222 
Sec. 5 “= Eq. 34-38 
mil 2 2. 2 ° 
: Nae _(&e) _ (ae fes\ far i 
(a Se | av i ue - ) (3) (G2) ) ae 
at the point J, since there the subscripts S and H are interchangeable for 
the outer differentiation. Combination of this result with Eq. (29) shows 
that 
il 
ot oe sae / =) es 2 = far \ | 
f fe (35) 
2 av 
WoJu eto (Se) P 
In general (am P/avo" )s >O (i.e., adiabatic expansion aS nate positive 
curvature) and for compression waves Vy > Vp, 80 that (a 2s avy” dy + 0, show- 
ing that Sp is a minimum at J. 
(26) shows that 
(=) UP Pa) iets (2) 
a5 My V, = V5 V1 - Vp \ Vo/H (36) 
Combination of this with Eq. (33) shows that 
i ge Po - Py =) (2) , 2 
lav/g “1 -%) ~ “lai, | * =e f. (57) 
For points above J (e.g. Z) (aS/aV) 5 is negative from Eq. (29) so that for 
those points 
rh 
fap Po - P 
Many | > Vp [=> (58) 
S Viating Ve 
or ¢ > D - Up, where U, is the mass velocity of the burnt cas. 
Now consider the entrooy at points Z and Y of Fig. 5-1. Becker? 
points out that an ordinary shock wave with initial P and T those 
at Y and final P and T those at Z would have the same velocity as the 
detonation wave with Pp and Vo at either Z or Y, In the shock wave the 
entropy is higher behind the wave than in front of it so that S is higher 
at Z than at Y, as previously asserted. 
There have been other arguments advanced for the particular choice of 
detonation velocity on the H curve, for example those of Scorah.’” However, 
the whole question of the theoretical justification of Chapman's condition 
does not seem to be in a very satisfactory state, although there appears to 
be little doubt of its correctness. 
