176 
III. PRESSURE WAVE 16 
6. THEORY OF SECONDARY IMPULSES 
covered by his measurements carried off about 1/4 of the energy available in exploded 
TNT. 
The total impulse at distant points must in any case be measured by the ve- 
locity of the afterflow, as stated in the foregoing; for at a distance the compres- 
sion of the water is always negligible. This fact furnishes an easy method of con- 
necting the impulse with the energy of the afterflow, as was pointed out by W. C. 
Herring (9). Estimates thus made in actual cases come out surprisingly large. Thus, 
in the case of 300 pounds of TNT exploded 34.5 feet under the surface, if we insert 
in the formula given in the foregoing for Jw—p,)at , W, = 300 x 1,200,000/2 foot- 
pounds, representing half of the initial energy that is available by expanding the 
exploded TINT to zero density, also p= 1.99 slugs per cubic foot and p = 2 x 14.7 
x 144 pounds per square foot, and then divide by 2 in order to have the impulse due 
to an outstroke alone, we find for the impulse in the primary wave, at a distance of 
50 feet from the charge, 3.3 pound-seconds of impulse per square inch. 
For comparison, the part of the pressure wave, 4 milliseconds in extent, 
that was measured by Hilliar represents an impulse of only 1.45 pound-seconds per 
square inch. The reason for this discrepancy is not clear. The observed pressure 
wave accounts for only a quarter of the energy in the TNT, so that the calculated 
value of 3.3 should be an underestimate. Perhaps an appreciable impulse may result 
from small pressures acting over relatively long times during a later phase than that 
covered by the measurements. 
It may be remarked that spherical symmetry has been assumed in the forego- 
ing discussion. If the motion is asymmetrical, the collapse may occur in such fash- 
ion as to break up the gas globe. Evidence of such occurrences in the case of small 
explosions has been secured by cinematic photography. 
III. PRESSURE ne 
7. TURBULENCE 
7. TURBULENCE 
The question may arise whether the motion of the water produced by an ex- 
plosion is turbulent or not. Turbulence can be produced only through the action of 
friction; and it seems that friction should have time to produce appreciable turbu- 
lence only near solid objects, such as fragments of a burst case. There exists no 
mechanism by which turbulence so produced can be propagated outwards with the pres- 
sure wave. 
