83 



turn out to be negllGible anyivay. It will be convenient 

 to separate the intej^rated equation into terras charac- 

 teristic of Incompressible laotion and tenns involving 



V'V s _JL. ^ (r*v) s (5", say. /ccordlngiy, v;e note that 

 r*- 3 r 



^oo oo — . _ ^- oo 



dr 



d a - 

 dF^ ' 



H-^^If 



The Intecrated equation (2) now becomes 



_ d _a _ 

 dt*^ 



da 



--- oo 



^ 14/^1^^^ 



o \ 2>r r 



'^r- oo 





or finally. 



a 1 

 dt 





(3) 



This equation should be valid even for rather early stages 



of the motion, when the shock v;ave front has advanced only 

 a few times the initial bubble radius- This is because the 

 ste.rting equation (1) is valid ric-b tliroujh the shock 



