89 



first vanishes at this radius. The effect of the second 

 terra may be larcer than that of the first Just after the 

 explosion takes place, but the present analysis is pre- 

 vented by other reasons from applying to those stages. The 

 larger the radius of the bubble, the smaller the effect of 

 the second term conpared with the first: a numerical cal- 

 culation gives a value of about .05 for the ratio of the 



a 1 



second tern to the first when 



Since the first 



*max ~ 3 * 

 term Itself is not very Important, we shall drop the 



second tern and write (17) as 



P(r, - ct,t) dtdr, «=* I §(a,0) 



1 d 



M<iij}'-^iE[^(i;j 



(18) 



We are now ready to solve (3) by using (10), 

 (13), and (4). The lest term, on the left of (3) clan now 

 be seen to be entirely negligible, since the principal part 

 of the correction to the non- compressive approximation is 

 the term cacr(a) in (13) : we have in fact, in c.g.s. units, 

 ^/^10"^while ca — 10*" to 10 '^ , We thus write (3) 



a ^ + 





oo / da \ 



dp _^ a dp(a) f, HF 



Now the left side of (19) It 



1 d fj/daY 4 a-' 



sipcHs r'-^/ 



(i/J 



(19) 



