596 





where C is a constant which in general should depend on q. If Eq. (1-3) is 

 to supply physically admissable radius-time ounces, (1-q/l+q) + £, must not 

 exceed unity. The best fit is obtained, however, when: 



i^ * e - 1. (1-4) 



Assuming that Eq. (I-4-) is generally valid, the parametric form of the empirical 

 radiua-time curve becomes: 



4-<^'[^-<i^' -f] 



W I? - ="" ¥ ] "-5) 



Figures 4-9 show the data mentioned previously along with curves cal'iulated 

 from Eq. (1-5). These ciu~ves show that, with a suitable choice of q, E(^ (1-5) 

 give a good analytic representation of the radius-time curve for the portions 

 of the bubble oscillation which are of interest; namely, for values of T/Ti 

 greater than 0.05. This follows from the fact tnat bubble phenomena such as 

 the migration to the time of the first minimum in the radius (A_i), the pressure 

 pulse emitted by the bubble, etc., are independent of the exact shape of the 

 radius-time curve in the early stages of the period. 



It should be noted that the empirical radiua-time curve in the form of 

 equation (1-5) involves only one arbitrary parameter, q, which has a direct 

 physical significance, as has been pointed out previously. Hence there are 

 two main uses to which the equations developed above can be put. One can 



-AO- 



