117 



c 1 I Crdm 



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

 as 



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



resistance is 



MK 



-—a,; 



M denoting the moment of inertia '\,r-dm. 



The differential equation of motion is, therefore, 



dix) Xu . - K 



-J- = — sm w. 



dt M H 



But w = — —', and, B being small, we may substitute for 

 sin B. The equation thus becomes 



■dF-^nli-^-^^-^- 



K. Xw 



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



= (c cos V b' - a'^ ^ 4- c' sin ^Z b' - a^. t) e-'^K 

 But, A being small, we have approximately 



e-*' = 1 — A^ ; 

 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/) [ c cos TT- + c' sinTT-j. 



Now, let 0, and B' denote the values of 0, when t becomes 

 l2 



