96 12 
other; there are very strong reasons for expecting that the dynamical conditions in 
and around the small charge after a time t will be geometrically and dynamically 
similar to those in and around the big charge after a time Rt; ‘that is to say, any two 
correspondingly situated particles at distances D and RD from the points at which 
detonation was started will have equal velocities and will be subject to equal pressures 
at moments t and Rt. 
It can be demonstrated that if this rule is true for any one pair of moments 
subsequent to complete detonation it must remain true thereafter. For if the rule 
holds good at moments ¢ and Rt every particle in the big system has the same velocity 
as the corresponding particle in the small system ; the displacement of any particle in 
the big system is R times that of the corresponding particle in the small system; on 
the other hand the pressure gradient operating on a particle of the small system, and 
therefore the acceleration of the particle, is R times as great as for the corresponding 
particle in the big system; consequently, after infinitesimal increments of time dt and 
Rdt corresponding particles in the two systems will have acquired equal increments of 
velocity, but the increment of displacement of the particle in the big system will be 
R times as great as in the small system; the rule therefore will still hold good at 
moments t + dt and R(t + dé), and by an extension of the same reasoning it will hold 
good at all subsequent times 'T and RT. To complete the proof of the rule it is 
necessary to show that it also holds good during detonation, when forces are being 
liberated by chemical change. The difficulty here is that the nature and laws of 
detonation are not yet fully understood, and any picture of the process must be to 
some extent hypothetical. Detonation, then, may be roughly conceived as a wave of 
chemical transformation which progresses from point to point with constant velocity, 
completing itself at each point practically instantaneously ; each layer of explosive is 
detonated by the temperature and pressure of the next layer within and generates a 
temperature and pressure of its own, which on the one hand maintains the temperature 
and pressure of the next inner layer and on the other hand produces detonation in the 
next outer layer; the front of the detonation wave divides a region of unchanged 
explosive, which no pressure has yet reached, from a region of transformed explosive 
under uniform intense pressure. On this provisional view, the similarity rule 
obviously holds good during detonation and would consequently be valid at all stages. 
It will be seen therefore that it is possible to go a long way towards a complete proof 
of the rule, though not quite all the way. 1t may also be pointed out that very natural 
conclusions result from accepting the rule, such as, that the energy radiated from a 
charge is proportional to the weight of the charge, that the rate of decay of the 
pressure is inversely proportional to the linear dimensions of the charge, &c. 
In dealing with charges of different sizes it is convenient to speak of distances in 
the ratio R as “‘ corresponding distances.” For example, 50 feet from a 300-Jb. charge 
and 25} feet from a 40-lb charge are corresponding distances, since— 
DON /300 
ODOM AO 
According to the above theory, when the pressure waves from a big and a small 
charge are compared at corresponding distances the maximum pressure should be the 
same in both cases, but the pressure from the big charge should be R times as 
sustained, that is to say, it takes R times as long in falling to any given fraction of its 
maximum intensity. The whole time-integral of pressure should be R times as great 
for the big charge as for the small one, and the time-integral of pressure of the big 
charge for any period Rt should be R times the time-integral of pressure of the small 
charge for the corresponding period t. In short, the time-pressure curve of the big 
charge should be a copy of that of the small charge with all the abscisse increased in 
the ratio R. 
To put the theory to a satisfactory test it is necessary to make comparisons with 
charges differing very widely in magnitude. Experiments were therefore made with 
charges weighing 40 lbs. and 1,900 lbs., giving a scale ratio R= 3°62. The small 
charges were of 40/60 amatol and the large ones of 50/50 amatol, but these two 
mixtures may be regarded as giving identical effects (see Section 12). With gauges 
at distances of 254 feet and 924 feet, which correspond to 50 feet from a 300-lb. 
charge, results were obtained which are shown in Figs. 13 and 15. It will be seen 
that the maximum pressure from the small charge (*78 ton per square inch) is about 
8 per cent. lower than that from the big charge (*85 ton per square inch), but the 
