I 
will  give  an  account  of  the  five  days.  There  are  a  good  many 
up  here  at  present,  and  we  get  on  very  jolly  on  the  whole;  but 
some  are  not  well,  and  some  are  going  to  be  plucked  or 
gulphed,  as  the  case  may  be,  and  others  are  reading  so  hard 
that  they  are  invisible.  I  go  to-morrow  to  breakfast  with 
shaky  men,  and  after  food  I  am  to  go  and  hear  the  list  read 
out,  and  whether  they  are  through,  and  bring  them  word. 
When  the  honour  list  comes  out  the  poll  men  act  as  messengers. 
Bob  Campbell  comes  in  occasionally  of  an  evening  now,  to 
discuss  matters  and  vary  sports.  During  examination  I  have 
had  men  at  night  working  with  gutta-percha,  mignets,  etc. 
It  is  much  better  than  reading  novels  or  talking  after  5| 
hours'  hard  waiting." 

His  father,  on  hearing  the  news,  wrote  from 
Edinburgh  :— 

"  I  heartily  congratulate  you  on  your  place  in  the  list.  I 
suppose  it  is  higher  than  the  speculators  would  have  guessed, 
and  quite  as  high  as  Hopkins  reckoned  on.  I  wish  you  success 
in  the  Smith's  Prizes  ;  be  sure  to  write  me  the  result.  I  will 
see  Mrs.  Morrieson,  and  I  think  I  will  call  on  Dr.  Gloag  to 
congratulate  him.  He  has  at  least  three  pupils  gaining 
honours." 

His  friends  in  Edinburgh  were  greatly  pleased. 

*  "Life  of  J.  C.  Maxwell,"  p.  195. 


AND  MODERN  PHYSICS.  37 

"I  get  congratulations  on  all  hands,"  his  father  writes  * 
"  including  Professor  Kelland  and  Sandy  Fraser  and 
all  others  competent,  .  .  .  To-night  or  on  Monday 
I  shall  expect  to  hear  of  the  Smith's  Prizes."  And 
again,  February  6th,  1854  :— "  George  Wedderburn 
came  into  my  room  at  2  a.m.  yesterday  morning, 
having  seen  the  Saturday  Times,  received  by  the 
express  train.  ...  As  you  are  equal  to  the 
Senior  in  the  champion  trial,  you  are  very  little 
behind  him." 

Or  again,  March  5th,  1854:  — 

"Aunt  Jane  stirred  me  up  to  sit  for  my  picture,  as  she 
said  you  wished  for  it  and  were  entitled  to  ask  for  it  qua 
Wrangler.  I  have  had  four  sittings  to  Sir  John  Watson 
Gordon,  and  it  is  now  far  advanced  ;  I  think  it  is  very  like. 
It  is  kitcat  size,  to  be  a  companion  to  Dyce's  picture  of  your 
mother  and  self,  which  Aunt  Jane  says  she  is  to  leave  to  you. 

And  now  the  long  years  of  preparation  were 
nearly  over.  The  cunning  craftsman  was  fitted  with 
his  tools  ;  he  could  set  to  work  to  unlock  the  secrets 
of  Nature  ;  he  was  free  to  employ  his  genius  and  his 
knowledge  on  those  tasks  for  which  he  felt  most 
fitted. 

*  "  Life  of  J.  C.  Maxwell,"  p.  207. 


38  JAMES   CLERK   MAXWELL 


CHAPTER   III. 

EARLY  RESEARCHES. — PROFESSOR  AT  ABERDEEN. 

From  this  time  on  Maxwell's  life  becomes  a  record 
of  his  writings  and  discoveries.  It  will,  however, 
probably  be  clearest  to  separate  as  far  as  possible 
biographical  details  from  a  detailed  account  of  his 
scientific  work,  leaving  this  for  consecutive  treatment 
in  later  chapters,  and  only  alluding  to  it  so  far  as 
may  prove  necessary  to  explain  references  in  his 
letters. 

He  continued  in  Cambridge  till  the  Long  Vacation 
of  1854,  reading  Mill's  "  Logic."  "  I  am  experiencing 
the  effects  of  Mill,"  he  writes,  March  25th,  1854,  "but 
I  take  him  slowly.  I  do  not  think  him  the  last  of 
his  kind.  I  think  more  is  wanted  to  bring  the  con- 
nexion  of  sensation  with  science  to  light,  and  to  show 
what  it  is  not."  He  also  read  Berkeley  on  "  The 
Theory  of  Vision  "  and  "  greatly  admired  it." 

About  the  same  time  he  devised  an  ophthalmo- 
scope.'55' 

"  I  have  made  an  instrument  for  seeing  into  the  eye 
through  the  pupil.  The  difficulty  is  to  throw  the  light  in  at 
that  small  hole  and  look  in  at  the  same  time  ;  but  that 
difficulty  is  overcome,  and  I  can  see  a  large  part  of  the  back 
of  the  eye  quite  distinctly  with  the  image  of  the  candle  on  it. 
People  find  no  inconvenience  in  being  examined,  and  I  have 
got  dogs  to  sit  quite  still  and  keep  their  eyes  steady.  Dogs' 
eyes  are  very  beautiful  behind— a  copper-coloured  ground,  with 

*  "  Life  of  J.  C.  Maxwell,"  p.  208. 


AND   M0DE11N   PHYSICS.  39 

glorious  bright  patches  and   networks  of  blue,  yellow,  and 
green,  with  blood-vessels  great  and  small." 

After  the  vacation  he  returned  to  Cambridge,  and 
the  letters  refer  to  the  colour-top.  Thus  to  Miss  Cay, 
November  24th,  1854,  p.  208  :— 

"  I  have  been  very  busy  of  late  with  various  things,  and 
am  just  beginning  to  make  papers  for  the  examination  at 
Cheltenham,  which  I  have  to  conduct  about  the  11th  of 
December.  I  have  also  to  make  papers  to  polish  off  my  pups, 
with.  I  have  been  spinning  colours  a  great  deal,  and  have  got 
most  accurate  results,  proving  that  ordinary  people's  eyes  are 
all  made  alike,  though  some  are  better  than  others,  and  that 
other  people  see  two  colours  instead  of  three  ;  but  all  those 
who  do  so  agree  amongst  themselves.  I  have  made  a  triangle 
of  colours  by  which  you  may  make  out  everything. 

"  If  you  can  find  out  any  people  in  Edinburgh  who  do  not 
see  colours  (I  know  the  Dicksons  don't),  pray  drop  a  hint  that 
I  would  like  to  see  them.  I  have  put  one  here  up  to  a  dodge 
by  which  he  distinguishes  colours  without  fail.  I  have  also 
constructed  a  pair  of  squinting  spectacles,  and  am  beginning 
operations  on  a  squinting  man." 

A  paper  written  for  his  own  use  originally  some 
time  in  1854,  but  communicated  as  a  parting  gift  to 
his  friend  Farrar,  who  was  about  to  become  a  master 
at  Marlborough,  gives  us  some  insight  into  his  view 
of  life  at  the  age  of  twenty-three. 

"  He  that  would  enjoy  life  and  act  with  freedom  must  have 
the  work  of  the  day  continually  before  his  eyes.  Not  yester- 
day's work,  lest  he  fall  into  despair  ;  nor  to-morrow's,  lest  he 
become  a  visionary — not  that  which  ends  with  the  day,  which 
is  a  worldly  work  ;  nor  yet  that  only  which  remains  to  eternity, 
for  by  it  he  cannot  shape  his  actions. 

"  Happy  is  the  man  who  can  recognise  in  the  work  of 
to-day  a   connected    portion  of   the   work    of   life   and    an 


40  JAMES   CLERK    MAXWELL 

embodiment  of  the  work  of  Eternity.  The  foundations  of 
his  confidence  are  unchangeable,  for  he  has  been  made  a 
partaker  of  Infinity.  He  strenuously  works  out  his  daily 
enterprises  because  the  present  is  given  him  for  a  possession. 

"Thus  ought  Man  to  be  an  impersonation  of  the  divine 
process  of  nature,  and  to  show  forth  the  union  of  the  infinite 
with  the  finite,  not  slighting  his  temporal  existence,  remem- 
bering that  in  it  only  is  individual  action  possible  ;  nor  yet 
shutting  out  from  his  view  that  which  is  eternal,  knowing  that 
Time  is  a  mystery  which  man  cannot  endure  to  contemplate 
until  eternal  Truth  enlighten  it." 

His  father  was  unwell  in  the  Christmas  vacation 
of  that  year,  and  he  could  not  return  to  Cambridge  at 
the  beginning  of  the  Lent  term.  "  My  steps,"  he 
writes*  to  C.  J.  Munro  from  Edinburgh,  February  19th, 
1855,  "will  be  no  more  by  the  reedy  and  crooked 
till  Easter  term.  ...  I  should  like  to  know  how 
many  kept  bacalaurean  weeks  go  to  each  of  these 
terms,  and  when  they  begin  and  end.  Overhaul  the 
Calendar,  and  when  found  make  note  of." 

He  was  back  in  Cambridge  for  the  May  term, 
working  at  the  motion  of  fluids  and  at  his  colour-top. 
A  paper  on  "  Experiments  on  Colour  as  Perceived  by 
the  Eye  "  was  communicated  to  the  Royal  Society  of 
Edinburgh  on  March  19th,  1855.  The  experiments 
were  shown  to  the  Cambridge  Philosophical  Society 
in  May  following,  and  the  results  are  thus  described 
in  two  letters!  to  his  father,  Saturday,  May  5th,  1855  : 

"  The  Eoyal  Society  have  been  very  considerate  in  sending 
me  my  paper  on  'Colours'  just  when  I  wanted  it  for  the 
Philosophical  here.   I  am  to  let  them  see  the  tricks  on  Monday 

*  "  Life  of  J.  C.  Maxwell,"  p.  210. 
f  "Life  of  J.  C.  Maxwell,"  p.  211. 


AND   MODERN   PHYSICS.  41 

evening,  and  I  have  been  there  preparing  their  experiments  in 
the  gaslight.  There  is  to  be  a  meeting  in  my  rooms  to-night 
to  discuss  Adam  Smith's  '  Theory  of  Moral  Sentiments,'  so  I 
must  clear  up  my  litter  presently.  I  am  working  away  at 
electricity  again,  and  have  been  working  my  way  into  the 
views  of  heavy  German  writers.  It  takes  a  long  time  to 
reduce  to  order  all  the  notions  one  gets  from  these  men,  but 
1  hope  to  see  my  way  through  the  subject  and  arrive  at  some- 
thing intelligible  in  the  way  of  a  theory 

"The  colour  trick  came  off  on  Monday,  7th.  I  had  the 
proof-sheets  of  my  paper,  and  was  going  to  read  ;  but  I 
changed  my  mind  and  talked  instead,  which  was  more  to  the 
purpose.  There  were  sundry  men  who  thought  that  blue  and 
yellow  make  green,  so  I  had  to  undeceive  them.  I  have  got 
Hay's  book  of  colours  out  of  the  Univ.  Library,  and  am 
working  through  the  specimens,  matching  them  with  the  top. 
I  have  a  new  trick  of  stretching  the  string  horizontally  above 
the  top,  so  as  to  touch  the  upper  part  of  the  axis.  The  motion 
of  the  axis  sets  the  string  a-vibrating  in  the  same  time  with 
the  revolutions  of  the  top,  and  the  colours  are  seen  in  the  haze 
produced  by  the  vibration.  Thomson  has  been  spinning  the 
top,  and  he  finds  my  diagram  of  colours  agrees  with  his 
experiments,  but  he  doubts  about  browns,  what  is  their 
composition.  I  have  got  colcothar  brown,  and  can  make  white 
with  it,  and  blue  and  green  ;  also,  by  mixing  red  with  a  little 
blue  and  green  and  a  great  deal  of  black,  I  can  match  colcothar 
exactly. 

"I  have  been  perfecting  my  instrument  for  looking  into 
the  eye.  Ware  has  a  little  beast  like  old  Ask,  which  sits  quite 
steady  and  seems  to  like  being  looked  at,  and  I  have  got 
several  men  who  have  large  pupils  and  do  not  wish  to  let  me 
look  in.  I  have  seen  the  image  of  the  candle  distinctly  in  all 
the  eyes  I  have  tried,  and  the  veins  of  the  retina  were  visible 
in  some ;  but  the  dogs'  eyes  showed  all  the  ramifications  of 
veins,  with  glorious  blue  and  green  network,  so  that  you  might 
copy  down  everything.  I  have  shown  lots  of  men  the  image 
in  my  own  eye  by  shutting  off  the  light  till  the  pupil  dilated 
and  then  letting  it  on. 


42  JAMES   CLERK   MAXWELL 

"I  am  reading  Electricity  and  working  at  Fluid  Motion, 
and  have  got  out  the  condition  of  a  fluid  being  able  to  flow 
the  same  way  for  a  length  of  time  and  not  wriggle  about." 

The  British  Association  met  at  Glasgow  in  Sep- 
tember, 1855,  and  Maxwell  was  present,  and  showed 
his  colour-top  at  Professor  Ramsay's  house  to  some  ot 
those  interested.  Letters'*  to  his  father  about  this 
time  describe  some  of  the  events  of  the  meeting  and 
his  own  plans  for  the  term. 

"We  had  a  paper  from  Brewster  on  'The  theory  of  three 
colours  in  the  spectrum,'  in  which  he  treated  Whewell  with 
philosophic  pity,  commending  him  to  the  care  of  Prof.  Wart- 
man  of  Geneva,  who  was  considered  the  greatest  authority  in 
cases  of  his  kind — cases,  in  fact,  of  colour-blindness.  Whewell 
was  in  the  room,  but  went  out  and  avoided  the  quarrel  ;  and 
Stokes  made  a  few  remarks,  stating  the  case  not  only  clearly 
but  courteously.  However,  Brewster  did  not  seem  to  see  that 
Stokes  admitted  his  experiments  to  be  correct,  and  the  news- 
papers represented  Stokes  as  calling  in  question  the  accuracy 
of  the  experiments. 

"  I  am  getting  my  electrical  mathematics  into  shape,  and  I 
see  through  some  parts  which  were  rather  hazy  before  ;  but  I 
do  not  find  very  much  time  for  it  at  present,  because  I  am 
reading  about  heat  and  fluids,  so  as  not  to  tell  lies  in  my 
lectures.  I  got  a  note  from  the  Society  of  Arts  about  the 
platometer,  awarding  thanks  and  offering  to  defray  the  ex- 
penses to  the  extent  of  £10,  on  the  machine  being  produced  in 
working  order.  When  I  have  arranged  it  in  my  head,  I  intend 
to  write  to  James  Bryson  about  it. 

"I  got  a  long  letter  from  Thomson  about  colours  and 
electricity.  He  is  beginning  to  believe  in  my  theory  about  all 
colours  being  capable  of  reference  to  three  standard  ones,  and 
he  is  very  glad  that  I  should  poach  on  his  electrical  preserves. 

"  .     .    .    It  is  difficult  to  keep  up  one's  interest  in  intel- 

*  "Life  of  J.  C.  Maxwell,"  p.  216. 


AND   MODERN   PHYSICS.  43 

lectual  matters  when  friends  of  the  intellectual  kind  are 
scarce.  However,  there  are  plenty  friends  not  intellectual 
who  serve  to  bring  out  the  active  and  practical  habits  of  mind, 
which  overly-intellectual  people  seldom  do.  Wherefore,  if  I 
am  to  be  up  this  term,  I  intend  to  addict  myself  rather  to  the 
working  men  who  are  getting  up  classes  than  to  pups.,  who 
are  in  the  main  a  vexation.  Meanwhile,  there  is  the  examina- 
tion to  consider. 

"  You  say  Dr.  Wilson  has  sent  his  book.  I  will  write  and 
thank  him.  I  suppose  it  is  about  colour-blindness.  I  intend 
to  begin  Poisson's  papers  on  electricity  and  magnetism  to- 
morrow. I  have  got  them  out  of  the  library.  My  reading 
hitherto  has  been  of  novels— 'Shirley '  and  'The  Newcomes,' 
and  now  '  Westward  Ho.' 

"  Macmillan  proposes  to  get  up  a  book  of  optics  with  my 
assistance,  and  I  feel  inclined  for  the  job.  There  is  great 
bother  in  making  a  mathematical  book,  especially  on  a  subject 
with  which  you  are  familiar,  for  in  correcting  it  you  do  as  you 
would  to  pups. — look  if  the  principle  and  result  is  right,  and 
forget  to  look  out  for  small  errors  in  the  course  of  the  work. 
However,  1  expect  the  work  will  be  salutary,  as  involving 
hard  work,  and  in  the  end  much  abuse  from  coaches  and 
students,  and  certainly  no  vain  fame,  except  in  Macmillan's 
puffs.  But,  if  I  havo  rightly  conceived  the  plan  of  an 
educational  book  on  optics,  it  will  be  very  different  in  manner, 
though  not  in  matter,  from  those  now  used." 

The  examination  referred  to  was  that  for  a 
Fellowship  at  Trinity,  and  Maxwell  was  elected  on 
October  10th,  1855. 

He  was  immediately  asked  to  lecture  for  the 
College,  on  hydrostatics  and  optics,  to  the  upper 
division  of  the  third  year,  and  to  set  papers  for  the 
questionists.  In  consequence,  he  declined  to  take 
pupils,  in  order  to  have  time  for  reading  and  doing 
private  mathematics,  and  for  seeing  the  men  who 
attended  his  lectures. 


44  JAMES  CLERK  MAXWELL 

In  November  he  writes :  "  I  have  been  lecturing 
two  weeks  now,  and  the  class  seems  improving  ;  and 
they  come  and  ask  questions,  which  is  a  good  sign. 
I  have  been  making  curves  to  show  the  relations  of 
pressure  and  volume  in  gases,  and  they  make  the 
subject  easier." 

Still,  he  found  time  to  attend  Professor  Willis's 
lectures  on  mechanism  and  to  continue  his  reading. 
'•  I  have  been  reading,"  he  writes,  "  old  books  on 
optics,  and  find  many  things  in  them  far  better  than 
what  is  new.  The  foreign  mathematicians  are  dis- 
covering for  themselves  methods  which  were  well 
known  at  Cambridge  in  1720,  but  are  now  forgotten." 

The  "  Poisson "  was  read  to  help  him  with  his 
own  views  on  electricity,  which  were  rapidly  maturing, 
and  the  first  of  that  great  series  of  works  which  has 
revolutionised  the  science  was  published  on  December 
10th,  1855,  when  his  paper  on  "  Faraday's  Lines  of 
Force "  was  read  to  the  Cambridge  Philosophical 
Society. 

The  next  term  found  him  back  in  Cambridge  at 
work  on  his  lectures,  full  of  plans  for  a  new  colour 
top  and  other  matters.  Early  in  February  he  received 
a  letter  from  Professor  Forbes,  telling  him  that  the 
Professorship  of  Natural  Philosophy  in  Marischal 
College,  Aberdeen,  was  vacant,  and  suggesting  that 
he  should  apply. 

He  decided  to  be  a  candidate  if  his  father 
approved.  "  For  my  own  part,"  he  writes,  "  I  think 
the  sooner  I  get  into  regular  work  the  better,  and 
that  the  best  way  of  getting  into  such  work  is  to 
profess  one's  readiness  by  applying  for  it."     On  the 


AND   MODERN   PHYSICS.  45 

20th  of  February  he  writes :  "  However,  wisdom  is  of 
many  kinds,  and  I  do  not  know  which  dwells  with 
wise  counsellors  most,  whether  scientific,  practical 
political,  or  ecclesiastical.  I  hear  there  are  candidates 
of  all  kinds  relying  on  the  predominance  of  one  or 
other  of  these  kinds  of  wisdom  in  the  constitution  ot 
the  Government." 

The  second  part  of  the  paper  on  "  Faraday's  Lines 
of  Force  "  was  read  during  the  term.  Writing  on  the 
4th  of  March,  he  expresses  the  hope  soon  to  be  able 
to  write  out  fully  the  paper.  "  I  have  done  nothing 
in  that  way  this  term,"  he  says,  "  but  am  just  begin- 
ning to  feel  the  electrical  state  come  on  again." 

His  father  was  working  at  Edinburgh  in  support 
of  his  candidature  for  Aberdeen,  and  when,  in  the 
middle  of  March,  he  returned  North,  he  found  every- 
thing well  prepared.  The  two  returned  to  Glenlair 
together  after  a  few  days  in  Edinburgh,  and  Maxwell 
was  preparing  to  go  back  to  Cambridge,  when,  on  the 
2nd  of  April,  his  father  died  suddenly. 

Writing  to  Mrs.  Blackburn,  he  says  :  "  My  father 
died  suddenly  to-day  at  twelve  o'clock.  He  had  been 
giving  directions  about  the  garden,  and  he  said  he 
would  sit  down  and  rest  a  little,  as  usual.  After  a 
few  minutes  I  asked  him  to  lie  down  on  the  sofa,  and 
he  did  not  seem  inclined  to  do  so ;  and  then  I  got 
him  some  ether,  which  had  helped  him  before. 
Before  he  could  take  any  he  had  a  slight  struggle, 
and  all  was  over.     He  hardly  breathed  afterwards." 

Almost  immediately  after  this,  Maxwell  was 
appointed  to  Aberdeen.  His  father's  death  had 
frustrated  some  at  least  of  the  intentions  with  which 


46  JAMES   CLERK    MAXWELL 

he  had  applied  for  the  post.  He  knew  the  old  man 
would  be  glad  to  see  him  the  occupant  of  a  Scotch 
chair.  He  hoped,  too,  to  be  able  to  live  with  his 
father  at  Glenlair  for  one  half  the  year ;  but  this  was 
not  to  be.  No  doubt  the  laboratory  and  the  freedom 
of  the  post,  when  compared  Avith  the  routine  work 
of  preparing  men  for  the  Tripos,  had  their  induce- 
ments ;  still,  it  may  bo  doubted  if  the  choice  was 
a  wise  one  for  him.  The  work  of  drilling  classes, 
composed,  for  the  most  part,  of  raw  untrained  lads, 
in  the  elements  of  physics  and  mechanics  was,  as 
Niven  says  in  his  preface  to  the  collected  works,  not 
that  for  which  he  was  best  fitted;  while  at  Cambridge, 
had  he  stayed,  he  must  always  have  had  among  his 
pupils  some  of  the  best  mathematicians  of  the  time ; 
and  he  might  have  founded  some  ten  or  fifteen  years 
before  he  did  that  Cambridge  School  of  Physicists 
which  looks  back  with  so  much  pride  to  him  as  their 
master. 

Leave-taking    at    Trinity   was   a    sad    task.     He 
writes  *  thus,  June  4th,  to  Mr.  R.  B.  Litchfield : — 

"  On  Thursday  evening  I  take  the  North-Western  route  to 
the  North.  I  am  busy  looking  over  immense  rubbish  of 
papers,  etc.,  for  some  things  not  to  be  burnt  lie  among  much 
combustible  matter,  and  some  is  soft  and  good  for  packing. 

"  It  is  not  pleasant  to  go  down  to  live  solitary,  but  it  would 

not  be  pleasant  to  stay  up  either,  when  all  one  had  to  do  lay 

elsewhere.     The  transition  state  from  a  man  into  a  Don  must 

come  at  last,  and  it  must  be  painful,  like  gradual  outrootingof 

nerves.     When  it  is  done  there  is  no  more  pain,  but  occasional 

reminders  from  some  suckers,  tap-roots,  or  other  remnants  of 

the  old  nerves,  just  to  show  what  was  there  and  what  might 

have  been." 

*  "  Life  of  J.  C.  Maxwell,"  p.  256, 


AND   MODERN   FHYSICS.  47 

The  summer  of  1856  was  spent  at  Glenlair, 
where  various  friends  were  his  guests — Lushington, 
MacLennan,  the  two  cousins  Cay,  and  others.  He 
continued  to  work  at  optics,  electricity,  and  magnetism, 
and  in  October  was  busy  with  "  a  solemn  address  or 
manifesto  to  the  Natural  Philosophers  of  the  North, 
which  needed  coffee  and  anchovies  and  a  roaring  hot 
fire  and  spread  coat-tails  to  make  it  natural."  This 
was  his  inaugural  lecture. 

In  November  he  was  at  Aberdeen.  Letters*  to 
Miss  Cay,  Professor  Campbell,  and  C.  J.  Munro  tell 
of  the  work  of  the  session.  The  last  is  from  Glenlair, 
dated  May  20th,  1S57,  after  work  was  over. 

"  The  session  went  off  smoothly  enough.  I  had  Sun,  all 
the  beginning  of  optics,  and  worked  off  all  the  experimental 
part  up  to  Fraunhofer's  lines,  which  were  glorious  to  see  with 
a  water-prism  I  have  set  up  in  the  form  of  a  cubical  box,  five 
inch  side.    .     .     . 

"I  succeeded  very  well  with  heat.  The  experiments  on 
latent  heat  came  out  very  accurate.  That  was  my  part,  and 
the  class  could  explain  and  work  out  the  results  better  than  I 
expected.  Next  year  I  intend  to  mix  experimental  physics  with 
mechanics,  devoting  Tuesday  and  THURSDAY  (what  would 
Stokes  say  1)  to  the  science  of  experimenting  accurately.    .    .   . 

"  Last  week  I  brewed  chlorophyll  (as  the  chemists  word  it), 
a  green  liquor,  which  turns  the  invisible  light  red.     .     .     . 

"  My  last  grind  was  the  reduction  of  equations  of  colour 
which  I  made  last  year.  The  result  was  eminently  satis- 
factory." 

Another  letter,t  June  5th,  1857,  also  to  Munro, 
refers  to  the  work  of  the  University  Commission  and 
the  new  statutes. 

*  "  Life  of  J.  C.  Maxwell,"  p.  267. 
t  "Life  of  J.  C.  Maxwell,"  p.  269. 


48  JAMES   CLERK   MAXWELL 

"  I  have  not  seen  Article  7,  but  I  agree  with  your  dissent 
from  it  entirely.  On  the  vested  interest  principle,  I  think  the 
men  who  intended  to  keep  their  fellowships  by  celibacy  and 
ordination,  and  got  them  on  that  footing,  should  not  be 
allowed  to  desert  the  virgin  choir  or  neglect  the  priestly 
office,  but  on  those  principles  should  be  allowed  to  live  out 
their  days,  provided  the  whole  amount  of  souls  cured  annually 
does  not  amount  to  £20  in  the  King's  Book.  But  my  doctrine 
is  that  the  various  grades  of  College  officers  should  be  set  on 
such  a  basis  that,  although  chance  lecturers  might  be  some- 
times chosen  from  among  fresh  fellows  who  are  going  away 
soon,  the  reliable  assistant  tutors,  and  those  that  have  a  plain 
calling  that  way,  should,  after  a  few  years,  be  elected  permanent 
officers  of  the  College,  and  be  tutors  and  deans  in  their  time, 
and  seniors  also,  with  leave  to  marry,  or,  rather,  never  pro- 
hibited or  asked  any  questions  on  that  head,  and  with  leave  to 
retire  after  so  many  years'  service  as  seniors.  As  for  the  men 
of  the  world,  we  should  have  a  limited  term  of  existence,  and 
that  independent  of  marriage  or  '  parsonage.' " 

It  was  more  than  twenty  years  before  the  scheme 
outlined  in  the  above  letter  came  to  anything ;  but, 
at  the  time  of  Maxwell's  death  in  1879,  another 
Commission  was  sitting,  and  the  plan  suggested  by 
Maxwell  became  the  basis  of  the  statutes  of  nearly 
all  the  colleges. 

For  the  winter  session  of  1857-58  he  was  again 
at  Aberdeen. 

The  Adams  Prize  had  been  established  in  18-18  by 
some  members  of  St.  John's  College,  and  connected 
by  them  with  the  name  of  Adams  "  in  testimony  of 
their  sense  of  the  honour  he  had  conferred  upon  his 
College  and  the  University  by  having  been  the  first 
among  the  mathematicians  of  Europe  to  determine 
from  perturbations  the  unknown  place  of  a  disturbing 


ANt)   MODERN   PHYSICS.  49 

planet  exterior  to  Uranus."  Professor  Cliallis,  Dr. 
Parkinson,  and  Sir  William  Thomson,  the  examiners, 
had  selected  as  the  subject  for  the  prize  to  be  awarded 
in  1857  the  "Motions  of  Saturn's  Rings."  For  this 
Maxwell  had  decided  to  compete,  and  his  letters  at 
the  end  of  1857  tell  of  the  progress  of  the  task. 
Thus,  writing*  to  Lewis  Campbell  from  Glenlair  on 
August  28th,  he  says  : — 

"  I  have  been  battering  away  at  Saturn,  returning  to  the 
charge  every  now  and  then.  I  have  effected  several  breaches 
in  the  solid  ring,  and  now  I  am  splash  into  the  fluid  one,  amid 
a  clash  of  symbols  truly  astounding.  When  I  reappear  it  will 
be  in  the  dusky  ring,  which  is  something  like  the  state  of  the 
air  supposing  the  siege  of  Sebastopol  conducted  from  a  forest 
of  guns  100  miles  one  way,  and  30,000  miles  the  other,  and  the 
shot  never  to  srop,  but  go  spinning  away  round  a  circle,  radius 
170,000  miles." 

And  again  t  to  Miss  Cay  on  the  28th  of  November  :— 

"  1  have  been  pretty  steady  at  work  since  I  came.  The 
class  is  small  and  not  bright,  but  I  am  going  to  give  them 
plenty  to  do  from  the  first,  and  I  find  it  a  good  plan.  I  have 
a  large  attendance  of  my  old  pupils,  who  go  on  with  the  higher 
subjects.  This  is  not  part  of  the  College  course,  so  they  come 
merely  from  choice,  and  I  have  begun  with  the  least  amusing 
part  of  what  I  intend  to  give  them.  Many  had  been  reading 
in  summer,  for  they  did  very  good  papers  for  me  on  the  old 
subjects  at  the  beginning  of  the  month.  Most  of  my  spare 
time  I  have  been  doing  Saturn's  rings,  which  is  getting  on 
now,  but  lately  I  have  had  a  great  many  long  letters  to  write 
— some  to  Glenlair,  some  to  private  friends,  and  some  all  about 
science.  ...  I  have  had  letters  from  Thomson  and  Challis 
about  Saturn — from  Hayward,  of  Durham  University,  about 

*  "  Life  of  J.  C.  Maxwell,"  p.  278. 
t  "  Life  of  J.  C.  Maxwell,"  p.  292. 


50  JAMES   CLERK   MAXWELL 

the  brass  top,  of  which  he  wants  one.  He  says  that  the  earth 
has  been  really  found  to  change  its  axis  regularly  in  the  way 
I  supposed.  Faraday  has  also  been  writing  about  his  own 
subjects.  I  have  had  also  to  write  Forbes  a  long  report  on 
colours  ;  so  that  for  every  note  I  Lave  got  I  have  had  to  write 
a  couple  of  sheets  in  reply,  and  reporting  progress  takes  a  deal 
of  writing  and  spelling. 

He  devised  a  model  (now  at  the  Cavendish 
Laboratory)  to  exhibit  the  motions  of  the  satellites 
in  a  disturbed  ring,  "  for  the  edification  of  sensible 
image- worshippers." 

The  essay  was  awarded  the  prize,  and  secured  for 
its  author  great  credit  among  scientific  men. 

In  another  letter,  written  during  the  same  session, 
he  says :  "  I  find  my  principal  work  here  is  teaching 
my  men  to  avoid  vague  expressions,  as  '  a  certain 
force,'  meaning  uncertain ;  may  instead  of  must ; 
will  be  instead  of  is  ;  proportional  instead  of  equal." 

The  death,  during  the  autumn,  of  his  College 
friend  Pomeroy,  from  fever  in  India,  was  a  great  blow 
to  him ;  his  letters  at  the  time  show  the  depth  of  his 
feelings  and  his  beliefs. 

The  question  of  the  fusion  of  the  twro  Colleges  at 
Aberdeen,  King's  College  and  the  Marischal  College, 
was  coming  to  the  fore.  "  Know  all  men,"  he  says, 
in  a  letter  to  Professor  Campbell,  "  that  I  am  a 
Fusionist." 

In  February,  1858,  he  was  still  engaged  on  Saturn's 
rings,  while  hard  at  work  during  the  same  time  with 
his  classes.  He  had  established  a  voluntary  class  for 
his  students  of  the  previous  year,  and  was  reading 
with  them  Newton's  "  Lunar  Theory  and  Astronomy." 
This  was  followed   by  "Electricity  and  Magnetism," 


AND  MODERN   PHYSICS.  51 

Faraday's  book  being  the  backbone  of  everything,  "  as 
he  himself  is  the  nucleus  of  everything  electric 
since  1830." 

In  February,  1858,  he  announced  his  engagement 
to  Katherine  Mary  Dewar,  the  daughter  of  the 
Principal  of  Marischal  College. 

"Dear  Aunt"  (he  says,*  February  18th,  1858),  "this  comes 
to  tell  you  that  I  am  going  to  have  a  wife.     .    .     . 

"  Don't  be  afraid ;  she  is  not  mathematical,  but  there  are 
other  things  besides  that,  and  she  certainly  won't  stop  mathe- 
matics. The  only  one  that  can  speak  as  an  eye-witness  is 
Johnnie,  and  he  only  saw  her  when  we  were  both  trying  to  act 
the  indifferent.  We  have  been  trying  it  since,  but  it  would 
not  do,  and  it  was  not  good  for  either." 

The  wedding  took  place  early  in  June.  Professor 
Campbell  has  preserved  some  of  the  letters  written 
by  Maxwell  to  Miss  Dewar,  and  these  contain  "  the 
record  of  feelings  which  in  the  years  that  followed 
were  transfused  in  action  and  embodied  in  a  married 
life  which  can  only  be  spoken  of  as  one  of  unexampled 
devotion." 

The  project  for  the  fusion  of  the  two  Colleges, 
to  which  reference  has  been  made,  went  on,  and  the 
scheme  was  completed  in  1860. 

The  two  Colleges  were  united  to  form  the  Uni- 
versity  of  Aberdeen,  and  the  new  chair  of  Natural 
Philosophy  thus  created  was  filled  by  the  appointment 
of  David  Thomson,  Professor  of  Natural  Philosophy 
in  King's  College,  and  Maxwell's  senior.  Mr.  W.  D. 
Niven,  in  his  preface  to  Maxwell's  works,  when 
dealing  with  this  appointment,  writes  : — 

*  "  Life  of  J.  C.  Maxwell,"  p.  303. 
D  2 


52  JAMES   CLERK   MAXWELL 

"  Professor  Thomson,  though  not  comparable  to  Maxwell 
as  a  physicist,  was  nevertheless  a  remarkable  man.  He  was 
distinguished  by  singular  force  of  character  and  great  ad- 
ministrative faculty,  and  he  had  been  prominent  in  bringing 
about  the  fusion  of  the  Colleges.  He  was  also  an  admirable 
lecturer  and  teacher,  and  had  done  much  to  raise  the  standard 
of  scientific  education  in  the  north  of  Scotland.  Thus  the 
choice  made  by  the  Commissioners,  though  almost  inevitable, 
had  the  effect  of  making  it  appear  that  Maxwell  failed  as  a 
teacher.  There  seems,  however,  to  be  no  evidence  to  support 
such  an  inference.  On  the  contrary,  if  we  may  judge  from  the 
number  of  voluntary  students  attending  his  classes  in  his  last 
College  session,  he  would  seem  to  have  been  as  popular  as  a 
professor  as  he  was  personally  estimable." 

The  question  whether  Maxwell  was  a  great  teacher 
has  sometimes  been  discussed.  I  trust  that  the 
following  pages  will  give  an  answer  to  it.  He  was 
not  a  prominent  lecturer.  As  Professor  Campbell 
says,*  "  Between  his  students'  ignorance  and  his  vast 
knowledge  it  was  difficult  to  find  a  common  measure. 
The  advice  which  he  once  gave  to  a  friend  whose 
duty  it  was  to  preach  to  a  country  congregation, 
'  Why  don't  you  give  it  them  thinner  ? '  must  often 
have  been  applicable  to  himself.  .  .  .  Illustra- 
tions of  ignotum  per  ignotius,  or  of  the  abstruse 
by  some  unobserved  property  of  the  familiar, 
Avere  multiplied  with  dazzling  rapidity.  Then  the 
spirit  of  indirectness  and  paradox,  though  he  was 
aware  of  its  dangers,  would  often  take  possession  of 
him  against  his  will,  and,  either  from  shyness  or 
momentary  excitement,  or  the  despair  of  making 
himself    understood,   would    land    him    in   '  chaotic 

*  "  Life  of  J.  C.  Maxwell,"  p.  259. 


AND   MODERN   PHYSICS.  53 

statements,'  breaking  off  with  some  quirk  of  ironical 
humour." 

But  teaching  is  not  all  done  by  lecturing.  His 
books  and  papers  are  vast  storehouses  of  suggestions 
and  ideas  which  the  ablest  minds  of  the  past  twenty 
years  have  been  since  developing.  To  talk  with  him 
for  an  hour  was  to  gain  inspiration  for  a  year's  work  ; 
to  see  his  enthusiasm  and  to  win  his  praise  or 
commendation  were  enough  to  compensate  for  many 
weary  struggles  over  some  stubborn  piece  of  apparatus 
which  would  not  &o  right,  or  some  small  source  of 
error  which  threatened  to  prove  intractable  and 
declined  to  submit  itself  to  calculation.  The  sure 
judgment  of  posterity  will  confirm  the  verdict  that 
Clerk  Maxwell  was  a  great  teacher,  though  lecturing 
to  a  crowd  of  untrained  undergraduates  was  a  task 
for  which  others  were  better  fitted  than  he. 


54  .TAMES    CLERK    MAXWELL 


CHAPTER    IV 


* 


PROFESSOB    AT    KINGS   COLLEGE,   LONDON. — LIFE 

AT   GLENLAIi:. 

In    1860    Forbes     resigned     the    chair    of    Natural 

Philosophy  at  Edinburgh.  Maxwell  and  Tait  were 
candidates,  and  Tait  was  appointed.  In  the  summer 
of  the  same  year  Maxwell  obtained  the  vacant 
Professorship  of  Natural  Philosophy  at  King's  College. 
London.  This  he  held  to  1865,  and  this  period  of 
his  life  is  distinguished  1  »y  the  appearance  of  some  of 
his  most  important  papers.  The  work  was  arduous ; 
the  College  course  extended  over  nine  months  of  the 
year ;  there  were  as  well  evening  lectures  to  artisans 
as  part  of  his  regular  duties.  His  life  in  London  was 
useful  to  him  in  the  opportunities  it  gave  him  for 
becoming  personally  acquainted  with  Faraday  and 
others.  He  also  renewed  his  intimacy  with  various 
Cambridge  friends. 

He  was  at  the  celebrated  Oxford  meeting  of  the 
British  Association  in  I860,  where  he  exhibited  his 
colour-box  for  mixing  the  colours  of  the  spectrum. 
In  1859,  at  the  meeting  at  Aberdeen,  he  had  read  to 
Section  A  his  first  paper  on  the  "Dynamical  Theory 
of  Gases,"  published  in  the  Philosophical  Magazine 
for  January,  1860.  The  second  part  of  the  paper, 
dealing  with  the  conduction  of  heat  and  other 
phenomena  in  a  gas,  was  published  in  July,  I860, 
after  the  Oxford  meeting. 

A  paper  on  the  "  Theory  of  Compound  Colours " 


AND   MODERN    PHYSICS.  55 

was  communicated  to  tho  Royal  Society  by  Professor 
Stokes  in  January,  I860.  It  contains  the  account  of 
his  colour-box  in  the  form  finally  adopted  (most  of 
the  important  parts  of  the  apparatus  are  still  at  the 
Cavendish  Laboratory),  and  a  number  of  observations 
by  Mrs.  Maxwell  and  himself,  which  will  be  more 
fully  described  later. 

In  November,  1 860,  he  received  for  this  work  the 
Rumford  medal  of  the  Royal  Society. 

The  next  year,  1861,  is  of  great  importance  in  the 
history  of  electrical  science.  The  British  Association 
met  at  Manchester,  and  a  Committee  was  appointed 
on  Standards  of  Electrical  Resistance.  Maxwell  was 
not  a  member.  The  committee  reported  at  the 
Cambridge  meeting  in  1862,  and  were  reappointed 
with  extended  duties.  Maxwell's  name,  among 
others,  was  added,  and  he  took  a  prominent  part  in 
the  deliberations  of  the  committee,  which,  as  their 
Report*  presented  in  1863  states,  came  to  the 
opinion,  "  after  mature  consideration,  that  the  sys- 
tem of  so-called  absolute  electrical  units,  based  on 
purely  mechanical  measurements,  is  not  only  the  best 
system  yet  proposed,  but  is  the  only  one  consistent 
with  our  present  knowledge  both  of  the  relations 
existing  between  the  various  electrical  phenomena  and 
of  the  connection  between  these  and  the  fundamental 
measurements  of  time,  space,  and  mass." 

Appendix  C  of  this  Report,  "  On  the  Elementary 

Relations  between  Electrical  Measurements,"  bears  the 

names  of  Clerk  Maxwell  and  Eleeming  Jenkin,  and  is 

the  foundation  of  everything  that  has  been  done  in 

*  B.A.  Report,  Newcastle,  1863. 


56  JAMES   CLERK   MAXWELL 

the  way  of  absolute  electrical  measurement  since  that 
date ;  while  Appendix  D  gives  an  account  by  the 
same  two  workers  of  the  ex}3eriments  on  the  absolute 
unit  of  electrical  resistance  made  in  the  laboratory  of 
King's  College  by  Maxwell,  Fleeming  Jenkin,  and 
Balfour  Stewart.  Further  experiments  are  described 
in  the  report  for  1864  The  work  thus  begun  was 
consummated  during  the  year  1894  by  the  legalisation 
throughout  the  civilised  world  of  a  system  of  electrical 
units  based  on  those  described  in  these  reports. 

Meanwhile,  Maxwell's  views  on  electro-magnetic 
theory  were  quietly  developing.  Papers  on  "  Physical 
Lines  of  Force,"  which  appeared  in  the  Philosophical 
Magazine  during  1861  and  1862,  contain  the  germs 
of  his  theory — expressed  at  that  time,  it  is  true,  in  a 
somewhat  material  form.  In  the  paper  published 
January,  1862,  the  now  well-known  relation  between 
the  ratio  of  the  electric  units  and  the  velocity  of  light 
was  established,  and  his  correspondence  Avith  Fleeming 
Jenkin  and  C.  J.  Munro  about  this  time  relates  in 
part  to  the  experimental  verification  of  this  relation. 
His  experiments  on  this  matter  were  published  in  the 
"  Philosophical  Transactions  "  for  1868. 

This  electrical  theory  occupied  his  mind  mainly 
during  1863  and  1864.  In  September  of  the  latter 
year  he  writes  *  from  Glenlair  to  C.  Hockin,  who  had 
taken  Balfour  Stewart's  place  during  the  second  series 
of  experiments  on  the  measurement  of  resistance. 

"  I  have  been  doing  several  electrical  problems.  I  have  got 
a  theory  of  '  electric  absorption,'  i.e.,  residual  charge,  etc.,  and 
I  very  much  want   determinations  of  the  specific  induction, 

*  "  Life  of  J.  C.  Maxwell,"  p.  340. 


AND   MODERN    PHYSICS.  57 

electric  resistance,  and  absorption  of  good  dielectrics,  such  as 
glass,  shell-lac,  gutta-percha,  ebonite,  sulphur,  etc. 

"I  have  also  cleared  the  electromagnetic  theory  of  light 
from  all  unwarrantable  assumption,  so  that  we  may  safely 
determine  the  velocity  of  light  by  measuring  the  attraction 
between  bodies  kept  at  a  given  difference  of  potential,  tho 
value  of  which  is  known  in  electromagnetic  measure. 

"  I  hope  there  will  be  resistance  coils  at  the  British  Associa- 
tion." 

This  work  resulted  in  his  greatest  electrical  paper, 
"  A  Dynamical  Theory  of  the  Electromagnetic  Field," 
read  to  the  Royal  Society  December  8th,  1864 

But  the  molecular  theory  of  gases  was  still 
prominently  before  his  mind. 

In  1862,  writing*  to  H.  R.  Droop,  he  says  :— 

"Some  time  ago,  when  investigating  Bernoulli's  theory 
of  gases,  I  was  surprised  to  find  that  the  internal  friction  of 
a  gas  (if  it  depends  on  the  collision  of  particles)  should  be 
independent  of  the  density. 

"Stokes  has  been  examining  Graham's  experiments  on  the 
rate  of  flow  of  gases  through  fine  tubes,  and  he  finds  that  the 
friction,  if  independent  of  density,  accounts  for  Graham's 
results  ;  but,  if  taken  proportional  to  density,  differs  from 
those  results  very  much.  This  seems  rather  a  curious  result, 
and  an  additional  phenomenon,  explained  by  the  '  collision  of 
particles  '  theory  of  gases.  Still  one  phenomenon  goes  against 
that  theory—  the  relation  between  specific  heat  at  constant 
pressure  and  at  constant  volume,  which  is  in  air  =  l-408, 
while  it  ought  to  be  T333." 

And   again  f   in  the  same  year,  21st  April,  1862,  to 
Lewis  Campbell : — 

"  Herr  Clausius  of  Zurich,  one  of  the  heat  philosophers,  has 
been  working  at  the  theory  of  gases  being  little  bodies  flying 

*  "  Life  of  J.  C.  Maxwell,"  p.  332. 
t  "  Life  of  J.  C.  Maxwell,"  p.  336, 


58  JAMES   CLERK   MAXWELL 

about,  and  Las  found  some  cases  in  which  he  and  I  don't  tally. 
So  I  am  working  it  out  again.  Several  experimental  results 
have  turned  up  lately  rather  confirmatory  than  otherwise  of 
that  theory. 

"  I  hope  you  enjoy  the  absence  of  pupils.  I  find  the  division 
of  them  into  smaller  classes  is  a  great  help  to  me  and  to  them  ; 
but  the  total  oblivion  of  them  for  definite  intervals  is  a 
necessary  condition  for  doing  them  justice  at  the  proper  time." 

The  experiments  on  the  viscosity  of  gases,  which 
formed  the  Bakerian  Lecture  to  the  Royal  Society 
read  on  February  8th,  18G6,  were  the  outcome  of  this 
work.  His  house  in  8,  Palace  Gardens,  Kensington, 
contained  a  large  garret  running  the  complete  length. 

'■  To  maintain  the  proper  temperature  a  large  fire 
was  for  some  days  kept  up  in  the  room  in  the  midst 
of  very  hot  weather.  Kettles  were  kept  on  the  fire  and 
large  quantities  of  steam  allowed  to  flow  into  the 
room.  Mrs.  Maxwell  acted  as  stoker,  which  was  very 
exhausting  work  when  maintained  for  several  consecu- 
tive hours.  After  this  the  room  was  kept  cool  for 
subsequent  experiments  by  the  employment  of  a 
considerable  amount  of  ice." 

Next  year,  May,  1866,  was  read  his  paper  on  the 
"  Dynamical  Theory  of  Gases,"  in  which  errors  in  his 
former  papers,  which  had  been  pointed  out  by 
( 'lausius,  were  corrected. 

Meanwhile  he  had  resigned  his  London  Professor- 
ship at  the  end  of  the  Session  of  1865,  and  had  been 
succeeded  by  Professor  W.  G.  Adams. 

For  the  next  four  years  he  lived  chiefly  at  Glenlair, 
working  at  his  theory  of  electricity,  occasionally,  as 
we  shall   see,  visiting   London   and   Cambridge,  and 


AND   MODERN   PHYSICS.  59 

takiuof  an  active  interest  in  the  affairs  of  his  own 
neighbourhood.  In  1865  he  had  a  serious  illness, 
through  which  he  was  nursed  with  great  care  by  Mrs. 
Maxwell.  His  correspondence  was  considerable,  and 
absorbed  much  of  his  time.  Much  also  was  given  to 
the  study  of  English  literature ;  he  was  fond  of 
reading  Chaucer,  Milton,  or  Shakespeare  aloud  to 
Mrs.  Maxwell. 

He  also  read  much  theological  and  philosophical 
literature,  and  all  he  read  helped  only  to  strengthen 
that  firm  faith  in  the  fundamentals  of  Christianity  in 
which  he  lived  and  died. 

