333 



and. his co-workers . Three hundred grams of Tetryl were 

 detonated at varying depths below the surface in water 

 23.5 feet deep. The period of oscillation, the peak 

 pressure and the distance the bubble moved were measured. 

 The agreement between theory and experiment as regards 

 periods is excellent; as regards pressure and distance 

 the bubble moves, the agreement is only fair. 



Since the agreement as regards periods is one of the 

 outstanding successes of the theory, it seems worthwhile 

 elaborating on it. Let f be the period of oscillation of 

 the bubble at a depth H feet beneath the surface. In 

 section II it is shown that f (H + 33) ' varies linearly 

 with 9?-, (H + 33)" ' where f^ is a complicated fiinction of 

 H, so that we have 



T(H + 33)^/^ = a + p^^(H + 33)"^/^ 



where a and p are constants independent ofH. It is also 



shown that a = C-,E ''^ and p = CnE ' where E is the 



amount of energy left in the bubble after the shock wave 



has passed and C-. and Co are two constants depending upon 



the exponent in the equation for the adiabatic expansion 



of the explosive . 



Prom the experimental data, T(H +' 33) ' and 

 • -1/3 

 f-, (H + 33) ' are calculated and then the constants oc and 



p are determined by the method of least squares. Prom the 

 values of a and p the amount of energy left in the bubble 

 and the adiabatic constant can be determined. In the par- 

 ticular case considered in section II it is found that 

 about 48 percent of the original energy of the explosive 

 is left in the bubble. 



Asstmiptions 



As in Report 37. IR we shall idealize the problem by 

 making the following assumptions: 



