ay 105 
piston at the moment of impact van be deduced from the shortening of the copper, 
and this gives a measure, in definite units, of the time-integral of the pressure in the 
water. 
Groups of these gauges gave exceedingly uniform results, but the question 
remained whether these results represented the whole time-integral of the pressure, 
because any pressure persisting after the moment of impact would fail to contribute 
to the momentum of the pistons and would be left out of account. It is obvious that 
no general answer is possible on this point, because the gauges might be able to catch 
the whole of the pressure from a given charge at a given distance but not from 
another charge or from the same charge at another distance. The question was 
investigated, for the case of a 30(-lb. amatol charge at a distance of 50 feet, by 
putting down a series of gauges with pistons having different amounts of free travel, 
and it was proved that in this particular case nearly the whole of the pressure was 
taken into account by a 3-inch piston with a 2-inch travel, as in Fig. 34. 
These experiments suggested a method by which similar gauges might be made 
to yield the complete time-history of the pressure. 
(18) Gauges for determining the complete 
Time-pressure Curve. 
Suppose it were possible to measure the velocity of the piston of the gauge 
shown in Fig. 34 at different distances from its starting point: it would clearly be a 
simple matter to reconstruct the history of the pressure from these measurements. 
Take any two successive measurements, velocity v, at distance s,, and velocity v, at 
distance s,; the average velocity during the intervening period may be taken as 
$ (v, + v)—this is not absolutely exact unless v, — », is infinitesimal, but in practice 
the error is altogether negligible ; the time of travel from s, to s, = distance divided 
by velocity 
— 282 — 81) 
V1 + Vy ; e 
the average acceleration during the same period = change of velocity divided by 
time 
— (Y= %) (1 +) , 
2(s, — 3,) 
and the pressure in the water = the acceleration of the piston multiplied by its mass 
and divided by its cross-sectional area 
—. M(vs — v1) (v1 + %) 
DAG(G;)—161) a 
Calculating all the measurements in this way, the result can be drawn diagrammati- 
cally as a series of rectangular steps, each representing a certain average pressure 
lasting a certain time, and a smooth curve drawn through all the steps in such a way 
as to leave out as much space as it takes in represents the reconstructed time-history 
of the pressure. 
In practice it is hardly possible to measure the velocity of a single piston at 
different stages of its travel, but a practical alternative which gives exactly the same 
information is to use a series of gauges with similar pistons having different amounts 
of free travel, the velocity of each piston at the end of its travel being measured by 
the effect of its impact on a copper, as in Fig. 34. When it came to designing a 
serics of gauges for this purpose it was found convenient to use eomparatively long 
pistons in the gauges with the largest amount of free travel and short pistons in the 
gauges with least free travel. The difference in the mass of the pistons causes no 
difficulty ; if a piston of mass M has a velocity V after travelling a distance S, a piston 
of unit mass acted on by the same pressure would have a velocity MV after travelling 
a distance MS; the results obtained with a series of pistons of unequal mass can 
therefore be translated to the basis of a series of pistons all of unit mass. 
The gauges (types GX, GY, GZ, GA, and GB) which were designed for trying 
this method are illustrated in Figs. 35 and 36. ‘They differ from the G gauge 
principally in being in nested form, the GX, GY, and GZ gauges taking six pistons 
each and the GA and GB gauges three. ‘The only other difference worth noting is the 
annular form of the air chamber. Each of the five types of gauge takes two sizes of 
C8 
