514 
- 18 - 
standard in the case when W= 100 1bs. Under these conditions a correction of 4% may be required to 
al) measured areas to give the true area up to infinity; i.e. fi pdt = 1.04 f pdt approximately. 
Thus for a 24 1bs. charge the area of the p/t curve was measure uB to a time 0.565 x 10°? second, 
whereas in the caseof 4 charge weighing 1000 Ibs. the measurement of area extended to t = 4.30 x 107 
second. In plotting results it is necessary first of all to bring all the observations to a standard 
distance of 1 foot and for this purpose the inverse distance law has been assumed. All the experimental 
evidence available supports the view that this law applies to momentum M as well as to P_y. In Figure 
17 are plotted the values of M ( = oft pdt) as a function of w the weight of charge — the logarithms 
° 
of those quantities being used as a convenient means of determining x (in M @ w) the slope of the line 
in the graph. 1t will be seen that the experimental points (each the mean of all reliable observations) 
lie well on the straight line given by 
log M = 0.65 log W + 0.26 
1.82 wrod M — momentum in lbs/sec. per sq. in. 
i = ae W- weight of charge in Ibs. 
D0 -— distance in feet. 
This has still to be corrected to bring the area observations to infinite time, i.e. 
-65 
Me pisg 0a Ne lbs/sq. in. secs. 
Dy) 
{It will be seen that in this case the experimental result is in good agreement with theory, that 
momentum is proportional to the 2/3 power of weight of charge. The experimental result now obtained is 
regarded as very reliable, for in this case there is no doubtful gauge correction to apply, the area of 
the recorded p/t curve being exactly equal to that of the actual curve, since f pdt is independent of 
the gauge dimensions. 
(d) Energy and weight of Charge. 
The p.e. records and graphs referred to in (c) above were also used in the measurement of energy 
which is proportional to f p? dt, All observations were reduced to the standard distance of 1 foot taking 
E= Daal p2 dt the law of inverse square of distance being assumed since the experimental data supports 
this law. In Figure 18 the results of all reliable observations are plotted in terms of log 
— = log of p? dt and log W—- the number of Individual observations at each point being indicated. it 
will at once be seen that the points lie well on a straight line, which can be expressed by the relation 
log E = 1.00 log W + 4.12 or E = 13200 W 
joes £ 13200 W W- 1bs. weight of charge 
2 p - 1bs/sq.in. 
D- feet 
t - secs. 
i.e, the energy in the pressure pulse is directly proportional to the weight of the charge. It will be , 
observed also that in all cases, Fray Mor E, the experimental observations for gun cotton and amato) lie 
well on the same straight line as those for T.N.T. (see Figures 16, 17 and 18) — an important point in 
dealing with the practical application of these results. 
A matter of some importance arising from the above experimental relation connecting energy and 
weight of charge, is the calculation of the proportion of the available chemical energy of the charge which 
ultimately appears in the pressure pulse. tf p is the pressure at a point at a distance 0 from the charge, 
v the particle velocity and the density of the water, and C the velocity of elastic waves in the water, 
i i i @ 3 . es 
then the energy per unit &rea in the wave ish pvdt. Since p=, Cv approximately this is equal to 
° 
1 fe 6) 
fe J p* dt. That is, the total energy passing across the surface of a sphere of radius D is 
° 
47 02 
foe) + “ oO P 
7 if R p2 dt. Now our experiments indicate that 0? J p? dt = 13200 per 1b. weight of explosive, 
° 
the sevcee 
