﻿Positive 
  Rays. 
  675 
  

  

  If 
  the 
  ions 
  travelled 
  without 
  deviation 
  parallel 
  to 
  the 
  axis 
  

   of 
  the 
  tunnel 
  in 
  N, 
  they 
  would 
  all 
  strike 
  against 
  the 
  disk 
  Q, 
  

   and 
  the 
  Faraday 
  cylinder 
  would 
  not 
  receive 
  any 
  charge. 
  If, 
  

   on 
  the 
  other 
  hand, 
  they 
  were 
  very 
  much 
  deflected 
  by 
  the 
  mag- 
  

   netic 
  field, 
  they 
  would 
  all 
  strike 
  against 
  the 
  Faraday 
  cylinder 
  

   and 
  the 
  disk 
  would 
  not 
  receive 
  any 
  charge. 
  If 
  we 
  measure 
  the 
  

   charges 
  received 
  by 
  the 
  disk 
  and 
  the 
  Faraday 
  cylinder 
  during 
  

   any 
  time, 
  the 
  ratio 
  of 
  the 
  charges 
  will 
  be 
  the 
  ratio 
  of 
  the 
  

   number 
  of 
  ions 
  which 
  strike 
  against 
  the 
  disk 
  to 
  the 
  number 
  

   striking 
  against 
  the 
  cylinder. 
  The 
  readings 
  of 
  the 
  electro- 
  

   scopes 
  do 
  not 
  give 
  us 
  directly 
  the 
  charges 
  received 
  by 
  the 
  

   systems 
  to 
  which 
  they 
  are 
  attached, 
  but 
  the 
  potentials 
  to 
  

   which 
  these 
  systems 
  are 
  raised. 
  We 
  can, 
  however, 
  if 
  we 
  know 
  

   the 
  ratio 
  of 
  the 
  potentials 
  easily 
  deduce 
  that 
  of 
  the 
  charges. 
  

   For 
  let 
  E^ 
  be 
  the 
  charge 
  and 
  potential 
  of 
  the 
  Faraday 
  

   cylinder, 
  E 
  2 
  , 
  V 
  2 
  the 
  corresponding 
  quantities 
  for 
  the 
  disk. 
  

  

  Thus 
  if 
  the 
  q's 
  represent 
  coefficients 
  of 
  capacity, 
  we 
  have 
  

  

  Ei 
  = 
  2iVi-f? 
  12 
  V 
  2 
  

  

  E 
  2 
  =<7i 
  2 
  Vi+? 
  2 
  V, 
  

   so 
  that 
  

  

  Ei_ 
  ?iVi 
  + 
  (7 
  12 
  V 
  2 
  n 
  

  

  E.-^+^V 
  W 
  

  

  To 
  determine 
  the 
  q's 
  by 
  experiment 
  we 
  proceed 
  as 
  follows. 
  

   Given 
  a 
  charge 
  to 
  the 
  disk, 
  the 
  cylinder 
  being 
  insulated 
  and 
  

   uncharged, 
  then 
  if 
  V/ 
  and 
  V 
  2 
  ' 
  are 
  respectively 
  the 
  potentials 
  

   of 
  the 
  cylinder 
  and 
  disk 
  as 
  determined 
  by 
  their 
  electroscopes, 
  

  

  91^1+912^2=0, 
  since 
  E 
  1= 
  0. 
  

  

  Thus 
  if 
  a 
  is 
  the 
  ratio 
  of 
  the 
  potential 
  of 
  the 
  cylinder 
  to 
  

   that 
  of 
  the 
  disk 
  when 
  the 
  cylinder 
  is 
  uncharged, 
  

  

  Similarly, 
  if 
  /3 
  is 
  the 
  ratio 
  of 
  the 
  potential 
  of 
  the 
  disk 
  to 
  

   that 
  of 
  the 
  cylinder 
  when 
  the 
  disk 
  is 
  uncharged, 
  we 
  have 
  

  

  Substituting 
  in 
  equation 
  (1) 
  we 
  have 
  

  

  Bi_fl 
  (Vi-«V 
  a 
  ) 
  

  

  E 
  2 
  a 
  Vs-zSVi 
  • 
  

  

  The 
  quantities 
  a 
  and 
  /3 
  are 
  very 
  easily 
  determined, 
  and 
  

  

  2 
  Y 
  2 
  

  

  