184 ELEMENTARY PRINCIPLES OF GUNNERY. 



with which the ball has travelled. As Robins remarks, 

 " This instrument thus fitted, if the weight of the pendulum 

 be known, and likewise the respective distances of its centre 

 of gravity, and of its centre of oscillation from its axis of 

 suspension, it will thence be known what motion will be 

 communicated to this pendulum by the percussion of a body 

 of a known weight, moving with a known degree of celerity, 

 and striking it at a given point ; that is, if the pendulum be 

 supposed at rest before the percussion, it will be known what 

 vibration it ought to make in consequence of such a de- 

 termined blow; and, on the contrary, if the pendulum, 

 being at rest, is struck by a body of a known weight, and 

 the vibration which the pendulum makes after the blow is 

 known, the velocity of the striking body may from thence 

 be determined. . . . The computation by which the velocity 

 of the ball is determined from the vibration of the pendulum 

 after the stroke requires a more particular explication ; and 

 for this purpose we will exhibit, as an example, the pen- 

 dulum made use of by us in some of our experiments. The 

 weight of the whole pendulum was 561bs. 3oz. ; its centre 

 of gravity was 52 inches distant from its axis of sus- 

 pension, and 200 of its small swings were performed in the 

 time of 253 seconds; whence its centre of oscillation is 

 62| inches distant from that axis. In the compound ratio 

 of 66 to 62| and 66 to 52, take the quantity of matter of 

 the pendulum to a fourth quantity, which will be 421bs. ^oz. 

 Now geometers will know that, if the blow be struck in the 

 centre of the plate (a), the pendulum will resent the stroke, 

 as if this last quantity of matter only (421bs. ^oz.) was con- 

 centrated in that point, and the rest of the pendulum was 

 taken away; whence, supposing the weight of the bullet 

 impinging on that point to be the twelfth of a pound, or 

 the -5~J- of this quantity of matter nearly, the velocity of 

 the point of oscillation after the stroke will, by the laws 

 observed in the congress of such bodies as rebound not from 

 each other, be the -gfo of the velocity the bullet moved 

 with before the stroke ; whence the velocity of this point of 

 oscillation being ascertained, that, multiplied by 505, will 

 give the velocity with which the ball impinged. 



" But the velocity of the point of oscillation after the 



