48 PROFESSOR KELLAND ON THE POLARIZATION OF LIGHT 



Hence the sum of the quantities, or the value of rj is reduced to the fol- 

 lowing very simple expression, 



Or Cl (r ( /T 1 _ x . , , _, . , .* _ . . . /i, "I iM / d I d rv\ 



-: =-?:{ (I R)sm0 + Tsm0 / cosa T'sm0'smo > + ( |sui0 



dP 2 I J e \dx dx) 



' sin0, cos 0-- sin 0' sin tf-DI^-D/r,* Q,,(a,-o) (9). 







d 2 a 

 This value of -j-g- is now in its simplest form involving only the vibrations and 



their differential coefficients with respect to x. 

 To find the value of . 



By interchanging y and x, y 1 and a/, ft and a, ft and a! in equation (5), we 

 have the folio whig expression as the first value. 



NOW 



+ 2 (0 r + r 2 sin 2 + jo 2 cos 2 0) 5 R 





cos 



^i 2 ) sin 2 5 I cos + 2 ((pr + ^p 2 ) cos 2 (p S I cos (J> + Sic. 



We have not deemed it requisite to work out this result at full ; a glance 

 will serve to shew that it is right, when AVC add that, by the first of equations (7) 



2l ( ( h r + ( ^p^ S in 2 ^= J and by the last 2 2 (0 r + ^L *) sin 2 ^f=-~ ; and like re- 



T & 2t T i & 



suits obtain for 2 (0 r + -^-p*) sin * i and 2 (0 r + J a' 2 ) sin Az. 



Again, 2 5 SxdySa differs from (b) in having 5 a in place of S /3, or, which 



is the same thing, (I - R) sin in place of (I + R) cos $ ; and in having a term con- 

 taining R, .'. by (b) we obtain, 



e \dx ax 



