404 PROFESSOR KEI.LAND ON FRESNEL'S FORMULjS FOR THE 



2 r ^ e ax 2 r e, dco / 



Similarly for the lower medium 



—4^= - =r^7 + 7, + 2(d)»-, + -i-— i-O;,-) sin 6p,--5-i^ 

 rf<^ 2 ' ^ r, '' ^'e, dx 



+ 2(d)r' + ^5s'-') sin5pl^ + 2(d)r + ^ac^)(7-7,) 

 r e dx r 



7. By substituting for -3-5- and ;' their values, and calling 



•S,{(pr + i^8d'-)&mSg =P 



2 (0 r, + -"^-^ ^ s/) sin 8g, = V, 



2{(pr + ^8z^) =Q 



r 



S(rf>r,+ -^a=;) =Q, 



we get -'''y=~2^y-'y'^+jdi'-v,di^'^'^'^'-'^^ 



^ r^ e\ X P<^7 P, 0^7, rx ^ X 



J e ax e, ax 



By means of these equations we obtain 



c'(7-T)-Q + y,7-T=0 

 or (c'-Q-Q,)(7-7,) = 0; 



P ^7 P, dy, 



And 7^ + trf^' + «-<^'('y-'^') = 



From the nature of the functions we cannot have 0^=0 + Q, , 



•■• 7— 7/=0 

 is the only mode of satisfying the first equation, and thus the second equation 



