﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  585 
  

  

  If 
  the 
  value 
  of 
  k 
  is 
  really 
  2°-l 
  centigrade, 
  as 
  computed 
  above, 
  the 
  calculated 
  maxi- 
  

   mum 
  theoretical 
  duty 
  in 
  Section 
  V. 
  is 
  too 
  small 
  by 
  about 
  one 
  one-hundred-and- 
  

   ninetieth 
  part 
  of 
  its 
  amount, 
  — 
  a 
  quantity 
  of 
  no 
  practical 
  importance 
  in 
  such 
  cal- 
  

   culations. 
  

  

  (61.) 
  It 
  may 
  be 
  anticipated, 
  that 
  when 
  Mr 
  Joule 
  and 
  Professor 
  Thomson 
  shall 
  

   have 
  performed 
  experiments 
  on 
  the 
  thermic 
  phenomena 
  exhibited 
  by 
  air 
  in 
  more 
  

   copious 
  currents, 
  and 
  by 
  gases 
  of 
  more 
  definite 
  composition, 
  and 
  more 
  simple 
  laws 
  

   of 
  elasticity, 
  much 
  more 
  precise 
  results 
  will 
  be 
  obtained. 
  

  

  When 
  a 
  gas 
  deviating 
  considerably 
  from 
  the 
  perfectly 
  gaseous 
  condition, 
  or 
  a 
  

   vapour 
  near 
  the 
  point 
  of 
  saturation, 
  is 
  employed, 
  it 
  will 
  no 
  longer 
  be 
  sufficiently 
  

   accurate 
  to 
  treat 
  the 
  specific 
  heat 
  at 
  constant 
  volume 
  as 
  a 
  constant 
  quantity, 
  nor 
  

   the 
  cooling 
  effect 
  as 
  very 
  small. 
  It 
  will 
  therefore 
  be 
  necessary 
  to 
  employ, 
  for 
  the 
  

   reduction 
  of 
  the 
  experiments, 
  the 
  integral 
  form 
  of 
  equation 
  (99) 
  ; 
  that 
  is 
  to 
  say, 
  

  

  = 
  a 
  T 
  = 
  A 
  [ 
  ft 
  t 
  + 
  ft 
  N 
  k 
  (hyp. 
  log 
  t 
  + 
  *) 
  + 
  Y(t 
  - 
  k) 
  ^ 
  - 
  1 
  \J* 
  P 
  d 
  V 
  ] 
  

   = 
  k(T 
  2 
  -r 
  1 
  ) 
  + 
  Ay( 
  T 
  ^-P) 
  Q 
  !V 
  

   -K 
  [Ay^cZV-ftN^A 
  • 
  * 
  + 
  A 
  hyp. 
  logr) 
  j 
  . 
  . 
  (110.) 
  

  

  (62.) 
  Preliminary 
  to 
  the 
  application 
  of 
  this 
  equation, 
  it 
  is 
  necessary 
  to 
  deter- 
  

   mine 
  the 
  mechanical 
  value 
  of 
  the 
  real 
  specific 
  heat 
  U. 
  Supposing 
  the 
  law 
  which 
  

   connects 
  the 
  pressure, 
  density, 
  and 
  temperature 
  of 
  the 
  gas 
  to 
  be 
  known, 
  it 
  is 
  suf- 
  

   ficient 
  for 
  this 
  purpose 
  to 
  have 
  an 
  accurate 
  experimental 
  determination, 
  either 
  of 
  

   the 
  apparent 
  specific 
  heat 
  at 
  constant 
  pressure 
  for 
  a 
  given 
  temperature, 
  or 
  the 
  

   velocity 
  of 
  sound 
  in 
  the 
  gas 
  under 
  given 
  circumstances. 
  

  

  First, 
  let 
  us 
  suppose 
  that 
  the 
  apparent 
  specific 
  heat 
  at 
  constant 
  pressure 
  is 
  

   known. 
  

  

  The 
  value 
  of 
  this 
  coefficient 
  (Centrifugal 
  Theory 
  of 
  Elasticity, 
  art. 
  12) 
  is 
  

  

  (dV\ 
  2 
  

  

  \drj 
  

  

  ' 
  T 
  2 
  "V 
  d 
  T 
  2 
  " 
  T 
  ' 
  T 
  

  

  ~dY 
  ' 
  

  

  In 
  order 
  that 
  the 
  lower 
  limit 
  of 
  the 
  integral 
  may 
  correspond 
  with 
  the 
  condition 
  

   of 
  perfect 
  gas, 
  it 
  is 
  convenient 
  to 
  transform 
  it 
  into 
  one 
  in 
  terms 
  of 
  the 
  density. 
  

   Let 
  D 
  be 
  the 
  weight 
  of 
  unity 
  of 
  volume, 
  then 
  

  

  AZ 
  2 
  P 
  ,„ 
  /-Di 
  d 
  2 
  P 
  ._ 
  , 
  n11 
  . 
  , 
  

  

  ** 
  o 
  

   If, 
  then, 
  we 
  have 
  the 
  pressure 
  of 
  the 
  gas 
  under 
  consideration 
  expressed 
  by 
  the 
  

   the 
  following 
  approximate 
  formula 
  : 
  — 
  

  

  vol. 
  xx. 
  part 
  iv. 
  7 
  T 
  

  

  k 
  p 
  = 
  s 
  + 
  (t 
  -J^ 
  + 
  /^v 
  + 
  %U 
  . 
  . 
  ( 
  m.) 
  

  

  