555 
from equations (4.5a), (4.6a) and (4.5). 
To the first order of small quantities, equation (4,9) becomes 
no tye bt Rad ie siehenbces Winer Mette "Se (4.10), 
PY 
and finally, from equations (%.8) and (4.10), remembering that of = E/Py in the present notation, 
y2 
—— 
Py ‘s ce 
= 
joa. coca  waes (4.11). 
yu? 
Naas Nata 
9° 
't follows from equation (4.2) that P is the pressure derived from the observed displacement 
¢ of the measuring end of the bar, using the procedure described in Section 3; equation (4.11) 
therefore gives the relationship between the ‘applied’ pressure Py and the 'measured' pressure, Pin 
the simple case visualised here. 
The wAlue of the shock wave velocity U is a function of r/Po. According to calculations, 
when rir, = 3.9, corresponding in our case to the pressure end of the bar, U is approximately 1.80 x 
10° cm./sec.; assuming that 0 = 0.29, C, = 5.26 X 10° cm./sec., it follows from equation (¥.11) that 
Py/P = 0.929 so that the appkied pressure corresponding to the maximum measured pressure given at the 
end of section 3 is 0.929 xX 18-01 = 16.73 tons/sq.in. When Gana = 8, Corresponding approximately to 
curve (4) in Figure 4, U = 1.61 x 10° cm./sec.; with this value of U and the previously assumed values 
of a and Cor Pile = 0.944. 
tn this simple case, the maximum difference between the values of P, and P is therefore of the 
order of 7% The conditions in the experiment are much more complex and it is difficult to discuss 
the general case, even though the correction does not appear to be large; hence, in order to compare 
the experimental results with the numerical gata it appears that the best procedure is to assume that 
the relationship (4.11) is correct even when U is variable and the pressure varies along the bar. 
On this hypothesis, the effect of pressure on the cylindrical surface of the bar may be seen from 
Figure 6, where the full-line curve shows the calculated shock wave pressure, Pye according to Penney, 
plotted against time t', reckoned from the instant of arrival of the shock wave at the pressure end of 
the bar. The chain-dotted lines in this diagram shows the variation with t* of the pressure P in the 
stress wave propagated along the bar, assuming that at time t' the lower portion.of the bar (region (1) 
of Figure 5) is subjected to a uniform hydrostatic pressure equal to Pp, and that this region travels 
along the bar with the velocity U of the shock wave front. 
1 
From these values of p, the velocity ¢ of the measuring end of the bar at time t, reckoned from 
the arrival of the stress wave, can be deduced using equation (3.4), and hence, by integration, the 
calculated value of the displavement ¢ of this end of the bar, The relationship between & and t, 
derived in this way, is shown by the brokenm-line curve (8) in Figure 3. 
The reason for the initial curvature of the experimental (¢, t) curve has already been discussed; 
apart from this, it is clear from Figure 3 that the differences between the experimental curve and the 
theoretical curve are ureater than the experimental error, !n particular, the theoretical curve shows 
a gradual but definite decrease of pressure as t increases, whereas the experimental curve is practically 
linear in the region in question, indicating that here the pressure ig constant. 
it is difficult to account for this discrepancy, — it may perhaps be due partly to errors in 
the calculations and to assuming that the charge is spherical whereas it is in fact cylindrical. 
{t may also be due partly to experimental errors, and it would be Interesting to repeat the experiment, 
using a spherical charge and a shorter pressure bar of smaller diameter with a parallel plate condenser 
unit to cut down dispersion effects, and fitted with some form of baffle tube to eliminate the effect 
of pressure on the cylindrical surface of the bar. 
Appendix wseoe, 
