﻿•222 
  Prof. 
  J. 
  H. 
  Jeans 
  on 
  the 
  

  

  become 
  identical. 
  It 
  follows 
  that, 
  as 
  regards 
  the 
  quantities 
  

   involved, 
  and 
  the 
  algebraic 
  dimensions 
  of 
  these 
  quantities, 
  

   £" 
  must 
  be 
  similar 
  to 
  pa 
  — 
  we 
  can 
  evaluate 
  e", 
  to 
  within 
  

   numerical 
  constants, 
  by 
  evaluating 
  p,i. 
  Or, 
  again, 
  e^ 
  must 
  

   be 
  given, 
  except 
  for 
  numerical 
  constants, 
  by 
  the 
  value 
  of 
  

   2hi+2/p2' 
  S^^ 
  ^^^ 
  difference 
  between 
  pn+2 
  and 
  p^ 
  lies 
  in 
  

   operating, 
  before 
  averaging, 
  with 
  ^^. 
  It 
  follows 
  that 
  e^ 
  is 
  

   similar, 
  as 
  regards 
  the 
  quantities 
  involved 
  and 
  their 
  algebraic 
  

   dimensions, 
  to 
  <&^, 
  regarded 
  as 
  a 
  multiplier. 
  

  

  The 
  operator 
  d^ 
  consists 
  of 
  sixteen 
  terms 
  of 
  which 
  typical 
  

   terms 
  are 
  

  

  Regarded 
  as 
  multipliers, 
  the 
  dimensions 
  of 
  these 
  terms 
  are 
  

   those 
  of 
  

  

  The 
  potentials 
  and 
  velocities 
  of 
  the 
  different 
  electrons 
  are 
  

   arranged 
  according 
  to 
  the 
  law 
  of 
  distribution 
  

  

  A 
  <,-(2^V+»»^+ 
  . 
  . 
  . 
  )/2RT 
  ^_^, 
  ^y 
  ^. 
  ^„ 
  ^p 
  ^,^^ 
  

  

  'SO 
  that 
  the 
  average 
  values 
  of 
  eY 
  and 
  miu^ 
  are 
  each 
  of 
  

   dimensions 
  RT. 
  We 
  know 
  that 
  the 
  average 
  value 
  of 
  my? 
  is 
  

   RT, 
  and 
  can 
  take 
  the 
  average 
  value 
  of 
  eV 
  to 
  be 
  aRT, 
  where 
  

   ■a 
  will, 
  in 
  general, 
  depend 
  on 
  the 
  structure 
  of 
  the 
  particular 
  

  

  substance 
  involved. 
  The 
  value 
  of 
  j- 
  is 
  given 
  by 
  equation 
  

  

  '(75). 
  Substituting 
  in 
  the 
  terms 
  (82), 
  we 
  find 
  that 
  all 
  the 
  

  

  terms 
  are 
  of 
  the 
  same 
  dimensions, 
  namely, 
  -^ 
  (^~ 
  ) 
  ? 
  which 
  

  

  iw^j 
  be 
  expressed 
  as 
  the 
  dimensions 
  of 
  ^^EyRTm. 
  

   We 
  must 
  accordingly 
  have 
  an 
  equation 
  of 
  the 
  form 
  

  

  '~mK- 
  VETm' 
  *■ 
  ^^ 
  

  

  Avhere 
  yS 
  is 
  a 
  numerical 
  constant 
  which 
  may 
  depend 
  on 
  the 
  

   structure 
  of 
  the 
  particular 
  substance, 
  

  

  40. 
  The 
  values 
  of 
  f^ 
  and 
  k 
  are 
  given 
  by 
  equations 
  (76) 
  

   and 
  (83). 
  Substituting 
  these 
  values 
  in 
  equation 
  (74) 
  we 
  

   obtain 
  

  

  \ 
  /3a^E 
  /' 
  

   which 
  is 
  satisfied 
  if 
  

  

  e^ 
  _ 
  6RT3 
  / 
  ^RP7 
  

   m^ 
  ~ 
  irma^ 
  

  

  ^^■^=W^ 
  («*) 
  

  

  