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31 IV. EFFECTS OF PRESSURE. WAVES 
10. ENERGY-MOMENTUM CONSIDERATIONS 
Aside from the practical difficulty of adopting such a mode of construc- 
tion, the following consideration raises doubts as to its complete efficacy. From 
a highly yielding structure, a compression wave is reflected as a wave of almost 
equal rarefaction. There is a limit, however, to the tension which water will stand, 
especially when in contact with solid objects. During the later phases of the motion, 
therefore, the water may pull loose from the yielding structure, with the result that 
the structure will not be brought entirely to rest during the rarefaction phase but 
will be left with a high inward velocity. Or, cavitation may occur in the water, with 
the result that a layer of water next to the structure will also be left moving in- 
ward. The supports may or may not be adequate to check this motion without damage. 
Little is known concerning the magnitude of the tension that natural sea-water can 
stand momentarily without breaking. 
Direct experiments on the effect of pressure waves upon highly yielding 
structures should be illuminating. 
[2¥- EFFECTS OF PRESSURE WAVES 
11. DAMAGING RANGE 
11. OBSERVATIONS OF DAMAGING RANGE 
In Hilliar's report (1) extensive observations are recorded of the damage 
inflicted upon empty H4 mine cases, made of mild steel 1/8 inch thick and 31 inches 
in diameter. The degree of damage was found to vary rapidly with distance from the 
exploding charge, being heavy at a distance equal to three-quarters of the minimun 
distance D at which no damage at all is produced. Thus it becomes of special impor- 
tance to determine the critical range D as a function of the weight Wof the charge. 
A partial answer is furnished by Hopkinson's rule of similarity: "The dan- 
age inflicted on a given structure by a giver charge at a given distance will be re- 
produced to scale if the linear dimensions of the charge and structure and the dis- 
tance between them are all increased or diminished in the same ratio." This rule can 
be deduced theoretically, and "its validity has been proved experimentally for charges 
differing very widely in magnitude." 
As the result of extensive observations, Hilliar concludes that, for a given 
structure, the damage range D is approximately proportional to the square root of the 
weight of the charge. 
By combining this result with Hopkinson's rule, a general formula can be 
deduced. Letting LZ stand for a convenient linear dimension of the structure, we have 
from Hilliar's result that 
p=w' f(t) 
where f is a function not yet known. Changing all linear dimensions in the ratior, 
we must have then 
TrD= (r3w)? f(r L) 
