﻿388 
  Prof. 
  A. 
  Anderson 
  on 
  the 
  Problem 
  of 
  Two 
  and 
  

  

  the 
  flame, 
  thus 
  causing 
  a 
  rise 
  in 
  temperature 
  of 
  the 
  latter. 
  

   The 
  temperature 
  is 
  highest 
  along 
  the 
  path 
  of 
  the 
  oxygen, 
  and 
  

   when 
  the 
  latter 
  flows 
  in 
  the 
  direction 
  of 
  the 
  substance 
  to 
  be 
  

   vaporized, 
  the 
  full 
  effect 
  of 
  the 
  temperature 
  is, 
  as 
  it 
  were, 
  

   concentrated 
  upon 
  it. 
  The 
  effect 
  is 
  greatest 
  near 
  the 
  base 
  

   of 
  the 
  flame, 
  where 
  combustion 
  is 
  only 
  beginning, 
  and 
  least 
  

   near 
  the 
  tip. 
  It 
  is 
  consequently 
  essential 
  that 
  the 
  oxygen, 
  

   prior 
  to 
  reaching 
  the 
  substance, 
  should 
  pass 
  through 
  a 
  region 
  

   of 
  the 
  flame 
  containing 
  unburnt 
  gases. 
  

  

  In 
  conclusion, 
  I 
  wish 
  to 
  thank 
  Lord 
  Rayleigh 
  for 
  having 
  

   provided 
  me 
  with 
  the 
  opportunity 
  of 
  paying 
  a 
  modest 
  

   tribute 
  to 
  the 
  work 
  of 
  one 
  who 
  came 
  so 
  near 
  to 
  discovering 
  

   spectrum 
  analysis. 
  

  

  Manchester, 
  Feb. 
  18, 
  1918. 
  

  

  XLIV. 
  On 
  the 
  Problem 
  of 
  Two 
  and 
  that 
  of 
  Three 
  Electrified 
  

   Spherical 
  Conductors. 
  By 
  Prof. 
  A. 
  Anderson, 
  M.A.* 
  

  

  WHEN 
  an 
  insulated 
  conducting 
  sphere 
  of 
  radius 
  a 
  is 
  

   charged 
  to 
  potential 
  A, 
  the 
  potential 
  V 
  T 
  due 
  to 
  the 
  

   charge 
  at 
  any 
  external 
  point, 
  P, 
  whose 
  distance 
  from 
  the 
  

   centre 
  of 
  the 
  sphere 
  is 
  r, 
  is 
  given 
  by 
  

  

  rV 
  = 
  a.A. 
  

  

  If 
  now, 
  charged 
  bodies 
  are 
  brought 
  into 
  the 
  field, 
  this 
  

   equation 
  no 
  longer 
  holds 
  : 
  we 
  have, 
  instead, 
  

  

  rV 
  + 
  aV' 
  = 
  rtA, 
  

  

  where 
  V 
  is 
  the 
  potential 
  that 
  the 
  introduced 
  bodies 
  have 
  

   at 
  P' 
  the 
  inverse 
  point 
  or, 
  as 
  we 
  may 
  call 
  it 
  for 
  shortness, 
  

   the 
  image 
  of 
  P 
  in 
  the 
  sphere. 
  A 
  has, 
  of 
  course, 
  altered 
  in 
  

   v;ilue 
  and 
  V 
  is, 
  as 
  before, 
  the 
  potential 
  due 
  to 
  the 
  charge 
  on 
  

   the 
  sphere. 
  

  

  This 
  equation 
  may 
  be 
  used 
  to 
  find 
  the 
  coefficients 
  of 
  capacity 
  

   and 
  induction 
  of 
  two 
  conducting 
  spheres. 
  

  

  Let 
  the 
  potentials 
  of 
  the 
  spheres 
  be 
  A 
  and 
  B, 
  their 
  centres 
  

   O 
  x 
  and 
  2 
  , 
  their 
  radii 
  a 
  and 
  6, 
  and 
  the 
  distance 
  apart 
  of 
  their 
  

   centres 
  c. 
  Also, 
  in 
  fig. 
  1, 
  let 
  L 
  be 
  the 
  image 
  of 
  O 
  x 
  in 
  B, 
  

   I 
  2 
  the 
  image 
  of 
  I 
  x 
  in 
  A, 
  I 
  3 
  the 
  image 
  of 
  I 
  2 
  in 
  B, 
  and 
  so 
  on, 
  

   I 
  M+ 
  i 
  in 
  either 
  sphere 
  being 
  the 
  image 
  of 
  I 
  n 
  in 
  that 
  sphere. 
  

   We 
  have 
  thus 
  a 
  series 
  of 
  points 
  I 
  l5 
  I 
  3 
  , 
  I 
  5 
  , 
  1 
  7 
  , 
  &c. 
  inside 
  the 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  