In  1867  he  and  Mrs.  Maxwell  paid  a  visit  to  Italy, 
which  was  a  source  of  great  pleasure  to  both. 

His  chief  scientific  work  was  the  preparation  of 
his  "  Electricity  and  Magnetism,"  which  did  not 
appear  till  1873 ;  the  time  was  in  the  main  one  of 
quiet  thought  and  preparation  for  his  next  great  task, 
the  foundation  of  the  School  of  Physics  in  Cambridge. 

In  1868  the  principalship  of  the  United  College 
in  the  University  of  St.  Andrews  was  vacant  by  the 
resignation  of  Forbes,  and  Maxwell  was  invited  by 
several  of  the  professors  to  stand.  He,  however, 
declined  to  submit  his  name  to  the  Crown. 


60  JAMES   CLERK    MAXWELL 


CHAPTER    V. 

CAMBRIDGE. — PROFESSOR   OF    PHYSICS. 

During  his  retirement  at  Glenlair  from  1865  to  1870 
Maxwell  was  frequently  at  Cambridge.  He  examined 
in  the  Mathematical  Tripos  in  1866  and  1867,  and 
again  in  1869  and  1870. 

The  regulations  for  the  Tripos  had  been  in  force 
practically  unchanged  since  1848,  and  it  was  felt  by 
many  that  the  range  of  subjects  included  was  not 
sufficiently  extensive,  and  that  changes  were  urgently 
needed  if  Cambridge  were  to  retain  its  position  as  the 
centre  of  mathematical  teaching.  Natural  Philosophy 
was  mentioned  in  the  Schedule,  but  Natural  Philosophy 
included  only  Dynamics  and  Astronomy,  Hydrostatics 
and  Physical  Optics,  with  some  simple  Hydrodynamics 
and  Sound. 

The  subjects  of  Heat,  Electricity  and  Magnetism, 
the  Theory  of  Elastic  Solids  and  Vibrations,  Yortex- 
Motion  in  Hydrodynamics,  and  much  else,  were 
practically  new  since  1848.  Stokes,  Thomson,  and 
Maxwell  in  England,  and  Helmholtz  in  German}',  had 
created  them. 

Accordingly  in  June,  1868,  a  new  plan  of  examina- 
tions was  sanctioned  by  the  Senate  to  come  into 
force  in  January,  1873,  and  these  various  subjects 
were  explicitly  included. 

Mr.  Niven,  who  was  one  of  those  examined  by 
Maxwell  in  1866,  writes  in  the  preface  to  the  collected 
works  :— 


AND   MODERN   PHYSICS.  61 

"For  some  years  previous  to  I860,  when  Maxwell  returned 
to  Cambridge  as  Moderator  in  the  Mathematical  Tripos,  the 
studies  in  the  University  had  lost  touch  with  the  great 
scientific  movements  going  on  outside  her  walls.  It  was  said 
that  some  of  the  subjects  most  in  vogue  had  but  little  interest 
for  the  present  generation,  and  loud  complaints  began  to  be 
heard  that  while  such  branches  of  knowledge  as  Heat,  Electri- 
city, and  Magnetism  were  left  out  of  the  Tripos  examination, 
the  candidates  were  wasting  their  time  and  energy  upon 
mathematical  trifles  barren  of  scientific  interest  and  of 
practical  results.  Into  the  movement  for  reform  Maxwell 
entered  warmly.  By  his  questions  in  18GG,  and  subsequent 
years,  he  infused  new  life  into  the  examination ;  he  took  an 
active  part  in  drafting  the  new  scheme  introduced  in  1873  ; 
but  most  of  all  by  his  writings  he  exerted  a  powerful  influence 
on  the  younger  members  of  the  University,  and  was  largely 
instrumental  in  bringing  about  the  change  which  has  been 
now  effected." 

But  the  University  possessed  no  means  of  teaching 
these  subjects,  and  a  Syndicate  or  Committee  was 
appointed,  November  25th,  1868,  "  to  consider  the 
best  means  of  giving  instruction  to  students  in 
Physics,  especially  in  Heat,  Electricity  and  Mag- 
netism, and  the  methods  of  providing  apparatus  for 
this  purpose." 

Dr.  Cookson,  Master  of  St.  Peter's  College,  took  an 
active  part  in  the  work  of  the  Syndicate.  Professor 
Stokes,  Professor  Liveing,  Professor  Humphry,  Dr. 
Phear,  and  Dr.  Routh  were  among  the  members. 
Maxwell  himself  was  in  Cambridge  that  winter,  as 
Examiner  for  the  Tripos,  and  his  work  as  Moderator 
and  Examiner  in  the  two  previous  years  had  done 
much  to  show  the  necessity  of  alterations  and  to 
indicate  the  direction  which  changes  should  take. 


62  JAMES   CLERK   MAXWELL 

The  Syndicate  reported  February  27th,  1869.  They 
called  attention  to  the  Report  of  the  Royal  Commis- 
sion of  1850.  The  Commissioners  had  "  prominently 
urged  the  importance  of  cultivating  a  knowledge  of 
the  great  branches  of  Experimental  Physics  in  the 
University";  and  in  page  118  of  their  Report,  after 
commending  the  manner  in  which  the  subject  of 
Physical  Optics  is  studied  in  the  University,  and 
pointing  out  that  "  there  is,  perhaps,  no  public  institu- 
tion where  it  is  better  represented  or  prosecuted  with 
more  zeal  and  success  in  the  way  of  original  research," 
they  had  stated  that  "  no  reason  can  be  assigned  why 
other  great  branches  of  Natural  Science  should  not 
become  equally  objects  of  attention,  or  why  Cambric! o-e 
should  not  become  a  great  school  of  physical  and 
experimental,  as  it  is  already  of  mathematical  and 
classical,  instruction." 

And  again  the  Commissioners  remark:  "In  a 
University  so  thoroughly  imbued  Avitli  the  mathe- 
matical spirit,  physical  study  might  be  expected  to 
assume  within  its  precincts  its  highest  and  severest 
tone,  be  studied  under  more  abstract  forms,  with 
more  continual  reference  to  mathematical  laws,  and 
therefore  with  better  hope  of  bringing  them  one  by 
one  under  the  domain  of  mathematical  investigation 
than  elsewhere." 

After  calling  attention  to  these  statements  the 
Report  of  the  Syndicate  then  continues  : — 

"  In  the  scheme  of  Examination  for  Honours  in 
the  Mathematical  Tripos  approved  by  Grace  of  the 
Senate  on  the  2nd  of  June,  1868,  Heat,  Electricity  and 
Magnetism,  if  not  introduced  for  the  first  time,  had  a 


AND   MODERN   PHYSICS.  G3 

much  greater  degree  of  importance  assigned  to  them 
than  at  any  previous  period,  and  these  subjects  will 
henceforth  demand  a  corresponding  amount  of  atten- 
tion from  the  candidates  for  Mathematical  Honours. 
The  Syndicate  have  limited  their  attention  almost 
entirely  to  the  question  of  providing  public  instruction 
in  Heat,  Electricity  and  Magnetism.  They  recognise 
the  importance  and  advantage  of  tutorial  instruction 
in  these  subjects  in  the  several  colleges,  but  they  are 
also  alive  to  the  great  impulse  given  to  studies  of  this 
kind,  and  to  the  large  amount  of  additional  training 
which  students  may  receive  through  the  instruction 
of  a  public  Professor,  and  by  knowledge  gained  in  a 
well-appointed  laboratory." 

"  In  accordance  with  these  views,  and  at  an  early 
period  in  their  deliberations,  they  requested  the  Pro- 
fessors* of  the  University,  who  are  engaged  in  teaching- 
Mathematical  and  Physical  Science,  to  confer  together 
upon  the  present  means  of  teaching  Experimental 
Physics,  especially  Heat,  Electricity  and  Magnetism, 
and  to  inform  them  how  the  increased  requirements 
of  the  University  in  this  respect  could  be  met  by 
them." 

"  The  Professors,  so  consulted,  favoured  the  Syndi- 
cate with  a  report  on  the  subject,  which  the  Syndicate 
now  beg  leave  to  lay  before  the  Senate.  It  points  out 
how  the  requirements  of  the  University  might  be 
"  partially  met,"  but  the  Professors  state  distinctly 
that  they  "  do  not  think  that  they  are  able  to  meet 
the  want  of  an  extensive  course  of  lectures  on  Physics 

*  The  Professors  who  were  consulted  were  Challis,  Willis,  Stokes, 
Cayley,  Adams,  and  Liveing'. 


64  James  clerk  maxwell 

treated  as  such,  and  in  great  measure  experimentally. 
As  Experimental  Physics  may  fairly  be  considered  to 
come  within  the  province  of  one  or  more  of  the  above- 
mentioned  Professors,  the  Syndicate  have  considered 
whether  now  or  at  some  future  time  some  arrange- 
mcnt  might  not  be  made  to  secure  the  effective 
teaching  of  this  branch  of  science,  without  having1 
resort  to  the  services  of  an  additional  Professor.  They 
are,  however,  of  opinion  that  such  an  arrangement 
cannot  be  made  at  the  present  time,  and  that  the 
exigencies  of  the  case  may  be  best  met  by  founding  a 
new  professorship  which  shall  terminate  with  the 
tenure  of  office  of  the  Professor  first  elected.  The 
services  of  a  man  of  the  highest  attainments  in 
science,  devoting  his  life  to  public  teaching  as  such 
Professor,  and  engaged  in  original  research,  would  be 
of  incalculable  benefit  to  the  University." 

The  Report  goes  on  to  point  out  that  a  laboratory 
would  be  necessary,  and  also  apparatus.  It  is 
estimated  that  £5,000  would  cover  the  cost  of  the 
laboratory,  and  £1,300  the  necessary  apparatus.  Pro- 
vision is  also  made  for  a  demonstrator  and  a  laboratory 
assistant,  and  the  Report  closes  with  a  recommenda- 
tion that  a  special  Syndicate  of  Finance  should  be 
appointed  to  consider  the  means  of  raising  the  funds. 

The  Professors  in  their  Report  to  the  Syndicate 
point  out  that  teaching  in  Experimental  Physics  is 
needed  for  the  Mathematical  Tripos,  the  Natural 
Sciences  Tripos,  certain  Special  examinations,  and  the 
first  examination  for  the  degree  of  M.B.  It  appeared 
to  them  clear  that  there  was  work  for  a  new  Professor. 

In   May,    1869,  the   Financial   Syndicate   recom- 


AND   MODERN   PHYSICS.  65 

mended  by  the  above  Report  was  appointed  "  to 
consider  the  means  of  raising  the  necessary  funds  for 
establishing  a  professor  and  demonstrator  of  Experi- 
mental Physics,  and  for  providing  buildings  and 
apparatus  required  for  that  department  of  science, 
and  further  to  consider  other  wants  of  the  University, 
and  the  sources  from  which  those  wants  may  be 
supplied." 

The  Syndicate  endeavoured  to  meet  the  expendi- 
ture by  inquiry  from  the  several  Colleges  whether 
they  would  be  willing  to  make  contributions  from 
their  corporate  funds,  but  without  success. 

'•The  answers  of  the  Colleges  indicated  such  a 
want  of  concurrence  in  any  proposal  to  raise  contri- 
butions from  the  corporate  funds  of  Colleges  by  any 
kind  of  direct  taxation  that  the  Syndicate  felt  obliged 
to  abandon  the  notion  of  obtaining  the  necessary  funds 
from  this  source,  and  accordingly  to  limit  the  number 
of  objects  which  the}>-  should  recommend  the  Senate 
to  accomplish." 

External  authority  was  necessary  before  the 
colleges  would  submit  to  taxation  for  University 
purposes,  and  it  was  left  to  the  Royal  Commission  of 
1877  to  carry  into  effect  many  of  the  suggestions  made 
by  the  Syndicate.  Meanwhile  they  contented  them- 
selves with  recommending  means  for  raising  an  annual 
stipend  of  £660  for  the  professor,  demonstrator,  and 
assistant,  and  a  capital  sum  of  £5,000,  or  thereabouts, 
for  the  expenses  of  a  building. 

The  Syndicate's  Report  was  issued  in  an  amended 
form  in  the  May  term  of  1870,  and  before  any  decision 
was  taken  on  it  the  Yicc-Chaneellor,  Dr.  Atkinson,  o  i 


66  JAMES   CLERK   MAXWELL 

October  13th,  1870,  published  "the  following  munifi- 
cent offer  of  his  grace  the  Duke  of  Devonshire,  the 
Chancellor  of  the  University,"  who  had  been  chairman 
of  the  Commission  on  Scientific  Education. 

"Holker  Hall, 

Grange,  Lancashire. 
"My  dear  Mr.  Vice-chancellor,— I  have  the  honour  to 
address  you  for  the  purpose  of  making  an  offer  to  the  University, 
which,  if  you  see  no  objection,  I  shall  be  much  obliged  to  you 
to  submit  in  such  manner  as  you  may  think  fit  for  the  con- 
sideration of  the  Council  and  the  University. 

"I  find  in  the  report  dated  February  29th,  18G9,  of  the 
Physical  Science  Syndicate,  recommending  the  establishment 
of  a  Professor  and  Demonstrator  of  Experimental  Physics,  that 
the  buildings  and  apparatus  required  for  this  department  of 
science  are  estimated  to  cost  £6,300. 

"  I  am  desirous  to  assist  the  University  in  carrying  this 
recommendation  into  effect,  and  shall  accordingly  be  prepared 
to  provide  the  funds  required  for  the  building  and  apparatus 
as  soon  as  the  University  shall  have  in  other  respects  completed 
its  arrangements  for  teaching  Experimental  Physics,  and  shall 
have  approved  the  plan  of  the  building. 

"  I  remain,  my  dear  Mr.  Vice-Chancellor, 
"  Yours  very  faithfully, 

"  Devonshire." 

By  his  generous  action  the  University  was  relieved 
from  all  expense  connected  with  the  building.  A 
Grace  establishing  a  Professorship  of  Experimental 
Physics  was  confirmed  by  the  Senate  February  9th, 
1871,  and  March  8th  was  fixed  for  the  election. 

Meanwhile  who  was  to  be  Professor  ?  Sir  W. 
Thomson's  name  had  been  mentioned,  but  he,  it  was 
known,  would  not  accept  the  post.  Maxwell  was  then 
applied  to,  and  at  first  he  was  unwilling  to  leave 
Glenlair.     Professor  Stokes,  the  Hon.   J.   W.   Strutt 


AND  MODERN  PHYSICS.  67 

(Lord   Rayleigh),    Mr.   Blore   of  Trinity,   and  others 
wrote  to  him.      Lord  Rayleigh's  letter  *  is  as  follows  : 

"Cambridge,  14th  February,  1871. 
"  When  I  came  here  last  Friday  I  found  everyone  talking 
about  the  new  professorship,  and  hoping  that  you  would  come. 
Thomson,  it  seems,  has  definitely  declined.  .  .  .  There  is 
no  one  here  in  the  least  fit  for  the  post.  What  is  wanted  by 
most  who  know  anything  about  it  is  not  so  much  a  lecturer  as 
a  mathematician  who  has  actual  experience  in  experimenting, 
and  who  might  direct  the  energies  of  the  younger  Fellows  and 
bachelors  into  a  proper  channel.  There  must  be  many  who 
would  be  willing  to  work  under  a  competent  man,  and  who, 
while  learning  themselves,  would  materially  assist  him.  .  .  . 
I  hope  you  may  be  induced  to  come ;  if  not,  I  don't  know 
who  it  is  to  be.  Do  not  trouble  to  answer  me  about  this,  as  I 
believe  others  have  written  to  you  about  it." 

On  tliQ  15th  of  February,  Maxwell  wrote  to  Mr. 
Blore : — 

"  I  had  no  intention  of  applying  for  the  post  when  I  got 
your  letter,  and  I  have  none  now,  unless  I  come  to  see  that  I 
can  do  some  good  by  it."  The  letter  continues  : — 

'•  The  class  of  Physical  Investigations,  which  might  be  under- 
taken with  the  help  of  men  of  Cambridge  education,  and  which 
would  be  creditable  to  the  University,  demand  in  general  a 
considerable  amount  of  dull  labour,  which  may  or  may  not  be 
attractive  to  the  pupils." 

However,  on  the  24th  of  February,  Mr.  Blore  wrote 
to  the  Electoral  Roll  :— 

"  I  am  authorised  to  give  notice  that  Mr.  John  (sic) 
Clerk  Maxwell,  F.R.S.,  formerly  Professor  of  Natural 
Philosophy  at  Aberdeen,  and  at  King's  College, 
London,  is  a  candidate  for  the  professorship  of 
Experimental  Physics." 

*  "  Life  of  J.  C.  Maxwell,"  p.  349. 
E  2 


08  JAMES    CLERK   MAXWELL 

Maxwell  was  elected  without  opposition.  Writing* 
to  his  wife  from  Cambridge,  20th  March,  1871,  he 
says  : — 

"  There  are  two  parties  about  the  professorship.  One  wants 
popular  lectures,  and  the  other  cares  more  for  experimental 
work.  I  think  there  should  be  a  gradation — popular  lectures 
and  rough  experiments  for  the  masses  ;  real  experiments  for 
real  students ;  and  laborious  experiments  for  first-rate  men 
like  Trotter  and  Stuart  and  Strutt." 

While  in  a  letter  f  from  Glenlair  to  C.  J.  Munro,  dated 
March  15th,  1871,  he  writes  : — -"The  Experimental 
Physics  at  Cambridge  is  not  built  yet,  but  we  are 
going  to  try.  The  desideratum  is  to  set  a  Don  and  a 
Freshman  to  observe  and  register  (say)  the  vibrations 
of  a  magnet  together,  or  the  Don  to  turn  a  watch  and 
the  Freshman  to  observe  and  govern  him." 

In  October  he  delivered  his  Introductory  Lecture. 
A  few  quotations  will  show  the  spirit  in  which  he 
approached  his  task. 

"In  a  course  of  Experimental  Physics  we  may  consider 
either  the  Physics  or  the  Experiments  as  the  leading  feature. 
We  may  either  employ  the  experiments  to  illustrate  the 
phenomena  of  a  particular  branch  of  Physics,  or  we  may 
make  some  physical  research  in  order  to  exemplify  a  particular 
experimental  method.  In  the  order  of  time,  we  should  begin, 
in  the  Lecture  Room,  with  a  course  of  lectures  on  some  branch 
of  Physics  aided  by  experiments  of  illustration,  and  conclude, 
in  the  Laboratory,  with  a  course  of  experiments  of  research. 

"Let  me  say  a  few  words  on  these  two  classes  of  experi- 
ments —  Experiments  of  Illustration  and  Experiments  of 
Research.      The  aim  of  an   experiment  of  illustration  is  to 

*  "  Life  of  J.  C.  Maxwell,"  p.  381. 
t  "  Life  of  J.  C.  Maxwell,"  p.  379. 


AND   MODERN   PHYSICS.  69 

throw  light  upon  some  scientific  idea  so  that  the  student  may 
be  enabled  to  grasp  it.  The  circumstances  of  the  experiment 
are  so  arranged  that  the  phenomenon  which  we  wish  to  observe 
or  to  exhibit  is  brought  into  prominence,  instead  of  being 
obscured  and  entangled  among  other  phenomena,  as  it  is  when 
it  occurs  in  the  ordinary  course  of  nature.  To  exhibit  illustra- 
tive experiments,  to  encourage  others  to  make  them,  and  to 
cultivate  in  every  way  the  ideas  on  which  they  throw  light, 
forms  an  important  part  of  our  duty.  The  simpler  the 
materials  of  an  illustrative  experiment,  and  the  more  familiar 
they  are  to  the  student,  the  more  thoroughly  is  he  likely  to 
acquire  the  idea  which  it  is  meant  to  illustrate.  The  educa- 
tional value  of  such  experiments  is  often  inversely  proportional 
to  the  complexity  of  the  apparatus.  The  student  who  uses 
home-made  apparatus,  which  is  always  going  wrong,  often 
learns  more  than  one  who  has  the  use  of  carefully  adjusted 
instruments,  to  which  he  is  apt  to  trust,  and  which  he  dares 
not  take  to  pieces. 

"  It  is  very  necessary  that  those  who  are  trying  to  learn  from 
books  the  facts  of  physical  science  should  be  enabled  by  the 
help  of  a  few  illustrative  experiments  to  recognise  these  facts 
when  they  meet  with  them  out  of  doors.  Science  appears  to 
us  with  a  very  different  aspect  after  we  have  found  out  that  it 
is  not  in  lecture-rooms  only,  and  by  means  of  the  electric  light 
projected  on  a  screen,  that  we  may  witness  physical  phenomena, 
but  that  we  may  find  illustrations  of  the  highest  doctrines  of 
science  in  games  and  gymnastics,  in  travelling  by  land  and  by 
water,  in  storms  of  the  air  and  of  the  sea,  and  wherever  there 
is  matter  in  motion. 

"  If,  therefore,  we  desire,  for  our  own  advantage  and  for  the 
honour  of  our  University,  that  the  Devonshire  Laboratory 
should  be  successful,  we  must  endeavour  to  maintain  it  in 
living  union  with  the  other  organs  and  faculties  of  our  learned 
body.  We  shall  therefore  first  consider  the  relation  in  which 
we  stand  to  those  mathematical  studies  which  have  so  long 
flourished  among  us,  which  deal  with  our  own  subjects,  and 
which  differ  from  our  experimental  studies  only  in  the  mode  in 
which  they  are  presented  to  the  mind. 


70  JAMES    CLERK    MAXWELL 

"There  is  no  more  powerful  method  for  introducing  know- 
ledge into  the  mind  than  that  of  presenting  it  in  as  many- 
different  ways  as  we  can.  When  the  ideas,  after  entering 
through  different  gateways,  effect  a  junction  in  the  citadel  of 
the  mind,  the  position  they  occupy  becomes  impregnable. 
Opticians  tell  us  that  the  mental  combination  of  the  views  of 
an  object  which  we  obtain  from  stations  no  further  apart  than 
our  two  eyes  is  sufficient  to  produce  in  our  minds  an  impression 
of  the  solidity  of  the  object  seen  ;  and  we  find  that  this  im- 
pression is  produced  even  when  we  are  aware  that  we  are 
really  looking  at  two  flat  pictures  placed  in  a  stereoscope.  It 
is  therefore  natural  to  expect  that  the  knowledge  of  physical 
science  obtained  by  the  combined  use  of  mathematical  analysis 
and  experimental  research  will  be  of  a  more  solid,  available, 
and  enduring  kind  than  that  possessed  by  the  mere  mathe- 
matician 01'  the  mere  experimenter. 

"But  what  will  be  the  effect  on  the  University  if  men 
pursuing  that  course  of  reading  which  has  produced  so  many 
distinguished  Wranglers  turn  aside  to  work  experiments  1 
Will  not  their  attendance  at  the  Laboratory  count  not  merely 
as  time  withdrawn  from  their  more  legitimate  studies,  but  as 
the  introduction  of  a  disturbing  element,  tainting  their  mathe- 
matical conceptions  with  material  imagery,  and  sapping  their 
faith  in  the  formulas  of  the  text-books?  Besides  this,  we  have 
already  heard  complaints  of  the  undue  extension  of  our  studies, 
and  of  the  strain  put  upon  our  questionists  by  the  weight  of 
learning  which  they  try  to  carry  with  them  into  the  Senate- 
House.  If  we  now  ask  them  to  get  up  their  subjects  not  only 
by  books  and  writing,  but  at  the  same  time  by  observation  and 
manipulation,  will  they  not  break  down  altogether?  The 
Physical  Laboratory,  we  are  told,  may  perhaps  be  useful  to 
those  who  are  going  out  in  Natural  Science,  and  who  do  not 
take  in  Mathematics,  but  to  attempt  to  combine  both  kinds  of 
study  during  the  time  of  residence  at  the  University  is  more 
than  one  mind  can  bear. 

"No  doubt  there  is  some  reason  for  this  feeling.  Many  of 
us  have  already  overcome  the  initial  difficulties  of  mathe- 
matical training.    When  we  now  go  on  with  our  study,  we  feel 


AND   MODERN   PHYSICS.  71 

that  it  requires  exertion  and  involves  fatigue,  but  we  are  con- 
fident that  if  we  only  work  hard  our  progress  will  be  certain. 

"Some  of  us,  on  the  other  hand,  may  have  had  some 
experience  of  the  routine  of  experimental  work.  As  soon  as 
we  can  read  scales,  observe  times,  focus  telescopes,  and  so  on, 
this  kind  of  work  ceases  to  require  any  great  mental  effort. 
We  may,  perhaps,  tire  our  eyes  and  weary  our  backs,  but  we 
do  not  greatly  fatigue  our  minds. 

"  It  is  not  till  we  attempt  to  bring  the  theoretical  part  of 
our  training  into  contact  with  the  practical  that  we  begin  to 
experience  the  full  effect  of  what  Faraday  has  called  '  mental 
inertia'— not  only  the  difficulty  of  recognising,  among  the 
concrete  objects  before  u?,  the  abstract  relation  which  we  have 
learned  from  books,  but  the  distracting  pain  of  wrenching  the 
mind  away  from  the  symbols  to  the  objects,  and  from  the 
objects  back  to  the  symbols.  This,  however,  is  the  price  we 
have  to  pay  for  new  ideas. 

"But  when  we  have  overcome  these  difficulties,  and 
successfully  bridged  over  the  gulph  between  the  abstract  and 
the  concrete,  it  is  not  a  mere  piece  of  knowledge  that  we  have 
obtained  ;  we  have  acquired  the  rudiment  of  a  permanent 
mental  endowment.  When,  by  a  repetition  of  efforts  of  this 
kind,  we  have  more  fully  developed  the  scientific  faculty,  the 
exercise  of  this  faculty  in  detecting  scientific  principles  in 
nature,  and  in  directing  practice  by  theory,  is  no  longer  irk- 
some, but  becomes  an  unfailing  source  of  enjoyment,  to  which 
we  return  so  often  that  at  last  even  our  careless  thoughts 
begin  to  run  in  a  scientific  channel. 

"  Our  principal  work,  however,  in  the  Laboratory  must  be 
to  acquaint  ourselves  with  all  kinds  of  scientific  methods,  to 
compare  them  and  to  estimate  their  value.  It  will,  I  think, 
be  a  result  worthy  of  our  University,  and  more  likely  to  be 
accomplished  here  than  in  any  private  laboratory,  if,  by  the 
free  and  full  discussion  of  the  relative  value  of  different 
scientific  procedures,  we  succeed  in  forming  a  school  of 
scientific  criticism  and  in  assisting  the  development  of  the 
doctrine  of  method. 

"  But  admitting   that  a  practical  acquaintance  with   the 


72  JAMES   CLERK   MAXWELL 

methods  of  Physical  Science  is  an  essential  part  of  a  mathe- 
matical and  scientific  education,  we  may  be  asked  whether  we 
are  not  attributing  too  much  importance  to  science  altogether 
as  part  of  a  liberal  education. 

"  Fortunately,  there  is  no  question  hero  whether  the 
University  should  continue  to  be  a  place  of  liberal  education, 
or  should  devote  itself  to  preparing  young  men  for  particular 
professions.  Hence,  though  some  of  us  may,  I  hope,  see  reason 
to  make  the  pursuit  of  science  the  main  business  of  our  lives, 
it  must  be  one  of  our  most  constant  aims  to  maintain  a  living 
connexion  between  our  work  and  the  other  liberal  studies  of 
Cambridge,  whether  literary,  philological,  historical,  or 
philosophical. 

"  There  is  a  narrow  professional  spirit  which  may  grow  up 
among  men  of  science  just  as  it  does  among  men  who  practise 
any  other  special  business.  But  surely  a  University  is  the 
very  place  where  we  should  be  able  to  overcome  this  tendency 
of  men  to  become,  as  it  were,  granulated  into  small  worlds, 
which  are  all  the  more  worldly  for  their  very  smallness  1  We 
lose  the  advantage  of  having  men  of  varied  pursuits  collected 
into  one  body  if  we  do  not  endeavour  to  imbibo  some  of  the 
spirit  even  of  those  whose  special  branch  of  learning  is  different 
from  our  own.1' 

Another  expression  of  his  views  on  the  position  of 
Physics  at  the  time  will  be  found  in  his  address  to 
Section  A  of  the  British  Association,  when  President 
at  the  Liverpool  meeting  of  1870. 


AND   MODERN   PHYSICS.  73 


CHAPTER    VI. 

CAMBRIDGE — THE  CAVENDISH  LABORATORY. 

But  the  laboratory  was  not  yet  built.  A  Syndicate, 
of  which  Maxwell  was  a  member,  was  appointed  to 
consider  the  question  of  a  site,  to  take  professional 
advice,  and  to  obtain  plans  and  estimates.  Professor 
Maxwell  and  Mr.  Trotter  visited  various  laboratories 
at  home  and  abroad  for  the  purpose  of  ascertaining 
the  best  arrangements.  Mr.  W.  M.  Fawcett  was 
appointed  architect ;  the  tender  of  Mr.  John  Loveday, 
of  Kebworth,  for  the  building  at  a  cost  of  £8,450, 
exclusive  of  gas,  water,  and  heating,  was  accepted  in 
March,  1872,  and  the  building*  was  begun  during  the 
summer. 

In  the  meantime  Maxwell  began  to  lecture,  finding 
a  home  where  he  could. 

''Lectures  begin  24th,"  lie  writes  from  Glenlair,  October 
19tb,  1872.  "Laboratory  rising,  I  hear,  but  I  have  no  place 
to  erect  my  chair,  but  move  about  like  the  cuckoo,  depositing 
my  notions  in  the  Chemical  Lecture-room  1st  term  ;  in  the 
Botanical  in  Lent,  and  in  Comparative  Anatomy  in  Easter." 

It  was  not  till  June,  1874,  that  the  building  was 
complete,  and  on  the  16th  the  Chancellor  formally 
presented  his  gift  of  the  Cavendish  Laboratory  to  the 
University.  In  the  correspondence  previous  to  this 
time  it  was  spoken  of  as  the  Devonshire  Laboratory. 
The  name  Cavendish  commemorated  the  work  of  the 
great  physicist  of  a  century  earlier,  whose  writings 

*  An  account  of  the  laboratory  is  given  in  Nature,  vol.  x.,  p.  139. 


74  JAMES   CLERK   MAXWELL 

Maxwell  was  shortly  to  edit,  as  well  as  the  generosity 
of  the  Chancellor. 

In  their  letter  of  thanks  to  the  Duke  of  Devonshire 
the  University  write  : — 

"Unde  vero  conventius  poterat  illis  artibus 
succurri  quam  e  tua  domo  quae  in  ipsis  jam  pridem 
inclaruerat.  Notum  est  Henricum  Cavendish  quern 
secutus  est  Coulombius  primuni  ita  docuisse,  quae  sit 
vis  electrica  ut  earn  numerornm  modulis  illustraret ; 
adhibitis  rationibus  quas  hodie  veras  esse  constat." 
And  they  suggest  the  name  as  suitable  for  the 
building.  To  this  the  Chancellor  replied,  after  re- 
ferring to  the  work  of  Henry  Cavendish :  "  Quod 
pono  in  officina  ipsa  nuncupanda  nomen  ejus  com- 
memorare  dignati  sitis,  id  grato  animo  accepi." 

The  building  had  cost  far  more  than  the  original 
estimate,  but  the  Chancellor's  generosity  was  not 
limited,  and  on  July  21st,  1874,  he  wrote  to  the  Yice- 
Chancellor : — 

"  It  is  m}'  wish  to  provide  all  instruments  for  the 
Cavendish  Laboratory  which  Professor  Maxwell  may 
consider  to  be  immediately  required,  either  in  his 
lectures  or  otherwise." 

Maxwell  prepared  a  list,  but  explained  while  doing 
it  that  time  and  thought  were  necessary  to  secure  the 
best  form  of  instruments  ;  and  he  continues,  writing  to 
the  Vice-Chancellor  :  "  I  think  the  Duke  fully  under- 
stood from  what  I  said  to  him  that  to  furnish  the 
Laboratory  will  be  a  matter  of  several  years'  duration. 
I  shall  consider  myself,  however,"  he  says,  "  at  liberty 
to  contribute  to  the  Laboratory  any  instruments 
which  I  have  had  constructed  in  former  years,  and 


AND  MODERN   PHYSICS.  75 

which  may  be  found  still  useful,  and  also  from  time  to 
time  to  procure  others  for  special  researches." 

In  1877  in  his  annual  report  Professor  Maxwell 
announced  that  the  Chancellor*  had  now  "  completed 
his  gift  to  the  University  by  furnishing  the  Cavendish 
Laboratory  with  apparatus  suited  to  the  present  state 
of  science." 

The  stock  of  apparatus,  however,  was  still  small, 
although  Maxwell  in  the  most  generous  manner 
himself  spent  large  sums  in  adding  to  it ;  for  the 
Professor  was  most  particular  in  procuring  only 
expensive  instruments  by  the  best  makers,  with  such 
additional  improvements  as  he  could  himself  suggest. 

In  March,  1874,  a  Demonstratorship  of  Physics 
had  been  established,  and  Mr.  Garnett  of  St.  John's 
College  was  appointed. 

Work  began  in  the  laboratory  in  October,  1874. 
At  first  the  number  of  students  Avas  small.  Only 
seventeen  names  appear  in  the  Natural  Sciences 
Triposj  list  for  1874,  and  few  of  those  did  Physics. 

The  fear  alluded  to  by  the  Professor  in  his  intro- 
ductory lecture,  that  men  reading  for  the  Mathematical 

*  The  Chancellor  continued  to  take  to  the  end  of  his  life  a  warm 
interest  in  the  work  at  the  laboratory.  In  1887,  the  Jubilee  year,  as 
Proctor— at  the  same  time  I  held  the  office  of  Demonstrator  — it  was 
my  duty  to  accompany  the  Chancellor  and  other  officers  to  Windsor 
to  present  an  address  from  the  University  to  Her  Majesty.  I  was 
introduced  to  the  Chancellor  at  Paddington,  and  he  at  once  began  to 
question  me  closely  about  the  progress  of  the  laboratory,  the  number 
of  students,  and  the  work  being  done  there,  showing  himself  fully 
acquainted  with  recent  progress. 

t  In  1894  the  list  contained,  in  Part  II.,  sixteen  names,  and  in 
Part  I.,  one  hundred  and  three  names. 


76  JAMES   CLERK   MAXWELL 

Tripos  Avould  not  find  time  for  attendance  at  the 
laboratory,  was  justified.  One  of  the  weaknesses  of 
our  Cambridge  plan  has  been  the  divorce  between 
Mathematics  and  experimental  work,  encouraged 
by  our  system  of  examinations.  Experimental 
knowledge  is  supposed  not  to  be  needed  for  the 
Mathematical  Tripos ;  the  Mathematics  permitted  in 
the  Natural  Sciences  Tripos  are  very  simple ;  thus 
it  came  about  that  few  men  while  reading  for  the 
Mathematical  Tripos  attended  the  laboratory,  and 
this  unfortunate  result  was  intensified  by  the  action 
of  the  University  in  1877-78,  when  the  regulations 
for  the  Mathematical  Tripos  were  again  altered.* 

Still  there  were  pupils  eager  and  willing  to  work, 
though  they  were  chiefly  men  who  had  already  taken 
their  B.A.  degree,  and  who  wished  to  continue 
Physical  reading  and  research,  even  though  it  in- 
volved "a  considerable  amount  of  dull  labour  not 
altogether  attractive."  My  own  work  there  began  in 
1876,  and  it  may  be  interesting  if  I  recall  my  remin- 
iscences of  that  time. 

The  first  experiments  I  can  recollect  related  to  the 
measurement  of  electrical  resistance.  I  well  remember 

*  Under  the  new  regulations  Physics  was  removed  from  the  first 
part  of  the  Tripos  and  formed,  with  the  more  advanced  parts  of 
Astronomy  and  Pure  Mathematics,  a  part  by  itself,  to  which  only  the 
Wranglers  were  admitted.  Thus  the  number  of  men  encouraged  to 
read  Thysics  was  very  limited.  This  pernicious  system  was  altered 
in  the  regulations  at  present  in  force,  which  came  into  action  in  1892. 
Part  I.  of  the  Mathematical  Tripos  now  contains  Heat,  Elementary 
Hydrodynamics  and  Sound,  and  the  simpler  paits  of  Electricity  and 
Magnetism,  and.  candidates  for  this  examination  do  come  to  the 
laboratory,  though  not  in  very  large  numbers.  The  more  advanced 
parts  both  of  Mathematics  and  Physics  are  included  in  Pait  II. 


AND   MODERN    PHYSICS.  77 

Maxwell  explaining  the  principle  of  Wheatstone's 
bridge,  and  my  own  wish  at  the  time  that  I  had  come 
to  the  laboratory  before  the  Tripos,  instead  of  after- 
wards. Lord  Rayleigh  had,  during  the  examination, 
set  an  easy  question  which  I  failed  to  do  for  want 
of  some  slight  experimental  knowledge,  and  the  first 
few  words  of  Maxwell's  talk  showed  me  the  solution. 

I  did  not  attend  his  lectures  regularly — they  were 
given,  I  think,  at  an  hour  which  I  was  obliged  to 
devote  to  teaching ;  besides,  there  was  his  book,  the 
"  Electricity  and  Magnetism,"  into  which  I  had  just 
dipped  before  the  Tripos,  to  work  at. 

Chrystal  and  Saunder  were  then  busy  at  their 
verification  of  Ohm's  law.  They  were  using  a  number 
of  the  Thomson  form  of  tray  Daniell's  cells,  and 
MaxAvell  was  anxious  for  tests  of  various  kinds  to 
be  made  on  these  cells ;  these  I  undertook,  and 
spent  some  time  over  various  simple  measurements 
on  them.  He  then  set  me  to  work  at  some  of  the 
properties  of  a  stratified  dielectric,  consisting,  if  I 
remember  rightly,  of  sheets  of  paraffin  paper  and 
mica.  By  this  means  I  became  acquainted  with 
various  pieces  of  apparatus.  There  were  no  regular 
classes  and  no  set  drill  of  demonstrations  arranged 
for  examination  purposes  ;  these  came  later.  In  Max- 
well's time  those  who  wished  to  work  had  the  use  of 
the  laboratory  and  assistance  and  help  from  him,  but 
they  were  left  pretty  much  to  themselves  to  find  out 
about  the  apparatus  and  the  best  methods  of  using  it. 

Rather  later  than  this  Schuster  came  and  did 
some  of  his  spectroscope  work.  J.  E.  H.  Gordon 
was  busy  with  the  preliminary  observations   for  his 


78  JAMES   CLERK   MAXWELL 

determination  of  Verdet's  constant,  and  Niven  had 
various  electrical  experiments  on  hand ;  while  Fleming 
was  at  work  on  the  B.  A.  resistance  coils. 

My  own  tastes  lay  in  the  direction  of  optics. 
Maxwell  was  anxious  that  I  should  investigate  the 
properties  of  certain  crystals.  I  think  they  were  the 
chlorate  of  potash  crystals,  about  which  Stokes  and 
Rayleigh  have  since  written ;  but  these  crystals  were 
to  be  grown,  a  slow  process  which  would,  he  supposed, 
take  years ;  and  as  I  wished  to  produce  a  dissertation 
for  the  Trinity  Fellowship  examination  in  1877,  that 
work  had  to  be  laid  aside. 

Eventually  I  selected  as  a  subject  the  form  of  the 
wave  surface  in  a  biaxial  crystal,  and  set  to  work  in 
a  room  assigned  to  me.  The  Professor  used  to  come 
in  on  most  days  to  see  how  I  was  getting  on.  Generally 
he  brought  his  dog,  which  sometimes  was  shut  up  in 
the  next  room  while  he  went  to  college.  Dogs  were 
not  allowed  in  college,  and  Maxwell  had  an  amusing 
way  of  describing  how  Toby  once  wandered  into 
Trinity,  and  by  some  doggish  instinct  discovered 
immediately,  to  his  intense  amazement,  that  he  was 
in  a  place  where  no  dogs  had  been  since  the  college 
was.  Toby  was  not  always  quiet  in  his  master's 
absence,  and  his  presence  in  the  next  room  was  some- 
what disturbing. 

When  difficulties  occurred  Maxwell  was  always 
ready  to  listen.  Often  the  answer  did  not  come  at 
once,  but  it  always  did  come  after  a  little  time.  I 
remember  one  day,  when  I  was  in  a  serious  dilemma, 
I  told  him  my  long  tale,  and  he  said  : — 

"  Well,    Chrystal   has   been    talking   to   me,   and 


AND   MODERN   PHYSICS.  79 

Garnett  and  Schuster  have  been  asking  questions, 
and  all  this  has  formed  a  good  thick  crust  round  my 
brain.  What  you  have  said  will  take  some  time  to 
soak  through,  but  we  will  see  about  it."  In  a  few 
days  he  came  back  with — "  I  have  been  thinking 
over  what  you  said  the  other  day,  and  if  you  do  so- 
and-so  it  will  be  all  right." 

My  dissertation  was  referred  to  him,  and  on  the 
day  of  the  election,  when  returning  to  Cambridge  for 
the  admission,  I  met  him  at  Bletchley  station,  and 
well  remember  his  kind  congratulations  and  words 
of  warm  encouragement. 

For  the  next  year  and  a  half  I  was  working 
regularly  at  the  laboratory  and  saw  him  almost  daily 
during  term  time. 

Of  these  last  years  there  really  is  but  little  to  tell. 
His  own  scientific  work  went  on.  The  ."  Electricity 
and  Magnetism "  was  written  mostly  at  Glenlair. 
About  the  time  of  his  return  to  Cambridge,  in  October, 
1872,  he  writes  *  to  Lewis  Campbell : — 

"  I  am  continually  engaged  in  stirring  up  the  Clarendon 
Press,  but  they  have  been  tolerably  regular  for  two  months.  I 
lind  nine  sheets  in  thirteen  weeks  is  their  average.  Tait  gives 
me  great  help  in  detecting  absurdities.  I  am  getting  converted 
to  quaternions,  and  have  put  some  in  my  book." 

The  book  was  published  in  1873.  The  Text-book 
of  Heat  was  written  during  the  same  period,  while 
"  Matter  and  Motion,"  "  a  small  book  on  a  great 
subject,"  was  published  in  1876. 

In  1873  and  1874  he  was  one  of  the  examiners  for 
the  Natural  Sciences  Tripos,  and  in  1873  he  was  the 

*  "  Life  of  J.  C.  Maxwell,"  p.  383. 


80  JAMES   CLERK    MAXWELL 

first  additional  examiner  for  the  Mathematical  Tripos, 
in  accordance  with  the  scheme  which  he  had  done  so 
much  to  promote  in  ls68. 

Many  of  his  shorter  papers  were  written  about  the 
same  tune.  The  ninth  edition  of  \he  Encyclopaedia 
Britannica  was  being  published,  and  Professor  Baynes 
had  enlisted  his  aid  in  the  work.  The  articles 
■  Atom."  ••  Attraction/'  "  Capillary  Action."'  "  Constitu- 
tion of  Bodies,"  "Diffusion,"  "Ether."  -Faraday.'"  and 
others  are  by  him. 

He  also  wrote  a  number  of  papers  for  Nature. 
S  me  of  these  are  reviews  of  books  or  accounts  of 
scientific  men,  such  as  the  notices  of  Faraday  and 
Helmholtz,  which  appeared  with  their  portraits  : 
others  again  are  original  contributions  to  science. 
Among  the  latter  manv  have  reference  to  the 
molecular  constitution  of  bodies.  Two  lectures — the 
first  on  "Molecules,"  delivered  before  the  British 
Association  at  Bradford  in  1">73  ;  the  second  on  the 
••  Dynamical  Evidence  of  the  Molecular  Constitution 
of  Bodies.""  delivered  before  the  Chemical  Society  in 
ls75 — were  of  special  importance.  The  closing 
sentences  of  the  first  lecture  have  been  often  quoted. 
They  run  as  follow :  — 

"  In  the  heavens  we  discover  by  their  light,  and  by  their 
light  alone,  stars  so  distant  from  each  other  that  no  material 
thing  can  ever  have  passed  from  one  to  another  :  and  yet  this 
light,  which  is  to  us  the  sole  evidence  of  the  existence  of  these 
distant  worlds,  tells  us  also  that  each  of  them  is  built  up  of 
molecules  of  the  same  kinds  as  those  which  we  find  on  earth. 
A  molecule  of  hydrogen,  for  example,  whether  in  Sirius  or  in 
Arcturus,  executes  its  vibrations  in  precisely  the  same  time. 

"Each  molecule  therefore  throughout  the  universe   Icars 


AND   MODERN   PHYSICS,  81 

impressed  upon  it  the  stamp  of  a  metric  system,  as  distinctly 
as  does  the  metre  of  the  Archives  at  Paris,  or  the  double  royal 
cubit  of  the  temple  of  Karnac. 

"  No  theory  of  evolution  can  be  formed  to  account  for  the 
similarity  of  molecules,  for  evolution  necessarily  implies  con- 
tinuous change,  and  the  molecule  is  incapable  of  growth  or 
decay,  of  generation  or  destruction. 

"None  of  the  processes  of  Nature,  since  the  time  when 
Nature  began,  have  produced  the  slightest  difference  in  the 
properties  of  any  molecule.  We  are  therefore  unable  to 
ascribe  either  the  existence  of  the  molecules  or  the  identity 
of  their  properties  to  any  of  the  causes  which  we  call  natural. 

"  On  the  other  hand,  the  exact  equality  of  each  molecule  to 
all  others  of  the  same  kind  gives  it,  as  Sir  John  Herschel  has 
well  said,  the  essential  character  of  a  manufactured  article, 
and  precludes  the  idea  of  its  being  eternal  and  self- existent. 

"Thus  we  have  been  led  along  a  strictly  scientific  path, 
very  near  to  the  point  at  which  Science  must  stop— not  that 
Science  is  debarred  from  studs'ingthe  internal  mechanism  of  a 
molecule  which  she  cannot  take  to  pieces  any  more  than  from 
investigating  an  organism  which  she  cannot  put  together.  But 
in  tracing  back  the  history  of  matter,  Science  is  arrested  when 
she  assures  herself,  on  the  one  hand,  that  the  molecule  has 
been  made,  and,  on  the  other,  that  it  has  not  been  made  by 
any  of  the  processes  we  call  natural. 

"Science  is  incompetent  to  reason  upon  the  creation  of 
matter  itself  out  of  nothing.  We  have  reached  the  utmost 
limits  of  our  thinking  faculties  when  we  have  admitted  that 
because  matter  cannot  be  eternal  and  self-existent,  it  must 
have  been  created. 

"  It  is  only  when  we  contemplate,  not  matter  in  itself,  but 
the  form  in  which  it  actually  exists,  that  our  mind  finds  some- 
thing on  which  it  can  lay  hold. 

"That  matter,  as  such,  should  have  certain  fundamental 
properties,  that  it  should  exist  in  space  and  be  capable  of 
motion,  that  its  motion  should  be  persistent,  and  so  on,  are 
truths  which  may,  for  anything  we  know,  be  of  the  kind  which 
metaphysicians  call  necessary.    "We  may  use  our  knowledge  of 

F 


82  JAMES   CLERK   MAXWELL 

such  truths  for  purposes  of  deduction,  but  we  have  no  data  for 
speculating  as  to  their  origin. 

"But  that  there  should  be  exactly  so  much  matter  and  no 
more  in  every  molecule  of  hydrogen  is  a  fact  of  a  very  different 
order.  We  have  here  a  particular  distribution  of  matter — a 
collocation,  to  use  the  expression  of  Dr.  Chalmers,  of  things 
which  we  have  no  difficulty  in  imagining  to  have  been  arranged 
otherwise. 

