Kerr  Effects  in  the  Infra-red  Spectrum.  45 
Method. 
The  method  adopted  has  some  points  in  common  both  with 
the  one  due  to  De  la  Provostaye  and  Desains  *  and  that  used 
by  Moreau  *.  A  beam  of  light  after  passing  in  turn  through 
a  polarizer,  rotating  substance  between  the  poles  of  an 
electromagnet,  and  analyser,  was  dispersed  and  formed  into 
a  spectrum  in  which  was  placed  the  strip  of  a  bolometer. 
Any  rotation  of  the  plane  of  polarization  such  as  would  be 
caused  by  exciting  the  magnet,  would  then  cause  an  increase 
or  diminution  of  intensity  of  the  beam  transmitted  by  the 
analyser,  which  effect  could  be  measured  for  any  desired 
wave-length  by  the  bolometer  and  the  rotation  calculated 
accordingly. 
If  the  principal  planes  of  the  polarizer  and  analyser  make 
an  angle  a,  the  intensity  at  any  chosen  wave-length  as 
measured  by  the  bolometer  may  be  represented  by 
I  =  kV  cos  2a, 
where  I'  is  the  intensity  of  this  radiation  incident  "on  the 
analyser,  and  k  takes  account  of  absorption.  Then  any  small 
rotation  8  of  the  plane  of  polarization,  produced  either  by 
turning  the  polarizer,  or  by  the  action  of  the  magnetic  field, 
will  produce  a  change  in  I,  disregarding  signs, 
dl  =  28kV  sin  a  cos  a, 
or,  dividing  by  I  and  solving  for  8, 
S=i?  cot «  radians,  or  ^cot«  degrees. 
2    1  IT     I  ° 
As  pointed  out  by  De  la  Provostaye  and  Desains,  dl  will 
evidently  be  greatest  for  a.  =  45°,  which  is  accordingly  the 
angle  chosen.  For  any  rotation  the  value  of  8  may  be 
obtained,  if  a  =  45°,  from 
dl^M' jcos2  (45°±o)-cos245°j-  =  +  £  sin  28 .  fcT, 
or 
8=  I  sin   lj. 
In  this  way  the  magnetic  rotation  for  any  chosen  wave- 
length may  be  determined  by  a  measurement  of  the  intensity  1 
of  that  wave-length  in  the  spectrum,  and  of  the  change  in 
intensity  dl  when  the  magnet  is  excited,  or  bettor,  when  it  is 
reversed,  since  this  gives  a  doubled  effect.  Both  L  and  </l 
are  determined  as  galvanometer-deflexions,  and  from  their 
*   Loc.  cif. 
