﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  577 
  

  

  When 
  the 
  question, 
  however, 
  is 
  confined 
  to 
  the 
  relations 
  between 
  tempera- 
  

   tures 
  and 
  quantities 
  of 
  heat, 
  a 
  more 
  simple 
  process 
  may 
  be 
  followed, 
  analogous 
  to 
  

   that 
  which 
  has 
  been 
  applied 
  in 
  the 
  preceding 
  article 
  to 
  the 
  hypothesis 
  of 
  Mole- 
  

   cular 
  Collisions. 
  

  

  If 
  a 
  mass 
  of 
  elastic 
  fluid, 
  so 
  much 
  rarefied 
  that 
  the 
  effect 
  of 
  molecular 
  attrac- 
  

   tion 
  is 
  insensible, 
  be 
  entirely 
  filled 
  with 
  vortices, 
  eddies, 
  or 
  circulating 
  currents 
  of 
  

   any 
  size 
  and 
  figure, 
  so 
  that 
  every 
  particle 
  moves 
  with 
  the 
  common 
  velocity 
  w, 
  

   then, 
  if 
  the 
  planes 
  of 
  revolution 
  of 
  these 
  eddies 
  be 
  uniformly 
  distributed 
  in 
  all 
  

   possible 
  positions, 
  it 
  follows, 
  from 
  reasoning 
  precisely 
  similar 
  to 
  that 
  employed 
  in 
  

   the 
  preceding 
  article, 
  that 
  the 
  pressure 
  exerted 
  by 
  the 
  fluid 
  against 
  a 
  plane, 
  in 
  

   consequence 
  of 
  the 
  centrifugal 
  force 
  of 
  the 
  eddies, 
  has 
  the 
  following 
  value 
  in 
  

   terms 
  of 
  gravity 
  : 
  — 
  

  

  a 
  7 
  • 
  v 
  ( 
  87 
  -) 
  

  

  or 
  two-thirds 
  of 
  the 
  hydrostatic 
  pressure 
  due 
  to 
  the 
  velocity 
  of 
  the 
  eddies 
  w 
  ; 
  

   V 
  being, 
  as 
  before, 
  the 
  volume 
  occupied 
  by 
  unity 
  of 
  weight. 
  

  

  It 
  is, 
  however, 
  reasonable 
  to 
  suppose, 
  that 
  the 
  motion 
  of 
  the 
  particles 
  of 
  atomic 
  

   atmospheres 
  does 
  not 
  consist 
  merely 
  in 
  circulating 
  currents 
  ; 
  but 
  that 
  those 
  cur- 
  

   rents 
  are 
  accompanied 
  with 
  a 
  certain 
  proportionate 
  amount 
  of 
  vibration, 
  — 
  a 
  kind 
  

   of 
  motion 
  which 
  does 
  not 
  produce 
  centrifugal 
  force. 
  To 
  these 
  we 
  have 
  to 
  add 
  

   the 
  oscillations 
  of 
  the 
  atomic 
  nuclei, 
  in 
  order 
  to 
  obtain 
  the 
  mechanical 
  equivalent 
  

   of 
  the 
  whole 
  molecular 
  motions 
  ; 
  which 
  is 
  thus 
  found 
  to 
  be 
  expressed 
  for 
  unity 
  

   of 
  weight 
  by 
  

  

  k 
  2j' 
  =( 
  * 
  ( 
  88 
  -) 
  

  

  k 
  being 
  a 
  specific 
  coefficient. 
  Hence 
  it 
  follows 
  (denoting 
  %- 
  by 
  N), 
  that 
  the 
  ex- 
  

  

  pansive 
  pressure 
  due 
  to 
  molecular 
  motions 
  in 
  a 
  perfect 
  gas, 
  is 
  equal 
  to 
  the 
  mecha- 
  

   nical 
  equivalent 
  of 
  those 
  motions 
  in 
  unity 
  of 
  volume 
  multiplied 
  by 
  a 
  specific 
  

   constant 
  

  

  N 
  • 
  | 
  (89.) 
  

  

  The 
  coefficient 
  N 
  has 
  to 
  be 
  determined 
  by 
  experiment 
  ; 
  its 
  value 
  for 
  atmo- 
  

   spheric 
  air 
  is 
  known 
  to 
  be 
  between 
  0'4 
  and 
  0*41. 
  

  

  In 
  order 
  to 
  account 
  for 
  the 
  transmission 
  of 
  pressure 
  throughout 
  the 
  molecular 
  

   atmospheres, 
  it 
  is 
  necessary 
  to 
  suppose 
  them 
  possessed 
  of 
  a 
  certain 
  amount 
  of 
  

   inherent 
  elasticity, 
  however 
  small, 
  varying 
  proportionally 
  to 
  density, 
  and 
  inde- 
  

   pendent 
  of 
  heat. 
  Let 
  this 
  be 
  represented 
  by 
  

  

  A 
  

   v 
  

  

  then 
  

  

  P 
  = 
  (NQ 
  + 
  A)A 
  (90.) 
  

  

  is 
  the 
  total 
  pressure 
  of 
  a 
  perfect 
  gas. 
  

  

  vol. 
  xx. 
  part 
  iv. 
  7 
  R 
  

  

  