"The  form  and  dimensions  of  the  orbits  of  the  planets,  for 
instance,  are  not  determined  by  any  law  of  nature,  but  depend 
upon  a  particular  collocation  of  matter.  The  same  is  the  case 
with  respect  to  the  size  of  the  earth,  from  which  the  standard 
of  what  is  called  the  metrical  system  has  been  derived.  But 
these  astronomical  and  terrestrial  magnitudes  are  far  inferior 
in  scientific  importance  to  that  most  fundamental  of  all 
standards  which  forms  the  base  of  the  molecular  system. 
Natural  causes,  as  we  know,  are  at  work  which  tend  to  modify, 
if  they  do  not  at  length  destroy,  all  the  arrangements  and 
dimensions  of  the  earth  and  the  whole  solar  system.  But 
though  in  the  course  of  ages  catastrophes  have  occurred  and 
may  yet  occur  in  the  heavens,  though  ancient  systems  may  be 
dissolved  and  new  systems  evolved  out  of  their  ruins,  the 
molecules  out  of  which  these  systems  are  built — the  foundation 
stones  of  the  material  universe— remain  unbroken  and  unworn. 
They  continue  this  day  as  they  were  created — perfect  in 
number  and  measure  and  weight ;  and  from  the  ineffaceable 
characters  impressed  on  them  we  may  learn  that  those  aspira- 
tions after  accuracy  in  measurement,  and  justice  in  action, 
which  we  reckon  among  our  noblest  attributes  as  men,  are 
ours  because  they  are  essential  constituents  of  the  image  of 
Him  who  in  the  beginning  created,  not  only  the  heaven  and 
the  earth,  but  the  materials  of  which  heaven  and  earth  consist." 

This  was  criticised  in  Nature  by  Mr.  C.  J.  Mimro, 
and  at  a  later  time  by  Clifford  in  one  of  his  essays. 

Some  correspondence  with  the  Bishop  of  Glou- 
cester and  Bristol  on  the  authority  for  the  com- 
parison  of  molecules   to    manufactured    articles     is 


AXD   MODERN   PHYSICS.  83 

given  by  Professor  Campbell,  and  in  it  Maxwell 
points  out  that  the  latter  part  of  the  article  "  Atom  " 
in  the  Encyclopcedia  is  intended  to  meet  Mr.  Munro's 
criticism. 

In  1874  the  British  Association  met  at  Belfast, 
under  the  presidency  of  Tyndall.  Maxwell  was  pre- 
sent, and  published  afterwards  in  Blackwood's  Maga- 
zine an  amusing  paraphrase  of  the  president's  address. 
This,  with  some  other  verses  written  at  about  the 
same  time,  may  be  quoted  here.  Professor  Campbell 
has  collected  a  number  of  verses  written  by  Maxwell 
at  various  times,  which  illustrate  in  an  admirable 
manner  both  the  grave  and  the  gay  side  of  his 
character. 

BRITISH   ASSOCIATION,    1874. 

Notes  of  the  President's  Address. 

In  the  very  beginnings  of  science,  the  parsons,  who  managed  things 

then, 
Being  handy  with  hammer  and  chisel,  made  gods  in  the  likeness  of 

men ; 
Till  commerce  arose,  and  at  length  some  men  of  exceptional  power 
Supplanted  both  demons  and  gods  by  the  atoms,  which  last  to  this 

hour. 
Yet  they  did  not  abolish  the  gods,  but  they  sent  them  well  out  of  the 

way, 
With  the  rarest  of  nectar  to  drink,  and  blue  fields  of  nothing  to  sway. 
From   nothing   comes   nothing,    they   told   us— naught   happens   by 

chance,  but  by  fate  ; 
There  "is  nothing  but  atoms  and  void,  all  else  is  mere  whims  out  of  date  ! 
Then  why  should  a  man  curry  favour  with  beings  who  cannot  exist, 
To  compass  some  petty  promotion  in  nebulous  kingdoms  of  mist  ? 
But  not  by  the  rays  of  the  sun,  nor  the  glittering  shafts  of  the  day, 
Must  the  fear  of   the  gods   be  dispelled,  but   by  words,  and   their 

wonderful  play. 

F    2 


84  JAMES   CLERK   MAXWELL 

So  treading  a  path  all  untrod,  the  poet-philosopher  sings 
Of  the  seeds  of  the  mighty  world — the  first-beginnings  of  things ; 
How  freely  he  scatters  his  atoms  before  the  beginning  of  years ; 
How  he  clothes  them  with  force  as  a  garment,  those  small  incom- 
pressible spheres  ! 
Nor  yet  does  he  leave  them  hard-hearted — he  dowers  them  with  love 

and  with  hate, 
Like  spherical  small  British  Asses  in  infinitesimal  state  ; 
Till  just  as  that  living  Plato,  whom  foreigners  nickname  Plateau,* 
Drops  oil  in  his  whisky-and-water  (for  foreigners  sweeten  it  so)  ; 
Each  drop  keeps  apart  from  the  other,  enclosed  in  a  flexible  skin, 
Till  touched  by  the  gentle  emotion  evolved  by  the  prick  of  a  pin  : 
Thus  in  atoms  a  simple  collision  excites  a  sensational  thrill, 
Evolved  through  all  sorts  of  emotion,  as  sense,  understanding,  and  will 
(For  by  laying  their  heads  all  together,  the  atoms,  as  councillors  do, 
May  combine  to  express  an  opinion  to  every  one  of  them  new). 
There  is  nobody  here,  I  should  say,  has  felt  true  indignation  at  all, 
Till  an  indignation  meeting  is  held  in  the  Ulster  Hall ; 
Then  gathers  the  wave  of  emotion,  then  noble  feelings  arise, 
Till  you  all  pass  a  resolution  which  takes  every  man  by  surprise. 
Thus  the  pure  elementary  atom,  the  unit  of  mass  and  of  thought, 
By  force  of  mere  juxtaposition  to  life  and  sensation  is  brought ; 
So,  down  through  untold  generations,  transmission  of  structureless  germs 
Enables  our  race  to  inherit  the  thoughts  of  beasts,  fishes,  and  worms. 
We  honour  our  fathers  and  mothers,  grandfathers  and  grandmothers 

too ; 
But  how  shall  we  honour  the  vista  of  ancestors  now  in  our  view  ? 
First,  then,  let  us  honour  the  atom,  so  lively,  so  wise,  and  so  small ; 
The  atomists  next  let  us  praise,  Epicurus,  Lucretius,  and  all. 
Let  us  damn  with  faint  praise  Bishop  Butler,  in  whom  many  atoms 

combined 
To  form  that  remarkable  structure  it  pleased  him  to  call — his  mind. 
Last,  praise  we  the  noble  body  to  which,  for  the  time,  we  belong, 
Ere  yet  the  swift  whirl  of  the  atoms  has  hurried  us,  ruthless,  along, 
The  British  Association — -like  Leviathan  worshipped  by  Hobbes, 
The  incarnation  of  wisdom,  built  up  of  our  witless  nobs, 
Which  will  carry  on  endless  discussions  whon  I,  and  probably  you, 
Have  melted  in  infinite  azure — in  English,  till  all  is  blue. 

*  "  Statique  Experimentale   et    Theorique  des   Liquides  soumis   aux   seules 
Forces  Moleculaires."    Par  J.  Plateau,  Professeur  a  l'Uuiversite  de  Gaud, 


AND   MODERN   PHYSICS.  85 

MOLECULAR    EVOLUTION. 

Belfast,  1874. 

At  quite  uncertain  times  and  places, 

The  atoms  left  their  heavenly  path, 
And  hy  fortuitous  embraces 

Engendered  all  that  being  hath. 
And  though  they  seem  to  cling  together, 

And  form  "  associations  "  here, 
Yet,  soon  or  late,  they  burst  their  tether, 

And  through  the  depths  of  space  career. 

So  we  who  sat,  oppressed  with  science, 

As  British  Asses,  wise  and  grave, 
Are  now  transformed  to  wild  Red  Lions,* 

As  round  our  prey  we  ramp  and  rave. 
Thus,  by  a  swift  metamorphosis, 

Wisdom  turns  wit,  and  science  joke, 
Nonsense  is  incense  to  our  noses, 

For  when  Red  Lions  speak  they  smoke. 

Hail,  Nonsense  !  dry  nurse  of  Red  Lions,  f 

From  thee  the  wise  their  wisdom  learn ; 
From  thee  they  cull  those  truths  of  science, 

Which  into  thee  again  they  turn. 
What  combinations  of  ideas 

Nonsense  alone  can  wisely  form  ! 
What  sage  has  half  the  power  that  she  has, 

To  take  the  towers  of  Truth  by  storm  ? 

Yield,  then,  ye  rules  of  rigid  reason ! 

Dissolve,  thou  too,  too  solid  sense  ! 
(  Melt  into  nonsense  for  a  season, 

Then  in  some  nobler  form  condense. 
Soon,  all  too  soon,  the  chilly  morning 

This  flow  of  soul  will  crystallise ; 
Then  those  who  Nonsense  now  are  scorning 

May  learn,  too  late,  where  wisdom  lies. 

*  The  "  Red  Lions  "  are  a  club  formed  by  Members  of  the  British  Association 
to  meet  for  relaxation  after  the  graver  labours  of  the  day. 
f  "Leonum  arida  nutrix." — Horace. 


86  JAMES   CLERK  MAXWELL 

TO   THE   COMMITTEE   OF  THE   CAYLEY 
PORTRAIT  FUND. 

1874. 

0  wretched  race  of  men,  to  space  confined  ! 
What  honour  can  ye  pay  to  him,  whose  mind 

To  that  which  lies  beyond  hath  penetrated? 
The  symbols  he  hath  formed  shall  sound  his  praise, 
And  lead  him  on  through  unimagined  ways 

To  conquests  new,  in  worlds  not  yet  created. 

First,  ye  Determinants  !  in  ordered  row 
And  massive  column  ranged,  before  him  go, 

To  form  a  phalanx  for  his  safe  protection. 
Ye  powers  of  the  nth  roots  of  —  1  ! 
Around  his  head  in  ceaseless  *  cycles  run, 

As  unembodied  spirits  of  direction. 

And  you,  ye  undevelopable  scrolls  ! 

Above  the  host  wave  your  emblazoned  rolls, 

Ruled  for  the  record  of  his  bright  inventions. 
Ye  cubic  surfaces  !  by  threes  and  nines 
Draw  round  his  camp  your  seven-and-twenty  line3  — 

The  seal  of  Solomon  in  three  dimensions. 

March  on,  symbolic  host !  with  step  sublime, 
Up  to  the  flaming  bounds  of  Space  and  Time  ! 

There  pause,  until  by  Dickinson  depicted, 
In  two  dimensions,  we  the  form  may  trace 
Of  him  whose  soul,  too  large  for  vulgar  space, 

In  n  dimensions  flourished  unrestricted. 


IN   MEMORY   OF  EDWARD   WILSON, 

Who  repented  of  what  was  in  his  mind  to  write  after  section. 

Rigid  Body  [slugs). 

C4i.v  a  body  meet  a  body- 
Fly  in'  through  the  air, 

Gin  a  body  hit  a  body, 
Will  it  fly?  and  where? 

*  v.r.,  endless. 


AND   MODERN   PHYSICS.  87 

Ilka  impact  has  its  measure, 

Ne'er  a  ane  hae  I ; 
Yet  a'  the  lads  they  measure  me, 

Or,  at  least,  they  try. 

Gin  a  body  meet  a  body 

Altogether  free, 
How  they  travel  afterwards 

AYe  do  not  always  see. 
I  Ilea  problem  has  its  method 

By  analytics  high ; 
For  me,  I  ken  na  ane  o'  them, 

But  what  the  waur  am  I  ? 

Another  task,  which  occupied  much  time,  from 
1874  to  1879,  was  the  edition  of  the  works  of  Henry 
Cavendish.  Cavendish,  who  was  great-uncle  to  the 
Chancellor,  had  published  only  two  electrical  papers, 
but  he  had  left  some  twenty  packets  of  manuscript 
on  Mathematical  and  Experimental  Electricity. 
These  were  placed  in  Maxwell's  hands  in  1874  by  the 
Duke  of  Devonshire. 

Niven,  in  his  preface  to  the  collected  papers 
dealing  with  this  book,  writes  thus  : — 

"This  work,  published  in  1879,  has  had  the  effect  of 
increasing  the  reputation  of  Cavendish,  disclosing  as  it  does 
the  unsuspected  advances  which  that  acute  physicist  had 
made  in  the  Theory  of  Electricity,  especially  in  the  measure- 
ment of  electrical  quantities.  The  work  is  enriched  by  a 
variety  of  valuable  notes,  in  which  Cavendish's  views  and 
results  are  examined  by  the  light  of  modern  theory  and 
methods.  Especially  valuable  are  the  methods  applied  to  the 
determination  of  the  electrical  capacities  of  conductors  and 
condensers,  a  subject  in  which  Cavendish  himself  showed  con- 
siderable skill  both  of  a  mathematical  and  experimental 
character. 


8$  JAMES  CLERK  MAXWELL 

;<  The  importance  of  the  task  undertaken  by  Maxwell  in 
connection  with  Cavendish's  papers  will  be  understood  from 
the  following  extract  from  his  introduction  to  them  :— 

'"It  is  somewhat  difficult  to  account  for  the  fact  that 
though  Cavendish  had  prepared  a  complete  description  of  his 
experiments  on  the  charges  of  bodies,  and  had  even  taken  the 
trouble  to  write  out  a  fair  copy,  and  though  all  this  seems  to 
have  been  done  before  1774,  and  he  continued  to  make  experi- 
ments in  electricity  till  1781,  and  lived  on  till  1810,  he  kept 
his  manuscript  by  him  and  never  published  it. 

Cavendish  cared  more  for  investigation  than  for  publica- 
tion. He  would  undertake  the  most  laborious  researches  in 
order  to  clear  up  a  difficulty  which  no  one  but  himself  could 
appreciate  or  was  even  aware  of,  and  we  cannot  doubt  that  the 
result  of  his  enquiries,  when  successful,  gave  him  a  certain 
degree  of  satisfaction.  But  it  did  not  excite  in  him  that 
desire  to  communicate  the  discovery  to  others,  which  in  the 
case  of  ordinary  men  of  science  generally  ensures  the  publica- 
tion of  their  results.  How  completely  these  researches  of 
Cavendish  remained  unknown  to  other  men  of  science  is  shown 
by  the  external  history  of  electricity.' 

"  It  will  probably  be  thought  a  matter  of  some  difficulty 
to  place  oneself  in  the  position  of  a  physicist  of  a  century 
ago,  and  to  ascertain  the  exact  bearing  of  his  experiments. 
But  Maxwell  entered  upon  this  undertaking  with  the  ut- 
most enthusiasm,  and  succeeded  in  identifying  himself  with 
Cavendish's  methods.  He  showed  that  Cavendish  had  really 
anticipated  several  of  the  discoveries  in  electrical  science 
which  have  been  made  since  his  time.  Cavendish  was  the 
first  to  form  the  conception  of  and  to  measure  Electrostatic 
Capacity  and  (Specific  Inductive  Capacity  ;  he  also  anticipated 
Ohm's  law." 

During  the  last  years  of  his  life  Mrs.  Maxwell  had 
a  serious  and  prolonged  illness,  and  Maxwell's  work 
was  much  increased  by  his  duties  as  sick  nurse.  On 
one  occasion  he  did  not  sleep  in  a  bed  for  three  weeks, 


and  Modern  physics.  89 

but   conducted  his   lectures  and  experiments  at  the 
laboratory  as  usual. 

About  this  time  some  of  those  who  had  been 
"Apostles"  in  1853-57  revived  the  habit  of  meeting 
together  for  discussion.  The  club,  which  included 
Professors  Lightfoot,  Hort  and  Westcott,  was  chris- 
tened the  "  Eranus,"  and  three  of  Maxwell's  contribu- 
tions to  it  have  been  preserved  and  are  printed  by 
Professor  Campbell. 

After  the  Cavendish  papers  were  finished,  Max- 
well had  more  time  for  his  own  original  researches, 
and  two  important  papers  were  published  in  1879. 
The  one  on  "  Stresses  in  Rarefied  Gases  arising  from 
Inequalities  of  Temperature "  was  printed  in  the 
Royal  Society's  Transactions,  and  deals  with  the 
Theory  of  the  Radiometer  ;  the  other  on  "  Boltzmann's 
Theorem  "  appears  in  the  Transactions  of  the  Cam- 
bridge Philosophical  Society.  In  the  previous  year 
he  had  delivered  the  Rede  lecture  on  "  The  Tele- 
phone." He  also  began  to  prepare  a  second  edition 
of  "  Electricity  and  Magnetism." 

His  health  gave  way  during  the  Easter  term  of 
1879  ;  indeed  for  two  years  previously  he  had  been 
troubled  with  dyspeptic  symptoms,  but  had  con- 
sulted no  one  on  the  subject.  He  left  Cambridge  as 
usual  in  June,  hoping  that  he  would  quickly  recover 
at  Glenlair,  but  he  grew  worse  instead.  In  October 
he  was  told  by  Dr.  Sanders  of  Edinburgh  that  he  had 
not  a  month  to  live.  He  returned  to  Cambridge  in 
order  to  be  under  the  care  of  Dr.  Paget,  wrho  was  able 
in  some  measure  to  relieve  his  most  severe  suffering 
but  the  disease,  of  which  his  mother  had  died  at  the 


90  JAMES   CLERK   MAXWELL 

same  age,  continued  its  progress,  and  he  died  on 
November  5th.  His  one  care  during  his  last  illness 
was  for  those  whom  he  left  behind.  Mrs.  Maxwell 
was  an  invalid  dependent  on  him  for  everything,  and 
the  thought  of  her  helplessness  was  the  one  thing 
which  in  these  last  days  troubled  him. 

A  funeral  service  took  place  in  the  chapel  at 
Trinity  College,  and  afterwards  his  remains  were  con- 
veyed to  Scotland  and  interred  in  the  family  burying- 
place  at  Corsock,  Kirkcudbright. 

A  memorial  edition  of  his  works  was  issued  by 
the  Cambridge  University  Press  in  1890.  A  portrait 
by  Lowes  Dickinson  hangs  in  the  hall  of  Trinity 
College,  and  there  is  a  bust  by  Boehm  in  the 
laboratory. 

After  his  death  Mrs.  Maxwell  gave  his  scientific 
library  to  the  Cavendish  Laboratory,  and  on  her 
death  she  left  a  sum  of  about  £G,000  to  found  a 
scholarship  in  Physics,  to  be  held  at  the  laboratory. 

The  preceding  pages  contain  some  account  of 
Clerk  Maxwell's  life  as  a  man  of  science.  His 
character  had  other  sides,  and  any  life  of  him 
would  be  incomplete  without  some  brief  reference  to 
these.  His  letters  to  his  wife  and  to  other  intimate 
friends  show  throughout  his  life  the  depth  of  his 
religious  convictions.  The  high  purpose  evidenced 
in  the  paper  given  to  the  present  Dean  of  Canterbury 
when  leaving  Cambridge,  animated  him  continually, 
and  appears  from  time  to  time  in  his  writings.  The 
student's  evening  hymn,  composed  in  1853  when  still 
an  undergraduate,  expresses  the  same  feelings — 


AND   MODERN   PHYSICS.  91 

Through  the  creatures  Thou  hast  made 

Show  the  brightness  of  Thy  glory, 
Be  eternal  truth  displayed 

In  their  substance  transitory, 
Till  green  earth  and  ocean  hoary, 

Massy  rock  and  tender  blade, 
Tell  the  same  unending  story, 

"  We  are  Truth  in  form  arrayed." 

Teach  me  so  Thy  works  to  read 

That  my  faith,  new  strength  accruing, 
May  from  world  to  world  proceed, 

Wisdom's  fruitful  search  pursuing, 
Till  Thy  breath  my  mind  imbuing, 

I  proclaim  the  eternal  creed, 
Oft  the  glorious  theme  renewing, 

God  our  Lord  is  God  indeed. 

His  views  on  the  relation  of  Science  to  Faith  are 
given  in  his  letter*  to  Bishop  Ellicott  already  referred 
to— 

"  But  I  should  be  very  sorry  if  an  interpretation  founded 
on  a  most  conjectural  scientific  hypothesis  were  to  get  fas- 
tened to  the  text  in  Genesis,  even  if  by  so  doing  it  got  rid  of 
the  old  statement  of  the  commentators  which  has  long  ceased 
to  be  intelligible.  The  rate  of  change  of  scientific  hypothesis 
is  naturally  much  more  rapid  than  that  of  Biblical  interpre- 
tations, so  that  if  an  interpretation  is  founded  on  such  an 
hypothesis,  it  may  help  to  keep  the  hypothesis  above  ground 
long  after  it  ought  to  be  buried  and  forgotten. 

"At  the  same  time  I  think  that  each  individual  man  should 

do  all  he  can  to  impress  his  own  mind  with  the  extent,  the 

order,  and  the  unity  of  the  universe,  and  should  carry  these 

ideas  with  him  as  he  reads  such  passages  as  the  1st  chapter  of 

the  Epistle  to  Colossians  (see  '  Lightfoot  on  Colossians,'  p.  182), 

just  as  enlarged  conceptions  of  the  extent  and  unity  of  the 

world  of  life  maybe  of  service  to  us  in  reading  Psalm  viii.. 

Heb.  ii.  6,  etc." 

*  "  Life  of  J.  C.  Maxwell,"  p.  394. 


92  JAMES   CLERK   MAXWELL 

And  again  in  his  letter*  to  the  secretary  of  the 
Victoria  Institute  giving  his  reasons  for  declining 
to  become  a  member — 

"  I  think  men  of  science  as  well  as  other  men  need  to  learn 
from  Christ,  and  I  think  Christians  whose  minds  are  scientific 
are  bound  to  study  science,  that  their  view  of  the  glory  of  God 
may  be  as  extensive  as  their  being  is  capable  of.  But  I  think 
that  the  results  which  each  man  arrives  at  in  his  attempts  to 
harmonise  his  science  with  his  Christianity  ought  not  to  be 
regarded  as  having  any  significance  except  to  the  man  himself, 
and  to  him  only  for  a  time,  and  should  not  receive  the  stamp 
of  a  society." 

Professor  Campbell  and  Mr.  Garnett  have  given 
us  the  evidence  of  those  who  were  with  him  in  his 
last  days,  as  to  the  strength  of  his  own  faith.  On  his 
death  bed  he  said  that  he  had  been  occupied  in 
trying  to  gain  truth  ;  that  it  is  but  little  of  truth  that 
man  can  acquire,  but  it  is  something  to  know  in 
whom  we  have  believed. 

*  "  Life  of  J.  C.  Maxwell,"  p.  404. 


AND   MODERN   THYSICS.  93 


CHAPTER    VII. 

SCIENTIFIC  WORK — COLOUR  VISION. 

Fifteen  years  only  have  passed  since  the  death  of 
Clerk  Maxwell,  and  it  is  almost  too  soon  to  hope 
to  form  a  correct  estimate  of  the  value  of  his  work 
and  its  relation  to  that  of  others  who  have  laboured 
in  the  same  field. 

Thus  Niven,  at  the  close  of  his  obituary  notice 
in  the  Proceedings  of  the  Royal  Society,  says :  "  It 
is  seldom  that  the  faculties  of  invention  and  exposi- 
tion, the  attachment  to  physical  science  and  capa- 
bility of  developing  it  mathematically,  have  been 
found  existing  in  one  mind  to  the  same  degree.  It 
would,  however,  require  powers  somewhat  akin  to 
Maxwell's  own  to  describe  the  more  delicate  features  of 
the  works  resulting  from  this  combination,  every  one 
of  which  is  stamped  with  the  subtle  but  unmistak- 
able impress  of  genius."  And  again  in  the  preface  to 
Maxwell's  works,  issued  in  1890,  he  wrote :  "  Nor 
does  it  appear  to  the  present  editor  that  the  time 
has  yet  arrived  when  the  quickening  influence  of 
Maxwell's  mind  on  modern  scientific  thought  can  be 
duly  estimated." 

It  is,  however,  the  object  of  the  present  series 
to  attempt  to  give  some  account  of  the  work  of  men 
of  science  of  the  last  hundred  years,  and  to  show  how 
each  has  contributed  his  share  to  our  present  stock  of 
knowledge.      This    task,  then,   remains    to   be   done. 


94  JAMES   CLERK   MAXWELL 

While  attempting  it  I  wish  to  express  my  indebted- 
ness to  others  who  have  already  written  about  Max- 
well's scientific  work,  especially  to  Mr.  W.  D.  Niven, 
whose  preface  to  the  Maxwell  papers  has  been  so  often 
referred  to ;  to  Mr.  Garnett,  the  author  of  Part  II. 
of  the  "  Life  of  Maxwell,"  which  deals  with  his  con- 
tributions to  science ;  and  to  Professor  Tait,  who  in 
Nature  for  February  5th,  18S0,  gave  an  account  of 
Clerk  Maxwell's  work,  "  necessarily  brief,  but  sufficient 
to  let  even  the  non-mathematical  reader  see  how 
very  great  were  his  contributions  to  modern  science  " 
— an  account  all  the  more  interesting  because,  again 
to  quote  from  Professor  Tait,  "  I  have  been  intimately 
acquainted  with  him  since  we  were  schoolboys 
together." 

Maxwell's  main  contributions  to  science  may  be 
classified  under  three  heads — "  Colour  Perception," 
"  Molecular  Physics,"  and  "  Electrical  Theories."  In 
addition  to  these  there  were  other  papers  of  the 
highest  interest  and  importance,  such  as  the  essay  on 
"  Saturn's  Rings,"  the  paper  on  the  "  Equilibrium  of* 
Elastic  Solids,"  and  various  memoirs  on  pure  geometry 
and  questions  of  mechanics,  which  would,  if  they  stood 
alone,  have  secured  for  their  author  a  distinguished 
position  as  a  physicist  and  mathematician,  but  which 
are  not  the  works  by  which  his  name  will  be  mostly 
remembered. 

The  work  on  "  Colour  Perception  "  was  begun  at 
an  early  date.  We  have  seen  Maxwell  while  still  at 
Edinburgh  interested  in  the  discussions  about  Hay's 
theories. 

His  first  published  paper  on  the  subject   was  a 


AND   MODERN   PHYSICS.  95 

letter  to  Dr.  G.  Wilson,  printed  in  the  Transactions  of 
the  Royal  Society  of  Arts  for  1855;  but  he  had  been 
mixing  colours  by  means  of  his  top  for  some  little  time 
previously,  and  the  results  of  these  experiments  are 
given  in  a  paper  entitled  "  Experiments  on  Colour," 
communicated  to  the  Royal  Society  of  Edinburgh 
by  Dr.  Gregory,  and  printed  in  their  Transactions, 
vol.  xxi. 

In  the  paper  on  "  The  Theory  of  Compound 
Colours,"  printed  in  the  Philosophical  Transactions 
for  1860,  Maxwell  gives  a  history  of  the  theory  as 
it  was  known  to  him. 

He  points  out  first  the  distinction  between  the 
optical  properties  and  the  chromatic  properties  of  a 
beam  of  light.  "The  optical  properties  are  those 
which  have  reference  to  its  origin  and  propagation 
through  media  until  it  falls  on  the  sensitive  organ  of 
vision ;  "  they  depend  on  the  periods  and  amplitudes 
of  the  ether  vibrations  which  compose  the  beam. 
"  The  chromatic  properties  are  those  which  have 
reference  to  its  power  of  exciting  certain  sensations  of 
colour  perceived  through  the  organ  of  vision."  It  is 
possible  for  two  beams  to  be  optically  very  different 
and  chromatically  alike.  The  converse  is  not  true ; 
two  beams  which  are  optically  alike  are  also  chroma- 
tically alike. 

The  foundation  of  the  theory  of  compound  colours 
was  laid  by  Newton.  He  first  shewed  that  "by  the 
mixture  of  homogeneal  light  colours  may  be  pro- 
duced which  are  like  to  the  colours  of  homoefeneal 
light  as  to  the  appearance  of  colour,  but  not  as  to  the 
immutability  of  colour  and  constitution  of  light."   Two 


96  JAMES   CLERK   MAXWELL 

beams  which  differ  optically  may  yet  be  alike  chroma- 
tically ;  it  is  possible  by  mixing  red  and  yellow  to 
obtain  an  orange  colour  chromatically  similar  to  the 
orange  of  the  spectrum,  but  optically  different  to  that 
orange,  for  the  compound  orange  can  be  analysed  by 
a  prism  into  its  component  red  and  yellow;  the 
spectrum  orange  is  incapable  of  further  resolution. 
Newton  also  solves  the  following  problem : — 
In  a  mixture  of  primary  colours,  the  quantity 
and  quality  of  each  being  given  to  know  the  colour 
of  the  compound  (Optics,  Book  1,  Part  2.  Prop.  6), 
and  his  solution  is  the  following : — He  arranges  the 
seven  colours  of  the  spectrum  round  the  circumfer- 
ence of  a  circle,  the  length  occupied  by  each  colour 
being  proportional  to  the  musical  interval  to  which, 
in  Newton's  views,  the  colour  corresponded.  At  the 
centre  of  gravity  of  each  of  these  arcs  he  supposes  a 
weight  placed  proportional  to  the  number  of  rays  of 
the  corresponding  colour  which  enter  into  the  mixture 
under  consideration.  The  position  of  the  centre  of 
gravity  of  these  weights  indicates  the  nature  of  the 
resultant  colour.  A  radius  drawn  through  this  centre 
of  gravity  points  out  the  colour  of  the  spectrum  which 
it  most  resembles;  the  distance  of  the  centre  of  gravity 
from  the  centre  gives  the  fulness  of  the  colour. 
The  centre  itself  is  white.  Newton  gives  no  proof 
of  this  rule  ;  he  merely  sa}Ts,  "  This  rule  I  conceive  to 
be  accurate  enough  for  practice,  though  not  mathe- 
matically accurate." 

Maxwell  proved  that  Newton's  method  of  finding 
the  centre  of  gravity  of  the  component  colours  was 
confirmed  by  his  observations,  and  that  it  involves 


AND    MODERN    PHYSICS.  ^>7 

mathematically  the  theory  of  three  elements  of  colour : 
but  the  disposition  of  the  colours  on  the  circle  was 
only  a  provisional  arrangement ;  the  true  relations 
of  the  colours  could  only  be  determined  by  direct 
experiment. 

Thomas  Young  appears  to  have  been  the  next,  after 
Newton,  to  work  at  the  theory  of  colour  sensation.  He 
made  observations  by  spinning  coloured  discs  much 
in  the  same  way  as  that  which  was  afterwards  adopted 
by  Maxwell,  and  he  developed  the  theory  that  three 
different  primary  sensations  may  be  excited  in  the  eye 
by  light,  while  the  colour  of  any  beam  depends  on 
the  proportions  in  which  these  three  sensations  are 
excited.  He  supposes  the  three  primary  sensations  to 
correspond  to  red,  green,  and  violet.  A  blue  ray  is 
capable  of  exciting  both  the  green  and  the  violet ;  a 
yellow  ray  excites  the  red  and  the  green.  Any  colour, 
according  to  Young's  theory,  may  be  matched  by  a 
mixture  of  these  three  primary  colours  taken  in  proper 
proportion ;  the  quality  of  the  colour  depends  on 
the  proportion  of  the  intensities  of  the  compon- 
ents; its  brightness  depends  on  the  sum  of  these 
intensities. 

Maxwell's  experiments  were  undertaken  with  the 
object  of  proving  or  disproving  the  physical  part  of 
Young's  theory.  He  does  not  consider  the  question 
whether  there  are  three  distinct  sensations  corre- 
sponding to  the  three  primary  colours ;  that  is  a 
physiological  inquiry,  and  one  to  which  no  completely 
satisfactory  answer  has  yet  been  given.  He  does  show 
that  by  a  proper  mixture  of  any  three  arbitrarily 
chosen  standard  colours  it  is  possible  to  match  any 


98  TAMES   CLERK    MAXWELL 

other  colour ;  the  words  "  proper  mixture,"  however, 
need,  as  will  appear  shortly,  some  development. 

We  may  with  advantage  compare  the  problem 
with  one  in  acoustics. 

When  a  compound  musical  note  consisting  of 
a  pure  tone  and  its  overtones  is  sounded,  the 
trained  ear  can  distinguish  the  various  overtones 
and  analyse  the  sound  into  its  simple  components. 
The  same  sensation  cannot  be  excited  in  two  different 
ways.  The  eye  has  no  such  corresponding  power. 
A  given  }^ellow  may  be  a  pure  spectral  yellow,  corre- 
sponding to  a  pure  tone  in  music,  or  it  may  be  a 
mixture  of  a  number  of  other  pure  tones ;  in  either 
case  it  can  be  matched  by  a  proper  combination  of 
three  standard  colours  —  this  Maxwell  proved.  It 
may  be,  as  Young  supposed,  that  if  the  three  standard 
colours  be  properly  selected  they  correspond  exactly 
to  three  primary  sensations  of  the  brain.  Maxwell's 
experiments  do  not  afford  any  light  on  this  point, 
which  still  remains  more  than  doubtful. 

When  Maxwell  began  his  work  the  theory  of 
colours  was  exciting  considerable  interest.  Sir  David 
Brewster  had  recently  developed  a  new  theory  of 
colour  sensation  which  had  formed  the  basis  of  some 
discussions,  and  in  1852  von  Helmholtz  published 
his  first  paper  on  the  subject.  According  to  Brewster, 
the  three  primitive  colours  were  red,  yellow  and  blue, 
and  he  supposed  that  they  corresponded  to  three 
different  kinds  of  objective  light.  Helmholtz  pointed 
out  that  experiments  up  to  that  date  had  been  con- 
ducted by  mixing  pigments,  with  the  exception  of  those 
in  which  the  rotating  disc  was  used,  and  that  it  is 


AND    MODERN    PHYSICS.  99 

necessary  to  make  them  on  the  rays  of  the  spectrin u 
itself.  He  then  describes  a  method  of  mixing  the 
light  from  two  spectra  so  as  to  obtain  the  combination 
of  every  two  of  the  simple  prismatic  rays  in  all 
degrees  of  relative  strength. 

From  these  experiments  results,  which  at  the  time 
were  unexpected,  but  some  of  which  must  have  been 
known  to  Young,  were  obtained.  Among  them  it 
was  shown  that  a  mixture  of  red  and  green  made 
yellow,  while  one  of  green  and  violet  produced  blue. 

In  a  later  paper  {Philosophical  Magazine,  1854) 
Helmholtz  described  a  method  for  ascertaining  the 
various  pairs  of  complementary  colours — colours,  that 
is,  which  when  mixed  will  give  white — which  had 
been  shown  by  Grassman  to  exist  if  Newton's  theory 
were  true.  He  also  gave  a  provisional  diagram  of 
the  curve  formed  by  the  spectrum,  which  ought  to 
take  the  place  of  the  circle  in  Newton's  diagram  ; 
for  this,  however,  his  experiments  did  not  give  the 
complete  data. 

Such  was  the  state  of  the  question  when  Maxwell 
began.  His  first  colour-box  was  made  in  1852. 
Others  were  designed  in  1855  and  1856,  and  the  final 
paper  appeared  in  1860.  But  before  that  time  he 
had  established  important  results  by  means  of  his 
rotatory  discs  and  colour  top.  In  his  own  description 
of  this  he  says :  "  The  coloured  paper  is  cut  into  the 
form  of  disc,  each  with  a  hole  in  the  centre  and 
divided  along  a  radius  so  as  to  admit  of  several  of 
them  being  placed  on  the  same  axis,  so  that  part  of 
each  is  exposed.  By  slipping  one  disc  over  another 
we  can  expose  any  given  portion  of  each  colour. 
g  2 


100  JAMES   CLERK    MAXWELL 

These  discs  are  placed  on  a  top  or  teetotum,  which 
is  spun  rapidly.  The  axis  of  the  top  passes  through 
the  centre  of  the  discs,  and  the  quantity  of  each 
colour  exposed  is  measured  by  graduations  on  the 
rim  of  the  top,  which  is  divided  into  100  parts. 
When  the  top  is  spun  sufficiently  rapidly,  the 
impressions  due  to  each  colour  separately  follow  each 
other  in  quick  succession  at  each  point  of  the  retina, 
and  are  blended  together;  the  strength  of  the  im- 
pression due  to  each  colour  is,  as  can  be  shown 
experimentally,  the  same  as  when  the  three  kinds  of 
light  in  the  same  relative  proportions  enter  the 
eye  simultaneously.  These  relative  proportions  are 
measured  by  the  areas  of  the  various  discs  which 
are  exposed.  Two  sets  of  discs  of  different  radius 
are  used ;  the  largest  discs  are  put  on  first,  then  the 
smaller,  so  that  the  centre  portion  of  the  top  shows 
the  colour  arising  from  the  mixture  of  those  of  the 
smaller  discs  ;  the  outer  portion,  that  of  the  larger 
discs." 

In  experimenting,  six  discs  of  each  size  are  used, 
black,  white,  red,  green,  yellow  and  blue.  It  is  found 
by  experiment  that  a  match  can  be  arranged  between 
any  five  of  these.  Thus  three  of  the  larger  discs  are 
placed  on  the  top — say  black,  yellow  and  blue — and 
two  of  the  smaller  discs,  red  and  green,  are  placed 
above  these.  Then  it  is  found  that  it  is  possible  so 
to  adjust  the  amount  exposed  of  each  disc  that  the  two 
parts  of  the  top  appear  when  it  is  spun  to  be  of  the 
same  tint.  In  one  series  of  experiments  the  chromatic 
effect  of  46-8  parts  of  black,  291  of  yellow,  and  24-1 
of  blue  was  found  to  be  the  same  as  that  of  GG'G  of 


AND   MODERN    PHYSICS.  101 

red  and  334  of  green  ;  each  set  of  discs  has  a  dirty 
yellow  tinge. 

Now,  in  this  experiment,  black  is  not  a  colour ; 
practically  no  light  reaches  the  eye  from  a  dead 
black.  We  have,  however,  to  fill  up  the  circumference 
of  the  top  in  some  way  Avhich  will  not  affect  the 
impression  on  the  retina  arising  from  the  mixture 
of  the  blue  and  yellow;  this  we  can  do  by  using 
the  black  disc. 

Thus  we  have  shown  that  66'6  parts  of  red  and 
334  parts  of  green  produce  the  same  chromatic  effect 
as  291  of  yellow  and  241  of  blue.  Similarly  in  this 
manner  a  match  can  be  arranged  between  any  four 
colours  and  black,  the  black  being  necessary  to 
complete  the  circumference  of  the  discs. 

Thus  using  A,  B,  C,  D  to  denote  the  various 
colours,  a,  b,  c,  d  the  amounts  of  each  colour  taken, 
we  can  get  a  series  of  results  expressed  as  follows: 
a  parts  of  A  together  with  b  parts  of  B  match  c  parts 
of  C  together  with  d  parts  of  D  ;  or  we  may  write  this 
as  an  equation  thus  : — 

aA  +  bB=cC  +  d  D, 

where  the  +  stands  for  "  combined  with,"  and  the  = 
for  "  matches  in  tint." 

We  may  also  write  the  above — 

dD=aA  +  bB-cG, 

or  (/  parts  of  D  can  be  matched  by  a  proper  combina- 
tion of  colours  A,  B,  C.  The  sign  -  shows  that  in 
order  to  make  the  match  we  have  to  combine  the 
colour  C  with  D ;  the  combination  then  matches 
a  mixture  of  A  and  B. 


102  JAMES   CLERK   MAXWELL 

In  this  way  we  can  form  a  number  of  equations 
for  all  possible  colours,  and  if  we  like  to  take  any 
three  colours  A,  B,  C  as  standards,  we  obtain  a  result 
which  may  be  written  generally — 

xX  =  aA  +  bB  +  c  C, 

or  x  parts  of  X  can  be  matched  by  a  parts  of  A, 
combined  with  b  parts  of  B  and  c  parts  of  C.  If  the 
sign  of  one  of  the  quantities  a,  b,  or  c  is  negative,  it 
indicates  that  that  colour  must  be  combined  with  X 
to  match  the  other  two. 

Now  Maxwell  was  able  to  show  that,  if  A,  B,  C 
be  properly  selected,  nearly  every  other  colour  can 
be  matched  by  positive  combinations  of  these 
three.  These  three  colours,  then,  are  primary  colours, 
and  nearly  every  other  colour  can  be  matched  by  a 
combination  of  the  three  primary  colours. 

Experiments,  however,  with  coloured  discs,  such 
as  were  undertaken  by  Young,  Forbes  and  Maxwell, 
were  not  capable  of  giving  satisfactory  results.  The 
colours  of  the  discs  were  not  pure  spectrum  colours, 
and  varied  to  some  extent  with  the  nature  of  the 
incident  light.  It  was  for  this  reason  that  Helmholtz 
in  1852  experimented  with  the  spectrum,  and  that 
Maxwell  about  the  same  time  invented  his  colour 
box. 

The  principle  of  the  latter  was  very  simple.  Sup- 
pose we  have  a  slit  S,  and  some  arrangement  for 
forming  a  pure  spectrum  on  a  screen.  Let  there 
now  be  a  slit  R  placed  in  the  red  part  of  the  spectrum 
on  the  screen.  When  light  falls  on  the  slit  S,  only 
the  red  rays  can  reach  R,  and  hence  conversely,  if  the 


AND   MODERN   PHYSICS.  103 

white  source  be  placed  at  the  other  end  of  the  appara- 
tus, so  that  R  is  illuminated  with  white  light,  only  red 
rays  will  reach  S.  Similarly,  if  another  slit  be  placed 
in  the  green  at  G,  and  this  be  illuminated  by  white 
light,  only  the  green  rays  will  reach  S,  while  from 
a  third  slit  V  in  the  violet,  violet  light  only  can 
arrive  at  S.  Thus  by  opening  the  three  slits  at  V, 
G  and  R  simultaneously,  and  looking  through  S,  the 
retina  receives  the  impression  of  the  three  different 
colours.  The  amount  of  light  of  each  colour  will 
depend  on  the  breadth  to  which  the  corresponding 
slit  is  opened,  and  the  relative  intensities  of  the  three 
different  components  can  be  compared  by  comparing 
the  breadths  of  the  three  slits.  Any  other  colour 
which  is  allowed,  by  some  suitable  contrivance  to 
enter  the  eye  simultaneously  can  now  be  matched, 
provided  the  red,  green  and  violet  are  primary 
colours. 

By  means  of  experiments  with  the  colour  box 
Maxwell  showed  conclusively  that  a  match  could  be 
obtained  between  any  four  colours ;  the  experiments 
could  not  be  carried  out  in  quite  the  simple  manner 
suggested  by  the  above  description  of  the  principle  of 
the  box.  An  account  of  the  method  will  be  found  in 
Maxwell's  own  paper.  It  consisted  in  matching  a 
standard  white  by  various  combinations  of  other 
colours. 

The  main  object  of  his  research,  however,  was 
to  examine  the  chromatic  properties  of  the  different 
parts  of  the  spectrum,  and  to  determine  the  form 
of  the  curve  which  ought  to  replace  the  circle  in 
Newton's  diagram  of  colour, 


104  JAMES    CLERK    MAXWELL 

Maxwell  adopted  as  his  three  standard  colours: 
red,  of  about  wave  length  0,302  ;  green,  wave  length 
5,281  ;  and  violet,  4,569  tenth  metres.  On  the  scale 
of  Maxwell's  instrument  these  are  represented  by  the 
numbers  24,  44  and  68. 

Let  us  take  three  points  A,  B,  C  at  the  corners 
of  an  equilateral  triangle  to  represent  on  a  diagram 
these  three  colours.  The  position  of  any  other  colour 
on  the  diagram  will  be  found  by  taking  weights 
proportional  to  the  amounts  of  the  colours  A,  B,  C 
required  to  make  the  match  between  A,  B,  C  and  the 
given  colour:  these  weights  are  placed  at  A,  B,  C 
respectively  ;  the  position  of  their  centre  of  gravity 
is  the  point  required.  Thus  the  position  of  white  is 
given  by  the  equation— 

W  =  18-6  (24)  +  31-4  (44)  +  I50-5  (68) 

which  means  that  weights  proportional  to  18  6,  31 '4 
and.  30  5  are  to  be  placed  at  A,  B,  C  respectively, 
and  their  centre  of  gravity  is  to  be  found.  The  point 
so  found  is  the  position  of  white.  Any  other  colour 
is  given  by  the  equation — 

X  =  a  (24)  +  b  (44)  +  c  (68). 

Again,  the  position  on  the  diagram  for  all  colours 
for  which  a,  b,  c  are  all  positive  lies  within  the 
triangle  A  B  C.  If  one  of  the  co-efficients,  say  c,  is 
negative  the  same  cons!  ruction  applies,  but  the 
weight  applied  at  C  must  be  treated  as  acting 
in  the  opposite  direction  to  those  at  A  and  B. 
A  mixture  of  the  given  colour  and  C  matches  a 
mixture  of  A  and  B.  It  is  clear  that  the  point 
corresponding  to  X  will  then  lie  outside  the  triangle 


AND    MODERN    I'lIVSK'S.  105 

A  I)  C.  Maxwell  showed  that,  with  his  standards, 
nearly  all  colours  could  be  represented  by  points 
inside  the  triangle.  The  colours  he  had  selected 
as  standards  were  very  close  to  primary  colours. 

Again,  he  proved  that  any  spectrum  colour  between 
red  and  green,  when  combined  with  a  very  slight 
admixture  of  violet,  could  be  matched,  in  the  case 
of  either  Mrs.  Maxwell  or  himself,  by  a  proper  mix- 
ture of  the  red  and  green.  The  positions,  therefore, 
of  the  spectrum  colours  between  red  and  green  lie 
just  outside  the  triangle  ABC,  being  very  close 
to  the  line  A  B,  while  for  the  colours  between  green 
and  violet  Maxwell  obtained  a  curve  lying  rather 
further  outside  the  side  B  C.  Any  spectrum  colour 
between  green  and  violet,  together  with  a  slight 
admixture  of  red,  can  be  matched  by  a  proper  mix- 
ture of  green  and  violet. 

Thus  the  circle  of  Newton's  diagram  should  be 
replaced  by  a  curve,  which  coincides  very  nearly 
with  the  two  sides  A  B  and  B  C  of  Maxwell's  figure. 

O 

Strictly,  according  to  his  observations,  the  curve  lies 
just  outside  these  two  sides.  The  purples  of  the 
spectrum  lie  nearly  along  the  third  side,  C  A,  of  the 
triangle,  being  obtained  approximately  by  mixing 
the  violet  and  the  red. 

To  find  the  point  on  the  diagram  corresponding 
to  the  colour  obtained  by  mixing  any  two  or  more 
spectrum  colours  we  must,  in  accordance  with  New- 
ton's rule,  place  weights  at  the  points  corresponding 
to  the  selected  colours,  and  find  the  centre  of  gravity 
of  these  weights. 

This,  then,  was  the  outcome  of  MaxAvell's  work  on 


106  JAMES   CLERK   MAXWELL 

colour.  It  verified  the  essential  part  of  Newton's 
construction,  and  obtained  for  the  first  time  the  true 
form  of  the  spectrum  curve  on  the  diagram. 

The  form  of  this  curve  Avill  of  course  depend 
on  the  eye  of  the  individual  observer.  Thus  Max- 
well and  Mrs.  Maxwell  both  made  observations,  and 
distinct  differences  were  found  in  their  eyes.  It 
appears,  however,  that  a  large  majority  of  persons 
have  normal  vision,  and  that  matches  made  by  one 
such  person  are  accepted  by  most  others  as  satis- 
factory. Some  peojole,  however,  are  colour  blind,  and 
Maxwell  examined  a  few  such.  In  the  case  of  those 
whom  he  examined  it  appeared  as  though  vision  was 
dichromatic,  the  red  sensation  seemed  to  be  absent ; 
nearly  all  colours  could  be  matched  by  combinations 
of  green  and  violet.  The  colour  diagram  was  reduced 
to  the  straight  line  B  C.  Other  forms  of  colour  blind- 
ness have  since  been  investigated. 

In  awarding  to  Maxwell  the  Rumford  medal  in 
1860,  Major-General  Sabine,  vice-president  of  the 
Royal  Society,  after  explaining  the  theory  of  colour 
vision  and  the  possible  method  of  verifying  it,  said : 
"Professor  Maxwell  has  subjected  the  theory  to  this 
verification,  and  thereby  raised  the  composition  of 
colours  to  the  rank  of  a  branch  of  mathematical 
physics,"  and  he  continues :  "  The  researches  for  which 
the  Rumford  medal  is  awarded  lead  to  the  remark- 
able result  that  to  a  very  near  degree  of  approxi- 
mation all  the  colours  of  the  spectrum,  and  therefore 
all  colours  in  nature  which  are  only  mixtures  of  these, 
can  be  perfectly  imitated  by  mixtures  of  three 
actually  attainable  colours,  which  are  the  red,  green 


AND   MODERN   PHYSICS.  107 

and  blue  belonging   respectively  to    three  particular 
parts  of  the  spectrum. 

