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  XXVII. 
  — 
  On 
  the 
  Centrifugal 
  Theory 
  of 
  Elasticity, 
  and 
  its 
  Connection 
  with 
  the 
  

   Theory 
  of 
  Heat. 
  By 
  William 
  John 
  Macquorn 
  Rankine, 
  C.E., 
  F.R.S.E., 
  

   F.R.S.S.A., 
  &c. 
  

  

  (Read 
  December 
  15, 
  1851.) 
  

  

  Section 
  First. 
  — 
  Relations 
  between 
  Heat 
  and 
  Expansive 
  Pressure. 
  

  

  (1.) 
  In 
  February 
  1850, 
  I 
  laid 
  before 
  the 
  Royal 
  Society 
  of 
  Edinburgh 
  a 
  paper, 
  

   in 
  which 
  the 
  laws 
  of 
  the 
  pressure 
  and 
  expansion 
  of 
  gases 
  and 
  vapours 
  were 
  de- 
  

   duced 
  from 
  the 
  supposition, 
  that 
  that 
  part 
  of 
  the 
  elasticity 
  of 
  bodies 
  which 
  depends 
  

   upon 
  heat, 
  arises 
  from 
  the 
  centrifugal 
  force 
  of 
  the 
  revolutions 
  of 
  the 
  particles 
  of 
  

   elastic 
  atmospheres 
  surrounding 
  nuclei, 
  or 
  atomic 
  centres. 
  A 
  summary 
  of 
  the 
  

   results 
  of 
  this 
  supposition, 
  which 
  I 
  called 
  the 
  Hypothesis 
  of 
  Molecular 
  Vortices, 
  

   was 
  printed 
  in 
  the 
  Transactions 
  of 
  this 
  Society, 
  volume 
  xx., 
  as 
  an 
  introduction 
  

   to 
  a 
  series 
  of 
  papers 
  on 
  the 
  Mechanical 
  Action 
  of 
  Heat 
  ; 
  and 
  the 
  original 
  paper 
  

   has 
  since 
  appeared 
  in 
  detail 
  in 
  the 
  Philosophical 
  Magazine. 
  

  

  In 
  that 
  paper, 
  the 
  bounding 
  surfaces 
  of 
  atoms 
  were 
  defined 
  to 
  be 
  imaginary 
  

   surfaces, 
  situated 
  between 
  and 
  enveloping 
  the 
  atomic 
  nuclei, 
  and 
  symmetrically 
  

   placed 
  with 
  respect 
  to 
  them, 
  and 
  having 
  this 
  property 
  — 
  that 
  at 
  these 
  surfaces 
  the 
  

   attractive 
  and 
  repulsive 
  actions 
  of 
  the 
  atomic 
  nuclei 
  and 
  atmospheres 
  upon 
  each 
  

   particle 
  of 
  atomic 
  atmosphere, 
  balance 
  each 
  other. 
  The 
  pressure 
  of 
  the 
  atomic 
  

   atmospheres 
  at 
  those 
  imaginary 
  boundaries 
  is 
  the 
  part 
  of 
  the 
  total 
  expansive 
  

   pressure 
  of 
  the 
  body 
  which 
  varies 
  with 
  heat 
  ; 
  the 
  effect 
  of 
  the 
  centrifugal 
  force 
  of 
  

   molecular 
  vortices 
  being 
  to 
  increase 
  it. 
  

  

  In 
  the 
  subsequent 
  investigation 
  it 
  was 
  assumed, 
  that 
  owing 
  to 
  the 
  symmetrical 
  

   action 
  of 
  the 
  particles 
  of 
  gases 
  in 
  all 
  directions, 
  and 
  the 
  small 
  amount 
  of 
  those 
  

   attractive 
  and 
  repulsive 
  forces 
  which 
  interfere 
  with 
  the 
  elasticity 
  of 
  their 
  atmo- 
  

   spheres, 
  no 
  appreciable 
  error 
  would 
  arise 
  from 
  treating 
  the 
  boundary 
  of 
  the 
  atmo- 
  

   sphere 
  of 
  a 
  single 
  atom, 
  in 
  calculation, 
  as 
  if 
  it 
  were 
  spherical 
  ; 
  an 
  assumption 
  

   which 
  very 
  much 
  simplified 
  the 
  analysis. 
  

  

  An 
  effect, 
  however, 
  of 
  this 
  assumption 
  was, 
  to 
  make 
  it 
  doubtful 
  whether 
  the 
  

   conclusions 
  deduced 
  from 
  the 
  hypothesis 
  were 
  applicable 
  to 
  any 
  substances 
  except 
  

   those 
  nearly 
  in 
  the 
  state 
  of 
  perfect 
  gas. 
  I 
  have, 
  therefore, 
  in 
  the 
  present 
  paper, 
  

   investigated 
  the 
  subject 
  anew, 
  without 
  making 
  any 
  assumption 
  as 
  to 
  the 
  arrange- 
  

   ment 
  of 
  the 
  atomic 
  centres, 
  or 
  the 
  form 
  of 
  the 
  boundaries 
  of 
  their 
  atmospheres. 
  

   The 
  equations 
  deduced 
  from 
  the 
  hypothesis, 
  between 
  expansive 
  pressure 
  and 
  heat, 
  

   are 
  therefore 
  applicable 
  to 
  all 
  substances 
  in 
  all 
  conditions 
  ; 
  and 
  it 
  will 
  be 
  seen 
  

   that 
  they 
  are 
  identical 
  with 
  those 
  in 
  the 
  original 
  paper 
  ; 
  shewing 
  that 
  the 
  assump- 
  

  

  VOL. 
  XX. 
  PART 
  III. 
  5 
  Y 
  

  

  