246 Dynamics. 



367. It may suffice in practice to divide the body into a great 

 number of parts, and multiply each part by the square of its 

 distance from the axis in order to obtain with sufficient exactness 

 the value of fmr 2 . 



Of the actual Length of the Seconds Pendulum. 



368. The number of vibrations performed in the same time 

 by two different pendulums, urged by the same gravity, being 

 inversely as the square roots of the lengths of these pendulums, 

 we can find very nearly the length of the seconds pendulum for 

 any given place by a very simple process. Having suspended 

 to a very fine wire of at least three feet in length, a small dense 

 body, as a ball of lead, gold, or platina, we ascertain the length 

 of this wire and the radius of the ball with great exactness. We 

 then cause this pendulum to vibrate by drawing it a little from 

 a vertical position, and count the number of vibrations performed 

 in a given time, as one hour, very carefully determined, and then 

 make use of the proportion ; as 3600, the number of vibrations 

 to be performed by the pendulum sought, is to the number actu- 

 ally performed by the above pendulum, so is the square root of 



346. the length of this latter pendulum to a fourth term or a?, which 

 will be the square root of the length of the pendulum sought ; 

 and by squaring this fourth term, we shall have very nearly the 

 length of the pendulum required to vibrate seconds. 



This result would be exact only on the supposition that the 

 wire or string is without weight, and that the ball consists only 

 of a single particle or has its matter concentrated at the centre. 



369. If we attempt to find geometrically the centre of oscil- 

 lation of the ball and wire, we shall still be liable to some small 

 error arising from irregularities in the form and distribution of 

 the matter in question. We accordingly have recourse to 

 another method, depending on a curious property of the com- 

 pound pendulum by which the distance between the point of sus- 

 pension and centre of oscillation, answering to the length of the 

 simple pendulum vibrating in the same time, can be ascertained 

 with the greatest precision. 



