﻿Energy 
  of 
  the 
  Ions 
  emitted 
  by 
  Hot 
  Bodies. 
  895 
  

  

  with 
  all 
  the 
  values 
  of 
  \mw 
  2 
  ^ 
  since 
  infinite 
  values 
  of 
  this 
  

   quantity 
  are 
  theoretically 
  possible 
  ; 
  but 
  the 
  number 
  o£ 
  such 
  

   cases 
  is 
  so 
  small 
  that 
  it 
  makes 
  no 
  difference 
  whether 
  they 
  are 
  

   included 
  or 
  not. 
  We 
  shall 
  suppose 
  that 
  the 
  condition 
  is 
  

   satisfied 
  if: 
  Ye 
  is 
  great 
  compared 
  with 
  the 
  average 
  value 
  of 
  

   ^77uvq 
  2 
  . 
  It 
  will 
  be 
  noticed 
  that 
  Ye/^mw 
  2 
  is 
  the 
  ratio 
  of 
  the 
  

   kinetic 
  energy 
  communicated 
  by 
  the 
  electric 
  field, 
  during 
  

   the 
  passage 
  from 
  the 
  strip 
  to 
  the 
  plate, 
  to 
  the 
  " 
  normal 
  com- 
  

   ponent 
  " 
  of 
  the 
  kinetic 
  energy 
  of 
  the 
  ion 
  when 
  it 
  was 
  

   emitted 
  from 
  the 
  strip. 
  

  

  If 
  |f 
  and 
  |f' 
  are 
  both 
  infinitesimal 
  and 
  x 
  =0 
  (4) 
  becomes 
  

  

  o 
  (M'f 
  , 
  WZfi 
  , 
  /' 
  Ye~\ 
  -W(i+4(i+v(i 
  +1 
  -^)) 
  2 
  ) 
  

   Zn^—^- 
  \ 
  dw 
  -o-t 
  ( 
  1 
  + 
  \ 
  / 
  1 
  + 
  t— 
  — 
  9 
  ) 
  e 
  K 
  ±*' 
  a 
  v 
  v 
  *—*' 
  ' 
  } 
  

  

  it* 
  Jo 
  &z 
  \ 
  V 
  \inwtf) 
  

  

  If 
  in 
  addition 
  Yej\mw 
  2 
  is 
  large 
  compared 
  with 
  unity, 
  this 
  

   reduces 
  to 
  

  

  nif 
  / 
  2kV< 
  

  

  iri 
  V 
  ±z' 
  2 
  

  

  e 
  i2 
  ' 
  2 
  

  

  The 
  number 
  of 
  ions 
  which 
  are 
  received 
  by 
  a 
  width 
  dec 
  of 
  the 
  

   lower 
  plane 
  at 
  x 
  is 
  therefore 
  

  

  rikYe 
  

  

  7T*V 
  ^ 
  

  

  

  and 
  the 
  total 
  number 
  of 
  ions 
  received 
  by 
  the 
  whole 
  of 
  the 
  

   lower 
  plane 
  is 
  

  

  ^ll 
  f 
  iky 
  e 
  — 
  r-77* 
  2 
  mi 
  x 
  7 
  

  

  Since 
  this 
  is 
  otherwise 
  obvious 
  the 
  result 
  may 
  be 
  considered 
  

   as 
  a 
  check 
  on 
  our 
  previous 
  calculations. 
  

  

  The 
  fraction 
  of 
  the 
  total 
  number 
  of 
  ions 
  received 
  by 
  the 
  

   lower 
  plane 
  which 
  pass 
  through 
  a 
  narrow 
  slit 
  of 
  width 
  |f, 
  

   distant 
  x 
  from 
  the 
  line 
  of 
  symmetry, 
  is 
  thus 
  

  

  f 
  ItkYe 
  

  

  2feV 
  

  

  / 
  z/c 
  x 
  e 
  - 
  

  

  sj 
  it 
  

  

  Since 
  k 
  = 
  ^d~a 
  where 
  1^ 
  is 
  the 
  gas 
  constant 
  reckoned 
  for 
  a 
  

  

  single 
  molecule, 
  and 
  6 
  is 
  the 
  absolute 
  temperature, 
  the 
  above 
  

   may 
  be 
  written, 
  changing 
  z' 
  to 
  z, 
  

  

  f 
  . 
  / 
  v 
  

  

  w 
  

  

  ne 
  

  

  Vne 
  

  

  z 
  ,e 
  4Kfe2 
  ...... 
  (5) 
  

  

  