34 o Rotation oj a Solid Body round a Fixed Point. 

 C and (?' having the values 



c = b J($^f )' ' = b J(TT)- 



\ \ / \ \ / 



The value of -~ deduced from (1) is 



i\ 



' sin 9 cos 9. 

 c' a" I \c l a* ' ' 



being the angle made by the plane of the circular section with 

 the plane (#, ?/), 



/a'-ZA a // 2 -c 2 \ 



- , 0080= T (- - r). 



\a 2 - c*J b\l\a?- c*J 



fJ'tJ 



Introducing these values of ~, sin 9 and cos 9, and for Pw its 



w c 



fl' 



value =, we obtain finally for the velocities 



I 1 



" 



(13) 



The velocity of each projection, therefore, varies as the ordinate 

 of the other. This theorem enables us to find a simple expression 

 for the time. Using the angle (0) marked in fig. 2, we obtain 



(^>, C, K] belonging to the projection parallel to axis of x. If 

 (i//, C', .fiT 7 ) be the corresponding quantities for the other projec- 

 tion, we obtain also 



= 7T 



