﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  571 
  

  

  This 
  expression 
  is 
  a 
  complete 
  differential, 
  and 
  may 
  be 
  written 
  thus 
  : 
  — 
  

  

  d(q+s)=d[q+ct>(q) 
  + 
  (q^-i^p^v 
  } 
  . 
  (so.) 
  

  

  (Q 
  being 
  treated 
  as 
  a 
  constant 
  in 
  performing 
  the 
  integration 
  J 
  PdV). 
  

  

  Its 
  integral, 
  Q 
  + 
  S, 
  the 
  sum 
  of 
  the 
  heat 
  of 
  the 
  body, 
  and 
  of 
  the 
  potential 
  of 
  its 
  

   molecular 
  actions, 
  is 
  the 
  same 
  quantity 
  which 
  I 
  have 
  denoted 
  by 
  the 
  symbol 
  y 
  

   in 
  the 
  10th 
  article 
  of 
  a 
  paper 
  on 
  the 
  Centrifugal 
  Theory 
  of 
  Elasticity, 
  and 
  whose 
  

   differences 
  are 
  there 
  stated 
  to 
  represent 
  the 
  total 
  amount 
  of 
  power 
  which 
  must 
  

   be 
  exercised 
  on 
  a 
  body, 
  whether 
  in 
  the 
  form 
  of 
  expansive 
  or 
  compressive 
  power, 
  

   or 
  in 
  that 
  of 
  heat, 
  to 
  make 
  it 
  pass 
  from 
  one 
  volume 
  and 
  temperature 
  to 
  another. 
  

   This 
  integral 
  corresponds 
  also 
  to 
  the 
  function 
  treated 
  of 
  by 
  Professor 
  William 
  

   Thomson 
  in 
  the 
  fifth 
  part 
  of 
  his 
  paper 
  on 
  the 
  Dynamical 
  Theory 
  of 
  Heat, 
  under 
  

   the 
  name 
  of 
  " 
  Total 
  Mechanical 
  Energy." 
  

  

  (52.) 
  We 
  have 
  now 
  obtained 
  a 
  system 
  of 
  formula?, 
  expressing 
  all 
  the 
  relations 
  

   between 
  heat 
  and 
  expansive 
  power, 
  analogous 
  to 
  those 
  deduced 
  from 
  a 
  considera- 
  

   tion 
  of 
  the 
  properties 
  of 
  temperature, 
  by 
  Messrs 
  Clausius 
  and 
  Thomson, 
  and 
  from 
  

   the 
  Hypothesis 
  of 
  Molecular 
  Vortices 
  in 
  the 
  previous 
  sections 
  of 
  this 
  paper 
  ; 
  but, 
  

   in 
  the 
  present 
  section, 
  both 
  the 
  theorems 
  and 
  the 
  investigations 
  are 
  distinguished 
  

   from 
  former 
  researches 
  by 
  this 
  circumstance; 
  — 
  that 
  they 
  are 
  independent, 
  not 
  only 
  

   of 
  any 
  hypothesis 
  respecting 
  the 
  constitution 
  of 
  matter, 
  but 
  of 
  the 
  properties, 
  

   and 
  even 
  of 
  the 
  existence, 
  of 
  such 
  a 
  function 
  as 
  Temperature 
  ; 
  being, 
  in 
  fact, 
  

   simply 
  the 
  necessary 
  consequences 
  of 
  the 
  following 
  

  

  DEFINITION 
  OF 
  EXPANSIVE 
  HEAT. 
  

  

  Let 
  the 
  term 
  Expansive 
  Heat 
  be 
  used 
  to 
  denote 
  a 
  kind 
  of 
  Physical 
  Energy 
  con- 
  

   vertible 
  with, 
  and 
  measurable 
  by, 
  equivalent 
  quantities 
  of 
  Mechanical 
  Power, 
  and 
  

   augmenting 
  the 
  Expansive 
  Elasticity 
  of 
  matter, 
  in 
  which 
  it 
  is 
  'present. 
  

  

  (52 
  A.) 
  It 
  is 
  further 
  to 
  be 
  remarked, 
  that 
  the 
  theorems 
  and 
  formula? 
  in 
  the 
  pre- 
  

   ceding 
  articles 
  of 
  this 
  section 
  are 
  applicable, 
  not 
  only 
  to 
  heat 
  and 
  expansive 
  power, 
  

   but 
  to 
  any 
  two 
  directly 
  convertible 
  forms 
  of 
  physical 
  energy, 
  one 
  of 
  which 
  is 
  

   actual, 
  and 
  the 
  other 
  potential. 
  They 
  are, 
  in 
  fact, 
  the 
  principles 
  of 
  the 
  conversion 
  

   of 
  energy 
  in 
  the 
  abstract, 
  when 
  interpreted 
  according 
  to 
  the 
  following 
  definitions 
  

   of 
  the 
  symbols. 
  

  

  Let 
  Q 
  denote 
  the 
  quantity 
  of 
  a 
  form 
  of 
  actual 
  physical 
  energy 
  present 
  in 
  a 
  

   given 
  body 
  ; 
  

  

  