Professor Mac Ctni-i-AGH's Lectures on Rotation. 149 



P (It ' p dt' 



C and C having the values 



The value of ^ deduced from (1) is, 

 at ^ ' 



6 being the angle made by the plane of the circular section with the plane (x, y). 



Introducing these values of -f, sin 6 and cos 0, and for Pw its value — ^, we 



dt fiK 



obtain finally for the velocities 



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 



Cdxf, 



dt 



K ^/(C"-C-sm'<p); 



(<p, C, K) belonging to the projection parallel to axis oi x. If {^, C, K') be 

 the corresponding quantities for the other projection, we obtain also 



K C 

 or, since it is easily seen that = = — , we obtain finally 



