264 .13. 



The equation (2. 15) shows that when the bubble is near 

 its minirauin size, the linear momention 3 a b remains constant. 

 Denote this constant value by s . Then 



(2.16) b=^ , 



and the energy equation (2.11) yields 



(3.1V, :^.^.^. j . 



The equations (2.16), (2.17) completely determine, in terms 

 of s, the motion of the bubble during its most interesting 

 phase when the radius a is small. An integration of (2.17) 

 and then of (2.16), yields a, b as functions of t. 



Equation (2.14) gives an expression for the quantity 

 (a a)*, which is important for the determination of the pressure; 



(2.18) (a^a)- = a | ^ I^ ^ | i^ ^ | -^ 



Substituting (2.16), (2.17) in (2.18), we obtain 



6« The minimum radius * 



The value of a quantity q at the time when the bubble 

 is exactly at its minimum size will be denoted by q. The 

 minimum radius a of the bubble is obtained by setting 

 a = in (2.17). The resulting equation is simplified by intro- 

 ducing, in place of a, the (non-dimensional) internal energy 



