1561 
R on logarithmic paper and were found to be approxim tely 
represented by power functions of average slope -0.11 and 
-0.08 respectively. (The lines actually show a slight downward 
curvatures) These calculations probably overestimate the 
viscous effect somewhat because of the approximation involved 
in equation (96). 
The asymptotic shock propagation theory of Kirkwood 
and Bethe (see reference 7, p- 126) predicts a peak pressure - 
distance dependence at long ranges of the form 
Ft one Be (Log & es 
R ae (146) 
where & is the charge radius. The logarithmic term in equation 
(146) measures the departure of the distance decay law from 
the R 
law of spherical sound waves, and represents, essentially, 
the effect upon the peak pressure of the continued spread of 
the profile of the wave. (Note that the quantity Py® @ /2 pC as 
calculated from equations 4-20 and 4.22 of reference 7 represents 
the energy flux of the shock wave and varies as Re, the 
logarithmic terms in the pressure and the time constant just 
serving to annul each other.) 
The effect of the logarithmic term in equation (146) 
can be ascertained by plotting on log-log paper, and it is found 
that this term contributes an average slope of about -0.06 to 
the Py, VS. R curve in the region between wi/3/R = 0.0053 and 
0.00022. (The line actually shows a slight upward curvature.) 
If we now combine the effects of viscous attenuation 
~ 8» 