It  should  be  noticed  in  concluding  our  remarks 
on  this  part  of  Maxwell's  Avork  that  his  results  are 
purely  physical.  They  are  not  inconsistent  with  the 
physiological  part  of  Young's  theory,  viz.,  that  there 
are  three  primary  sensations  of  colour  which  can  be 
transmitted  to  the  brain,  and  that  the  colour  of  any 
object  depends  on  the  relative  proportions  in  which 
these  sensations  are  excited,  but  they  do  not  prove 
that  theory.  Any  physiological  theory  which  can  be 
accepted  as  true  must  explain  Maxwell's  observations, 
and  Young's  theory  does  this  ;  but  it  is,  of  course, 
possible  that  other  theories  may  explain  them  equally 
well,  and  be  more  in  accordance  with  physiological 
observations  than  Young's.  Maxwell  has  given  us 
the  physical  facts  which  have  to  be  explained  ;  it  is 
for  the  physiologists  to  do  the  rest. 


10$  JAMES   CLERK   MAXWELL 


CHAPTER    VIII. 

SCIENTIFIC    WORK — MOLECULAR   THEORY. 

Maxwell  in  his  article  "Atom,"  in  the  ninth  edition  of 
the  Encyclopaedia  Britannica,  has  given  some  account 
of  Modern  Molecular  Science,  and  in  particular  of  the 
molecular  theory  of  gases.  Of  this  science,  Clausius 
and  Maxwell  are  the  founders,  though  to  their  names 
it  has  recently  been  shown  that  a  third,  that  of 
Waterston,  must  be  added.  In  the  present  chapter 
it  is  intended  to  give  an  outline  of  Maxwell's  contri- 
butions to  molecular  science,  and  to  explain  the 
advances  due  to  him. 

The  doctrine  that  bodies  are  composed  of  small 
particles  in  rapid  motion  is  very  ancient.  Democritus 
was  its  founder,  Lucretius — de  Rerum  Natura— ex- 
plained its  principles.  The  atoms  do  not  fill  space ; 
there  is  void  between. 

"  Quapropter  locus  e.st  intactus  inane  vacansque, 
Quod  si  non  esset,  nulla  ratione  moveri 
Res  possent ;  namque  officium  quod  corporis  extat 
Olficere  atqnc  obstare,  id  in  omni  tempore  adesset 
Omnibus.     Hand  igitur  quicquam  procedere  posset 
Principium  quoniam  cedendi  nulla  daret  res." 

According-  to  Boscovitch  an  atom  is  an  indivisible 
point,  having  position  in  space,  capable  of  motion,  and 
possessing  mass.  It  is  also  endowed  with  the  power 
of  exerting  force,  so  that  two  atoms  attract  or  repel 
each  other  with  a  force  depending  on  their  distance 


.VXD    MODERN    PHYSICS.  109 

apart.  It  has  no  parts  or  dimensions:  it  is  a  more 
geometrical  point  w ithout  extension  in  space :  it  has 
not  the  property  of  impenetrability,  for  two  atoms 
can,  it  is  supposed,  exist  at  the  same  point. 

In  modern  molecular  science  according  to 
Maxwell,  "  we  begin  by  assuming  that  bodies  are 
made  up  of  parts  each  of  which  is  capable  of  motion, 
and  that  these  parts  act  on  each  other  in  a  manner 
consistent  with  the  principle  of  the  conservation  of 
energy.  In  making  these  assumptions  we  are 
justified  by  the  facts  that  bodies  may  be  divided  into 
smaller  parts,  and  that  all  bodies  Avith  Avhich  we  are 
acquainted  are  conservative  systems,  which  would  not 
be  the  case  unless  their  parts  were  also  conservative 
systems. 

"  We  may  also  assume  that  these  small  parts  are  in 
motion.  This  is  the  most  general  assumption  we  can 
make,  for  it  includes  as  a  particular  case  the  theory 
that  the  small  parts  are  at  rest.  The  phenomena  of 
the  diffusion  of  gases  and  liquids  through  each  other 
show  that  there  may  be  a  motion  of  the  small  parts  of 
a  body  which  is  not  perceptible  to  us. 

"  We  make  no  assumption  with  respect  to  the 
nature  of  the  small  parts — whether  they  are  all  of 
one  magnitude.  We  do  not  even  assume  them  to 
have  extension  and  figure.  Each  of  them  must  be 
measured  by  its  mass,  and  any  two  of  them  must, 
like  visible  bodies,  have  the  power  of  acting  on  one 
another  when  they  come  near  enough  to  do  so.  The 
properties  of  the  body  or  medium  are  determined  by 
the  configuration  of  its  parts." 

These  small  particles  are  called  molecules,  and  a 


110  JAMES    CLERK   MAXWELL 

molecule   in    its    physical    aspect    was    defined    by 
Maxwell  in  the  following  terms  : — 

"  A  molecule  of  a  substance  is  a  small  body,  such  that  if,  on 
the  one  hand,  a  number  of  similar  molecules  were  assembled 
together,  they  would  form  a  mass  of  that  substance  ;  while  on 
the  other  hand,  if  any  portion  of  this  molecule  were  removed,  it 
would  no  longer  be  able,  along  with  an  assemblage  of  other 
molecules  similarly  treated,  to  make  up  a  mass  of  the  original 
substance." 

We  are  to  look  upon  a  gas  as  an  assemblage  of 
molecules  flying  about  in  all  directions.  The  path  of 
any  molecule  is  a  straight  line,  except  during  the 
time  when  it  is  under  the  action  of  a  neighbouring 
molecule  ;  this  time  is  usually  small  compared  with 
that  during  which  it  is  free. 

The  simplest  theory  we  could  formulate  would  be 
that  the  molecules  behaved  like  elastic  spheres,  and 
that  the  action  between  any  two  was  a  collision  follow- 
ing the  laws  which  Ave  know  apply  to  the  collision  of 
elastic  bodies.  If  the  average  distance  between  two 
molecules  be  great  compared  with  their  dimensions, 
the  time  during  which  any  molecule  is  in  collision 
will  be  small  compared  with  the  interval  between  the 
collisions,  and  this  is  in  accordance  with  the  funda- 
mental assumption  just  mentioned.  It  is  not, 
however,  necessary  to  suppose  an  encounter  between 
two  molecules  to  be  a  collision.  One  molecule  may 
act  on  another  with  a  force,  which  depends  on  the 
distance  between  them,  of  such  a  character  that  the 
force  is  insensible  except  when  the  molecules  are 
extremely  close  together. 

It  is  not  difficult  to  see  how  the  pressure  exerted 


AND    MODERN    PHYSICS.  Ill 

by  a  gas  on  the  sides  of  a  vessel  which  contains  it- 
may  be  accounted  for  on  this  assumption.  Each 
molecule  as  it  strikes  the  side  has  its  momentum 
reversed — the  molecules  arc  here  assumed  to  be 
perfectly  elastic. 

Thus  each  molecule  of  the  gas  is  continually 
gaining  momentum  from  the  sides  of  the  vessel,  while 
it  gives  up  to  the  vessel  the  momentum  which  it 
possessed  before  the  impact.  The  rate  at  which  this 
change  of  momentum  proceeds  across  a  given  area 
measures  the  force  exerted  on  that  area  ;  the  pressure 
of  the  gas  is  the  rate  of  change  of  momentum  per 
unit  of  area  of  the  surface. 

Again,  it  can  be  shown  that  this  pressure  is  pro- 
portional to  the  product  of  the  mass  of  each  molecule, 
the  number  of  molecules  in  a  unit  of  volume,  and 
the  square  of  the  velocity  of  the  molecules. 

Let  us  consider  in  the  first  instance  the  case  of  a 
jet  of  sand  or  water  of  unit  cross  section  which  is 
playing  against  a  surface.  Suppose  for  the  present 
that  all  the  molecules  which  strike  the  surface  have 
the  same  velocity. 

Then  the  number  of  molecules  which  strike  the 
surface  per  second,  will  be  proportional  to  this  velocity. 
If  the  particles  are  moving  quickly  they  can  reach  the 
surface  in  one  second  from  a  greater  distance  than  is 
possible  if  they  be  moving  slowly.  Again,  the  number 
reaching  the  surface  will  be  proportional  to  the 
number  of  molecules  per  unit  of  volume.  Hence,  if 
we  call  v  the  velocity  of  each  particle,  and  N  the 
number  of  particles  per  unit  of  volume,  the  number 
which  strike  the  surface  in  one  second  will  be  N  v ; 


112  JAMES   CLERK    MAXWELL 

if  m  be  the  mass  of  each  molecule,  the  mass  which 
strikes  the  surface  per  second  is  N  m  v ;  the  velocity 
of  each  particle  of  this  mass  is  v,  therefore  the 
momentum  destroyed  per  second  by  the  impact  is 
N  m  v  x  v,  or  N  m  v2,  and  this  measures  the  pressure. 
Hence  in  this  case  if  p  be  the  pressure 

p  =  N  m  u2. 

In  the  above  we  assume  that  all  the  molecules  in 
the  jet  are  moving'  with  velocity  v  perpendicular  to 
the  surface.  In  the  case  of  a  crowd  of  molecules 
flying  about  in  a  closed  space  this  is  clearly  not  true. 
The  molecules  may  strike  the  surface  in  any  direction  : 
they  will  not  all  be  moving  normal  to  the  surface. 
To  simplify  the  case,  consider  a  cubical  box  filled 
with  gas.  The  box  has  three  pairs  of  equal  faces  at 
right  angles.  We  may  suppose  one- third  of  the 
particles  to  be  moving  at  right  angles  to  each  face, 
and  in  this  case  the  number  per  unit  volume  which 
Ave  have  to  consider  is  not  N,  but  }  X.  Hence  the 
formula  becomes  p  =  ±  N  m  v". 

Moreover,  if  p  be  the  density  of  the  gas — that  is, 
the  mass  of  unit  volume — then  Nra  is  equal  to  p, 
for  m  is  the  mass  of  each  particle,  and  there  are  N 
particles  in  a  unit  of  volume. 

Hence,  finally,  p  =  }  p  v2. 

Or,  again,  if  V  be  the  volume  of  unit  mass  of  the 
gas,  then  p  V  is  unity,  or  p  is  equal  to  1/1'. 

Hence  ]>Y  =  %vl. 

Formula?  equivalent  to  these  appear  first  to  have 
been  obtained  by  Herapath  about  the  year  1816 
(Thomson's   "Annals    of    Philosophy,"    1816).      The 


AND   MODERN   PHYSICS.  113 

results  only,  however,  were  stated  in  that  year.  A 
paper  which  attempted  to  establish  them  was  pre- 
sented to  the  Royal  Society  in  1820.  It  gave  rise  to 
very  considerable  correspondence,  and  was  withdrawn 
by  the  author  before  being  read.  It  is  printed  in  full 
in  Thomson's  "  Annals  of  Philosophy  "  for  1821,  vol.  i., 
pp.  273,  340,  401.  The  arguments  of  the  author  are 
no  doubt  open  to  criticism,  and  are  in  many  points 
far  from  sound.  Still,  by  considering  the  problem  of 
the  impact  of  a  large  number  of  hard  bodies,  he 
arrived  at  a  formula  connecting  the  pressure  and 
volume  of  a  given  mass  of  gas  equivalent  to  that 
just  given.  These  results  are  contained  in  Proposi- 
tions viii.  and  ix.  of  Herapath's  paper. 

In  his  next  step,  however,  Herapath,  as  we  know 
now,  was  wrong.  One  of  his  fundamental  assumptions 
is  that  the  temperature  of  a  gas  is  measured  by  the 
momentum  of  each  of  its  particles.  Hence,  assuming 
this,  we  have  T  =  m  u,  if  T  represents  the  tempera- 
ture; and 

p  =  £  N  m  v~  =  i  N  tm  v)\ 

in 

Or,  again — 

These  results  are  practically  given  in  Proposition  viii., 
Gorr.  (1)  and  (2),  and  Proposition  ix.*     The  tempera- 

*  In  his  "  Hydrodynamics,"  published  in  1738,  Daniel  Bernouilli 
had  discussed  the  constitution  of  a  gas,  and  had  proved  from  general 
considerations  that  the  pressure,  if  it  arose  from  the  impact  of  a 
number  of  moving  particles,  must  be  proportional  to  the  square 
f)f  their  velocity.  (See  "Fogg.  Ann.,"  Bd.  107,  1859,  p.  490.) 
H 


114  JAMES    CLERK    MAXWELL 

tu re  as  thus  defined  by  Herapath  is  an  absolute 
temperature,  and  lie  calculates  the  absolute  zero  of 
temperature  at  which  the  gas  would  have  no  volume 
from  the  above  results.  The  actual  calculation  is  of 
course  wrong,  for,  as  we  know  now  by  experiment,  the 
pressure  is  proportional  to  the  temperature,  and  not 
to  its  square,  as  Herapath  supposed.  It  will  be  seen, 
however,  that  Herapath's  formula  gives  Boyle's  law : 
for  if  the  temperature  is  constant,  the  formula  is 
equivalent  to 

p  V  =  a  constant. 

Herapath  somewhat  extended  his  work  in  his 
"  Mathematical  Physics "  published  in  1847,  and 
applied  his  principles  to  explain  diffusion,  the  relation 
between  specific  heat  and  atomic  weight,  and  other 
properties  of  bodies.  He  still,  however,  retained  his 
erroneous  supposition  that  temperature  is  to  be 
measured  by  the  momentum  of  the  individual 
particles. 

The  next  step  in  the  theory  was  made  by 
Waterston.  His  paper  was  read  to  the  Royal  Society 
on  March  5th,  1846.  It  was  most  unfortunately 
committed  to  the  Archives  of  the  Society,  and  was 
only  disinterred  by  Lord  Rayleigh  in  1892  and 
printed  in  the  Transactions  for  that  year. 

In  the  account  just  given  of  the  theory,  it  has 
been  supposed  that  all  the  particles  move  with  the 
same  velocity.  This  is  clearly  not  the  case  in  a  gas. 
If  at  starting  all  the  particles  had  the  same  velocity, 
the  collisions  would  change  this  state  of  affairs.  Some 
particles  will  be  moving  quickly,  some  slowly.  We  may, 


AND    MODERN    PHYSICS.  115 

however,  still  apply  the.  theory  by  splitting  up  the 
particles  into  groups,  and,  supposing  that  each  group 
has  a  constant  velocity,  the  particles  in  this  group 
will  contribute  to  the  pressure  an  amount — pl — equal 
to  I  N,  m  iy2,  where  c,  is  the  velocity  of  the  group 
and  N\  the  number  of  particles  having  that  velocity. 
The  whole  pressure  will  be  found  by  adding  that  due 
to  the  various  groups,  and  will  be  given  as  before  by 
p  =  I  N  m  v~,  where  v  is  not  now  the  actual  velocity 
of  the  particles,  but  a  mean  velocity  given  by  the 
equation 

N  v°<  =  Nt  V  +  N2  v2~  + , 

which  will  produce  the  same  pressure  as  arises  from 
the  actual  impacts.  This  quantity  v2  is  known  as  the 
mean  square  of  the  molecular  velocity,  and  is  so  used 
by  Waterston. 

In  a  paper  in  the  Philosophical  Magazine  for 
1858  Waterston  gives  an  account  of  his  own  paper 
of  1846  in  the  following  terms: — "Mr.  Herapath 
unfortunately  assumed  heat  or  temperature  to  be 
represented  b}^  the  simple  ratio  of  the  velocity  instead 
of  the  square  of  the  velocity,  being  in  this  apparently 
led  astray  by  the  definition  of  motion  generally  re- 
ceived, and  thus  was  baffled  in  his  attempts  to 
reconcile  his  theory  with  observation.  If  we  make 
this  change  in  Mr.  Herapath's  definition  of  heat  or 
temperature — viz.,  that  it  is  proportional  to  the  vis- 
viva  or  square  velocity  of  the  moving  particle,  not  to 
the  momentum  or  simple  ratio  of  the  velocity — we 
can  without  much  difficulty  deduce  not  only  the 
primary   laws   of  elastic    fluids,   but   also   the   other 

H   2 


116  JAMES   CLERK   MAXWELL 

physical  properties  of  gases  enumerated  above  in  the 
third  objection  to  Newton's  hypothesis.  [The  paper 
from  which  the  quotation  is  taken  is  on  '  The  Theory 
of  Sound.']  In  the  Archives  of  the  Royal  Society  for 
1845-46  there  is  a  paper  on  '  The  Physics  of  Media 
that  consist  of  perfectly  "  Elastic  Molecules  in  a 
State  of  Motion,"  which  contains  the  synthetical 
reasoning  on  which  the  demonstration  of  these 
matters  rests.  .  .  .  This  theory  does  not  take 
account  of  the  size  of  the  molecules.  It  assumes 
that  no  time  is  lost  at  the  impact,  and  that  if  the 
impacts  produce  rotatory  motion,  the  vis  viva  thus 
invested  bears  a  constant  ratio  to  the  rectilineal  vis 
viva,  so  as  not  to  require  separate  consideration.  It 
does,  also,  not  take  account  of  the  probable  internal 
motion  of  composite  molecules ;  yet  the  results  so 
closely  accord  with  observation  in  every  part  of  the 
subject  as  to  leave  no  doubt  that  Mr.  Herapath's  idea 
of  the  physical  constitution  of  gases  approximates 
closely  to  the  truth." 

In  his  introduction  to  Waterston's  paper  (Phil. 
Trans.,  1892)  Lord  Rayleigh  writes: — "Impressed 
with  the  above  passage,  and  with  the  general  in- 
genuity and  soundness  of  Waterston's  views,  I  took 
the  first  opportunity  of  consulting  the  Archives,  and 
saw  at  once  that  the  memoir  justified  the  large  claims 
made  for  it,  and  that  it  marks  an  immense  advance 
in  the  direction  of  the  now  generally  received  theory." 
In  the  first  section  of  the  paper  Waterston's  great 
advance  consisted  in  the  statement  that  the  mean 
square  of  the  kinetic  energy  of  each  molecule 
measures  the  temperature. 


AND    MODERN    PHYSICS.  117 

According  to  this  we  are  thus  to  put  in  the  pres- 
sure equation — |  m  v2  =  T,  the  temperature,  and  Ave 
have  at  once — p  V  =  f  N  ■  T. 

Now  this  equation  expresses,  as  we  know,  the 
laws  of  Boyle  and  Gay  Lussac. 

The  second  section  discusses  the  properties  of 
media,  consisting  of  two  or  more  gases,  and  arrives  at 
the  result  that  "  in  mixed  media  the  mean  square 
molecular  velocity  is  inversely  proportional  to  the 
specific  weights  of  the  molecules."  This  was  the 
great  law  rediscovered  by  Maxwell  fifteen  years  later. 
With  modern  notation  it  may  be  put  thus : — If 
ut1.  m2  be  the  masses  of  each  molecule  of  two  dif- 
ferent sots  of  molecules  mixed  together,  then,  when 
a  steady  state  has  been  reached,  since  the  temperature 
is  the  same  throughout,  mj  v,2  is  equal  to  m3  v2z.  The 
average  kinetic  energy  of  each  molecule  is  the  same. 

From  this  Avogadros'  law  follows  at  once — for  if 
pu  lh  ^e  ,jh°  pressures,  N,,  N2  the  numbers  of  molecules 
per  unit  volume  — 

ih  =  3  Ni  »h  v:\ 

Pi  =    a  N.,  m:i  i\/. 

Hence,  if  pl  is  equal  to  p.,,  since  m.L  v?  is  equal  to 
•in.-,  v.f,  we  must  have  Nx  equal  to  N3,  or  the  number 
of  molecules  in  equal  volumes  of  two  gases  at  the 
same  pressure  and  temperature  is  the  same.  The 
proof  of  this  proposition  given  by  Waterston  is  not 
satisfactory.  On  this  point,  however,  we  shall  have 
more  to  say.  The  third  section  of  the  paper  deals  with 
adiabatic expansion, and  in  it  there  is  an  error  in  calcula- 
tion which  prevented  correct  results  from  being  attained. 


118  JAMES    CLERK    .MAXWELL 

At  the  meeting  of  the  British  Association  at 
Ipswich,  in  1851,  a  paper  by  J.  J.  Waterston  of 
Bombay,  on  "  The  General  Theory  of  Gases,"  was  read. 
The  following  is  an  extract  from  the  Proceedings  : — 

The  author  "  conceives  that  the  atoms  of  a  gas, 
being  perfectly  elastic,  are  in  continual  motion  in  all 
directions,  being  constrained  Avithin  a  limited  space 
by  their  collisions  with  each  other,  and  with  the 
particles  of  surrounding  bodies. 

"  The  vis  viva  of  these  motions  in  a  given  portion 
of  a  gas  constitutes  the  quantity  of  heat  contained 
in  it. 

"  He  shows  that  the  result  of  this  state  of  motion 
must  be  to  give  the  gas  an  elasticity  proportional 
to  the  mean  square  of  the  velocity  of  the  molecular 
motions,  and  to  the  total  mass  of  the  atoms  contained 
in  unity  of  bulk-'  (unit  <»i  volume) — that  is  to  say,  to 
the  density  of  the  medium. 

"The  elasticity  in  a  given  gas  is  the  measure 
of  temperature.  Equilibrium  of  pressure  and  heat 
between  two  gases  takes  place  when  the  number 
of  atoms  in  unit  of  volume  is  equal  and  the  vis 
viva  of  each  atom  equal.  Temperature,  therefore, 
in  all  gases  is  proportional  to  the  mass  of  one  atom 
multiplied  by  the  mean  square  of  the  velocity  of  the 
molecular  motions,  being  measured  from  an  absolute 
zero  491°  below  the  zero  of  Fahrenheit's  ther- 
mometer." 

It  appears,  therefore,  from  these  extracts  that  the 
discovery  of  the  laws  that  temperature  is  measured  by 
the  mean  kinetic  energy  of  a  single  molecule,  and 
that  in  a  mixture  of  gases  the  mean  kinetic  energy  of 


\NJ>    .MODERN    PHYSICS.  L19 

each  molecule  is  the  same  for  each  gas,  is  due  to 
Waterston.  They  were  contained  in  his  paper  of 
1846,  and  published  by  him  in  1851.  Both  these 
papers,  however,  appear  to  have  been  unnoticed  by 
all  subsequent  writers  until  1892. 

Meanwhile,  in  1848,  Joule's  attention  Avas  called 
by  his  experiments  to  the  question,  and  he  saw  that 
Herapath's  result  gave  a  means  of  calculating  the 
mean  velocity  of  the  molecules  of  a  gas.  For  ac- 
cording to  the  result  given  above,  p  —  I  p  v~ ;  thus 
v"  =  3  p/p,  and  p  and  p  being  known,  we  find  t>3.  Thus 
for  hydrogen  at  freezing-point  and  atmospheric  pres- 
sure Joule  obtains  for  v  the  value  6,055  feet  per  second, 
or,  roughly,  six  times  the  velocity  of  sound  in  air. 

Clausius  was  the  next  writer  of  importance  on  the 
subject.  His  first  paper  is  in  "  Foggendorff's  Anna- 
len,"  vol.  c,  1857,  "  On  the  Kind  of  Motion  we  call 
Heat.''  It  gives  an  exposition  of  the  theory,  and 
establishes  the  fact  that  the  kinetic  energy  of  the 
translatory  motion  of  a  molecule  does  not  represent 
the  whole  of  the  heat  it  contains.  If  we  look  upon 
;i  molecule  as  a  small  solid  we  must  consider  the 
energy  it  possesses  in  consequence  of  its  rotation 
ubout  its  centre  of  gravity,  as  well  as  the  energy  due 
to  the  motion  of  translation  of  the  whole. 

Clausius'  second  paper  appeared  in  1859.  In  it 
he  considers  the  average  length  of  the  path  of  a 
molecule  during  the  interval  between  two  collisions. 
He  determines  this  path  in  terms  of  the  average 
distance  between  the  molecules  and  the  distance 
between  the  centres  of  two  molecules  at  the  time 
when  a  collision  is  taking  place. 


120  JAMES   CLERK    MAXWELL 

These  two  papers  appear  to  have  attracted  Max- 
well's attention  to  the  matter,  and  his  first  paper, 
entitled  "  Illustrations  of  the  Dynamical  Theory  of 
Gases,"  was  read  to  the  British  Association  at  Aber- 
deen and  Oxford  in  1859  and  1860,  and  appeared  in 
the  Philosophical  Magazine,  January  and  July,  1860. 

In  the  introduction  to  this  paper  Maxwell  points 
out,  while  there  was  then  no  means  of  measuring  the 
quantities  which  occurred  in  Clausius'  expression  for 
the  mean  free  path,  "  the  phenomena  of  the  internal 
friction  of  gases,  the  conduction  of  heat  through  a  gas, 
and  the  diffusion  of  one  gas  through  another,  seem  to 
indicate  the  possibility  of  determining  accurately  the 
mean  length  of  path  which  a  particle  describes  between 
two  collisions.  In  order,  therefore,  to  lay  the  founda- 
tion of  such  investigations  on  strict  mechanical  prin- 
ciples," he  continues,  "  I  shall  demonstrate  the  laws 
of  motion  of  an  indefinite  number  of  small,  hard  and 
perfectly  elastic  spheres  acting  on  one  another  only 
during  impact/' 

Maxwell  then  proceeds  to  consider  in  the  first  case 
the  impact  of  two  spheres. 

But  a  gas  consists  of  an  indefinite  number  of 
molecules.  Now  it  is  impossible  to  deal  with  each 
molecule  individually,  to  trace  its  history  and  follow 
its  path.  In  order,  therefore,  to  avoid  this  difficulty 
Maxwell  introduced  the  statistical  method  of  dealing 
with  such  problems,  and  this  introduction  is  the  first 
great  step  in  molecular  theory  with  which  his  name 
is  connected. 

He  was  led  to  this  method  by  his  investigation 
into  the  theoiy  of  Saturn's  rings,  which  had  been  com- 


AND   MODERN    PHYSICS.  121 

pletert  in  185G,  and  in  which  he  had  shown  that  the 
conditions  of  stability  required  the  supposition  that 
the  rings  are  composed  of  an  indefinite  number  of  free 
particles  revolving  round  the  planet,  with  velocities 
depending  on  their  distances  from  the  centre.  These 
particles  may  either  be  arranged  in  separate  rings,  or 
their  motion  may  be  such  that  they  are  continually 
coming  into  collision  with  each  other. 

As  an  example  of  the  statistical  method,  let  us 
consider  a  crowd  of  people  moving  along  a  street. 
Taken  as  a  whole  the  crowd  moves  steadily  forwards. 
Any  individual  in  the  crowd,  however,  is  jostled  back- 
wards and  forwards  and  from  side  to  side  ;  if  a  line 
were  drawn  across  the  street  we  should  find  people 
crossing  it  in  both  directions.  In  a  considerable  in- 
terval  more  people  would  cross  it,  going  in  the  direc- 
tion in  which  the  crowd  is  moving,  than  in  the  other. 
and  the  velocity  of  the  crowd  might  be  estimated 
by  counting  the  number  which  crossed  the  line  in 
a  given  interval.  This  velocity  so  found  would  differ 
greatly  from  the  velocity  of  any  individual,  which 
might  have  any  value  within  limits,  and  which  is 
continually  changing.  If  we  knew  the  velocity  of 
each  individual  and  the  number  of  individuals  we 
could  calculate  the  average  velocity,  and  this  would 
agree  with  the  value  found  by  counting  the  resultant 
number  of  people  who  cross  the  line  in  a  given  in- 
terval. 

Again,  the  people  in  the  crowd  will  naturally  fall 
into  groups  according  to  their  velocities.  At  any 
moment  there  will  be  a  certain  number  of  people 
whose  velocities  are  all   practically  equal,  or,    to  be 


122  JAMES    CLERK    MAXWELL 

more  accurate,  do  not  differ  among  themselves  by 
more  than  some  small  quantity.  The  number  of 
people  at  any  moment  in  each  of  these  groups  will 
be  very  different.  The  number  in  any  group,  which 
has  a  velocity  not  differing  greatly  from  the  mean 
velocity  of  the  whole,  will  be  large  ;  comparatively  few 
will  have  either  a  very  large  or  a  very  small  velocity. 

Again,  at  any  moment,  individuals  are  changing 
from  one  group  to  another ;  a  man  is  brought  to 
a  stop  by  some  obstruction,  and  his  velocity  is  con- 
siderably altered — he  passes  from  one  group  to  a 
different  one  ;  but  while  this  is  so,  if  the  mean  velocity 
remains  constant,  and  the  size  of  the  crowd  be  very 
great,  the  number  of  people  at  any  moment  in  a 
given  group  remains  unchanged.  People  pass  from 
that  group  into  others,  but  during  any  interval  the 
same  number  pass  back  again  into  that  group. 

It  is  clear  that  if  this  condition  is  satisfied  the 
distribution  is  a  steady  one,  and  the  crowd  will  continue 
to  move  on  with  the  same  uniform  mean  velocity. 

Now,  Maxwell  applies  these  considerations  to  a 
crowd  of  perfectly  elastic  spheres,  moving  anyhow  in 
a  closed  space,  acting  upon  each  other  only  when 
in  contact.  He  shows  that  they  may  be  divided  into 
groups  according  to  their  velocities,  and  that,  when 
the  steady  state  is  reached,  the  number  in  each  group 
will  remain  the  same,  although  the  individuals  change. 
Moreover,  it  is  shown  that,  if  A  and  B  represent  any 
two  groups,  the  state  will  only  be  steady  when  the 
numbers  which  pass  from  the  group  A  to  the  group 
B  are  equal  to  the  numbers  which  pass  back  from  the 
group  B  to  the  group  A.     This  condition,  combined 


AND    MODERN    PHYSICS.  123 

with  the  fact  that  the  total  kinetic  energy  of  the 
motion  remains  unchanged,  enables  him  to  calculate 
the  number  of  particles  in  any  group  in  terms  of  the 
whole  number  of  particles,  the  mean  velocity,  and  the 
actual  velocity  of  the  group. 

From  this  an  accurate  expression  can  be  found  for 
the  pressure  of  the  gas,  and  it  is  proved  that  the  value 
found  by  others,  on  the  assumption  that  all  the 
particles  were  moving  with  a  common  velocity,  is 
correct.  Previous  to  this  paper  of  Maxwell's  it  had 
been  realised  that  the  velocities  could  not  be  uniform 
throughout.  There  had  been  no  attempt  to  determine 
the  distribution  of  velocity,  or  to  submit  the  problem 
to  calculation,  making  allowance  for  the  variations  in 
velocity. 

Maxwell's  mathematical  methods  are,  in  their 
generality  and  elegance,  far  in  advance  of  anything 
previously  attempted  in  the  subject. 

So  far  it  has  been  assumed  that  the  particles  in  the 
vessel  are  all  alike.  Maxwell  next  takes  the  case  of 
a  mixture  of  two  kinds  of  particles,  and  inquires  what 
relation  must  exist  between  the  average  velocities  of 
these  different  particles,  in  order  that  the  state  may 
be  steady. 

Now,  it  can  be  shown  that  when  two  elastic  spheres 
impinge  the  effect  of  the  impact  is  always  such  as  to 
reduce  the  difference  between  their  kinetic  energies. 

Hence,  after  a  very  large  number  of  impacts  the 
kinetic  energies  of  the  two  balls  must  be  the  same  : 
the  steady  state,  then,  will  be  reached  when  each  ball 
has  the  same  kinetic  energy. 

Thus  if  mu  m*  be  the  masses  of  the  particles  in 


124  JAMES    CLERK    MAXWELL 

the  two  sets  respectively,  vu  >\,  their  mean  velocities 
we  must  have  finally — 

i  »?!  v*  =  %  m2  v,~ 

This  is  the  second  of  the  two  great  laws  enunciated 
by  Waterston  in  1845  and  1851,  but  which,  as  we 
have  seen,  had  remained  unknown  until  1859,  when 
it  was  again  given  by  Maxwell. 

Now,  when  gases  are  mixed  their  temperatures 
become  equal.  Hence  we  conclude,  in  Maxwell's 
words,  "  that  the  physical  condition  which  determines 
that  the  temperature  of  two  gases  shall  be  the  same, 
is  that  the  mean  kinetic  energy  of  agitation  of  the 
individual  molecules  of  the  two  gases  are  equal." 

Thus,  as  the  result  of  Maxwell's  more  exact  re- 
searches on  the  motion  of  a  system  of  spherical 
particles,  we  find  that  we  again  can  obtain  the 
equations — 


T  =*«!»» 

p  =  i  Nmi)3   = 

|  NT  = 

T 

From  these  results  we  obtain  as  before  the  laws  of 
Boyle,  Charles  and  Avrogadro. 

Again  if  u  be  the  specific  heat  of  the  gas  at 
constant  volume,  the  quantity  of  heat  required  to 
raise  a  single  molecule  of  mass  m  one  degree  will  be 
a  m. 

Thus,  when  a  molecule  is  heated,  the  kinetic 
energy  must  increase  by  this  amount.  But  the 
increase  of  temperature,  which  in  this  case  is  1°,  is 
measured  by  the   increase   of  kinetic  energy  of  the 


AND    MODERN    THYSICS.  125 

single  molecule.  Hence  the  amount  of  heat  required 
to  raise  the  temperature  of  a  single  molecule  of  all 
gases  1°  is  the  same.  Thus  the  quantity  <r  m  is 
the  same  for  all  gases ;  or,  in  other  words,  the 
specific  heat  of  a  gas  is  inversely  proportional  to  the 
mass  of  its  individual  molecules.  The  density  of  a 
gas — since  the  number  of  molecules  per  unit  volume 
at  a  given  pressure  and  temperature  is  the  same  for 
all  gases — is  also  proportional  to  the  mass  of  each  in- 
dividual molecule.  Thus  the  specific  heats  of  all  gases 
are  inversely  proportional  to  their  densities.  This 
is  the  law  discovered  experimentally  by  Dulong  and 
Petit  to  be  approximately  true  for  a  large  number  of 
substances. 

In  the  next  part  of  the  paper  Maxwell  proceeded 
to  determine  the  average  number  of  collisions  in  a 
given  time,  and  hence,  knowing  the  velocities,  to 
determine,  in  terms  of  the  size  of  the  particles  and 
their  numbers,  the  mean  free  path  of  a  particle  ;  the 
result  so  found  differed  somewhat  from  that  already 
obtained  by  Clausius. 

Having  done  this  he  showed  how,  by  means  of 
experiments  on  the  viscosity  of  gases,  the  length  of 
the  mean  free  path  could  be  determined. 

An  illustration  due  to  Professor  Balfour  Stewart 
will  perhaps  make  this  clear.  Let  us  suppose  we 
have  two  trains  running  with  uniform  speed  in 
opposite  directions  on  parallel  lines,  and,  further,  that 
the  engines  continue  to  work  at  the  same  rate, 
developing  just  sufficient  energy  to  overcome  the 
resistance  of  the  line,  etc..  and  to  maintain  the  speed 


126  JAMES   CLERK   MAXWELL 

constant,  Now  suppose  passengers  commence  to 
jump  across  from  one  train  to  the  other.  Each  man 
carries  with  him  his  own  momentum,  which  is  in  the 
opposite  direction  to  that  of  the  train  into  which  he 
jumps ;  the  result  is  that  the  momentum  of  each 
train  is  reduced  by  the  process ;  the  velocities  of  the 
two  decrease ;  it  appears  as  though  a  frictional  force 
were  acting  between  the  two.  Maxwell  suggests  that 
a  similar  process  will  account  for  the  apparent 
viscosity  of  gases. 

Consider  two  streams  of  gas,  moving  in  opposite 
directions  one  over  the  other  ;  it  is  found  that  in 
each  case  the  layers  of  gas  near  the  separating  sur- 
face move  more  slowly  than  those  in  the  interior  of 
the  streams  ;  there  is  apparently  a  frictional  force 
between  the  two  streams  along  this  surface,  tending 
to  reduce  their  relative  velocity.  Maxwell's  explana- 
tion of  this  is  that  at  the  common  surface  particles 
from  the  one  stream  enter  the  other,  and  carry  with 
them  their  own  momentum ;  thus  near  this  surface 
the  momentum  of  each  stream  is  reduced,  just  as  the 
momentum  of  the  trains  is  reduced  by  the  people 
jumping  across.  Internal  friction  or  viscosity  is  due 
to  the  diffusion  of  momentum  across  this  common 
surface.  The  effect  does  not  penetrate  far  into  the 
gas,  for  the  particles  soon  acquire  the  velocity  of  the 
stream  to  which  they  have  come. 

Now,  the  rate  at  Avhich  the  momentum  is  diffused 
will  measure  the  frictional  force,  and  will  depend  on 
the  mean  free  path  of  the  particles.  If  this  is  consider- 
able, so  that  on  the  average  a  particle  can  penetrate  a 
considerable  distance  into  the   second   gas   before  a 


AND    MODERN    PHYSICS.  127 

collision  takes  place  and  its  motion  is  changed,  the 
viscosity  will  be  considerable;  if,  on  the  other  hand, 
the  mean  free  path  is  small,  the  reverse  will  be  true. 
Thus  it  is  possible  to  obtain  a  relation  between 
the  mean  free  path  and  the  coefficient  of  viscosity, 
and  from  this,  if  the  coefficient  of  viscosity  be  known, 
a  value  for  the  mean  free  path  can  be  found. 

Maxwell,  in  the  paper  under  discussion,  was  the 
first  to  do  this,  and,  using  a  value  found  by  Professor 
Stokes  for  the  coefficient  of  viscosity,  obtained  as  the 
length  of  the  mean  free  path  of  molecules  of  air 
n^-  of  an  inch,  while  the  number   of  collisions  per 

44(000  '  *- 

second  experienced  by  each  molecule  is  found  to  be 
about  8,077,200,000. 

Moreover,  it  appeared  from  his  theory  that  the  co- 
efficient of  viscosity  should  be  independent  of  the 
number  of  molecules  of  gas  present,  so  that  it  is  not 
altered  by  varying  the  density.  This  result  Maxwell 
characterises  as  startling,  and  he  instituted  an  elaborate 
series  of  experiments  a  few  years  later  with  a  view  of 
testing  it.  The  reason  for  this  result  will  appear  if 
we  remember  that,  when  the  density  is  decreased,  the 
mean  free  path  is  increased  ;  relatively,  then,  to  the 
total  number  of  molecules  present,  the  number  which 
cross  the  surface  in  a  given  time  is  increased.  And  it 
appears  from  Maxwell's  result  that  this  relative  in- 
crease is  such  that  the  total  number  crossing  remains 
unchanged.  Hence  the  momentum  conveyed  across 
each  unit  area  per  second  remains  the  same,  in  spite 
of  the  decrease  in  density. 

Another  consequence  of  the  same  investigation  is 
that  the  coefficient  of  viscosity  is  proportional  to  the 


128  JAMES    CLERK    MAXWELL 

mean  velocity  of  the  molecules.  Since  the  absolute 
temperature  is  proportional  to  the  square  of  the 
velocity,  it  follows  that  the  coefficient  of  viscosity  is 
proportional  to  the  square  root  of  the  absolute 
temperature. 

The  second  part  of  the  paper  deals  with  the 
process  of  diffusion  of  two  or  more  kinds  of  moving 
particles  among  one  another. 

If  two  different  gases  are  placed  in  two  vessels 
separated  by  a  porous  diaphragm  such  as  a  piece  of 
unglazed  earthenware,  or  connected  by  means  of  a 
narrow  tube,  Graham  had  shewn  that,  after  sufficient 
time  has  elapsed,  the  two  are  mixed  together. 
The  same  process  takes  place  when  two  gases 
of  different  density  are  placed  together  in  the  same 
vessel.  At  first  the  denser  gas  may  be  at  the  bottom, 
the  less  dense  above,  but  after  a  time  the  two  are 
found  to  be  uniformly  distributed  throughout. 

Maxwell  attempted  to  calculate  from  his  theory 
the  rate  at  which  the  diffusion  takes  place  in  these 
cases.  The  conditions  of  most  of  Graham's  experi- 
ments were  too  complicated  to  admit  of  direct  com- 
parison with  the  theory,  from  which  it  appeared  that 
there  is  a  relation  between  the  mean  free  path  and 
the  rate  of  diffusion.  One  experiment,  however,  was 
found,  the  conditions  of  which  could  be  made  the 
subject  of  calculation,  and  from  it  Maxwell  obtained 
as  the  value  of  the  mean  free  path  in  air  :1^(1  of  an 
inch. 

The  number  was  close  enough  to  that  found  from 
the  viscosity  to  afford  some  confirmation  of  his 
theory. 


AND   MODERN   PHYSICS.  129 

However,  a  few  years  later  Clausius  criticised  the 
details  of  this  part  of  the  paper,  and  Maxwell,  in  his 
memoir  of  1866,  admits  the  calculation  to  have  been 
erroneous.  The  main  principles  remained  unaffected, 
the  molecules  pass  from  one  gas  to  the  other,  and  this 
constitutes  diffusion. 

Now,  suppose  we  have  two  sets  of  particles  in 
contact  of  such  a  nature  that  the  mean  kinetic 
energy  of  the  one  set  is  different  from  that  of  the 
other;  the  temperatures  of  the  two  will  then  be  dif- 
ferent. These  two  sets  will  diffuse  into  each  other,  and 
the  diffusing  particles  will  carry  with  them  their 
kinetic  energy,  which  will  gradually  pass  from  those 
which  have  the  greater  energy  to  those  which  have 
the  less,  until  the  average  kinetic  energy  is  equalised 
throughout.  But  the  kinetic  energy  of  translation  is 
the  heat  of  the  particles.  This  diffusion  of  kinetic 
energy  is  a  diffusion  of  heat  by  conduction,  and  we 
have  here  the  mechanical  theory  of  the  conduction 
of  heat  in  a  gas. 

Maxwell  obtained  an  expression,  which,  however, 
he  afterwards  modified,  for  the  conductivity  of  a  gas 
in  terms  of  the  mean  free  path.  It  followed  from  this 
that  the  conductivity  of  air  was  only  about  ^  of 
that  of  copper. 

Thus  the  diffusion  of  gases,  the  viscosity  of  gases, 
and  the  conduction  of  heat  in  gases,  are  all  connected 
with  the  diffusion  of  the  particles  carrying  with  them 
their  momenta  and  their  energy  ;  while  values  of  the 
mean  free  path  can  be  obtained  from  observations  on 
any  one  of  these  properties. 

In  the  third  part  of  his  paper  Maxwell  considers 
i 


130  JAMES   CLERK   MAXWELL 

the  consequences  of  supposing  the  particles  not  to  be 
spherical.  In  this  case  the  impacts  would  tend  to  set 
up  a  motion  of  rotation  in  the  particles.  The  direction 
of  the  force  acting  on  any  particle  at  impact  would 
not  necessarily  pass  through  its  centre;  thus  by  impact 
the  velocity  of  its  centre  would  be  changed,  and  in 
addition  the  particles  would  be  made  to  spin.  Some 
part,  therefore,  of  the  energy  of  the  particles  will 
appear  in  the  form  of  the  translational  energy 
of  their  centres,  while  the  rest  will  take  the 
form  of  rotational    energy   of    each    particle    about 

its  centre. 

It  follows  from  Maxwell's  work  that  for  each  par- 
ticle the  average  value  of  these  two  portions  of  energy 
would  be  equal.  The  total  energy  will  be  half  trans- 
lational and  half  rotational. 

This  theorem,  in  a  more  general  form  which  was 
afterwards  given  to  it,  has  led  to  much  discussion, 
and  will  be  again  considered  later.  For  the  present 
we  will  assume  it  to  be  true.  Clausius  had  already 
called  attention  to  the  fact  that  some  of  the  energy 
must  be  rotational  unless  the  molecules  be  smooth 
spheres,  and  had  given  some  reasons  for  supposing 
that  the  ratio  of  the  whole  energy  to  the  energy 
of  translation  is  in  a  steady  state  a  constant.  Max- 
well shows  that  for  rigid  bodies  this  constant  is  2. 
Let  us  denote  it  for  the  present  by  the  symbol  /3. 
Thus,  if  the  translational  energy  of  a  molecule  is 
|  Tii  v2,  its  whole  energy  is  |  /3  m  v3. 

The  temperature  is  still  measured  by  the  trans- 
lational energy,  or  \  m  v" ;  the  heat  depends  on  the 
whole  energy.     Hence  if  H  represent  the  amount  of 


AND   MODERN    PHYSICS.  131 

heat — measured  as   energy — contained    by    a    single 
molecule,  and  T  its  temperature,  we  have — 

H  =  ft  T 

From  this  it  can  be  shewn*  that  if  7  represent  the 
ratio  of  the  specific  heat  of  a  gas  at  constant  pressure 
to  the  specific  heat  at  constant  volume,  then — 

1 


ft  = 


3     y-1 


For  air  and  some  other  gases  the  value  of  7  has 
been  shown  to  be  T408.     From  this  it  follows  that 

*  The  proof  is  as  follows  : — 

If  ff  be  the  specific  heat  at  constant  volume,  tr'at  constant  pressure, 
and  consider  a  unit  of  mass  of  gas  at  pressure  p  and  volume  v,  let  the 
volume  increase  by  an  amount  dv,  while  the  temperature  dy. 
Thus  <r'dT=<rdT  +  pdv 

2  T 

But         p  v  =  -  — 

3  m 

Hence  p  being  constant, 

2  dT 

p  d  v  =  -  

3  m 

Therefore         a'  =  cr  +  —  — 

3    m 

Now  suppose  an  amount  of  heat,  dH,  is  given  to  a  single  molecule 
and  that  its  temperature  is  T.     Its  specific  heat  is  «r,  and 

dH  =  <rmdT 
But        dH  =  /3dT 

Therefore         jS^irm 

Hence         —  =  — 
m         0 

Thus         ff'  =  '(l+g^j) 

And         a  'fa  =  y 
o 
Therefore  7=1-)-  — — 

6  P 


»'      *  =  m7^T) 


I    2 


132  JAMES    CLERK    MAXWELL 

ft  =  1*634.  Now,  Maxwell's  theory  required  that  for 
smooth  hard  particles,  approximately  spherical  in 
shape,  ft  should  be  2,  and  hence  he  concludes  "  we 
have  shown  that  a  system  of  such  particles  could  not 
possibly  satisfy  the  known  relation  between  the  two 
specific  heats  of  all  gases." 

Since  this  statement  was  made  many  more  experi- 
ments on  the  value  of  7  have  been  undertaken ;  it  is 
not  equal  to  1*408  for  all  gases.  Hence  the  value  of 
ft  is  different  for  various  gases. 

It  is  of  some  importance  to  notice  that  the 
value  of  ft  just  found  for  air  is  very  approximately 
1-66  or  f. 

For  mercury  vapour  the  value  of  7  has  been  shown 
by  Kundt  to  be  1*33  or  11,  and  hence  ft  is  equal  to  1- 
Thus  all  the  energy  of  a  particle  of  mercury  vapour  is 
translational,  and  its  behaviour  in  this  respect  is  con- 
sistent with  the  assumption  that  a  particle  of  mercury 
vapour  is  a  smooth  sphere. 

The  two  results  of  this  theory  which  seemed  to 
lend  themselves  most  readily  to  experimental  verifi- 
cation were  (1)  that  the  viscosity  of  a  gas  is 
independent  of  its  density,  and  (2)  that  it  is  pro- 
portional to  the  square  ro3t  of  the  absolute 
temperature.  The  next  piece  of  work  connected  with 
the  theory  was  an  attempt  to  test  these  consequences, 
and  a  description  of  the  experiments  was  published 
in  the  "  Philosophical  Transactions "  for  1865,  in  a 
paper  on  the  "  Viscosity  or  Internal  Friction  of  Air 
and  other  Gases,"  and  forms  the  Bakerian  lecture  for 
that  year. 

The   first   result   was  completely   proved.      It   is 


AND  MODERN  PHYSICS.  133 

shewn  that  the  value  of  the  coefficient*  of  viscosity 
"  is  the  same  for  air  at  0  5  inch  and  at  30  inches 
pressure,  provided  that  the  temperature  remains  the 
same." 

It  was  clear  also  that  the  viscosity  depended  on 
the  temperature,  and  the  results  of  the  experiments 
seemed  to  show  that  it  was  nearly  proportional  to  the 
absolute  temperature.  Thus  for  two  temperatures, 
185°  Fah.  and  51°  Fah.,  the  ratio  of  the  two  co- 
efficients found  was  12624;  the  ratio  of  the  two 
temperatures,  each  measured  from  absolute  zero,  is 
1-2605. 

