252 
Sec. 20 -4}- Eq. 110-115 
Using the method of Sec. 13, we see that (since the stick is 
infinitely long) the whole region in the burnt gases is covered by r 
type lines originating in the region of uniform pressure and velocity 
(Pow) back of the detonation front. These lines run parallel to the de- 
tonation front in this region and curve Site on passing through the 
rarefaction wave. Consequently, since r = 3 (w+ U) is everywhere the 
same (in the burnt gases), 
Uz = - (a+ const. (110) 
fete ) aP ; (111) 
On choosing foie the const. becomes w, the mass-velocity back of 
lo 2? , 
{I 
where &) 
the detonation front. 
To summarize: the burnt gas expands reversibly, at the same time 
increasing its forward velocity and reducing its pressure and temperature, 
The air is compressed and acquires a forward velocity. The solution is 
assumed to be the situation reached when the pressures and velocities are 
equal across the boundary. 
b. Use of a general equation of state, The equation of state will be 
written in the general form 
Py = nRTF (x) (112) 
where x = (K/v) h(T) , (113 ) 
in which P is the pressure (c.2.8. ), v the volume occupied by the gases 
resulting from the explosion of M grams of explosive, v=VM, n is the number 
of moles of products (all products are assumed to be gases), R is the gas 
constant per mole (c.g.s.), F (x) is some function of x, K 4s a constant 
for a given composition of the gases and for the given quantity M, and h 
(T) is a function of the temperature T. It will be assumed that the 
composition (therefore n and K) is independent of T and P. 
The velooity Us of the burnt gases is connected with the density 
through the equation 
Us aoa y(ar/a ? ae afi (114) 
as shown above. It is convenient to write the integral in the form 
1 
mun. tae) ee 
xe ($ bg (Mak Dg eC , (115) 
in which the integrand is expressed as a function of x. We therefore 
need (aP/a CP dg and (a ( [)s: In addition we shall want P as a function 
