412 PROFESSOR KELLAND ON FRESNEL'S FORMULA FOR THE 





0'/ 





= — 2" ^ ^^^ r cos20' + — -i — sm 0' cos '0' 



By adding this term to that just found, we get 



W/(a,-a)-o A sind)' + ^— sin0'-D T 



Hence 



14. From this equation we obtain, by interchanging the quantities (I- R) sin 0, 

 T sin 0' &c. 



-^= - 2 (I-I^ sin + T sin 0') 



e ^ \dx dx ) e, ^ dx 

 -D,T-DI, 

 By subtraction 



d^a d?a, _ 



= -(Q>+Q)(a-a.) 



Now Q, + Q differs from e by a finite quantity: hence this equation can only be. 

 satisfied by making 



d"^ a^ d^a 

 'd7~Tf^^ 



the second of which equations is a consequence of the first. 

 By adding the two equations we get 



d^ a d^ a. 



^+^'=-c2(I-Rsin0 + Tsin0') 



+ (Q - Q.) («-«.)-- 2 D.I,- 2 D,T, 



2M . , /dl dR\ 2M, dT 



+ -— sin0 I V- - -7- ) -f- sm 0' -T- 



e ^ \dx dx) e^ ^ dx 



