360 
= ith = 
At small distances, however, the two theories are in fundamental disagreement as to what 
exactly the effect of adding Aluminium is. This disagreement is particularly serious because, in 
each pair of results, nothing has been changed except the adiabatic of the explosion products so that 
it is clear that either one or the other theory cannot be relied on near the charge, even for 
Comparison purposes. 
(f) The effect of neglecting the ingoing wave in the water. 
Comparison of the two sets of curves indicates at once that Kirkwood's(3) theory tends to give 
too high values for both peak pressure and time constant, but that the correction involved may well 
differ considerably for different explosives. 
(g) The effect of Kirkwood's exponential assumption. 
Kirkwood"s theory apparently involves a straight assumption that the pressure-time curve is 
exponential. The constants are determined by the initial conditions of continuity of pressure and 
velocity at the gas-water interface, and once this has been done the subsequent behaviour of the 
pressure pulse is determined entircly by the properties of water, the properties of the gas having 
no further chance of influencing the answer. We think that our results, showing as they do that the 
predicted form of the pulse is exponential, represent a distinct improvement, and also that there may 
be some way of determining the time constant which shall take account, by some averaging process, of 
part of the early history of the gas bubble, as distinct from the conditions at the initial instant 
only. At later instants, tne Q function in the water will have to be considered explicitly. This 
point will be investigated further. 
Conclusions. 
Apart from the exceptions noted above, it will be seen that the various theories are in 
reasonable agreement with one another and with experiment, and that the causes of many of the apparent 
discrepancies can be traced. The step-by-step calculations justify Kirkwood's(3) assumption of an 
exponent ial pressure pulse, but indicate that the determination of the constants of the exponential 
curve needs some method more elaborate than that used by Kirkwood(3), even if only comparisons of 
different explosives are wanted. It is probable that this method will need to take explicit account 
of conditions at the surface of the gas bubble at instants other than the Initial one. The Q 
function in the water is then not negligible near the gas bubble, and will probably have to be 
allowed for also. 
References. 
(1) Taylor and Davies. "A Measurement of the Pressure close to an Explosive Underwater" 
(2) Kirkwood and Others. U.S. Report U.E. 24 
(3) Bethe, Kirkwood "The Pressure-wave produced by an Underwater Explosion". A 
et al. series of teports beginning with 0.S.R.0. 588, Most of the 
information is summarised in 0.S.R.D. 2022 which supersedes 
some of the earlier reports. 
(4) Wood. “Nature of the Pressure Impulse produced by the detonation of 
explosives under water. An investigation by the Piezo-electric 
cathode-ray oscillograph method", 
