260 _14- 



of tiie bubble due to the absence of water and the second 

 term G(A) is the internal energy of the gas. If the 

 gas obeys the adiabatic law, the internal energy is 



, , K M^ 

 G(A) = -3(* -IT 



where ^ is the adiabatic exponent, K is a constant depend- 

 ing on the explosive, and M is the mass of the explosive 

 used* 



The energy equation is 



(2.4) 'J^-»-U=E 



where E is the constant total energy in the system (after 

 the passage of the initial shock wave due to the explosion). 



3» Non-dimensional variables . 



A considerable simplification in the writing of the 

 equations is obtained by introducing non-dimensional quantities 

 with appropriate scaling factors. Likewise, in part III, it 

 is even more important to introduce non-dimensional quantities. 

 For the purpose of comparing the formulas developed in this 

 part with those in part III, we shall use the scaling factors 

 convenient for part III. It should be mentioned that these are 

 not the most convenient factors to use if the results of part 

 II were the sole objective. 



Set 



(2.5) A = La, B = Lb, T = Ct, 



where L,C are scaling factors with the dimensions of length, 

 time, respectively, and a, b, t are non-dimensional variables. 

 (Henceforth, capital letters will indicate dimensional quantities 

 and small letters non-dimensional quantities.) The scaling factors 



