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  XXXI. 
  — 
  On 
  the 
  Dynamical 
  Theory 
  of 
  Heat. 
  Part 
  V.* 
  On 
  the 
  Quantities 
  of 
  

   Mechanical 
  Energy 
  contained 
  in 
  a 
  Fluid 
  in 
  Different 
  States, 
  as 
  to 
  Temperature 
  

   and 
  Density. 
  By 
  William 
  Thomson, 
  M.A., 
  Professor 
  of 
  Natural 
  Philosophy 
  

   in 
  the 
  University 
  of 
  Glasgow. 
  

  

  (Read 
  December 
  15, 
  1851.) 
  

  

  81. 
  A 
  body 
  which 
  is 
  either 
  emitting 
  heat, 
  or 
  altering 
  its 
  dimensions 
  against 
  

   resisting 
  forces, 
  is 
  doing 
  work 
  upon 
  matter 
  external 
  to 
  it. 
  The 
  mechanical 
  

   effect 
  of 
  this 
  work, 
  in 
  one 
  case, 
  is 
  the 
  excitation 
  of 
  thermal 
  motions, 
  and 
  in 
  the 
  

   other, 
  the 
  overcoming 
  of 
  resistances. 
  The 
  body 
  must 
  itself 
  be 
  altering 
  in 
  its 
  cir- 
  

   cumstances, 
  so 
  as 
  to 
  contain 
  a 
  less 
  store 
  of 
  work 
  within 
  it, 
  by 
  an 
  amount 
  precisely 
  

   equal 
  to 
  the 
  aggregate 
  value 
  of 
  the 
  mechanical 
  effects 
  produced 
  : 
  and 
  conversely, 
  

   the 
  aggregate 
  value 
  of 
  the 
  mechanical 
  effects 
  produced, 
  must 
  depend 
  solely 
  on 
  the 
  

   initial 
  and 
  final 
  states 
  of 
  the 
  body, 
  and 
  is 
  therefore 
  the 
  same, 
  whatever 
  be 
  the 
  

   intermediate 
  states 
  through 
  which 
  the 
  body 
  passes, 
  provided 
  the 
  initial 
  and 
  final 
  

   states 
  be 
  the 
  same. 
  

  

  82. 
  The 
  total 
  mechanical 
  energy 
  of 
  a 
  body 
  might 
  be 
  defined 
  as 
  the 
  mechanical 
  

   value 
  of 
  all 
  the 
  effect 
  it 
  would 
  produce, 
  in 
  heat 
  emitted 
  and 
  in 
  resistances 
  over- 
  

   come, 
  if 
  it 
  were 
  cooled 
  to 
  the 
  utmost, 
  and 
  allowed 
  to 
  contract 
  indefinitely 
  or 
  to 
  

   expand 
  indefinitely 
  according 
  as 
  the 
  forces 
  between 
  its 
  particles 
  are 
  attractive 
  or 
  

   repulsive, 
  when 
  the 
  thermal 
  motions 
  within 
  it 
  are 
  all 
  stopped 
  ; 
  but 
  in 
  our 
  present 
  

   state 
  of 
  ignorance 
  regarding 
  perfect 
  cold, 
  and 
  the 
  nature 
  of 
  molecular 
  forces, 
  we 
  

   cannot 
  determine 
  this 
  " 
  total 
  mechanical 
  energy" 
  for 
  any 
  portion 
  of 
  matter, 
  nor 
  

   even 
  can 
  we 
  be 
  sure 
  that 
  it 
  is 
  not 
  infinitely 
  great 
  for 
  a 
  finite 
  portion 
  of 
  matter. 
  

   Hence 
  it 
  is 
  convenient 
  to 
  choose 
  a 
  certain 
  state, 
  as 
  standard 
  for 
  the 
  body 
  under 
  

   consideration, 
  and, 
  to 
  use 
  the 
  unqualified 
  term, 
  mechanical 
  energy, 
  with 
  reference 
  

   to 
  this 
  standard 
  state 
  ; 
  so 
  that 
  the 
  " 
  mechanical 
  energy 
  of 
  a 
  body 
  in 
  a 
  given 
  

   state," 
  will 
  denote 
  the 
  mechanical 
  value 
  of 
  the 
  effects 
  the 
  body 
  would 
  produce 
  in 
  

   passing 
  from 
  the 
  state 
  in 
  which 
  it 
  is 
  given, 
  to 
  the 
  standard 
  state, 
  or 
  the 
  mechanical 
  

   value 
  of 
  the 
  whole 
  agency 
  that 
  would 
  be 
  required 
  to 
  bring 
  the 
  body 
  from 
  the 
  

   standard 
  state 
  to 
  the 
  state 
  in 
  which 
  it 
  is 
  given. 
  

  

  83. 
  In 
  the 
  present 
  communication, 
  a 
  system 
  of 
  formulae 
  founded 
  on 
  proposi- 
  

  

  * 
  A 
  preceding 
  communication 
  (April 
  21, 
  1851) 
  published 
  in 
  the 
  Transactions 
  (Vol. 
  xx., 
  Part 
  ii.), 
  

   under 
  the 
  title, 
  " 
  On 
  a 
  Method 
  of 
  Discovering 
  Experimentally 
  the 
  Eelation 
  between 
  the 
  Mechanical 
  Work 
  

   spent, 
  and 
  the 
  Heat 
  produced 
  by 
  the 
  Compression 
  of 
  a 
  Gaseous 
  Fluid," 
  will 
  be 
  referred 
  to 
  as 
  Part 
  

   IV. 
  of 
  a 
  series 
  of 
  Papers 
  on 
  the 
  Dynamical 
  Theory 
  of 
  Heat 
  ; 
  and 
  the 
  numbers 
  of 
  its 
  sections 
  will 
  be 
  

   altered 
  accordingly, 
  so 
  that 
  its 
  first 
  section 
  will 
  be 
  referred 
  to 
  as 
  § 
  61, 
  and 
  its 
  20th 
  and 
  last, 
  as 
  § 
  80. 
  

  

  VOL. 
  XX. 
  PART 
  III. 
  6 
  M 
  

  

  