﻿428 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  CENTRIFUGAL 
  THEORY 
  OF 
  ELASTICITY, 
  

  

  The 
  suffix 
  l 
  being 
  used 
  to 
  distinguish 
  the 
  value 
  of 
  quantities 
  at 
  those 
  surfaces. 
  

   Hence 
  o> 
  1 
  is 
  a 
  maximum 
  or 
  minimum. 
  Those 
  surfaces 
  are 
  symmetrical 
  in 
  form 
  

   round 
  each 
  nucleus, 
  and 
  equidistant 
  between 
  pairs 
  of 
  adjacent 
  nuclei. 
  Their 
  

   equation 
  is 
  

  

  0-^ 
  = 
  0. 
  

  

  Let 
  M 
  denote 
  the 
  total 
  weight 
  of 
  an 
  atom 
  ; 
  m 
  that 
  of 
  its 
  atmospheric 
  part, 
  and 
  

   M—fx 
  that 
  of 
  its 
  nucleus 
  ; 
  then 
  

  

  M 
  V 
  is 
  the 
  volume 
  of 
  the 
  atom, 
  — 
  

  

  jyPy 
  the 
  mean 
  density 
  of 
  the 
  atmospheric 
  part, 
  measured 
  by 
  weight, 
  the 
  

  

  nucleus 
  being 
  supposed 
  to 
  be 
  of 
  insensible 
  magnitude 
  ; 
  — 
  

   and 
  we 
  have 
  the 
  following 
  equations 
  

  

  dy 
  dz 
  \ 
  

  

  (2.) 
  

  

  M 
  V 
  = 
  '// 
  dz 
  dy 
  dz 
  

  

  ^■wNlII^ 
  dxdydz= 
  IIlQ^ 
  dxd 
  y 
  dz 
  

  

  The 
  suffix 
  (,) 
  denoting 
  that 
  the 
  integration 
  is 
  to 
  be 
  extended 
  to 
  all 
  points 
  

   within 
  the 
  surface 
  

  

  ($-^ 
  = 
  0). 
  

  

  According 
  to 
  the 
  hypothesis 
  now 
  under 
  consideration, 
  Heat 
  consists 
  in 
  a 
  re- 
  

   volving 
  motion 
  of 
  the 
  particles 
  of 
  the 
  atomic 
  atmosphere, 
  communicated 
  to 
  them 
  

   by 
  the 
  nuclei. 
  Let 
  v 
  be 
  the 
  common 
  mean 
  velocity 
  possessed 
  by 
  the 
  nucleus 
  of 
  

   an 
  atom 
  and 
  the 
  atmospheric 
  particles, 
  when 
  the 
  distribution 
  of 
  this 
  motion 
  has 
  

   been 
  equalised. 
  I 
  use 
  the 
  term 
  mean 
  velocity 
  to 
  denote, 
  that 
  the 
  velocity 
  of 
  each 
  

   particle 
  may 
  undergo 
  small 
  periodic 
  changes, 
  which 
  it 
  is 
  unnecessary 
  to 
  consider 
  

   in 
  this 
  investigation. 
  

  

  Then 
  the 
  quantity 
  of 
  heat 
  in 
  unity 
  of 
  weight 
  is 
  

  

  «-& 
  

  

  being 
  equal 
  to 
  the 
  mechanical 
  power 
  of 
  unity 
  of 
  weight 
  falling 
  through 
  the 
  height 
  

  

  2~ 
  ■ 
  The 
  quantity 
  of 
  heat 
  in 
  one 
  atom 
  is 
  of 
  course 
  M 
  Q, 
  and 
  in 
  the 
  atmospheric 
  

  

  part 
  of 
  an 
  atom, 
  /x 
  Q. 
  

  

  I 
  shall 
  leave 
  the 
  form 
  of 
  the 
  paths 
  described 
  by 
  the 
  atmospheric 
  particles 
  in- 
  

   determinate, 
  except 
  that 
  they 
  must 
  be 
  closed 
  curves 
  of 
  permanent 
  figure, 
  and 
  in- 
  

   cluded 
  within 
  the 
  surface 
  (* 
  -*! 
  = 
  ()). 
  Let 
  the 
  nucleus 
  be 
  taken 
  as 
  the 
  origin 
  of 
  

   co-ordinates, 
  and 
  let 
  a, 
  (3, 
  7, 
  be 
  the 
  direction-cosines 
  of 
  the 
  motion 
  of 
  the 
  particles 
  

   at 
  any 
  point 
  [x, 
  y, 
  z). 
  Then 
  the 
  equations 
  of 
  a 
  permanent 
  condition 
  of 
  motion 
  at 
  

   that 
  point, 
  are 
  

  

  