254 THEORY OF HEAT. [CHAP. IV. 



a=^N + JV e * versin ^ + JVe * versin ^ + & c . 



= o + sn ^ + cos & e 



+ (3/ 2 sin 2 + JV 2 cos qj 6 &amp;lt;versin ^ + &c. 



= N + (M, sin 2q l + N t cos 2^) 6 * versin * 



+ (M z sin 2g 2 + ^ cos 2g 2 ) 6 &amp;lt; vershl * + &c. 



. = JV + {,, sin ( j - 1) ^ + ^ cos (j - 1) grj e 



+ M sin - 1 + ^&quot; cos - 1 e versin + &c. 



n = i o + sn 71 - q, + , cos n - Sl e 



+ {M z sin ( - 1) q z + JV; cos - 1) 2 } e * versin + &c. 

 In these equations 



_ , 27T 27T Q 27T 



e = e , ^y , 2 2 = 2 &amp;gt; ^= 3 &c., 



273. The equations which we have just set down contain the 

 complete solution of the proposed problem ; it is represented by 

 the general equation 



o,= -2a,+ -sin(j-l)~Sasin(i-l)-^- 



2 .xSTT^ -.N^Tr&quot;! -^ 



+ - cos ( i 1) 2a cos (i 1) 

 n n n\ 



n n n 



(e), 



