﻿Charge 
  of 
  the 
  Ions 
  emitted 
  by 
  Hot 
  Bodies. 
  751 
  

  

  expand 
  the 
  sines 
  and 
  cosines 
  in 
  powers 
  of* 
  t, 
  obtaining 
  

   1H* 
  , 
  2| 
  /Z 
  \HV 
  f3 
  

  

  Z 
  \H«. 
  H 
  2 
  * 
  

  

  

  ^-^^' 
  

  

  It 
  is 
  easy 
  to 
  show 
  that 
  with 
  the 
  values 
  o£ 
  the 
  variables 
  

   which 
  occurred 
  in 
  the 
  experiments 
  the 
  terms 
  involving 
  

   powers 
  of 
  t 
  higher 
  than 
  the 
  third 
  introduced 
  changes 
  which 
  

   were 
  small 
  compared 
  with 
  the 
  errors 
  of 
  observation. 
  

  

  The 
  problem 
  now 
  is 
  to' 
  eliminate 
  t 
  between 
  these 
  two 
  

   equations 
  so 
  as 
  to 
  obtain 
  x 
  — 
  x 
  Q 
  as 
  a 
  function 
  of 
  z 
  &c. 
  It 
  is 
  

   advisable 
  at 
  this 
  stage 
  to 
  consider 
  what 
  further 
  approxi- 
  

   mations 
  are 
  permissible. 
  To 
  do 
  this 
  we 
  shall 
  evaluate 
  each 
  

   of 
  the 
  terms 
  in 
  the 
  above 
  series, 
  using 
  the 
  actual 
  values 
  of 
  

   the 
  quantities 
  which 
  occurred 
  in 
  a 
  typical 
  experiment. 
  These 
  

   were 
  Z 
  = 
  146 
  x 
  10 
  8 
  E.M. 
  units, 
  H 
  = 
  4670 
  E.M. 
  units, 
  

   ^ 
  = 
  •534 
  cua.,e/ra 
  = 
  330 
  E.M. 
  units, 
  and 
  u 
  =w 
  = 
  6 
  x 
  10 
  4 
  cms. 
  

   per 
  sec. 
  approximately. 
  The 
  above 
  mean 
  value 
  for 
  u 
  and 
  io 
  

   follows, 
  assuming 
  that 
  the 
  charge 
  on 
  a 
  positive 
  ion 
  is 
  equal 
  

   to 
  that 
  carried 
  by 
  the 
  hydrogen 
  ion 
  in 
  electrolysis, 
  from 
  

   researches 
  not 
  yet 
  published 
  by 
  Mr. 
  F. 
  C. 
  Brown 
  and 
  by 
  

   the 
  author 
  on 
  the 
  kinetic 
  energy 
  of 
  the 
  positive 
  ions 
  emitted 
  

   by 
  hot 
  metals. 
  We 
  may 
  write 
  the 
  expression 
  for 
  Z\ 
  

  

  Ze 
  2 
  He 
  „ 
  We 
  2 
  w 
  . 
  

  

  Z 
  X 
  = 
  W 
  t 
  + 
  <r- 
  t 
  2 
  - 
  U 
  -—t 
  2 
  -. 
  - 
  /- 
  t\ 
  

  

  lm 
  Am 
  bm" 
  

  

  2-7tfxl0- 
  2 
  51'lXlO 
  -2 
  -93xl0- 
  2 
  ^XlO" 
  3 
  

  

  The 
  number 
  underneath 
  each 
  term 
  is 
  the 
  value 
  of 
  that 
  term 
  

   obtained 
  by 
  putting 
  t 
  = 
  4*6 
  x 
  10~ 
  7 
  . 
  This 
  is 
  the 
  value 
  which 
  t, 
  

   the 
  time 
  required 
  by 
  the 
  ion 
  to 
  reach 
  the 
  lower 
  plate, 
  would 
  

   have 
  if 
  there 
  were 
  no 
  magnetic 
  field. 
  It 
  will 
  be 
  observed 
  

   that 
  the 
  term 
  ±Ze/mt 
  2 
  is 
  by 
  far 
  the 
  most 
  important, 
  and 
  that 
  

   both 
  the 
  terms 
  involving 
  H 
  are 
  comparatively 
  small. 
  

  

  We 
  shall 
  see 
  below 
  that 
  the 
  measurements 
  were 
  made 
  for 
  

   those 
  ions 
  for 
  which 
  u 
  = 
  0, 
  so 
  that 
  the 
  third 
  term 
  vanishes 
  in 
  

   any 
  case 
  from 
  the 
  equation 
  which 
  represents 
  the 
  experimental 
  

   conditions. 
  The 
  only 
  term 
  involving 
  H 
  which 
  remains 
  is 
  

   the 
  last 
  and 
  the 
  omission 
  of 
  this 
  term 
  will 
  only 
  change 
  the 
  

   value 
  of 
  t 
  by 
  about 
  '2 
  per 
  cent, 
  a 
  quantity 
  small 
  compared 
  

   with 
  the 
  probable 
  error 
  of 
  observation. 
  Within 
  this 
  order 
  

   of 
  accuracy 
  t 
  will 
  be 
  given 
  by 
  solving 
  the 
  quadratic 
  equation 
  

  

  ■ 
  i} 
  — 
  t 
  2 
  ±iv 
  t 
  = 
  z 
  lt 
  and 
  with 
  practically 
  the 
  same 
  degree 
  of 
  

  

  