337 



and 



(1.9) ^(x) =t4-T + (1 - ^)t§ ^^ 5 +^'^]- 



■^ "^ ^ 1 (2n + 1)^ - x^ ^ 



Tables and graphs of the functions f(x) and t^ (x) are 

 given in the appendix (see Plgvires 13, 14 and 15 and 

 Tables 3 and 4) . Note that if the water is infinitely 

 deep, B = C30 so that from (1.7), (1.9) and (1.6) we have 



(1.10) X = 1, ^(x) = 1/2, <p^ = -1/2H. 



Bubble Quantities at Time of Maximum Size 



Small letters, a, b, h, etc., will be used to repre- 

 sent the non-dimensional values of the quantities repre- 

 sented by the corresponding capital letters. The sub- 

 script zero attached to these quantities will indicate 

 their value at the beginning of the bubble motion, the 

 subscript one their value at the time of maximtun size, 

 and a bar attached to them will indicate their value at 

 the time of recompression when the bubble size is a mini- 

 mum. 



The non-dimensional time from the beginning of the 

 bubble motion to the stage of maximum size is 



