﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  167 
  

  

  Ratio 
  of 
  those 
  two 
  specific 
  heats 
  : 
  — 
  

  

  |?=1 
  + 
  N 
  .... 
  (21.) 
  

  

  This 
  ratio 
  is 
  the 
  quantity 
  called 
  by 
  Poisson 
  7, 
  in 
  his 
  researches 
  on 
  the 
  pro- 
  

   pagation 
  of 
  sound. 
  

  

  (11.) 
  It 
  is 
  unnecessary 
  to 
  do 
  more 
  than 
  to 
  refer 
  to 
  the 
  researches 
  of 
  Poisson, 
  

   and 
  to 
  those 
  of 
  Laplace, 
  for 
  the 
  proof 
  that 
  the 
  effect 
  of 
  the 
  production 
  of 
  heat 
  by 
  

   the 
  compression 
  of 
  air 
  is 
  the 
  same 
  as 
  if 
  the 
  elasticity 
  varied 
  in 
  proportion 
  to 
  that 
  

   power 
  of 
  the 
  density 
  whose 
  index 
  is 
  the 
  ratio 
  of 
  the 
  two 
  specific 
  heats 
  ; 
  so 
  that 
  

   the 
  actual 
  velocity 
  of 
  sound 
  is 
  greater 
  than 
  that 
  which 
  it 
  would 
  have 
  if 
  there 
  were 
  

   no 
  such 
  development 
  of 
  heat, 
  in 
  the 
  proportion 
  of 
  the 
  square 
  root 
  of 
  that 
  ratio. 
  

  

  The 
  following 
  is 
  the 
  value 
  of 
  the 
  velocity 
  of 
  sound 
  in 
  a 
  gas, 
  as 
  given 
  by 
  

   Poisson, 
  in 
  the 
  second 
  volume 
  of 
  his 
  Traite 
  de 
  Mecanique 
  : 
  — 
  

  

  *=Jsr 
  - 
  7. 
  (1 
  + 
  ET)^ 
  .... 
  (22.) 
  

  

  where 
  a 
  denotes 
  the 
  velocity 
  of 
  sound, 
  g 
  the 
  velocity 
  generated 
  by 
  gravity 
  in 
  

   unity 
  of 
  time, 
  E 
  the 
  coefficient 
  of 
  increase 
  of 
  elasticity 
  with 
  temperature, 
  at 
  the 
  

   freezing 
  point 
  of 
  water, 
  T 
  the 
  temperature 
  measured 
  from 
  that 
  point, 
  m 
  the 
  spe- 
  

   cific 
  gravity 
  of 
  mercury, 
  a 
  that 
  of 
  the 
  gas 
  at 
  the 
  temperature 
  of 
  melting 
  ice, 
  and 
  

   pressure 
  corresponding 
  to 
  a 
  column 
  of 
  mercury 
  of 
  the 
  height 
  h. 
  It 
  follows 
  that 
  

   the 
  ratio 
  7 
  is 
  given 
  by 
  the 
  formula 
  

  

  a 
  2 
  A 
  

  

  7=1 
  + 
  N 
  nearly 
  = 
  ^ 
  — 
  =-= 
  . 
  . 
  . 
  (23.) 
  

  

  ' 
  J 
  g 
  m 
  h 
  (1 
  + 
  E 
  T) 
  v 
  ' 
  

  

  Calculations 
  have 
  been 
  made 
  to 
  determine 
  the 
  ratio 
  7 
  from 
  the 
  velocity 
  of 
  

   sound 
  ; 
  but 
  as 
  many 
  of 
  them 
  involve 
  erroneous 
  values 
  of 
  the 
  coefficient 
  of 
  elasti- 
  

   city 
  E, 
  the 
  experiments 
  have 
  to 
  be 
  reduced 
  anew. 
  

  

  The 
  following 
  calculation 
  is 
  founded 
  on 
  an 
  experiment 
  quoted 
  by 
  Poisson 
  

   on 
  the 
  velocity 
  of 
  sound 
  in 
  atmospheric 
  air, 
  the 
  values 
  of 
  E, 
  m, 
  and 
  a 
  being 
  taken 
  

   from 
  the 
  experiments 
  of 
  M. 
  Regnault. 
  

  

  a 
  = 
  340-89 
  metres 
  per 
  second. 
  

   g 
  = 
  9 
  m 
  -80896. 
  h 
  = 
  m 
  -76. 
  T 
  = 
  15°-9 
  Centigrade. 
  

  

  E 
  = 
  0003665 
  ; 
  - 
  = 
  10513. 
  

  

  A 
  

  

  Consequently, 
  for 
  atmospheric 
  air, 
  

  

  7 
  = 
  1-401. 
  

  

  The 
  results 
  of 
  a 
  reduction, 
  according 
  to 
  correct 
  data, 
  of 
  the 
  experiments 
  of 
  

   Dulong 
  upon 
  the 
  velocity 
  of 
  sound 
  in 
  atmospheric 
  air, 
  oxygen, 
  and 
  hydrogen, 
  

   are 
  as 
  follows 
  : 
  — 
  

  

  Atmospheric 
  air, 
  . 
  . 
  . 
  . 
  7 
  = 
  1-410 
  

  

  Oxygen, 
  1-426 
  

  

  Hydrogen, 
  1'426 
  

  

  VOL. 
  XX. 
  PART 
  I. 
  2 
  Y 
  

  

  