﻿d 
  2 
  \oe, 
  H, 
  

  

  436 
  MR 
  W. 
  J. 
  M. 
  EANKINE 
  ON 
  THE 
  CENTRIFUGAL 
  THEORY 
  OF 
  ELASTICITY, 
  

  

  and, 
  therefore, 
  

  

  m 
  r 
  t 
  

  

  Log,^ 
  = 
  -j— 
  J 
  'pdV 
  - 
  -log 
  e 
  V 
  +/(t) 
  + 
  constant. 
  

  

  / 
  (t) 
  is 
  easily 
  found 
  to 
  be 
  = 
  — 
  log 
  e 
  t 
  for 
  a 
  perfect 
  gas, 
  and 
  being 
  independent 
  of 
  

   the 
  density, 
  is 
  the 
  same 
  for 
  all 
  substances 
  in 
  all 
  conditions 
  ; 
  Hence 
  we 
  find 
  (the 
  

   integrals 
  being 
  so 
  taken 
  that 
  for 
  a 
  perfect 
  gas 
  they 
  shall 
  = 
  0) 
  

  

  •■«*&_ 
  /■/*£_ 
  i)„j 
  

  

  « 
  T 
  J 
  \h 
  fj.d 
  T 
  AC 
  V 
  / 
  T 
  

  

  log 
  1 
  H 
  L 
  _^I 
  rd*p 
  1 
  

  

  tfr 
  2 
  _ 
  A//7 
  dr* 
  + 
  t 
  2 
  

  

  dT 
  dY 
  ~ 
  h 
  fxd 
  t 
  acV 
  

  

  and, 
  therefore, 
  

  

  »«-(^{»-(&+/£6«v)+«V.g} 
  . 
  . 
  (25.) 
  

  

  is 
  the 
  variation 
  of 
  latent 
  heat, 
  expressed 
  in 
  terms 
  of 
  the 
  pressure, 
  volume, 
  and 
  

   temperature 
  ; 
  to 
  which 
  if 
  the 
  variation 
  of 
  sensible 
  heat, 
  8 
  Q=U 
  8 
  T 
  , 
  be 
  added, 
  the 
  

   complete 
  variation 
  of 
  heat, 
  8 
  Q 
  I 
  + 
  8Q 
  I 
  '=8 
  . 
  Q, 
  in 
  unity 
  of 
  weight 
  of 
  the 
  substance, 
  

   corresponding 
  to 
  the 
  variations 
  8 
  V 
  and 
  8 
  t 
  of 
  volume 
  and 
  temperature, 
  will 
  be 
  

   ascertained. 
  

  

  It 
  is 
  obvious 
  that 
  equation 
  (25), 
  with 
  its 
  consequences, 
  is 
  applicable 
  to 
  any 
  

   mixture 
  of 
  atoms 
  of 
  different 
  substances 
  in 
  equilibrio 
  of 
  pressure 
  and 
  temperature 
  ; 
  

  

  for 
  in 
  that 
  case 
  t, 
  ~ 
  and 
  -^-K, 
  are 
  the 
  same 
  for 
  each 
  substance. 
  We 
  have 
  only 
  

  

  ' 
  d 
  t, 
  d 
  t 
  2 
  J 
  

  

  to 
  substitute 
  for 
  -^ 
  the 
  following 
  expression 
  : 
  — 
  

  

  n 
  i 
  M 
  1 
  + 
  2 
  M 
  2 
  +A 
  - 
  C 
  ' 
  

   where 
  n 
  Y 
  , 
  n 
  2 
  , 
  &c, 
  are 
  the 
  proportions 
  of 
  the 
  different 
  ingredients 
  in 
  unity 
  of 
  weight 
  

   of 
  the 
  mixture, 
  so 
  that 
  w 
  l 
  + 
  w 
  2 
  + 
  &c.=l. 
  

  

  Equation 
  (25) 
  agrees 
  exactly 
  with 
  equation 
  (6) 
  in 
  the 
  first 
  section 
  of 
  my 
  

   original 
  paper 
  on 
  the 
  Theory 
  of 
  the 
  Mechanical 
  Action 
  of 
  Heat. 
  It 
  is 
  the 
  funda- 
  

   mental 
  equation 
  of 
  that 
  theory 
  ; 
  and 
  I 
  shall 
  now 
  proceed 
  to 
  deduce 
  the 
  more 
  

   important 
  consequences 
  from 
  it. 
  

  

  (10.) 
  Equivalence 
  of 
  Heat 
  and 
  Expansive 
  Power. 
  Joule's 
  Law. 
  — 
  From 
  the 
  

   variation 
  of 
  the 
  heat 
  communicated 
  to 
  the 
  body, 
  let 
  us 
  subtract 
  the 
  variation 
  of 
  

   the 
  expansive 
  power 
  given 
  out 
  by 
  it, 
  or 
  

  

  P8v={p+/(V)}8v 
  

   The 
  result 
  is 
  the 
  variation 
  of 
  the 
  total 
  power 
  exercised 
  upon 
  or 
  communicated 
  to 
  

  

  * 
  This 
  coefficient 
  corresponds 
  to 
  — 
  — 
  in 
  the 
  notation 
  of 
  my 
  previous 
  paper 
  on 
  the 
  Mechanical 
  

  

  K 
  

  

  Action 
  of 
  Heat. 
  

  

  