﻿88 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  2. 
  The 
  difference 
  between 
  two 
  of 
  the 
  pressures 
  is 
  proportional 
  to 
  the 
  difference 
  

   oj 
  the 
  compressions 
  which 
  they 
  produce. 
  

  

  The 
  equations 
  deduced 
  from 
  these 
  axioms 
  contain 
  two 
  coefficients, 
  and 
  differ 
  

   from 
  those 
  of 
  Navier 
  only 
  in 
  not 
  assuming 
  any 
  invariable 
  ratio 
  between 
  the 
  

   cubical 
  and 
  linear 
  elasticity. 
  They 
  are 
  the 
  same 
  as 
  those 
  obtained 
  by 
  Professor 
  

   Stokes 
  from 
  his 
  equations 
  of 
  fluid 
  motion, 
  and 
  they 
  agree 
  with 
  all 
  the 
  laws 
  of 
  

   elasticity 
  which 
  have 
  been 
  deduced 
  from 
  experiments. 
  

  

  In 
  this 
  paper 
  pressures 
  are 
  expressed 
  by 
  the 
  number 
  of 
  units 
  of 
  weight 
  to 
  the 
  

   unit 
  of 
  surface 
  ; 
  if 
  in 
  English 
  measure, 
  in 
  pounds 
  to 
  the 
  square 
  inch, 
  or 
  in 
  atmo- 
  

   spheres 
  of 
  15 
  pounds 
  to 
  the 
  square 
  inch. 
  

  

  Compression 
  is 
  the 
  proportional 
  change 
  of 
  any 
  dimension 
  of 
  the 
  solid 
  caused 
  

   by 
  pressure, 
  and 
  is 
  expressed 
  by 
  the 
  quotient 
  of 
  the 
  change 
  of 
  dimension 
  divided 
  

   by 
  the 
  dimension 
  compressed.* 
  

  

  Pressure 
  will 
  be 
  understood 
  to 
  include 
  tension, 
  and 
  compression 
  dilatation 
  ; 
  

   pressure 
  and 
  compression 
  being 
  reckoned 
  positive. 
  

  

  Elasticity 
  is 
  the 
  force 
  which 
  opposes 
  pressure, 
  and 
  the 
  equations 
  of 
  elasticity 
  

   are 
  those 
  which 
  express 
  the 
  relation 
  of 
  pressure 
  to 
  compression.! 
  

  

  Of 
  those 
  who 
  have 
  treated 
  of 
  elastic 
  solids, 
  some 
  have 
  confined 
  themselves 
  

   to 
  the 
  investigation 
  of 
  the 
  laws 
  of 
  the 
  bending 
  and 
  twisting 
  of 
  rods, 
  without 
  con- 
  

   sidering 
  the 
  relation 
  of 
  the 
  coefficients 
  which 
  occur 
  in 
  these 
  two 
  cases 
  ; 
  while 
  

   others 
  have 
  treated 
  of 
  the 
  general 
  problem 
  of 
  a 
  solid 
  body 
  exposed 
  to 
  any 
  forces. 
  

  

  The 
  investigations 
  of 
  Leibnitz, 
  Bernoulli, 
  Euler, 
  Varignon, 
  Young, 
  La 
  

   Hire, 
  and 
  Lagrange, 
  are 
  confined 
  to 
  the 
  equilibrium 
  of 
  bent 
  rods 
  ; 
  but 
  those 
  of 
  

   Navier, 
  Poisson, 
  Lame 
  and 
  Clapeyron, 
  Cauchy, 
  Stokes, 
  and 
  Wertheim, 
  are 
  

   principally 
  directed 
  to 
  the 
  formation 
  and 
  application 
  of 
  the 
  general 
  equations. 
  

  

  The 
  investigations 
  of 
  Navier 
  are 
  contained 
  in 
  the 
  seventh 
  volume 
  of 
  the 
  

   Memoirs 
  of 
  the 
  Institute, 
  page 
  373 
  ; 
  and 
  in 
  the 
  Annates 
  de 
  Chimie 
  et 
  de 
  Physique, 
  

   2 
  e 
  Serie, 
  xv., 
  264, 
  and 
  xxxviii., 
  435 
  ; 
  L' 
  Application 
  de 
  la 
  Mecanique, 
  torn. 
  i. 
  

  

  Those 
  of 
  Poisson 
  in 
  Mem. 
  de 
  VInstitut, 
  viii., 
  429 
  ; 
  Annates 
  de 
  Chimie, 
  2 
  e 
  Serie, 
  

   xxxvi., 
  334 
  ; 
  xxxvii., 
  337 
  ; 
  xxxviii., 
  338 
  ; 
  xlii. 
  Journal 
  de 
  VEcole 
  Polytechnique, 
  

   cahier 
  xx., 
  with 
  an 
  abstract 
  in 
  Annates 
  de 
  Chimie 
  for 
  1829. 
  

  

  The 
  memoir 
  of 
  MM. 
  Lame 
  and 
  Clapeyron 
  is 
  contained 
  in 
  Crelle's 
  Mathe- 
  

   matical 
  Journal, 
  vol. 
  vii. 
  ; 
  and 
  some 
  observations 
  on 
  elasticity 
  are 
  to 
  be 
  found 
  

   in 
  Lame's 
  Cours 
  de 
  Physique. 
  

  

  M. 
  Cauchy's 
  investigations 
  are 
  contained 
  in 
  his 
  Exercises 
  de 
  Analyse, 
  vol. 
  iii., 
  

   p. 
  180, 
  published 
  in 
  1828. 
  

  

  Instead 
  of 
  supposing 
  each 
  pressure 
  proportional 
  to 
  the 
  linear 
  compression 
  

   which 
  it 
  produces, 
  he 
  supposes 
  it 
  to 
  consist 
  of 
  two 
  parts, 
  one 
  of 
  which 
  is 
  propor- 
  

  

  * 
  The 
  laws 
  of 
  pressure 
  and 
  compression 
  may 
  be 
  found 
  in 
  the 
  Memoir 
  of 
  Lame 
  and 
  Clapeyron. 
  

   See 
  note 
  A. 
  

  

  \ 
  See 
  note 
  B. 
  

  

  