﻿576 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  the 
  fraction 
  cos 
  6 
  only 
  strikes 
  the 
  plane; 
  while 
  the 
  force 
  of 
  the 
  blow 
  also 
  is 
  less 
  

   than 
  that 
  of 
  a 
  normal 
  blow 
  in 
  the 
  ratio 
  cos 
  6 
  : 
  1 
  . 
  Hence 
  the 
  mean 
  force 
  of 
  col- 
  

   lision 
  is 
  

  

  f. 
  

  

  2 
  cos 
  2 
  6 
  sin 
  6 
  dd 
  = 
  I 
  

   o 
  3 
  

  

  of 
  the 
  force 
  of 
  a 
  perpendicular 
  collision 
  ; 
  so 
  that 
  the 
  expansive 
  pressure 
  is 
  repre- 
  

   sented 
  by 
  

  

  1 
  vj_ 
  1_ 
  _2 
  (^ 
  

  

  3 
  ' 
  g 
  ' 
  V 
  3 
  " 
  V 
  

  

  Hence, 
  according 
  to 
  this 
  hypothesis, 
  we 
  should 
  have 
  for 
  a 
  perfect 
  gas 
  

  

  or 
  the 
  product 
  of 
  the 
  pressure 
  and 
  volume 
  of 
  a 
  mass 
  of 
  a 
  perfect 
  gas 
  equal 
  to 
  two- 
  

   thirds 
  of 
  the 
  mechanical 
  equivalent 
  of 
  its 
  total 
  heat. 
  

  

  It 
  is 
  known, 
  however, 
  that 
  the 
  product 
  of 
  the 
  pressure 
  and 
  volume 
  of 
  a 
  mass 
  

   of 
  sensibly 
  perfect 
  gas 
  is 
  only 
  about 
  four-tenths 
  of 
  the 
  equivalent 
  of 
  its 
  total 
  heat. 
  

   The 
  hypothesis, 
  therefore, 
  requires 
  modification. 
  

  

  By 
  supposing 
  the 
  particles 
  to 
  attract 
  each 
  other, 
  or 
  to 
  be 
  of 
  appreciable 
  bulk 
  

   compared 
  with 
  the 
  distances 
  between 
  them, 
  the 
  ratio 
  in 
  question 
  is 
  diminished 
  ; 
  

   but 
  either 
  of 
  these 
  suppositions 
  is 
  inconsistent 
  with 
  the 
  perfectly 
  gaseous 
  con- 
  

   dition. 
  

  

  It 
  appears 
  to 
  me, 
  that, 
  besides 
  this 
  difficulty 
  connected 
  with 
  the 
  gaseous 
  con- 
  

   dition, 
  there 
  exists 
  also 
  great 
  difficulty 
  in 
  conceiving 
  how 
  the 
  hypothesis 
  can 
  be 
  

   applied 
  to 
  the 
  solid 
  condition, 
  in 
  which 
  the 
  particles 
  preserve 
  definite 
  arrange- 
  

   ments. 
  The 
  limited 
  amount 
  of 
  time 
  and 
  attention, 
  however, 
  which 
  I 
  have 
  

   hitherto 
  bestowed 
  on 
  this 
  hypothesis, 
  is 
  not 
  sufficient 
  to 
  entitle 
  me 
  to 
  pronounce 
  

   whether 
  these 
  difficulties 
  admit 
  of 
  a 
  solution. 
  

  

  (58.) 
  The 
  idea 
  of 
  ascribing 
  expansive 
  elasticity 
  to 
  the 
  centrifugal 
  force 
  of 
  

   vortices 
  or 
  eddies 
  in 
  elastic 
  atmospheres 
  surrounding 
  nuclei 
  of 
  atoms, 
  originated 
  

   with 
  Sir 
  Humphry 
  Davy. 
  The 
  peculiarity 
  of 
  the 
  view 
  of 
  the 
  hypothesis 
  taken 
  

   in 
  this 
  paper 
  consists 
  in 
  the 
  function 
  ascribed 
  to 
  the 
  nuclei 
  or 
  central 
  physical 
  

   points 
  of 
  the 
  atoms, 
  which, 
  besides 
  retaining 
  the 
  atmospheres 
  round 
  them 
  by 
  

   their 
  attraction, 
  are 
  supposed, 
  by 
  their 
  actions 
  on 
  each 
  other, 
  to 
  constitute 
  the 
  

   medium 
  which 
  transmits 
  radiant 
  heat 
  and 
  light 
  ; 
  so 
  that 
  heat 
  is 
  radiant 
  or 
  ther- 
  

   mometric, 
  according 
  as 
  it 
  affects 
  the 
  nuclei 
  or 
  their 
  atmospheres. 
  

  

  In 
  this 
  form 
  the 
  hypothesis 
  of 
  Molecular 
  Vortices 
  is 
  not 
  a 
  mere 
  special 
  suppo- 
  

   sition, 
  to 
  elucidate 
  the 
  theory 
  of 
  expansive 
  heat, 
  but 
  becomes 
  connected 
  with 
  the 
  

   theory 
  of 
  the 
  elasticity 
  of 
  matter 
  in 
  all 
  conditions, 
  from 
  solid 
  to 
  gaseous, 
  and 
  

   with 
  that 
  of 
  the 
  transmission 
  of 
  radiations. 
  

  

  I 
  have 
  already 
  investigated 
  mathematically 
  the 
  consequences 
  of 
  this 
  hypo- 
  

   thesis 
  by 
  two 
  different 
  processes, 
  which 
  are 
  necessarily 
  somewhat 
  complicated. 
  

  

  