This  result,  then,  does  not  agree  with  the  hypothesis 
that  a  gas  consists  of  spherical  molecules  acting  only 
on  each  other  by  a  kind  of  impact,  for,  if  this  were  so, 
the  coefficient  would,  as  we  have  seen,  depend  on  the 
square  root  of  the  absolute  temperature.  But  Max- 
well's result,  connecting  viscosity  with  the  first  power 
of  the  absolute  temperature,  has  not  been  confirmed 
by  other  investigators.  According  to  it  we  should 
have  as  the  relation  between  /x,  the  coefficient  of 
viscosity  at  t°  and  fi0,  that  at  zero  the  equation — 

H  =  jia(l  +  .00365 1). 

The  most  recent  results  of  Professor  Holman 
(Philosophical  Magazine,  Vol.  xxi.,  p.  212)  give — 

h  =  Ho  {1  +  .00275 1     .00000034t-}. 
And  results  similar  to  this  are  given  by  O.  E.  Meyer 

*  Owing  to  an  error  of  calculation  the  actual  value  obtained  by 
Maxwell  from  these  observations  for  the  coefficient  of  viscosity  is  too 
great.  More  recent  observers  have  found  lower  values  than  those 
given  by  him;  the  difference  is  thus  explained. 


134  JAMES    CLERK    MAXWELL 

Puluj,  and  Obermeyer.  Maxwell's  coefficient  -00365 
is  too  large,  but  -00182,  the  coefficient  obtained  by 
supposing  the  viscosity  proportional  to  the  square 
root  of  the  temperature,  would  be  too  small. 

It  still  remains  true,  therefore,  that  the  laws  of  the 
viscosity  of  gases  cannot  be  explained  by  the  hypothesis 
of  the  impact  of  hard  spheres ;  but  some  deductions 
drawn  by  Maxwell  in  his  next  paper  from  his  sup- 
posed law  of  proportionality  to  the  first  power  of  the 
absolute  temperature  require  modification. 

It  was  clear  from  his  experiments  just  described 
that  the  simple  hypothesis  of  the  impact  of  elastic 
bodies  would  not  account  for  all  the  phenomena 
observed.  Accordingly,  in  I860,  Maxwell  took  up 
the  problem  in  a  more  general  form  in  his  paper  on 
the  "  Dynamical  Theory  of  Gases,"  Phil.  Trans.,  1866. 

In  it  he  considered  the  molecules  of  the  gas  not 
as  elastic  spheres  of  definite  radius,  but  as  small 
bodies,  or  groups  of  smaller  molecules,  repelling  one 
another  with  a  force  whose  direction  always  passes 
very  nearly  through  the  centre  of  gravity  ot  the 
molecules,  and  whose  magnitude  is  represented  very 
nearly  by  some  function  of  the  distance  of  the  centres 
of  gravity.  "  I  have  made,"  he  continues,  "  this 
modification  of  the  theory  in  consequence  of  the 
results  of  my  experiments  on  the  viscosity  of  air  at 
different  temperatures,  and  I  have  deduced  from 
these  experiments  that  the  repulsion  is  inversely  as 
the  fifth  power  of  the  distance." 

Since  more  recent  observation  has  shown  that  the 
numerical  results  of  Maxwell's  work  connecting 
viscosity   and    temperature   are   erroneous,  this   last 


AND   MODERN   PHVSICS.  If  5 

deduction  does  not  hold  ;  the  inverse  fifth  power  law 
of  force  will  not  give  the  correct  relation  between 
viscosity  and  temperature.  Maxwell  himself  at  a 
later  date,  "  On  the  Stresses  in  Rarefied  Gases,"  Phil. 
Trans.,  1879,  realised  this  ;  but  even  in  this  last  paper 
ho  adhered  to  the  fifth  power  law  because  it  leads  to 
an  important  simplification  in  the  equations  to  be 
dealt  with. 

The  paper  of  1866  is  chiefly  important  because  it 
contains  for  the  first  time  the  application  of  general 
dynamical  methods  to  molecular  problems.  The  law 
of  the  distribution  of  velocities  among:  the  molecules 
is  again  investigated,  and  a  result  practically  identical 
with  that  found  for  the  elastic  spheres  is  arrived  at. 
In  obtaining  this  conclusion,  however,  it  is  assumed 
that  the  distribution  of  velocities  is  uniform  in  all 
directions  about  any  point,  whatever  actions  may  be 
taking  place  in  the  gas.  If,  for  example,  the  tempera- 
ture is  different  at  different  points,  then,  for  a  given 
velocity,  all  directions  are  not  equally  probable. 
Maxwell's  expression,  therefore,  for  the  number  of 
molecules  which  at  any  moment  have  a  given  velocity 
only  applies  to  the  permanent  state  in  which  the  dis- 
tribution of  temperature  is  uniform.  When  dealing, 
for  example,  with  the  conduction  of  heat,  a  modifi- 
cation of  the  expression  is  necessary.  This  was 
pointed  out  by  Boltzmann* 

In  the  paper  of  1806,  Maxwell  applies  his  gener- 
alised results  to  the  final  distribution  of  two  gases 

*  Studien  uber  das  Gleichgewicbt  der  lebendigen  Kraft  zwiscben 
bewegten  materiellen  Punkten  Sitz  d.  k.  Akad  Wicn,  Band  LVIIL> 
1838. 


13G  JAMES   CLERK    MAXWELL 

under  the  action  of  gravity,  the  equilibrium  of  tem- 
perature between  two  gases,  and  the  distribution  of 
temperature  in  a  vertical  column.  These  results  are, 
as  he  states,  independent  of  the  law  of  force  between 
the  molecules.  The  dynamical  causes  of  diffusion 
viscosity  and  conduction  of  heat  are  dealt  with,  and 
these  involve  the  law  of  force. 

It  follows  also  from  the  investigation  that,  on  the 
hypotheses  assumed  as  its  basis,  if  two  kinds  of  gases 
be  mixed,  the  difference  between  the  average  kinetic 
energies  of  translation  of  the  gases  of  each  kind 
diminishes  rapidly  in  consequence  of  the  action 
between  the  two.  The  average  kinetic  energy  of 
translation,  therefore,  tends  to  become  the  same  for 
each  kind  of  gas,  and  as  before,  it  is  this  average 
energy  of  translation  which  measures  the  tem- 
perature. 

A  molecule  in  the  theory  is  a  portion  of  a  gas" 
which  moves  about  as  a  single  body.  It  may  be  a 
mere  point,  a  centre  of  force  having  inertia,  capable 
of  doing  work  while  losing  velocity.  There  may 
be  also  in  each  molecule  systems  of  several  such 
centres  of  force  bound  together  by  their  mutual 
actions.  Again,  a  molecule  may  be  a  small  solid 
body  of  determinate  form ;  but  in  this  case  we  must, 
as  Maxwell  points  out,  introduce  a  new  set  of  forces 
binding  together  the  parts  of  each  molecule :  we  must 
have  a  molecular  theory  of  the  second  order.  In  any 
case,  the  most  general  supposition  made  is  that  a 
molecule  consists  of  a  series  of  parts  which  stick 
together,  but  are  capable  of  relative  motion  among 
each  other. 


AND   MODERN   PHYSICS.  137 

In  this  case  the  kinetic  energy  of  the  molecule 
consists  of  the  energy  of  its  centre  of  gravity,  together 
with  the  energy  of  its  component  parts,  relative  to  its 
centre  of  gravit}'.* 

Now  Clausius  had,  as  Ave  have  seen,  given  reasons 
for  believing  that  the  ratio  of  the  whole  energy  of  a 
molecule  to  the  energy  of  translation  of  its  centre  of 
gravity  tends  to  become  constant.  We  have  already 
used  /3  to  denote  this  constant.  Thus,  while  the  tem- 
perature is  measured  by  the  average  kinetic  energy 
of  translation  of  the  centre  of  gravity  of  each  mole- 
cule, the  heat  contained  in  a  molecule  is  its  whole 
energy,  and  is  /3  times  this  quantity.  Thus  the  con- 
clusions as  to  specific  heat,  etc.,  already  given  on  page 
130,  apply  in  this  case,  and  in  particular  we  have  the 
result  that  if  7  be  the  ratio  of  the  specific  heat  at 
constant  pressure  to  that  at  constant  volume,  then — 

p    2    ' 


3  7  -  1 

Maxwell's  theorem  of  the  distribution  of  kinetic 
energy  among  a  system  of  molecules  applied,  as  he 
gave  it  in  I860,  to  the  kinetic  energy  of  translation  of 
the  centre  of  gravity  of  each  molecule.  Two  years 
later   Dr.   Boltzmann,  in  the  paper  we  have  already 

*  Another  supposition  which  might  he  made,  and  which  is  necessary 
in  order  to  explain  various  actions  ohserved  in  a  compound  gas  under 
electric  force,  is  that  the  parts  of  which  a  molecule  is  composed  are 
continually  changing.  Thus  a  molecule  of  steam  consists  of  two 
parts  of  hydrogen,  one  of  oxygen,  hut  a  given  molecule  of  oxygen  is 
not  always  combined  with  the  same  two  molecules  of  hydrogen  ;  the 
particles  are  continually  changed.  In  Maxwell's  paper  an  hypothesis 
of  this  kind  is  not  dealt  with. 


138  JAMES   CLERK   MAXWELL 

referred  to,  extended  it  (under  certain  limitations)  to 
the  parts  of  which  a  molecule  is  composed.  According 
to  Maxwell  the  average  kinetic  energy  of  the  centre 
of  gravity  of  each  molecule  tends  to  become  the  same. 
According  to  Boltzmann  the  average  kinetic  energy 
of  each  part  of  the  molecule  tends  to  become  the 
same. 

Maxwell,  in  the  last  paper  he  wrote  on  the  subject 
("  On  Boltzmann's  Theorem  on  the  Average  Distri- 
bution of  Energy  in  a  System  of  Material  Points," 
Cavnb.  Phil.  Trans.,  XII.),  took  up  this  problem. 
AVatson  had  given  a  proof  of  it  in  1876  differing  from 
13  jltzmann's,  but  still  limited  by  the  stipulation  that 
the  time,  during  which  a  particle  is  encountering  other 
particles,  is  very  small  compared  with  the  time  during 
which  there  is  no  sensible  action  between  it  and  other 
particles,  and  also  that  the  time  during  which  a 
particle  is  simultaneously  within  the  distance  of  more 
than  one  other  particle  may  be  neglected. 

Maxwell  claims  that  his  proof  is  free  from  any 
such  limitation.  The  material  points  may  act  on 
each  other  at  all  distances,  and  according  to  any  law 
which  is  consistent  with  the  conservation  of  energy  ; 
they  may  also  be  acted  on  by  forces  external  to  the 
system,  provided  these  are  consistent  with  that  law. 

The  only  assumption  which  is  necessary  for  the 
direct  proof  is  that  the  system,  if  left  to  itself  in  its 
actual  state  of  motion,  will  sooner  or  later  pass 
through  every  phase  which  is  consistent  with  the 
conservation  of  energy. 

In  this  paper  Maxwell  finds  in  a  very  general 
manner  an  expression  for  the  number  of  molecules 


AND   MODERN   PHYSICS.  130 

which  at  any  time  have  a  given  velocity,  and  this, 
when  simplified  by  the  assumptions  of  the  former 
papers,  reduces  to  the  form  already  found.  He  also 
shows  that  the  average  kinetic  energy  corresponding 
to  any  one  of  the  variables  which  define  his  system 
is  the  same  for  every  one  of  the  variables  of  his  system. 
Thus,  according  to  this  theorem,  if  each  molecule 
be  a  single  small  solid  body,  six  variables  will  be  re- 
quired to  determine  the  position  of  each,  three 
variables  will  give  us  the  position  of  the  centre  of 
gravity  of  the  molecule,  while  three  others  will  deter- 
mine the  position  of  the  body  relative  to  its  centre  of 
gravity.  If  the  six  variables  be  properly  chosen,  the 
kinetic  energy  can  be  expressed  as  a  sum  of  six 
squares,  one  square  corresponding  to  each  variable. 
According  to  the  theorem  the  part  of  the  kinetic 
energy  depending  on  each  square  is  the  same.  Thus, 
the  whole  energy  is  six  times  as  great  as  that  which 
arises  from  any  one  of  the  variables.  The  kinetic 
energy  of  translation  is  three  times  as  great  as  that 
arisino-  from  each  variable,  for  it  involves  the  three 
variables  which  determine  the  position  of  the  centre 
of  gravity.  Hence,  if  we  denote  by  K  the  kinetic 
energy  due  to  one  variable,  the  whole  energy  is  6  K, 
and  the  translational  energy  is  3  K ;  thus,  for  this 
case— 

ft  =   G  X     =     2 
'  3  K 

Or,  again,  if  we  suppose  that  the  molecule  is  such  that 
m  variables  are  required  to  determine  its  position 
relatively  to  its  centre  of  gravity,  since  3  are 
needed  to  fix  the  centre  of  gravity,  the  total  number 


140  JAMES   CLERK   MAXWELL 

of  variables  defining  the  position  of  the  molecule  is 
m  +  3,  and  it  is  said  to  have  m  +  3  degrees  of  freedom. 
Hence,  in  this  case,  its  total  energy  is  (m  +  3)  K  and 
its  energy  of  translation  is  3  K,  thus  we  find — 

n       ni  +  3 

/ ~>  = 


3 


2 


Hence         y  =  1   +  -       -5  =  1  4- 

'  m  +  6 


n 


if  n  be  the  number  of  degrees  of  freedom  of  the 
molecule. 

Thus,  if  this  Boltzmann-Maxwell  theorem  be  true, 
the  specific  heat  of  a  gas  will  depend  solely  on  the 
number  of  degrees  of  freedom  of  each  of  its  molecules. 
For  hard  rigid  bodies  we  should  have  n  equal  to  6, 
and  hence  7=1*333.  Now  the  fact  that  this  is  not 
the  value  of  7  for  any  of  the  known  gases  is  a 
fundamental  difficulty  in  the  way  of  accepting  the 
complete  theory. 

Boltzmann  has  called  attention  to  the  fact  that  if 
n  be  equal  to  five,  then  7  has  the  value  1*40.  And  this 
agrees  fairly  with  the  value  found'  by  experiment  for 
air,  oxygen,  nitrogen,  and  various  other  gases.  We 
will,  however,  return  to  this  point  shortly. 

Thei*e  is,  perhaps,  no  result  in  the  domain  of 
physical  science  in  recent  years  which  has  been  more 
discussed  than  the  two  fundamental  theorems  of  the 
molecular  theory  which  we  owe  to  Maxwell  and  to 
Boltzmann. 

The  two  results  in  question  are  (1)  the  expression 
for  the  number  of  molecules  which  at  any  moment 
will  have  a  given   velocity,  and  (2)   the  proposition 


AND   MODERN   PHYSICS.  141 

that  the  kinetic  energy  is  ultimately  equally  divided 
among  all  the  variables  which  determine  the  system. 

With  regard  to  (1)  Maxwell  showed  that  his  error 
law  was  one  possible  condition  of  permanence.  If  at 
any  moment  the  velocities  are  distributed  according 
to  the  error  law,  that  distribution  will  be  a  permanent 
one.  He  did  not  prove  that  such  a  distribution  is  the 
only  one  which  can  satisfy  all  the  conditions  of  the 
problem. 

The  proof  that  this  law  is  a  necessaiy,  as  well  as  a 
sufficient,  condition  of  permanence  was  first  given  by 
Boltzmann,  for  a  single  monatomic  gas  in  1872,  for  a 
mixture  of  such  gases  in  1886,  and  for  a  polyatomic  gas 
in  1887.  Other  proofs  have  been  given  since  by  Watson 
and  Burbury.  It  would  be  quite  beyond  the  limits  of 
this  book  to  go  into  the  question  of  the  completeness 
or  sufficiency  of  the  proofs.  The  discussion  of  the 
question  is  still  in  progress. 

The  British  Association  Report  for  1894  contains 
an  important  contribution  to  the  question,  in  the 
shape  of  a  report  by  Mr.  G.  H.  Bryan,  and  the  dis- 
cussion he  started  at  Oxford  by  reading  this  report 
has  been  continued  in  the  pages  of  Nature  and  else- 
where since  that  time. 

Mr.  Bryan  shows  in  the  first  place  what  may  be 
the  nature  of  the  systems  of  molecules  to  which  the 
results  will  apply,  and  discusses  various  points  of 
difficulty  in  the  proof. 

The  theorem  in  question,  from  which  the  result  (1) 
follows  as  a  simple  deduction,  has  been  thus  stated  by 
Dr.  Larmor.* 

*  Nature,  vol.  1.,  p.  152  (December  13th,  1894). 


H2  JAMES   CLERK    MAXWELL 

"  There  exists  a  positive  function  belonging  to  a 
group  of  molecules  which,  as  they  settle  themselves 
into  a  steady  state — on  the  average  derived  from  a 
great  number  of  configurations — maintains  a  steady 
downward  trend.  The  Maxwell-Boltzmann  steady  state 
is  the  one  in  which  this  function  has  finally  attained 
its  minimum  value,  and  is  thus  a  unique  steady  state, 
it  still  being  borne  in  mind  that  this  is  only  a  pro- 
position of  averages  derived  from  a  great  number  of 
instances  in  which  nothing  is  conserved  in  encounters, 
except  the  energy,  and  that  exceptional  circumstances 
may  exist,  comparatively  very  few  in  number,  in 
which  the  trend  is,  at  any  rate,  temporarily  the 
other  way." 

This  theorem,  when  applied  to  cases  of  motion, 
such  as  that  of  a  gas  at  constant  temperature  en- 
closed in  a  rigid  envelope  impermeable  to  heat, 
appears  to  be  proved.  For  such  a  case,  therefore, 
the  Maxwell-Boltzmann  law  is  the  only  one  possible. 

But  whether  this  be  so  or  not,  the  taw  first  intro- 
duced by  Maxwell  is  one  of  those  possible,  and  the 
advance  in  molecular  science  due  to  its  introduction 
is  enormous. 

We  come  now  to  the  second  result,  the  equal 
partition  of  the  energy  among  all  the  degrees  of 
freedom  of  each  molecule.  Lord  Kelvin  has  pointed 
out  a  flaw  in  Maxwell's  proof,  but  Boltzmann  showed 
(Philosophical  3Iagazine,March,  1893)  how  this  flaw 
can  easily  be  corrected,  and  it  may  be  said  that  in  all 
cases  in  which  the  Boltzmann-Maxwell  law  of  the 
distribution  of  velocities  holds,  Maxwell's  law  of  the 
equal  partition  of  energy  holds  also. 


AND   MODERN    PHYSICS.  143 

Three  cases  are  considered  by  Mr.  Bryan,  in  which 
the  law  of  distribution  fails  for  rigid  molecules :  the 
first  is  when  the  molecules  have  all,  in  addition  to 
their  velocities  of  agitation,  a  common  velocity  of 
translation  in  a  fixed  direction  ;  the  second  is  when  the 
gas  has  a  motion  of  uniform  rotation  about  a  fixed 
axis ;  while  the  third  is  when  each  molecule  has  an 
axis  of  symmetry.  In  this  last  case  the  forces  acting 
during  a  collision  necessarily  pass  through  the  axis 
of  symmetry,  the  angular  velocity,  therefore,  of  any 
molecule  about  this  axis  remains  constant,  the 
number  of  molecules  having  a  given  angular  velocity 
will  remain  the  same  throughout  the  motion,  and  the 
part  of  the  kinetic  energy  which  depends  on  this 
component  of  the  motion  will  remain  fixed,  and  will 
not  come  into  consideration  when  dealing  with  the 
equal  partition  of  the  energy  among  the  various 
degrees  of  freedom. 

Such  a  molecule  has  five,  and  not  six,  degrees  of 
freedom  ;  three  quantities  are  needed  to  determine  the 
position  of  its  centre  of  gravity,  and  two  to  fix  the 
position  of  the  axis  of  symmetry. 

In  this  case,  then,  as  Boltzmann  points  out,  in  the 
expression  for  the  ratio  of  the  specific  heats,  we  must 
have  n  equal  to  5,  and  hence 

9  9 

y  =  l+£=l+|     =     l-4 

n  o 

agreeing  fairly   with    the   value   found   for   air    and 
various  other  permanent  gases. 

For  cases,  then,  in  which  we  consider  each  atom 
as    a    single    rigid    body,    the    Boltzmann  -  Maxwell 


144-  JAMES   CLERK   MAXWELL 

theorem  appears  to  give  a  unique  solution,  and  the 
Maxwell  law  of  the  distribution  of  the  energy  to  be 
in  fair  accordance  with  the  results  of  observation.* 

If  we  can  never  go  further — and  it  must  be 
admitted  that  the  difficulties  in  the  way  of  further 
advanca  are  enormous — it  may,  I  think,  be  claimed 
for  Maxwell  that  the  progress  already  made  is  greatly 
due  to  him.  Both  these  laws,  for  the  case  of  elastic 
spheres,  are  contained  in  his  first  paper  of  1860; 
and  while  it  is  to  the  genius  of  Boltzmann  that  we  owe 
their  earliest  generalisation,  and  in  particular  the 
proof  of  the  uniqueness  of  the  solution  under  proper 
restrictions,  Maxwell's  last  paper  contributed  in  no 
small  degree  to  the  security  of  the  position.  Not 
merely  the  foundations,  but  much  of  the  super- 
structure of  molecular  science  is  his  work. 

The  difficulties  in  the  way  of  advance  are,  as  we 
have  said,  enormous.  Boltzmann,  in  one  of  his  papers, 
has  considered  the  properties  of  a  complex  molecule 
of  a  gas,  consisting  maybe  of  a  number  of  atoms 
and  possibly  of  ether  atoms  bound  with  them,  and  he 
concludes  that  such  a  molecule  will  behave  in  its 
progressive  motion,  and  in  its  collisions  with  other 
molecules,  nearly  like  a  rigid  body.  But  to  quote 
from  Mr.  Bryan  :  "  The  case  of  a  polyatomic  mole- 
cule, whose  atoms  are  capable  of  vibrating  relative 
to  one  another,  affords  an  interesting  field  for  investi- 
gation and  speculation.  Is  the  Boltzmann  distribu- 
tion still  unique,  or  do  other  permanent  distribu- 
tions exist  in  which  the  kinetic  energy  is  unequally 
divided  ? " 

*  See  papers  by  Mr.  Capstick,~P/«?.  Trans  ,  vols.  185-18G. 


AND   MODERN   PHYSICS.  i45 

Again,  the  spectroscope  reveals  to  us  vibrations 
of  the  ether,  which  are  connected  in  some  way  with 
the  vibrations  of  the  molecules  of  gas,  whose  spectrum 
we  are  observing.  It  seems  clear  that  the  law  of 
equal  partition  does  not  apply  to  these,  and  yet, 
if  we  are  to  suppose  that  the  ether  vibrations  are 
due  to  actual  vibrations  of  the  atoms  which  con- 
stitute a  molecule,  why  does  it  not  apply  ?  Where 
does  the  condition  come  in  which  leads  to  failure  in 
the  proof  ?  Or,  again,  is  it,  as  has  been  suggested,  the 
fact  that  the  complex  spectrum  of  a  gas  represents 
the  terms  of  a  Fourier  Series,  into  which  some 
elaborate  vibration  of  the  atoms  is  resolved  by  the 
ether  ?  or  is  the  spectrum  due  simply  to  electro- 
magnetic vibrations  on  the  surface  of  the  molecules 
— vibrations  whose  period  is  determined  chiefly  by  the 
size  and  shape  of  the  molecule,  but  in  which  the 
atoms  of  which  it  is  composed  take  part  ?  There  are 
grave  difficulties  in  the  way  of  either  of  these  ex- 
planations, but  we  must  not  let  our  dread  of  the  task 
which  remains  to  be  done  blind  our  eyes  to  the  great- 
ness of  Maxwell's  work. 

One  other  important  paper,  and  a  number  of 
shorter  articles,  remain  to  be  mentioned. 

The  Boltzmann-Maxwell  law  applies  only  to  cases 
in  which  the  temperature  is  uniform  throughout.  In 
a  paper  published  in  the  Philosophical  Transactions 
for  1879,  on  "  Stresses  in  Rarefied  Gases  Arising  from 
Inequalities  of  Temperature,"  Maxwell  deals,  among 
other  matters,  with  the  theory  of  the  radiometer.  He 
shows  that  the  observed  motions  will  not  take  place 
unless  gas,  in  contact  with  a  solid,  can  slide  along 
j 


14G  JAMES   CLERK   MAXWELL 

the  surface  of  the  solid  with  a  finite  velocity  between 
places  where  the  temperature  is  different ;  and  in  an 
appendix  he  proves  that,  on  certain  assumptions  re- 
garding the  nature  of  the  contact  of  the  solid  and 
the  gas,  there  will  be,  even  when  the  pressure  is  con- 
stant, a  flow  of  gas  along  the  surface  from  the  colder 
to  the  hotter  parts. 

Among  his  less  important  papers  bearing  on 
molecular  theory  must  be  mentioned  a  lecture  on 
"  Molecules  "  to  the  British  Association  at  its  Bradford 
meeting  ;  "  Scientific  Papers  of  Clerk  Maxwell,"  vol.  ii., 
p.  361 ;  and  another  on  "  The  Molecular  Constitution 
of  Bodies,"  Scientific  Papers,  vol.  ii.,  p.  418. 

In  this  latter,  and  also  in  a  review  in  Nature  of 
Van  der  Waal's  book  on  "  The  Continuity  of  the 
Gaseous  and  Liquid  States,"*  he  explains  and  dis- 
cusses Clausius'  virial  equation,  by  means  of  which 
the  variations  of  the  permanent  gases  from  Boyle's 
law  are  explained.  The  lecture  gives  a  clear  account, 
in  Maxwell's  own  inimitable  style,  of  the  advances 
made  in  the  kinetic  theory  up  to  the  date  at  which  it 
was  delivered,  and  puts  clearly  the  difficulties  it  has 
to  meet.  Maxwell  thought  that  those  arising  from 
the  known  values  of  the  ratio  of  the  specific  heats 
were  the  most  serious. 

In  the  articles,  "  Atomic  Constitution  of  Bodies " 
and  "  Diffusion,"  in  the  ninth  edition  of  the  Encyclo- 
paedia Britannica,  we  have  Maxwell's  later  views  on 
the  fundamental  assumptions  of  the  molecular  theory. 

The  text-book  on  "  Heat "  contains  some  further 
developments  of  the  theory.     In  particular  he  shows 

*  Nature,  vol.  x." 


AND   MODERN   PHYSICS.  147 

how  the  conclusions  of  the  second  law  of  thermo-dyna- 
mics  are  connected  with  the  fact  that  the  coarseness 
of  our  faculties  will  not  allow  us  to  grapple  with 
individual  molecules. 

The  work  described  in  the  foregoing  chapters 
would  have  been  sufficient  to  secure  to  Maxwell  a 
distinguished  place  among  those  who  have  advanced 
our  knowledge  ;  it  remains  still  to  describe  his  greatest 
work,  his  theory  of  Electricity  and  Magnetism. 


j2 


148  JAMES   CLERK    MAXWELL 


CHAPTER    IX. 

SCIENTIFIC   WORK. — ELECTRICAL   THEORIES. 

Clerk  Maxwell's  first  electrical  paper — that  on 
Faraday's  "  Lines  of  Force  " — was  read  to  the  Cam- 
bridge Philosophical  Society  on  December  10th,  1855, 
and  Part  II.  on  February  11th,  1856.  The  author 
was  then  a  Bachelor  of  Arts,  only  twenty-three  years 
in  age,  and  of  less  than  one  year's  standing  from  the 
time  of  taking  his  degree. 

The   opening  words   of  the  paper  are  as  follows 
(Scientific  Papers,  vol.  i.,  p.  155)  : — ■ 

"The  present  state  of  electrical  science  seems  peculiarly 
unfavourable  to  speculation.  The  laws  of  the  distribution  of 
electricity  on  the  surface  of  conductors  have  been  analytically 
deduced  from  experiment ;  some  parts  of  the  mathematical 
theory  of  magnetism  are  established,  while  in  other  parts  the 
experimental  data  are  wanting ;  the  theory  of  the  conduction 
of  galvanism,  and  that  of  the  mutual  attraction  of  conductors, 
have  been  reduced  to  mathematical  formulae,  but  have  not 
fallen  into  relation  with  the  other  parts  of  the  science.  No 
electrical  theory  can  now  be  put  forth,  unless  it  shows  the 
connection,  not  only  between  electricity  at  rest  and  current 
electricity,  but  between  the  attractions  and  inductive  effects  of 
electricity  in  both  states.  Such  a  theory  must  accurately 
satisfy  those  laws,  the  mathematical  form  of  which  is  known, 
and  must  afford  the  means  of  calculating  the  effects  in  the 
limiting  cases  where  the  known  formulae  are  inapplicable.  In 
order,  therefore,  to  appreciate  the  requirements  of  the  science, 
the  student  must  make  himself  familiar  with  a  consider- 
able bcdy  of  most  intricate  mathematics,  the  mere  retention 
of  which  in  the  memory  materially  interferes  with  further 


AND   MODERN   PHYSICS.  149 

progress.  The  first  process,  therefore,  in  the  effectual  study 
of  the  science,  must  be  one  of  simplification  and  reduction  of 
the  results  of  previous  investigation  to  a  form  in  which  the 
mind  can  grasp  them.  The  results  of  this  simplification  may- 
take  the  form  of  a  purely  mathematical  formula  or  of  a  physical 
hypothesis.  In  the  first  case  we  entirely  lose  sight  of  the 
phenomena  to  be  explained  ;  and  though  we  may  trace  out 
the  consequences  of  given  laws,  we  can  never  obtain  more 
extended  views  of  the  connections  of  the  subject.  If,  on  the 
other  hand,  we  adopt  a  physical  hypothesis,  we  see  the 
phenomena  only  through  a  medium,  and  are  liable  to  that 
blindness  to  facts  and  rashness  in  assumption  which  a  partial 
explanation  encourages.  We  must  therefore  discover  some 
method  of  investigation  which  allows  the  mind  at  every  step 
to  lay  hold  of  a  clear  physical  conception,  without  being  com- 
mitted to  any  theory  founded  on  the  physical  science  from 
which  that  conception  is  borrowed,  so  that  it  is  neither  drawn 
aside  from  the  subject  in  pursuit  of  analytical  subtleties,  nor 
carried  beyond  the  truth  by  a  favourite  hypothesis. 

"  In  order  to  obtain  physical  ideas  without  adopting  a 
physical  theory  we  must  make  ourselves  familiar  with  the 
existence  of  physical  analogies.  By  a  physical  analogy  I 
mean  that  partial  similarity  between  the  laws  of  one  science 
and  those  of  another  which  makes  each  of  them  illustrate  the 
other.  Thus  all  the  mathematical  sciences  are  founded  on 
relations  between  physical  laws  and  laws  of  numbers,  so  that 
the  aim  of  exact  science  is  to  reduce  the  problems  of  Nature  to 
the  determination  of  quantities  by  operations  with  members. 
Passing  from  the  most  universal  of  all  analogies  to  a  very 
partial  one,  we  find  the  same  resemblance  in  mathematical 
form  between  two  different  phenomena  giving  rise  to  a 
physical  theory  of  light. 

"  The  changes  of  direction  which  light  undergoes  in  passing 
from  one  medium  to  another  are  identical  with  the  deviations 
of  the  path  of  a  particle  in  moving  through  a  narrow  space  in 
which  intense  forces  act.  This  analogy,  which  extends  only  to 
the  direction,  and  not  to  the  velocity  of  motion,  was  long 
believed  to  be  the  true  explanation  of  the  refraction  of  light ; 


150  JAMES   CLERK   MAXWELL 

and  we  still  find  it  useful  in  the  solution  of  certain  problems, 
in  which  we  employ  it  without  danger  as  an  artificial  method. 
The  other  analogy,  between  light  and  the  vibrations  of  an 
elastic  medium,  extends  much  farther,  but,  though  its  import- 
ance and  fruitfulness  cannot  be  over-estimated,  we  must 
recollect  that  it  is  founded  only  on  a  resemblance  in  form 
between  the  laws  of  light  and  those  of  vibrations.  By  stripping 
it  of  its  physical  dress  and  reducing  it  to  a  theory  of  '  transverse 
alternations,'  we  might  obtain  a  system  of  truth  strictly  founded 
on  observation,  but  probably  deficient  both  in  the  vividness  of 
its  conceptions  and  the  fertility  of  its  method.  I  have  said 
thus  much  on  the  disputed  questions  of  optics,  as  a  preparation 
for  the  discussion  of  the  almost  universally  admitted  theory  of 
attraction  at  a  distance. 

"We  have  all  acquired  the  mathematical  conception  of  these 
attractions.  We  can  reason  about  them  and  determine  their 
appropriate  forms  or  formulae.  These  formulae  have  a  distinct 
mathematical  significance,  and  their  results  are  found  to  be  in 
accordance  with  natural  phenomena.  There  is  no  formula  in 
applied  mathematics  more  consistent  Avith  Nature  than  the 
formula  of  attractions,  and  no  theory  better  established  in  the 
minds  of  men  than  that  of  the  action  of  bodies  on  one  another 
at  a  distance.  The  laws  of  the  conduction  of  heat  in  uniform 
media  appear  at  first  sight  among  the  most  different  in  their 
physical  relations  from  those  relating  to  attractions.  The 
quantities  which  enter  into  them  are  temperature,  flow  of  heat-, 
conductivity.  The  word  force  is  foreign  to  the  subject.  Yet 
we  find  that  the  mathematical  laws  of  the  uniform  motion  of 
heat  in  homogeneous  media  are  identical  in  form  with  those  of 
attractions  varying  inversely  as  the  square  of  the  distance.  We 
have  only  to  substitute  source  of  heat  for  centre  of  attraction, 
4ow  of  heat  for  accelerating  effect  of  attraction  at  any  point, 
and  temperature  for  potential,  and  the  solution  of  a  problem  in 
attractions  is  transformed  into  that  of  a  problem  in  heat. 

"  This  analogy  between  the  formulae  of  heat  and  attraction 
was,  I  believe,  first  pointed  out  by  Professor  William  Thomson 
in  the  Cambridge  Mathematical  Journal,  Vol.  III. 

"  Now  the  conduction  of  heat  is  supposed  to  proceed  by  an 


AND   MODERN   PHYSICS.  151 

action  between  contiguous  parts  of  a  meJium,  while  the  force 
of  attraction  is  a  relation  between  distant  bodies,  and  yet,  if 
we  knew  nothing  more  than  is  expressed  in  the  mathematical 
formulae,  there  would  be  nothing  to  distinguish  between  tho 
one  set  of  phenomena  and  the  other. 

"  It  is  true  that,  if  we  introduce  other  considerations  and 
observe  additional  facts,  the  two  subjects  will  assume  very 
different  aspects,  but  the  mathematical  resemblance  of  some  of 
their  laws  will  remain,  and  may  still  be  made  useful  in  exciting 
appropriate  mathematical  ideas. 

"It  is  by  the  use  of  analogies  of  this  kind  that  I  have  at- 
tempted to  bring  before  the  mind,  in  a  convenient  and  manage- 
able form,  those  mathematical  ideas  which  are  necessary  to  the 
study  of  the  phenomena  of  electricity.  The  methods  are  gener- 
ally those  suggested  by  the  processes  of  reasoning  which  are 
found  in  the  researches  of  Faraday,  and  which,  though  they 
have  been  interpreted  mathematically  by  Professor  Thomson 
and  others,  are  very  generally  supposed  to  be  of  an  indefinite 
and  unmathematical  character,  when  compared  with  those 
employed  by  the  professed  mathematicians.  By  the  method 
which  I  adopt,  I  hope  to  render  it  evident  that  I  am  not 
attempting  to  establish  any  physical  theory  of  a  science  in 
which  I  have  hardly  made  a  single  experiment,  and  that  the 
limit  of  my  design  is  to  show  how,  by  a  strict  application  of 
the  ideas  and  methods  of  Faraday,  the  connection  of  the  very 
different  orders  of  phenomena  which  he  has  discovered  may  be 
clearly  placed  before  the  mathematical  mind.  I  shall  therefore 
avoid  as  much  as  I  can  the  introduction  of  anything  which  does 
not  serve  as  a  direct  illustration  of  Faraday's  methods,  or  of 
the  mathematical  deductions  which  may  be  made  from  them. 
In  treating  the  simpler  parts  of  the  subject  I  shall  use  Faraday's 
mathematical  methods  as  well  as  his  ideas.  When  the  com- 
plexity of  the  subject  requires  it,  I  shall  use  analytical  notation, 
still  confining  myself  to  the  development  of  ideas  originated  by 
the  same  philosopher. 

"  I  have  in  the  first  place  to  explain  and  illustrate  the  idea 
of  '  lines  of  force.' 

'"When  a  body  is  electrified  in  any  manner,  a  small  body 


152  JAMES   CLERK    MAXWELL 

charged  with  positive  electricity,  and  placed  in  any  given 
position,  will  experience  a  force  urging  it  in  a  certain  direction. 
If  the  small  body  be  now  negatively  electrified,  it  will  beurged 
by  an  equal  force  in  a  direction  exactly  opposite. 

"  The  same  relations  hold  between  a  magnetic  body  and  the 
north  or  south  poles  of  a  small  magnet.  If  the  north  pole  is 
urged  in  one  direction,  the  south  pole  is  urged  in  the  opposite 
direction. 

"  In  this  way  we  might  find  a  line  passing  through  any 
point  of  space,  such  that  it  represents  the  direction  of  the  force 
acting  on  a  positively  electrified  particle,  or  on  an  elementary 
north  pole,  and  the  reverse  direction  of  the  force  on  a  negatively 
electrified  particle  or  an  elementary  south  pole.  Since  at  every 
point  of  space  such  a  direction  may  be  found,  if  we  commence 
at  any  point  and  draw  a  line  so  that,  as  we  go  along  it,  its 
direction  at  any  point  shall  always  coincide  with  that  of  the 
resultant  force  at  that  point,  this  curve  will  indicate  the 
direction  of  that  force  for  every  point  through  which  it  passes, 
and  might  be  called  on  that  account  a  line  of  force.  We  might 
in  the  same  way  draw  other  lines  of  force,  till  we  had  filled  all 
space  with  curves  indicating  by  their  direction  that  of  the  force 
at  any  assigned  point. 

"  We  should  thus  obtain  a  geometrical  model  of  the  physical 
phenomena,  which  would  tell  us  the  direction  of  the  force,  but 
we  should  still  require  some  method  of  indicating  the  intensity 
of  the  force  at  any  point.  If  we  consider  these  curves  not  as 
mere  lines,  but  as  fine  tubes  of  variable  section  carrying  an 
incompressible  fluid,  then,  since  the  velocity  of  the  fluid  is 
inversely  as  the  section  of  the  tube,  we  may  make  the  velocity 
vary  according  to  any  given  law,  by  regulating  the  section  of 
the  tube,  and  in  this  way  we  might  represent  the  intensity  of 
the  force  as  well  as  its  direction  by  the  motion  of  the  fluid  in 
these  tubes.  This  method  of  representing  the  intensity  of  a 
force  by  the  velocity  of  an  imaginary  fluid  in  a  tube  is 
applicable  to  any  conceivable  system  of  forces,  but  it  is 
capable  of  great  simplification  in  the  case  in  which  the  forces 
are  such  as  can  be  explained  by  the  hypothesis  of  attractions 
varying  inversely  as  the  square  of  the  distance,  such  as  those 


AND   MODERN   PHYSICS.  153 

observed  in  electrical  and  magnetic  phenomena.  In  the  case 
of  a  perfectly  arbitrary  system  of  forces,  there  will  generally  bo 
interstices  between  the  tabes  ;  but  in  the  case  of  electric  and 
magnetic  forces  it  is  possible  to  arrange  the  tubes  so  as  to 
leave  no  interstices.  The  tubes  will  then  be  mere  surfaces, 
directing  the  motion  of  a  fluid  filling  up  the  whole  space.  It 
has  been  usual  to  commence  the  investigation  of  the  laws  of 
these  forces  by  at  once  assuming  that  the  phenomena  are  due 
to  attractive  or  repulsive  forces  acting  between  certain  points. 
We  may,  however,  obtain  a  different  view  of  the  subject,  and 
one  more  suited  to  our  more  difficult  inquiries,  by  adopting  for 
the  definition  of  the  forces  of  which  we  treat,  that  they  may  be 
represented  in  magnitude  and  direction  by  the  uniform  motion 
of  an  incompressible  fluid. 

"  I  propose,  then,  first  to  describe  a  method  by  which  the 
motion  of  such  a  fluid  can  be  clearly  conceived  ;  secondly  to 
trace  the  consequences  of  assuming  certain  conditions  of 
motion,  and  to  point  out  the  application  of  the  method  to 
some  of  the  less  complicated  phenomena  of  electricity, 
magnetism,  and  galvanism  ;  and  lastly,  to  show  how  by  an 
extension  of  these  methods,  and  the  introduction  of  another 
idea  due  to  Faraday,  the  laws  of  the  attractions  and  inductive 
actions  of  magnets  and  currents  may  be  clearly  conceived, 
without  making  any  assumptions  as  to  the  physical  nature  of 
electricity,  or  adding  anything  to  that  which  has  been  already 
proved  by  experiment. 

"  By  referring  everything  to  the  purely  geometrical  idea  of 
the  motion  of  an  imaginary  fluid,  I  hope  to  attain  generality 
and  precision,  and  to  avoid  the  dangers  arising  from  a  pre- 
mature theory  professing  to  explain  the  cause  of  the 
phenomena.  If  the  results  of  mere  speculation  which  I  have 
collected  are  found  to  be  of  any  use  to  experimental  philo- 
sophers, in  arranging  and  interpreting  their  results,  they  will 
have  served  their  purpose,  and  a  mature  theory,  in  which 
physical  facts  will  be  physically  explained,  will  be  formed  by 
those  who  by  interrogating  Nature  herself  can  obtain  the  only 
true  solution  of  the  questions  which  the  mathematical  theory 
suggests." 


154  JAMES   CLERK   MAXWELL 

The  idea  was  a  bold  one :  for  a  youth  of  twenty- 
three  to  explain,  by  means  of  the  motions  of  an 
incompressible  fluid,  some  of  the  less  complicated 
phenomena  of  electricity  and  magnetism,  to  show  how 
the  laws  of  the  attractions  of  magnets  and  currents 
may  be  clearly  conceived  without  making  any  as- 
sumption as  to  the  physical  nature  of  electricity,  or 
adding  anything  to  that  which  has  already  been 
proved  by  experiment. 

It  may  be  useful  to  review  in  a  very  few  words 
the  position  of  electrical  theory*  in  1855. 

Coulomb's  experiments  had  established  the  funda- 
mental facts  of  electrostatic  attraction  and  repulsion, 
and  Coulomb  himself,  about  1785,  had  stated  a  theory 
based  on  these  experiments  which  could  "  only  be 
attacked  by  proving  his  experimental  results  to  be 
inaccurato."t 

Coulomb  supposes  the  existence  of  two  electric 
fluids,  the  theory  developed  previously  by  Franklin, 
but  says — 

"  Je  previens  pour  mettre  la  theorie  qui  va  suivre  a  l'abri 
de  toute  dispute  systematique,  que  dans  la  supposition  de 
deux  flu  ides  electriques,  je  n'ai  autre  intention  que  de  presenter 
avec  le  moins  d'elements  possible  les  resultats  du  calcul  et 
de  1'experience,  et  non  d'indiquer  les  veritables  causes  de 
i'electriciteV' 

Cavendish  was  working  in  England  about  the 
same  time  as  Coulomb,  but  ho  published  very  little, 

*  An  historical  account  of  the  development  of  the  science  of 
electricity  will  he  found  in  the  article  "  Electricity  "  in  the  Encyclo- 
peedia  Britaimiea,  ninth  edition,  hy  Professor  Chrystal. 

t  Thomson  (Lord  Kelvin),*" Papers  on  Electrostatics  and  Mag- 
netism,'' p.  15. 


AND   MODERN   PHYSICS.  155 

and  the  value  and  importance  of  his  work  was  not 
recognised  until  the  appearance  in  1879  of  the 
"  Electrical  Kesearches  of  Henry  Cavendish,"  edited 
by  Clerk  Maxwell. 

Early  in  the  present  century  the  application  of 
mathematical  analysis  to  electrical  problems  was 
begun  by  Laplace,  who  investigated  the  distribution 
of  electricity  on  spheroids,  and  about  1811  Poisson's 
great  work  on  the  distribution  of  electricity  on  two 
spheres  placed  at  any  given  distance  apart  was  pub- 
lished. Meanwhile  the  properties  of  the  electric 
current  were  being  investigated.  Galvani's  discovery 
of  the  muscular  contraction  in  a  frog's  leg,  caused  by 
the  contact  of  dissimilar  metals,  was  made  in  1790. 
Volta  invented  the  voltaic  pile  in  1800,  and  Oersted  in 
1820  discovered  that  an  electric  current  produced 
magnetic  force  in  its  neighbourhood.  On  this  Ampere 
laid  the  foundation  of  his  theory  of  electro-dynamics, 
in  which  he  showed  how  to  calculate  the  forces  be- 
tween circuits  carrying  currents  from  an  assumed  law 
of  force  between  each  pair  of  elements  of  the  circuits. 
His  experiments  proved  that  the  consequences  which 
follow  from  this  law  are  consistent  with  all  the 
observed  facts.  They  do  not  prove  that  Ampere's  law 
alone  can  explain  the  facts. 

Maxwell,  writing  on  this  subject  in  the  "  Electricity 
and  Magnetism,"  vol.  ii.,  p.  162,  says — ■ 

"  The  experimental  investigation  by  which  Ampere  estab- 
lished the  laws  of  the  mechanical  action  between  electric 
currents  is  one  of  the  most  brilliant  achievements  in  science. 

"  The  whole,  theory  and  experiment,  seems  as  if  it  had 
leaped  full  grown  and  full  armed  from  the  brain    of    the 


156  JAMES   CLERK   MAXWELL 

'  Newton  of  Electricity.'  It  is  perfect  in  form  and  unassail- 
able in  accuracy,  and  it  is  summed  up  in  a  formula  from 
which  all  the  phenomena  may  be  deduced,  and  Avhich  must 
always  remain  the  cardinal  formula  of  electro-dynamics. 

"The  method  of  Ampere,  however,  though  cast  into  an 
inductive  form,  does  not  allow  us  to  trace  the  formation  of  the 
ideas  which  guided  it.  We  can  scarcely  believe  that  Ampere 
really  discovered  the  law  of  action  by  means  of  the  experi- 
ments which  he  describes.  We  are  led  to  suspect,  what,  indeed, 
he  tells  us  himself,  that  he  discovered  the  law  by  some  process 
which  he  has  not  shown  us,  and  that  when  he  had  afterwards 
built  up  a  perfect  demonstration,  he  removed  all  traces  of  the 
scaffolding  by  which  he  had  built  it." 

The  experimental  evidence  for  Ampere's  theory, 
so  far,  at  least,  as  it  was  possible  to  obtain  it  from 
experiments  on  closed  circuits,  was  rendered  unim- 
peachable by  W.  Weber  about  1846,  while  in  the 
previous  year  Grassman  and  F.  E.  Neumann  both 
published  laws  for  the  attraction  between  two  elements 
of  current  which  differ  from  that  of  Ampere,  but  lead 
to  the  same  result  for  closed  circuits.  In  a  paper 
published  in  1846  Weber  announced  his  hypothesis 
connecting  together  electrostatic  and  electro-dynamic 
action.  In  this  paper  he  supposed  that  the  force 
between  two  particles  of  electricity  depends  on  the 
motion  of  the  particles  as  well  as  on  their  distance 
apart.  A  somewhat  similar  theory  was  proposed  by 
Gauss  and  published  after  his  death  in  his  collected 
works.  It  has  been  shown,  however,  that  Gauss' 
theory  is  inconsistent  with  the  conservation  of  energy. 
Weber's  theory  avoids  this  inconsistency  and  leads,  for 
closed  circuits,  to  the  same  results  as  Ampere.  It  has 
been  proved,  however,  by  Von  Helmholtz,  that,  under 
certain  circumstances,  according  to  it,  a  body  would 


AND   MODERN   PHYSICS.  157 

behave  as  though  its  mass  were  negative — it  would 
move  in  a  direction  opposite  to  that  of  the  force."* 

Since  1846  many  other  theories  have  been  pro- 
posed to  explain  Ampere's  laws.  Meanwhile,  in  1821, 
Faraday  observed  that  under  certain  circumstances  a 
wire  carrying  a  current  could  be  kept  in  continuous 
rotation  in  a  magnetic  field  by  the  action  between  the 
magnets  and  the  current.  In  1824  Arago  observed 
the  motion  of  a  magnet  caused  by  rotating  a  copper 
disc  in  its  neighbourhood,  while  in  1831  Faraday 
began  his  experimental  researches  into  electro-magnetic 
induction.  About  the  same  period  Joseph  Henry,  of 
Washington,  was  making,  independently  of  Faraday, 
experiments  of  fundamental  importance  on  electro- 
magnetic induction,  but  sufficient  attention  was  not 
called  to  his  work  until  comparatively  recent  years. 

