434 
when G- (t) is known as a function of time, Eq. 5.16 determines Cy as 
a function of @ at the shock front, since y is a function of O~ alone 
by Eq. 5.14. By Eqe 509, Q” may in turn be expressed as a function of Fe 
and ic, and thus Eq. 5.16 determines ce as a function of R e in order to 
put this relationship into a more explicit form, we introduce the following 
definitions, 
% 
BuGe)- = eee: Gat) dt, 
XB) = |leIG, (5.17) 
xg = 7a, . 
From Eq. 5.9 and the definition of ZL as | + '/Ae, we find that Z is a 
function of 4 alone, 27 
2 RE SP sora a ere Ge 2s ‘| 2 
£ 207 [ i; (5 =) , (5.18) 
i ffs £2 a Lee a 
where () , is the initial value 1,6 O) of the kinetic enthalpy of the water 
at the gas sphere surface, Since Yy is a function of Z alone, it is by 
Eqe 518 a function of q alone, In fact, for large tT we get the asymptotic 
relation, 
= Ato = /7 
4 ae (5.19) 
[erg te fo, ZL t,. 
J (én | aA 2 Zy 
The definition of the characteristic time ee) is particularly useful 
when we employ a peak approximation to G,(t) e 
With the definitions of Eq. 5.17, Eq. 516 may be written in the 
form 
47 
