806 Lieut.-Colonel A. G. Hadcock [May 24, 



Most artillerists have so far treated the problem of internal 

 ballistics either {a) as if the gun was a closed vessel for each position 

 of the projectile, as in Centerval's and Mansel's methods, or (b) that 

 the pressure, for each position of the projectile, bears some definite 

 relationship to the pressure which would have been developed had 

 the charge been burnt in a closed vessel of capacity equal to that of 

 the chamber of the gun. This method of treatment has been adopted 

 by (losset, Heffernan, Charbonnier, and others. 



Both these assumptions require some qualification, because in a 

 closed vessel no linear motion is given to the charge, while in a gun 

 a considerable amount of energy is absorbed by the charge having to 

 be put into motion. Thus we find that the pressure on the breech of 

 the gun is higher than that on the projectile. The pressure on the 

 base of the shot is that due to putting the shot alone into motion, 

 while the higher pressure on the breech is due to the additional 

 work required to be done in putting also into motion the weight of 

 the gas or charge. Direct experiment proves this to be the case, and 

 usually the difference in pressure on the breech and on the base of 

 the shot amounts to between 1 and 2 tons per square inch. 



By assuming that the pressure falls uniformly from breech to the 

 base of the shot and that the mean velocity of the gases and uncon- 

 sumed part of the charge is four-tenths to one-half that of the 

 projectile, we can prove that the following relation holds between 

 the pressure on the breech and that on the shot — 



Pressure per square inch on breech _ 4 ?^ ^ , ^ 

 Pressure per square inch on shot 10 W 



where iv weight of charge in pounds ; W the weight of the shot ; 

 and / the factor of effect. 



Another way of looking at this is to remember that when a 

 column of fluid under pressure is put into motion a certain amount 

 of the pressure is lost. The amount so lost depends on the velocity. 

 In our case we have the gas under high pressure. Part of it is in 

 contact with the shot and moving at the same velocity as the shot ; 

 the remainder has a gradually less linear motion, until at the breech 

 end of the gun there is no relative motion. It follows then that 

 the forward part of the gas, which has a considerable velocity, will 

 have less pressure than that part in contact with the breech end of 

 the gun. 



In a gun the space behind the projectile continually increases as 

 the projectile travels along the bore ; thus each portion of the gas as 

 generated may, for our purpose, be considered to expand according to 

 the law p iv' - aj = k (a constant), and do work on the shot. In doing 

 so it would lose heat, but at the same time the charge continues to 

 burn and additional heat is given to the already generated gases ; 

 thus our hypothetical expansion is neither adiabatic nor is it iso- 

 thermal. For simplicity we suppose that no heat is imparted to the 