In  1833  Lenz  made  some  important  researches, 
which  led  him  to  discover  the  connection  between  the 
direction  of  the  induced  currents  and  Ampere's  laws, 
summed  up  in  his  rule  that  the  direction  of  the 
induced  current  is  always  such  as  to  oppose  by  its 
electro-magnetic  action  the  motion  which  induces  it. 

In  1845  F.  E.  Neumann  developed  from  this  law 
the  mathematical  theory  of  electro-magnetic  induction, 
and  about  the  same  time  W.  Weber  showed  how  it 
might  be  deduced  from  his  elementary  law  of 
electrical  action. 

The  great  name  of  Von  Helmholtz  first  appears  in 
connection  with  this  subject  in  1851,  but  of  his 
writings  we  shall  have  more  to  say  at  a  later  stage. 

*  J.    J.  Thomson,    B.A.,  Report,   1885,  pp.    109,    113,  Report   on 
Electrical  Theories. 


158  JAMES   CLERK   MAXWELL 

Meanwhile,  during  the  same  period,  various 
writers,  Murphy,  Plana,  Charles,  Sturm,  and  Gauss, 
extended  Poisson's  work  on  electrostatics,  treating  the 
questions  which  arose  as  problems  in  the  distribution 
of  an  attracting  fluid,  attracting  or  repelling  according 
to  Newton's  law,  though  here  again  the  greatest 
advances  were  made  by  a  self-taught  Nottingham 
shoemaker,  George  Green  by  name,  in  his  paper  "  On 
the  Application  of  Mathematical  Analysis  to  the 
Theories  of  Electricity  and  Magnetism,"  1828. 

Green's  researches,  Lord  Kelvin  writes,  "  have  led  to 
the  elementary  proposition  which  must  constitute  the 
legitimate  foundation  of  every  perfect  mathematical 
structure  that  is  to  be  made  from  the  materials  fur- 
nished by  the  experimental  laws  of  Coulomb." 

Green,  it  may  be  remarked,  was  the  inventor  of 
the  term  Potential.  His  essay,  however,  lay  neglected 
from  1828,  until  Lord  Kelvin  called  attention  to  it  in 
1845.  Meanwhile,  some  of  its  most  important  results 
had  been  re-discovered  by  Gauss  and  Charles  and 
Thomson  himself. 

Until  about  1845,  the  experimental  work  on  which 
these  mathematical  researches  in  electrostatics  were 
based  was  that  of  Coulomb.  An  electrified  body  is 
supposed  to  have  a  charge  of  some  imponderable  fluid 
"  electricity."  Particles  of  electricity  repel  each  other 
according  to  a  certain  law,  and  the  fluid  distributes 
itself  in  equilibrium  over  the  surface  of  any  charged 
conductor  in  accordance  with  this  law.  There  are  on 
this  theory  two  opposite  kinds  of  electric  fluid,  positive 
and  negative,  two  charges  of  the  same  kind  repel,  two 
charges   of  opposite  kinds  attract;  the  repulsion  or 


AND   MODERN   PHYSICS.  159 

attraction  is  proportional  to  the  product  of  the  charges, 
and  inversely  proportional  to  the  square  of  the 
distance  between  them. 

The  action  between  two  charges  is  action  at  a 
distance  taking  place  across  the  space  which  separates 
the  two. 

Faraday,  in  1837,  in  the  eleventh  series  of  his 
"  Experimental  Researches,"  published  his  first  paper 
on  "  Electrostatic  Induction."  He  showed — as  indeed 
Cavendish  had  proved  long  previously,  though  the 
result  remained  unpublished — that  the  force  between 
two  charged  bodies  will  depend  on  the  insulating 
medium  which  surrounds  them,  not  merely  on  their 
shape  and  position.  Induction,  as  he  expresses  it, 
takes  place  along  curved  lines,  and  is  an  action  of 
contiguous  particles ;  these  curved  lines  he  calls  the 
"  lines  of  force." 

Discussing  these  researches  in  1845,  Lord  Kelvin 
writes* : — 

"Mr.  Faraday's  researches  .  .  .  were  undertaken  with  a 
view  to  test  an  idea  which  he  had  long  possessed  that  the 
forces  of  attraction  and  repulsion  exercised  by  free  electricity 
are  not  the  resultants  of  actions  exercised  at  a  distance,  but  are 
propagated  by  means  of  molecular  action  among  the  con- 
tiguous particles  of  the  insulating  medium  surrounding  the 
electrified  bodies,  which  he  therefore  calls  the  dielectric.  By 
this  idea  he  has  been  led  to  some  very  remarkable  views  upon 
induction,  or,  in  fact,  upon  electrical  action  in  general.  As  it 
is  impossible  that  the  phenomena  observed  by  Faraday  can  be 
incompatible  with  the  results  of  experiment  which  constitute 
Coulomb's  theory,  it  is  to  be  expected  that  the  difference  of 
his  ideas  from  those  of  Coulomb  must  arise  solely  from  a 
different   method  of  stating  and  interpreting  physically  the 

*  Tapers  on  "  Electrostatics,"  etc.,  p.  26. 


100  JAMES   CLERK   MAXWELL 

same  laws ;  and  further,  it  may,  I  think,  be  shown  that  either 
method  of  viewing  this  subject,  when  carried  sufficiently  far, 
may  be  made  the  foundation  of  a  mathematical  theory  which 
would  lead  to  the  elementary  principles  of  the  other  as  conse- 
quences. This  theory  would,  accordingly,  be  the  expression  of 
the  ultimate  law  of  the  phenomena,  independently  of  any 
physical  hypothesis  we  might  from  other  circumstances  be  led 
to  adopt.  That  there  are  necessarily  two  distinct  elementary 
ways  of  viewing  the  theory  of  electricity  may  be  seen  from  the 
following  considerations.  .  .  ." 

In  the  pages  which  follow.  Lord  Kelvin  develops 
the  consequences  of  an  analogy  between  the  conduc- 
tion of  heat  and  electrostatic  action,  which  he  had 
pointed  out  three  years  earlier  (1842),  in  his  paper  on 
"  The  Uniform  Motion  of  Heat  in  Homogeneous  Solid 
Bodies,"  and  discusses  its  connection  with  the  mathe- 
matical theory  of  electricity. 

The  problem  of  distributing  sources  of  heat  in  a 
given  homogeneous  conductor  of  heat,  so  as  to  pro- 
duce a  definite  steady  temperature  at  each  point  or 
the  conductor  is  shewn  to  be  mathematically  identical 
with  that  of  distributing  electricity  in  equilibrium,  so 
as  to  produce  at  each  point  an  electrical  potential 
having  the  same  value  as  the  temperature. 

Thus  the  fundamental  laws  of  the  conduction  of 
heat  ma}<  be  made  the  basis  of  the  mathematical 
theory  of  electricity,  but  the  physical  idea  which 
they  suggest  is  that  of  the  propagation  of  some  effect 
by  means  of  the  mutual  action  of  contiguous  particles, 
rather  than  that  of  material  particles  attracting  or 
repelling  at  a  distance,  which  naturally  follows  from 
the  statement  of  Coulomb's  law. 

Lord  Kelvin  continues : — ■ 


AND   MODERN   PHYSICS.  1G1 

''  All  the  views  which  Faraday  has  brought  forward  and 
illustrated,  as  demonstrated  by  experiment,  lead  to  this  method 
of  establishing  the  mathematical  theory,  and,  as  far  as  the 
analysis  is  concerned,  it  would  in  most  general  propositions  be 
more  simple,  if  possible,  than  that  of  Coulomb.  Of  course  the 
analysis  of  particular  problems  would  be  identical  in  the  two 
methods.  It  is  thus  that  Faraday  arrives  at  a  knowledge  of 
some  of  the  most  important  of  the  mathematical  theorems 
which  from  their  nature  seemed  destined  never  to  be  perceived 
except  as  mathematical  truths." 

Lord  Kelvin's  papers  on  "The  Mathematical 
Theory  of  Electricity,"  published  from  1848  to  1850, 
his  "  Propositions  on  the  Theory  of  Attraction " 
(1842),  his  "Theory  of  Electrical  Images"  (1847), 
and  his  paper  on  "The  Mathematical  Theory  of 
Magnetism  "  (1849),  contain  a  statement  of  the  most 
important  results  achieved  in  the  mathematical 
sciences  of  Electrostatics  and  Magnetism  up  to  the 
time  of  Maxwell's  first  paper. 

The  opening  sentences  of  that  paper  have  already 
been  quoted.  In  the  preface  to  the  "  Electricity  and 
Magnetism  "  Maxwell  writes  thus  : — 

"Before  I  began  the  study  of  electricity  I  resolved  to  read 
no  mathematics  on  the  subject  till  1  had  first  read  through 
4  Experimental  Researches  on  Electricity.'  I  was  aware  that 
there  was  supposed  to  be  a  difference  between  Faraday's  way 
of  conceiving  phenomena  and  that  of  the  mathematicians,  so 
that  neither  he  nor  they  were  satisfied  with  each  other's 
language.  I  had  also  the  conviction  that  this  discrepancy  did 
not  arise  from  either  party  being  wrong.  I  was  first  convinced 
of  this  by  Sir  William  Thomson,  to  whose  advice  and  assist- 
ance, as  well  as  to  his  published  papers,  I  owe  most  of  what  I 
have  learned  on  the  subject. 

"As  I  proceeded  with  tin  study  of  Faraday,  I  perceived 
that   his   method   of  conceiving  the    pheno.nena   was  also   a 

K 


1G2  JAMES   CLERK   MAXWELL 

mathematical  one,  though  not  exhibited  in  the  conventional 
form  of  mathematical  symbols.  I  also  found  that  these 
methods  were  capable  of  being  expressed  in  the  ordinary 
mathematical  forms,  and  thus  compared  with  those  of  the  pro- 
fessed mathematicians. 

"  For  instance,  Faraday,  in  his  mind's  eye,  saw  lines  of 
force  traversing  all  space  where  the  mathematicians  saw 
centres  of  force  attracting  at  a  distance.  Faraday  saw  a 
medium  where  they  saw  nothing  but  distance.  Faraday 
sought  the  seat  of  the  phenomena  in  real  actions  going  on  in 
the  medium.  They  were  satisfied  that  they  had  found  it 
in  a  power  of  action  at  a  distance  impressed  on  the  electric 
fluids." 

Now,  Maxwell  saw  an  analogy  between  electro- 
statics and  the  steady  motion  of  an  incompressible 
fluid  like  water,  and  it  is  this  analogy  which  he  develops 
in  the  first  part  of  his  paper.  The  water  flowTs  along- 
definite  lines ;  a  surface  which  consists  wholly  of  such 
lines  of  flow  will  have  the  property  that  no  water  ever 
crosses  it.  In  any  stream  of  water  we  can  imagine  a 
number  of  such  surfaces  drawn,  dividing  it  up  into  a 
series  of  tubes ;  each  of  these  will  be  a  tube  of  flow,  each 
of  these  tubes  remain  always  filled  with  water.  Hence, 
the  quantity  of  wrater  which  crosses  per  second  any 
section  of  a  tube  of  flow  perpendicular  to  its  length  is 
always  the  same.  Thus,  from  the  form  of  the  tube, 
we  can  obtain  information  as  to  the  direction  and 
strength  of  the  flow,  for  where  the  tube  is  wide  the 
flow  will  be  proportionately  small,  and  vice  versa. 

Again,  wre  can  draw  in  the  fluid  a  number  of  sur- 
faces, over  each  of  which  the  pressure  is  the  same ; 
these  surfaces  will  cut  the  tubes  of  flow  at  right 
angles.  Let  us  suppose  they  are  drawn  so  that  the 
difference  of  pressure  between  any  two   consecutive 


AND   MODERN   PHYSICS.  1G3 

surfaces  is  unity,  then  the  surfaces  will  be  close 
together  at  points  at  which  the  pressure  changes 
rapidly ;  where  the  variation  of  pressure  is  slow,  the 
distance  between  two  consecutive  surfaces  will  be 
considerable. 

If,  then,  in  any  case  of  motion,  we  can  draw  the 
pressure  surfaces,  and  the  tubes  of  flow,  we  can  de- 
termine the  motion  of  the  fluid  completely.  Now, 
the  same  mathematical  expressions  which  appear  in 
the  hydro-dynamical  theory  occur  also  in  the  theory 
of  electricity,  the  meaning  only  of  the  symbols  is 
changed.  For  velocity  of  fluid  we  have  to  write 
electrical  force.  For  difference  of  fluid  pressure  we 
substitute  work  done,  or  difference  of  electrical 
potential  or  pressure. 

The  surfaces  and  tubes,  drawn  as  the  solution 
of  any  hydro-dynamical  problem,  give  us  also  the 
solution  of  an  electrical  problem  ;  the  tubes  of  flow  are 
Faraday's  tubes  of  force,  or  tubes  of  induction,  the 
surfaces  of  constant  pressure  are  surfaces  of  equal 
electrical  potential.  Induction  may  take  place  in 
curved  lines  just  as  the  tubes  of  flow  may  be  bent  and 
curved  ;  the  analogy  between  the  two  is  a  complete 
one. 

But,  as  Maxwell  shows,  the  analogy  reaches  further 
still.  An  electric  current  flowing  along  a  wire  had 
been  recognised  as  having  many  properties  similar  to 
those  of  a  current  of  liquid  in  a  tube.  When  a  steady 
current  is  passing  through  any  solid  conductor,  there 
are  formed  in  the  conductor  tubes  of  electrical  flow 
and  surfaces  of  constant  pressure.  These  tubes  and 
surfaces  are  the  same  as  those  formed  by  the  flow  of 
k  2 


164  JAMES   CLERK   MAX  WELL 

liquid  through  a  solid  whose  boundary  surface  is  the 
same  as  that  of  the  conductor,  provided  the  flow  of 
liquid  is  properly  proportioned  to  the  flow  of  elec- 
tricity. 

These  analogies  refer  to  steady  currents  in  which, 
therefore,  the  flow  at  any  point  of  the  conductor  does 
not  depend  on  the  time.  In  Part  II.  of  his  paper  Max- 
well deals  with  Faraday's  electro-tonic  state.  Faraday 
had  found  that  when  changes  are  produced  in  the  mag- 
netic phenomena  surrounding  a  conductor,  an  electric 
current  is  set  up  in  the  conductor,  which  continues  so 
long  as  the  magnetic  changes  are  in  progress,  but 
which  ceases  when  the  magnetic  state  becomes  stead}7. 

"Considerations  of  this  kind  led  Professor  Faraday  to 
connect  with  his  discovery  of  the  induction  of  electric  currents 
the  conception  of  a  state  into  which  all  bodies  are  thrown  by 
the  presence  of  magnets  and  currents.  This  state  does  not 
manifest  itself  by  any  known  phenomena  as  long  as  it  is  un- 
disturbed, but  any  change  in  this  state  is  indicated  by  a 
current  or  tendency  towards  a  current.  To  this  state  he  gave 
the  name  of  the  '  Electro-tonic  State,'  and  although  he  after- 
wards succeeded  in  explaining  the  phenomena  which  suggested 
it  by  means  of  less  hypothetical  conceptions,  he  has  on  several 
occasions  hinted  at  the  probability  that  some  phenomena 
might  be  discovered  which  would  render  the  electro-tonic 
state  an  object  of  legitimate  induction.  These  speculations, 
into  which  Faraday  had  been  led  by  the  study  of  laws  which 
he  has  well  established,  and  which  he  abandoned  only  for 
want  of  experimental  data  for  the  direct  proof  of  the  unknown 
state,  have  not,  I  think,  been  made  the  subject  of  mathematical 
investigation.  Perhaps  it  may  be  thought  that  the  quantitative 
determinations  of  the  various  phenomena  are  not  sufficiently 
rigorous  to  be  made  the  basis  of  a  mathematical  theory. 
Faraday,  however,  has  not  contented  himself  with  simply 
stating  the  numerical  results  of  his  experiments  and  leaving 


AND   MODERN   PHYSICS.  165 

the  law  to  be  discovered  by  calculation.  Where  he  has  per- 
ceived a  law  he  has  at  once  stated  it,  in  terms  as  unambiguous 
as  those  of  pure  mathematics,  and  if  the  mathematician,  re- 
ceiving this  as  a  physical  truth,  deduces  from  it  other  laws 
capable  of  being  tested  by  experiment,  he  has  merely  assisted 
the  physicist  in  arranging  his  own  ideas,  which  is  confessedly 
a  necessary  step  in  scientific  induction. 

"In  the  following  investigation,  therefore,  the  laws  estab- 
lished by  Faraday  will  be  assumed  as  true,  and  it  will  be 
shown  that  by  following  out  his  speculations  other  and  more 
general  laws  can  be  deduced  from  them.  If  it  should,  then, 
appear  that  these  laws,  originally  devised  to  include  one  set  of 
phenomena,  may  be  generalised  so  as  to  extend  to  phenomena 
of  a  different  class,  these  mathematical  connections  may 
suggest  to  physicists  the  means  of  establishing  physical  con- 
nections, and  thus  mere  speculation  may  be  turned  to  account 
in  experimental  science." 

Maxwell  shows  how  to  obtain  a  mathematical  ex- 
pression for  Faraday's  electro-tonic  state.  In  his 
"  Electricity  and  Magnetism,"  this  electro-tonic  state 
receives  a  new  name.  It  is  known  as  the  Vector 
Potential*  and  the  paper  under  consideration  contains, 

*  It  is  difficult  to  explain  without  analysis  exactly  what  is 
measured  by  Maxwell's  Vector  Potential.  Its  rate  of  change  at  any 
point  of  space  measures  the  electromotive  force  at  that  point,  so  far 
as  it  is  due  to  variations  of  the  electric  current  in  neighbouring  con- 
ductors ;  the  magnetic  induction  depends  on  the  first  differential 
coefficients  of  the  components  of  the  electro-tonic  state ;  the  electric 
current  is  related  to  their  second  differential  coefficients  in  the  same 
manner  as  the  density  of  attracting  matter  is  related  to  the  potential 
it  produces.  In  language  which  is  now  frequently  used  in  mathe- 
matical physics,  the  electromotive  force  at  a  point  due  to  magnetic 
induction  is  proportioned  to  the  rate  of  change  of  the  Vector  Potential, 
the  magnetic  induction  depends  on  the  "curl"  of  the  Vector  Potential, 
while  the  electric  current  is  measured  by  the  "concentration  "  of  the 
Vector  Potential.  From  a  knowledge  of  the  Vector  Potential  these 
Other  quantities  can  be  obtained  by  processes  of  differentiation. 


166  JAMES   CLERK   MAXWELL 

though  in  an  incomplete  form,  his  first  statement  or 
those  equations  of  the  electric  field  which  are  so  in- 
dissolubly  bound  up  with  Maxwell's  name. 

The  great  advance  in  theory  made  in  the  paper  is 
the  distinct  recognition  of  certain  mathematical 
functions  as  representing  Faraday's  electro  tonic-state, 
and  their  use  in  solving  electro-magnetic  problems. 

The  paper  contains  no  new  physical  theory  of 
electricity,  but  in  a  few  years  one  appeared.  In  his 
later  writings  Maxwell  adopted  a  more  general  view 
of  the  electro-magnetic  field  than  that  contained 
in  his  early  papers  on  "Physical  Lines  of  Force."  It 
must,  therefore,  not  be  supposed  that  the  somewhat 
gross  conception  of  cog-wheels  and  pulleys,  which  we 
are  about  to  describe,  were  anything  more  to  their 
author  than  a  model,  which  enabled  him  to  realise 
how  the  changes,  which  occur  when  a  current  of 
electricity  passes  through  a  wire,  might  be  represented 
by  the  motion  of  actual  material  particles. 

The  problem  before  him  was  to  devise  a  physical 
theory  of  electricity,  which  would  explain  the  forces 
exerted  on  electrified  bodies  by  means  of  action 
between  the  contiguous  parts  of  the  medium  in  the 
space  surrounding  these  bodies,  rather  than  by  direct 
action  across  the  distance  which  separates  them.  A 
similar  question,  still  unanswered,  had  arisen  in  the 
case  of  gravitation.  Astronomers  have  determined 
the  forces  between  attracting  bodies ;  they  do  not 
know  how  those  forces  arise. 

Maxwell's  fondness  for  models  has  already  been 
alluded  to ;  it  had  led  him  to  construct  his  top  to 
illustrate  the  dynamics  of  a  rigid  body  rotating  about 


AND   MODERN   PHYSICS.  107 

a  fixed  point,  and  his  model  of  Saturn's  rings  (now  in 
the  Cavendish  Laboratory)  to  illustrate  the  motion  of 
the  satellites  in  the  rings.  He  had  explained  many  of 
the  gaseous  laws  by  means  of  the  impact  of  molecules, 
and  now  his  fertile  ingenuity  was  to  imagine  a 
mechanical  model  of  the  state  of  the  electro-magnetic 
field  near  a  system  of  conductors  carrying  currents. 

Faraday,  as  we  have  seen,  looked  upon  electro- 
static and  magnetic  induction  as  taking  place  along 
curved  lines  of  force.  He  pictures  these  lines  as 
ropes  of  molecules  starting  from  a  charged  conductor, 
or  a  magnet,  as  the  case  may  be,  and  acting  on  other 
bodies  near.  These  ropes  of  molecules  tend  to 
shorten,  and  at  the  same  time  to  swell  outwards 
laterally.  Thus  the  charged  conductor  tends  to  draw 
other  bodies  to  itself,  there  is  a  tension  along  the 
lines  of  force,  while  at  the  same  time  each  tube  of 
molecules  pushes  its  neighbours  aside ;  a  pressure  at 
right  angles  to  the  lines  of  force  is  combined  with 
this  tension.  Assuming  for  a  moment  this  pressure 
and  tension  to  exist,  can  we  devise  a  mechanism  to 
account  for  it  ?  Maxwell  himself  has  likened  the 
lines  of  force  to  the  fibres  of  a  muscle.  As  the  fibres 
contract,  causing  the  limb  to  which  they  are  attached 
to  move,  they  swell  outwards,  and  the  muscle  thickens. 

Again,  from  another  point  of  view,  we  might  con- 
sider a  line  of  force  as  consisting  of  a  string  of  small 
cells  of  some  flexible  material  each  filled  Avith  fluid. 
If  we  then  suppose  this  series  of  cells  caused  to 
rotate  rapidly  about  the  direction  of  the  line  of  force, 
the  cells  will  expand  laterally  and  contract  longi- 
tudinally ;  there  will  again  be  tension  along  the  lines 


168  JAMES   CLERK    MAXWELL 

of  force  and  pressure  at  right  angles  to  them.  It  was 
this  last  idea,  as  we  shall  see  shortly,  of  which  Max- 
well made  use — 

"  I  propose  now  "  [he  writes  ("  On  Physical  Lines  of  Force," 
Phil.  Mag.,  vol.  xxi.)]  "  to  examine  magnetic  phenomena  from 
a  mechanical  point  of  view,  and  to  determine  what  tensions 
in,  or  motions  of,  a  medium  are  capable  of  producing  the 
mechanical  phenomena  observed.  If  by  the  same  hypothesis 
we  can  connect  the  phenomena  of  magnetic  attraction  with 
electro-magnetic  phenomena,  and  with  those  of  induced  cur- 
rents, we  shall  have  found  a  theory  which,  if  not  true,  can 
only  be  proved  to  be  erroneous  by  experiments,  which  will 
greatly  enlarge  our  knowledge  of  this  part  of  physics." 

Lord  Kelvin  had  in  1847  given  a  mechanical 
representation  of  electric,  magnetic  and  galvanic  forces 
by  means  of  the  displacements  of  an  elastic  solid  in  a 
state  of  strain.  The  angular  displacement  at  each 
point  of  the  solid  was  taken  as  proportional  to  the 
magnetic  force,  and  from  this  the  relation  between 
the  various  other  electric  quantities  and  the  motion 
of  the  solid  was  developed.  But  Lord  Kelvin  did  not 
attempt  to  explain  the  origin  of  the  observed  forces 
by  the  effects  due  to  these  strains,  but  merely  made 
use  of  the  mathematical  analogy  to  assist  the  imagi- 
nation in  the  study  of  both. 

Maxwell  considered  magnetic  action  as  existing 
in  the  form  of  pressure  or  tension,  or  more  gener- 
ally, of  some  stress  in  some  medium.  The  existence 
of  a  medium  capable  of  exerting  force  on  material 
bodies  and  of  withstanding  considerable  stress,  both 
pressure  and  tension,  is  thus  a  fundamental  hypothesis 
with  him ;  this  medium  is  to  be  capable  of  motion, 


AND   MODERN   PHYSICS.  1G9 

and  electro-magnetic  forces  arise  from  its  motion  and 
its  stresses. 

Now,  Maxwell's  fundamental  supposition  is  that, 
in  a  magnetic  field,  there  is  a  rotation  of  the  mole- 
cules  continually  in  progress  about  the  lines  of  mag- 
netic force.  Consider  now  the  case  of  a  uniform 
magnetic  field,  whose  direction  is  perpendicular  to 
the  paper ;  we  are  to  look  upon  the  lines  of  force 
as  parallel  strings  of  molecules,  the  axes  of  these 
strings  being  perpendicular  to  the  paper.  Each 
string  is  supposed  to  be  rotating  in  the  same  direc- 
tion about  its  axis,  and  the  angular  velocity  of  rota- 
tion is  a  measure  of  the  magnetic  force.  In  conse- 
quence of  this  rotation  there  will  be  differences  of 
pressure  in  different  directions  in  the  medium ;  the 
pressure  along  the  axes  of  the  strings  will  be  less  than 
it  would  be  if  the  medium  were  at  rest,  that  in  the 
directions  at  right  angles  to  the  axes  will  be  greater, 
the  medium  will  behave  as  though  it  were  under 
tension  along  the  axes  of  the  molecules  under 
pressure  at  right  angles  to  them.  Moreover,  it  can 
be  shown  that  the  pressure  and  the  tension  are  both 
proportional  to  the  square  of  the  angular  velocity 
• — the  square,  that  is,  of  the  magnetic  force — and 
this  result  is  in  accordance  with  the  consequences 
of  experiment. 

More  elaborate  calculation  shows  that  this  state- 
ment is  true  generally.  If  we  draw  the  lines  of  force 
in  any  magnetic  field,  and  then  suppose  the  molecules 
of  the  medium  set  in  rotation  about  these  lines  of 
force  as  axes,  with  velocities  which  at  each  point  are 
proportional  to  the  magnetic  force,  the  distribution  of 


170  JAMES   CLERK   MAXWELL 

pressure  throughout  is  that  which  we  know  actually 
to  exist  in  the  magnetic  field. 

According  to  this  hypothesis,  then,  a  permanent 
bar  magnet  has  the  power  of  setting  the  medium 
round  it  into  continuous  molecular  rotation  about  the 
lines  of  force  as  axes.  The  molecules  which  are  set 
in  rotation  we  may  consider  as  spherical,  or  nearly 
spherical,  cells  filled  with  a  fluid,  or  an  elastic  solid 
substance,  and  surrounded  by  a  kind  of  membrane,  or 
sack,  holding  the  contents  together. 

So  far  the  model  does  not  give  any  account  of 
electrical  actions  which  go  on  in  the  magnetic  field. 

The  energy  is  wholly  rotational,  and  the  forces 
wholly  magnetic. 

Consider,  however,  any  tAvo  contiguous  strings  of 
molecules.  Let  them  cut  the  paper  as  shown  in  the 
two  circles  in  Fig.  1  : — 


Fig.1. 

Then  these  cells  are  both  rotating  in  the  same 
direction,  hence  at  A,  where  they  touch,  their  points  of 
contact  will  be  moving  in  opposite  directions,  as  shown 
by  the  arrow  heads,  and  it  is  difficult  to  imagine  how 
such  motion  can  continue ;  it  would  require  the  sur- 
faces of  the  cells  to  be  perfectly  smooth,  and  if  this 
were  so  they  would  lose  the  power  of  transmitting 
action  from  one  cell  to  the  next. 

The  cells  A  and  B  may  be  compared  to  two  cog- 


AND   MODERN    PHYSICS.  171 

wheels  placed  close  together,  which  we  wish  to  turn 
in  the  same  direction.  If  the  cogs  can  interlock,  as  in 
Fig.  2,  this  is  impossible  :  consecutive  wheels  in  the 
train  must  move  in  opposite  directions. 

But  in  many  machines  the  desired  end  is  attained 
by  inserting  between  the  two  wheels  A  and  B  a  third 
idle  wheel  C,  as  shewn  in  Fig.  3.  *  This  may  be  very 


Fig.  3. 

small,  its  only  function  is  to  transmit  the  motion  of  A 
to  B  in  such  a  way  that  A  and  B  may  both  turn  in  the 
same  direction.  It  is  not  necessary  that  there  should 
be  cogs  on  the  wheels;  if  the  surfaces  be  perfectly 
rough,  so  that  no  slipping  can  take  place,  the  same 
result  follows  without  the  cogs. 

Guided  by  this  analogy  MaxAvell  extended  his 
model  by  supposing  each  cell  coated  with  a  number 
of  small  particles  which  roll  on  its  surface.  These 
particles  play  the  part  of  the  idle  wheels  in  the 
machine,  and  by  their  rolling  merely  enable  the 
adjacent  parts  of  two  cells  to  move  in  opposite 
directions. 

Consider  now  a  number  of  such  cells  and  their  idle 
wheels  lying  in  a  plane,  that  of  the  paper,  and  suppose 
each  cell  is  rotating:  with  the  same  uniform  angular 
velocity  about  an  axis  at  right  angles  to  that  plane, 
each  idle  wheel  will  be  acted  on  by  two  equal  and 
opposite  forces  at  the  ends  of  the  diameter  in  which 


172  JAMES   CLERK   MAXWELL 

it  is  touched  by  the  adjacent  cells ;  it  will  therefore 
be  set  in  rotation,  but  there  will  be  no  force  tending 
to  drive  it  onwards ;  it  does  not  matter  whether  the 
axis  on  which  it  rotates  is  free  to  move  or  fixed,  in 
either  case  the  idle  wheel  simply  rotates.  But  suppose 
now  the  adjacent  cells  are  not  rotating  at  the  same 
rate.  In  addition  to  its  rotation  the  idle  wheel  will  be 
urged  onward  with  a  velocity  which  depends  on  the 
difference  between  the  rotations,  and,  if  it  can  move 
freely,  it  will  move  on  from  between  the  two  cells. 
Imagine  now  that  the  interstices  between  the  cells 
are  fitted  with  a  string  of  idle  wheels.  So  long  as  the 
adjacent  cells  move  with  different  velocity  there  will 
be  a  continual  stream  of  rolling  particles  or  idle  wheels 
between  them.  Maxwell  in  the  paper  considered 
these  rolling  particles  to  be  particles  of  electricity. 
Their  motion  constitutes  an  electric  current.  In  a 
uniform  magnetic  field  there  is  no  electric  current ; 
if  the  strength  of  the  field  varies,  the  idle  wheels  are 
set  in  motion  and  there  may  be  a  current. 

These  particles  are  very  small  compare  1  with  the 
magnetic  vortices.  The  mass  of  all  the  particles  is  in- 
appreciable compared  with  the  mass  of  the  vortices, 
and  a  great  many  vortices  with  their  surrounding 
particles  are  contained  in  a  molecule  of  the  medium  ; 
the  particles  roll  on  the  vortices  without  touching 
each  other,  so  that  so  long  as  they  remain  within  the 
same  molecule  there  is  no  loss  of  energy  by  resistance. 
When,  however,  there  is  a  current  or  general  trans- 
ference of  particles  in  one  direction  they  must  pass 
from  one  molecule  to  another,  and  in  doing  so  may 
experience  resistance  and  generate  heat. 


and  modern  physics.  173 

Maxwell  states  that  the  conception  of  a  particle, 
having  its  motion  connected  with  that  of  a  vortex  by 
perfect  rolling  contact,  may  appear  somewhat  awkward. 
"  I  do  not  bring  it  forward,"  he  writes,  "  as  a  mode  of 
connection  existing:  in  Nature,  or  even  as  that  which 
I  would  willingly  assent  to  as  an  electrical  hypothesis. 
It  is,  however,  a  mode  of  connection  which  is  mechani- 
cally conceivable  and  easily  investigated,  and  it  serves 
to  bring  out  the  actual  mechanical  connections 
between  the  known  electro-magnetic  phenomena,  so 
that  I  venture  to  say  that  anyone  who  understands 
the  provisional  and  temporary  character  of  this 
hypothesis  will  find  himself  rather  helped  than 
hindered  by  it  in  his  search  after  the  true  interpreta- 
tion of  the  phenomena." 

The  first  part  of  the  paper  deals  with  the  theory 
of  magnetism  ;  in  the  second  part  the  hypothesis  is 
applied  to  the  phenomena  of  electric  currents,  and  it 
is  shown  how  the  known  laws  of  steady  currents  and 
of  electro-ma<metic  induction  can  be  deduced  from  it. 
In  Part  III,  published  January  and  February,  1862,  the 
theory  of  molecular  vortices  is  applied  to  statical 
electricity. 

The  distinction  between  a  conductor  and  an 
insulator  or  dielectric  is  supposed  to  be  that  in  the 
former  the  particles  of  electricity  can  pass  with  more 
or  less  freedom  from  molecule  to  molecule.  In  the 
latter  such  transference  is  impossible,  the  particles  can 
only  be  displaced  within  the  molecule  with  which 
they  are  connected;  the  cells  or  vortices  of  the 
medium  are  supposed  to  be  elastic,  and  to  resist  by 
their  elasticity  the  displacement  of  the  particles  within 


174  JAMES   CLERK   MAXWELL 

them.  When  electrical  force  acts  on  the  medium  this 
displacement  of  the  particles  within  each  molecule 
takes  place  until  the  stresses  due  to  the  elastic  re- 
action of  the  vortices  balance  the  electrical  force  ;  the 
medium  behaves  like  an  elastic  body  yielding  to 
pressure  until  the  pressure  is  balanced  by  the  elastic 
stress.  When  the  electric  force  is  removed  the  cells 
or  vortices  recover  their  form,  the  electricity  returns 
to  its  former  position. 

In  a  medium  such  as  this  waves  of  periodic 
displacement  could  be  set  up,  and  would  travel  with 
a  velocity  depending  on  its  electric  properties.  The 
value  for  this  velocity  can  be  obtained  from  electrical 
observations,  and  Maxwell  showed  that  this  velocity, 
so  found,  was,  within  the  limits  of  experimental  error, 
the  same  as  that  of  light.  Moreover,  the  electrical 
oscillations  take  place,  like  those  of  light,  in  the  front 
of  the  wave.  Hence,  he  concludes,  "  the  elasticity  of 
the  magnetic  medium  in  air  is  the  same  as  that  of 
the  luminiferous  medium,  if  these  two  coexistent, 
coextensive,  and  equally  elastic  media  are  not  rather 
one  medium." 

The  paper  thus  contains  the  first  germs  of  the 
electro-magnetic  theory  of  light.  Moreover,  it  is 
shown  that  the  attraction  between  two  small  bodies 
charged  with  given  quantities  of  electricity  depends 
on  the  medium  in  which  they  are  placed,  Avhile  the 
specific  inductive  capacity  is  found  to  be  proportional 
to  the  square  of  the  refractive  index. 

The  fourth  and  final  part  of  the  paper  investigates 
the  propagation  of  light  in  a  magnetic  field. 

Faraday  had  shown  that  the  direction  of  vibration 


AND   MODERN   PHYSICS.  175 

in  a  wave  of  polarised  light  travelling  parallel  to  the 
lines  of  force  in  a  magnetic  field  is  rotated  by  its 
passage  through  the  field.  The  numerical  laws  of 
this  relation  had  been  investigated  by  Verdet,  and 
Maxwell  showed  how  his  hypothesis  of  molecular 
vortices  led  to  laws  which  agree  in  the  main  with  » 
those  found  by  Verdet. 

He  points  out  that  the  connection  between 
magnetism  and  electricity  has  the  same  mathe- 
matical form  as  that  between  certain  other  pairs  of 
phenomena,  one  of  which  has  a  linear  and  the  other 
a  rotatory  character ;  and,  further,  that  an  analogy 
may  be  worked  out  assuming  either  the  linear 
character  for  magnetism  and  the  rotatory  character 
for  electricity,  or  the  reverse.  He  alludes  to  Prof. 
Challis'  theory,  according  to  which  magnetism  is  to 
consist  in  currents  in  a  fluid  whose  directions  corre- 
spond with  the  lines  of  magnetic  force,  while  electric 
currents  are  supposed  to  be  accompanied  by,  if  not 
dependent  upon,  a  rotatory  motion  of  the  fluid  about 
the  axis  of  the  current;  and  to  Von  Helmholtz's 
theory  of  a  somewhat  similar  character.  He  then 
gives  his  own  reasons — agreeing  with  those  of  Sir 
W.  Thomson  (Lord  Kelvin) — for  supposing  that  there 
must  be  a  real  rotation  going  on  in  a  magnetic  field 
in  order  to  account  for  the  rotation  of  the  plane  of 
polarisation,  and,  accepting  these  reasons  as  valid,  he 
develops  the  consequences  of  his  theory  with  the 
results  stated  above. 

His  own  verdict  on  the  theory  is  given  in  the 
"Electricity  and  Magnetism"  (vol.  ii.,  §  831,  first 
edition,  p.  41G)  : — 


176  JAMES  CLERK   MAXWELL 

"  A  theory  of  molecular  vortices,  which  I  worked  out  at  con- 
siderable length,  was  published  in  the  Phil.  Mag.  for  March, 
April,  and  May,  1861 ;  Jan.  and  Feb.,  1862. 

"  I  think  we  have  good  evidence  for  the  opinion  that  some 
phenomenon  of  rotation  is  going  on  in  the  magnetic  field,  that 
this  rotation  is  performed  by  a,  great  number  of  very  small 
portions  of  matter,  each  rotating  on  its  own  axis,  this  axis 
being  parallel  to  the  direction  of  the  magnetic  force,  and  that 
the  rotations  of  these  different  vortices  are  made  to  depend  on  one 
another  by  means  of  some  kind  of  mechanism  connecting  them. 

"The  attempt  which  I  then  made  to  imagine  a  working 
model  of  this  mechanism  must  be  taken  for  no  more  than  it 
really  is,  a  demonstration  that  mechanism  may  be  imagined 
capable  of  producing  a  connection  mechanically  equivalent  to 
the  actual  connection  of  the  parts  of  the  electro-magnetic  field. 
The  problem  of  determining  the  mechanism  required  to 
establish  a  given  species  of  connection  between  the  motions  of 
the  parts  of  a  system  always  admits  of  an  infinite  number  of 
solutions.  Of  these,  some  may  be  more  clumsy  or  more  com- 
plex than  others,  but  all  must  satisfy  the  conditions  of 
mechanism  in  general. 

"  The  following  results  of  the  theory,  however,  arc  of 
higher  value  : — 

"(1)  Magnetic  force  s  the  effect  of  the  centrifugal  force  of 
the  vortices. 

"(2)  Electro-magnetic  induction  of  currents  is  the  effect  of 
the  forces  called  into  play  when  the  velocity  of  the  vortices  is 
changing. 

"(3)  Electromotive  force  arises  from  the  stress  on  the  con- 
necting mechanism. 

"(4)  Electric  displacement  arises  from  the  elastic  yielding 
of  the  connecting  mechanism." 

In  studying  this  part  of  Maxwell's  work,  it  must 
clearly  be  remembered  that  he  did  not  look  upon  the 
ether  as  a  series  of  cog-wheels  with  idle  wheels  be- 
tween, or  anything  of  the  kind.  He  devised  a  mechan- 
ical model  of  such  cogs  and  idle  wheels,  the  properties 


AND   MODERN    PHYSICS.  1  "7  7 

of  which  would  in  some  respects  closely  resemble 
those  of  the  ether ;  from  this  model  he  deduced, 
among  other  things,  the  important  fact  that  electric 
waves  would  travel  outwards  with  the  velocity  of 
light.  Other  such  models  have  been  devised  since 
his  time  to  illustrate  the  same  laws.  Prof.  Fitzgerald 
has  actually  constructed  one  of  wheels  connected 
together  by  elastic  bands,  which  shows  clearly  the  kind 
of  processes  which  Maxwell  supposed  to  go  on  in  a 
dielectric  when  under  electric  force.  Professor  Lodge, 
in  his  book,  "  Modern  Views  of  Electricity,"  has  very 
fully  developed  a  somewhat  different  arrangement  of 
cog-wheels  to  attain  the  same  result. 

Maxwell's  predictions  as  to  the  propagation  of 
electric  waves  have  in  recent  days  received  their  full 
verification  in  the  brilliant  experiments  of  Hertz  and 
his  followers ;  it  remains  for  us,  before  dealing  with 
these,  to  trace  their  final  development  in  his  hands. 

The  papers  we  have  been  discussing  were  perhaps 
too  material  to  receive  the  full  attention  they 
deserved ;  the  ether  is  not  a  series  of  cogs,  and  elec- 
tricity is  something  different  from  material  idle 
wheels.  In  his  paper  on  'The  Dynamical  Theory  of  the 
Electro-magnetic  Field,"  Phil.  Trans.,  1864,  Maxwell 
treats  the  same  questions  in  a  more  general  manner. 
On  a  former  occasion  he  says,  "  I  have  attempted  to 
describe  a  particular  kind  of  motion  and  a  particular 
kind  of  strain  so  arranged  as  to  account  for  the 
phenomena.  In  the  present  paper  I  avoid  any 
hjrpothesis  of  this  kind  ;  and  in  using  such  words  as 
electric  momentum  and  electric  elasticity  in  reference 
to  the  known  phenomena  of  the  induction  of  currents 


178  JAMES   CLERK   MAXWELL 

and  the  polarisation  of  dielectrics,  I  wish  merely  to 
direct  the  mind  of  the  reader  to  mechanical  pheno- 
mena, which  will  assist  him  in  understanding  the 
electrical  ones.  All  such  phrases  in  the  present 
paper  are  to  be  considered  as  illustrative  and  not  as 
explanatory."     He  then  continues : — 

"  In  speaking  of  the  energy  of  the  field,  however,  I  wish  to 
be  understood  literally.  All  energy  is  the  same  as  mechanical 
energy,  whether  it  exists  in  the  form  of  motion  or  in  that  of 
elasticity,  or  in  any  other  form. 

"  The  energy  in  electro-magnetic  phenomena  is  mechanical 
energy.     The  only  question  is,  Where  does  it  reside  1 

"  On  the  old  theories  it  resides  in  the  electrified  bodies,  con- 
ducting circuits,  and  magnets,  in  the  form  of  an  unknown 
quality  called  potential  energy,  or  the  power  of  producing 
certain  effects  at  a  distance.  On  our  theory  it  resides  in  the 
electro-magnetic  field,  in  the  space  surrounding  the  electrified 
and  magnetic  bodies,  as  well  as  in  those  bodies  themselves, 
and  is  in  two  different  forms,  which  may  be  described  without 
hypothesis  as  maguetic  polarisation  and  electric  polarisation, 
or,  according  to  a  very  probable  hypothesis,  as  the  motion  and 
the  strain  of  one  and  the  same  medium. 

"  The  conclusions  arrived  at  in  the  present  paper  are  inde- 
pendent of  this  hypothesis,  being  deduced  from  experimental 
facts  of  three  kinds  : — 

"(1)  The  induction  of  electric  currents  by  the  increase  or 
diminution  of  neighbouring  currents  according  to  the  changes 
in  the  lines  of  force  passing  through  the  circuit. 

"  (2)  The  distribution  of  magnetic  intensity  according  to 
the  variations  of  a  magnetic  potential. 

"  (3)  The  induction  (or  influence)  of  statical  electricity 
through  dielectrics. 

"  We  may  now  proceed  to  demonstrate  from  these  principles 
the  existence  and  laws  of  the  mechanical  forces,  which  act 
upon  electric  currents,  magnets,  and  electrified  bodies  placed 
in  the  electro-magnetic  field." 


AND   MODERN   PHYSICS.  179 

In  his  introduction  to  the  paper,  he  discusses  in  a 
general  way  the  various  explanations  of  electric  pheno- 
mena which  had  been  given,  and  points  out  that — 

"It  appears,  therefore,  that  certain  phenomena  in  electricity 
and  magnetism  lead  to  the  same  conclusion  as  those  of  optics, 
namely,  that  there  is  an  setherial  medium  pervading  all  bodies, 
and  modified  only  in  degree  by  their  presence  ;  that  the  parts 
of  this  medium  are  capable  of  being  set  in  motion  by  electric 
currents  and  magnets  ;  that  this  motion  is  communicated  from 
one  part  of  the  medium  to  another  by  forces  arising  from  the 
connection  of  those  parts  ;  that  under  the  action  of  these 
forces  there  is  a  certain  yielding  depending  on  the  elasticity  of 
these  connections  ;  and  that,  therefore,  energy  in  two  different 
forms  may  exist  in  the  medium,  the  one  form  being  the  actual 
energy  of  motion  of  its  parts,  and  the  other  being  the  potential 
energy  stored  up  in  the  connections  in  virtue  of  their  elasticity. 

"  Thus,  then,  -\ve  are  led  to  the  conception  of  a  complicated 
mechanism  capable  of  a  vast  variety  of  motion,  but  at  the 
same  time  so  connected  that  the  motion  of  one  part  depends, 
according  to  definite  relations,  on  the  motion  of  other  parts, 
these  motions  being  communicated  by  forces  arising  from  the 
relative  displacement  of  the  connected  parts,  in  virtue  of  their 
elasticity.  Such  a  mechanism  must  be  subject  to  the  general 
laws  of  dynamics,  and  we  ought  to  be  able  to  work  out  all  the 
consequences  of  its  motion,  provided  we  know  the  form  of  the 
relation  between  the  motions  of  the  parts." 

These  general  laws  of  dynamics,  applicable  to  the 
motion  of  any  connected  system,  had  been  developed 
by  Lagrange,  and  are  expressed  in  his  generalised 
equations  of  motion.  It  is  one  of  Maxwell's  chief 
claims  to  fame  that  he  saw  in  the  electric  field  a 
connected  system  to  which  Lagrange's  equations  could 
be  applied,  and  that  he  was  able  to  deduce  the 
mechanical  and  electrical  actions  which  take  place  by 
means  of  fundamental  propositions  of  dynamics. 
l  2 


180  JAMES   CLERK   MAXWELL 

The  methods  of  the  paper  now  under  discussion 
were  developed  further  in  the  "  Treatise  on  Electricity 
and  Magnetism,"  published  in  1873  ;  in  endeavouring 
to  give  some  slight  account  of  Maxwell's  work,  we 
shall  describe  it  in  the  form  it  ultimately  took. 

The  task  which  Maxwell  set  himself  was  a  double 
one ;  he  had  first  to  express  in  symbols,  in  as  general 
a  form  as  possible,  the  fundamental  laws  of  electro- 
magnetism  as  deduced  from  experiments,  chiefly  the 
experiments  of  Faraday,  and  the  relations  between 
the  various  quantities  involved ;  when  this  was  done 
he  had  to  show  how  these  laws  could  be  deduced  from 
the  general  dynamical  laws  applicable  to  any  system 
of  moving  bodies. 

