﻿constituting 
  Full 
  Radiation 
  or 
  White 
  Light. 
  789 
  

  

  if 
  Ave 
  are 
  given 
  that 
  the 
  energy 
  between 
  a 
  and 
  u 
  + 
  dcc 
  is 
  

   proportional 
  to 
  F 
  (a) 
  du^ 
  we 
  have 
  

  

  (2) 
  

  

  F(a) 
  = 
  r 
  i 
  /(/^) 
  COS 
  aya 
  ^/ij 
  + 
  j^ 
  j 
  /(yLt) 
  sin 
  a//, 
  (^yU, 
  J 
  . 
  . 
  (^ 
  

  

  This 
  equation 
  solved 
  for 
  / 
  will 
  be 
  the 
  solution 
  of 
  the 
  

   problem. 
  

  

  Two 
  particular 
  solutions 
  may 
  very 
  easily 
  be 
  obtained, 
  

   first 
  when 
  the 
  pulse 
  is 
  an 
  even 
  function, 
  and 
  second 
  when 
  it 
  

   is 
  an 
  odd 
  function. 
  In 
  the 
  first 
  case 
  (2) 
  reduces 
  to 
  

  

  r/(/.)cos«;c.^/. 
  = 
  F(..)^ 
  .... 
  (3) 
  

  

  Jo 
  

  

  Jo 
  

  

  and 
  in 
  the 
  second 
  case 
  to 
  

  

  oo 
  

  

  f{fju) 
  sin 
  afi 
  dfM 
  = 
  F(a)^ 
  (4) 
  

  

  

  

  Now, 
  in 
  Fourier's 
  Theorem 
  

  

  (j)(ji) 
  = 
  - 
  I 
  da 
  \ 
  (f>(X) 
  COS 
  c<,(\— 
  cv) 
  dX, 
  

  

  "^ 
  J 
  J 
  -30 
  

  

  let 
  </)(ci') 
  be 
  equal 
  to 
  zero 
  if 
  a?<0, 
  and 
  be 
  equal 
  to 
  /[.x) 
  if 
  

   .u>0./'Then 
  we 
  have 
  

  

  1 
  r* 
  ^^ 
  L*^ 
  

  

  COS 
  ci{\^,ii)d\ 
  .... 
  (5) 
  

  

  is 
  equal 
  to/(.r) 
  for 
  positive 
  values 
  of 
  a? 
  and 
  equal 
  to 
  zero 
  for 
  

   negative 
  values 
  of 
  x. 
  Hence 
  

  

  -\ 
  da 
  \ 
  f(\) 
  cos 
  cc(\ 
  + 
  jj)d\ 
  .... 
  (6) 
  

  

  '^Jo 
  Jo 
  

  

  is 
  equal 
  to 
  zero 
  for 
  positive 
  values 
  of 
  <r. 
  

  

  Adding 
  and 
  subtracting 
  (5) 
  and 
  (6), 
  we 
  obtain 
  

  

  f(ai) 
  = 
  — 
  \ 
  cos 
  ax 
  da 
  I 
  /(X) 
  cos 
  a\ 
  dX 
  , 
  . 
  . 
  (7) 
  

  

  '^Jo 
  Jo 
  

  

  9 
  /» 
  00 
  /'CO 
  

  

  = 
  " 
  I 
  sin 
  ax 
  da 
  \ 
  /(A,) 
  sin 
  a\ 
  dX 
  . 
  . 
  . 
  (S) 
  

  

  '^ 
  Jo 
  Jo 
  

  

  for 
  positive 
  values 
  of 
  ^. 
  

  

  In 
  much 
  of 
  what 
  follows 
  we 
  shall 
  frequently 
  have 
  an 
  

   equation 
  involving 
  a 
  cosine 
  with 
  a 
  similar 
  one 
  involving 
  a 
  sine. 
  

  

  