284 PHILOSOPHICAL TRANSACTIONS. [aNNO 1778. 



city of the ball may be reduced in any proportion, or to any slow velocity, which 

 may conveniently be measured, by making the body struck to be sufficiently 

 large; for it is well known, that the common velocity, with which the ball and 

 block of blood would move forward after the stroke, bears to the original velo- 

 city of the ball only, the same ratio which the weight of the ball has to that of 

 the ball and block together. Thus then velocities of 1000 feet in a second are 

 easily reduced to those of 2 or 3 feet only; which small velocity being measured 

 by any convenient means, then the number denoting it being increased in 

 the proportion of the weight of the ball to the weight of the ball and block 

 together, the original velocity of the ball itself will thus be obtained. In these 

 experiments, this reduced velocity is rendered easy to be measured by a very 

 simple and curious contrivance, which is this: the block of wood, which is 

 struck by the ball, is not left at liberty to move straight forward in the direction 

 of the motion of the ball, but it is suspended, as the weight or ball of a pen- 

 dulum, by a strong iron stem, having a horizontal axis at top, on the ends of 

 which it vibrates freely when struck by the ball. The consequence of this simple 

 contrivance is evident: this large ballistic pendulum, after being struck by the 

 ball, will be penetrated by it to a small depth, and it will then swing round its 

 axis describing an arch, which will be greater or less according to the force of the 

 blow struck; and from the size of the arch described by the vibrating pendulum, 

 the velocity of any point of the pendulum itself can be easily computed; for a 

 body acquires the same velocity by falling from the same height, whether it de- 

 scends perpendicularly down, or otherwise; therefore, the length of the arch 

 described, and of its radius, being given, its versed sine becomes known, which 

 is the height perpendicularly descended by the corresponding point of the pen- 

 dulum. The height descended being thus known, the velocity acquired in falling 

 through that height becomes known, from the common rules for the descent of 

 bodies by the force of gravity; and this is the velocity of that point of the pen- 

 dulum: this velocity of any known point whatever is then to be reduced to the 

 velocity at the centre of oscillation, by the proportion of their radii or distances 

 from the axis of motion; and the velocity of this centre, thus obtained, is to 

 be esteemed the velocity of the whole pendulum itself; which being now given, 

 that of the ball before the stroke becomes known from the given weights of the 

 ball and pendulum. Thus then the mensuration of the very great velocity of 

 the ball is reduced to the observation of the magnitude of the arch described by 

 the pendulum, in consequence of the blow struck. This arch may be measured 

 after various ways: in the following experiments it was ascertained by measuring 

 tV)e length of its chord by means of a piece of tape or small ribband, one end of 

 which was fastened to the bottom of the pendulum, and the rest of it inatle to 

 slide through a small machine contrived for the purpose hereafter described; for 



