﻿Charge 
  of 
  the 
  Ions 
  emitted 
  by 
  Hot 
  Bodies. 
  753 
  

  

  the 
  direction 
  of 
  the 
  displacement 
  depending 
  on 
  the 
  direction 
  

   of 
  the 
  magnetic 
  field. 
  This 
  result 
  might 
  of 
  course 
  have 
  been 
  

   anticipated 
  from 
  the 
  relative 
  magnitude 
  of 
  the 
  different 
  

   terms 
  in 
  the 
  last 
  equation. 
  It 
  is 
  clear, 
  therefore, 
  that 
  the 
  

   new 
  position 
  of 
  the 
  maximum 
  will 
  again 
  represent 
  the 
  

   position 
  of 
  the 
  particles 
  for 
  which 
  n 
  = 
  ; 
  so 
  that 
  by 
  

   measuring 
  the 
  displacement 
  of 
  the 
  maximum 
  we 
  obtain 
  the 
  

   value 
  of 
  x 
  for 
  the 
  particles 
  whose 
  sideways 
  component 
  of 
  

   initial 
  velocity 
  is 
  equal 
  to 
  zero. 
  The 
  displacement 
  x 
  of 
  this 
  

   maximum 
  will 
  therefore 
  be 
  obtained 
  if 
  we 
  put 
  u 
  equal 
  to 
  

   zero 
  in 
  the 
  last 
  equation. 
  

   We 
  thus 
  get 
  

  

  liezi^mz^ 
  _ 
  Hiv 
  2 
  z 
  1 
  (2mz-^ 
  

   Xx 
  ~-~Z^\Ze~) 
  Z~\Ze~) 
  ' 
  

  

  The 
  values 
  of 
  these 
  two 
  terms 
  in 
  the 
  experiment 
  cited 
  are 
  

   129 
  x 
  10 
  -3 
  and 
  *29 
  x 
  10~ 
  3 
  respectively 
  ; 
  so 
  that 
  within 
  an 
  

   accuracy 
  of 
  about 
  '2 
  per 
  cent, 
  it 
  will 
  be 
  sufficient 
  to 
  take 
  

  

  _ 
  IW 
  f~2e~~ 
  

  

  where 
  x 
  is 
  the 
  displacement 
  of 
  the 
  maximum 
  and 
  V 
  is 
  the 
  

   potential- 
  difference 
  between 
  the 
  upper 
  and 
  lower 
  plates. 
  

  

  The 
  legitimacy 
  of 
  the 
  approximations 
  has 
  been 
  illustrated 
  

   by 
  means 
  only 
  of 
  a 
  single 
  instance, 
  but 
  with 
  all 
  the 
  values 
  

   of 
  the 
  magnetic 
  and 
  electric 
  fields 
  which 
  were 
  used 
  the 
  

   quantities 
  neglected 
  were 
  always 
  of 
  the 
  order 
  indicated 
  and 
  

   small 
  compared 
  with 
  the 
  experimental 
  error. 
  From 
  the 
  last 
  

   equation 
  the 
  formula 
  for 
  e/m 
  will 
  be 
  seen 
  to 
  be 
  

  

  e 
  _ 
  9 
  V,?! 
  2 
  

   m 
  ~ 
  2 
  H 
  V 
  * 
  

  

  The 
  value 
  of 
  e/m 
  is 
  thus 
  inversely 
  proportional 
  to 
  the 
  

   fourth 
  power 
  of 
  z 
  x 
  . 
  In 
  the 
  experiments 
  Z\ 
  was 
  always 
  about 
  

   6 
  mm., 
  and 
  could, 
  on 
  paper, 
  easily 
  be 
  measured 
  to 
  an 
  

   accuracy 
  of 
  one 
  per 
  cent. 
  But 
  there 
  was 
  always 
  a 
  chance 
  

   of 
  something 
  having 
  gone 
  wrong 
  with 
  this 
  distance 
  due 
  to 
  

   mechanical 
  imperfections, 
  a 
  fact 
  which 
  probably 
  gave 
  rise 
  

   to 
  more 
  trouble 
  than 
  anything 
  else, 
  particularly 
  in 
  the 
  

   initial 
  stages 
  of 
  the 
  investigation. 
  For 
  this 
  reason 
  it 
  is 
  

   quite 
  necessary 
  to 
  use 
  apparatus 
  as 
  elaborate 
  as 
  that 
  shown 
  

   in 
  fig. 
  1. 
  

  

  § 
  5. 
  Results 
  of 
  the 
  Experiments. 
  

  

  In 
  discussing 
  the 
  theory 
  of 
  these 
  experiments 
  we 
  have 
  

   assumed 
  that 
  the 
  motion 
  of 
  the 
  ions 
  after 
  leaving 
  the 
  metal 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  16. 
  No. 
  95. 
  Nov. 
  1908. 
  3 
  D 
  

  

  