513 
- 17 - 
or combining this with the inverse distance )aw,we have 
12,000 
Pp a w38  * ~—1bs/sq. in. 
(at distance D feet) 
The relation obtained by plotting Hilliar maximum pressure gauge (G.F) observations® is identical 
with this — see Figure 16b. Now the simple theory of explosion pressures, as outlined by Hilliar (p.12 
R.£.142/19) indicates that Prax should be proportional to w'32 = see dotted line in Figure 16b. The 
difference between the two curves shown is quite outside the limits of experimental error. {t has not 
been possible, however, to obtain a definite physical explanation of this difference between experimental 
results and simple theory, but it must be realised in the first place that the simple theory given by 
Hilliar does not include all the facts. The resistance offered by the charge case, for example, is 
ignored - it is probable that the elastic constants and dimensions of the charge case exert a definite 
Influence on the maximum pressure imparted to the water. The question has been examined by Mr. Butterworth¢ 
who gives a rough theoretical estimate that on this account the recorded pressure will be about 6% lower 
than without the above - the correction being practically the same for all sizes of charge since the 
thickness of the metal cases employed increases in proportion to the linear dimensions of the charge (see 
Figure j1). |t would appear therefore that under these circumstances the difference between the experimental 
result Roos x w*38 and the theoretical deduction Pony c w'?3 remains unexplained. 
Again it is probable that air cavities in, or near, the chargé affect P_. — but such an effect 
would probably be of an irregular nature and would affect 211 charges, large and small, by about the same 
extent. It is realised, of course, that the method of recording oar is open to criticism, for the p.e. 
gauges used have a finite size and measure only average pressure around the point of maximum compression 
in the pulse. On this account a positive correction, increasing as the size of the charge (and 
consequently the thickness of pulse) diminishes, must be applied to the recorded pressures. This would 
tend towards the cube root law but would require positive corrections to the observed values of 32% for 
2i1ds. 174% for 184 1bs. and 11% for 100 lbs. charges, assuming no appreciable correction is necessary in 
the record of a 1000 1b. charge. 
This question of correction to the recorded values of P x will be dealt with more fully ina later 
section where the form of the p/t curve is discussed. (See Section 4). 
A point of some interest and importance in connection with the experimental results shown graphical ly 
in Figures 16a and b, is the fact that observations of Rae with gun cotton and amatol charges lie on the 
same straight line as the observations with T.N.T. Charges. The results indicate therefore that there is 
no appreciable difference in maximum pressure developed by equal weights of these three explosives. 
(c) Momentum a pdt) and weight of Charge. 
AS in the case of maximum pressure, it has been found that the value of momentum, as measured by 
the area of the p/t curve, for a given size of charge is a very variable quantity. It is only by taking 
the average of a large number of observations therefore that reliable data can be obtained. with this end 
in view a careful analysis has been made of 116 records the area of the p/t curve being in each case 
measured by means of 2n Amsler integrator. |t was neceesary for this purpose first of all to analyse the 
original records and plot on an enlarged scale the graph of the pressure-time curve. 
These graphs were then used in the planimeter measurements of area. Since it is impossible to 
extend the measurement to infinity along the time axis it was decided to measure areas up to a definite 
time 't' which is taken as proportion to Wi * a value of t = 2.00 x 10°? second being adopted as a 
Standard ...... 
od The Hilliar gauge results used in this curve were cbtained simultaneously for the same shots 
and are directly comparable with the p.e. records. The difference between 'G.F." (3 copper) 
and 'G.J.' (9 Copper) gauges has been dealt with in a report by Mr. Butterworth. See appendix. 
¢ See appendix 8, 
* Any small error involved in this assumption, only affects the result in the second order of 
small quantities. 
