13 97 
greater part of this discrepancy is probably due to the gauges, which tend to under- 
estimate the maximum pressure from a small charge, as explained in Section 19. The 
time taken for the pressure to fall to -2 ton per square inch is ‘60 X 10-*second in 
one case and 1°80 X 10 in the other, giving a ratio 30. which is fairly near the 
scale ratio R = 3°62. The time-integral of pressure of the small charge for a period 
t = 10-*second is 0°30, while that of the big charge for a period Rt = 3°62 x 10-°is 
1:02, giving a ratio 3°4, which is very close to the scale ratio. The results with 
300-lb. charges at 50 feet (Fig. 1) are in equally good agreement with the theory, and 
so are the comparisons between other large and small charges shown in Figs. 12 and 
20, 7 and 17, 1 and 29. The small discrepancies between theory and results may be 
imputed to experimental errors and to differences in the make-up of the charges. 
Putting together the results described in the last three sections, it will be seen 
that when once the time-pressure curve has been determined for a given charge at a 
given distance it is possible to construct the time-pressure curve for a similar charge 
of any size under any conditions of distance and depth. For example, suppose it is 
required to know what effect will be produced at a point 10 feet below the surface 
by the explosion of a 5-ton charge of 50/50 amatol 100 feet below the surface and 
200 feet away horizontally. The curve for a 1,900-lb. charge at a distance of 924 feet 
is shown in Fig. 15; the corresponding distance for a 5-ton charge is 
3 D 
92h x ae = 167 feet, 
and the time-pressure curve for a 5-ton charge at this distance is obtained from 
Fig. 15 by increasing all the abscissw in the ratio 
§/11200 -Q]. 
1900 Pehi 
the ordinates of this curve are then diminished in the ratio ae giving the time- 
pressure curve of a 5-ton charge at a distance of 219 feet, which is the direct distance 
from the centre of the charge to the point of reference ; finally, since the difference 
between the direct and reflected paths from the charge to the point of reference, by 
the construction shown in Fig. 2, is 9 feet, the pressure is cut off after 1:8 x 10° 
second. The result is shown in Fig. 19. Other examples of predicted pressure curves 
are shown (in broken lines) in Figs. 17, 22, 24, and 29. 
If the effect of the surface is left out of account, the maximum pressure P, the 
time-integral of pressure I, and the energy flux F from a charge of weight W at 
distance D can be expressed in the form— 
~ Wt 
e— Kip 
+ 
I=Ky 
WwW 
ES i 
K,, K,, and K,; being constants depending on the nature of the explosive and its 
container. Neither these formule nor the above method of predicting the time- 
pressure curve can properly be applied in the region near the charge, where the 
pressure exceeds 2 tons per square inch, this region being outside the scope of the 
present investigation. 
(10) Bottom Effects. 
The experiments described in Section 24 show that the pressure wave is reflected 
from a mud bottom with much diminished intensity; the time-integral of the 
reflected pressure is less than half what it would be if complete reflection occurred. 
Another point that was investigated was the effect of firing a charge on the 
bottom, instead of in mid-water. It is natural to expect that a stronger pressure 
wave would be generated ; the difference should be more marked the greater the 
elastic resistance and density of the bottom, both these factors making it relatively 
unyielding to a sudden pressure, with the result that the radiated energy is 
concentrated in the water. In the limit, when the bottom is perfectly unyielding, the 
radiation of energy would be entirely vonfined to the water, and the pressure wave 
