50 Experiments upon Gunpowder. 



any given case by suspending the gun in an horizontal 

 position by two pendulous rods, and measuring the arc 

 of its ascent by means of a ribbon, according to the 

 method already described ; and this will give the mo- 

 mentum of the gun (its weight being known), and con- 

 sequently 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 produce that 

 recoil. 



That part of the recoil which arises from the expan- 

 sion 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, as I have found by a great 

 variety of experiments. 



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 

 quantity 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 veloci- 

 ties, 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 it is fired with 

 any given charge of powder, without any bullet, 



V = the velocity of the recoil, when the same charge 

 is made to impel a bullet, 



B = the weight of the bullet, and 



v = its velocity, 



It will be _ynr- 



