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appears from the calculations of Kirkwood(3) and others, to be discussed later, that smal] changes 
in the chemistry of the decomposition make surprisingly little difference to the final results. 
In this report we shall use the adiabatics for T.N.T. and (T.N.T./Aluminium 85/15) obtained by Booth. 
We may therefore take it that the two equations of state are known with sufficient accuracy 
for practical purposes. A more difficult question is to decide the initial conditions from which 
to start our hydrodynamical calculations. It is known from Taylor's theoretical work that a 
spherical detonation wave is a theoretical possibility, but there is no definite evidence that it 
really exists. We nave therefore two possible choices. We might take the gas to be initially at 
rest at a high, but uniform, pressure, or we might take initial conditions based on the assumption 
of a spherical detonation wave. It is desirable to obtain data using both assumptions. 
Calculations already carried out. 
The first attempt was made at this problem by Penney. He obtained results which give the 
correct value for the peak pressure at great distances, but the wrong form for the pressure-time curve, 
the pressure very quickly dropping to zero, then rising again, an effect which is not observed 
experimentally. In a secmd attempt Penney and Dasyupta attacked the problem again, obtaining a 
curve very like those observed experimentally. It is difficult to compare these two reports directly, 
because, although in both substantially the same method of following the changes in pressure is used 
(a step-by-step method based on the Riemann hydrodynamical equations) two of the assumptions are 
Changed. In the first paper the initial conditions are those of a gas at rest at uniform pressure, 
in the second those proper to the region just behind a detonation wave. In addition, different 
equations of state for water are used in the two papers, It was partly in order to sort out the 
effects of these two changes that the present calculations were undertaken. 
Independently, Kirkwood and others(3) have attempted to obtain a theory of the propagation of 
the pressure pulse which shall enable results to be obtained in analytic form for differant explosives, 
without having to report the laborious step-by-step process for each one, In all cases the initial 
conditions assumed are the same as those of Penney's original paper (gases initially at rest), but 
the equation of state for water is practically identical with that used by Penney and Dasgupta, so 
that here again no direct comparison is possible. Kirkwood(3) and his collaborators have carried 
out the work for a large range of explosives, and have 21so examined the effect of smal) variations 
in the equation of state of the gaseous products, and of temperature and salinity variations in the 
water. It appears that the effect of all tnese can be neglected for practical purposes. 
The calculations actually carried out, the results of which are presented in this report, used 
the step-by-step method described by Penney. To try to maintain accuracy the steps were kept quite 
small, so that in 30 —- 40 steps the shock front at the head of the pressure pulse had attained a radius 
of about six times the original radius of the charge (taken for convenience as 50 cm). These results 
were extrapolated to greater distances by a method suggested by Dasgupta, to be described later. The 
equation of state for water was that used by Penney and Dasgupta and was practically identical with 
that used by Kirkwood and others(3). The equation of state for the gas was that calculated by Booth, 
while the initial conditions were that the gas was at rest at uniform pressure. In addition to T.N.T., 
the calculations were carried out for a T.N.T./Aluminium 85/15 mixture, to obtain a direct assessment 
of the effect of adding aluminium to a high explosive, and for comparison with Kirkwood's(3) work. 
With these calculations avallable, we are in a position to make the following comparisons:— 
(a) To ascertain the reason for the discrepancy between Penney‘'s earlier results and Penney 
and Dasgupta's later results. 
(b) To make a direct comparison between the step-by-step and Kirkwood methods. 
(c) To obtain an assessment of the effect of adding aluminium to a high explosive. 
Criticism of the methods. 
The methods have both been fully described elsewhere, so that it is sufficient to say here 
that the step-by-step method is based on the equations:— 
oe 
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