332  The  Hon.  J.  W.  Strutt  on  the  Reflection  and 
similar  to  that  used  for  vibrations  normal  to  the  plane  of  inci- 
dence and  with  the  same  notation,  we  find  that  the  intensity  of 
the  reflected  light  is  represented  by  tan  (g—  j  ),  where 
cot g  —  cos  (ot—u)  sin  2  tan-1  ( ^ ^  ), 
\Rcos0a 
while  the  change  of  phase  d!  is  given  by 
tan  d'=  sin  (a  —  u)  tan  2  tan-1  ( ~ ^ ). 
\K  cos  6  J 
However,  what  we  should  most  require  for  comparison  with 
experiment  relates  to  the  relative  intensities  and  changes  of 
phase  of  the  two  polarized  components ;  and  these  are  directly 
obtained  by  Eisenlohr  by  transforming  FresneFs  corresponding 
expression*  after  the  introduction  of  the  complex  refractive  index. 
If  the  ratio  of  the  amplitudes  be  called  tan  /3,  we  have 
cos  2/3  =  cos  (a  +  u)  sin  2  tan- 1 1  -= ^  V 
\cK  cos  0/ 
tan  (d'—d)=  sin  (a  +u)  tan  2  tan-1  ( -= ^), 
\  CiX  COS  C7/ 
c  and  u  being  determined  as  before.  Eisenlohr  has  compared 
these  formulas  with  measurements  made  by  Jamin  relating  to 
the  so-called  principal  angle  of  incidence  (making  d'  —  d  equal  to 
rrr 
-)  and  the  corresponding  ratio  of  amplitudes,  and  has  deduced, 
as  I  have  already  remarked,  values  of  the  constants  which  make 
the  real  part  of  y?  negative,  and  are  therefore  inadmissible.  An- 
other argument  leading  to  the  same  conclusion  is  as  follows. 
Consider  a  case  in  which  fi2  is  so  considerable  that  c  is  sen- 
sibly equal  to  unity  and  a.  to  zero,  or,  in  other  words,  so  refrac- 
tive that  the  entering  ray  is  always  sensibly  parallel  to  the  nor- 
mal of  the  surface;  and  let  the  incident  ray  strike  the  surface 
at  that  particular  angle  which  gives  a  relative  phase-difference 
of  a  quarter  of  a  period.  The  angle  in  question  is  that  deter- 
mined by 
sm2fl 
cR  cos  6       ' 
so  that 
cos  2/3=  cos  a. 
Since  a  must  lie  between  0  and  —  j,  cos  2/5  must  be  comprised 
*  cos(4+fl) 
cos  (0,-0)' 
