110 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 



elasticity of the fluid directly, and inversely as its density ; if therefore the den- 

 sity of the fluid generated from powder was 4 times less than it is, its elasticity 

 remaining the same, it would issue out at the vent, and escape by the side of 

 the bullet in the bore, with nearly 4 times as great a velocity as it does at pre- 

 sent ; but we know from experiment that the loss of force on these accounts is 

 now very considerable. 



An elastic bow, made of very light wood, will throw an arrow, and especially 

 a light one, with greater velocity than a bow of steel of the same degree of 

 stiffness : but, for practice, gunpowder may be supposed to be so light as to be 

 rendered entirely useless : and for some purposes it seems probable, that it would 

 not be the worse for being even heavier than it is now made. Vents are abso- 

 lutely necessary in fire-arms, and in large pieces the windage must be consider- 

 able, in order that the bullets, which are not always so round as they should be, 

 may not stick in the bore ; and those who have been present at the firing of 

 heavy artillery and large mortars with shot and shells, must have observed, that 

 there is a sensible space of time elapses between the lighting of the prime and the 

 explosion ; and that, during that interval, the flame is continually issuing out at 

 the vent with a hissing noise, and with a prodigious velocity, as appears by the 

 height to which the stream of fire mounts up in the air. 



As it appears from these experiments, says Mr. T. that the relation of the 

 velocities of bullets to their weights is different from that which Mr. Robins's 

 theory supposes, it remains to inquire what the law is which actually obtains. 

 And first, as the velocities bear a greater proportion to each other than the re- 

 ciprocal sub-duplicate ratio of the weights of the bullets, Mr. T. examines how 

 near they come to the reciprocal sub-triplicate ratio of their weights: and here 

 the velocities computed on the last supposition appear to agree rather better with 

 the experiments than those computed on Mr. Robins's principles ; but still there 

 is a considerable difference between the actual and the computed velocities in the 

 3 last experiments in the table, which it has been observed were the erroneous 

 ones. 



As the powder itself is heavy, it may be considered as a weight that is put in 

 motion along with the bullet ; and if we suppose the density of the generated 

 fluid is always uniform from the bullet to the breech, the velocity of the centre 

 of gravity of the powder, or, which amounts to the same thing, of the elastic 

 fluid, and the gross matter generated from it, will be just half as great as the 

 velocity of the bullet. If therefore we put p to denote the weight of the pow- 

 der, b the weight of the bullet, and u its initial velocity ; then bv + -Ipv = 

 (b + ip) X v will express the momentum of the charge at the instant when the 

 bullet quits the bore. If now, instead of ascertaining the relation of the velo- 

 cities to the weights of the bullets, we add halt the weight of the powder to the 



