75 



flow of heat outward In one period has the orier of magnitude 



A^Ja^. K^dt (19) 



Jo a 



where K Is the thermal conductivity of the gas and Ae the 



difference in temoerature between the center of the bubble 

 and the water at the boundary. The ratio of (19) to Q or W 

 becomes smaller the larger the explosion. However, it is 

 easily verified that (19) is entirely negligible as compared 

 with the total energy Q or W, even for the smallest explosions. 

 It seems unlikely that there can be any appreciable departure 

 from a<Jlabatic conditions, even when convection inside the 

 bubble is taken into account. 



(Iv) A l-^g In the achievement of ther-"al equilibrium 

 In the gas 3° it is comoressed. If such a lag is present the 

 work done by the water in compressing the gas will be greater 

 than the work given up by the gas in re-expanding, and the dif- 

 ference will be manifested as an irreversible heating of the 

 gas. It is not unlikely that such an effect exists , especially 

 since soot particles and possibly water droplets may be present 

 in the gas. However, if this is the predominant cause of the 

 energy loss, the unbalance in the energy equation ought to depend 

 strongly on the scale of the explosion. For the dissipation 

 due to the lag In equilibrium should become very small when the 

 duration of the contracted stage becomes either very short or 

 very long comnared with the time required to establish thermal 

 equilibrium in the gas. To the best of the author's knowledge, 

 no such dependence on scale has been noticed; however, there 

 is not a very wide range of charge sizes for which accurate 



