Kerr  Effects  in  the  Infra-red  Spectrum*  55 
When  set  with  principal  plane  parallel  to  that  of  polarizer 
or  analyser,  respectively,  the  intensity  will  be  given  by 
or 
I8=i  KiKaKs  V  (cos2  *  +  b  sin2  «), 
I4  =  ^K,K2K3I/  (cos2  a -I- a  sin2  a). 
Making  a  =  45°,  and  dropping  the  second  terms  of  the 
four  equations,  as  they  may  be  neglected  with  respect  to  the 
first,  a  and  b  become  on  solving, 
a  =  I1/Is  =  IJ/I4,     6=I2/I3=I2/I4, 
and  hence  may  be  readily  measured  as  the  ratio  o£  two 
intensities. 
It  might  reasonably  be  expected,  since  the  plates  were  set 
at  the  same  angle  for  all  wave-lengths,  that  a  and  b  would 
depend  largely  on  the  wave-length  tested.  Such,  however, 
has  not  been  found  to  be  the  case,  at  least  to  any  appreciable 
extent,  over  the  range  of  spectrum  for  which  a  nicol  was 
transparent  enough  to  be  used  in  measuring  them,  say  as  far 
as  A,  =  2*5  [jl.  Then,  since  from  there  to  A,  =  4*3  //.  the  varia- 
tion in  the  refractive  index  of  glass,  and  hence  of  the 
polarizing  angle,  is  small,  a  and  b  could  be  regarded  as  con- 
stant, within  the  limits  of  accuracy  required  in  the  work,  over 
the  whole  range  of  spectrum  for  which  it  was  possible  to 
measure  rotations.  This  was  undoubtedly  because  the  varia- 
tion of  the  angle  of  complete  polarization  with  wave-length 
was  much  smaller  than,  the  unavoidable  variation  of  the 
angle  of  incidence  over  the  surface  of  the  plates.  The  tests 
gave  the  value  of  a  as  *025  and  b  as  *035,  making  a  correction 
of  12-8  per  cent,  to  be  applied  to  the  rotations  as  determined  by 
the  expressions  I  dl/L  or  I-  sin-1  dl/I ;  for  while  the  correction 
has  been  calculated  only  for  small  angles  of  rotation,  it  may 
be  applied  to  any  rotation  actually  measured,  with  sufficient 
accuracy.  With  regard  to  the  magnitude  of  the  correction, 
it  may  be  noted  too  that,  so  long  as  it  applies  equally  fco 
all  wave-lengths,  its  actual  value  is  a  matter  o:  secondary 
importance. 
The  use  of  non-parallel  light  resulted  in  the  edges  ot^  the 
beam  being  polarized  in  slightly  different  planes  from  that  of 
the  centre.  This  would  cause  an  effective  variation  of  a  Eor 
different  parts  of  the  beam,  but  such  small  uncertainty  would 
be  less  than  that  of  the  determination  of  x  itself.  Fortu- 
nately such  errors,  as  well  as  those  incidental  to  the  setting  o( 
the  polarizer  and  analyser,  were  also  of  secondary  importance, 
being  non-selective  in  character.  To  be  Eree  from  elliptical 
polarization  which  might  resull  from  reflexion  at  the  mirrors 
