﻿Kinetic 
  Theory 
  of 
  Matter, 
  697 
  

  

  number 
  of 
  particles 
  escaping 
  per 
  second 
  for 
  which 
  u 
  lies 
  

   between 
  Uq 
  and 
  u^ 
  + 
  diiQ 
  will 
  be 
  the 
  same 
  as 
  the 
  number 
  of 
  

   those 
  striking 
  the 
  surface 
  per 
  second 
  inside 
  for 
  which 
  u 
  lies 
  

   between 
  iii 
  and 
  Ui-\-dui, 
  where 
  

  

  2 
  

   iiQ^=iu^-— 
  -<J) 
  and 
  UQdiiQ= 
  uidui. 
  

  

  This 
  is, 
  from 
  (3), 
  

  

  'NQ{uQ)duQ 
  = 
  nl 
  — 
  j 
  uidu 
  

  

  p—kmu^ 
  

  

  = 
  n(^yu,du,e-^^-^-^^i^). 
  . 
  (4) 
  

  

  where 
  n 
  is 
  the 
  number 
  of 
  molecules 
  per 
  c.c. 
  inside 
  the 
  

   boundary. 
  The 
  total 
  number 
  Xq 
  which 
  escape 
  per 
  second 
  

   will 
  be 
  those 
  for 
  which 
  uq 
  is 
  greater 
  than 
  zero, 
  i. 
  e. 
  

  

  (5) 
  

  

  2 
  {7rkm)i 
  

  

  Substituting 
  for 
  n 
  in 
  (4) 
  we 
  therefore 
  have 
  

  

  l^o{uo)duo 
  = 
  2hnuQNQe-^"'"^^duo, 
  

   whence 
  

  

  F{uo)duo= 
  ^^'^^^''' 
  ='2hnuoe-^'--^duo 
  . 
  . 
  (6) 
  

  

  It 
  follows 
  that 
  the 
  distribution, 
  among 
  the 
  particles 
  leaving 
  

   any 
  surface, 
  of 
  the 
  component 
  of 
  velocity 
  normal 
  to 
  the 
  

   surface, 
  is 
  independent 
  of 
  the 
  amount 
  of 
  work 
  done 
  by 
  the 
  

   particles 
  in 
  crossing 
  the 
  surface, 
  including 
  the 
  usual 
  case 
  

   where 
  the 
  work 
  has 
  the 
  particular 
  value 
  zero. 
  

  

  The 
  application 
  of 
  this 
  result 
  to 
  the 
  evaporation 
  of 
  

   electricity, 
  or 
  thermionics, 
  has 
  been 
  considered 
  in 
  numerous 
  

   previous 
  papers. 
  It 
  is, 
  however, 
  equally 
  applicable 
  to 
  

   ordinary 
  molecular 
  evaporation. 
  If 
  we 
  suppose, 
  as 
  in 
  the 
  

   theory 
  of 
  surface 
  tension, 
  that 
  the 
  molecules 
  of 
  a 
  liquid, 
  in 
  

   order 
  to 
  escape 
  into 
  the 
  vapour, 
  have 
  to 
  get 
  through 
  a 
  skin 
  

   in 
  which 
  they 
  are 
  acted 
  on 
  by 
  forces 
  which 
  on 
  the 
  average 
  

   are 
  directed 
  along 
  the 
  inward 
  normal 
  : 
  then 
  it 
  follows 
  from 
  

   the 
  above 
  calculations 
  that 
  the 
  proportion 
  of 
  the 
  molecules 
  

   escaping 
  in 
  a 
  given 
  time, 
  for 
  which 
  u 
  lies 
  between 
  u 
  and 
  

   u 
  + 
  du, 
  is 
  '2kmue~^''"'"^du. 
  It 
  is 
  therefore 
  independent 
  of 
  the 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  18. 
  No. 
  107. 
  Nov. 
  1909. 
  3 
  A 
  

  

  