OF THE MOTIONS OF A SOLID BODY. Q6\ 



— d4'.(cos dsin ^^-fcos 6 cos V) 



-f d^.(sin V + cos «5 cos V + sin ^9 cos V) > -f 



y" J — d5.(sin cos 9 cos ^(p — sin cos cos ^^) 

 — d4'.(cos B sin cos (p — cos 9 sin cos tp) 

 + d^.(sin cos ^— cos *d sin cos ^ — sin ^9 sin cos ^) J -1- 



z" J dfi.(cos ^9 cos ^-fsin H cos <p) 



— d^' . sin 6 sin 9 > = 



a'X — dtj. . cos 9-f d^)-fz'X^^-cos ^ — d^* sin 9 sin (p)zzdt.']{px" 

 —qz")=0. 



Secondly, multiplying the first equation by cos ^, the 

 second by cos 6 sin ^, and the third by — sin 9 sin (p, we 

 have 



[x"< d9.( — sin cos dsin *^H-sin cos 9 sin ^^) 



-f-d4'.(cos 9 sin cos ^ — cos 9 sin cos ^) 



■f d^.( — sin cos ^ + cos ^5 sin cos ^ + sin ^d sin cos ^) J + 



y" < dd.(— sin cos 9 sin cos ^H-sincos dsin cos^) 

 +d4'(cos 9 cos V+cos 9 sin V) 

 -fd^(— cos V — cos 25 sin V— sin ^9 sin V) ( + 



z" J d5.(cos *^fl sin 9-fsin *fl sin ^) 



-Hd4. . sin 6 cos <p >=: 



^"(diP . cos 9 — d(p)+2fXd9.sm <p d^. sin 9 cos ^)=:(— py'^H- 

 r2f')dt=:0; and];?/— rz"=0. 

 Lastly, if we multiply the second equation by sin 9, and 

 the third by cos 9, and add them together, or more simply, 



