﻿440 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  CENTRIFUGAL 
  THEORY 
  OF 
  ELASTICITY. 
  

   If 
  the 
  body 
  be 
  a 
  perfect 
  gas, 
  then 
  

  

  V^ 
  /£]M 
  K 
  4 
  _ 
  K^ 
  T-K 
  dY\ 
  

  

  t 
  \2/jl 
  + 
  t- 
  T 
  S 
  + 
  V 
  ' 
  dr) 
  

  

  Y 
  /kM 
  K 
  k-\ 
  

   Ky 
  -T 
  V277 
  + 
  T-^j 
  

  

  (32.) 
  

  

  v 
  T 
  o 
  V 
  T 
  / 
  T 
  o 
  \2 
  yu 
  t 
  2 
  7 
  

  

  The 
  fact 
  that 
  the 
  specific 
  heats 
  of 
  all 
  simple 
  gases 
  for 
  unity 
  of 
  weight 
  are 
  in- 
  

  

  k 
  M 
  

   versely 
  proportional 
  to 
  their 
  specific 
  gravities, 
  shews 
  that 
  ~ 
  — 
  is 
  the 
  same 
  for 
  them 
  

  

  all. 
  

  

  (13.) 
  Velocity 
  of 
  Sound 
  in 
  Fluids. 
  — 
  Let 
  a 
  denote 
  the 
  velocity 
  of 
  sound 
  in 
  a 
  

   fluid, 
  and 
  d 
  . 
  P 
  the 
  total 
  differential 
  of 
  the 
  pressure. 
  Then 
  

  

  fl 
  =,(,.^) 
  = 
  v{^(---^.-)} 
  

  

  d. 
  y 
  

  

  (33.) 
  

  

  If 
  it 
  were 
  possible 
  to 
  maintain 
  the 
  temperature 
  of 
  each 
  particle 
  of 
  the 
  fluid 
  in- 
  

   variable 
  during 
  the 
  passage 
  of 
  sound, 
  this 
  velocity 
  would 
  be 
  simply 
  

  

  ("d-l) 
  

  

  V 
  

  

  But 
  we 
  have 
  reason 
  to 
  believe, 
  that 
  there 
  is 
  not 
  time, 
  during 
  the 
  passage 
  of 
  

   sound, 
  for 
  an 
  appreciable 
  transfer 
  of 
  heat 
  from 
  atom 
  to 
  atom 
  ; 
  so 
  that 
  for 
  each 
  

   particle 
  

  

  d 
  Q 
  + 
  d 
  Q' 
  = 
  ; 
  or, 
  K 
  = 
  in 
  equation 
  (29). 
  

  

  To 
  fulfil 
  this 
  condition, 
  we 
  must 
  have 
  

  

  dr 
  r—K 
  dp 
  

  

  TV 
  = 
  ~ 
  TT~ 
  ' 
  rfT 
  

  

  V 
  

  

  Consequently, 
  

  

  or, 
  by 
  equation 
  (31) 
  

  

  ,/ 
  d¥ 
  K 
  P 
  \ 
  

  

  V 
  

  

  That 
  is 
  to 
  say, 
  the 
  action 
  of 
  heat 
  increases 
  the 
  velocity 
  of 
  sound 
  in 
  a 
  fluid, 
  beyond 
  

   what 
  it 
  mould 
  be, 
  if 
  heat 
  did 
  not 
  act, 
  in 
  the 
  ratio 
  of 
  the 
  square 
  root 
  of 
  the 
  specific 
  

   heat 
  at 
  constant 
  pressure, 
  to 
  the 
  square 
  root 
  of 
  the 
  specific 
  heat 
  at 
  constant 
  volume. 
  

  

  This 
  is 
  Laplace's 
  law 
  of 
  the 
  propagation 
  of 
  sound 
  ; 
  which 
  is 
  here 
  shewn 
  to 
  be 
  

   applicable, 
  not 
  only 
  to 
  perfect 
  gases, 
  but 
  to 
  all 
  fluids 
  whatsoever. 
  

  

  