of minute Forces on the Rate of the Seconds Pendulum. 347 



Under, the rod must be lengthened by a quantity equal to half 

 the diameter of the cylinder ; provided that the cylinder, or 

 a small portion of it, be fixed in such a manner, that its sur- 

 face shall be at the exact point of the rod previously occupied 

 by the knife-edge. 



hi my experiments with the convertible pendulum, no part 

 of the rod extended beyond the point of suspension at the 

 light end, with the exception of a brass nut, which did not 

 extend beyond the centre of the cylinder. Conceiving the cy- 

 linder to be a separate part of the pendulum, I equalized the 

 matter on each side of the centre or axis, by making it equally 

 heavy on balancing it with additional weight on both sides, in 

 the direction of its length, and then adjusted the pendulum 

 anew. I expected that this adjustment would cause the vi- 

 brations to be performed in the same time as when it was ad- 

 justed with the knife-edge. 



The pendulum, however, now lost one vibration in 8 mi- 

 nutes, a quantity of loss on its rate nearly twice the amount 

 of its former loss. From this result, I inferred that if all the 

 weight or matter beyond the surface on which the cylinder 

 rolls were removed, it would have the effect of producing 

 vibrations synchronous with those performed by a pendulum 

 vibrating on a knife-edge; and that the effect of the cylindric 

 surface in quickening the vibrations of the pendulum is the 

 same as that of shortening the rod of the pendulum by a quan- 

 tity equal to half the diameter of the cylinder. 



The conclusions to be drawn from these experiments are, 

 that when a convertible adjusted pendulum is made to roll or 

 vibrate on a cylinder instead of a knife-edge, the surface on 

 which it rolls is the point of suspension, and the centre of the 

 cylinder that is lowest is the point of oscillation, and that they 

 reciprocally take the places of each other when inverted. 



When the detached pendulum vibrated on a cylinder, the 

 long vibrations were slower than when it vibrated on a knife- 

 edge; I suppose the principal cause of this to be, the lengthen- 

 ing of the pendulum in proportion as the vibration extends. 

 For the portions of the cylinder on each side of the vertical 

 passing through the point of rest, become more distant from 

 the point of oscillation in proportion as the vibration extends, 



I and consequently the times of the longer vibrations are pro- 

 portionably slower. 

 There is a vertical motion, as well as a small horizontal mo- 

 tion, both of which increase in proportion as cylinders of a 

 larger diameter are employed; — but why cylinders of 1*8 inch, 

 with a seconds pendulum, produce more isochronous vibra- 

 .„ 



