114 30 
takes no more than a few hundred-thousandths of a second to reach its maximum. 
In the time-pressure diagrams tlie pressure has heen represented as rising to its 
maximum instantaneously ; in the absence of fuller knowledge this seems a reasonable 
supposition, for the pressure in the exploded charge is no doubt greater immediately 
after detonation than at any subsequent moment, and the part of the wave in which 
the pressure is greatest may be expected to travel fastest (Section 23) and to remain 
in front. It should be pointed out, however, that the mathematical theory of an 
intense pressure wave with a vertical front has not proved soluble up to the present. 
(Rayleigh, ‘‘ Theory of Sound,” § 251.) 
It will be recognised that the crusher gauge commonly used for measuring the 
pressure developed in ordnance by the propellant belongs to the type discussed in 
this section. A similar gauge with lead cylinders (Eley’s lead crushers) in place of 
coppers is employed for measuring the lower pressures developed in shot-guns, and 
was used by Abbot and Schuyler for their investigations on explosion pressures in 
water. It is impossible, however, with lead crushers to get nearly so small a time- 
constant as with coppers. As shown in Section 28, the value of k for Eley’s lead 
crushers is about 5°6 lbs. per 10~* inch, compared with k = 62 for the coppers used 
in the present experiments, so that the time-constant of a gauge "sing these leads is— 
T = '534/M (in thousandths of a second), 
that is to say, with pistons of equal mass the time-constant for leads is more than 
three times that for coppers. ‘The pistons used by Abbot appear also to have been 
much more massive than was necessary, and although Abbot’s description of his 
gauges is very incomplete it may be gathered that they had time-constants ranging 
from 4 x 1U-* to 8 x 10~*; they were therefore far too sluggish to give anything 
like correct indications of the maximum pressure; the more transient pressures from 
small charges would be relatively under-estimated compared with the more sustained 
pressures from hig charges. Moreover, the gauges for measuring low pressures had 
larger pistons and a higher time-constant than those for measuring high pressures, 
with the result that low pressures were relatively underestimated. ‘These considera- 
tions are probably suthcient to account for the fact that Abbot found the pressure to 
s Wwe? : ; Sql 
vary, roughly speaking, as pre? while the present investigation shows that the 
; : Wi . , 
maximum pressure varies as >> (Section 9). 
(20) Gauges for Empirical Comparisons of Pressure 
(Plasticine Gauges). 
The simple gauge shown in Fig. 38 was designed for certain auxiliary purposes 
which required only an empirical measurement of the pressure, especially for investi- 
gating the symmetry of the pressure wave in different directions round the charge. 
The working element is a cup of plasticine, exposed at one face to the pressure in 
the water, which squeezes part of the plasticine through a narrow neck into an 
air-chamber forming the body of the gauge. The extruded plasticine is cut off and 
weighed. 
Very consistent results are obtained from groups of these gauges if they are 
carefully prepared, the variability being only about 2 per cent. The batch of 
plasticine is thoroughly mixed by repeated rolling and folding. Jn filling the cups 
special care is taken to avoid including any air. Each cup, with the plasticine 
heaped up a little, is clamped in a vice, the plasticine is hammered until a length 
of one or two inches has been extruded through the neck, and the superfluous 
plasticine at top and bottom of the cup is shaved away flush. After an experiment 
the exposed face of the plasticine is scraped clean and heaped up with some more 
plasticine from the same hatch, which is hammered through as before, and the gauge 
is ready for use again. 
A comparison of the results given by these gauges under widely varying 
conditions leads to the conclusion that the weight of extruded plasticine is pro- 
portional to the time-integral of the pressure as long as the pressure exceeds about 
-30 ton per square inch, but that when the pressure falls below this value it is unable 
to overcome the static resistance of the plasticine. Figures supporting this con- 
clusion are shown in the following table. The time-integral of pressure I(p> 30) 
is calculated in each case from the time-pressure curve indicated in the next column, 
or from a curve derived from this curve by diminishing all the ordinates in pro- 
