392 
7a is the density of water at zero pressure, In the discussion of the 
asymptotic behavior of the wave at large distances, the relation between the 
destruction of the wave crest and the dissipation of energy at the wave front 
is clarified. In the section 7, the method of calculating the pressure -time 
curve of the shock wave is outlined, the necessary formulas are assembled, 
and typical results of the application of the theory to service explosives 
are exhibited. 
In the development of the kinetic enthalpy propagation theory all 
elements of the fluid are assumed to be on the same adiabatic. This is not 
strictly true, since the entropy increment of an element of fluid at a shock 
front of changing intensity depends upon the time at which it passes through 
the front. Kirkwood and Brinkley” have developed a propagation theory which 
takes proper account of the finite entropy increment in the fluid resulting 
from the passage of the shock wave. The partial differential equations of 
hydrodynamics and the Hugoniot relation between pressure and particle veloc- 
ity are used to provide three relations between the four partial derivatives 
of pressure and particle velocity, with respect to time and distance from the 
source, at the shock front. An approximate fourth relation is set up by im- 
posing a similarity restraint on the shape of the energy-time curve of the 
shoek wave and by utilizing the second law of thermodynamics to determine, 
at ayn arbitrary distance, the distribution of the initial energy input be- 
tween dissipated energy residual in the fluid already traversed by the shock 
wave and exergy available for further propagations. The four relations are 
used to formulate a pair of ordinary differential equations for peak pressure 
and shock-wave energy as functions of distance from the source and in addition 
8/7 J. G. Kirkwood and S. R. Brinkley, Jr., OSRD Report No. 4814 (1945). 
S. R. Brinkley, Jr. and J. G. Kirkwood, Phys. Rev., 71, 606 (1947). 
