433 
where C, , O| , and aie refer to the initial values of these variables on 
the gas sphere at time t = 0. Introduction of a new variable y » defined 
as o est 
ea ‘Utfpe')? 
oo 7 Via 
(5-14) 
= do + te —- - f (4 -—_ 
Nee a esl eee 
into Eqe 5.13 and differentiation with respect to c gives the following. 
linear differential equation, 
’ & t 
dy 2 641%) Bajar, ot HME Die 
et Ge PP Gl) (5.15) 
Nie jae | Ge es | 
te) = 3 [Stas - 
Solution of Eq. 5.15 yields the result 
Co Vo u GaaiG: f dp 
= —— eee — “oe 
I ee J erat "ep CF alias) ~ 2 
Eke nS Cuma, exta(a 2 (5.16) 
AG, a ) i = Fl (e/a, ) doy - 
% 
24 To obtain Eq. 516 we first integrate the linear equation 5,15 in stand- 
ard form, using the condition 43 O for t=O. Then 
Co ‘ 
4.5 2, |" Ge) [tent] at, 
BG, 
: Galt) a ¢ 
Rian. | ep eaeet PE 4 o.ce Soc) | 
Integrating the first term of Ga(t)N‘Cé) directly and the second 
term by parts, we obtain Eq. 5.16. 
46 
