117 



r^dm 



— Kai § r^ds ■=. — Kw V 



where h = -7-. The ratio, h, is constant for all bodies of 



prismatic form ; and for these, therefore, the moment of 

 resistance is 



MK 



M denoting the moment of inertia ^r-dm. 



The differential equation of motion is, therefore, 



db) Xu . . K 



-77= — sm y 0). 



at M H 



m 

 But u) = • — T7 ; and, being small, we may substitute for 



sin B. The equation thus becomes 



^0 KrfO X^ 



Making, for abridgment, - = 2a, — = b^ the integral is 

 ° H M " 



B = [c cos V B^ — A^ # + c' sin V b^ — a^. t) e-^K 

 But, A being small, we have approximately 



g-A< =:: 1 _ Af ; 

 and, if t denote the time of vibration. 



V B^ — A^ . T = TT. 



Hence the preceding equation may be put under the form 

 = (1 — A^) fccos TT- + c'sinTr-j- 

 Now, let B, and B' denote the values of B, when t becomes 

 L 2 



