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^54 
PHYSICS: A. G. WEBSTER 
Proc. N. a. S. 
(w + Xco)^ = (5 — 6) 
Jdtjpdt 
(11) 
If p is given in the form of a curve by the indicator, and the two integrals 
are evaluated for the whole time the shot is in the barrel, the determina- 
tion of the muzzle velocity and of the whole length of the barrel, every- 
thing else being known, will furnish two linear equations for the deter- 
mination of Ro and b. On the other hand if the times at which the shot 
passes a number of points are known, or if x is experimentally given as a 
function of t either of the equations (10) or (11) gives a means of verifying 
the assumption (7) and as many points as may be for determining the 
constants by least squares. 
It will now be necessary to take account of the first law of thermo- 
dynamics. If U is the energy of the hot gas per unit of mass, dQ the 
amount of heat taken in, and Rdx the work done against friction, which 
is converted into heat, which stays in the gas, we have 
dO -f Rdx = d{c^zU) + pdV. ' (12) 
