514 PROFESSOR KELLAND ON THE VIBRATIONS OF 



+ ~e ~d~x COS ^' COS 6 sin kf } + 2 "7;- sin 0' cos $' (-o 2 +jw 2 ) (2 T' cos 0' sin & sin 2 y 



the sum of which is 



2 (Qr' + p^ (-2 T sin 0, cos sin 2 ^ + 2 T' sin 0' sin & sin 2 

 / 2t 2 



1 < T 1 </ T' 



+ - - sin 0, cos 6 sin & y e -- - sin 0' sin 6' sin &' o) 

 e, dx e' dx 



^2 .2 Al // T 



^Tsm0 /C osO+ -T'sind)'sine' + ' si 

 * ^ e t dx 



M' rfT' . ,, . ^ F, rfT v 



sm ffl' sin & ' 



X - - 

 ^ rfa: / dy 



Lastly, 2 (^ / + &JL 8 ^ ( a/ - a) = Q^ (a, - a). 



Hence, adding these terms together, we get 

 d*a c 2 fc . T . M . . (dl 



M A/ T 



^ ' sin (/>, cos 



, 

 e' dx f dy f dy 



+ Q-, (,-) 



By a precisely similar process we find 



<**& 2 A /T ox M /rfl 



7F = ~2 cos * P + R) + T fc + 



-^Tcos0 /C osa + | 2 T' cos 0' sin 6' + ' cos </>, cos 



W dT ,, . A , F dE, F t dT, n 

 -- r - cos 0' sm 0' -f - -r-' + -~ -~- D R y - D ( T y 

 e' dx f dy f dy 



M/rfl' ?R'\ M, <^T . . M' dT f , 

 -( -j -- -3- ) + ' sm0+ -- cos6'- 

 e\aa: dx ] e, dx e dx 



