﻿432 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  CENTRIFUGAL 
  THEORY 
  OF 
  ELASTICITY, 
  

  

  Hence, 
  temperature 
  depends 
  on 
  the 
  above 
  function 
  only 
  ; 
  for 
  the 
  definition 
  of 
  

   temperature 
  is, 
  that 
  bodies 
  at 
  the 
  same 
  temperature 
  are 
  in 
  a 
  permanent 
  condition 
  

   as 
  to 
  heat, 
  so 
  far 
  as 
  their 
  mutual 
  action 
  is 
  concerned. 
  

  

  The 
  ratio 
  of 
  the 
  real 
  specific 
  heat 
  of 
  (a) 
  to 
  that 
  of 
  (b) 
  is 
  obviously 
  

  

  hj 
  a 
  :h 
  h 
  k 
  b 
  (14.) 
  

  

  (7.) 
  Measure 
  of 
  Temperature 
  and 
  Specific 
  Heat. 
  — 
  The 
  function 
  is 
  proportional 
  

   to 
  the 
  pressure 
  of 
  a 
  perfect 
  gas 
  at 
  a 
  constant 
  density. 
  That 
  pressure, 
  therefore, 
  

   is 
  the 
  most 
  convenient 
  measure 
  of 
  temperature. 
  

  

  Let 
  t 
  denote 
  absolute 
  temperature, 
  as 
  measured 
  by 
  the 
  pressure 
  of 
  a 
  perfect 
  

   gas 
  at 
  constant 
  density, 
  and 
  reckoned 
  from 
  a 
  certain 
  absolute 
  zero, 
  274°6 
  Centi- 
  

   grade, 
  or 
  494 
  0- 
  28 
  Fahrenheit 
  below 
  the 
  temperature 
  of 
  melting 
  ice. 
  Let 
  k 
  be 
  a 
  

   constant 
  which 
  depends 
  on 
  the 
  length 
  of 
  a 
  degree 
  on 
  the 
  thermometric 
  scale, 
  and 
  

   is 
  the 
  same 
  for 
  all 
  substances 
  in 
  nature. 
  

  

  Then 
  

  

  a 
  2/cQ 
  

   h 
  k 
  

  

  r\ 
  t 
  \ 
  h 
  k 
  I 
  

  

  and 
  the 
  real 
  specific 
  heat 
  of 
  the 
  substance, 
  that 
  is 
  to 
  say, 
  the 
  depth 
  of 
  fall, 
  under 
  

   the 
  influence 
  of 
  gravity, 
  which 
  is 
  equivalent 
  to 
  a 
  rise 
  of 
  one 
  degree 
  of 
  temperature 
  

   in 
  the 
  body, 
  is 
  represented 
  by 
  

  

  '-*-* 
  w 
  

  

  The 
  pressure 
  of 
  a 
  perfect 
  gas 
  is 
  represented 
  in 
  terms 
  of 
  temperature 
  by 
  

  

  * 
  = 
  wn 
  < 
  17 
  -) 
  

  

  It 
  may 
  also 
  be 
  expressed 
  thus 
  : 
  let 
  t 
  denote 
  the 
  absolute 
  temperature 
  of 
  melt- 
  

   ing 
  ice 
  in 
  degrees 
  of 
  the 
  scale 
  employed, 
  and 
  V 
  the 
  volume 
  of 
  unity 
  of 
  weight 
  of 
  

   the 
  substance 
  in 
  the 
  theoretical 
  state 
  of 
  perfect 
  gas, 
  at 
  the 
  temperature 
  of 
  melting 
  

   ice 
  and 
  pressure 
  unity 
  : 
  — 
  then 
  

  

  V 
  T 
  

  

  *=vV 
  < 
  18 
  -) 
  

  

  v 
  'o 
  

  

  On 
  comparing 
  this 
  with 
  equation 
  (17) 
  we 
  see 
  that 
  

  

  h 
  JL- 
  Yn 
  . 
  

  

  h 
  fl 
  t 
  h 
  p. 
  _ 
  K 
  

  

  iv; 
  ; 
  mt 
  - 
  r- 
  

  

  l 
  (19-) 
  

  

  Now 
  h 
  is 
  the 
  specific 
  elasticity 
  of 
  the 
  atomic 
  atmosphere 
  of 
  the 
  substance 
  ; 
  ^-^ 
  

  

  is 
  the 
  mean 
  specific 
  gravity 
  of 
  that 
  atmosphere, 
  when 
  the 
  body 
  is 
  in 
  the 
  theoretical 
  

   state 
  of 
  perfect 
  gas 
  ; 
  and 
  k 
  and 
  r 
  are 
  the 
  same 
  for 
  all 
  substances 
  in 
  nature. 
  There- 
  

  

  