345 



Formulas (1.35) and (1.34) shov/ that a ana 6 depend 

 on the value of E and of I, and I_. If we consider the 

 ratio ct /p we have 



2 T 2 



(2.3) ^ = 4l2i-l(2g/3)-^/2 or ^ = 1.155 ^ 



o 

 which is independent of E. A graph of I-i/lp ^°r different 



values of k and y is given in Figure 9. 



Three physical quantities are needed to fiilly describe 

 the bubble motion — the values of K, Y and E. Since we have 

 only two constants a and p determined, we must assume the 

 value of one of the three quantities, we shall asstmie that 

 Y = 1.25, the value proposed by Jones for T.N.T.j and then 

 by the use of Figure 9 we find that k = .23. From this 

 value of k, using Figures 1 and 2 and formulas (1.35) and 

 (1.34), we find that rQ = 500 calories/gram. Since the 

 detonation energy of Tetryl is 1060 calories/gram, this 

 value for rQ is another confirmation of the theory. 



Since we know the value of E = rQJjI, we can use (1.1) 3 



and get 



(2.4) L = 13.88 (w/Zq)-"-/^ 



where L is in feet, Vv in pounds and Z in feet, and 



C = 2.997 W^/^Z"^/^. 

 o 



Y-1 



Since k varies with depth as Z' , the value, k = .23, 

 is really an average value over the range Z^ = 33 to 

 Z = 56.5. If we assume that this value of k corresponds 

 to a depth halfv/ay between the bottom and the surface of 

 the water, we find that k varies from .215 to .244. This 

 change in k can be neglected in the calcxilation of the 

 period, momentum and migration. However, in the calcula- 

 tion of the peak pressiire it must be taken into accoimt 



-2/3 ("^-1 ) 

 since the pressure varies as k ' ^ ' ' . 



