﻿AND 
  ITS 
  CONNECTION 
  WITH 
  THE 
  THEORY 
  OF 
  HEAT. 
  427 
  

  

  as 
  the 
  heat 
  is 
  less 
  ; 
  but 
  their 
  sum, 
  so 
  far 
  as 
  elasticity 
  of 
  volume 
  is 
  concerned, 
  is 
  a 
  

   function 
  of 
  the 
  density 
  only. 
  

  

  That 
  is 
  to 
  say, 
  as 
  in 
  equation 
  (12) 
  of 
  my 
  paper 
  on 
  the 
  laws 
  of 
  the 
  elasticity 
  of 
  

   solids 
  {Cambridge 
  and 
  Dublin 
  MathematicalJournal, 
  February 
  1851), 
  let 
  the 
  total 
  

   coefficient 
  of 
  elasticity 
  of 
  volume 
  be 
  denoted 
  thus 
  

  

  ^=J 
  + 
  0(C 
  1 
  ,C 
  2S 
  C 
  3 
  ) 
  (IB.) 
  

  

  C 
  , 
  C. 
  , 
  C 
  , 
  being 
  the 
  coefficients 
  of 
  rigidity 
  round 
  the 
  three 
  axes 
  of 
  elasticity, 
  and 
  

   J 
  a 
  coefficient 
  of 
  fluid 
  elasticity 
  ; 
  then 
  

  

  J=-^ 
  r 
  F(V,Q)-^(V,Q).^ 
  r 
  /(V) 
  

   (0 
  15 
  C 
  2 
  , 
  C 
  3 
  ) 
  = 
  - 
  ( 
  1 
  - 
  4 
  (V, 
  Q) 
  ) 
  .-£-/ 
  (V) 
  

  

  (10.) 
  

  

  V 
  

   For 
  the 
  present, 
  we 
  have 
  to 
  take 
  into 
  consideration 
  that 
  portion 
  only 
  of 
  the 
  

   expansive 
  pressure 
  which 
  depends 
  on 
  density 
  and 
  heat 
  jointly, 
  and 
  is 
  the 
  means 
  

   of 
  mutually 
  converting 
  heat 
  and 
  expansive 
  power 
  ; 
  that 
  is 
  to 
  say, 
  the 
  pressure 
  at 
  

   the 
  boundaries 
  of 
  the 
  atomic 
  atmospheres 
  ; 
  which 
  I 
  shall 
  denote 
  by 
  

  

  P 
  =F 
  (V, 
  Q) 
  

  

  Pressures, 
  throughout 
  this 
  paper, 
  are 
  supposed 
  to 
  be 
  measured 
  by 
  units 
  of 
  

   weight 
  upon 
  unity 
  of 
  area; 
  densities, 
  by 
  the 
  weight 
  of 
  unity 
  of 
  volume. 
  

  

  (3.) 
  Determination 
  of 
  the 
  External 
  Pressure 
  of 
  an 
  Atomic 
  Atmosphere. 
  — 
  Let 
  a 
  

   body 
  be 
  composed 
  of 
  equal 
  and 
  similar 
  atomic 
  nuclei, 
  arranged 
  in 
  any 
  symmetrical 
  

   manner, 
  and 
  enveloped 
  by 
  an 
  atmosphere, 
  the 
  parts 
  of 
  which 
  are 
  subject 
  to 
  attrac- 
  

   tive 
  and 
  repulsive 
  forces, 
  exercised 
  by 
  each 
  other, 
  and 
  by 
  the 
  nuclei. 
  Let 
  it 
  further 
  

   be 
  supposed, 
  that 
  this 
  atmosphere, 
  at 
  each 
  point, 
  has 
  an 
  elastic 
  pressure 
  proportional 
  

   to 
  the 
  density 
  at 
  that 
  point, 
  multiplied 
  by 
  a 
  specific 
  coefficient 
  depending 
  on 
  the 
  

   nature 
  of 
  the 
  substance, 
  which 
  I 
  shall 
  denote 
  by 
  h. 
  (This 
  coefficient 
  was 
  denoted 
  

   by 
  b 
  in 
  previous 
  papers). 
  

  

  Let 
  Q 
  and 
  p' 
  denote 
  the 
  density 
  and 
  pressure 
  of 
  the 
  atomic 
  atmosphere 
  at 
  any 
  

   point 
  ; 
  then 
  

  

  T 
  , 
  d 
  <J> 
  d 
  <J> 
  </<E> 
  

  

  Let 
  - 
  ff 
  d^'-^dj'-^rz 
  

  

  be 
  the 
  accelerative 
  forces 
  operating 
  on 
  a 
  particle 
  of 
  atomic 
  atmosphere, 
  in 
  virtue 
  

   of 
  the 
  molecular 
  attractions 
  and 
  repulsions, 
  which 
  I 
  have 
  made 
  explicitly 
  negative, 
  

   attractions 
  being 
  supposed 
  to 
  predominate. 
  The 
  property 
  of 
  the 
  surfaces 
  called 
  

   the 
  boundaries 
  of 
  the 
  atoms 
  is 
  this 
  

  

  63,-* 
  <£).-* 
  (£).-* 
  

  

  