﻿Properties 
  of 
  Films 
  of 
  Magnetic 
  Metals. 
  853 
  

  

  and 
  minor 
  axis 
  twice 
  their 
  difference. 
  The 
  ratio 
  of 
  minor 
  

   to 
  major 
  axis 
  is 
  then 
  

  

  A 
  r 
  — 
  Ai 
  

  

  E 
  = 
  

  

  A 
  r 
  + 
  A/ 
  

  

  This 
  we 
  designate 
  the 
  ellipticity 
  of 
  the 
  vibration. 
  If 
  

   A 
  r 
  and 
  Aj 
  be 
  equal 
  we 
  have 
  zero 
  ellipticity, 
  a 
  plane 
  vibration. 
  

   After 
  passing 
  a 
  distance 
  x 
  through 
  a 
  medium 
  possessing 
  the 
  

   extinction 
  coefficients 
  k' 
  r 
  and 
  hi 
  (defined 
  in 
  terms 
  of 
  the 
  

   amplitude) 
  the 
  two 
  vibrations 
  will 
  have 
  the 
  amplitudes 
  

   respectively 
  

  

  A 
  r 
  e~ 
  JcrX 
  and 
  A*"** 
  

  

  and 
  will 
  combine 
  to 
  form 
  an 
  elliptic 
  vibration 
  possessing 
  as 
  

   ratio 
  between 
  the 
  axes 
  the 
  value 
  

  

  E= 
  A 
  r 
  e- 
  k 
  r*-A 
  l 
  e-^ 
  x 
  

   A 
  r 
  e~ 
  krX 
  +A 
  t 
  e- 
  k 
  ix' 
  

  

  For 
  A 
  r 
  and 
  Ai 
  equal, 
  which 
  is 
  the 
  case 
  at 
  the 
  incident 
  

   face 
  of 
  the 
  film, 
  when 
  there 
  is 
  no 
  ellipticity 
  of 
  the 
  reflected 
  

   light, 
  this 
  equation 
  readily 
  takes 
  the 
  form 
  

  

  - 
  *» 
  o 
  

  

  -Ei 
  - 
  hi-k 
  r 
  ki-kr 
  r 
  

  

  e 
  ~ 
  -\-e 
  2 
  

  

  = 
  tanh 
  l 
  9 
  L 
  r 
  x 
  . 
  

  

  For 
  values 
  of 
  E 
  ^ 
  *15 
  we 
  may 
  write 
  this 
  (within 
  an 
  error 
  

   of 
  less 
  than 
  one 
  per 
  cent.) 
  

  

  Within 
  the 
  accuracy 
  of 
  our 
  measurements 
  (which 
  do 
  not 
  

   exceed 
  an 
  ellipticity 
  of 
  '02) 
  the 
  ellipticity 
  arising 
  from 
  dif- 
  

   ferential 
  absorption 
  in 
  the 
  films 
  should 
  therefore 
  be 
  propor- 
  

   tional 
  to 
  their 
  thickness. 
  For 
  those 
  films 
  in 
  which 
  the 
  

   ellipticity 
  is 
  proportional 
  to 
  the 
  thickness, 
  the 
  tabulated 
  values 
  

   of 
  the 
  ellipticity 
  divided 
  by 
  the 
  thickness 
  represent 
  therefore 
  

   ki 
  — 
  k 
  r 
  

  

  