﻿Cloud 
  of 
  similar 
  small 
  Particles 
  of 
  any 
  Shape. 
  381 
  

   For 
  the 
  sphere 
  {e 
  = 
  0} 
  

  

  L 
  = 
  M 
  = 
  N==~ 
  (30) 
  

  

  In 
  the 
  case 
  of 
  a 
  very 
  elongated 
  ovoid, 
  L 
  and 
  M 
  approximate 
  

   to 
  the 
  value 
  2ir, 
  while 
  N 
  approximates 
  to 
  the 
  form 
  

  

  N=4^(log|-l), 
  .... 
  (31) 
  

  

  vanishing 
  when 
  e=l. 
  It 
  appears 
  that, 
  when 
  K'/K 
  is 
  finite, 
  

   mere 
  elongation 
  does 
  not 
  suffice 
  to 
  render 
  A 
  and 
  B 
  negli- 
  

   gible 
  in 
  comparison 
  with 
  C. 
  The 
  limiting 
  value 
  of 
  C 
  : 
  A 
  is 
  

   in 
  fact 
  J(l-fK'/K). 
  If, 
  however, 
  as 
  for 
  a 
  perfectly 
  con- 
  

   ducting 
  body, 
  K' 
  = 
  x>, 
  then 
  becomes 
  paramount, 
  and 
  the 
  

   simplified 
  values 
  alread}' 
  given 
  for 
  this 
  case 
  acquire 
  

   validity*. 
  

  

  Another 
  question 
  which 
  naturally 
  presents 
  itself 
  is 
  whether 
  

   a 
  want 
  of 
  equality 
  among 
  the 
  coefficients 
  A, 
  B, 
  C 
  interferes 
  

   with 
  the 
  relation 
  between 
  attenuation 
  and 
  refractive 
  index, 
  

   explained 
  in 
  my 
  paper 
  of 
  1899 
  f 
  . 
  The 
  answer 
  appears 
  to 
  

   be 
  in 
  the 
  affirmative, 
  since 
  the 
  attenuation 
  depends 
  upon 
  

   A 
  2 
  + 
  B 
  2 
  + 
  C 
  2 
  , 
  while 
  the 
  refractive 
  index 
  depends 
  upon 
  

   A-f-B-i-O, 
  so 
  that 
  no 
  simple 
  relation 
  obtains 
  in 
  general. 
  

   But 
  it 
  may 
  well 
  be 
  that 
  in 
  cases 
  of 
  interest 
  the 
  disturbance 
  

   thus 
  arising 
  is 
  not 
  great. 
  

  

  The 
  problem 
  of 
  an 
  ellipsoidal 
  particle 
  of 
  uniform 
  dielectric 
  

   quality 
  can 
  be 
  no 
  more 
  than 
  illustrative 
  of 
  what 
  happens 
  

   in 
  the 
  case 
  of 
  a 
  molecule 
  ; 
  but 
  we 
  may 
  anticipate 
  that 
  the 
  

   general 
  form 
  with 
  suitable 
  values 
  of 
  A, 
  B, 
  C 
  still 
  applies, 
  

   except 
  it 
  may 
  be 
  under 
  special 
  circumstances 
  where 
  reso- 
  

   nance 
  occurs 
  and 
  where 
  the 
  effective 
  values 
  of 
  the 
  co- 
  

   efficients 
  may 
  vary 
  greatly 
  with 
  the 
  wave-length 
  of 
  the 
  

   light. 
  

  

  * 
  But 
  the 
  particle 
  must 
  still 
  be 
  small 
  relatively 
  to 
  the 
  wave-length 
  

   within 
  the 
  medium 
  of 
  which 
  it 
  is 
  composed. 
  

  

  t 
  An 
  equivalent 
  formula 
  was 
  given 
  by 
  Lorenz 
  in 
  1890, 
  'CEuvres 
  

   Scientifiques,' 
  t. 
  i. 
  p. 
  496, 
  Copenhagen, 
  1898. 
  See 
  also 
  Schuster's 
  

   ' 
  Theory 
  of 
  Optics,' 
  2nd 
  ed. 
  p. 
  326 
  (1909). 
  

  

  