﻿750 
  Prof. 
  0. 
  W. 
  Richardson 
  on 
  the 
  Sjiecific 
  

  

  cent, 
  from 
  the 
  mean 
  value 
  anywhere 
  in 
  the 
  region 
  where 
  

   motion 
  of 
  the 
  ions 
  was 
  investigated. 
  

  

  Care 
  was 
  taken 
  that 
  no 
  iron 
  was 
  used 
  in 
  the 
  construction 
  

   of 
  the 
  apparatus. 
  The 
  strength 
  of 
  the 
  magnetic 
  field 
  was 
  

   determined 
  by 
  means 
  of 
  a 
  bismuth 
  spiral 
  supplied 
  and 
  

   calibrated 
  by 
  Hartmann 
  and 
  Braun. 
  

  

  A 
  Dolezalek 
  electrometer 
  was 
  used. 
  Its 
  sensitiveness 
  was 
  

   made 
  to 
  vary 
  from 
  80 
  to 
  900 
  divisions 
  per 
  volt, 
  according 
  to 
  

   the 
  magnitude 
  of 
  the 
  currents 
  to 
  be 
  measured. 
  The 
  capacity 
  

   taken 
  out 
  of 
  the 
  condenser 
  was 
  always 
  '001 
  microfarad 
  and 
  

   the 
  width 
  of 
  the 
  slit 
  between 
  cc 
  was 
  usually 
  about 
  *03 
  cm. 
  

  

  § 
  4. 
  Theory 
  of 
  the 
  Method. 
  

  

  Let 
  the 
  two 
  connecting 
  planes 
  be 
  perpendicular 
  to 
  the 
  

   axis 
  of 
  z, 
  the 
  plane 
  which 
  contains 
  the 
  strip 
  being 
  determined 
  

   by 
  z 
  = 
  0, 
  and 
  that 
  containing 
  the 
  slit 
  being 
  determined 
  by 
  

   : 
  = 
  cj. 
  The 
  electric 
  force 
  Z 
  is 
  everywhere 
  constant 
  and 
  

   perpendicular 
  to 
  the 
  two 
  planes. 
  Let 
  the 
  axis 
  of 
  y 
  be 
  taken 
  

   parallel 
  to 
  the 
  edges 
  of 
  the 
  strip 
  and 
  slit. 
  This 
  is 
  also 
  the 
  

   direction 
  of 
  the 
  uniform 
  magnetic 
  force 
  H. 
  The 
  equations 
  

   of 
  motion 
  of 
  an 
  ion 
  whore 
  mass 
  is 
  m 
  and 
  charge 
  e, 
  under 
  the 
  

   influence 
  of 
  the 
  electric 
  and 
  magnetic 
  fields, 
  are 
  

  

  <!-.r 
  -u- 
  dz 
  d 
  2 
  ?/ 
  . 
  d?z 
  r 
  , 
  TT 
  dx 
  

  

  "'W 
  = 
  Re 
  dt' 
  m 
  2#= 
  ' 
  m 
  d? 
  =Ze 
  - 
  m 
  Tf 
  

  

  The 
  solution 
  of 
  these 
  equations 
  is 
  fully 
  discussed 
  in 
  J. 
  J. 
  

   Thomson's 
  ' 
  Conduction 
  of 
  Electricity 
  through 
  Gases/ 
  

   chapter 
  iv. 
  If 
  the 
  ion 
  starts 
  at 
  the 
  instant 
  £ 
  = 
  from 
  the 
  

   point 
  a? 
  y 
  0, 
  with 
  velocity 
  components 
  i< 
  v 
  w 
  , 
  the 
  dis- 
  

   placement 
  xy 
  z 
  at 
  time 
  t 
  is 
  given 
  by 
  

  

  Z 
  /Z 
  \m 
  . 
  He. 
  t 
  w 
  m/, 
  H^\ 
  

  

  y— 
  yo=^. 
  

  

  Z 
  \ 
  m 
  / 
  He 
  \ 
  iv 
  m 
  . 
  He 
  

  

  ( 
  L 
  \ 
  m 
  ( 
  lie 
  \ 
  w 
  m 
  . 
  

  

  t. 
  

   m 
  

  

  The 
  x 
  and 
  z 
  displacements 
  are 
  independent 
  of 
  y. 
  Since 
  the 
  

   object 
  of 
  the 
  experiment 
  is 
  to 
  determine 
  the 
  value 
  of 
  x 
  — 
  x 
  

   forjjgiven 
  values 
  of 
  Z, 
  H, 
  and 
  g 
  1<f 
  the 
  y 
  displacement 
  is 
  not 
  

  

  He 
  

  

  required. 
  As 
  — 
  t 
  was 
  always 
  less 
  than 
  unity, 
  we 
  may 
  

  

  