461 
function in a Taylor series in the time, the well-known peak approximation, 
is appropriate for an initial estimate of y « This corresponds to an expo- 
nential f(?), ae 
= © , 
i (8.17) 
For the asymptotic quadratic energy-time curve, corresponding to the linear 
pressure-time curve of the positive phase of a shock wave, 
pie sf7 PE) orap- Sk, 
f = oO y) ~~ d24, 
y= 2/3, 
As a convenient empirical interpolation formula between the two extreme 
(8.18) 
values of -¥ » we have found the following expression to be satisfactory. 
- Pin7P 
p= cone (8.19) 
For explosion waves in water, the value v = | is suitable for all but very 
great distances from the charge, Kt >? 100 charge radii. 
Elimination of ie between the first two of Eqs. 8.15 and combina- 
tion with Eqs. 8.8 yield a set of four eauations for the four partial deriv- 
atives (dp/at), (du/dt) i (dp/ on) ‘ and (Ou/3 ty) at the shock front, 
4, 
Bap), Io fow\ "eine 2". at pas 
(5) ; u., (52) a ag D(R) 
& (§ + passe) ae (24)=- 4/2) 2 4820) 
duy's u(dey= 2 () © 2(st), 
72 
