Faraday  and  Kerr  Effects  in  the  Infra-red  Spectrum.     41 
its  expression  in  isosceles  functions  is 
and  its  harmonic  expression  is 
rir 
Hence  the  rth  component 
L  f  .             .         .  .  sin.Sr//.    sin  3rw/       p     "1 
-  <  sin  r/^  sm  ?W  + LZ +  &c.  > 
n       2(tanA  +  tanB)   f.  .  sm  Sr^u  sm  Srcot 
Ur  = s <  smru  sinrct)f+ rp; 
r  7rr2  L  & 
sin  5^Lt  sin  5^0)^      „ 
H ^ +&c 
■}■ 
If  7t  be  the  altitude  of  either  of  the  given  triangles,  then 
h—ju  tan  A=  (ir  —  /i)  tan  B, 
and  the  development  for  the  complete  wave  is 
2h        f  .         .  sin  2/u,  sin  2a>^ 
/(O  =  — ? \  "I  sin  /*  sm  <°t  + 
,  sin  3/Ltsin  3^6      p      1 
+ g: +4?-). 
III.    On  the  Faraday  and  Kerr  Effects  in  the  Infra-red 
Spectrum.     By  L.  E.  Ingersoll  *. 
Introduction. 
THE  aim  of  the  present  work  is  a  study  of  electromagnetic 
rotatory  dispersion,  particularly  in  the  infra-red  spectrum. 
Because  of  the  important  bearing  of  the  phenomenon  of 
magnetic  rotation  of  the  plane  of  polarization  of  light  in  the 
field  of  electro-optics,  the  subject  has  been  investigated  in  all 
its  various  aspects  by  many  observers  during  the  last  halt- 
century,  and  the  effects  of  the  different  factors  which  govern 
the  rotation,  such  as  strength  of  magnetic  field,  angle  o( 
incidence,  and  temperature,  carefully  determined.  The  most 
important  factor  of  all,  however,  if  one  considers  the  place  it 
must  have  in  any  explanation  of  the  phenomenon — the  depend- 
ence of  the  magnetic  rotation  on  wave-length,  or  magnetic 
rotatory  dispersion — has  been  studied  only  over  a  very  limited 
range   of  spectrum.     Thus  while  the  rotatory  dispersion  in 
*  Thesis  submitted  tor  the  Ph.D.  degree,  University  of  Wisconsin, 
1905.    Communicated  by  Prof.  C,  E.  Mendenhall, 
