50 



pulsatlona can be regarded as small oscillations in the neigh- 

 borhood of the radius at which the gas proHsur-? eqn&.le the 

 surrounding hydrostatic ^oreosure. For these grnall oscillations 

 Q is essential, but the calculation of the period la simplified 

 by the assumption of small airplitudess 



In Appendix 1 it is shown that when G a in (5). the 

 period of the motion is 



1. -5/6 1/3 

 T„ .-s 1.135 /o «^ p ' W ' (6) 



o ' ■^ 



This formula has been derived by Willis and others. Of course, 

 the comparison of this formula with observation Is not complete 

 unless a definite value can be Inserted for W. From the 

 discussion given above It Is clear that W will be appreciably 

 less than the total energy release's by the explosion. 

 Theoretical calculations reported in Volume I of this Compendium 

 agree with observation in assigning to the first pulsation 

 of the bubble a value of W of the order of half the chemical 

 energy Q released by the explosive, the remaining energy being 

 distributed in comparable proportions between energy carried 

 off to appreciable distances by the shock wave and energy 

 dissipated as heat by irreversible processes at the shock 

 front In the very early stages of its motion. A convenient 



10 



See the article by Willis in this Volume. 



■'•■'■See the article by Arons and Yennle in Volume I of 



this Compendium, or Rev. Mod. Phys. 20, 519 (1948). 



