﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  151 
  

  

  I 
  have 
  integrated 
  the 
  differential 
  equation 
  which 
  results 
  from 
  this 
  condition, 
  

   for 
  substances 
  in 
  the 
  gaseous 
  state, 
  in 
  which 
  the 
  forces 
  that 
  interfere 
  with 
  the 
  

   centrifugal 
  force 
  and 
  atmospheric 
  elasticity 
  are 
  comparatively 
  small 
  ; 
  and 
  the 
  

   result 
  is 
  

  

  P=6 
  H 
  D 
  (37« 
  + 
  1 
  ) 
  (I 
  - 
  F) 
  + 
  /(D) 
  ' 
  ' 
  • 
  (VI) 
  

  

  P 
  is 
  the 
  entire 
  elasticity 
  of 
  the 
  gas, 
  and 
  D 
  its 
  mean 
  density. 
  M 
  represents 
  

   the 
  total 
  mass 
  of 
  an 
  atom, 
  measured 
  by 
  weight, 
  and 
  /j. 
  that 
  of 
  its 
  atmospheric- 
  

   part 
  ; 
  so 
  that 
  ^ 
  D 
  is 
  the 
  mean 
  density 
  of 
  the 
  atomic 
  atmospheres. 
  

  

  /(D) 
  denotes 
  the 
  effect 
  of 
  the 
  mutual 
  actions 
  of 
  separate 
  atoms. 
  

  

  The 
  first 
  term 
  represents 
  the 
  superficial-atomic 
  elasticity. 
  F 
  denotes 
  the 
  

   effect 
  of 
  the 
  attraction 
  of 
  the 
  nucleus 
  in 
  modifying 
  that 
  elasticity, 
  and 
  can 
  be 
  

   represented 
  approximately 
  by 
  a 
  converging 
  series, 
  in 
  terms 
  of 
  the 
  negative 
  powers 
  

  

  w 
  2 
  

  

  of 
  h 
  — 
  r 
  + 
  1, 
  commencing 
  with 
  the 
  inverse 
  square, 
  the 
  coefficients 
  being 
  functions 
  

  

  of 
  the 
  density 
  D.. 
  

  

  By 
  using 
  the 
  first 
  term 
  of 
  such 
  a 
  series, 
  and 
  determining 
  its 
  coefficient, 
  and 
  

   the 
  quantity/ 
  (D) 
  empirically, 
  I 
  have 
  obtained 
  formulse 
  agreeing 
  closely 
  with 
  the 
  

   results 
  of 
  M. 
  Regnault's 
  experiments 
  on 
  the 
  Expansion 
  of 
  Atmospheric 
  Air, 
  

   Carbonic 
  Acid, 
  and 
  Hydrogen. 
  

  

  In 
  a 
  perfect 
  gas, 
  the 
  above 
  expression 
  is 
  reduced 
  to 
  

  

  •= 
  J 
  M 
  D 
  (3T? 
  +1 
  ) 
  • 
  • 
  • 
  • 
  < 
  VIL 
  > 
  

  

  Let 
  11, 
  as 
  before, 
  denote 
  the 
  number 
  of 
  atoms 
  of 
  a 
  substance 
  which, 
  in 
  the 
  

   state 
  of 
  perfect 
  gas, 
  occupy 
  unity 
  of 
  volume 
  under 
  unity 
  of 
  pressure 
  at 
  the 
  tem- 
  

   perature 
  of 
  melting 
  ice, 
  so 
  that 
  n 
  M 
  is 
  its 
  specific 
  gravity 
  in 
  that 
  state 
  : 
  then 
  

  

  *-;&"''* 
  (j£j 
  +1 
  ) 
  " 
  • 
  • 
  • 
  (VIIL) 
  

  

  The 
  factor 
  by 
  which 
  -^ 
  is 
  here 
  multiplied 
  fulfils 
  the 
  condition 
  of 
  being 
  a 
  

   function 
  of 
  -r, 
  and 
  of 
  constants 
  which 
  are 
  the 
  same 
  for 
  all 
  substances, 
  and 
  is 
  

  

  therefore 
  fitted 
  for 
  a 
  measure 
  of 
  temperature. 
  It 
  obviously 
  varies 
  proportionally 
  

   to 
  the 
  pressure 
  of 
  a 
  perfect 
  gas 
  of 
  a 
  given 
  density, 
  or 
  its 
  volume 
  under 
  a 
  given 
  

   pressure. 
  

  

  Let 
  T 
  , 
  therefore, 
  denote 
  temperature, 
  as 
  measured 
  from 
  an 
  imaginary 
  zero, 
  

   C 
  degrees 
  of 
  the 
  scale 
  adopted, 
  below 
  the 
  temperature 
  of 
  melting 
  ice, 
  at 
  which 
  

  

  VOL. 
  XX. 
  PART 
  I. 
  2 
  S 
  

  

  