﻿356 
  Prof. 
  Richardson 
  and 
  Mr. 
  Brown 
  on 
  the 
  Kinetic 
  

  

  (5) 
  

  

  we 
  get 
  

  

  P 
  =wt 
  y 
  ' 
  ' 
  

  

  • 
  • 
  

  

  where 
  X= 
  — 
  ^ 
  — 
  is 
  supposed 
  to 
  be 
  constant. 
  

  

  

  The 
  equation 
  to 
  the 
  path 
  is 
  thus 
  

  

  

  

  

  (6) 
  

  

  If 
  #o 
  is 
  the 
  distance 
  between 
  the 
  two 
  plates 
  and 
  p 
  Q 
  the 
  

   radius 
  of 
  the 
  upper 
  one 
  the 
  condition 
  that 
  the 
  particle 
  should 
  

   just 
  reach 
  the 
  boundary 
  of 
  the 
  upper 
  plate 
  is 
  

  

  •m.r 
  W 
  2 
  — 
  mu 
  Q 
  p 
  W 
  = 
  ^'Kepo 
  2 
  (7) 
  

  

  If 
  the 
  value 
  of 
  W 
  considered 
  as 
  a 
  function 
  of 
  u 
  , 
  a 
  , 
  and 
  

   p 
  is 
  < 
  that 
  given 
  by 
  equation 
  (7) 
  the 
  particle 
  will 
  reach 
  the 
  

   upper 
  plate, 
  provided 
  u 
  also 
  satisfies 
  the 
  inequality 
  (2), 
  

   otherwise 
  it 
  will 
  either 
  be 
  returned 
  to 
  the 
  lower 
  plate 
  or 
  it 
  

   will 
  reach 
  the 
  guard-ring. 
  Solving 
  the 
  quadratic 
  equation 
  

   we 
  see 
  that 
  the 
  particle 
  will 
  just 
  reach 
  the 
  edge 
  of 
  the 
  plate 
  

   if 
  

  

  w 
  =*S( 
  wo± 
  \/^- 
  2 
  ^ 
  Y 
  ) 
  

  

  when 
  

  

  W 
  u 
  

  

  v=o 
  

  

  Po 
  

  

  so 
  that 
  the 
  positive 
  sign 
  is 
  the 
  one 
  to 
  take. 
  Hence 
  for 
  the 
  

   particle 
  to 
  reach 
  the 
  upper 
  plate 
  W 
  must 
  lie 
  between 
  the 
  limits 
  

  

  and 
  \ 
  — 
  (u 
  -\-\/ 
  u 
  2 
  — 
  2 
  — 
  Vj, 
  whilst 
  u 
  must 
  lie 
  between. 
  

  

  x) 
  and 
  \/ 
  2 
  — 
  Y. 
  If 
  the 
  fraction 
  of 
  the 
  ions 
  emitted 
  whose 
  

   V 
  m 
  

  

  velocity 
  parallel 
  to 
  the 
  plates 
  lies 
  between 
  W 
  and 
  W 
  + 
  dW 
  

   is 
  F(W)^W, 
  the 
  current 
  received 
  by 
  the 
  upper 
  plate 
  will 
  be 
  

  

  ... 
  (8) 
  

  

  J 
  2 
  x 
  V 
  ° 
  v 
  u 
  

   V(wmw. 
  

   o 
  

  

  Particular 
  Case 
  of 
  MaxwelVs 
  Law 
  of 
  Distribution. 
  

   If 
  we 
  assume 
  tentatively 
  that 
  the 
  law 
  of 
  distribution 
  of 
  

   velocity 
  among 
  the 
  emitted 
  ions 
  is 
  the 
  same 
  as 
  that 
  among 
  

  

  