486 
where O° isthe Riemann finction in the gas sphere and Ut) is the 
shock velocity in the exterior medium, determined as a function of pres- 
sure by the Hugoniot conditions. The asterisked quantities refer to the 
explosion products and the unasterisked to the exterior medium. The sub- 
script D refers to the Chapman—Jouguet detonation state. The first of 
Eqs. 9.24 expresses the fact that the eenannaye 2 computed normal to the 
generating surface, initially vanishes in the receding rarefaction wave. 
In the limit of infinite detonation velocity, the first of 
Eqs. 9.24 reduces to 
Baie epee, (9.25) 
which is in agreement with the expression of section 2 for the determination 
of the initial pressure from the instantaneous constant volume explosion 
state, 
In the development of the propagation equations, the rate of 
energy delivery has been approximated by an exponential function of time. 
As in section 8, we may assume that the integral of this exponential func- 
tion is equal to about one-half the total energy of explosion. The disad- 
vantages of this procedure are minimized by the circumstance that except 
in the immediate vicinity of the charge, the shock-wave parameters are not 
very sensitive to the initial energy. Accordingly, the initial value of 
the energy variable D is taken to be 
a 
D, = 3 [7x ei ) 
(9.26) 
96 
