Manchester Memoirs, Vol. Hi. (1908), No. 8. 7 



Now, during the cycle, the mean angular velocity 



= — (ii» + (.>,) 



Vh „ 



Vh \ Vh 



h" + k-'J h' + k'^ ' ' ' ^^^'^ 



Similarly, during the succeeding cycle, the mean angular 

 velocity 



/ Vh \ Vh ^ , , 



Therefore, from (iv) and (v.), the change in mean angular 

 velocity 



. Y V/i \ Vh .„ „, 



. • . from (iii.) 



Vh , s ( Vh V/« a^ 



. • . from (i.) 



Vh W ^ 



change in mean angular velocity in cycle 2r_ _ / Vh V 

 2r \/r + hy 



when small quantities of the second order are neglected. 



Thus the mean angular acceleration is directed towards 



the position of equilibrium, and is equal to (-p — 73) x the 



angular displacement — the result obtained previously. 



It is of interest to compare this case of constant pivot 

 speed with the motion when the pivot has a simple vibra- 



