474 



DR G. PLARR ON THE DETERMINATION OF 



Hence 



The equation in Mx becomes 



' u 2 y 2 — 2u 2 vy = — Sk<bk 



u 2 z 2 — 2u 2 wz = — Si chj 



Or, 



0=-™ 

 m 



+ u 2 [wy(u 2 z 2 — 2u 2 wz) + vz(u 2 y 2 — m 2 vy)] 

 +u % yz. 



vw 



= 



m 



+ u 2 yzTu 2 wz — 2 -uPw 2 + u 2 vy — 2u 2 v 2 ~\ 



Assembling the terms in u 2 , v 2 , w 2 , and remarking 



u 2 + v 2 + w 2 = 2Si<j>-H = 2a 2 = l x 



(l t becoming later = a 2 + 2b 2 ), and having 



u* - 2u 2 w 2 - 2u 2 v 2 = u\u 2 - 2(v 2 + w 2 )] 

 = u 2 [u 2 -2(l 1 -u 2 )] 

 = u 2 [3u 2 -2^], 



we get 



771 



(3) +u 2 yz[u 2 (vy+wz)+u%3u 2 -2l 1 )] . 



The expressions (1) (2) give 



2u\vy + wz) = u 2 (y 2 + z 2 ) 



-ksj<pj+sk<pk). 



But the last term 



Putting y 2 + z 2 = r 



m 



we get 



+ -(S^+m 2 ), as ESi0i = s(+- 2 j=- 



2u 2 (vy + wz) = v?r 2 -\ — ($i<pi + m 2 ) 



m„ 



and the equation in Mj becomes 



m 



0=- 



2vw 



m 

 r 



+u 2 yz 



u 2 r 2_j (Sid)i+m„) 



m 



+ w 2 (6u 2 -4£ 1 ) 



