﻿constituting 
  Full 
  Radiation 
  or 
  White 
  Light. 
  791 
  

  

  putting 
  n 
  = 
  0. 
  Transforming 
  this 
  so 
  as 
  to 
  obtain 
  the 
  energy 
  

  

  between 
  a 
  and 
  « 
  + 
  <:/« 
  where 
  a 
  = 
  ^, 
  we 
  get 
  

  

  A, 
  

  

  where 
  2h 
  = 
  ^r—^. 
  

  

  -TTt/ 
  

  

  Hence, 
  dropping 
  factors 
  outside 
  the 
  integral 
  sign, 
  the 
  

   forms 
  of 
  the 
  pulses 
  are 
  given 
  by 
  

  

  — 
  5—n 
  

  

  Putting 
  n 
  = 
  l 
  for 
  Lord 
  Rajleigh's 
  formula, 
  the 
  expressions 
  

   reduce 
  to 
  

  

  b'-a^^ 
  ^ 
  2Kv 
  

  

  and 
  

  

  Taking 
  Planck's 
  formula 
  for 
  the 
  distribution 
  of 
  energy, 
  

  

  (?A9— 
  1 
  

  

  this 
  transforms 
  into 
  

  

  F(cc)du 
  = 
  —. 
  -, 
  where 
  2h 
  =-r-r> 
  as 
  before. 
  

  

  Extracting 
  the 
  square 
  root 
  of 
  this 
  expression 
  by 
  expanding 
  

   the 
  denominator 
  in 
  ascending 
  powers 
  of 
  e~*% 
  substituting 
  

   the 
  result 
  in 
  (10) 
  and 
  (11), 
  and 
  integrating 
  term 
  by 
  term, 
  

   we 
  get 
  for 
  the 
  form 
  of 
  the 
  pulses 
  

  

  cos 
  f 
  5 
  , 
  _i 
  ./; 
  ) 
  cos 
  (5 
  _, 
  ,v 
  ) 
  

  

  3 
  sm 
  (2 
  5l>) 
  

  

  ^^'"^ 
  (A2 
  + 
  .v;2)f 
  ~^2 
  (32/^^ 
  + 
  ^') 
  

  

  To 
  the 
  eye 
  these 
  pulses 
  have 
  much 
  the 
  same 
  form^as 
  the 
  

   simple 
  ones 
  obtained 
  from 
  Lord 
  Rayleigh^s 
  formula. 
  

  

  