101 



The rise of the bubble during the first expansion is thus 

 proportional to T^, and the ratio of the distance risen to 

 fljaax proportional to T. The rise Is therefore negllcible 

 for sraall explosions, but considerable for large ones. 



A conspicuous feature of (12) is that the rise 

 is enomously accelerated during the contracting stage, 

 because of the a in the denominator. This is an illus- 

 tration of the general instability of the contracting 

 stage. Even for rather sraall explosions, the velocity 

 of rise will probably become so groat during the con- 

 traction that the approximation of treating the gravity 

 correction as sraall will break dovm. It is certain, 

 hovifover, that a very rapid vortical acceleration vdll 

 take place, which will tend to create turbulence much 

 sooner* than it v;ould be created in the absence of gravity. 



