VOL. XLII.j PHILOSOPHICAL TRANSACTIONS. 679 



elasticity of common air, or, which is the same thing, 1000* times greater than 

 the pressure of the atmosphere. 



But, besides the determination of the quantity of fluid produced from a given 

 quantity of powder, the method on which this deduction is founded, there is 

 another method of discovering the same thing, which, though less obvious, is 

 yet, as hath been already observed, more accurate : that is, by examining the 

 actual velocities communicated to bullets by the explosion of given charges in 

 given cylinders ; and this is the subject of the 7th, 8th, and Qth propositions. 



And first, it is evident, that this examination cannot take place, unless a 

 method of discovering the velocities of bullets be previously established. Now 

 the only known means of effecting this was, either by observing the time of 

 the flight of bullets through a given space ; or by finding their ranges when 

 they were projected at a given angle, and thence computing their velocity on 

 the hypothesis of their parabolic motion. The first of these methods was often 

 impracticable, and in all great velocities extremely inaccurate, both on account 

 of the shortness of the time of their flight, and the resistance of the air. The 

 2d is still more exceptionable, since, by reason of the air's resistance, the velo- 

 cities thus found may be less in any ratio given, than the real velocity sought. 

 Now, to avoid these difficulties, the author invented a method of determining 

 the velocities of bullets, which may be carried to any required degree of exact- 

 ness, and is nowise liable to the forementioned exceptions ; for, by this inven- 

 tion, the velocity of the bullet is found in any point of its track, independent 

 of the velocity it had before it arrived at that point, or of the velocity it would 

 have after it had passed it : so that not only the original velocity, with which it 

 issues from the piece, is hence known, but also its velocity, after it has passed 

 to any given distance ; and therefore the variations of its velocity from the 

 resistance of the air may be also ascertained with great facility. The machine 

 for this purpose is described in the 8th proposition, and the principle it is 

 founded on is this simple axiom of mechanics ; that if a body in motion strikes 

 on another at rest, and they are not separated after the stroke, but move on 

 with one common motion, then that common motion is equal to the motion 

 with which the first body moved before the stroke : whence, if that cotnmon 

 motion and the masses of the two bodies are known, the motion of the first 



• By more accurate and extensive experiments, since made, I have found that this number, 

 denoting tlie first strength of the fired gunpowder, varies very much on several accounts, but chiefly 

 on the different quantities that are employed in the experiments. Thus, by firing different quanti- 

 ties at a time, I have found that, by using from 4 to 8 ounces at once, that number varies from 1150 

 to near l600 ; being gradually always larger as the charge is higher. See the end of prop. 18 of my 

 Course of Mathematics, voL ii. p. 357, ed. 4th. C. H. 



