﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  

  

  153 
  

  

  The 
  coefficient 
  k 
  (which 
  enters 
  into 
  the 
  value 
  of 
  specific 
  heat) 
  being 
  the 
  ratio 
  

   of 
  the 
  vis 
  viva 
  of 
  the 
  entire 
  motion 
  impressed 
  on 
  the 
  atomic 
  atmospheres 
  by 
  the 
  

   action 
  of 
  their 
  nuclei, 
  to 
  the 
  vis 
  viva 
  of 
  a 
  peculiar 
  kind 
  of 
  motion, 
  may 
  be 
  conjec- 
  

   tured 
  to 
  have 
  a 
  specific 
  value 
  for 
  each 
  substance 
  depending 
  in 
  a 
  manner 
  as 
  yet 
  

   unknown 
  on 
  some 
  circumstance 
  in 
  the 
  constitution 
  of 
  its 
  atoms. 
  Although 
  it 
  

   varies 
  in 
  some 
  cases 
  for 
  the 
  same 
  substance 
  in 
  the 
  solid, 
  liquid, 
  and 
  gaseous 
  states, 
  

   there 
  is 
  no 
  experimental 
  evidence 
  that 
  it 
  varies 
  for 
  the 
  same 
  substance 
  in 
  the 
  same 
  

   condition. 
  In 
  the 
  investigation 
  which 
  follows, 
  therefore, 
  I 
  have 
  treated 
  it 
  as 
  sen- 
  

   sibly 
  constant. 
  

  

  The 
  following, 
  then, 
  are 
  the 
  expressions 
  for 
  quantity 
  of 
  heat 
  in 
  terms 
  of 
  

   temperature. 
  In 
  one 
  atom 
  : 
  — 
  

  

  3kM 
  

  

  q= 
  lT 
  -M= 
  

  

  * 
  2g 
  2 
  Cn 
  [X 
  

  

  (r 
  — 
  C 
  n 
  fx 
  b) 
  

  

  In 
  unity 
  of 
  weight 
  : 
  — 
  

  

  Q: 
  

  

  3k 
  

  

  '2g 
  2 
  Cn/j. 
  

  

  (r-Cn/JLb) 
  

  

  (XII.) 
  

  

  Real 
  specific 
  heat 
  is 
  consequently 
  expressed 
  by 
  the 
  following 
  equations 
  : 
  — 
  

   For 
  one 
  atom 
  : 
  — 
  

  

  For 
  unity 
  of 
  weight 
  : 
  

  

  d 
  q 
  

  

  3&M 
  

  

  dr 
  

  

  2Gn}x 
  

  

  dq 
  

  

  3k 
  

  

  dr 
  

  

  ~2Cnfx 
  

  

  \ 
  

  

  For 
  so 
  much 
  of 
  a 
  perfect 
  gas 
  as 
  occupies 
  unity 
  of 
  

   volume 
  under 
  unity 
  of 
  pressure 
  at 
  the 
  temperature 
  of 
  

  

  melting 
  ice 
  :- 
  

  

  dg_ 
  3kM. 
  

  

  2G/JL 
  

  

  n 
  T- 
  

  

  (XIII.) 
  

  

  The 
  laws 
  established 
  experimentally 
  by 
  Dulong, 
  that 
  the 
  specific 
  heats 
  of 
  

   simple 
  atoms, 
  and 
  of 
  certain 
  groups 
  of 
  compound 
  atoms, 
  bear 
  to 
  each 
  other 
  simple 
  

   ratios, 
  generally 
  that 
  of 
  equality, 
  and 
  that 
  the 
  specific 
  heats 
  of 
  equal 
  volumes 
  of 
  

  

  k 
  M 
  

   all 
  simple 
  gases 
  are 
  equal, 
  shew 
  that 
  the 
  specific 
  factor 
  — 
  depends 
  on 
  the 
  che- 
  

  

  mical 
  constitution 
  of 
  the 
  atom, 
  and 
  thus 
  confirm 
  the 
  conjecture 
  I 
  have 
  stated 
  

   respecting 
  the 
  coefficient 
  k. 
  

  

  As 
  I 
  shall 
  have 
  occasion, 
  in 
  the 
  investigation 
  which 
  follows, 
  to 
  refer 
  to 
  and 
  

   to 
  use 
  the 
  equation 
  for 
  the 
  elasticity 
  of 
  vapours 
  in 
  contact 
  with 
  their 
  liquids, 
  which 
  

   I 
  published 
  in 
  the 
  Edinburgh 
  New 
  Philosophical 
  Journal 
  for 
  July 
  1849, 
  I 
  shall 
  

   here 
  state 
  generally 
  the 
  nature 
  of 
  the 
  reasoning 
  from 
  which 
  it 
  was 
  deduced. 
  

  

  