r ^ 2 4 V 



/,= — p a> a ' 



^ (27i + 3)(2n+l)[4 -(2n+l)2] 



_ po?a^ ^ I 1 *_^_ *\ 



477 L—i 1 271-1 271+1 2n + 3 {2n+&f 



Of the four series into which the last sum may be broken up, the terms of the first three cancel 

 each other except for one term out of the second, which equals 4. Furthermore 





1 1 1 



-^ (271 + 3)2 1^ 3^ 5^ 



see Carslaw's Fourier Series, 3d ed. (1930), p. 235. Hence 



T = 1 pa'^(^^( L 0.1553 aM — TrpaM oj^. [102e] 



(See Reference 1, Article 72; Reference 10, page 102.) 



103. MOTION WITHIN A ROTATING TRIANGULAR PRISM. 

 If 



w = <l> + iiP = iAz^, 2 = re'^, [103a, b] 



then 



cf> = - Ar^ sm^ d, ip = Ar^ cos S 0, [103c, d] 



iP = A {x^ -S xy^) 



from 



z = {x + iy) , where x = r cos 6, y = r sin 

 Substituting for ip in Equation [99c], 



A{x^ -3 xy^)-~ a;(a;2^/) = C. 



This is satisfied for all values oi y \i x = a and 



1 



3^ffi+— (u = 0. 



2 



253 