There  are  two  classes  of  phenomena,  electric  and 
magnetic,  which  have  been  known  from  very  early 
times,  and  which  are  connected  together.  When  a 
piece  of  sealing-wax  is  rubbed  it  is  found  to  attract 
other  bodies,  it  is  said  to  exert  electric  force  through- 
out the  space  surrounding  it ;  when  two  different 
metals  are  dipped  in  slightly  acidulated  water  and 
connected  by  a  wire,  certain  changes  take  place  in  the 
plates,  the  water,  the  wire,  and  the  space  round  the 
wire,  electric  force  is  again  exerted  and  a  current  of 
electricity  is  said  to  flow  in  the  wire.  Again,  certain 
bodies,  such  as  the  lodestone,  or  pieces  of  iron  and 
steel  which  have  been  treated  in  a  certain  manner, 
exhibit  phenomena  of  action  at  a  distance :  they  are 
said  to  exert  magnetic  force,  and  it  is  found  that  this 
magnetic  force  exists  in  the  neighbourhood  of  an 
electric  current  and  is  connected  with  the  current. 

Again,  when  electric  force  is  applied  to  a  body,  the 


AND  MODERN   PHYSICS.  181 

effects  may  be  in  part  electrical,  in  part  mechanical ; 
the  electrical  state  of  the  body  is  in  general  changed, 
while  in  addition,  mechanical  forces  tending  to  move 
the  body  are  set  up.  Experiment  must  teach  us  how 
the  electrical  state  depends  on  the  electric  force,  and 
what  is  the  connection  between  this  electric  force  and 
the  magnetic  forces  which  may,  under  certain  circum- 
stances, be  observed.  Now,  in  specifying  the  electric 
and  magnetic  conditions  of  the  system,  various  other 
quantities,  in  addition  to  the  electric  force,  will  have 
to  be  introduced ;  the  first  step  is  to  formulate  the 
necessary  quantities,  and  to  determine  the  relations 
between  them  and  the  electric  force. 

Consider  now  a  wire  connecting  the  two  poles  of 
an  electric  battery — in  its  simplest  form,  a  piece  of 
zinc  and  a  piece  of  copper  in  a  vessel  of  dilute  acid — 
electric  force  is  produced  at  each  point  of  the  wire. 
Let  us  suppose  this  force  known ;  an  electric  current 
depending  on  the  material  and  the  size  of  the  wire 
flows  alonor  it,  its  value  can  be  determined  at  each 
point  of  the  wire  in  terms  of  the  electric  force  by 
Ohm's  law.  If  we  take  either  this  current  or  the 
electric  force  as  known,  we  can  determine  by  known 
laws  the  electric  and  magnetic  conditions  elsewhere. 
If  we  suppose  the  wire  to  be  straight  and  very  long, 
then,  so  long  as  the  current  is  steady  and  we  neglect 
the  small  effect  due  to  the  electrostatic  charge  on  the 
wire,  there  is  no  electric  force  outside  the  wire.  There 
is,  however,  magnetic  force,  and  it  is  found  that  the 
lines  of  magnetic  force  are  circles  round  the  wire.  It 
is  found  also  that  the  work  done  in  travelling  once 
completely  round  the  wire  against  the  magnetic  force 


1 82  JAMES   CLERK   MAXWELL 

is  measured  by  the  current  flowing  through  the  wire, 
and  is  obtained  in  the  system  of  units  usually  adopted 
by  multiplying  the  current  by  4>7r.  This  last  result  then 
gives  us  one  of  the  necessary  relations,  that  between 
the  magnetic  force  due  to  a  current  and  the  strength 
of  the  current. 

Again,  consider  a  steady  current  flowing  in  a 
conductor  of  any  form  or  shape,  the  total  flow  of 
current  across  any  section  of  the  conductor  can  be 
measured  in  various  ways,  and  it  is  found  that  at  any 
time  this  total  flow  is  the  same  for  each  section  of  the 
conductor.  In  this  respect  the  flow  of  a  current  re- 
sembles that  of  an  incompressible  fluid  through  a 
pipe  ;  where  the  pipe  is  narrow  the  velocity  of  flow 
is  greater  than  it  is  where  the  pipe  is  broad,  but  the 
total  quantity  crossing  each  section  at  any  given 
instant  is  the  same. 

Consider  now  two  conducting  bodies,  two  spheres, 
or  two  flat  plates  placed  near  together  but  insulated. 
Let  each  conductor  be  connected  to  one  of  the  poles 
of  the  battery  by  a  conducting  wire.  Then,  for  a  very 
short  interval  after  the  contact  is  made,  it  is  found 
that  there  is  a  current  in  each  wire  which  rapidly  dies 
away  to  zero.  In  the  neighbourhood  of  the  balk 
there  is  electric  force ;  the  balls  are  said  to  be  charged 
with  electricity,  and  the  lines  of  force  are  curved  lines 
running  from  one  ball  to  the  other.  It  is  found  that 
the  balls  slightly  attract  each  other,  and  the  space 
between  them  is  now  in  a  different  condition  from  what 
it  was  before  the  balls  were  charged.  According  to 
Maxwell,  Electric  Displacement  has  been  produced 
in  this  space,  and  the  electric  displacement  at  each 


AND   MODERN    PHYSICS.  183 

point  is  proportional  to  the  electric  force  at  that 
point. 

Thus,  (i)  when  electric  force  acts  on  a  conductor,  it 
produces  a  current,  the  current  being  by  Ohm's  law 
proportional  to  the  force :  (ii)  when  it  acts  on  an 
insulator  it  produces  electric  displacement,  and  the 
displacement  is  proportional  to  the  force  ;  while  (iii) 
there  is  magnetic  force  in  the  neighbourhood  of  the 
current,  and  the  work  done  in  carrying  a  magnetic 
pole  round  any  complete  circuit  linked  with  the 
current  is  proportional  to  the  current.  The  first  two 
of  these  principles  give  us  two  sets  of  equations  con- 
necting together  the  electric  force  and  the  current 
in  a  conductor  or  the  displacement  in  a  dielectric 
respectively ;  the  third  connects  the  magnetic  force 
and  the  current. 

Now  let  us  go  back  to  the  variable  period  when 
the  current  is  flowing  in  the  wires ;  and  to  make  ideas 
precise,  let  the  two  conductors  be  two  equal  large  flat 
plates  placed  with  their  faces  parallel,  and  at  some 
small  distance  apart.  In  this  case,  when  the  plates 
are  charged,  and  the  current  has  ceased,  the  electric 
displacement  and  the  force  are  confined  almost  entirely 
to  the  space  between  the  plates.  During  the  variable 
period  the  total  flow  at  any  instant  across  each  section 
of  the  wire  is  the  same,  but  in  the  ordinary  sense  of 
the  word  there  is  no  flow  of  electricity  across  the 
insulating  medium  between  the  plates.  In  this  space, 
however,  the  electric  displacement  is  continuously 
changing,  rising  from  zero  initially  to  its  final  steady 
value  when  the  current  ceases.  It  is  a  fundamental 
part  of  Maxwell's  theory  that  this  variation  of  electric 


184  JAMES  CLERK  MAXWELL 

displacement  is  equivalent  in  all  respects  to  a  current. 
The  current  at  any  point  in  a  dielectric  is  measured 
by  the  rate  of  change  of  displacement  at  that  point. 

Moreover,  it  is  also  an  essential  point  that  if  we 
consider  any  section  of  the  dielectric  between  the  two 
plates,  the  rate  of  change  of  the  total  displacement 
across  this  section  is  at  each  moment  equal  to  the 
total  flow  of  current  across  each  section  of  the  con- 
ducting wire. 

Currents  of  electricity,  therefore,  including  dis- 
placement currents,  always  flow  in  closed  circuits, 
and  obey  the  laws  of  an  incompressible  fluid  in 
that  the  total  flow  across  each  section  of  the  circuit 
— conducting  or  dielectric — is  at  any  moment  the 
same. 

It  should  be  clearly  remembered  that  this  funda- 
mental hypothesis  of  Maxwell's  theory  is  an  assump- 
tion only  to  be  justified  by  experiment.  Von 
Helmholtz,  in  his  paper  on  "  The  Equations  of 
Motion  of  Electricity  for  Bodies  at  Rest,"  formed 
his  equations  in  an  entirely  different  manner  from 
Maxwell,  and  arrived  at  results  of  a  more  general 
character,  which  do  not  require  us  to  suppose  that 
currents  flow  always  in  closed  circuits,  but  permit  of 
the  condensation  of  electricity  at  points  in  the  circuit 
where  the  conductors  end  and  the  non-conducting 
part  of  the  circuit  begins.  We  leave  for  the  present 
the  question  which  of  the  two  theories,  if  either, 
represents  the  facts. 

We  have  obtained  above  three  fundamental  rela- 
tions— (i)  that  between  electric  force  and  electric 
current   in   a   conductor ;    (ii)   that  between  electric 


AND  MODERN   PHYSICS.  185 

force  and  electric  displacement  in  a  dielectric  ;  (iii) 
that  between  magnetic  force  and  the  current  which 
gives  rise  to  it.  And  we  have  seen  that  an  electric 
current — i.e.  in  a  dielectric  the  variation  of  the 
strength  of  an  electric  field  of  force — gives  rise  to 
magnetic  force.  Now,  magnetic  force  acting1  on  a 
medium  produces  "  magnetic  displacement,"  or  mag- 
netic induction,  as  it  is  called.  In  all  media  except 
iron,  nickel,  cobalt,  and  a  few  other  substances,  the 
magnetic  induction  is  proportional  to  the  magnetic 
force,  and  the  ratio  between  the  magnetic  induction 
produced  by  a  given  force  and  the  force  is  found  to 
be  very  nearly  the  same  for  all  such  media.  This 
ratio  is  known  as  the  permeability,  and  is  generally 
denoted  by  the  symbol  //,. 

A  relation  reciprocal  to  that  given  in  (iii)  above 
might  be  anticipated,  and  was,  in  fact,  discovered  by 
Faraday.  Changes  in  a  field  of  magnetic  induction 
give  rise  to  electric  force,  and  hence  to  displacement 
currents  in  a  dielectric  or  to  conduction  currents  in 
a  conductor.  In  considering  the  relation  between 
these  changes  and  the  electric  force,  it  is  simplest 
at  first  not  to  deal  with  magnetic  matter  such  as 
iron,  nickel,  or  cobalt ;  and  then  we  may  say  that  (iv) 
the  work  which  at  any  instant  would  be  done  in 
carrying  a  unit  quantity  of  electricity  round  a 
closed  circuit  in  a  magnetic  field  against  the  electric 
forces  due  to  the  field  is  equal  to  the  rate  at  which 
the  total  magnetic  induction  which  threads  the 
circuit  is  being  decreased.  This  law,  summing  up 
Faraday's  experiments  on  electro-magnetic  induction, 
gives  a  fourth  principle,  leading  to  a  fourth  series 


186  JAMES   CLERK   MAXWELL 

of  equations  connecting  together  the  electric  and 
magnetic  quantities  involved. 

The  equations  deduced  from  the  above  four 
principles,  together  with  the  condition  implied  in 
the  continuity  of  an  electric  current,  constitute 
Maxwell's  equations  of  the  electro-magnetic  field. 

If  we  are  dealing  only  with  a  dielectric  medium, 
the  reciprocal  relation  between  the  third  and  fourth 
principle  may  be  made  more  clear  by  the  following 
statement : — 

(A)  The  work  done  at  any  moment  in  carrying 
a  unit  quantity  of  magnetism  round  a  closed  circuit 
in  a  field  in  which  electric  displacement  is  varying,  is 
equal  to  the  rate  of  change  of  the  total  electric 
displacement  through  the  circuit  multiplied  by  4  7r.  :<~ 

(B)  The  work  done  at  any  moment  in  carrying  a 
unit  quantity  of  electricity  round  a  circuit  in  a  field 
in  which  the  magnetic  induction  is  varying,  is  equal 
to  the  rate  of  change  of  the  total  magnetic  induction 
through  the  circuit. 

From  these  two  principles,  combined  with  the 
laws  connecting  electric  force  and  displacement, 
magnetic  force  and  induction,  and  with  the  condition 
of  continuity,  Maxwell  obtained  his  equations  of  the 
field. 

Faraday's  experiments  on  electro-magnetic  induc- 
tion afford  the  proof  of  the  truth  of  the  fourth 
principle.  It  follows  from  those  experiments  that 
when   the   number   of  lines   of   magnetic   induction 

*  The  4  it  is  introduced  because  of  the  system  of  units  usually 
employed  to  measure  electrical  quantities.  If  we  adopted  Mr.  Oliver 
Heaviside's  "  rational  units,"  it  would  disappear,  as  it  does  in  (B). 


AND   MODERN    PHYSICS.  1ST 

which  are  linked  with  any  closed  circuit  are  made 
to  vary,  an  induced  electromotive  force  is  brought 
into  play  round  that  circuit.  This  electromotive  force 
is,  according  to  Faraday's  results,  measured  by  the 
rate  of  decrease  in  the  number  of  lines  of  magnetic 
induction  which  thread  the  circuit.  Maxwell  applies 
this  principle  to  all  circuits,  whether  conducting  or  not. 

In  obtaining  equations  to  express  in  symbols 
the  results  of  the  fourth  principle  just  enunciated, 
Maxwell  introduces  a  new  quantity,  to  which  he  gives 
the  name  of  the  "vector  potential."  This  quantity 
appears  in  his  analysis,  and  its  physical  meaning  is 
not  at  first  quite  clear.  Professor  Poynting  has,  how- 
ever, put  Maxwell's  principles  in  a  slightly  different 
form,  which  enables  us  to  see  definitely  the  meaning  of 
the  vector  potential,  and  to  deduce  Maxwell's  equations 
more  readily  from  the  fundamental  statements. 

We  are  dealing  with  a  circuit  with  which  lines 
of  magnetic  induction  are  linked,  while  the  number 
of  such  lines  linked  with  the  circuit  is  varying.  Now, 
let  us  suppose  the  variation  to  take  place  in  con- 
sequence of  the  lines  of  induction  moving  outwards 
or  inwards,  as  the  case  may  be,  so  as  to  cut  the  circuit. 
Originally  there  are  none  linked  with  the  circuit.  As 
the  magnetic  field  has  grown  to  its  present  strength 
lines  of  magnetic  induction  have  moved  inwards. 
Each  little  element  of  the  circuit  has  been  cut  by  some, 
and  the  total  number  linked  with  the  circuit  can  be 
found  by  adding  together  those  cut  by  each  element. 
Now,  Professor  Poynting's  statement  of  Maxwell's 
fourth  principle  is  that  the  electrical  force  in  the 
direction  of  any  element  of  the  circuit  is  found  by 


188  JAMES   CLERK   MAXWELL 

dividing  by  the  length  of  the  element  the  number  of 
lines  of  magnetic  induction  which  are  cut  in  one 
second  by  it. 

Moreover,  the  total  number  of  lines  of  magnetic  in- 
duction which  have  been  cut  by  an  element  of  unit 
length  is  defined  as  the  component  of  the  vector 
potential  in  the  direction  of  the  element ;  hence  the 
electrical  force  in  any  direction  is  the  rate  of  decrease 
of  the  component  of  the  vector  potential  in  that 
direction.  We  have  thus  a  physical  meaning  for  the 
vector  potential,  and  shall  find  that  in  the  dynamical 
theory  this  quantity  is  of  great  importance. 

Professor  Poynting  has  modified  Maxwell's  third 
principle  in  a  similar  manner ;  he  looks  upon  the 
variation  in  the  electric  displacement  as  due  to  the 
motion  of  tubes  of  electric  induction,*  and  the  mag- 
netic force  along  any  circuit  is  equal  to  the  number 
of  tubes  of  electric  induction  cutting  or  cut  by  unit 
length  of  the  circuit  per  second,  multiplied  by  4>tt. 

From  the  equations  of  the  field,  as  found  by 
Maxwell,  it  is  possible  to  derive  two  sets  of  sym- 
metrical equations.  The  one  set  connects  the  rate  of 
change  of  the  electric  force  with  quantities  depending 
on  the  magnetic  force ;  the  other  set  connects  in  a 
similar  manner  the  rate  of  change  of  the  magnetic 
force  with  quantities  depending  on  the  electric  force. 

*  For  an  exact  statement  as  to  the  rel  ttion  between  the  directions 
of  the  lines  of  electric  displacement  and  of  the  magnetic  force,  refer- 
ence must  be  made  to  Professor  Poynting's  paper,  Phil.  Trans,,  188.5, 
Part  11.,  pp.  280,  281.  The  ideas  are  further  developed  in  a  series  of 
articles  in  the  Electrician,  September,  1895.  Reference  should  also  be 
made  to  J.  J.  Thomson's  "  Recent  Researches  in  Electricity  and 
Magnetism." 


AND    MODERN   PHYSICS.  189 

Several  writers  in  recent  years  adopt  these  equations 
as  the  fundamental  relations  of  the  field,  establishing 
them  by  the  argument  that  they  lead  to  consequences 
which  are  found  to  be  in  accordance  with  experiment. 

We  have  endeavoured  to  give  some  account  of 
Maxwell's  historical  method,  according  to  which  the 
equations  are  deduced  from  the  laws  of  electric 
currents  and  of  electro-magnetic  induction  derived 
directly  from  experiment. 

While  the  manner  in  which  Maxwell  obtained 
his  equations  is  all  his  own,  he  was  not  alone  in 
stating  and  discussing  general  equations  of  the  electro- 
magnetic field.  The  next  steps  which  we  are  about 
to  consider  are,  however,  in  a  special  manner  duo 
to  him.  An  electrical  or  magnetic  system  is  the 
seat  of  energy  ;  this  energy  is  partly  electrical,  partly 
magnetic,  and  various  expressions  can  be  found  for 
it.  In  Maxwell's  theory  it  is  a  fundamental  assump- 
tion that  energy  has  position.  "The  electric  and  mag- 
netic energies  of  any  electro-magnetic  system,"  says 
Professor  Poynting,  "  reside,  therefore,  somewhere  in 
the  field."  It  follows  from  this  that  they  are  present 
wherever  electric  and  magnetic  force  can  be  shown  to 
exist.  Maxwell  showed  that  all  the  electric  energy  is 
accounted  for  by  supposing  that  in  the  neighbourhood 
of  a  point  at  which  the  electric  force  is  R  there  is 
an  amount  of  energy  per  unit  of  volume  equal  to 
KR2/87r,  K  being  the  inductive  capacity  of  the 
medium,  while  in  the  neighbourhood  of  a  point  at 
which  the  magnetic  force  is  H,  the  magnetic  energy 
per  unit  of  volume  is  /jlJ^/Stt,  /j,  being  the  per- 
meability.    He  supposes,  then,  that  at  each  point  of 


190  JAMES   CLERK   MAXWELL 

an  electro-magnetic  system  energy  is  stored  accord- 
ing to  these  laws.  It  follows,  then,  that  the  electro- 
magnetic field  resembles  a  dynamical  system  in 
which  energy  is  stored.  Can  we  discover  more  of 
the  mechanism  by  which  the  actions  in  the  field 
are  maintained  ?  Now  the  motion  of  any  point  of  a 
connected  system  depends  on  that  of  other  points  of 
the  system  ;  there  are  generally,  in  any  machine,  a 
cartain  number  of  points  called  driving-points,  the 
motion  of  which  controls  the  motion  of  all  other 
parts  of  the  machine ;  if  the  motion  of  the  driving- 
points  be  known,  that  of  any  other  point  can  be  deter- 
mined. Thus  in  a  steam  engine  the  motion  of  a 
point  on  the  fly-wheel  can  be  found  if  the  motion  of 
the  piston  and  the  connections  between  the  piston 
and  the  wheel  be  known. 

In  order  to  determine  the  force  which  is  acting  on 
any  part  of  the  machine  we  must  find  its  momentum, 
and  then  calculate  the  rate  at  which  this  momentum 
is  being  changed.  This  rate  of  change  will  give  us 
the  force.  The  method  of  calculation  which  it  is 
necessary  to  employ  was  first  given  by  Lagrange,  and 
afterwards  developed,  with  some  modifications,  by 
Hamilton.  It  is  usually  referred  to  as  Hamilton's 
principle ;  when  the  equations  in  the  original  form 
are  used  they  are  known  as  Lagrange's  equations. 

Now  Maxwell  showed  how  these  methods  of  calcu- 
lation could  be  applied  to  the  electro-magnetic  field. 
The  energy  of  a  dynamical  system  is  partly  kinetic, 
partly  potential.  Maxwell  supposes  that  the  magnetic 
energy  of  the  field  is  kinetic  energy,  the  electric 
energy  potential.      When    the    kinetic    energy  of  a 


AND   MODERN    PHYSICS.  191 

system  is  known,  the  momentum  of  any  part  of  the 
system  can  be  calculated  by  recognised  processes. 
Thus  if  we  consider  a  circuit  in  an  electro-magnetic 
field  we  can  calculate  the  energy  of  the  field,  and 
hence  obtain  the  momentum  corresponding  to  this 
circuit.  If  we  deal  with  a  simple  case  in  which  the 
conducting  circuits  are  fixed  in  position,  and  only  the 
current  in  each  circuit  is  allowed  to  vary,  the  rate  of 
change  of  momentum  corresponding  to  any  circuit 
will  give  the  force  in  that  circuit.  The  momentum 
in  question  is  electric  momentum,  and  the  force  is 
electric  force.  Now  we  have  already  seen  that  the 
electric  force  at  any  point  of  a  conducting  circuit  is 
given  by  the  rate  of  change  of  the  vector  potential 
in  the  direction  considered.  Hence  we  are  led  to 
identify  the  vector  potential  with  the  electric  mo- 
mentum of  our  dynamical  system ;  and,  referring  to 
the  original  definition  of  vector  potential,  we  see  that 
the  electric  momentum  of  a  circuit  is  measured  by  the 
number  of  lines  of  magnetic  induction  which  are 
interlinked  with  it. 

Again,  the  kinetic  energy  of  a  dynamical  system 
can  be  expressed  in  terms  of  the  squares  and  products 
of  the  velocities  of  its  several  parts.  It  can  also  be 
expressed  by  multiplying  the  velocity  of  each  driving- 
point  by  the  momentum  corresponding  to  that  driving- 
point,  and  taking  half  the  sum  of  the  products. 
Suppose,  now,  we  are  dealing  with  a  system  consisting 
of  a  number  of  wire  circuits  in  which  currents  are 
running,  and  let  us  suppose  that  we  may  represent 
the  current  in  each  wire  as  the  velocity  of  a  driving- 
point  in  our  dynamical  system.     We  can  also  express 


192  JAMES   CLERK    MAXWELL 

in  terms  of  those  currents  the  electric  momentum  of 
each  wire  circuit;  let  this  be  done,  and  let  half  the 
sum  of  the  products  of  the  corresponding  velocities 
and  momenta  be  formed. 

In  maintaining  the  currents  in  the  wires  energy  is 
needed  to  supply  the  heat  which  is  produced  in  each 
wire  ;  but  in  starting  the  currents  it  is  found  that 
more  energy  is  needed  than  is  requisite  for  the  supply 
of  this  heat.  This  excess  of  energy  can  be  calculated, 
and  when  the  calculation  is  made  it  is  found  that  the 
excess  is  equal  to  half  the  sum  of  the  products  of  the 
currents  and  corresponding  momenta.  Moreover,  if 
this  sum  be  expressed  in  terms  of  the  magnetic  force, 
it  is  found  to  be  equal  to  fi  H2/8  7r,  which  is  the  mag- 
netic energy  of  the  field.  Now,  when  a  dynamical 
system  is  set  in  motion  against  known  forces,  more 
energy  is  supplied  than  is  needed  to  do  the  work 
against  the  forces ;  this  excess  of  energy  measures  the 
kinetic  energy  acquired  by  the  system. 

Hence,  Maxwell  was  justified  in  taking  the  mag- 
netic energy  of  the  field  as  the  kinetic  energy  of  the 
mechanical  system,  and  if  the  strengths  of  the  currents 
in  the  wires  be  taken  to  represent  the  velocities  of  the 
driving-points,  this  energy  is  measured  in  terms  of 
the  electrical  velocities  and  momenta  in  exactly  the 
same  way  as  the  energy  of  a  mechanical  system  is 
measured  in  terms  of  the  velocities  and  momenta  of 
its  driving-points. 

The  mechanical  system  in  which,  according  to 
Maxwell,  the  energy  is  stored  is  the  ether.  A  state  of 
motion  or  of  strain  is  set  up  in  the  ether  of  the  field. 
The  electric  forces  which  drive  the  currents,  and  also 


AX1>    MODERN    PHYSICS.  198 

the  mechanical  forces  acting  on  the  conductors  carry- 
ing the  currents,  are  due  to  this  state  of  motion,  or  it 
may  be  of  strain,  in  the  other.  It  must  not  be  sup- 
posed that  the  term  electric  displacement  in  Maxwell's 
mind  meant  an  actual  bodily  displacement  of  the 
particles  of  the  ether ;  it  is  in  some  way  connected 
Avith  such  a  material  displacement.  In  his  view,  with- 
out motion  of  the  ether  particles  there  would  be  no 
electric  action,  but  he  does  not  identify  electric 
displacement  and  the  displacement  of  an  ether 
particle. 

His  mechanical  theory,  however,  does  account  for 
the  electro-magnetic  forces  between  conductors  carry- 
ing currents.  The  energy  of  the  system  depends  on 
the  relative  positions  of  the  currents  which  form  part 
of  it.  Now,  any  conservative  mechanical  system 
tends  to  set  itself  in  such  a  position  that  its  potential 
energy  is  least,  its  kinetic  energy  greatest.  The 
circuits  of  the  system,  then,  will  tend  to  set  themselves 
so  that  the  electro-kinetic  energy  of  the  system  may 
be  as  large  as  possible ;  forces  will  be  needed  to  hold 
them  in  any  position  in  which  this  condition  is  not 
satisfied. 

We  have  another  proof  of  the  correctness  of  the 
value  found  for  the  energy  of  the  field  in  that  the 
forces  calculated  from  this  value  agree  with  those 
which  are  determined  by  direct  experiment. 

Again,  the  forces  applied  at  the  various  driving- 
points  are  transmitted  to  other  points  by  the  con- 
nections of  the  machine ;  the  connections  are  thrown 
into  a  state  of  strain ;  stress  exists  throughout  their 
substance.    When  we  see  the  piston-rod  and  the  shaft 

M 


194  JAMES    CLERK    MAXWELL 

of  an  engine  connected  by  the  crank  and  the  connect- 
ing-rod, we  recognise  that  the  work  done  on  the 
piston  is  transmitted  thus  to  the  shaft.  So,  too,  in 
the  electro-magnetic  field,  the  ether  forms  the  con- 
nection between  the  various  circuits  in  the  field ; 
the  forces  with  which  those  circuits  act  on  each  other 
are  transmitted  from  one  circuit  to  another  by  the 
stresses  set  up  in  the  ether. 

To  take  another  instance,  consider  the  electro- 
static attraction  between  two  charged  bodies.  Let  us 
suppose  the  bodies  charged  by  connecting  each  to 
the  opposite  pole  of  a  battery  ;  a  current  flows  from 
the  battery  setting  up  electric  displacement  in  the 
sp;ice  between  the  bodies,  and  throwing  the  ether  into 
a  state  of  strain.  As  the  strain  increases  the  current 
gets  less ;  the  reaction  resulting  from  the  strain  tends 
to  stop  it,  until  at  last  this  reaction  is  so  great  that 
the  current  is  stopped.  When  this  is  the  case  the 
wires  to  the  battery  may  be  removed,  provided  this  is 
done  without  destroying  the  insulation  of  the  bodies  ; 
the  state  of  strain  will  remain  and  shows  itself  in  the 
attraction  between  the  balls. 

Looking  at  the  problem  in  this  manner,  we  are 
face  to  face  with  two  great  questions — the  one,  What 
is  the  state  of  strain  in  the  ether  which  will  enable  it 
to  produce  the  observed  electro-static  attractions  and 
repulsions  between  charged  bodies  ?  and  the  other, 
What  is  the  mechanical  structure  of  the  ether  which 
would  give  rise  to  such  a  state  of  strain  as  will 
account  for  the  observed  forces  ?  Maxwell  gives  one 
answer  to  the  first  question ;  it  is  not  the  only  answer 
which  could    be    given,  but   it  does  account  for  the 


AND   MODERN   PHYSICS.  195 

facts.     He   failed   to   answer   the   second.     He   says 

("  Electricity  and  Magnetism,"  vol.  i.  p.  1 32)  :— 

"  It  must  be  carefully  borne  in  mind  that  we  have  made 
only  one  step  in  the  theory  of  the  action  of  the  medium.  We 
have  supposed  it  to  be  in  a  state  of  stress,  but  have  not  in  any 
way  accounted  for  this  stress,  or  explained  how  it  is  maintained. 
...  I  have  not  been  able  to  make  the  next  step,  namely,  to 
account  by  mechanical  considerations  for  these  stresses  in  the 
dielectric." 

Faraday  had  pointed  out  that  the  inductive  action 
between  two  bodies  takes  place  along  the  lines  of 
force,  which  tend  to  shorten  along  their  length  and 
to  spread  outwards  in  other  directions.  Maxwell 
compares  them  to  the  fibres  of  a  muscle,  which 
contracts  and  at  the  same  time  thickens  when 
exerting  force.  In  the  electric  field  there  is,  on 
Maxwell's  theory,  a  tension  along  the  lines  of  electric 
force  and  a  pressure  at  right  angles  to  those  lines. 
Maxwell  proved  that  a  tension  K  K2/8  it  along  the 
lines  of  force,  combined  with  an  equal  pressure  in 
perpendicular  directions,  would  maintain  the  equili- 
brium of  the  field,  and  would  give  rise  to  the  observed 
attractions  or  repulsions  between  electrified  bodies. 
Other  distributions  of  stress  might  be  found  which 
would  lead  to  the  same  result.  The  one  just  stated 
will  always  be  connected  with  Maxwell's  name.  It 
Avill  be  noticed  that  the  tension  along  the  lines  of 
force  and  the  pressure  at  right  angles  to  them  are 
each  numerically  equal  to  the  potential  energy  stored 
per  unit  of  volume  in  the  field.  The  value  of  each  of 
the  three  quantities  is  K  R2/8  tt. 

In  the  same  way,  in  a  magnetic  field,  there  is 
a  state  of  stress,  and  on  Maxwell's  theory  this,  too, 
m  2 


196  JAMES   CLERK    MAXWELL 

consists  of  a  tension  .along  the  lines  of  force  and  an 
equal  pressure  at  right  angles  to  them,  the  values 
of  the  tension  and  the  pressure  being  each  equal 
to  that  of  the  magnetic  energy  per  unit  of  volume, 
or  fju  H2/8  7r. 

In  a  case  in  which  both  electric  and  magnetic 
force  exists,  these  two  states  of  stress  are  super- 
posed. The  total  energy  per  unit  of  volume  is 
K  R2/8  7r  +  fi  H'/S  7r  ;  the  total  stress  is  made  up 
of  tensions  K  RL>/8  it  and  /x  H2/8  tt  along  the  lines 
of  electric  and  magnetic  force  respectively,  and  equal 
pressures  at  right  angles  to  these  lines. 

We  see,  then,  from  Maxwell's  theory,  that  electric 
force  produced  at  any  given  point  in  space  is  trans- 
mitted from  that  point  by  the  action  of  the  ether. 
The  question  suggests  itself,  Does  the  transmission 
take  time,  and  if  so,  does  it  proceed  with  a  definite 
velocity  depending  on  the  nature  of  the  medium 
through  which  the  change  is  proceeding  ? 

According  to  the  molecular-vortex  theory,  we 
have  seen  that  waves  of  electric  force  are  transmitted 
with  a  definite  velocity.  The  more  general  theory 
developed  in  the  "  Electricity  and  Magnetism  "  leads 
to  the  same  result.  Electric  force  produced  at  any 
point  travels  outwards  from  that  point  with  a  velocity 
given  by  I/a^K/a.  At  a  distant  point  the  force  is 
zero,  until  the  disturbance  reaches  it.  If  the  dis- 
turbance last  only  for  a  limited  interval,  its  effects 
will  at  any  future  time  be  confined  to  the  space 
within  a  spherical  shell  of  constant  thickness  depend- 
ing' on  the  interval ;  the  radii  of  this  shell  increase 
with  uniform  speed  l/\/  K  yu. 


AND   MODERN   PHYSICS.  197 

If  the  initial  disturbance  be  periodic,  periodic 
waves  of  electric  force  will  travel  out  from  the  centre, 
just  as  waves  of  sound  travel  out  from  a  bell,  or  waves 
of  light  from  a  candle  flame.  A  wire  carrying  an 
alternating  current  may  be  such  a  source  of  periodic 
disturbance,  and  from  the  wire  waves  travel  outwards 
into  space. 

Now,  it  is  known  that  in  a  sound  wave  the  dis- 
placements of  the  air  particles  take  place  in  the 
direction  in  which  the  wave  is  travelling  ;  they  lie 
at  right  angles  to  the  wave  front,  and  are  spoken  of 
as  longitudinal.  In  light  waves,  on  the  other  hand, 
the  displacements  are,  as  Fresnel  proved,  in  the  wave 
front,  at  right  angles,  that  is,  to  the  direction  of 
propagation  ;  they  are  transverse. 

Theory  shows  that  in  general  both  these  waves 
may  exist  in  an  elastic  solid  body,  and  that  they 
travel  with  different  velocities.  Of  which  nature  are 
the  waves  of  electric  displacement  in  a  dielectric  ? 
It  can  be  shewn  to  follow  as  a  necessary  consecuience 
of  Maxwell's  views  as  to  the  closed  character  of  all 
electric  currents,  that  waves  of  electric  displacement 
are  transverse.  Electric  vibrations,  like  those  of  light, 
are  in  the  wave  front  and  at  right  angles  to  the  direction 
of  propagation  ;  they  depend  on  the  rigidity  or  quasi- 
rigidity  of  the  medium  through  ivhich  they  travel, 
not  on  its  resistance  to  compression. 

Again,  an  electric  current,  whether  due  to  varia- 
tion of  displacement  in  a  dielectric  or  to  conduction 
in  a  conductor,  is  accompanied  by  magnetic  force. 
A  wave  of  periodic  electric  displacement,  then,  will 
be  also  a  wave  of  periodic  magnetic  force  travelling  at 


198  JAMES   CLERK   MAXWELL 

the  same  rate  ;  and  Maxwell  shewed  that  the  direc- 
tion of  this  magnetic  force  also  lies  in  the  wave  front, 
and  is  always  at  right  angles  to  the  electric  displace- 
ment. In  the  ordinary  theory  of  light  the  wave  of 
linear  displacement  is  accompanied  by  a  wave  of 
periodic  angular  twist  about  a  direction  lying  in 
the  wave  front  and  perpendicular  to  the  linear  dis- 
placement. 

In  many  respects,  then,  waves  of  electric  dis- 
placement resemble  waves  of  light,  and,  indeed,  as  we 
proceed  we  shall  find  closer  connections  still.  Hence 
comes  Maxwell's  electro-magnetic  theory  of  light. 

It  is  only  in  dielectric  media  that  electric  force  is 
propagated  by  wave  motion.  In  conductors,  although 
the  third  and  fourth  of  Maxwell's  principles  given  on 
page  185  still  are  true,  the  relation  between  the  electric 
force  and  the  electric  current  differs  from  that  which 
holds  in  a  dielectric.  Hence  the  equations  satisfied 
by  the  force  are  different.  The  laws  of  its  propagation 
resemble  those  of  the  conduction  of  heat  rather  than 
those  of  the  transmission  of  light. 

Again,  light  travels  with  different  velocities  in 
different  transparent  media.  The  velocity  of  electric 
waves,  as  has  been  stated,  is  equal  to  l/\//xR;  but 
in  making  this  statement  it  is  assumed  that  the 
simple  laws  which  hold  where  there  is  no  gross 
matter — or,  rather,  where  air  is  the  only  dielectric 
with  which  we  are  concerned — hold  also  in  solid  or 
liquid  dielectrics.  In  a  solid  or  a  liquid,  as  in  vacuo, 
the  waves  are  propagated  by  the  ether.  We  assume, 
as  a  first  step  towards  a  complete  theory,  that  so  far 
as  the  electric  waves  are  concerned   the  sole  effect 


AND   MODERN    PHYSICS.  199 

produced  by  the  matter  shews  itself  in  a  change  of 
inductive  capacity  or  of  permeability.  It  is  not  likely 
that  such  a  supposition  should  be  the  whole  truth, 
and  Ave  may,  therefore,  expect  results  deduced  from  it 
to  be  only  approximation  to  the  true  result. 

Now,  electro-magnetic  experiments  show  that, 
excluding  magnetic  substances,  the  permeability  of 
all  bodies  is  very  nearly  the  same,  and  differs  very 
slightly  from  that  of  air.  The  inductive  capacity, 
however,  of  different  bodies  is  different,  and  hence 
the  velocity  with  which  electro-magnetic  waves  travel 
differs  in  different  bodies. 

But  the  refraction  of  waves  of  light  depends  on 
the  fact  that  light  travels  with  different  velocities  in 
different  media;  hence  we  should  expect  to  have 
waves  of  electric  displacement  reflected  and  refracted 
when  they  pass  from  one  dielectric,  such  as  air,  to 
another,  such  as  glass  or  gutta-percha;  moreover, 
for  light  the  refractive  index  of  a  medium  such  as 
glass  is  the  ratio  of  the  velocity  in  air  to  the  velocity 
in  the  glass. 

Thus  the  electrical  refractive  index  of  glass  is  the 
ratio  of  the  velocity  of  electric  waves  in  air  to  their 
velocity  in  glass. 

Now  let  K0  be  the  inductive  capacity  of  air,  Kx  that 
of  glass,  taking  the  permeability  of  air  and  glass  to  be 
the  same,  we  have  the  result  that — 


Electrical  refractive  index  =  v  Ki  /  K0. 

But  the  ratio  of  the  inductive  capacity  of  glass  to 
that  of  air  is  known  as  the  specific  inductive  capacity 
of  glass, 


200  JAMES    CLERK    MAXWELL 

Hence,  the  specific  inductive  capacity  of  any 
medium  is  equal  to  the  square  of  the  electrical  refrac- 
tive index  of  that  medium. 

Since  Maxwell's  time  the  mathematical  laws  of 
the  reflexion  and  refraction  of  electric  waves  have 
been  investigated  by  various  writers,  and  it  has  been 
shewn  that  they  agree  exactly  with  those  enunciated 
by  Fresnel  for  light. 

Hitherto  we  have  been  discussing  the  propagation 
of  electric  waves  in  an  isotropic  medium,  one  which 
has  identical  properties  in  all  directions  about  a  point. 
Let  us  now  consider  how  these  laws  are  modified  if 
the  dielectric  be  crystalline  in  structure. 

Maxwell  assumes  that  the  crystalline  character 
of  the  dielectric  can  be  sufficiently  represented  by 
supposing  the  inductive  capacity  to  be  different  in 
different  directions;  experiments  have  since  shewn 
that  this  is  true  for  crystals  such  as  Iceland 
Spar  and  Aragonite  ;  he  assumes  also,  and  this,  too, 
is  justified  by  experiment,  that  the  magnetic  per- 
meability does  not  depend  on  the  direction.  It 
follows  from  these  assumptions  that  a  crystal  will 
produce  double  refraction  and  polarisation  of  electric 
waves  which  fall  upon  it,  and,  further,  that  the  laws 
of  double  refraction  will  be  those  given  by  Fresnel 
for  light  waves  in  a  doubly  refracting  medium. 
There  will  be  two  waves  in  the  crystal.  The  dis- 
turbance in  each  of  these  will  be  plane  polarised  ; 
their  velocity  and  the  position  of  their  plane  of 
polarisation  can  be  found  from  the  direction  in  which 
they  are  travelling  by  Fresnel's  construction  exactly. 

Maxwell's  theory,  then,  would  appear  to  indicate 


AND    MODERN    PHYSICS.  201 

some  close  connection  between  electric  waves  and 
those  of  light.  Faraday's  experiments  on  the  rota- 
tion of  the  plane  of  polarisation  by  magnetic  force 
shew  one  phenomenon  in  which  the  two  are  con- 
nected, and  Maxwell  endeavoured  to  apply  his  theory 
to  explain  this.  Here,  however,  it  became  necessary 
to  introduce  an  additional  hypothesis — there  must  be 
some  connection  between  the  motion  of  the  ether 
to  which  magnetic  force  is  due  and  that  which  con- 
stitutes light.  It  is  impossible  to  give  a  mechanical 
account  of  the  rotation  of  the  plane  of  polarisation 
without  some  assumption  as  to  the  relation  between 
these  two  kinds  of  motion.  Maxwell,  therefore, 
supposes  the  linear  displacements  of  a  point  in  the 
ether  to  be  those  which  give  rise  to  light,  while  the 
components  of  the  magnetic  force  are  connected  with 
these  in  the  same  way  as  the  components  of  a  vortex 
in  a  liquid  in  vortex  motion  are  connected  with  the 
displacements  of  the  liquid.  He  further  assumes  the 
existence  of  a  term  of  special  form  in  the  expression 
for  the  kinetic  energy,  and  from  these  assumjations  he 
deduces  the  laws  of  the  propagation  of  polarised 
light  in  a  magnetic  field.  These  laws  agree  in  the 
main  with  the  results  of  Verdet's  experiments. 


202  JAMES   CLERK    MAXWELL 

CHAPTER   X. 

DEVELOPMENT   OF   MAXWELL'S   THEORY. 

We  have  endeavoured  in  the  preceding  pages  to  give 
some  account  of  Maxwell's  contributions  to  electrical 
theory  and  the  physics  of  the  ether.  We  must  now 
consider  very  briefly  what  evidence  there  is  to  support 
these  views.  At  Maxwell's  death  such  evidence, 
though  strong,  was  indirect.  His  supporters  were 
limited  to  some  few  English-speaking  pupils,  young 
and  enthusiastic,  who  were  convinced,  it  may  be,  in 
no  small  measure,  by  the  affection  and  reverence  with 
which  they  regarded  their  master.  Abroad  his  views 
had  made  very  little  way. 

In  the  last  Avords  of  his  book  he  writes,  speaking 
of  various  distinguished  workers — 

"There  appears  to  be  in  the  minds  of  these  eminent  men 
some  prejudice,  or  a  priori  objection,  against  the  hypothesis  of 
a  medium  in  which  the  phenomena  of  radiation  of  light  and 
heat,  and  the  electric  actions  at  a  distance,  take  place.  It  is 
true  that,  at  one  time,  those  who  speculated  as  to  the  causes  of 
physical  phenomena  were  in  the  habit  of  accounting  for  each 
kind  of  action  at  a  distance  by  means  of  a  special  aetherial 
fluid,  whose  function  and  property  it  was  to  produce  these 
actions.  They  filled  all  space  three  and  four  times  over  with 
aethers  of  different  kinds,  the  properties  of  which  were  in- 
vented merely  to  'save  appearances,'  so  that  more  rational 
enquirers  were  willing  rather  to  accept  not  only  Newton's 
definite  law  of  attraction  at  a  distance,  but  even  the  dogma  of 
Cotes,*  that  action  at  a  distance  is  one  of  the  primary  pro- 
perties of  matter,  and  that  no  explanation  can  be  more  intel- 
ligible than  this  fact.  Hence  the  undulatory  theory  of  light 
*  Preface  to  Newton's  "  Principia,"  2nd  edition. 


AND    MODERN    PHYSICS.  203 

has  met  with  much  opposition,  directed  not  against  its  failure 
to  explain  the  phenomena,  but  against  its  assumption  of  the 
existence  of  a  medium  in  which  light  is  propagated. 

"  We  have  seen  that  the  mathematical  expression  for 
electro-dynamic  action  led,  in  the  mind  of  Gauss,  to  the  con- 
viction that  a  theory  of  the  propagation  of  electric  action  in 
time  would  be  found  to  be  the  very  key-stone  of  electro- 
dynamics. Now  we  are  unable  to  conceive  of  propagation  in 
time,  except  either  as  the  flight  of  a  material  substance  through 
space,  or  as  the  propagation  of  a  condition  of  motion,  or  stress, 
in  a  medium  already  existing  in  space. 

"  In  the  theory  of  Neumann,  the  mathematical  conception 
called  potential,  which  we  are  unable  to  conceive  as  a  material 
substance,  is  supposed  to  be  projected  from  one  particle  to 
another  in  a  manner  which  is  quite  independent  of  a  medium, 
and  which,  as  Neumann  has  himself  pointed  out,  is  extremely 
different  from  that  of  the  propagation  of  light. 

"  In  the  theories  of  Eiemann  and  Betti  it  would  appear 
that  the  action  is  supposed  to  be  propagated  in  a  manner 
somewhat  more  similar  to  that  of  light. 

"  But  in  all  of  these  theories  the  question  naturally  occurs  : — 
If  something  is  transmitted  from  one  particle  to  another  at  a 
distance,  what  is  its  condition  after  it  has  left  one  particle  and 
before  it  has  reached  the  other  1  If  this  something  is  the 
potential  energy  of  the  two  particles,  as  in  Neumann's  theory, 
how  are  we  to  conceive  this  energy  as  existing  in  a  point  of 
space,  coinciding  neither  with  the  one  particle  nor  with  the 
other  1  In  fact,  whenever  energy  is  transmitted  from  one  body 
to  another  in  time,  there  must  be  a  medium  or  substance  in 
which  the  energy  exists  after  it  leaves  one  body  and  before  it 
reaches  the  other,  for  energy,  as  Torricelli*  remarked,  'is  a 
quintessence  of  so  subtle  a  nature  that  it  cannot  be  contained 
in  any  vessel  except  the  inmost  substance  of  material  things.' 
Hence  all  these  theories  lead  to  a  conception  of  a  medium  in 
which  the  propagation  takes  place,  and  if  we  admit  this 
medium  as  an  hypothesis,  I  think  it  ought  to  occupy  a  pro- 
minent place  in  our  investigations,  and  that  we  ought  to 
*  "  Lezioni  Accademiche  "  (Firenze,  1715),  p.  25. 


204  JAMES    CLERK    MAXWELL 

endeavour  to  construct  a  mental  representation  of  all  the 
details  of  its  action,  and  this  has  been  my  constant  aim  in  this 
treatise." 

Let  us  see,  then,  what  were  the  experimental 
grounds  in  Maxwell's  day  for  accepting  as  true  his 
views  on  electrical  action,  and  how  since  then,  by  the 
genius  of  Heinrich  Hertz  and  the  labours  of  his 
followers,  those  grounds  have  been  rendered  so  sure 
that  nearly  the  whole  progress  of  electrical  science 
during  the  last  twenty  years  has  consisted  in  the 
development  of  ideas  which  are  to  be  found  in  the 
"  Treatise  on  Electricity  and  Magnetism." 

The  purely  electrical  consequences  of  Maxwell's 
theory  were  of  course  in  accord  with  all  known  elec- 
trical observations.  The  equations  of  the  field  ac- 
counted for  the  electro-magnetic  forces  observed  in 
various  experiments,  and  from  them  the  laws  of  electro- 
magnetic induction  could  be  correctly  deduced  ;  but 
there  was  nothing  very  special  in  this.  Similar  equa- 
tions had  been  obtained  from  the  theory  of  action  at 
a  distance  by  various  writers  ;  in  fact,  Helmholtz's 
theory,  based  on  the  most  general  form  of  expression 
for  the  force  between  two  elements  of  current  con- 
sistent with  certain  experiments  of  Ampere's,  was 
more  general  in  its  character  than  Maxwell's.  The 
destructive  features  of  Maxwell's  theory  were  : 

(1)  The  assumption  that  all  currents  flow  in  closed 
circuits. 

(2)  The  idea  of  energy  residing  throughout  the 
electro-magnetic  field  in  consequence  of  the  strains 
and  stresses  set  up  in  the  electro-magnetic  medium 
by  the  actions  to  which  it  was  subject. 


AND    MODERN    PHYSICS.  205 

(3)  Tho  identification  of  this  electro-magnetic 
medium  with  the  lnminiferous  ether,  and  the  con- 
sequent view  that  light  is  an  electro-magnetic 
phenomena. 

(4)  The  view  that  electro-magnetic  forces  arise 
entirely  from  strains  and  stresses  set  up  in  the  ether ; 
the  electro-static  charge  of  an  insulated  conductor 
being  one  of  the  forms  in  which  the  ether  strain  is 
manifested  to  us. 

(5)  A  dielectric  under  the  action  of  electric  force 
is  said  to  become  polarised,  and,  according  to  Maxwell 
(vol.  i.  p.  133),  all  electrification  is  the  residual  effect 
of  the  polarisation  of  the  dielectric. 

