106 oa 
piston, making a total of ten steps in the time scale; one extreme is a piston # inch 
long with a free travel of sj inch, the other extreme is a 6}inch piston with a 4-inch 
travel. Each gauge is filled with pistons of one size only, so that ten gauges must be 
put down to get a complete time-pressure curve. The six or three coppers in each 
gauge are merely to check one another, the average shortening of the coppers in each 
gauge being taken as the basis of calculation. 
While these gauges were being made, the coppers were carefully calibrated by 
attacking them with pistons of known mass and velocity, both these factors being 
varied over a wide range. These experiments, which are described in Appendix II., 
proved that the shortening of the copper is entirely a function of energy ; two pistons 
with the same kinetic energy produce exactly the same shortening, though one may be 
many times heavier than the other. The relation between shortening and energy, 
shown in a table in Appendix IL, is the basis on which all the gauge results were 
calculated. The coppers in these calibration experiments behaved with great. 
uniformity, an observation that was borne out by the whole of the subsequent sea 
trials, in which many thousands of them were expended. 
When the gauges were tried they at once gave successful results, which can best 
be illustrated by quoting the complete figures of an actual experiment. ‘This will also 
serve to explain the way in. which the calculations are made, including various 
corrections which it has been convenient to leave out of sight in describing the simple 
theory of the method. The charge consisted of 300 Ibs. of 40/60 amatol (Shot 4) at a 
depth of 34}-feet below the surface, and the gauges were hung in a vertical line, 1 foot 
apart, at a horizontal distance of 50 feet, the middle gauges being at the same depth 
as the charge. Referring to Table V., L represents the length, S the nominal free travel, 
and M the mass of the ten sizes of piston. The mass M includes not only the steel 
piston but also the copper, and the water which follows the piston into its bore up to 
the moment of impact, since these contribute their share to the inertia and energy of 
the moving system. Another point which has to be taken into account is the 
downward impulse which the pressure communicates to the whole gauge. __ It is clear 
that the body of the gauge is acted on by a force equal and opposite to that which 
propels the group of pistons, and that at each moment it has an acceleration, velocity, 
‘ ees : 3 ; 
and displacement — times that of the pistons, x being the ratio of the mass of the body 
of the gauge to-that of the group of pistons. The momentum of the gauge is equal to 
that of the pistons, but its kinetic energy is less in the ratio zy «CA the moment of 
impact the momentum on both sides is cancelled, and the energy on both sides is 
absorbed by the coppers. The energy contributed by the pistons is therefore less than 
the total kinetic energy in the ratio on The real travel S’ of the pistons up to the 
moment of impact is less than the nominal travel S in the same ratio. The equivalent 
travel of a l-oz. piston, that is to say, the distance a l-oz. piston would be moved 
if acted on by the same pressure up to the same moment, is s = MS’. 
Thus far the figures in the table are merely characteristic of the gauges, and 
would be the same for any experiment; the figures which follow are special to this 
particular shot. 
A represents the shortening of the coppers and F the corresponding enerpy, 
ascertained from the calibration table. The energy which a copper registers is 
principally kinetic, but not entirely, because the pressure existing in the water at 
the moment of impact does a certain amount of work on the copper while the latter 
is being shortened. The work done in this way ia equal to the pressure multiplied 
by the cross-sectional area of the piston multiplied by the shortening of the copper, 
= °036 p A foot-pounds, if p is expressed in tons per square inch. ‘Io apply this 
correction it is necessary to guess the pressure p; if the event shows that the guess 
was a bad one it may be necessary to repeat the calculation to a second approximation, 
but it is generally possible to make a good enough guess by comparing the figures 
for 4 with cases previously worked out. The remaihing energy, E’ = E — ‘036 p 4, 
, 
is from kinetic sources, and the part derived from the piston is gy = SF 
Knowing the mass M and the kinetic energy FE’ of the piston it is a simple matter 
to calculate its velocity V at the moment of impact, and the equivalent velocity of 
