-31- 277 



The last equation (3.9) Is noteworthy, since a^ repre- 

 sents the non-dimensional maximum radius of the bubble. 

 The actual maximum radius A, is thus 



A^ = .924 L. 



If the Internal energy -375 of the gas were neglected, 



the maximum radius would be exactly L. 



The quantity ^1 + f^ in the integral (3.7) is 



very closely equal to 1 + ^ = 1 + _|l as Is shown in 



2 3bo 



appendix II. Making this approximation, we can evaluate 

 the Integral (3.7) niMierically, This numerical evaluation 

 Is discussed in appendix III, the result being 



t, = .735 + 



.136 



1 - '"^^ -^ ^ 



The total (non-dimensional) period t of the pulsation is 

 therefore 



(3.10) t = 2t^ = 1.47 + ^1^ = 1.47 I 1 + i^ j . 



Formula (3.10) shows that if no rigid walls are 

 present (b =00), the actual period T in seconds would 

 be 



T = 1.47 C, 



or about 3/2 times C • This provides the physical inter- 

 pretation of the scaling factor C mentioned in section 3 

 of part II, 



Substituting b = b , b = in (3.5), we obtain for 



