447 
where u, and {1 are the initial values of material velocity and 
kinetic enthalpy of the water at the gasesphere surface a; 
A, ) ¢ ie W, » the initial density, sound velocity, and enthalpy 
of the water at a; Se ¢ ; Ww, the initial values of the same 
quantities in the gas just interior to the sphere surface a). 
The equation of propagation, Eq. 5.24, has been written 
in the form, 
ms -t/0 
M20Rt) =X (9) 2, é : (7-2) 
where t' is the time measured from the instant t, at which the wave 
front arrives at point R. At distances at which RR, t) can be 
represented by its acoustical approximation, we have obtained (Eq. 6.1) 
p= x(g)Rer” 
P= AX, 5) Srey aie 
(7.3) 
where Ps is the density of water at zero pressure. For most ex— 
plosives, the acoustical approximation to Q is entirely adequate 
at values of R/a, 2D 25 . For smaller values of R/a,, it is preferable 
to use Eq. 7.2 rather than Eq. 7.3. 
In order to calculate the dissipation parameter x and the 
time-espread parameter, Y » we again introduce the variable q 
R/a, = ¥%- (7.4) 
Neglecting the relatively small terms in J, and J, Eqs. 5.20 yield 
