421 
-S 
asymptotically on time as ( (+ t/¢,) » where 8, is a characteristic time. 
The initial peak approximation to the term au’/ 2 in G@,(t) is there- 
fore poor, but due to the rapid change in sign of Du/Dt, a(t) may be 
treated as a slowly varying function of time. 
The peak approximation to the enthalpy) is to be obtained as 
follows, -t/6, 
We () = W,e ys 
1/8, = ~ [Dlg w/Dt] | (448) 
- (1/P, w,) [Dp/Dt] : 
where w, is the initial value of UW, (t) on the gas sphere. Using the first 
of Eqs. 4.7 to get the limit on the right-hand side of Eq. 4.8, we obtain 
8 > Ag/Cg, ) 
a os 3 i 9e 
/, 14, i C, + J, C, (409) 
ee ee Cn 
8, wo, fr ¢, +f, ¢, 
where the subscript 1 denotes as usual initial values of the quantities on 
¢ 
the gas sphere surface. Since act) is a slowly varying function of time, 
the appropriate peak approximation to a(t) Walt ) is 
-t/ 
alt), (t) = 40,6 9% (44410) 
Eqe 4.10 therefore determines the first term in Gt) » equal to 
ait) w(t) + u./2] » &B a function of time and of parameters depending 
upon the initial conditions at the gas sphere surface. 
In order to investigate the manner in which u( t) » the 
velocity of the gas sphere surface depends upon time, we return to Eqs. 4.6, 
the first of which may be written in the alternative form 
3k 
