﻿Radiation 
  in 
  a 
  Magnetic 
  Field, 
  351 
  

  

  and 
  

  

  S 
  = 
  f</> 
  (x) 
  sin 
  kxdx 
  y 
  

  

  the 
  integration 
  extending 
  over 
  the 
  whole 
  spectrum. 
  

   But 
  by 
  Fourier's 
  formula 
  

  

  /"•to 
  p 
  » 
  

  

  <f>{x) 
  = 
  1 
  cos 
  kosdk 
  + 
  I 
  S 
  sin 
  &# 
  d£ 
  ; 
  

  

  Jo 
  Jo 
  

  

  so 
  that 
  if 
  C 
  and 
  S 
  are 
  both 
  known, 
  <f>{x) 
  can 
  be 
  determined. 
  

   In 
  general 
  this 
  is 
  not 
  the 
  case 
  unless 
  another 
  relation 
  between 
  

   C 
  and 
  S 
  is 
  given. 
  Such 
  a 
  relation 
  is 
  furnished 
  by 
  the 
  " 
  phase 
  

   curve/' 
  which 
  gives 
  the 
  displacement 
  of 
  the 
  fringes 
  from 
  the 
  

   position 
  they 
  would 
  have 
  occupied 
  had 
  the 
  source 
  been 
  homo- 
  

   geneous. 
  If 
  8 
  is 
  this 
  displacement 
  and 
  = 
  27rS/\, 
  then 
  

  

  C 
  = 
  Vcos0 
  and 
  S 
  = 
  Vsin<9. 
  

  

  In 
  general 
  the 
  curve 
  is 
  troublesome 
  to 
  obtain, 
  on 
  account 
  

   of 
  the 
  difficulty 
  in 
  securing 
  a 
  sufficiently 
  homogeneous 
  com- 
  

   parison 
  source 
  ; 
  but 
  in 
  the 
  present 
  instance 
  this 
  is 
  furnished 
  

   by 
  the 
  non-magnetized 
  radiations 
  *. 
  

  

  Usually, 
  however, 
  the 
  assumption 
  was 
  made 
  that 
  the 
  spec- 
  

   trum 
  was 
  symmetrical, 
  and 
  in 
  only 
  a 
  few 
  cases 
  was 
  the 
  

   solution 
  verified 
  by 
  the 
  complete 
  analysis. 
  In 
  this 
  simpler 
  

   form 
  we 
  have 
  = 
  0, 
  S 
  = 
  ; 
  and 
  C 
  = 
  V, 
  whence 
  

  

  *w 
  = 
  f 
  

  

  Jo 
  

  

  V 
  cos 
  kx 
  dk. 
  

  

  This 
  integral 
  may 
  frequently 
  be 
  calculated 
  when 
  V 
  can 
  be 
  

   expressed 
  in 
  simple 
  analytical 
  form 
  as 
  a 
  function 
  of 
  k. 
  In 
  

   general 
  this 
  is 
  not 
  the 
  case, 
  and 
  it 
  was 
  for 
  the 
  solution 
  of 
  

   such 
  problems 
  that 
  the 
  harmonic 
  analyser 
  f 
  was 
  devised. 
  

   The 
  curve 
  V=/(&) 
  is 
  u 
  fed 
  " 
  to 
  the 
  machine, 
  which 
  then 
  

   draws 
  the 
  curve 
  y 
  = 
  <p(x), 
  the 
  whole 
  operation 
  taking 
  but 
  a 
  

   few 
  minutes. 
  

  

  It 
  was 
  found 
  on 
  completing 
  the 
  analysis 
  of 
  some 
  fifty 
  or 
  

   more 
  visibility-curves, 
  that 
  the 
  resulting 
  spectra 
  could 
  be 
  

   classified 
  under 
  three 
  types 
  ; 
  there 
  were 
  some 
  interesting 
  

   variations 
  which 
  would 
  merit 
  a 
  separate 
  investigation, 
  but 
  

   most 
  of 
  the 
  cases 
  could 
  be 
  identified 
  at 
  a 
  glance. 
  

  

  The 
  three 
  types 
  of 
  visibility-curve 
  are 
  given 
  in 
  figs. 
  2, 
  3, 
  

  

  * 
  These 
  are 
  not 
  always 
  sufficiently 
  simple 
  as 
  in 
  the 
  case 
  of 
  the 
  green 
  

   thallium 
  line. 
  

   t 
  Phil. 
  Mag., 
  Jan. 
  1898. 
  

  

  2 
  B 
  2 
  

  

  