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  IV.— 
  On 
  the 
  Equilibrium 
  of 
  Elastic 
  Solids. 
  By 
  James 
  Clerk 
  Maxwell, 
  Esq. 
  

  

  (Read 
  18th 
  February, 
  1850). 
  

  

  There 
  are 
  few 
  parts 
  of 
  mechanics 
  in 
  which 
  theory 
  has 
  differed 
  more 
  from 
  

   experiment 
  than 
  in 
  the 
  theory 
  of 
  elastic 
  solids. 
  

  

  Mathematicians, 
  setting 
  out 
  from 
  very 
  plausible 
  assumptions 
  with 
  respect 
  to 
  

   the 
  constitution 
  of 
  bodies, 
  and 
  the 
  laws 
  of 
  molecular 
  action, 
  came 
  to 
  conclusions 
  

   which 
  were 
  shewn 
  to 
  be 
  erroneous 
  by 
  the 
  observations 
  of 
  experimental 
  philosophers. 
  

   The 
  experiments 
  of 
  (Ersted 
  proved 
  to 
  be 
  at 
  variance 
  with 
  the 
  mathematical 
  theo- 
  

   ries 
  of 
  Navier, 
  Poisson, 
  and 
  Lamb 
  and 
  Clapeyron, 
  and 
  apparently 
  deprived 
  this 
  

   practically 
  important 
  branch 
  of 
  mechanics 
  of 
  all 
  assistance 
  from 
  mathematics. 
  

  

  The 
  assumption 
  on 
  which 
  these 
  theories 
  were 
  founded 
  may 
  be 
  stated 
  thus 
  :— 
  

  

  Solid 
  bodies 
  are 
  composed 
  of 
  distinct 
  moleades, 
  which 
  are 
  kept 
  at 
  a 
  certain 
  dis- 
  

   tance 
  from 
  each 
  other 
  by 
  the 
  opposing 
  principles 
  of 
  attraction 
  and 
  heat. 
  When 
  the 
  

   distance 
  between 
  two 
  molecules 
  is 
  changed, 
  they 
  act 
  on 
  each 
  other 
  with 
  a 
  force 
  whose 
  

   direction 
  is 
  in 
  the 
  line 
  joining 
  the 
  centres 
  of 
  the 
  molecules, 
  and 
  whose 
  magnitude 
  is 
  

   equal 
  to 
  the 
  change 
  of 
  distance 
  multiplied 
  into 
  a 
  function 
  of 
  the 
  distance 
  which 
  

   vanishes 
  when 
  that 
  distance 
  becomes 
  sensible. 
  

  

  The 
  equations 
  of 
  elasticity 
  deduced 
  from 
  this 
  assumption 
  contain 
  only 
  one 
  

   coefficient, 
  which 
  varies 
  with 
  the 
  nature 
  of 
  the 
  substance. 
  

  

  The 
  insufficiency 
  of 
  one 
  coefficient 
  may 
  be 
  proved 
  from 
  the 
  existence 
  of 
  

   bodies 
  of 
  different 
  degrees 
  of 
  solidity. 
  

  

  No 
  effort 
  is 
  required 
  to 
  retain 
  a 
  liquid 
  in 
  any 
  form, 
  if 
  its 
  volume 
  remain 
  un- 
  

   changed 
  ; 
  but 
  when 
  the 
  form 
  of 
  a 
  solid 
  is 
  changed, 
  a 
  force 
  is 
  called 
  into 
  action 
  

   which 
  tends 
  to 
  restore 
  its 
  former 
  figure 
  ; 
  and 
  this 
  constitutes 
  the 
  difference 
  be- 
  

   tween 
  elastic 
  solids 
  and 
  fluids. 
  Both 
  tend 
  to 
  recover 
  their 
  volume, 
  but 
  fluids 
  do 
  

   not 
  tend 
  to 
  recover 
  their 
  shape. 
  

  

  Now, 
  since 
  there 
  are 
  in 
  nature 
  bodies 
  which 
  are 
  in 
  every 
  intermediate 
  state 
  

   from 
  perfect 
  solidity 
  to 
  perfect 
  liquidity, 
  these 
  two 
  elastic 
  powers 
  cannot 
  exist 
  in 
  

   every 
  body 
  in 
  the 
  same 
  proportion, 
  and 
  therefore 
  all 
  theories 
  which 
  assign 
  to 
  

   them 
  an 
  invariable 
  ratio 
  must 
  be 
  erroneous. 
  

  

  I 
  have 
  therefore 
  substituted 
  for 
  the 
  assumption 
  of 
  Navier 
  the 
  following 
  

   axioms 
  as 
  the 
  results 
  of 
  experiments. 
  

  

  If 
  three 
  pressures 
  in 
  three 
  rectangular 
  axes 
  be 
  applied 
  at 
  a 
  point 
  in 
  an 
  

   elastic 
  solid, 
  — 
  

  

  1. 
  The 
  sum 
  of 
  the 
  three 
  pressures 
  is 
  proportional 
  to 
  the 
  sum 
  of 
  the 
  compressions 
  

   which 
  they 
  produce. 
  

  

  VOL. 
  XX. 
  PART 
  I. 
  2A 
  

  

  