459 
The integral of the energy-time curve, Di {) » is thus expressible, 
through Eq. &el4, in terms of the peak pressure-distance curve of the shock 
wave at distances beyond R - It is to be remarked that Eq. 8.14 and the dis- 
sipation assumption do not violate conservation of momentum, since, through 
spreading of the wave, it is possible for the total momentum to remain finite 
while the particle velocity everywhere and the total kinetic energy tend to 
zero, Our dissipation assumption breaks down if the first shock wave can be 
overtaken by secomd shocks built up in its rear. This will not be the case 
if the pressure-time curve is initially monotone decreasing with asymptotic 
value b, e if the excess pressure p has a negative phase, a second shock 
will develop in the negative part of the pressure-time curve but cannot over- 
take the initial positive shock. In this case our theory will apply to the 
positive phase if the time integrals of Eqs. 8.9 to 8.14 are extended not to 
infinity but to the time es at which the excess pressure in the positive 
phase vanishes, The general theory of shock waves is not sufficiently 
developed to permit one to say that there is proof for the foregoing state- 
ments, or even that a spherical shock is stable, but the statements can 
nevertheless be accepted with some assurance as plausible, 
We now shall express the energy-—time integral in reduced form, 
GR) ies R* Pm Um ) vd, 7 
1 2 ‘a (=?) + (Ou Ys Zula) 
(Fn) (8.15) 
re t —¢(R) 
y= F(R, Pdr , = ia ) 
6 
FOR, 23) = re *pulR® Pm “Pod . 
70 
