410 
Thus G¢ €) is the value of the function G on the surface of the gas 
sphere at time t . We are now provided with the following relation be- 
tween the kinetic enthalpy Q at any point Crt) and the value of G on 
the surface of the gas sphere, G (T) at a retarded time Y determined 
by Eqe 3230, 
Oiler) 2G, (t)/r = alti yi7r , (3.33) 
where $2, (t) is the value of Q on the surface of the gas sphere at time 
t. 
At first glance it might seem that the solution 3.33 would differ 
from the incompressible solution, Eq. 3.21, only in the detail that the wave 
requires a finite interval of time to reach a given point J”. However, if 
€ diminishes with diminishing {2 and if the value of € at the shock front 
exceeds the wave~front velocityyU , then there are other important differ- 
ences, There will occur a progressive destruction of the crest of the wave 
at the shock front and, when G.( t ) is a monotone decreasing function of 
t 9» & progressive broadening of the profile of the wave as it advances 
outward. 
To illustrate these points, we consider the value of [°([{}t the 
shock front, given by Eq, 3.30, 
R : 
dr’ ar 
¥ Ul[r ar) | Peet 
(hee , (3.34) 
where the integral ie Ar'/ U is the time t, required for the shock 
front to travel to the point R. We remark that it € >U , T  ini- 
tially zero, is an increasing function of R. Thus at a specified point 
23 
