114 



Appendix 4, is /t / xi 



/ »^ (^) - 



I surface tcnn i _ 3 /O 



j gravity term ", " ? /t 



gh / a"* dt 



The intesrels can be evaluated for t*T, by the methods 

 of Appendix 1, in the approximation which neglects gas 

 pressure. The results are 



dt = 0.30 V-f? af_ (34) 



;, 



{^J ""fg ma. 



'o 



a^ dt = 1.14 Y:f a^^ (35) 



^°° 



so that the ratio is 



I surffgg ^e™ ( - 0.20 _Z- » .^SSX (36) 



I gravity term | " p gh Ti ^ 



For small explosions in shallow water or close to a rigid 

 surface this ratio can become appreciably greater than one, 

 so that the bubble can, for example, sink instead of rise. 

 It must be renembered of course that when h is as small 

 as two or three times a^j^^^ the rate of drift given by (32) 

 becomes so large during the contraction that it can by no 

 means bo regarded a s a small correction to the motion, 

 llov/ever, (32) should give the drift fairly well over the 

 greater part of the first period, so the qualitative con- 

 clusion that a bubble will rise or sink in a given experi- 

 ment is probably safe. 



