48 



gas bubble (and therefore that, In the water) changes 

 by only a very small fraction of its value in the 

 time required for an acoustic wave to be propagated 

 through a distance of the order of the radius of the 

 bubble. This ensures that the flow in the bubble 

 region will teeep in phase with the motion of the 

 boundary of the bubble. 



(d) In many cases, though not all, the unilateral 

 migration of the bubble in its first period, due to 

 gra-wlty or other influences, is of fairly small 

 magnitude compared with the maximum radius of the 

 bubble, and the bubble remains fairly accurately spherical 

 in shape. As will be shown later, this is the case 

 when the sixe of the explosive charge is sufficiently 

 small in oompartson with the external hydrostatic 

 pressure. 

 The more refined theories to be considered later in this article 

 will explain the validity and limitations of the simple 

 theory in a more quantitative way. 



We shall therefore assume for the present that the water 

 moves radially outward or Inward in such manner that the 

 amounts of water crossing any two concentric spheres in a 

 given time are always the same; if the motion is spherically 

 symmetrical this means that the variation of velocity v with 

 radius r Is given by 



