46 



Of the equations enumerated above, only those enumerated under 

 (b) are needed to determine the latter motion. In the absence 

 of gravity these equations are invariant under any scale changes 

 for pressures, lengths and times which satisfy Pi/Pp ' 

 (L-j/Lp) /(t-|/tp) . In this approximation explosion bubbles from 

 all sizes of cb«rs^ at all depths execute homologous motions. 

 Taylor has shown that if gravity is not neglected, this homology 

 rule does not completely disappear, but reduces to a homology 

 over one degree of freedom instead of two. 



Departures from the scaling law (1) can be produced by 

 irreversible processes taking place inside the bubble, and de- 

 partures from both types of scaling law may be expected if 

 turbulence becomes serious in the water. Failures of scaling, 

 if properly ihterpreted, may thus be of considerable significance 

 in detecting the presence of irreversible phenomena. 



See the article by Taylor, this Volume. " 



A 



