﻿90 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  The 
  accounts 
  of 
  experimental 
  researches 
  on 
  the 
  values 
  of 
  the 
  coefficients 
  are 
  

   so 
  numerous 
  that 
  I 
  can 
  mention 
  only 
  a 
  few. 
  

  

  Canton, 
  Perkins, 
  (Ersted, 
  Aime, 
  Colladon 
  and 
  Sturm, 
  and 
  Kegnault, 
  

   have 
  determined 
  the 
  cubical 
  compressibilities 
  of 
  substances 
  ; 
  Coulomb, 
  Duleau, 
  

   and 
  Giulio, 
  have 
  calculated 
  the 
  linear 
  elasticity 
  from 
  the 
  torsion 
  of 
  wires 
  ; 
  and 
  a 
  

   great 
  many 
  observations 
  have 
  been 
  made 
  on 
  the 
  elongation 
  and 
  bending 
  of 
  beams. 
  

  

  I 
  have 
  found 
  no 
  account 
  of 
  any 
  experiments 
  on 
  the 
  relation 
  between 
  the 
  

   doubly 
  refracting 
  power 
  communicated 
  to 
  glass 
  and 
  other 
  elastic 
  solids 
  by 
  com- 
  

   pression, 
  and 
  the 
  pressure 
  which 
  produces 
  it 
  ;* 
  but 
  the 
  phenomena 
  of 
  bent 
  glass 
  

   seem 
  to 
  prove, 
  that, 
  in 
  homogeneous 
  singly-refracting 
  substances 
  exposed 
  to 
  pres- 
  

   sures, 
  the 
  principal 
  axes 
  of 
  pressure 
  coincide 
  with 
  the 
  principal 
  axes 
  of 
  double 
  

   refraction 
  ; 
  and 
  that 
  the 
  difference 
  of 
  pressures 
  in 
  any 
  two 
  axes 
  is 
  proportional 
  to 
  

   the 
  difference 
  of 
  the 
  velocities 
  of 
  the 
  oppositely 
  polarised 
  rays 
  whose 
  directions 
  are 
  

   parallel 
  to 
  the 
  third 
  axis. 
  On 
  this 
  principle 
  I 
  have 
  calculated 
  the 
  phenomena 
  

   seen 
  by 
  polarised 
  light 
  in 
  the 
  cases 
  where 
  the 
  solid 
  is 
  bounded 
  by 
  parallel 
  planes. 
  

  

  In 
  the 
  following 
  pages 
  I 
  have 
  endeavoured 
  to 
  apply 
  a 
  theory 
  identical 
  with 
  

   that 
  of 
  Stokes 
  to 
  the 
  solution 
  of 
  problems 
  which 
  have 
  been 
  selected 
  on 
  account 
  

   of 
  the 
  possibility 
  of 
  fulfilling 
  the 
  conditions. 
  I 
  have 
  not 
  attempted 
  to 
  extend 
  

   the 
  theory 
  to 
  the 
  case 
  of 
  imperfectly 
  elastic 
  bodies, 
  or 
  to 
  the 
  laws 
  of 
  permanent 
  

   bending 
  and 
  breaking. 
  The 
  solids 
  here 
  considered 
  are 
  supposed 
  not 
  to 
  be 
  com- 
  

   pressed 
  beyond 
  the 
  limits 
  of 
  perfect 
  elasticity. 
  

  

  The 
  equations 
  employed 
  in 
  the 
  transformation 
  of 
  co-ordinates 
  may 
  be 
  found 
  

   in 
  Gregory's 
  Solid 
  Geometry. 
  

  

  I 
  have 
  denoted 
  the 
  displacements 
  by 
  8x, 
  8y, 
  8z. 
  They 
  are 
  generally 
  denoted 
  

   by 
  a, 
  /?, 
  7 
  ; 
  but 
  as 
  I 
  had 
  employed 
  these 
  letters 
  to 
  denote 
  the 
  principal 
  axes 
  at 
  

   any 
  point, 
  and 
  as 
  this 
  had 
  been 
  done 
  throughout 
  the 
  paper, 
  I 
  did 
  not 
  alter 
  a 
  

   notation 
  which 
  to 
  me 
  appears 
  natural 
  and 
  intelligible. 
  

  

  The 
  laws 
  of 
  elasticit} 
  r 
  express 
  the 
  relation 
  between 
  the 
  changes 
  of 
  the 
  dimen- 
  

   sions 
  of 
  a 
  body 
  and 
  the 
  forces 
  which 
  produce 
  them. 
  

  

  These 
  forces 
  are 
  called 
  Pressures, 
  and 
  their 
  effects 
  Compressions. 
  Pressures 
  

   are 
  estimated 
  in 
  pounds 
  on 
  the 
  square 
  inch, 
  and 
  compressions 
  in 
  fractions 
  of 
  the 
  

   dimensions 
  compressed. 
  

  

  Let 
  the 
  position 
  of 
  material 
  points 
  in 
  space 
  be 
  expressed 
  by 
  their 
  co-ordinates 
  

   ■r, 
  y, 
  and 
  'z, 
  then 
  any 
  change 
  in 
  a 
  system 
  of 
  such 
  points 
  is 
  expressed 
  by 
  giving 
  to 
  these 
  

   co-ordinates 
  the 
  variations 
  8 
  x, 
  8y, 
  8 
  z, 
  these 
  variations 
  being 
  functions 
  of 
  x, 
  y, 
  z. 
  

  

  The 
  quantities 
  8 
  x, 
  8y, 
  8 
  z, 
  represent 
  the 
  absolute 
  motion 
  of 
  each 
  point 
  in 
  the 
  

   directions 
  of 
  the 
  three 
  co-ordinates 
  ; 
  but 
  as 
  compression 
  depends 
  not 
  on 
  absolute, 
  

   but 
  on 
  relative 
  displacement, 
  we 
  have 
  to 
  consider 
  only 
  the 
  nine 
  quantities 
  — 
  

  

  * 
  See 
  note 
  C. 
  

  

  