VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 103 



the fine invisible elastic fluid, generated from the powder in its inflammation, 

 cannot put itself in motion without re-acting against the gun at the same time. 

 Thus we see pieces when they are fired with powder alone, recoil as well as when 

 their charges are made to impel a weight of shot, though the recoil is not in 

 the same degree in both cases. 



It is easy to determine the velocity of the recoil in any given case, by sus- 

 pending the gun in a horizontal position by two pendulous rods, and measuring 

 the arc of its ascent, by means of a ribbon according to the method already des- 

 cribed, and this will give the momentum of the gun, its weight being known, 

 and consequently the momentum of its charge. But in order to determine the 

 velocity of the bullet from the recoil, it will be necessary to find out how much 

 the weight and velocity of the elastic fluid contributes to it. That part of the 

 recoil which arises from the expansion of this fluid is always very nearly the same, 

 whether the powder is fired alone, or whether the charge is made to impel one 

 or more bullets ; which Mr. T. says he has found by a great variety of experi- 

 ments.* If therefore a gun, suspended according to the method prescribed, be 

 fired with any given charge of powder, but without any bullet or wad, and the 

 recoil be observed ; and if the same piece be afterwards fired with the same quan- 

 tity of powder, and a bullet of a known weight, the excess of the velocity of 

 the recoil in the latter case, over that in the former, will be proportional to the 

 velocity of the bullet ; for the difference of these velocities, multiplied into the 

 weight of the gun, will be equal to the weight of the bullet multiplied into its 

 velocity. 



Thus if w be put equal to the weight of the gun, 



u = the velocity of its recoil when fired without a bullet, 



v = the velocity of the recoil when the same charge impels a bullet, 



b = the weight of the bullet, and 



v = its velocity ; then it will be 



V — u 



v = X w. 



B 



Let us see how this method of determining the velocities of bullets will an- 

 swer in practice. In the 94th exper. the recoil, with l65 gr. of powder, without 

 a bullet, was 5.5 inches, and in the 95th exper. with the same charge, the recoil 

 was 5.6 inches. The mean is 5.55 inches; and the length of the rods by which 

 the barrel was suspended being 64 inches, the velocity of the recoil u, answering 

 to 5.55 inches measured on the ribbon, is that of 1.1358 feet in a second. Now 

 in 5 experiments, viz. exper. -20, 21, 22, 23, 24, with the same charge of 

 powder, and a bullet weighing 580 gr., the medium recoil was 14.6 inches. 



* Remarked in Robins's New Principles of Gunnery, prop. 11, p. 111. But it is not generally 

 true. 



