﻿158 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  wave 
  of 
  sound, 
  is 
  to 
  alter 
  slowly 
  the 
  form 
  of 
  the 
  function 
  representing 
  the 
  wave, 
  

   still 
  that 
  effect 
  is 
  not 
  sufficiently 
  great 
  to 
  make 
  Laplace's 
  theory 
  practically 
  erro- 
  

   neous. 
  I 
  have, 
  therefore, 
  in 
  the 
  sequel, 
  adhered 
  to 
  the 
  experiments 
  of 
  Dulong, 
  

   and 
  to 
  those 
  quoted 
  by 
  Poisson, 
  on 
  the 
  velocity 
  of 
  sound, 
  as 
  the 
  best 
  data 
  for 
  

   determining 
  the 
  mechanical 
  equivalent 
  of 
  heat. 
  

  

  (4.) 
  The 
  expression 
  already 
  given 
  for 
  the 
  real 
  specific 
  heat 
  of 
  unity 
  of 
  weight 
  

   of 
  a 
  given 
  substance 
  may 
  be 
  resolved 
  into 
  two 
  factors, 
  thus 
  : 
  — 
  

  

  The 
  first 
  factor, 
  ~ 
  — 
  ^, 
  may 
  be 
  considered 
  in 
  general 
  as 
  a 
  known 
  quantity 
  ; 
  for 
  C 
  

  

  represents, 
  as 
  already 
  stated, 
  274 
  -6 
  centigrade 
  degrees, 
  the 
  absolute 
  temperature 
  

   of 
  melting 
  ice, 
  and 
  wM 
  the 
  theoretical 
  weight, 
  in 
  the 
  perfectly 
  gaseous 
  state, 
  of 
  

   unity 
  of 
  volume 
  of 
  the 
  substance, 
  under 
  unity 
  of 
  pressure, 
  at 
  that 
  temperature 
  ; 
  

  

  or 
  what 
  is 
  the 
  same 
  thing, 
  -^ 
  is 
  the 
  height 
  of 
  an 
  imaginary 
  column 
  of 
  the 
  sub- 
  

   stance, 
  of 
  uniform 
  density, 
  and 
  at 
  the 
  temperature 
  of 
  melting 
  ice, 
  whose 
  pressure 
  

   by 
  weight 
  upon 
  a 
  given 
  area 
  of 
  base 
  is 
  equal 
  to 
  its 
  pressure 
  by 
  elasticity, 
  sup- 
  

  

  3 
  k 
  M 
  

   posing 
  it 
  to 
  be 
  perfectly 
  gaseous. 
  The 
  determination 
  of 
  the 
  ratio 
  -s 
  — 
  is 
  neces- 
  

  

  sary, 
  to 
  complete 
  the 
  solution 
  of 
  the 
  problem. 
  

  

  (5.) 
  The 
  relation 
  now 
  to 
  be 
  investigated 
  between 
  heat 
  and 
  mechanical 
  power, 
  

   is 
  that 
  which 
  exists 
  between 
  the 
  power 
  expended 
  in 
  compressing 
  a 
  body 
  into 
  a 
  

   smaller 
  volume, 
  and 
  the 
  increase 
  of 
  heat 
  in 
  consequence 
  of 
  such 
  a 
  compression, 
  

   and 
  conversely, 
  between 
  the 
  heat 
  which 
  disappears, 
  or, 
  as 
  it 
  is 
  said, 
  becomes 
  

   latent, 
  during 
  the 
  expansion 
  of 
  a 
  body 
  to 
  a 
  greater 
  volume, 
  and 
  the 
  mechanical 
  

   power 
  gained 
  or 
  developed 
  by 
  that 
  expansion. 
  Those 
  phenomena, 
  according 
  to 
  

   :he 
  hypothesis 
  now 
  under 
  consideration, 
  as 
  well 
  as 
  every 
  hypothesis 
  which 
  

   iscribes 
  heat 
  to 
  motion, 
  are 
  simply 
  the 
  transformation 
  of 
  mechanical 
  power 
  from 
  

   one 
  shape 
  into 
  another. 
  

  

  It 
  is 
  obvious, 
  in 
  the 
  first 
  place, 
  without 
  the 
  aid 
  of 
  algebraical 
  symbols, 
  that 
  

   the 
  general 
  effect 
  of 
  the 
  compression 
  of 
  an 
  oscillating 
  atomic 
  atmosphere, 
  or 
  

   molecular 
  vortex, 
  must 
  be 
  to 
  accelerate 
  its 
  motion, 
  and 
  of 
  its 
  dilatation, 
  to 
  retard 
  

   its 
  motion 
  ; 
  for 
  every 
  portion 
  of 
  such 
  an 
  atmosphere 
  is 
  urged 
  towards 
  the 
  nucleus 
  

   or 
  atomic 
  centre 
  by 
  a 
  centripetal 
  force 
  equal 
  to 
  the 
  centrifugal 
  force 
  arising 
  from 
  

   the 
  oscillation 
  ; 
  so 
  that 
  when, 
  by 
  compression, 
  each 
  portion 
  of 
  the 
  atmosphere 
  is 
  

   made 
  to 
  approach 
  the 
  centre 
  by 
  a 
  given 
  distance, 
  the 
  vis 
  viva 
  of 
  its 
  motion 
  will 
  

   be 
  increased 
  by 
  the 
  amount 
  corresponding 
  to 
  the 
  centripetal 
  force 
  acting 
  through 
  

   that 
  distance 
  ; 
  and 
  conversely, 
  when 
  by 
  expansion 
  each 
  portion 
  of 
  the 
  atmosphere 
  

   is 
  made 
  to 
  retreat 
  from 
  the 
  centre, 
  the 
  vis 
  viva 
  of 
  its 
  motion 
  will 
  be 
  diminished 
  

   by 
  a 
  similar 
  amount. 
  

  

  It 
  is 
  not, 
  however, 
  to 
  be 
  taken 
  for 
  granted, 
  that 
  all 
  the 
  power 
  expended 
  in 
  

  

  