404 PROFESSOR KELLAND ON FRESNEL'S FORMULA FOR THE 



J 



' + 2 



Similarly for the lower medium 



'^= - ^7T^+2(*n + ^a.;) sin Sp.lfT^ 



7. By substituting for -^ and -^^ their values, and caUing 



2(0r + -^5s2)sm^'p =P 



2 (0 r, + -*^-^ a 0/) sin ^ (), = P, 



l{(Pr + ^8z^) =Q 



r 



l{cpr,+ tlL8z,^) = Q^ 



we get -..7 = -^(7 + 7,) +^g^|'g- + Q,(7._7) 



-<^7.= -^(7 + X) +? ^+5^1:!!-'+ Q (7-7,) 



^ ^ da: e, ax 



0=i'(7-7,).?g^^S^.Q,(7,-7) 



By means of these equations we obtain 



«" (7 - 7.) - Q + Q, 7^,= O 



or (c'-Q-Q.)(7-X) = 0; 



. , P(/7 P, ^7, - 



And -T-^ + — T^ + Q-Q,(7-7) = 



From the nature of the functions we cannot have c2= Q + Q, , 



••• 7-X=0 

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



