﻿708 
  Prof. 
  J. 
  de 
  Kowalski 
  and 
  Dr. 
  U. 
  J. 
  Rappel 
  

  

  on 
  

  

  Formulw 
  for 
  the 
  Electrical 
  Intensity 
  hetween 
  Spherical 
  

   Electrodes. 
  

  

  The 
  formulae 
  for 
  the 
  electrical 
  intensity 
  between 
  two 
  spheres 
  

   of 
  the 
  same 
  radius 
  have 
  been 
  given 
  already 
  by 
  Kirchhoff 
  *, 
  and 
  

   have 
  been 
  lately 
  brought 
  into 
  a 
  more 
  elegant 
  form 
  by 
  

   Russell. 
  

  

  If 
  the 
  two 
  spheres 
  have 
  respectively 
  a 
  potential 
  of 
  Yi 
  and 
  

   y2 
  the 
  following 
  formula 
  applies 
  : 
  — 
  

  

  a 
  ' 
  l-q 
  1 
  (l 
  + 
  q'^-^y^ 
  ' 
  

  

  where 
  a 
  is 
  the 
  radius 
  of 
  the 
  sphere, 
  and 
  q 
  defined 
  by 
  the 
  

   following 
  equation 
  

  

  ^ 
  A 
  \/A2-4a2 
  

  

  2q= 
  - 
  — 
  , 
  

  

  ^ 
  a 
  a 
  

  

  where 
  A 
  represents 
  the 
  distance 
  between 
  the 
  centres 
  of 
  the 
  

  

  Y 
  

   spheres. 
  In 
  case 
  Yi= 
  — 
  V2=: 
  -^ 
  we 
  have 
  

  

  " 
  -I 
  / 
  

  

  ^max. 
  — 
  'A 
  

  

  where 
  

  

  when 
  X 
  represents 
  the 
  shortest 
  distance 
  betweeil 
  the 
  centres 
  

   of 
  the 
  spheres. 
  

  

  When 
  Vi 
  = 
  V 
  and 
  V2 
  = 
  0, 
  as 
  is 
  the 
  case 
  in 
  our 
  problem, 
  we 
  

   have 
  

  

  ^=y. 
  

  

  where 
  

  

  '^ 
  a' 
  \-q 
  1 
  (l+^4"-^)2^ 
  • 
  

  

  * 
  KirchhofF, 
  Crelle's 
  Journal, 
  p. 
  89 
  (1860\ 
  

  

  