﻿574 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  where 
  J 
  is 
  Joule's 
  equivalent, 
  and 
  \x 
  a 
  function 
  of 
  the 
  temperature, 
  the 
  same 
  for 
  

   all 
  substances, 
  to 
  be 
  determined 
  empirically 
  ; 
  and 
  consequently, 
  

  

  1 
  Cr 
  

  

  hyp. 
  log. 
  (4 
  . 
  t 
  — 
  4. 
  . 
  /c) 
  = 
  = 
  / 
  fidr 
  

  

  or 
  if 
  TlJjdr 
  

  

  4 
  . 
  t— 
  4. 
  K 
  = 
  € 
  J 
  

  

  1 
  A 
  a 
  

  

  and 
  Q=*(+.T-+.«)=*.eV 
  " 
  

  

  These 
  expressions 
  will 
  be 
  recognised 
  by 
  those 
  who 
  have 
  studied 
  Professor 
  Thom- 
  

   son's 
  papers 
  on 
  the 
  Dynamical 
  Theory 
  of 
  Heat. 
  By 
  introducing 
  the 
  value 
  given 
  

   above 
  of 
  the 
  quantity 
  of 
  heat 
  in 
  unity 
  of 
  weight, 
  into 
  the 
  formulae 
  of 
  the 
  preceding 
  

   articles 
  of 
  this 
  section, 
  they 
  are 
  at 
  once 
  transformed 
  to 
  those 
  of 
  Professor 
  

   Thomson, 
  and 
  in 
  particular, 
  the 
  formulae 
  79 
  and 
  82 
  become 
  the 
  following: 
  — 
  

  

  \f 
  7 
  ^dr 
  \f 
  V 
  **at 
  lA^r 
  

  

  * 
  Effect 
  of 
  Mac 
  hine 
  _ 
  e 
  J 
  - 
  e 
  iJ 
  _JJ 
  r 
  2 
  

  

  Heat 
  Expended 
  T~77 
  = 
  1 
  - 
  e 
  . 
  (85.) 
  

  

  _ 
  / 
  J 
  udr 
  

  

  Sub-Section 
  3. 
  — 
  On 
  the 
  Hypothesis 
  of 
  Molecular 
  Vortices. 
  

  

  (56.) 
  The 
  use 
  of 
  a 
  Mechanical 
  Hypothesis 
  in 
  the 
  Theory 
  of 
  Heat, 
  as 
  in 
  other 
  

   branches 
  of 
  physics, 
  is 
  to 
  render 
  it 
  a 
  branch 
  of 
  Mechanics, 
  the 
  only 
  complete 
  phy- 
  

   sical 
  science 
  ; 
  and 
  to 
  deduce 
  its 
  principles 
  from 
  the 
  laws 
  of 
  Force 
  and 
  Motion, 
  

   which 
  are 
  better 
  understood 
  than 
  those 
  of 
  any 
  other 
  phenomena. 
  

  

  The 
  results 
  of 
  the 
  investigations 
  in 
  the 
  preceding 
  part 
  of 
  this 
  section 
  are 
  con- 
  

   sistent 
  alike 
  with 
  all 
  conceivable 
  hypotheses 
  which 
  ascribe 
  the 
  phenomena 
  of 
  

   heat 
  to 
  invisible 
  motions 
  amongst 
  the 
  particles 
  of 
  bodies. 
  

  

  Those 
  investigations, 
  however, 
  leave 
  undetermined 
  the 
  relation 
  between 
  tem- 
  

   perature 
  and 
  quantity 
  of 
  heat, 
  except 
  in 
  so 
  far 
  as 
  they 
  shew 
  that 
  it 
  must 
  follow 
  

   the 
  same 
  law 
  of 
  variation 
  in 
  all 
  substances. 
  

  

  By 
  adopting 
  a 
  definite 
  hypothesis, 
  we 
  are 
  conducted 
  to 
  a 
  definite 
  relation 
  be- 
  

   tween 
  temperature 
  and 
  quantity 
  of 
  heat 
  ; 
  which, 
  being 
  introduced 
  into 
  the 
  formulae, 
  

   leads 
  to 
  specific 
  results 
  respecting 
  the 
  phenomena 
  of 
  the 
  mutual 
  transformation 
  

   of 
  heat 
  and 
  visible 
  mechanical 
  power 
  ; 
  and 
  those 
  results, 
  being 
  compared 
  with 
  

   experiment, 
  furnish 
  a 
  test 
  of 
  the 
  soundness 
  of 
  the 
  hypothesis. 
  

  

  Thus 
  the 
  hypothesis 
  of 
  Molecular 
  Vortices, 
  which 
  forms 
  the 
  basis 
  of 
  the 
  in- 
  

   vestigations- 
  in 
  the 
  first 
  five 
  sections 
  of 
  this 
  paper, 
  and 
  in 
  a 
  paper 
  on 
  the 
  Centri- 
  

   fugal 
  Theory 
  of 
  Elasticity, 
  leads 
  to 
  the 
  conclusion, 
  that, 
  if 
  temperature 
  be 
  mea- 
  

  

  * 
  It 
  is 
  to 
  be 
  observed, 
  that 
  in 
  Professor 
  Thomson's 
  notation, 
  heat 
  is 
  supposed 
  to 
  be 
  measured 
  

   by 
  an 
  arbitrary 
  unit, 
  whose 
  ratio 
  to 
  a 
  unit 
  of 
  mechanical 
  power 
  is 
  denoted 
  by 
  J 
  ; 
  while 
  in 
  this 
  paper, 
  

   the 
  same 
  unit 
  is 
  employed 
  in 
  expressing 
  quantities 
  of 
  heat 
  and 
  of 
  mechanical 
  power. 
  

  

  