﻿580 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  Sub-Section 
  4. 
  Thermic 
  Phenomena 
  of 
  Currents 
  of 
  Elastic 
  Fluids. 
  

   (60.) 
  When 
  a 
  gas 
  previously 
  compressed 
  is 
  allowed 
  to 
  escape 
  through 
  small 
  

   apertures, 
  as 
  in 
  the 
  experiments 
  of 
  Mr 
  Joule 
  and 
  Professor 
  Thomson, 
  and 
  has 
  

   its 
  velocity 
  destroyed 
  entirely 
  by 
  the 
  mutual 
  friction 
  of 
  its 
  particles, 
  without 
  im- 
  

   pediment 
  from 
  any 
  other 
  substance, 
  and 
  without 
  conduction 
  of 
  heat 
  to 
  or 
  from 
  

   any 
  other 
  substance 
  ; 
  then 
  its 
  condition 
  is 
  expressed 
  by 
  making 
  

  

  dY 
  = 
  

  

  that 
  is 
  to 
  say, 
  

  

  1 
  f 
  (dV 
  P\ 
  dV\ 
  7Tr 
  

  

  If 
  we 
  assume 
  (as 
  is 
  really 
  the 
  case 
  in 
  the 
  experiments) 
  that 
  the 
  specific 
  heat 
  

   of 
  the 
  gas 
  at 
  constant 
  volume 
  does 
  not 
  sensibly 
  vary 
  within 
  the 
  limits 
  of 
  the 
  

   experiments 
  as 
  to 
  temperature 
  and 
  volume, 
  so 
  that 
  K 
  v 
  is 
  sensibly 
  constant, 
  and 
  

   also 
  that 
  the 
  variation 
  of 
  temperature 
  is 
  very 
  small 
  as 
  compared 
  with 
  the 
  absolute 
  

   temperatures, 
  then 
  we 
  have 
  the 
  following 
  approximate 
  integral 
  : 
  — 
  

  

  A 
  T 
  

  

  =ib/;-(?r-iyv-«f;-£-«v} 
  ■ 
  <**> 
  

  

  which 
  represents 
  the 
  cooling 
  effect 
  of 
  an 
  expansion 
  from 
  the 
  volume 
  V 
  x 
  to 
  the 
  

   volume 
  V 
  2 
  . 
  

  

  If 
  it 
  were 
  possible 
  to 
  obtain 
  any 
  substance 
  in 
  the 
  state 
  of 
  perfect 
  gas 
  to 
  be 
  

   used 
  in 
  experiments 
  of 
  this 
  kind, 
  the 
  first 
  integral 
  in 
  the 
  above 
  expression 
  would 
  

   disappear, 
  because, 
  for 
  a 
  perfect 
  gas, 
  

  

  dY 
  P 
  

  

  d 
  T 
  T 
  

  

  and 
  as 
  the 
  other 
  term 
  is 
  negative, 
  the 
  result 
  would 
  be 
  a 
  slight 
  heating 
  effect. 
  As 
  

  

  dP 
  P 
  

  

  no 
  gas, 
  however, 
  is 
  perfect, 
  and 
  as 
  j- 
  always 
  exceeds 
  -, 
  the 
  mode 
  of 
  reducing 
  

  

  the 
  experimental 
  data 
  is 
  to 
  calculate 
  the 
  value 
  of 
  the 
  first 
  term, 
  which 
  represents 
  

   the 
  effect 
  of 
  cohesion, 
  from 
  the 
  known 
  properties 
  of 
  the 
  gas, 
  to 
  subtract 
  from 
  it 
  

   the 
  actual 
  cooling, 
  and 
  from 
  the 
  remainder 
  to 
  compute 
  values 
  of 
  k, 
  the 
  tempera- 
  

   ture 
  of 
  absolute 
  privation 
  of 
  heat, 
  according 
  to 
  the 
  following 
  formula 
  : 
  — 
  

  

  k 
  = 
  k 
  v 
  J, 
  % 
  U. 
  -) 
  \ 
  _ 
  ; 
  

  

  J_ 
  r"-arp 
  

  

  K, 
  dV 
  

  

  When 
  the 
  gas 
  is 
  nearly 
  perfect, 
  as 
  in 
  the 
  case 
  of 
  atmospheric 
  air, 
  it 
  is 
  unne- 
  

   cessary 
  to 
  take 
  into 
  consideration 
  its 
  deviation 
  from 
  the 
  perfect 
  condition 
  in 
  com- 
  

   puting 
  the 
  integral 
  in 
  the 
  denominator 
  ; 
  whose 
  approximate 
  value 
  is 
  found 
  to 
  be 
  

  

  