410 PROFESSOR KELLAND ON FRESNEL'S FORMULA FOR THE 



„_ , . Ka^ „„ . ^ . KiT" dl 1 . _, . ^^ ^ dR 1 . ^ . ^^ ^, 



= — 2Isma)sm'— H— + 2Rsm(psm2— s — + -r- • - sin sin Kir' j smffismKa/' ^ 



^2 ^ 2 dx e ^ dx e ^ j 



5^=(5I + 5R)cos0 



^ , „^ . Ka?- l«;i . „ , „„ . aKir" 1(7R . „ „, 

 =cosd) -2Isin2 --— + -— -sinKir'-2Rsm^— ^r— + --^smK^' 

 ^1 2 edx 2 e dx ) 



5a,= aTsm0' + 5T, 



=sm 0' {c. cos (e,ir,+ 5ir,+/jr,+ 5y, + ci!+^)-c cos e,a7,+/y, + c<+5f} 



+ C«~"'''''"^*'''cos(/y, + 5y, + c!; + /i + »i,)-Ce-"'''^'cos/,2^, + ci! + /* + i, 



= -2 T sinrf.' sin2^ + ^- - sm(/)'sinKir"-T,(l- -"''^"cos/c/y)+ ^' Je-^-^^sin/rfy 



5ft=5Tcos0' 



= — 2 T cos d)' sm2 — jr — i- - t— cos (p %va.e,ox 



Ky \d1 ^, . ^^ „ 

 = — 2 T cos rf)' sin^ -^r- + - -^- cos 9' sin K. «^ 



13. The equation of motion in the upper surface parallel to the axis of x is 



^=-zUr + ^8x^\ §a+l'^ 8x82,8^ 

 df \ r / r 



d,V 



+ 2 Uf' + i-J^SarA (a,-o) + 2-^5yay(ft-j8) 



retaining the limitations to 2. 



-"o 



But 2 (<pr+'^ 8x^^ 8a = 



2 (^r + ^ 8 af^ cos^(p + 8 f sin ^(p\ sin^x j -21 sin^-^-H- j j^sin Ka^j 

 + 2 ((pr + ^8 X'" cos ^(p + 8^" sin ^c/)) sin^x |2 Rsin^^-^ ^sinKa"j 

 ^2 ^9, + ^'- 5^^) X j-I,.(l-.-"''%os/5y)j 



= -| sin (sin 20 - 2 cos 20) (I - R) 



+ -sin0(sin^0-2cos=0) (^-J^j-DI- 



