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explosive and those of water. A description of the theory divides itself 
naturally into three parts: The specification of the initial conditions 
at the boundary between the water and the gaseous products of the explo- 
sion; the formulation of a new and adequate theory of propagation of the 
spherical shock wave in water; the investigation of the motion of the sur- 
face of the gas sphere composed of the explosion products. Our discussion 
follows closely the exposition of the original wiceweees 
In the section 2, initial conditions are formulated and a method 
is outlined for calculating Pp, and u,, the initial pressure and initial 
particle velocity at the surface of the gas sphere. In section 3, the 
theory of propagation of the spherical shock wave in water is developed. 
It is found that to an adequate approximation a quantity ef is propagated 
outward from the surface of the gas sphere with a velocity c+u, where FP is 
the distance from the center of the charge, c the local velocity of sound, 
and u the particle velocity of the water. The function{2 , called the 
kinetic enthalpy, is equal to We u’/2 » Where W) is the enthalpy incre- 
ment 4 H-relative to the undisturbed water ahead of the shock front. Owing 
to the fact that ctu exceeds the velocity of the shock front, the crest of 
the pressure wave is progressively destroyed as the disturbance travels out- 
ward. Also, owing to the fact that c+u depends upon the local intensity of 
the wave, the wave profile is progressively broadened as it travels outward. 
In the section 4, the motion of the gas sphere surface is inves- 
tigated, and the quantity G,(t), equal to a(t) <2, ¢t) , is determined 
as a function of time t, a(t) being the radius of the gas sphere at the time 
