PERIOD OF VIBRATION OF STEAM VESSELS. 125 



if we call — which is the square of the radius of gyration, =: k\ 

 3 

 Similarly for any intermediate position B, 



If the chord DE have the length .S"i, and the chord HE the length S, then 

 Ji = ^ » and>' = — -. where S is the radius to the center of gravity ^y^L. SubstJ- 



20 20 



tuting the values of ji and y in (i8), we have 



«=^J'S-/-5^ (21) 



where 5"! and ^ are chords with radius S. 



The maximum angular velocity of the simple pendulum from (13) would be — 



where Si = Idg = arc with radius /. 



Similarly from (20), the maximum angular velocity of the compound pendulum 

 would be — 



«o = H>|J^ = ^o /f- (23) 



From a comparison of equations (22) and (23), it appears that for the com- 

 pound pendulum ^ corresponds to / for the simple pendulum, and the formula for the 

 period of the compound pendulum would be — 



^- '" Jf (24) 



V7>/^ 



t2 



where -^replaces / in formula (17). 



