VOL. LXVIII.] PHILOSOPHICAL TRANSACTIONS. 285 



thus the length of the tape drawn out, was equal to the length of the chord ol 

 the arch described by the bottom of the pendulum. 



This description may convey a general idea of the nature and principle of the 

 experiment; but besides the centre of oscillation, and the weights of the ball 

 and pendulum, the effect of the blow depends also on the place of the centre of 

 gravity and the point of impact: it will therefore be now necessary to give a more 

 particular description of the machine, and of the methods of finding the above- 

 mentioned requisites, and then investigate our general rule for determining the 

 velocity of the ball, in all cases, from them and the chord of the arch of vibration. 



Of the Particular Description of the Machine, and of the Determination of 

 the Centres of Gravity and Osciltation. — Plate 4, fig. I, is a representation of 

 the machine used in these experiments; the first pendulum consisted of a block 

 of sound and dry elm, being nearly a cube of 20 inches long, which was fastened 

 to a strong iron stem on the back part by screw-bolts, having a thick iron axis 

 at the top, the ends being turned truly cylindrical, to roll pretty freely in sockets 

 made to receive them; the whole being supported by a four-legged stand of very 

 strong timber, firmly fixed in the ground, a is the face of the cube into which 

 the balls were fired; by means of the blow it is made to swing round the axis bc, 

 and the chord of the arch described is measured by the tape def fastened to 

 the bottom of the wood at d, and sliding with some slight friction through a 

 small machine, fixed at e for that purpose, the tape being marked with inches 

 and tenths, for more easily measuring the chord or part of it drawn through by 

 the pendulum. The whole length of this pendulum, from the middle of the 

 axis to the ribband at d, was 102^ inches. The weight and the other dimensions 

 were taken each day when the experiments were made, and then registered; and 

 the manner of discovering the places of the centres of gravity and oscillation 

 was as follows. 



To find the centre of oscillation, the pendulum was hung up, and made to 

 vibrate in small arcs, and the time of making 2 or 300 vibrations was observed 

 by a half-second pendulum. Having thus obtained the time answering to a cer- 

 tain number of vibrations, the finding of the centre of oscillation is easy: for if 

 V denote the number of vibrations made in s seconds, then it is well known that 



vv : ss :: 30.2 : — ^^— = the distance in inches from the axis of motion to the 



^ vv 



centre of oscillation ; and by this rule the place of that centre was found for 

 each day. 



The centre of gravity was ascertained by one or both Avt 



of the 2 following methods. First, a triangular prism 

 of iron ab, being placed on the ground with an edge 

 upwards, the pendulum was laid across it, and moved 

 forward or backward on the stem or block as the case B ii 



