22 -'°- 



perioa as beinj aetermined oy the pressure D^ of tne first pulse ana tne second half as determined 

 by the value- n, for the second pjls:-. The time int=rval can than be taken to be proportional to 

 (TI ^ + n ^''), In practict little difference is involved, otherwise equation (l2a) would require 

 correction for danpinj. The above result can be jeneraliscd for any t*o consecutive pulses of a 

 train arising from -i sinjle detonator. If 0^, H^ ^. ^ are the amplitudes of the nth, (n + i)th 

 pulses and T , ^ the time interval between them, then 



j^_ ^^ ^ c (n^i/' . n^ ^ ^1/') (31) 



This relation has Been tested ajainst experinental fijures. Relative values of U^ 

 appropriat2 to successive pulses have been measured off from the C.R.O. records. This cannot be 

 done satisfactorily from one single photojrapn because 11^^ decreases too rapidly with n to allow of 

 accurate measurement over a numciir of pulses. However, a series of photographs wer? taken in which 

 the amplification was progressively Increased. These enabled mean values to oe given to the 

 ratios n /n from various pairs of consecutive pulses. In this way it was found that the 

 pressure amplitudes cf the first five pulses were in tne ratio 



n. : n, : n, : n : n. 



From equation (3l) the corresponding time intervals --re calculated to be In the ratio 



1.45: 1.29: 1.12: 1.00 



Tne corresponding values got oy direct measurement from Figure 2 are 

 1.67: 1.23: 1.10: 1.00 



Agreement is considered satisf:^ctory in view cf the fact that complete reliance cannot be placed in 

 the amplitudes of the pulses shown in Figure 2. The initial pulses are richer than tne late ones 

 in nigh frequency sound of the oraer of several hunored Kc/s., ;nd the receiver and amplifier do not 

 necessarily repriuce them in true proportion to tne others. This woulj affect the calculation of 

 T,,more than the other intervals. 



C on SI (jerot ton s of the assum-ptions m ade. 



The foregoing rosults have been derived on the basis of certain assumptions. These 

 assumptions are now considered in the light of tne results obtained 



(a) The compressibility of the water . 



It is legitimate to treat tne water as an IncomoressiOle fluid only in so far as tne radial 

 velocity of the bubble Is small compared with that of sound in water. From equation (P) It may be 

 shown that the maximum r.=.Jlal velocity of the bubble occurs when j- - j < ^nJ that this mc.ximum 

 velocity is ° 



i. 

 16 



For the small detorators this amounts to 2.7 lo" cms/second. The velocity of sound is 16 10* cms/second, 

 so that the radial velocity Is at most 1/6 that of sound. The assumption of incompressibul ity is 

 therefore quite reasonable as a first approximation when It is remembered that this maximum velocity 

 is operative for only a relatively short part of tne expansion. 



(b) T he finite duration of the explosi on. 



It was assumed that the exoloslon took place instantaneously, whereas in fact for the 

 detonators It lasts about 2 micro seconds. Assuming an instantaneous explosion, the expansion which 

 takes place in the first 2 fi secondsis now considered. Equation (s), for small values of t, can 



