393 
to determine the initial slope of the pressure-time curve of the shock wave. 
This theory permits using the exact Hugoniot equations of the fluid in the 
numerical integration of the propagation equations. While less flexible 
than the propagation theory of Kirkwood and Bethe, the approximations em- 
ployed are less drastic than those of the latter authors, In section eight, 
this alternative propagation theory is described in detail for the case of 
underwater shock waves of spherical symmetry. 
In section 9, we discuss briefly the results obtained by Rice 
and Gine112/ in their application of the methods of Kirkwood and Bethe to 
the shock wave of cylindrical symmetry generated by an infinite cylinder of 
explosive detonated simultaneously at all points of its axis. These results 
are less satisfactory than for the case of spherical symmetry because the 
propagation velocity of the kinetic enthalpy is not well approximated by CTU, 
The shock wave of cylindrical symmetry can be satisfactorily described by 
the methods of Kirkwood and Brinkley, 29/ and we describe their application 
to the shock wave generated by an infinite cylinder of explosive in which 
the detonation wave travels in the axial direction. 
2. Specification of Initial Conditions 
In this section, we wish to examine the initial conditions at the 
boundary between explosive and water leading to the emission of the shock wave. 
When the detonation front arrives at the surface of the sphere of radius a, 
forming the boundary between the initially intact explosive and the water, a 
shock wave travels into the water and the following boundary conditions are 
established. 
pat) = Pi aa out ing ae ib) Cees an 
3/ O. K. Rice and R. Ginell, OSRD Report No. 2023 (1943), OSRD Report No. 
10/ AEE ens aJ irkwood, OSRD Report No. _56 
Salts Bra: ey, Jr., and J. G. Kirkwoo epo Oo ’ 
Phys. Rev., 72; 1109 (1947), Proc. Symposia App. Math., 1, 18 {134332 
7 
