﻿676 
  Prof. 
  J. 
  J. 
  Thomson 
  

  

  on 
  

  

  from 
  this 
  equation 
  we 
  can 
  deduce 
  the 
  ratio 
  of 
  the 
  charges 
  

   when 
  we 
  know 
  that 
  of 
  the 
  potentials. 
  By 
  using 
  two 
  electro- 
  

   scopes 
  and 
  determining 
  by 
  means 
  of 
  them 
  the 
  ratio 
  of 
  the 
  

   charges 
  received 
  by 
  the 
  cylinder 
  and 
  disk, 
  we 
  eliminate 
  any 
  

   irregularities 
  that 
  might 
  arise 
  from 
  variations 
  in 
  the 
  working 
  

   of 
  the 
  coil 
  used 
  to 
  produce 
  the 
  cathode 
  rays 
  which 
  ionize 
  the 
  

   gas 
  in 
  the 
  ionization 
  chamber. 
  

  

  If 
  an 
  ion 
  is 
  projected 
  through 
  the 
  tunnel 
  in 
  N 
  along 
  the 
  

   axis 
  of 
  the 
  tunnel, 
  it 
  will, 
  if 
  there 
  is 
  no 
  magnetic 
  field 
  acting 
  

   iupon 
  it, 
  travel 
  along 
  a 
  straight 
  line 
  and 
  hit 
  the 
  disk. 
  If 
  there 
  

   s 
  a 
  magnetic 
  field 
  its 
  path, 
  after 
  getting 
  through 
  the 
  hole, 
  

   will 
  be 
  a 
  circle, 
  since 
  if 
  it 
  is 
  free 
  when 
  once 
  it 
  has 
  got 
  

   through 
  the 
  hole 
  from 
  any 
  electric 
  force, 
  it 
  will, 
  however, 
  

   continue 
  to 
  hit 
  the 
  disk 
  until 
  the 
  radius 
  of 
  this 
  circle 
  is 
  less 
  

   than 
  the 
  radius 
  of 
  the 
  circle 
  passing 
  through 
  the 
  hole, 
  the 
  

   edge 
  of 
  the 
  disk, 
  and 
  touching 
  at 
  the 
  hole 
  the 
  axis 
  of 
  the 
  

   tunnel. 
  If 
  d 
  is 
  the 
  distance 
  of 
  the 
  disk 
  below 
  the 
  hole, 
  a 
  

   the 
  radius 
  of 
  the 
  disk, 
  r 
  the 
  radius 
  of 
  this 
  circle 
  is 
  equal 
  to 
  

  

  d 
  2 
  + 
  a 
  2 
  

  

  — 
  s 
  — 
  . 
  When 
  the 
  radius 
  of 
  the 
  path 
  of 
  the 
  ion 
  is 
  less 
  than 
  

  

  2a 
  L 
  

  

  this, 
  the 
  ion 
  will 
  give 
  up 
  its 
  charge 
  to 
  the 
  Faraday 
  cylinder; 
  

   when 
  it 
  is 
  greater 
  than 
  this 
  it 
  will 
  give 
  up 
  its 
  charge 
  to 
  the 
  

   disk. 
  

  

  If 
  H 
  is 
  the 
  magnetic 
  force 
  acting 
  on 
  the 
  ion, 
  e 
  its 
  charge, 
  

   m 
  its 
  mass, 
  and 
  r 
  the 
  radius 
  of 
  its 
  circular 
  orbit, 
  

  

  JIer 
  = 
  mv, 
  

  

  if 
  V 
  is 
  the 
  potential-difference 
  between 
  the 
  gauze 
  and 
  the 
  

   top 
  of 
  the 
  box 
  

  

  Ye 
  = 
  \mv 
  2 
  ; 
  

  

  thus 
  HV*=2V. 
  

  

  in 
  

  

  Thus 
  when 
  H 
  increases 
  through 
  the 
  value 
  given 
  by 
  the 
  

   equation 
  

  

  R 
  JMV 
  £= 
  . 
  2Y 
  (2) 
  

  

  \ 
  2a 
  / 
  m 
  v 
  y 
  

  

  there 
  ought 
  to 
  be 
  a 
  large 
  increase 
  in 
  the 
  ratio 
  of 
  the 
  charge 
  

   on 
  the 
  Faraday 
  cylinder 
  to 
  that 
  on 
  the 
  disk. 
  If 
  the 
  pencil 
  of 
  

   ions 
  coming 
  through 
  the 
  hole 
  were 
  indefinitely 
  thin, 
  and 
  if 
  

   all 
  the 
  ions 
  travelled 
  with 
  the 
  same 
  velocity 
  in 
  the 
  same 
  

   direction, 
  the 
  transference 
  of 
  the 
  charge 
  from 
  the 
  disk 
  to 
  the 
  

   cylinder 
  would 
  be 
  quite 
  abrupt. 
  With 
  a 
  magnetic 
  force 
  less 
  

   than 
  a 
  certain 
  value, 
  all 
  the 
  charge 
  would 
  be 
  on 
  the 
  disk, 
  

   while 
  with 
  a 
  force 
  greater 
  than 
  this 
  all 
  the 
  charge 
  would 
  be 
  

  

  