660 PHILOSOPHICAL TRANSACTIONS. [aNNO 1742-3. 



body before the stroke is thence determined. On this principle then it follows, 

 that the velocity of a bullet may be diminished in any given ratio, by its being 

 made to impinge on a body of a weight properly proportioned to it ; and hereby 

 the most violent motions, which would otherwise escape our examination, are 

 easily determined by these retarded motions, which have a given relation to 

 them. Hence then, if a heavy body greatly exceedmg the weight of the bullet, 

 whose velocity is wanted, be suspended so that it may vibrate freely on an axis 

 in the manner of a pendulum, and the bullet impinges on it when it is at rest, 

 the velocity of the pendulum after the stroke will be easily known by the extent 

 of its vibration, and from thence, and the known relation of the weight of the 

 bullet and the pendulum, and the position of the axis of oscillation, the velo- 

 city with which the bullet is impinged will be determined, as is largely explained 

 in the 8th proposition. Where note, that there is a paragraph by mistake 

 omitted in that proposition, which should increase the velocity there found in 

 the duplicate proportion of the distances of the points of oscillation and per- 

 cussion from the axis of suspension ; but this only affects that particular num- 

 ber, for it was remembered in the computations of the succeeding experiments, 

 . the numbers of which are truly stated. 



It being explained how the velocities of bullets may be discovered by experi- 

 ment : the next consideration is, from those velocities to determine the force 

 which produced them. And the author thought, the best method of effecting 

 this was by computing what velocities would arise from the action of fired 

 powder, supposing its force to be rightly assumed by the process in the preced- 

 ing part; that is, supposing the elasticity of the fluid thence arising to be at 

 first 1000 times greater than that of common air; for then, by comparing the 

 result of these computations with a great nuniber of different experiments, it 

 would appear whether that force was rightly assigned ; and if not, in what de- 

 gree it was to be corrected. 



The 7th proposition is employed in computing the velocity which would be 

 communicated to a bullet in a given piece by a given charge of powder, on the 

 principles hitherto laid down, that is, supposing the elasticity of fired powder to 

 be at first 1000 times greater than that of common air. 



In the Qth proposition these computations are compared with a great number 

 of experiments, made in barrels of various lengths, from 7 inches to 45 inches, 

 and with different quantities of powder, from 6 dwt. to 36 ; and the coincidence 

 between the theory and these experiments is very singular, and such as occurs 

 in but few philosophical subjects of so complicated a nature. 



By this agreement between the theory and the experiments, each part of the 

 theory is separately confirmed ; for by firing different quantities of powder in 



