102 ie 
results are consistent with the supposition that the damaging power of a pressure 
wave is determined by its energy flux; on this view an H 4 niine, case begins to be 
damaged when the energy flux exceeds about 5 foot-pounds per square inch; but, at 
best, this can only be true approximately and within limits, for it is possible to 
conceive of a very prolonged pressure wave with an energy flux exceeding 5 foot- 
pounds per square inch.but with a maximum pressure much lower than the mine 
could withstand under statical conditions, and such a pressure wave would obviously 
have no effect. It is much more probable that damage is a function of the time- 
integral of the excess of pressure over a fixed value, 
f o-®) a, 
k depending on the strength of the structure ; for example, if k is taken as 0°1 ton per 
square inch, 
[ @-%) ae 
has nearly the same value (about 0°2) for a 40-Ib. charge at 26 feet, for a 300-lb. 
charge at 68 feet, and for a 1,900-lb. charge at 175 feet, which is in good agreement 
with the results in Tablé IV. ; on this view an H. 4 mine case begins to be damaged 
when 
j (p-0"1) dt 
exceeds about 0°16, p being expressed in tons per square inch and t in thousandths 
of a second. 
On general considerations, and quite apart from the above results, it is very 
difficult to suppose that the kind of damage at present in question can be determined 
simply by the maximum intensity of the pressure. A crack, such as is produced by 
a guncotton slab detonated in contact with a steel plate, may take only a few 
millionths of a second to form, but the damage actually inflicted is not of this kind ; 
it is in the nature of deformation, and must take.a relatively considerable time to 
become at all serious ; the pressure on the mine case is only of the order of 1 ton per 
square inch, and the formation of even a shallow dent 1 inch deep must take at: least 
several ten-thousandths of a second, in which time the pressure has fallen very much 
below its maximum intensity ; it is clear, therefore, that the extent of the damage will 
depend very much on the rate at which the pressure falls. It is an instructive fact 
that an H 4 mine case is generally not damaged at all by a 40-]b. amatol charge at 
a distance of 29 feet, though the pressure at this distance (apart from any increase by 
reflection) is 0°7 ton per square inch, which is many times as great as the mine case 
could stand under statical conditions; the only possible explanation is that the 
pressure does not last long enough to deform the structure beyond its power of elastic 
recovery. 
Damage to a hull by a distant charge will probably be governed by much the 
saine considerations as damage to a mine case; deformation will be the primary effect, 
and where the metal is torn or rivets sheared, this will be a secondary effect arising 
out of the other; the rate of decay of pressure will have just the same importance in 
determining the extent of the damage. 
It is very desirable that any experiments that may be made against hulls should 
include (1) a determination of the time-history of the movement of the hull itself at 
the point nearest to the charge, (2) a measurement by gauges of the time-pressure 
curve in the water just outside the hull at the same point. 
Experimental results on the damage sustained by a given structure can be applied 
to similar structures of different dimensions by mezns of a rule first stated by 
Hopkinson. This rule is as follows :—the damage inflicted on a given structure by a 
given charge at a given distance will be reproduced to scale if the linear dimensions 
of the charge and structure and the distance between them are all increased or 
diminished in the same ratio. For example, it is known that a 300-lb. charge of 
amatol at a distance of 70 feet produces dents about 2 inches deep in a spherical mild 
steel shell 31 inches in diameter and 4 inch thick; consequently it may be predicted 
that a 2,400-lb. charge at a distance of 140 feet will produce dents about 4 inches 
deep in a shell 62 inches in diameter and } inch thick. This rule provides a link 
between the effects of a small charge on a small structure and of a big charge on a big 
