- A - 



42 



damage which the high pressure accompanying this stage is 

 capable of doing to neighboring structures; moreover, the form 

 of the plumes sent up by the explosion will obviously depend on 

 the way the bubble is moving when it breaks the surface. A the- 

 oretical discussion of the migration effects due to gravity and 

 to neighboring surfaces is given in Section 5, with mathematical 

 details in Appendices 4 and 5, respectively. The mathematical 

 methods used here, and those used in most of the other theoretical 

 papers of this volume dealing with the migration effect, have not 

 been elaborated far enough to provide a quantitative calculation 

 of the extent of the departures of the bubble from spherical shape. 

 However, some qualitative comments on these departures are given 

 in Section 6. 



Experiments on the various aspects of the pulsation 

 phenomenon have usually shown a quite satisfactory agreement with 

 the predictions of the theory. A notable exception has to do 

 with the apparent loss of energy between successive pulsations, 

 a loss which occurs in the brief time when the radius of the 

 bubble is near its minimum. It has been established that some 

 as yet unelucidated mechanism of dissipation does away with an 

 amount of energy of the same order as the known energy loss from 

 acouotic radiation. Some brief speculations on this topic are 

 given in Section ?• 



^A. B. Arons, J. P. Sliffco, and A. Carter, J. Acous. Soc. 

 Am. 20,271 (194^); A. B. Arons and D. H. Yennie, hev. iMod. 

 l^hys. 20,519 (1943), also Volume I of this Compendium. 



