﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  575 
  

  

  sured 
  by 
  the 
  expansion 
  of 
  a 
  perfect 
  gas, 
  the 
  total 
  quantity 
  of 
  heat 
  in 
  a 
  body 
  is 
  

   simply 
  proportional 
  to 
  the 
  elevation 
  of 
  its 
  temperature 
  above 
  the 
  temperature 
  of 
  

   absolute 
  privation 
  of 
  heat 
  ; 
  or, 
  in 
  the 
  notation 
  of 
  the 
  preceding 
  article, 
  

  

  4< 
  • 
  t 
  =- 
  t, 
  -4/ 
  . 
  t 
  = 
  1, 
  and 
  

  

  Q 
  = 
  fe(T-/0 
  (86.) 
  

  

  It 
  being 
  the 
  real 
  specific 
  heat 
  of 
  the 
  body. 
  

  

  If 
  this 
  value 
  be 
  substituted 
  for 
  the 
  quantity 
  of 
  heat 
  Q, 
  in 
  all 
  the 
  formulae, 
  

   from 
  67 
  to 
  80 
  inclusive, 
  which 
  are 
  founded 
  simply 
  on 
  the 
  definition 
  of 
  expansive 
  

   heat, 
  it 
  reproduces 
  all 
  the 
  formulae 
  which, 
  in 
  this 
  and 
  the 
  other 
  paper 
  referred 
  to, 
  

   have 
  been 
  deduced 
  directly 
  from 
  the 
  hypothesis. 
  In 
  the 
  sequel 
  I 
  shall 
  apply 
  one 
  

   of 
  these 
  formulae 
  to 
  the 
  calculation, 
  from 
  the 
  experiments 
  of 
  Professor 
  Thomson 
  

   and 
  Mr 
  Joule 
  on 
  the 
  heating 
  of 
  currents 
  of 
  air 
  by 
  friction, 
  of 
  approximate 
  values 
  

   of 
  the 
  absolute 
  temperature 
  corresponding 
  to 
  total 
  privation 
  of 
  heat, 
  that 
  the 
  

   mutual 
  consistency 
  of 
  those 
  values 
  may 
  serve 
  as 
  a 
  test 
  of 
  the 
  soundness 
  of 
  the 
  

   hypothesis, 
  and 
  the 
  accuracy 
  of 
  the 
  formulas 
  deduced 
  from 
  it. 
  

  

  (57.) 
  Before 
  proceeding 
  further, 
  it 
  may 
  be 
  desirable 
  to 
  point 
  out 
  how 
  far 
  this 
  

   hypothesis 
  agrees 
  with, 
  and 
  how 
  far 
  it 
  diners 
  from, 
  that 
  proposed 
  by 
  Mr 
  Hera- 
  

   path 
  and 
  Mr 
  Waterston, 
  which 
  supposes 
  bodies 
  to 
  consist 
  of 
  extremely 
  small 
  and 
  

   perfectly 
  elastic 
  particles, 
  which 
  fly 
  about 
  in 
  all 
  directions 
  with 
  a 
  velocity 
  whose 
  

   half-square 
  is 
  the 
  mechanical 
  equivalent 
  of 
  the 
  heat 
  possessed 
  by 
  unity 
  of 
  weight, 
  

   and 
  are 
  prevented 
  from 
  dispersing 
  by 
  their 
  collisions 
  with 
  each 
  other 
  and 
  with 
  

   the 
  particles 
  of 
  surrounding 
  bodies. 
  Let 
  v 
  be 
  the 
  velocity 
  of 
  motion, 
  then 
  

  

  represents 
  the 
  heat 
  possessed 
  by 
  unity 
  of 
  weight, 
  expressed 
  in 
  terms 
  of 
  the 
  force 
  

   of 
  gravity. 
  

  

  The 
  expansive 
  pressure 
  due 
  to 
  such 
  motions 
  is 
  found 
  by 
  conceiving 
  a 
  hard, 
  

   perfectly 
  elastic 
  plane 
  of 
  the 
  area 
  unity 
  to 
  be 
  opposed 
  to 
  the 
  collision 
  of 
  the 
  par- 
  

   ticles, 
  and 
  calculating 
  the 
  pressure 
  which 
  would 
  be 
  required 
  to 
  maintain 
  its 
  posi- 
  

   tion 
  against 
  them. 
  If 
  all 
  the 
  particles 
  were 
  to 
  strike 
  and 
  rebound 
  from 
  such 
  a 
  

   plane 
  at 
  right 
  angles, 
  the 
  pressure 
  would 
  be 
  represented 
  thus 
  : 
  

  

  9 
  ' 
  V 
  

   where 
  V 
  is 
  the 
  volume 
  which 
  contains 
  so 
  many 
  particles 
  as 
  amount 
  to 
  unity 
  of 
  

   weight. 
  But 
  the 
  particles 
  are 
  supposed 
  to 
  fly 
  in 
  equal 
  numbers 
  in 
  all 
  directions. 
  

   Then 
  if 
  6 
  denote 
  the 
  angle 
  of 
  incidence 
  on 
  the 
  plane 
  

  

  sin 
  6d6 
  

  

  = 
  sm 
  

  

  Odd 
  

  

  f. 
  

  

  2 
  sin 
  6dd 
  

  

  

  

  represents 
  the 
  proportion 
  of 
  the 
  whole 
  particles 
  which 
  fly 
  in 
  those 
  directions 
  

   which 
  make 
  the 
  angle 
  6 
  with 
  the 
  normal 
  to 
  the 
  plane. 
  Of 
  this 
  proportion, 
  again, 
  

  

  