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

 C and C' having the values 



The value of -j- deduced from (1) is 

 tit 



- z - - P p' sin cos 9. 

 dt \c 2 ay \ c V 



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

 the plane (#, ?/), 



a c //fl 2 -& 2 \ a 



smO = - / - , cos 9 = T 



z 



Introducing these values of -^, sin 6 and cos 0, and for Pw its 



P 



value =r, we obtain finally for the velocities 



G 



"' 



(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 



dt 



(^, (7, K] belonging to the projection parallel to axis of x. If 

 (i//, (7', K') be the corresponding quantities for the other projec- 

 tion, we obtain also 



