﻿910 
  Prof. 
  0. 
  W. 
  Richardson 
  on 
  the 
  Kinetic 
  

  

  more 
  general 
  method 
  of 
  attacking 
  the 
  problem, 
  especially 
  in 
  

   view 
  of 
  the 
  fact, 
  demonstrated 
  by 
  the 
  author 
  mid 
  Dr. 
  Brown 
  

   (loc. 
  ceV.), 
  thai 
  the 
  distribution 
  of 
  the 
  component 
  of 
  velocity 
  

   normal 
  to 
  the 
  emitting 
  surface 
  only 
  follows 
  Maxwell's 
  

   law 
  under 
  somewhat 
  restricted 
  conditions. 
  The 
  following 
  

   graphical 
  method 
  doe** 
  nor 
  depend 
  on 
  any 
  assumption 
  as 
  

   to 
  fho 
  mode 
  of 
  distribution 
  of 
  any 
  part 
  of 
  the 
  kinetic 
  

   energv. 
  

  

  If 
  Ve 
  is 
  larg3 
  compared 
  with 
  ^mw 
  Q 
  2 
  the 
  ions 
  which 
  reach 
  

   the 
  plate 
  at 
  a 
  distance 
  ■ 
  from 
  the 
  line 
  of 
  symmetry 
  are 
  

   emitted 
  by 
  the 
  strip 
  (oi 
  infinitesimal 
  width) 
  with 
  the 
  side- 
  

  

  We 
  \ 
  l/2 
  

   ways 
  velocity 
  r/ 
  n 
  = 
  - 
  (" 
  ) 
  . 
  The 
  part 
  of 
  their 
  kinetic 
  

   - 
  mz* 
  ' 
  

  

  energy 
  which 
  depen 
  Is 
  on 
  I 
  is 
  velocity 
  component 
  is 
  therefore 
  

  

  . 
  .. 
  *? 
  Ve 
  

  

  "o 
  = 
  .[ 
  .- 
  

  

  If 
  y 
  i- 
  th«- 
  vertical 
  or 
  linal 
  i 
  in 
  the 
  ?', 
  x 
  diagram 
  and 
  v 
  is 
  the 
  

  

  number 
  of 
  ions 
  corresponding 
  to 
  unit 
  area 
  oi 
  the 
  figure, 
  then 
  

  

  the 
  number 
  which 
  c 
  I 
  to 
  a 
  strip 
  of 
  heighl 
  y 
  and 
  

  

  breadth 
  <l.f 
  is 
  vydx. 
  ions 
  fa- 
  the 
  sideways 
  

  

  •'- 
  V, 
  ' 
  . 
  , 
  ., 
  , 
  . 
  . 
  

  

  energy 
  , 
  ., 
  . 
  so 
  that 
  th 
  ■ 
  i 
  >tal 
  si 
  leways 
  kinetic 
  energy 
  is 
  

  

  1 
  :- 
  

  

  SI 
  

  

  x\l 
  

  

  The 
  total 
  number 
  of 
  ions 
  is 
  v 
  I 
  y&r, 
  so 
  that 
  the 
  average 
  

  

  J 
  — 
  CO 
  

  

  sideways 
  kinetic 
  energy 
  is 
  

  

  jj 
  y^dx 
  \ 
  ydx. 
  . 
  . 
  . 
  (16) 
  

  

  J 
  — 
  X 
  I 
  J 
  — 
  00 
  

  

  The 
  integral 
  in 
  the 
  denominator 
  is 
  the 
  area 
  included 
  in 
  

   the 
  /. 
  x 
  diagram. 
  The 
  other 
  can 
  easily 
  be 
  obtained 
  by 
  

   plotting 
  /,/■- 
  against 
  x 
  and 
  measuring 
  the 
  area 
  enclosed 
  

   by 
  the 
  resulting 
  curve. 
  The 
  last 
  curve, 
  it 
  will 
  be 
  observed, 
  

   is 
  a 
  complete 
  graphical 
  expression 
  of 
  the 
  law 
  of 
  distribution 
  

   of 
  ?/,,- 
  among 
  the 
  ions. 
  In 
  a 
  precisely 
  similar 
  way 
  the 
  

   distribution 
  of 
  u 
  could 
  he 
  expressed 
  graphically. 
  

  

  We 
  shall 
  now 
  consider 
  the 
  application 
  of 
  this 
  method 
  to 
  

   the 
  results 
  already 
  obtained, 
  commencing 
  with 
  the 
  negative 
  

   ions. 
  

  

  