﻿Energy 
  of 
  the 
  Ions 
  emitted 
  by 
  Hot 
  Bodies. 
  893 
  

  

  It 
  is 
  to 
  be 
  borne 
  in 
  mind 
  that 
  only 
  positive 
  values 
  of 
  w 
  are 
  

   admissible 
  in 
  this 
  expression. 
  Those 
  which 
  start 
  from 
  the 
  

   back 
  of 
  the 
  strip 
  are 
  supposed 
  to 
  be 
  caught 
  by 
  the 
  upper 
  

   plate 
  and 
  have 
  no 
  opportunity 
  to 
  reach 
  the 
  plane 
  below. 
  

   The 
  conditions 
  which 
  have 
  to 
  be 
  satisfied 
  are 
  therefore 
  

  

  ^'^(V^W))) 
  ■ 
  • 
  (3) 
  

   u> 
  >0. 
  J 
  

  

  Suppose 
  that 
  out 
  of 
  any 
  large 
  number 
  n 
  x 
  of 
  ions 
  emitted 
  by 
  

   the 
  strip, 
  the 
  number 
  which 
  have 
  velocity 
  components 
  lying, 
  

   at 
  the 
  same 
  time, 
  between 
  u 
  and 
  u 
  + 
  du 
  and 
  w 
  and 
  w 
  + 
  dw 
  

   is 
  denoted 
  by 
  %F(w 
  , 
  to 
  ) 
  du 
  dw 
  . 
  Then 
  the 
  number 
  which 
  

   reach 
  the 
  lower 
  plane 
  at 
  points 
  to 
  the 
  right 
  of 
  the 
  line 
  x 
  = 
  x 
  

   will 
  be 
  

  

  dwA 
  du 
  ¥(u 
  ,w 
  ). 
  

  

  J^o-^(l+v'(l+I^)J 
  

  

  If, 
  as 
  in 
  the 
  kinetic 
  theory 
  of 
  gases, 
  the 
  probabilities 
  of 
  given 
  

   values 
  of 
  the 
  components 
  of 
  velocity 
  along 
  two 
  mutually 
  

   perpendicular 
  directions 
  are 
  independent 
  of 
  each 
  other, 
  the 
  

   last 
  expression 
  may 
  be 
  written 
  

  

  I 
  = 
  nA 
  f'(u< 
  ) 
  du- 
  \ 
  >VK), 
  

  

  J° 
  ^*-o-ir- 
  (i+v(i+^^)J 
  

  

  where 
  ?i 
  1 
  f(u 
  )du 
  and 
  Qi 
  1 
  f(w 
  Q 
  )dw 
  are 
  respectively 
  the 
  number 
  

   of 
  emitted 
  ions 
  having 
  velocity 
  components 
  between 
  u 
  and 
  

   u 
  + 
  du 
  and 
  zc 
  and 
  ic 
  -\-dw 
  . 
  

  

  If 
  we 
  consider 
  a 
  narrow 
  slit 
  of 
  width 
  £ 
  in 
  the 
  lower 
  plane, 
  

   bounded 
  by 
  the 
  lines 
  x 
  — 
  x 
  — 
  x 
  -\-%/2 
  and 
  x 
  = 
  x 
  — 
  x 
  — 
  ^/2 
  it 
  

   follows 
  from 
  the 
  preceding 
  expressions 
  that 
  the 
  number 
  of 
  

   ions 
  which 
  pass 
  through 
  the 
  slit 
  will 
  be 
  equal 
  to 
  

  

  n 
  ± 
  \div 
  \ 
  dii 
  F(u 
  , 
  w 
  ) 
  . 
  

  

  f 
  P 
  

  

  \dw 
  \ 
  

  

  Jo 
  J 
  1 
  * 
  1 
  

  

  ■a-o-fe 
  

  

  ?(l4V(l+ 
  r 
  ^ 
  T 
  )) 
  

   \ 
  V 
  pnwtfJJ 
  

  

  If 
  in 
  addition 
  the 
  strip 
  is 
  of 
  finite 
  width 
  f 
  and 
  extends 
  from 
  

   #0= 
  — 
  f'/2 
  to 
  x 
  = 
  -t- 
  f/2, 
  the 
  total 
  number 
  which 
  pass 
  through 
  

   the 
  slit 
  will 
  be 
  

  

  ~\ 
  dx 
  \ 
  dw 
  Q 
  \ 
  da 
  F(u 
  , 
  w 
  Q 
  ). 
  

  

  