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Sec. 1. ape 
The rarefaction wave may affect the observed detonation velocity if the 
rarefaction wave follows so closely on the detonation front that the region 
of reaction is overlapped by the rarefaction. This phenomenon has been 
little studied but may account for the lower velocity observed in narrow 
tubes, in which the radial expansion also produces a rarefaction wave. 
ad. Theory of finite waves. Many of the above statements can be 
verified by direct experiment, while others are consequences cf the hydro- 
dynamic theory of detonation and shock waves, the subject of this report. 
This theory has been developed over the past century by many investigators 
and is now quite universally accepted as a valid treatment of the general 
features of the problem, The theory originally arose from a consideration of 
sound waves of finite amplitude so that it is worth while discussing these 
here. 
The ordinary theory of sound is applicable only tc waves of infinitesimal 
amplitude. Investigation shows that that part of a compressional pulse which 
is of sreater amplitude travels faster than the parts of lower amplitude. 
Therefore the shape cf the pulse changes as it moves along, the top tending 
to catch up with the front. The pulse thus becomes steeper and steeper. If 
viscosity and thermal conduction (and the finite time required to establish 
equilibrium) are neglected, the pulse will ultimately acquire an infinitely 
steep front; i.e. a discontinuity in pressure and temperature will be formed. 
This 1s called a shock wave. The material behind the shock wave also 
acquires a forward material velocity. 
The formation of a discontinuous shock wave may be made to seem reason- 
able by the following qualitative argument. Let a piston in a long tube be 
given a sudden small velocity. A sound pulse will be formed which advances 
ahead of the moving piston with the velocity of sound in the medium, The gas 
in front cf the piston and behind the sound pulse will be moving with the 
velocity of the piston. Now increase the velocity of the piston by another 
sudden small increment. A second pulse will start travelling with the 
velocity of sound rolative tc the moving gas and therefore actually travelling 
with the velocity of sound plus tho previous velocity of the piston. This 
pulse will thus catch up to the first one. Carry this procedure further and 
it is clear that a piling up cf pulses will occur which will produce a dis- 
continuity. 
e. Rarefaction waves contrasted with shock waves. Reversing the above 
arguments, we see that rarefaction waves of finite amplitude will tend to 
Spread out instead of piling up. In the absence of viscosity stc., rarse- 
faction waves are thermodynamically reversible phenomena, i.e., no change of 
entropy is involved and the ordinary laws of adiabatic expansion can be ap- 
plied. Shock waves on the other hand are irreversible; there is a continual 
dissipation of energy into heat. This may seem strange when viscosity, etc., 
are neglected but if the shock front is infinitely steep, dissipation can be 
caused by infinitely small values of the viscosity and neat conduction. 
f. Basic principles of hydrodynamic theory. It is assumed that every- 
where in the material there is conservation of mass 4nd energy and that all 
motions are governed by Newton's Jews. Furthermore, for simplicity it is 
usually but not necessarily assumed that the viscosity, thermai conduction 
