91 



Appendix 3, where it is shown that only a negligible 

 aino\ant of enercy is radiated v;hen t he bubble is lar^o, 

 but t!iat at the first contraction an appreciable 

 radiation of energy may ta'<ce place. 



Before concluding, it should be mentioned that 

 the preceding analysis disposes of an objection v/hich may 

 be raised against the simple theory of Appendix 1. The 

 objection is that for a certain range of depths the 

 pressure j\imp at the shock v/ave remains {"greater than poo 

 for a larce part of the period of the first pulsation. 

 It is therefore not irjiediately obvious that the notion 

 of the bubble ivill be the same in the actual case as in 

 the non-compressive approximation, for which the prossure- 

 radiufl curve of I''icu.re 1 would be replaced by a monotonic 

 curve with asymptote pc© • 



