395 
of the gas sphere, the Hugoniot conditions Eqs. 2.2 or 2.3 provide one 
relationship, 
u FC py), 
ul@,,0), p, + p(a,,0), 
between the initial pressure Py and initial velocity u, at the surface of 
(2.4) 
mi 
MW 
the gas sphere. 
To obtain a second relation between Py and Uy to be used in 
conjunction with Eq. 2.4, we must consider what is happening in the interior 
of the gas sphere. At precisely the initial instant of time the situation 
is rather complicated. The front of the advancing detonation wave is co- 
incident with the spherical surface ao and its tail extends back into 
the gas in the interior. Near the detonation front both pressure and 
particle velocity are high, although the pressure does not greatly exceed 
the equilibrium pressure pg corresponding to adiabatic conversion at con- 
stant volume of the solid explosive into its decomposition products. Ac- 
cording to G. i. Taylor, /2/ the detonation wave is of appreciable intensity 
only in an outer spherical shell bounded by radii 3a,/5 and a,, the gas 
in the interior being at rest. The velocity of the detonation wave is in 
general of the order of 5000 meters/sec, Thus the time width of the head 
of the wave is quite small, of the order of 10 aj), if a, is expressed in 
meters, We shall find that @,, equal to ao/C, where c, is the velocity of 
sound in water at zero pressure, is a convenient unit of time to employ in 
discussing underwater explosions. The breadth of the head of the detonation 
12/ G. 1. Taylor, British Report RC 178 (1941). 
