200 



"We must, therefore, carefully seek out all terms in the development 

 of it, whose argument is either 2<3 - 0 or 0. The latter, however, will 

 be found to disappear. Then, 



a 15 / 



= • — 2 (yx x - xy x ) — ( x*x? + y*y? + z% 2 + 2xy x x y x + 2xz x x % x + 2yz y^, 



-i- • i 5 j- - 2 + Oi 2 - yi) m 



+ lL HL 15 [ a? cos 2(3 - 20 + 2a/3 COS 2(3 + /3 2 COS 2(3 + 20 



C r* \ 



x y x z x sin * sin 0 



H -I — fa 2 sin 2(3 - 20 + a/3 sin2p+/3 2 sin 2<3 + 20 W 2 -y, 2 ) 

 C r* 2 \ / 



sin t sin 0 



-i ^ (a 3 - 2 a/3) a^s, sin i sin 2<3 - 0 

 1 15 



_ il _ ( a * _ 2a/3) (a?! 2 - y^) sin t cos 20 - 0) 



Now, taking the value of i found above, we shall have 



. A 1 + B 2 . 



*» + 2 o V S111 2 ^ " W l+ 



neglecting, for the present, the other term, 



= sm «, + h cos t x — r sin 2w - n x \ 



A + B 



cos t = cos i, - i sin t, — sin 2n - n x -, &c. 



44 2w-w 



Then, since a stands for ^ + < ?° S , we shall have 



a 2 = i f 1 + cos «! 2 - 1 + cos i x sin ^ + ^ A x + B 2 sin 2n - n 1 

 * y 2n-n x 



and 



2a/3 = - \ sin 2 t = - \ ( sin 2 *; + sin ii cos i x — sm 2w - w 



JiTl — 7l x 



