332 



center moves during the first oscillation, the maximum 

 and minimum radius of the bubble and, finally, the peak 

 pressure emitted by the bubble. The formulas are given 

 in terms of certain integrals which can be evaluated by 

 the method given in Report 37. IR. Numerical integration 

 of the differential equations of motion of the bubble is 

 completely unnecessary. For convenience Pigiires 1-6 con- 

 tain graphs of these integrals for the most frequently 

 occurring values of the parameters. 



Section III contains a discussion of these formulas 

 and a short Indication of their proof. A careful analy- 

 sis is made of the dependence of the parameters in the 

 bubble motion upon the properties of the explosive. It 

 is shown that, by a study of the periods of bubbles 

 placed at different depths, it is possible to determine 

 the amount of energy left in the bubble after the shock 

 wave has passed and also to determine the exponent in the 

 equation for the adiabatic expansion of the explosive. 

 This seems to be one of the very few methods by which 

 this exponent can be found. 



A similar procedure can be used to determine the 

 amount of energy left in the second bubble oscillation. 

 The experiments indicate that only about 16 percent of 

 the original energy of the explosive remains. Calcula- 

 tions show that the energy radiated by the pressure pulse 

 emitted by the bubble at minimvun size is not large enough 

 to explain the energy loss . The explanation of this high 

 dissipation of energy is one of the major xinsolved prob- 

 lems of the theory. 



As was mentioned before. Section IV contains a solu- 

 tion of the "electrostatic problem" equivalent to the 

 problem of a bubble placed between a rigid bottom and a 

 free surface. 



In Section II the theory is applied to the analysis 

 of some experimental data obtained at Woods Hole by Arons 