Now  it  must,  I  think,  be  admitted  that  in  Max- 
well's day  there  Avas  direct  proof  of  very  few  of  these 
propositions.  No  one  has  even  yet  so  measured  the 
displacement  currents  in  a  dielectric  as  to  show  that 
the  total  flow  across  every  section  of  a  circuit  is  at 
any  given  moment  the  same,  though  there  are  other 
experiments  of  an  indirect  character  which  have  now 
completely  justified  Maxwell's  hypothesis.  Experi- 
ments by  Schiller  and  Von  Helmholtz  prove  it  is 
true  that  some  action  in  the  dielectric  must  be  taken 
into  consideration  in  any  satisfactory  theory ;  they 
therefore  upset  various  theories  based  on  direct  action 
at  a  distance,  "  but  they  tell  us  nothing  as  to  whether 
any  special  form  of  the  dielectric  theory,  such  as 
Maxwell's  or  Helmholtz's,  is  true  or  not."  (J.  J. 
Thomson,  "  Report  on  Electrical  Theories,"  B.A.  Re- 
port, 1885,  p.  149.) 

When  Maxwell  died  there  had  been  little  if  any 
experimental  evidence  as  to  the  stresses  set  up  in  a 


206  JAMES    CLERK    MAXWELL 

body  by  electric  force.  Fontana,  Govi,  and  Duter 
had  all  observed  that  changes  take  place  in  the 
volume  of  the  dielectric  of  a  condenser  when  it  is 
charged.  Quincke  had  taken  up  the  work,  and  the 
first  of  his  classic  papers  on  this  subject  was  published 
in  1880,  the  year  following  Maxwell's  death.  Maxwell 
himself  was  fond  of  shewing  an  experiment  in  which 
a  charged  insulated  sphere  Avas  brought  near  to  the 
surface  of  paraffin  ;  the  stress  on  the  surface  causes  a 
heaping  up  of  the  paraffin  under  the  sphere. 

Kerr  had  shewn  in  1875  that  many  substances 
become  doubly  refracting  under  electric  stress  ;  his 
complete  determination  of  the  laws  of  this  action  was 
published  at  a  later  date. 

As  to  direct  measurements  on  electric  waves,  there 
were  none  ;  the  value  of  the  velocity  with  which,  if 
Maxwell's  theory  were  true,  they  must  travel  had 
been  determined  from  electrical  observations  of  quite 
a  different  character.  Weber  and  Kohlrausch  had 
measured  the  value  of  K  for  air,  for  which  //,  is  unity, 
and  from  their  observations  it  follows  that  the  value 
of  the  wave  velocity  for  electro-magnetic  waves  is 
about  31  x  109  centimetres  per  second.  The  velocity 
of  light  was  known,  from  the  experiments  of  Fizeau 
and  Foucault,  to  have  about  this  value,  and  it  was  the 
near  coincidence  of  these  two  values  which  led  Max- 
well to  write  in  1864  : — 

"  The  agreement  of  the  results  seems  to  show  that 
light  and  magnetism  are  affections  of  the  same 
substance,  and  that  light  is  an  electro-magnetic 
disturbance  propagated  through  the  field  according 
to  electro- magnetic  laws." 


AND    MODERN    PHYSICS.  207 

By  the  time  the  first  edition  of  the  "  Electricity 
and  Magnetism"  was  published,  Maxwell  and  Thomson 
(Lord  Kelvin)  had  both  made  determinations  of  K, 
and  had  shewn  that  for  air  at  least  the  resulting  value 
for  the  velocity  of  electro-magnetic  waves  was  very 
nearly  that  of  light. 

For  other  substances  at  that  date  the  observations 
were  fewer  still.  Gibson  and  Barclay  had  determined 
the  specific  inductive  capacity  of  paraffin,  and  found 
that  its  square  root  was  T405,  while  its  refractive  index 
for  long  waves  is  1422.  Maxwell  himself  thought 
that  if  a  similar  agreement  could  be  shewn  to  hold 
for  a  number  of  substances,  we  should  be  warranted 
in  concluding  that  "  the  square  root  of  K,  though  it 
may  not  be  the  complete  expression  for  the  index  of 
refraction,  is  at  least  the  most  important  term  in  it." 

Between  this  time  and  Maxwell's  death  enough 
had  been  done  to  more  than  justify  this  statement. 
It  was  clear  from  the  observations  of  Boltzmann, 
Silow,  Hopkinson,  and  others  that  there  were  many 
substances  for  which  the  square  root  of  the  speciiic 
inductive  capacity  was  very  nearly  indeed  equal  to 
the  refractive  index,  and  good  reason  had  been  given 
why  in  some  cases  there  should  be  a  considerable 
difference  between  the  two. 

Hopkinson  found  that  in  the  case  of  glass  the 
differences  were  very  large,  and  they  have  since  been 
found  to  be  considerable  for  most  solids  examined, 
with  the  exception  of  paraffin  and  sulphur.  For 
petroleum  oil,  benzine,  toluene,  carbon-bisulphide,  and 
some  other  liquids  the  agreement  between  Maxwell's 
theory  and  experiment  is  close.     For  the  fatty  oils, 


208  JAMES    CLERK    MAXWELL 

such  as  castor  oil,  olive  oil,  sperm  oil,  neatsfoot  oil, 

and  also  for  ether,  the  differences  are  considerable. 

It  seems  probable  that  the  reason  for  this  difference 
lies  in  the  feet  that,  in  the  light  waves,  we  are  dealing 
with  the  wave  velocity  of  a  disturbance  of  an  ex- 
tremely short  period.  Now,  we  know  that  the  sub- 
stances mentioned  shew  optical  dispersion,  and  we 
have  at  present  no  completely  satisfactory  theory  from 
which  we  can  calculate,  from  experiments  on  very 
short  waves,  what  the  velocity  for  very  long  waves 
will  be.  In  most  cases  Cauchy's  formula  has  been 
used  to  obtain  the  numbers  given.  The  value  of  K, 
however,  as  found  by  experiment,  corresponds  to  these 
infinitely  long  waves,  and  to  quote  Professor  J.  J. 
Thomson's  words,  "  the  marvel  is  not  that  there 
should  not  be  substances  for  which  the  relation  K 
=  fi~  does  not  hold,  but  that  there  should  be  an}'  for 
which  it  does."  * 

It  has  been  shewn,  moreover,  both  by  Professor  J. 
J.  Thomson  himself  and  by  Blondlot,  that  when  the 
value  of  K  is  measured  under  very  rapidly  varying 
electrifications,  changing  at  the  rate  of  about  25,000,000 
to  the  second,  the  value  of  the  inductive  capacity  for 
glass  is  reduced  from  about  6-8  or  7  to  about  2"7 ;  the 
square  root  of  this  is  1*6,  which  does  not  differ  much 
from  its  refractive  index.  The  values  of  the  inductive 
capacity  of  paraffin  and  sulphur,  which  it  will  be 
remembered  agree  fairly  with  Maxwell's  theory,  were 
found  to  be  not  greatly  different  in  the  steady  and 
in  the  rapidly  varying  field. 

On  the  other  hand,   some  experiments  of  Arons 

*  In  his  sentence  fi  stands  for  the  refractive  index. 


AND   MODERN    PHYSICS.  209 

and  Rubens  in  rapidly  varying  fields  lead  to  values 
which  do  not  differ  greatly  from  those  given  by  other 
methods.  The  theory,  however,  of  these  experiments 
seems  open  to  criticism. 

To  attempt  anything  like  a  complete  account  of 
modern  verifications  of  Maxwell's  views  and  modern 
developments  of  his  theory  is  a  task  beyond  our 
limits,  but  an  account  of  Maxwell  written  in  1895 
would  be  incomplete  without  a  reference  to  the  work 
of  Heinrich  Hertz. 

Maxwell  told  us  what  the  properties  of  electro- 
magnetic waves  in  air  must  be.  Hertz*  in  1887  enabled 
us  to  measure  those  properties,  and  the  measurements 
have  verified  completely  Maxwell's  views. 

The  method  of  producing  electrical  oscillations  in 
a  conductor  had  long  been  known.  Thomson  and  Von 
Helmholtz  had  both  pointed  it  out.  Schiller  had 
examined  such  oscillations  in  1874,  and  had  deter- 
mined the  inductive  capacity  of  glass  by  their  means, 
using  oscillations  whose  period  varied  from  "000056  to 
•00012  of  a  second. 

These  oscillations  were  produced  by  discharging 
a  condenser  through  a  coil  of  wire  having  self- 
induction.  If  the  electrical  resistance  of  the  coil  be 
not  too  great,  the  charge  oscillates  backwards  and 
forwards  between  the  plates  of  the  condenser  until  its 
energy  is  dissipated  in  the  heat  produced  in  the  wire, 
and  in  the  electro-magnetic  radiations  which  leave  it. 

The  period  of  these  oscillations  under  proper 
conditions  is  given  by  the  formula  T  =  2  7r  y/C  L  where 

*  Hertz's  papers  have  been  translated  into  English  by  D.  E.  Jones, 
and  are  published  under  the  title  of  Electric  Waves, 
X 


210  JAMES    CLERK    MAXWELL 

L,  the  coefficient  of  self  induction,  and  C  the  capacity 
of  the  condenser.  These  quantities  can  be  calculated, 
and  hence  the  time  of  an  oscillation  is  known.  From 
such  an  arrangement  waves  radiate  out  into  space.  If 
Ave  could  measure  by  any  method  the  length  of  such  a 
wave  we  could  determine  its  velocity  by  dividing  the 
wave  length  by  the  period.  But  it  is  clear  that  since 
the  velocity  is  comparable  with  that  of  light  the  wave 
length  will  be  enormous,  unless  the  period  is  very 
short.  Thus,  a  wave,  travelling  with  the  velocity  of 
light,  whose  period  was  '0001  second,  such  as  the 
waves  Schiller  worked  with,  would  have  a  length  of 
■0001  x  30,000,000,000  or  3,000,000  centimetres,  and 
would  be  quite  immeasurable.  Before  measurements 
on  electric  waves  could  be  made  it  was  necessary  (1) 
to  produce  waves  of  sufficiently  rapid  period,  (2)  to 
devise  means  to  detect  them.  This  is  what  Hertz  did. 
The  wave  length  of  the  electrical  oscillations 
can  be  reduced  by  reducing  either  the  electrical 
capacity  of  the  system,  or  the  coefficient  of  self- 
induction  of  the  wire.  Hertz  adopted  both  these 
expedients.  His  vibrator,  in  some  of  his  more  im- 
portant experiments,  consisted  of  two  square  brass 
plates  40  cm.  in  the  side.  To  each  of  these  is  attached 
a  piece  of  copper  wire  about  30  cm.  in  length,  and  each 
wire  ends  in  a  small  highly-polished  brass  ball.  The 
plates  are  placed  so  that  the  wires  lie  in  the  same 
straight  line,  the  brass  balls  being  separated  by  a  very 
small  air  gap.  The  two  plates  are  then  charged,  the 
one  positively  the  other  negatively,  until  the  insulation 
resistance  of  the  air  gap  breaks  down  and  a  discharge 
passes  across.     Under  these  conditions  the  discharge 


AND    MODERN    PHYSICS.  211 

is  oscillatory.  It  does  not  consist  of  a  single  spark, 
but  of  a  series  of  sparks,  which  pass  and  repass  in 
opposite  directions,  until  the  energy  of  the  original 
charge  is  radiated  into  space  or  dissipated  as  heat ; 
the  plates  are  then  recharged  and  the  process  repeated. 
In  Hertz's  experiments  the  oscillator  was  charged  by 
being  connected  to  the  secondary  terminals  of  an 
induction  coil. 

In  1883  Professor  Fitzgerald  had  called  attention 
to  this  method  of  producing  electric  waves  in  air,  and 
had  given  two  metres  as  the  minimum  wave  length 
which  might  be  attained.  In  1870  Herr  von  Bezold 
had  actually  made  observations  on  the  propagation 
and  reflection  of  electrical  oscillations,  but  his  work, 
published  as  a  preliminary  communication,  had  at- 
tracted little  notice.  Hertz  was  the  first  to  undertake 
in  1887  in  a  systematic  manner  the  investigation  of 
the  electric  waves  in  air  which  proceed  from  such  an 
oscillator  with  a  view  to  testing  various  theories  of 
electro-magnetic  action. 

It  remained,  however,  necessary  to  devise  an 
apparatus  for  detecting  the  waves.  When  the  waves 
are  incident  on  a  conductor,  electric  surgings  are  set 
up  in  the  conductor,  and  may,  under  proper  conditions, 
be  observed  as  tiny  sparks.  Hertz  used  as  his  de- 
tector a  loop  of  wire,  the  ends  of  which  terminated  in 
two  small  brass  balls.  The  wire  was  bent  so  that  the 
balls  were  very  close  together,  and  the  sparks  could 
be  seen  passing  across  the  tiny  air  gap  which  separated 
them.  Such  a  wire  will  have  a  definite  period  of  its 
own  for  oscillations  of  electricity  with  which  it  may 
be  charged,  and  if  the  frequency  of  the  electric  waves 
n  2 


212  JAMES    CLERK    MAXWELL 

which  fall  on  it  agrees  with  that  of  the  waves  which 
it  can  itself  emit,  the  oscillations  which  are  set  up  in 
the  wire  will  be  stronger  than  under  other  conditions, 
the  sparks  seen  will  be  more  brilliant*  Hertz's  re- 
sonator was  a  circle  of  wire  thirty-five  centimetres  in 
radius,  the  period  for  such  a  resonator  would,  he 
calculated,  be  the  same  as  that  of  his  vibrator. 

There  is,  however,  very  considerable  difficulty  in 
determining  the  period  of  an  electric  oscillator  from  its 
dimensions,  and  the  value  obtained  from  calculation 
for  that  of  Hertz's  radiator  is  not  very  trustworthy. 
The  complete  period  is,  however,  comparable  with  two 
one  hundredth  millionths  of  a  second ;  in  his  original 
papers,  Hertz,  through  an  error,  gave  a  value  greater 
than  this. 

With  these  arrangements  Hertz  was  able  to  detect 
the  presence  of  electrical  radiation  at  considerable 
distances  from  the  radiator;  he  was  also  able  to 
measure  its  wave  length.  In  the  case  of  sound  waves 
the  'existence  of  nodes  and  loops  formed  under  proper 
conditions  is  well  known.  When  waves  are  directly 
reflected  from  a  flat  surface,  interference  takes  place 
between  the  incident  and  reflected  waves,  stationary 
vibrations  are  set  up,  and  nodes  and  loops — places,  that 
is,  of  minimum  and  of  maximum  motion  respectively — 
are  formed.  The  position  of  these  nodes  and  loops 
can  be  determined  by  the  aid  of  suitable  apparatus, 
and  it  can  be  shewn  that  the  distance  between  two 
consecutive  nodes  is  half  the  wave  length. 

*  Some  of  the  consequences  of  this  electrical  resonance  have 
been  very  strikingly  shown  by  Professor  Oliver  Lodge.  See  Nature, 
February  20th,  1890. 


AND    MODERN    PHYSICS.  213 

Similarly  when  electrical  vibrations  fall  on  a  re- 
flector, a  large  flat  surface  of  metal,  for  example, 
stationary  vibrations  due  to  the  interference  between 
the  incident  and  reflected  waves  are  produced,  and 
these  give  rise  to  electrical  nodes  and  loops.  The 
position  of  such  nodes  and  loops  can  be  found  by  the 
use  of  Hertz's  apparatus,  or  in  other  ways,  and  hence 
the  length  of  the  electrical  waves  can  be  found.  The 
existence  of  the  nodes  and  loops  shews  that  the 
electric  effects  are  propagated  by  wave  motion.  The 
length  of  the  waves  is  found  to  be  definite,  since  the 
nodes  and  loops  recur  at  equal  intervals  apart. 

If  it  be  assumed  that  the  frequency  is  known,  the 
velocity  of  wave  propagation  can  be  determined. 
Hertz  found  from  his  experiments  that  in  air  the 
waves  travelled  with  the  velocity  of  light.  It  appears, 
however,  that  there  were  two  errors  in  the  calculation 
which  happened  to  correct  each  other,  so  that  neither 
the  value  of  the  frequency  given  in  Hertz's  paper 
nor  the  wave  length  observed  is  correct. 

By  modifying  the  apparatus  it  was  possible  to 
measure  the  Avave  length  of  the  waves  transmitted 
along  a  copper  wire,  and  hence,  again  assuming  the 
period  of  oscillation,  to  calculate  the  velocit}'  of  wave 
propagation  along  the  wire.  Hertz  made  the  experi- 
ment, and  found  from  his  first  observations  that  the 
waves  were  propagated  along  the  wire  with  a  finite 
velocity,  but  that  the  velocity  differed  from  that  in 
air.  The  half-wave  length  in  the  wire  Avas  onby  about 
2-8  metres ;  that  in  air  was  about  4  5  metres. 

Now,  this  experiment  afforded  a  crucial  test 
between  the  theories  of  Maxwell  and  Von  Helmholtz. 


214  JAMES   CLERK   MAXWELL 

According  to  the  former,  the  waves  do  not  travel  in 
the  wire  at  all ;  they  travel  through  the  air  alongside 
the  wire,  and  the  wave  length  observed  by  Hertz 
ought  to  have  been  the  same  as  in  air.  According  to 
Von  Helmholtz,  the  two  velocities  observed  by  Hertz 
should  have  been  different,  as,  indeed,  they  were,  and 
the  experiment  appeared  to  prove  that  Maxwell's 
theory  was  insufficient  and  that  a  more  general  one, 
such  as  that  of  Von  Helmholtz,  was  necessary.  But 
other  experiments  have  not  led  to  the  same  result. 
Hertz  himself,  using  more  rapid  oscillations  in  some 
later  measurements,  found  that  the  wave  length  of 
the  electric  waves  from  a  given  oscillator  was  the 
same  whether  they  were  transmitted  through  free 
space  or  conducted  along  a  wire.*  Lecher  and  J.  J. 
Thomson  have  arrived  at  the  same  result ;  but  the 
most  complete  experiments  on  this  point  are  those  of 
Sarasin  and  De  la  Rive. 

It  may  be  taken,  then,  as  established  that 
Maxwell's  theory  is  sufficient,  and  that  the  greater 
generality  of  Von  Helmholtz  is  unnecessary. 

In  a  later  paper  Hertz  showed  that  electric 
waves  could  be  reflected  and  refracted,  polarised  and 
analysed,  just  like  light  waves.  In  his  introduction 
to  his  "  Collected  Papers"  he  writes  (p.  19) : — 

"  Casting  now  a  glance  backwards,  we  see  that  by  the 
experiments  above   sketched   the  propagation   in   time   of  a 

*  Hertz's  original  results  were  no  doubt  affected  by  waves 
reflected  from  the  walls  and  floor  of  the  room  in  which  he  worked. 
An  iron  stove  also,  which  was  near  his  apparatus,  may  have  had 
a  disturbing  influence ;  but  for  all  this,  it  is  to  his  genius  and  his 
brilliant  achievements  that  the  complete  establishment  of  Maxwell's 
theory  is  due. 


AND   MODERN   PHYSICS.  215 

supposed  action  at  a  distance  is  for  the  first  time  proved. 
This  fact  forms  the  philosophic  result  of  the  experiments,  and 
indeed,  in  a  certain  sense,  the  most  important  result.  The 
proof  includes  a  recognition  of  the  fact  that  the  electric  forces 
can  disentangle  themselves  from  material  bodies,  and  can 
continue  to  subsist  as  conditions  or  changes  in  the  state  of 
space.  The  details  of  the  experiments  further  prove  that  the 
particular  manner  in  which  the  electric  force  is  propagated 
exhibits  the  closest  analogy  *  with  the  propagation  of  light ; 
indeed,  that  it  corresponds  almost  completely  to  it.  The 
hypothesis  that  light  is  an  electrical  phenomenon  is  thus  made 
highly  probable.  To  give  a  strict  proof  of  this  hypothesis 
would  logically  require  experiments  upon  light  itself. 

"  What  we  here  indicate  as  having  been  accomplished  by 
the  experiments  is  accomplished  independently  of  the  correct- 
ness of  particular  theories.  Nevertheless,  there  is  an  obvious 
connection  between  the  experiments  and  the  theory  in  connec- 
tion with  which  they  were  really  undertaken.  Since  the  year 
1861  science  has  been  in  possession  of  a  theory  which  Maxwell 
constructed  upon  Faraday's  views,  and  which  we  therefore 
call  the  Faraday-Maxwell  theory.  This  theory  affirms  the 
possibility  of  the  class  of  phenomena  here  discovered  just  as 
positively  as  the  remaining  electrical  theories  are  compelled 
to  deny  it.  From  the  outset  Maxwell's  theory  excelled  all 
others  in  elegance  and  in  the  abundance  of  the  relations 
between  the  various  phenomena  which  it  included. 

"  The  probability  of  this  theory,  and  therefore  the  number 
of  its  adherents,  increased  from  year  to  year.  But  as  long  as 
Maxwell's  theory  depended  solely  upon  the  probability  of  its 
results,  and  not  on  the  certainty  of  its  hypotheses,  it  could  not 
completely  displace  the  theories  which  were  opposed  to  it. 

"  The  fundamental  hypotheses  of  Maxwell's  theory  con- 
tradicted the  usual  views,  and  did  not  rest  upon  the  evidence 
of  decisive  experiments.  In  this  connection  we  can  best 
characterise  the  object  and  the  result  of  our  experiments  by 

*  The  analogy  does  not  consist  only  in  the  agreement  between 
the  more  or  less  accurately  measured  velocities.  The  approximately 
equal  velocity  is  only  one  element  among  many  others. 


216  JAMES    CLERK    MAXWELL 

saying  :  The  object  of  these  experiments  was  to  test  the 
fundamental  hypotheses  of  the  Faraday-Maxwell  theory,  and 
the  result  of  the  experiments  is  to  confirm  the  fundamental 
hypotheses  of  the  theory." 

Since  Maxwell's  death  volumes  have  been  written 
on  electrical  questions,  which  have  all  been  inspired 
by  his  work.  The  standpoint  from  which  electrical 
theory  is  regarded  has  been  entirely  changed.  The 
greatest  masters  of  mathematical  physics  have  found, 
in  the  development  of  Maxwell's  views,  a  task  that 
called  for  all  their  powers,  and  the  harvest  of  new 
truths  which  has  been  garnered  has  proved  most  rich. 
But  while  this  is  so,  the  question  is  still  often  asked, 
What  is  Maxwell's  theory  ?  Hertz  himself  concludes 
the  introduction  just  referred  to  with  his  most  in- 
teresting answer  to  this  question.  Prof.  Boltzmann 
has  made  the  theory  the  subject  of  an  important 
course  of  lectures.  Poincare,  in  the  introduction  to 
his  "  Lectures  on  Maxwell's  Theories  and  the  Electro- 
magnetic Theory  of  Light,"  expresses  the  difficulty, 
which  many  feel,  in  understanding  what  the  theory  is. 
"  The  first  time,"  he  says,  "  that  a  French  reader  opens 
Maxwell's  book  a  feeling  of  uneasiness,  often  even  of 
distrust,  is  mingled  with  his  admiration.  It  is  only 
after  prolonged  study,  and  at  the  cost  of  many  efforts, 
that  this  feeling  is  dissipated.  Some  great  minds 
retain  it  always."  And  again  he  writes  :  "  A  French 
savant,  one  of  those  who  have  most  completely 
fathomed  Maxwell's  meaning,  said  to  me  once,  !  I 
understand  everything  in  the  book  except  what  is 
meant  by  a  body  charged  with  electricity.' ' 

In    considering     this     question,    Poincare's    own 


AND   MODERN   PHYSICS.  217 

remark- — "  Maxwell  does  not  give  a  mechanical  ex- 
planation of  electricity  and  magnetism,  he  is  only 
concerned  to  show  that  such  an  explanation  is 
possible  " — is  most  important. 

We  cannot  find  in  the  "  Electricity  "  an  answer  to 
the  question — What  is  an  electric  charge  ?  Maxwell 
did  not  pretend  to  know,  and  the  attempt  to  give  too 
great  definiteness  to  his  views  on  this  point  is  apt  to 
lead  to  a  misconception  of  what  those  views  were. 

On  the  old  theories  of  action  at  a  distance  and  of 
electric  and  magnetic  fluids  attracting  according  to 
known  laws,  it  was  easy  to  be  mechanical.  It  was  only 
necessary  to  investigate  the  manner  in  which  such 
fluids  could  distribute  themselves  so  as  to  be  in  equi- 
librium, and  to  calculate  the  forces  arising  from  the 
distribution.  The  problem  of  assigning  such  a 
mechanical  structure  to  the  ether  as  will  permit  of 
its  exerting  the  action  which  occurs  in  an  electro- 
magnetic field  is  a  harder  one  to  solve,  and  till  it  is 
solved  the  question — What  is  an  electric  charge  ? — 
must  remain  unanswered.  Still,  in  order  to  grasp 
Maxwell's  theory  this  knowledge  is  not  necessary. 

The  properties  of  ether  in  dielectrics  and  in  con- 
ductors must  be  quite  different.  In  a  dielectric  the 
ether  has  the  power  of  storing  energy  by  some  change 
in  its  configuration  or  its  structure  ;  in  a  conductor  this 
power  is  absent,  owing  probably  to  the  action  of  the 
matter  of  which  the  conductor  is  composed. 

When  we  are  said  to  charge  an  insulated  conductor 
we  really  act  on  the  ether  in  the  neighbourhood  of  the 
body  so  as  to  store  if,  with  energy  ;  if  there  be  another 
conductor  in  the  field  we  cannot  store  energy  in  the 


218  JAMES    CLERK   MAXWELL 

ether  it  contains.  As,  then,  we  pass  from  the  outside 
of  this  conductor  to  its  interior  there  is  a  sudden 
change  in  some  mechanical  quantity  connected  with 
the  ether,  and  this  change  shows  itself  as  a  force  of 
attraction  between  the  two  conductors.  Maxwell 
called  the  change  in  structure,  or  in  property,  which 
occurs  when  a  dielectric  is  thus  stored  with  electro- 
static energy,  Electric  Displacement ;  if  we  denote 
it  by  I),  then  the  electric  force  R  is  equal  to  47rI)/K, 
and  hence  the  energy  in  a  unit  of  volume  is  27rD"/K, 
where  K  is  a  quantity  depending  on  the  insulator. 

Now,  D,  the  electric  displacement,  is  a  quantity 
which  has  direction  as  well  as  magnitude.  Its  value, 
therefore,  at  any  point  can  be  represented  by  a  straight 
line  in  the  usual  way ;  inside  a  conductor  it  is  zero. 
The  total  change  in  D,  which  takes  place  all  over 
the  surface  of  a  conductor  as  we  enter  it  from  the 
outside  measures,  according  to  Maxwell,  the  total 
charge  on  the  conductor.  At  points  at  which  the 
lines  representing  D  enter  the  conductor  the  charge 
is  negative ;  at  points  at  which  they  leave  it  the 
charge  is  positive ;  along  the  lines  of  the  displacement 
there  exists  throughout  the  ether  a  tension  measured 
by  27rD2/K;  at  right  angles  to  these  lines  there  is 
a  pressure  of  the  same  amount. 

In  addition  to  the  above  the  components  of  the 
displacement  D  must  satisfy  certain  relations  which 
can  only  be  expressed  in  mathematical  form,  the 
physical  meaning  of  which  it  is  difficult  to  state  in 
non-mathematical  language. 

When  these  relations  are  so  expressed  the  problem 
of  finding  the  value  of  the  displacement  at  all  points 


AND    MODERN    PHYSICS.  219 

of  space  becomes  determinate,  and  the  forces  acting 
on  the  conductors  can  be  obtained.  Moreover,  the 
total  change  of  displacement  on  entering  or  leaving 
a  conductor  can  be  calculated,  and  this  gives  the 
quantity  which  is  known  as  the  total  electrical  charge 
on  the  conductor.  The  forces  obtained  by  the  above 
method  are  exactly  the  same  as  those  which  would 
exist  if  we  supposed  each  conductor  to  be  charged  in 
the  ordinary  sense  with  the  quantities  just  found,  and 
to  attract  or  repel  according  to  the  ordinary  laws. 

If,  then,  we  define  electric  displacement  as  that 
change  which  takes  place  in  a  dielectric  when  it 
becomes  the  seat  of  electrostatic  energy,  and  if, 
further,  we  suppose  that  the  change,  whatever  it  be 
mechanically,  satisfies  certain  well-known  laws,  and 
that  in  consequence  certain  pressures  and  tensions 
exist  in  the  dielectric,  electrostatic  problems  can  be 
solved  without  reference  to  a  charge  of  electricity 
residing  on  the  conductors. 

Something  such  as  this,  it  appears  to  me,  is  Max- 
well's theory  of  electricity  as  applied  to  electrostatics. 
It  is  not  necessary,  in  order  to  understand  it,  to  know 
what  change  in  the  ether  constitutes  electric  displace- 
ment, or  what  is  an  electric  charge,  though,  of  course, 
such  knowledge  would  render  our  views  more  definite, 
and  would  make  the  theory  a  mechanical  one. 

When  we  turn  to  magnetism  and  electro-maor- 
netism,  Maxwell's  theory  develops  itself  naturally. 
Experiment  proves  that  magnetic  induction  is  con- 
nected with  the  rate  of  change  of  electric  displace- 
ment, according  to  the  laws  already  given.  If,  then, 
we  knew  the  nature  of  the  change  to  which  the  name 


220  JAMES    CLERK    MAXWELL 

"  electric  displacement "  has  been  given,  the  nature  of 
magnetic  induction  would  be  known.  The  difficulties 
in  the  way  of  any  mechanical  explanation  are,  it 
is  true,  very  great ;  assuming,  however,  that  some 
mechanical  conception  of  "  electric  displacement "  is 
possible,  Maxwell's  theory  gives  a  consistent  account 
of  the  other  phenomena  of  electro-magnetism. 

Again,  we  have,  it  is  true,  an  electro-magnetic 
theory  of  light,  but  we  do  not  know  the  nature  of  the 
change  in  the  ether  which  affects  our  eyes  with  the 
sensation  of  light.  Is  it  the  same  as  electric  displace- 
ment, or  as  magnetic  induction,  or  since,  when  electric 
displacement  is  varying,  magnetic  induction  always 
accompanies  it,  is  the  sensation  of  light  due  to  the 
combined  effect  of  the  two  ? 

These  questions  remain  unanswered.  It  may  be 
that  light  is  neither  electric  displacement  nor  magnetic 
induction,  but  some  quite  different  periodic  change  of 
structure  of  the  ether,  which  travels  through  the 
ether  at  the  same  rate  as  these  quantities,  and  obeys 
many  of  the  same  laws. 

In  this  respect  there  is  a  material  difference  be- 
tween the  ordinary  theory  of  light  and  the  electro- 
magnetic theory.  The  former  is  a  mechanical  theory  ; 
it  starts  from  the  assumption  that  the  periodic  change 
which  constitutes  light  is  the  ordinary  linear  dis- 
placement of  a  medium — the  ether — having  certain 
mechanical  properties,  and  from  those  properties  it 
deduces  the  laws  of  optics  with  more  or  less  success. 

Lord  Kelvin,  in  his  labile  ether,  has  devised  a 
medium  which  could  exist  and  which  has  the 
necessary  mechanical  properties.     The  periodic  linear 


AND    MODERN    PHYSICS.  221 

displacements  of  the  labile  ether  would  obey  the  laws 
of  light,  and  from  the  fundamental  hypotheses  of  the 
theory,  a  mechanical  explanation,  reasonably  satis- 
factory in  its  main  features,  can  be  given  of  most 
purely  optical  phenomena.  The  relations  between 
light  and  electricity,  or  light  and  magnetism,  are  uot, 
however,  touched  by  this  theory ;  indeed,  they  cannot 
be  touched  without  making  some  assumption  as  to 
what  electric  displacement  is. 

In  recent  years  various  suggestions  have  been 
made  as  to  the  nature  of  the  change  which  constitutes 
electric  displacement.  One  theory,  due  to  Yon  Helm- 
holtz,  supposes  that  the  electro-kinetic  momentum,  or 
vector  potential  of  Maxwell,  is  actually  the  momen- 
tum of  the  moving  ether ;  according  to  another,  sug- 
gested, it  would  appear  originally  in  a  crude  form 
by  Challis,  and  developed  within  the  last  few  months 
in  very  satisfactory  detail  by  Larmor,  the  velocity 
of  the  ether  is  magnetic  force ;  others  have  been 
devised,  but  we  are  still  waiting  for  a  second  Newton 
to  give  us  a  theory  of  the  ether  which  shall  include 
the  facts  of  electricity  and  magnetism,  luminous  radi- 
ation, and  it  may  be  gravitation.* 

Meanwhile  we  believe  that  Maxwell  has  taken  the 
first  steps  towards  this  discovery,  and  has  pointed  out 
the  lines  along:  which  the  future  discoverer  must  direct 
his  search,  and  hence  we  claim  for  him  a  foremost 
place  among  the  leaders  of  this  century  of  science. 

*  For  a  very  suggestive  account  of  some  possible  theories,  reference 
should  be  made  to  the  presidential  address  of  Professor  W.  M.  Hicks 
to  Section  A  of  the  British  Association  at  Ipswich  in  1895. 


INDEX. 


Aberdeen,  Maxwell  fleeted  Professor  at, 
45  ;  formation  of  University  of,  51 

Adams, W.  G. ,  succeeds  Maxwell  as  Pro- 
fessorat  King's  College,  London,  5S 

Adams  Prize,  The,  48  ;  gained  by  Max- 
well, 50 

Ampere,  155,  204 

Ampere's  Law,  155,  156 

Annals  of  Philosophy,  Thomson's,  112, 
113 

"  Apostles,"  club  so  called,  30,  89 

Arago,  157 

Arragonite,  200 

Atom,  article  by  Maxwell  in  Encyclo- 
paedia Britannica,  108 

Avogadros'  Law,  117,  124 

Bakerian  Lecture,  delivered  by  Max- 
well, 58 

Berkeley  on  the  Theory  of  Vision,  38 

Bernouilli,  D.,  113 

Blackburne,  Professor,  16 

Blore,  Rev.  E.  W.,  07 

Boehm,  Bust  of  Maxwell  by,  90 

Boltzmann,  Dr.,  135,  137,138,  144,  216 

Boltzinaun-Maxwell  Theory,  The,  140, 
145 

Boscovitch  on  Atoms,  108,  109 

Boyle's  Law,  114,  117,  124 

Brewster,  Sir  David,  on  Colour  Sensa- 
tion, 99 

British  Association,  Maxwell  and,  42, 
54  ;  Lecture  before,  80-82  ;  Lines  on 
President's  address,  S3,  S4 

Butler,  Dr.  H.  M.,  extract  from  sermon 
on  Maxwell,  32-35 

Bryan,  G.  H.,  141,  143 

Cambridge,  Maxwell  at,  28-40  ;  Mathe- 
matical Tripos  at,  60;  Foundation 
of  Professorship  of  Experimental 
Physics  at.  66 

Cambridge  and  Dublin  Mathematical 
Journal,  Papers  by  Maxwell  in,  HO 

Campbell,  Professor  L.,  9,  10,  12,14,  22, 
52,  57,  79 

Cauchy's  Formula,  208 

Cavendish,  Henry,  73,  74;  Works  of, 
edited  by  Maxwell,  87, 154,  155 

Cavendish  Laboratory,  built  and  pre- 
sented to  University  of  Cambridge, 
73,  74 

Cay.  Miss  Frances,  11 

Cayley  Portrait  Fund,  lines  to  Com- 
mitter. 86 

Challis,  Professor,  40 

Charles'  Law,  124 

Chemical  Society,  Maxwell's  lecture 
before,  80-S2 


Clausius,    on   kinetic   theory  of  gases, 

119,  129,  130,  137 
Clerks  of  Penicuik,  The,  9,  10 
Colour  Perception,  94 
Colour  Sensation,    Young  on,   97,   98  ; 

Sir  D.  Brewster  on,  99 
Colours,   paper  by  Maxwell,  on,  40,  41  ; 

Helmholtz  on,  00 
Conductors  and  Insulators,  Distinction 

between,  173 
Cookson,  Dr.,  61 
Corsoek,  Maxwell  buried  at,  90 
Cotes,  202 
Coulomb,  154 
Curves,  investigated  by  Maxwell,  19 

Daniell's  cells,  77 
Demoeritus,  108 

Demonstrator  of  Physics,  W.  Garnett 
appointed,  75 

Description  of  Oval  Curves,  first  paper 
by  Maxwell    19 

Devonshire,  Duke  of,  Cavendish  La- 
boratory built  by,  73,  74  ;  Letter  of 
Thanks  from  University  of  Cam- 
bridge, 74 

Dewar,  Miss  K.  M.,  her  marriage  to 
Maxwell,  51 

Dickinson,  Lowes;  Portrait  of  Maxwell 
by,  90 

Diffusion  of  gases,  128 

Discs  for  colour  experiments.  99-101 

Droop,  H.  R.,  57         • 

Dynamical  Theory  of  the  Electromag- 
netic Field,  Maxwell  on,  57,  177 

Dynamical  Theory  of  Gases,  Maxwell 
on,  58,  134 

Edinburgh  Academy,  Maxwell's  school- 
life  at,  13-18 
Edinburgh,  Royal  Society  of,  Maxwell 

at  meetings  of,  IS 
Edinburgh, University  of,  Maxwell  at,  22 
Elastic  Spheres,  144 
Electric  Displacement,  218,  219,  220 
Electrical  Theories,  94,  154,  155 
Electricity   and  Magnetism,  Maxwell's 
book  on,  59,  77,  79,  147,  155,  156, 
176,  1S0-201  ;  papers  by  Lord  Kelvin 
on,    161-2  ;  Application  of  Mathe- 
matical Analysis  to,  paper  by    G. 
Green,  15S 
Electricity,  Modern  Views   of,  by   Pro- 
fessor Lodge,  177 
Electro-kinetic  Momentum,  221 
Electro-magnetic      Field,      Dynamical 

Theory  of,  Maxwell  on,  57,  177 
Electro-magnetic  Induction,  157 
Electro-magnetic  Theory  of  Light,  174 


INDEX. 


223 


Electro-tonic  State,  164 

Electrostatic    Induction,    Faraday   on, 

159 
Encyclopaedia  Britannica,,  articles    by 

Maxwell  in,  80,  108,  140 
Ether,  labile,  220 
Experimental    Physics,    foundation  of 

Professorship    at   Cambridge,    60  ; 

Election  of  Maxwell,  68 

Faraday  on  electrical  science,  107;  on 
electrostatic  induction,  159 

Faraday's  Lines  of  Force,  paper  by 
Maxwel]  on,  14,  45,  1 18-  153 

Fawcett,  \V.  M  ,  architect  of  Cavendish 
Laboratory,  7:; 

Fitzgerald,  Professor,  177,  211 

Forbes,  Professor  J.  D.,  IS,  41,  54; 
friendship  with  Maxwell,  19;  paper 
on  Theory  of  Glaciers,  19;  resigns 
Professorship  at  Edinburgh,  54 

Galvani,  155 

Garnett,   W.,  appointed    Demonstrator 

of  Physics  at  Cambridge,  75  ;    Life 

of  Maxwell  by,  94 
Gases,  Molecular  theory  of,   57,    108 ; 

Waterston  on  general  theory  of,118  ; 

Clausius  on,  J 19;  diffusion  of,  128 
Gauss'  Theory,  150 
Gay  Lussac's  Law,  117 
General  Theory  of  Gases,  Waterston  on, 

118  ;  Clausius  on,  119 
Glenlair,'  home    of    Maxwell,   11,   23; 

laboratory  at,  24  ;  Maxwell's  lit''  at, 

■".8.  59  ;  "  Electricity  and   Magnet- 
ism "  written  at,  ,9 
Gordon,  J.  E.  11.,  77,  78 
Green,   G.,  of    Nottingham,   paper  on 

electricity    and     magnetism,    158 ; 

inventor  of  term  "  Potential,"  158 

Hamilton,  sir  W.  U.,  22 
Hamilton's  Principle,  190 
Heat,  Text-book  on,  by  Maxwell,  79 
Helmholtz,  99,  156,  157,  175,  221 
Henry,   .1.,  of  Washington,  on  electro- 
magnetic induction,  157 
Herapath.  on  molecules,  112-116 
Hertz,  Heinrich,  204,  209—213 
1 1  irks,  W.M.,  221 
Hockin,  C,  56 
Ilolman,  Professor,  133 

Iceland  Spar,  200 

Insulators  and  Conductors,  liistiuctioii 
between,  173 

Jenkin,  Fleeming,  55,  56 

Kelland,  Professor,  22 
Kelvin,  Lord,  16, 142, 158, 159,  100,  16S  ; 
on  the  Uniform  Motion  of  Heat,  M0; 


papers  on  Electricity  and  Mag- 
netism, ltd,  102 

Kinetic  energy,  124,  129,  136,  139,  191 

King's  College,  London,  Maxwell  elected 
Professor  at,  54 

Kohlrausch,  200 

Kundt,  132 

Labile  Ether,  220 

Lab  iratory  at  Glenlair,  24 

Lagrange,  179 

I  ^grange's  Equations,  179,  190 

Laplace,  155 

Larmor,  J.,  141,  142 

Lecher,  211 

Lenz,  157 

Litchfield,  R.  1!.,  46 

Light,  Electro-magnetic  Theory  of,  171 ; 

Waves  of,  198,  199 
Lodge,  Professor,  book  on  ModernViews 

of  Electricity,  177 
Lucretius,  198 
Luminous  Radiation,  221 

Mathematical  Tripos  at  Cambridge, 
subjects,  Oil;  Maxwell  an  examiner 
for,  00,  ,sj>  ;  experimental  work  in, 70 
Matter  and  Motion,  Maxwell  on,  79 
.Maxwell,  James  Clerk,  parentage  and 
birthplace,  10,  11 ;  childhood  and 
school-days,  12-18  ;  his  mother's 
death,  13  ;  first  lessons  in  geometry, 
17;  attends  meetings  of  Royal 
Society  of  Edinburgh,  18;  his  first 
published  paper,  19 ;  friendship 
with  Professor  Forbes,  19;  his  polari- 
scope,  20;  enters  the  University  of 
Edinburgh,  22 ;  papers  on  Rolling 
Curves  and  Elastic  Solids,  23  ;  vaca- 
tions at  Glenlair,  23  ;  laboratory  at 
Glenlair,  24;  undergraduate  life  at 
Cambridge,  28-36 ;  elected  scholar 
of  Trinity,  29  ;  illness  at  Lowestoft, 
29;  his  friends  at  Cambridge,  30; 
Tripos  ami  degree,  35-37  ;  early  re- 
searches, 38-44  ;  paper  011  Colours, 
10.  11  ;  elected  Fellow  of  'trinity, 
43;  Lecturer  at  Trinity,  43  ;  Pro- 
fessor al  Aberdeen,  45;  his  father's 
death,  45  ;  gains  the  Adams  Prize, 
5u;  marriage,  51  ;  powers  as  teacher 
and  lecturer,  52,  53;  Professor  at 
King's  College,  London,  54:  gains 
the  Rumford  Medal,  55;  delivers 
Bakerian  lecture,  58  ;  resigns  Pro- 
fessorship al  King's  College.  Lou- 
don, 58;  life  at  Glenlair,  58,  ^>  ; 
visit  to  Italy.  :•'.< ;  Examiner  for 
Mathematical  Tripos,  60,  80;  elected 
Professor  of  Experimental  Physics 
at  Cambridge,  OS  ;  Introductory 
Lecture,  0.8-72;  Examiner  for 
Natural  Sciences  Tripos,  79  ;  articles 


224 


INDEX. 


in  Encyclopcedia  Britannica,,SO,  118, 
1  10 ;  papers  in  Nature,  80  ;  lectures 
before  British  Association  and 
Chemical  .Society,  80-82  ;  humorous 
poems,  8?-87  ;  delivers  Rede  Lec- 
ture on  the  Telephone,  80 ;  last 
illness  and  death,  89,  00  ;  buried  at 
Corsock,  00  ;  bust  and  portrait,  00  ; 
religious  views,  91,  02 

Maxwell,  John  Clerk,  10,  11 

Meyer,  O.  E.,  133 

Mill's  Logic,  38 

Molecular  Evolution,  Lines  on,  85 

Physics,  04 

Constitution  of   Bodies,   Maxwell 

on,  140 

Theory  of  Gases,  57,  108 

Molecules,  100,  110  ;  Herapath  on,  112- 
110  ;  lecture  by  Maxwell  on,  140 

Motion  of  Saturn's  Rings,  subject  for 
Adams  Prize,  49 

Munro,  J.  C,  40,  50,  68,  82 

Natural  Sciences  Tripos,  Maxwell  Ex- 
aminer for,  79 

Nature,  papers  by  Maxwell  in,  SO 

Neumann,  F.  E.,  150,  157 

Newton's  Lunar  Theory  and  Astronomy, 
50 

Principia,  202 

Nicol,  "Win.,  inventor  of  the  polarising 
prism,  20 

Niven,  W.  D.,  27,  40,  51,  52,  60,  7S,  S7, 
SS.  03 


<  Mienneyer,  134 

Ohm's  Law,  77 

( Ophthalmoscope  devised  by  Mnxwell,83 

Oval  Curves,  Description  of,  Maxwell's 
first  paper,  10 

Parkinson,  Dr..  49 

Philosophical  Magazine,  56,  99,115,  120, 

133,  142 
Philosophical  Transictions,   50,  SO,  132, 

145 
Physical    Linos  of  Fore  •,    Maxwell  on, 

50,  158 
Physics.  Instruction  in,  at  Cambridge, 

01  ;  Report  of  Syndicate  on,  02-04  ; 

Demonstrator  appointed,  75 
Poincare,  216 

Poisson,   44:    on   distribution   of  elec- 
tricity, 15a 
Polariscope,  made  by  Maxwell,  20 
"Potential,"    term     invented     by     G. 

Green,  158;  the  Vector,  105,  221 
Poynting,  Professor,  1S7-1S9 
Puluj,  134 


Quincke,  200 

Radiation,  Luminous,  221 

Rarefied  Gases,  Stresses  in,  paper  by 
Maxwell,  135,  145 

Rayleigh,  Lord,  67,  77 

Rede  Lecture  on  the  Telephone,  de- 
livered by  Maxwell,  80 

Report  on  Electrical  Theories,  J.  J. 
Thomson,  204 

of  Syndicate  as  to  instruction  in 

Physics  at  Cambridge,  02-04 

Robertson,  C.  H.,  28 

Rolling  Curves,  Maxwell  on,  23 

Royal  Society,  The,  Maxwell  and,  55  ; 
Transactions  of,  89 

Rumford  Medal  gained  by  Maxwell,  55, 
100 

Sabine,    Major-General,   Vice-President 

of  [loyal  Society,  106 
Smith's  Prizes,  36 
Standards    of     Electrical     Resistance, 

Committee  on,  55 
Stewart,  Balfour,  56,  125 
Stresses  in  Rarefied  Gases,  Maxwell  on, 

135,  155 

Tait,  Professor  P.  G.,  21,  20,  94 

Tayler,  Rev.  C.  B.,  29 

Telephone,  Rede  Lecture   by  Maxwell 

on,  89 
Theory  of  Glaciers,  Prof.  Forbes  on,  19 
Thomson,  J.  J.,  157,   20S ;  Report   on 

Electrical  Theories,  205 
Thomson's  Annals  of  Philosophy,  112,113 

Uniform  Motion  of  Heat  in  Homo- 
geneous Solid  Bodies,  paper  by  Lord 
Kelvin,  100,  161 

University  Commission,  47,  48,  62 

Urr,  Vale' of,  11 

Vector  Potential,  The,  165,  221 
Viscosity   of   Gases,    Experiments   on, 

58,  125,  132 
Volta,  Inventor  of  voltaic  pile,  155 

Waterston,  J.  J.,  on  molecular  theory 
of  gases,  114,  115  ;  cm  general  theory 
of  gases,  118 

Waves  of  Light,  198,  199 

Weber,  W.,  150,  200 

Wedderbum,  Mrs.,  14 

Wheatstone's  Bridge,  77 

Williams,  J.,  Archdeacon  of  Cardigan,  10 

Willis,  Professor,  44 

Wilson,  E  ,  lines  in  memory  of,  80,  87 

Young,  T.,  on  colour  sensation,  07,  98 


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