51 



alteinative to deriving W from Q la to derive It from the 



maximum radius a of the bubble, If measurements of this 



max 



12 

 quantity are available. If (^(amax^ ^^ neglected , 



5 m (4ir/3) a^ax' p^ , and so (6) becomes 



T^ = 1.829 ^ * pj^ a^^ (V) 



The corresponding expression for the period of small oscillations 

 about the eq-alllbrlum radius a-|_ is, a(?ccrding to Appendix 1, 





2X f=^ p -* a, (S) 



where / is tl\G ratio of tho specific heats of the gac. For 

 / 2 1,5. (8) becomes 



3.13 /o ^ P ^ a^ 



Willis^ has shown that (6) does In fact describe the 

 periods of oscillation of the bubbles produced by charges of 

 various sizes at various depths. With a suitable choice of 



12 



The rather Indirect experimental determination of G-la^^j^) 



reporte-^ In reference 11 gives a value of the order of 0.2W at the 



maximum of the first pulsation, presumably at 500 feet depth; however, 



this value is open to suspicion since It is 50^ higher than the value 



obtained in a similar way for the second pulsation, whereas it should 



be smaller. Thus the correct '^{a^^g^y) might be as small as O.IW at 



this depth; at the surface, where p^ Is 16 times smaller, a 3 will 



be roughly 16 times larger, and ^(a^^^)/^ will be smaller by 



1- T 

 a factor 16 ^^ \ , "if tiq use Arons' value of 1.25 for the 



effective ratio of specific heats / . 



1"^ 

 ^See the article by Willis in this Volume. 



