585 



In each case the value of the hubble energy ia also given neglecting 

 the internal energy of the gas (k - 0), which fixes the values ajj = 1 and 

 t = 1.492. Here it is to be expected that the radius calculation will 

 give a lower value than that obtained from the tjerlod constajit, since t is 

 relatively insensitive to k, whereas a^, when the internal energy is taken 

 into account, may decrease 10^ by comparison with its value for no 

 internal energy. This is found to be true in nil , cases except the two 

 involving tetryl charges very near the surface. Consistent calculations 

 of the energy cannot be made in these two cases, since the energy cal- 

 culated from the maximum radius is apparently higher than that obtained 

 from the period of oscillation (this leads to values of t/ay lower than 

 any found in Fig. 3). 



No complete explanation of this anomaly can be given at present. 

 However, it is interesting to see what the theory predicts for a case in 

 which the adiabatic law, Eq. (9.1), is replaced by the simple assumption 

 that the gas pressiire is a constant, pg. This assumption may be a rough 

 representation of the facts, if, during a large part of the motion, the 

 condition of the gas is largely determined by the condensation of water 

 vapor, a condition which might be true when the explosion occurs at the 

 shallowest depths described in this report. 



The resultant expressions for non-dimensional radius and period are, 

 respectively: 



'[-?J 



-^' (10.4) 



1.492 1-^ (10.5) 



Although the ratio t/ay is never less than 1.492 for positive pressure 

 ratios, Pg/p , and thus cannot explain the low value t/ajj = 1.46 found 

 experimentally, it seems noteworthy that both the radius and period 

 constants should be larger on the basis of Eqs. (10.4) and (10.5) than 

 in the case wl-iere the adiabatic law holds and that the observed constants 

 are indeed found to be larger near the surface than at greater depths. 



Calculations for the second period of bubble oscillation are given 

 in Table XXIII. 



From this discussion it is seen that suitable data are not available 

 at present to determine the most appropriate value of the specific heat 

 ratio. It should be mentioned that the theoretical calculations of Jones 

 indicate an effective value of Y = 1.25 for TNT of the density used m 

 these experiments. 



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