﻿150 
  MR 
  W. 
  J. 
  M. 
  EANKINE 
  ON 
  THE 
  

  

  any 
  substance, 
  b 
  its 
  coefficient 
  of 
  elasticity, 
  and 
  n 
  the 
  number 
  of 
  atoms 
  which, 
  in 
  

   the 
  state 
  of 
  perfect 
  gas, 
  occup3 
  T 
  unity 
  of 
  volume 
  under 
  unity 
  of 
  pressure 
  at 
  the 
  

   temperature 
  of 
  melting 
  ice 
  ; 
  — 
  then 
  

  

  nfJLb 
  (I.) 
  

  

  is 
  a 
  constant 
  quantity 
  for 
  all 
  substances. 
  

  

  Secondly, 
  The 
  superficial 
  elasticity 
  of 
  a 
  vortex 
  must 
  not 
  be 
  a 
  function 
  of 
  its 
  

   diameter 
  : 
  to 
  fulfil 
  which 
  condition, 
  the 
  linear 
  velocity 
  of 
  revolution 
  must 
  be 
  equal 
  

   throughout 
  all 
  parts 
  of 
  each 
  individual 
  vortex. 
  

  

  Thirdly, 
  In 
  all 
  contiguous 
  vortices 
  of 
  the 
  same 
  substance, 
  the 
  velocities 
  of 
  

   revolution 
  must 
  be 
  equal 
  ; 
  and 
  in 
  contiguous 
  vortices 
  of 
  different 
  substances, 
  the 
  

   squares 
  of 
  the 
  velocities 
  must 
  be 
  proportional 
  to 
  the 
  coefficients 
  of 
  elasticity 
  of 
  

   the 
  molecular 
  atmospheres. 
  

  

  The 
  second 
  and 
  third 
  conditions 
  are 
  those 
  of 
  equilibrium 
  of 
  heat, 
  and 
  are 
  

   equivalent 
  to 
  this 
  law 
  : 
  — 
  

  

  Temperature 
  is 
  a 
  function 
  of 
  the 
  square 
  of 
  the 
  velocity 
  of 
  revolution 
  in 
  the 
  mo- 
  

   lecular 
  vortices 
  divided 
  by 
  the 
  coefficient 
  of 
  elasticity 
  of 
  the 
  atomic 
  atmospheres 
  ; 
  — 
  or 
  

  

  Temperature 
  = 
  <p 
  ('^—\ 
  (II.) 
  

  

  where 
  w 
  represents 
  that 
  velocity. 
  

  

  The 
  mean 
  elasticity 
  which 
  a 
  vortex 
  exerts 
  endways 
  is 
  not 
  affected 
  by 
  its 
  

   motion, 
  being 
  equal 
  to 
  

  

  ^ 
  an.) 
  

  

  where 
  g 
  is 
  its 
  mean 
  density. 
  The 
  superficial 
  elasticity 
  at 
  its 
  lateral 
  surfaces, 
  

   however, 
  is 
  expressed 
  by 
  

  

  W 
  2 
  Q 
  

  

  27 
  + 
  6 
  P 
  ( 
  IV 
  -) 
  

  

  w 
  2 
  o 
  

   The 
  additional 
  elasticity 
  -—-, 
  being 
  that 
  which 
  is 
  due 
  to 
  the 
  motion, 
  is 
  

  

  independent 
  of 
  the 
  diameter. 
  The 
  divisor 
  g 
  (the 
  force 
  of 
  gravity) 
  is 
  introduced, 
  

   on 
  the 
  supposition 
  of 
  the 
  density 
  o 
  being 
  measured 
  by 
  weight. 
  

  

  Supposing 
  the 
  atmosphere 
  of 
  an 
  atom 
  to 
  be 
  divided 
  into 
  concentric 
  spherical 
  

   layers, 
  it 
  may 
  be 
  shewn 
  that 
  the 
  effect 
  of 
  the 
  coexistence 
  of 
  a 
  great 
  number 
  of 
  

   small 
  vortices 
  in 
  one 
  of 
  those 
  layers 
  whose 
  radius 
  is 
  r, 
  and 
  mean 
  density 
  g, 
  is 
  to 
  

   give 
  it 
  a 
  centrifugal 
  force, 
  expressed 
  by 
  

  

  *- 
  (V.) 
  

  

  gr 
  ' 
  

  

  which 
  tends 
  to 
  increase 
  the 
  density 
  and 
  elasticity 
  of 
  the 
  atmosphere 
  at 
  the 
  sur- 
  

   face, 
  which 
  I 
  have 
  called 
  the 
  boundary 
  of 
  the 
  atom. 
  The 
  layer 
  is 
  also 
  acted 
  upon 
  

   by 
  the 
  difference 
  between 
  the 
  mean 
  elasticities 
  at 
  its 
  two 
  surfaces, 
  and 
  by 
  the 
  

   attraction 
  towards 
  the 
  atomic 
  centre 
  ; 
  and 
  these 
  three 
  forces 
  must 
  balance 
  each 
  

   other. 
  

  

  