﻿394 
  Prof. 
  A. 
  Anderson 
  on 
  the 
  Problem 
  of 
  Tico 
  and 
  

   Thus 
  

  

  L 
  c 
  . 
  AIi 
  J 
  Lc 
  c 
  AI 
  X 
  . 
  BIj 
  J 
  ' 
  

  

  c 
  2 
  — 
  B 
  2 
  a?c 
  

  

  or, 
  since 
  AI^ 
  — 
  » 
  and 
  BI 
  2 
  = 
  c 
  — 
  g 
  — 
  ™, 
  

  

  "-A[»A 
  + 
  '-]- 
  B 
  Pf 
  + 
  ^fc?( 
  + 
  -]- 
  

  

  As 
  an 
  example, 
  suppose 
  we 
  have 
  three 
  small 
  equal 
  con- 
  

   ducting 
  spheres, 
  whose 
  centres 
  are 
  at 
  the 
  corners 
  of 
  an 
  

   equilateral 
  triangle 
  the 
  length 
  of 
  whose 
  side 
  is 
  c. 
  The 
  terms 
  

  

  we 
  have 
  found 
  will 
  give 
  q 
  n 
  , 
  g 
  12 
  , 
  (Ju 
  correctly 
  to 
  ( 
  - 
  ) 
  • 
  

  

  A 
  2u 
  2 
  2a 
  3 
  \ 
  

  

  a 
  2 
  /, 
  a 
  2a 
  3 
  \ 
  

  

  ^12 
  = 
  ^13 
  = 
  923= 
  -■" 
  [1- 
  - 
  + 
  - 
  c2 
  -j, 
  

  

  from 
  which 
  we 
  obtain 
  the 
  coefficients 
  of 
  potential 
  

  

  1 
  (\ 
  2« 
  2 
  2«- 
  ] 
  \ 
  

  

  ^11 
  = 
  ^2=^=^(1-^+^, 
  

  

  1 
  /, 
  da 
  a 
  2 
  16ot\ 
  

   Pu=Pu=Px= 
  Ta 
  (1+ 
  - 
  + 
  6 
  , 
  - 
  -jT). 
  

  

  The 
  energy 
  of 
  the 
  system, 
  each 
  sphere 
  being 
  supposed 
  to 
  

   have 
  unit 
  charge, 
  is 
  

  

  1/3 
  da 
  15« 
  3 
  \ 
  

   a\2 
  + 
  c 
  ~ 
  c 
  3 
  /' 
  

  

  and 
  the 
  force 
  acting 
  on 
  one 
  of 
  them 
  is 
  

  

  \/3 
  

   the 
  force 
  being 
  — 
  g- 
  in 
  the 
  case 
  of 
  point 
  charges. 
  

   c 
  

  

  By 
  the 
  above 
  method 
  the 
  potential 
  due 
  to 
  two 
  charged 
  

   conducting 
  spheres 
  at 
  an 
  external 
  point 
  can 
  be 
  written 
  down 
  

   easily. 
  Let 
  the 
  centres 
  of 
  the 
  spheres 
  be 
  A 
  and 
  B, 
  their 
  

   radii 
  a 
  and 
  b, 
  the 
  distance 
  between 
  the 
  centres 
  c, 
  and 
  the 
  

   potentials 
  U 
  and 
  V. 
  Let 
  the 
  image 
  of 
  an}' 
  external 
  point 
  

   P 
  in 
  B 
  be 
  P„ 
  the 
  image 
  of 
  P, 
  in 
  A, 
  P 
  2 
  , 
  the 
  image 
  of 
  P 
  2 
  in 
  B, 
  

   P 
  ;5 
  , 
  and 
  so 
  on. 
  Also, 
  let 
  the 
  image 
  of 
  P 
  in 
  A 
  be 
  Q 
  1? 
  the 
  

   image 
  of 
  Q 
  l 
  in 
  B, 
  Q 
  2 
  , 
  the 
  image 
  of 
  Q 
  2 
  in 
  A, 
  Q 
  3 
  , 
  and 
  so 
  on. 
  

  

  