425 
from ees long times. A suitable compromise between Eqs. 4.18 and 
4.19 appears to consist in using Eq. 4.19 for calculating v and x, the 
retarded time and time spread, and then using Eq. 4.18 for the explicit 
calculation of the pressure behind the front for Y eh 4 However, the 
complete theory based upon Eq. 4.19 yields surprisingly satisfactory results 
and is probably adequate for most engineering calculations requiring an 
estimate of the intensity and duration of the initial pressure pulse produced 
by an underwater explosion. 
Equations 4.18 and 4.19 together with the propagation theory of 
Section 2, provide a complete description of the shock wave emitted by a 
spherical charge of explosive in terms of the initial conditions on the 
boundary between the gaseous products of the explosive and the water. 
5. Dissipation and Spread Parametersl9/ 
In this section, we wish to complete the evaluation of the retarded 
time ante of the shock front and of the timeespread parameter & for use in the 
propagation theory, Eq. 3.33, and in the asymptotic theory of Eq. 3.37. The 
latter theory is appropriate for the calculation of the pressure-time curve 
of the shock wave at distances from the charge exceeding about 25 charge 
radii, and. it forms a basis for the discussion of the limiting properties 
of the shock wave at great distances from the charge. In this section, 
we shall explicitly employ several properties of water that are derivable 
from the equation of state, and it is necessary at this point to introduce a 
particular equation of state. 
The Tait20/ equation may be written in the form 
1 See Reference 7, Section 2. 
20/ P. G. Tait, "Report on Some of the Physical Properties of Fresh Water 
and Sea Water." The Physics and Chemistry of the Voyage of H.M,S. 
Challenger., vol. II, Part IV, S. P. LXI (ses). 
See also R. E. Gibson, J. Am. Chem. Soc., 56, 4 (1934); 57, 284 (1935). 
38 
