410 PROFESSOR KELLAND ON FRESNEL'S FORMULiE FOR THE 



8a=idl-8R)smcl) + 8l, 



«T . . . Ka/ „„ . ^ . Ka/' dl 1 . ^ . ^^ dR 1 . ^ . ^^ 



= — 2Ism0sin2— s — l-2Ksxn©sm2 — ^r — + -j- • - sm0 sin Ka/ 7— • - sin ffl sm K a/' \ 



^2 ^ 2 dx e ^ dx e ^ j 



\-I,(l-e cosfOy)+j--je sm/Oy 



8^=idl + 8R)eos(p 



=cosd) )-2Ism2 — — _ + ---_sinKa/-2Rsm^— jr— + --— sinKj/'l 



5 a,= 5 T sin 0' + 5 T, 



=sin (^' {c . cos (g, x,-\-8x, ■\-fy, + ^y, + c i H-^f)— c cos e, ir, +fy, + c t+g} 



= -2T sincp' sm^^ + ^-^sm(j>'smKaf'-TXl-e-'^'^'eos/dy) + ^je-''^'^%m/dy 

 5i8,= 5Tcos0' 



= — 2 T cos ffi' sin^ —77 — I J — cos sin e.Ox 



^ 2 e^dx ^ 



^ . Kx" IdT ^, . ^^ „ 

 = — 2 T cos d)' sm2 -s- + - -r- cos 0' sm K x" 



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



^=^Ur^^8x^\ 8a+2'^8x8y8^ 

 df \ r ) r " 



+ 2 ^0/ + -^^^^) icc-a)+l^ 8af 81/ (^-^) 



retaining the limitations to 2. 

 But 2 (<pr + ^ 8xA 8a = 



2 ((f)r + — 8af^ cos ^ + 81/^ sin ^<pj sixKpx j -21 sin^— ^-H-- ^ sin K^c'j 



.+ 2Ur + ^8x"^cos'cf> + 8z/''sm^(l>^ sin0x J2 Rsin^^-^ ^sinKa^'j 



+ 2 (0r + ^'*5^^) X \-l,.(l-e-"'''eos/8y)\ 



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

 M . , _ „, ^ „_ /c?I (^R 



H Sin 



e 



</>(sin2</>-2cos^<^) (^-^)-DI, 



