396 
wave is about €,/6 in the typical case, We may reasombly expect that after 
an interval of time of this magnitude, the head of the detonation wave will 
have disappeared in the gas sphere by transmission of a shock wave to the 
water and by the smoothing effect of receding rarefaction waves. 
In the theory of propagation of the shock wave in water, we 
shall find that the crest of the shock wave is progressively destroyed as 
it advances outward and that the wave emitted from the gas sphere before 
a certain time TU (®) is dissipated before the shock front arrives at a 
distance R from the center of the charge. In the typical case of TNT, 15 
is about @,/2 at a distance of 25a,. Thus,except in the immediate neigh- 
borhood of the charge, we may assume that the initial details of profile 
impressed upon the shock wave by transmission of the head of the deto- 
nation wave into the water are not extremely important. We therefore 
specify initial conditions in the gas sphere which are closely approxi- 
mated after the very short initial period of time @)/6. These are the 
same conditions as those employed by Penney. At time t = 0, the gas sphere 
is assumed to be at a uniform pressure - the equilibrium pressure corres-— 
ponding to adiabatic conversion at constant density of the solid explosive 
into its decomposition products, The pressure Pe may be calculated from 
the heat of the explosion reaction and the heat capacity and equation of 
state of the products, 
The pressure discontinuity Pe-Po at the boundary a, is at once 
propagated into the water, the boundary conditions 2.1 are established, and 
Eqe 204 is satisfied, At the same time a rarefaction wave starts into the 
gas. By the Riemann theory, the value of a certain function ¥ is initially 
10 
