484 
Taylorst/ has shown that the Chapman-Jouguet2o/ conditions can 
be satisfied at the front of a stationary detonation wave by solutions of 
the equations of hydrodynamics. which depend only on Si / t - For solutions 
of the Taylor type, 
FD DY sed bs eee a oa (9.29) 
The solutions of Eqs. 9.1 and 9.19 for the exterior medium are compatible 
with the conditions on the boundary between explosion products and the ex= 
terior medium if solutions of the Taylor type are valid in the explosion 
products behind the detonation wave. 
At any finite distance from an infinite cylinder of explosive, 
r /t=0 » and 
DADE. = MeV. (9.20) 
Eq. 9.20 can be employed to provide three relations between the derivatives 
with respect to time and the distance coordinates of the pressure and the 
components of the particle velocity. These relations and Eqs. 9.1, spec- 
ialized to the shock front, together with Eqs. 9.3 and 9.12, provide nine 
nonhomogeneous linear equations between nine partial derivatives with coef- 
ficients that are functions of R U, » and Jae The equations can be solved 
for the derivatives and an ordimry differential equation, a bf d R : r( pp, I? ) 
formulated with the aid of Eq. 9.2. The result is 
3 
dp,,, b, YR, 
aia = Pip Uy | N(p) + Dir) m (Pus) ) (9.21) 
34] G. I. Taylor, Btitish Report RC-178 (1941) 
35/ H. L. Chapman, Phil. Mag. (5) 47, 90 (1889). 
E. Jouguet, Comptes rendus, 132, 573 (1901). 
See also S. R. Brinkley, Jr., and J. G, Kirkwood, Proc. Third Symposium 
on Combustion, Flame, and Explosion Phenomena, Williams and Wilkins Co. 
Baltimore (1949), p. 586. 9 
