652 
PHYSICS: A. G. WEBSTER 
Proc. N. a. S. 
the density of loading as A = co/F = I/t;, while if the fraction of 
the load z has been converted into gas we have v = V/o)Z. Accordingly 
RT RT RTz 
(3) 
V/z - 
V 
zrj 
It is frequently assumed that during the burning the temperature of the 
gas remains constant, although this can hardly be the case during the 
expansion in the gun. Although the specific heats of the gases vary 
largely with the temperature, as shown by the classical experiments of 
Mallard and Le Chatelier (who found them to be linear functions of 
the temperature) we shall here consider them as constant, taking mean 
values. This hypothesis can be corrected later. 
SI 
If the powder is contained in a variable volume c and oiz has been 
burned, while aj(l — z) remains in solid form, of density b, the gases will 
have the space V = [c — o:{l — z) / b] to occupy, so that the specific volume 
will be 7; = 
- (1 — z) \ /o)Z and we have 
b 
P = 
RTc^z 
(4) 
c — aj(l — z)/b — cjozt] 
as the relation between p, z, c, and T. Let 5 be the area of the bore, 
c' the volume of the chamber, and x the position or "travel" of the shot, 
so that 
c = c' Sx. (5) 
