67 

 It will be noticed that (IS) consists of a periodic 

 terra and a monotonic one, the latter corresponding to repulsion 

 from a free surface and attraction to a rigid one. This can be 

 understood qualitatively from the fact that the pressure gradient 

 due to the image is most effective, in imparting normal momentum 

 to the bubble, when the bubble is large. At this time the image 

 pressure gradient is toward a free surface or away from a rigid 

 surface. The predominant motion is in the direction opposite to 

 this pressure gradient. Just as in the case of the rise due to 

 gravity, the velocity of migration due to the surface contains a 

 term proportional to the reciprocal of the volume of the bubble, 

 which becomes extremely large in the contracted stages. 



In making comparisons of theoretical and observed migra- 

 tion rates, one must usually deal with cases where both gravity and 

 boundary surfaces are present. To the order of approximation used 

 in Appendices 4 and 5, the velocities (17) and (18) can merely be 

 added in such cases. The relative importance of the migration 

 effects (17) and (18) as compared with the rest of the motion can 

 be measured by a ratio such as (dh/dt )/(da/dt ) . For (18) this 

 ratio at any stage is essentially a function of h/a , and is 

 practically independent of p or the size of the explosion. For 

 (17), however, the corresponding ratio is proportional to 



'^^max-^Poo ' ^° ^^^^ ^^^ gravit 

 the explosion or the smaller p 

 For the experiments o 

 duction and described in Appendix 8, the combined effects of 



pga /p , so that the gravity rise is more important the larger 



uloLX OO 



ion nr* t-.ho cimallor" n 



00 



For the experiments of Ramsauer mentioned in the intro- 



