﻿434 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  CENTRIFUGAL 
  THEORY 
  OF 
  ELASTICITY, 
  

   of 
  volume 
  8 
  V. 
  Let 
  8 
  . 
  Q 
  be 
  divided 
  into 
  two 
  parts 
  

  

  of 
  which 
  8 
  Q, 
  being 
  directly 
  employed 
  in 
  varying 
  the 
  velocity 
  of 
  the 
  particles, 
  is 
  

   the 
  variation 
  of 
  the 
  actual 
  or 
  sensible 
  heat 
  possessed 
  by 
  the 
  body 
  ; 
  while 
  8 
  Q', 
  

   being 
  employed 
  in 
  varying 
  then 
  orbits, 
  represents 
  the 
  amount 
  of 
  the 
  mutual 
  

   transformation 
  of 
  heat 
  with 
  expansive 
  power 
  and 
  molecular 
  action, 
  or 
  the 
  varia- 
  

   tion 
  of 
  what 
  is 
  called 
  the 
  latent 
  heat 
  ; 
  that 
  is 
  to 
  say, 
  of 
  a 
  molecular 
  condition 
  con- 
  

   stituting 
  a 
  source 
  of 
  power, 
  out 
  of 
  which 
  heat 
  may 
  be 
  developed. 
  (8 
  Q' 
  in 
  this 
  

   paper 
  corresponds 
  to 
  — 
  8 
  Q' 
  in 
  my 
  former 
  papers.) 
  

  

  The 
  variation 
  of 
  sensible 
  heat 
  has 
  evidently 
  this 
  value 
  

  

  8q 
  = 
  U8r 
  , 
  (22.) 
  

  

  Let 
  8 
  x, 
  8 
  y, 
  8 
  z, 
  be 
  the 
  displacements 
  of 
  the 
  orbit 
  of 
  the 
  particles 
  of 
  atomic- 
  

   atmosphere 
  at 
  the 
  point 
  (x,y, 
  z.) 
  A 
  molecule 
  gdxdydz 
  is 
  acted 
  upon 
  by 
  the 
  

   accelerative 
  forces 
  (see 
  equation 
  3 
  A.) 
  

  

  parallel 
  to 
  the 
  three 
  axes 
  respectively. 
  

  

  The 
  sum 
  of 
  the 
  actions 
  of 
  those 
  forces 
  on 
  the 
  molecule 
  g 
  dxdy 
  d 
  z 
  during 
  the 
  

   change 
  of 
  temperature 
  and 
  volume, 
  is 
  

  

  = 
  — 
  2 
  Q8 
  (p 
  Q 
  d 
  x 
  dy 
  d 
  z 
  

  

  The 
  sum 
  of 
  such 
  actions 
  upon 
  all 
  the 
  particles 
  in 
  unity 
  of 
  weight 
  is 
  equal 
  in 
  

   amount 
  and 
  opposite 
  in 
  sign 
  to 
  the 
  variation 
  of 
  latent 
  heat 
  : 
  that 
  is 
  to 
  say, 
  

  

  $$= 
  2: 
  ^rJjJo9S<t>dxdydz 
  (23.) 
  

  

  To 
  determine 
  the 
  value 
  of 
  the 
  variation 
  8 
  <£, 
  let 
  it 
  be 
  divided 
  into 
  two 
  parts, 
  

  

  thus 
  : 
  — 
  

  

  8 
  cp 
  = 
  8 
  cf) 
  x 
  + 
  8 
  A(p 
  

   where 
  A<p=<p—(p 
  1 
  

  

  First, 
  With 
  respect 
  to 
  8 
  p 
  it 
  is 
  obvious 
  that 
  because, 
  according 
  to 
  equations 
  

  

  (6,7) 
  

  

  we 
  must 
  have 
  

  

  8V 
  = 
  kV8cp 
  i 
  arid8ct) 
  l 
  =^ 
  

  

  rC 
  V 
  

  

  Hence 
  the 
  first 
  part 
  of 
  the 
  integral 
  (23) 
  is 
  

   2Q 
  

   M 
  

  

  '*/#&)'*■*'*•- 
  5ft$-« 
  T 
  

  

  