1275 
But s is the slope of D and c + u is the slope of a P- 
characteristic. Hence D is intersected by successive values 
of P. Since these values decrease, the result is that P de- 
cays at the shock front. Since any shock will decay if not 
supported from behind, the physical meaning of the approxi- 
mation (20.1) is that this decay is negligible during the 
period of reflection. Aside from its numerical success, this 
assumption has in its favor two facts which make it plausible: 
first, the time of reflection is short; and second, since the 
shock travels faster with respect to My than with respect 
to the wall, the wall behaves as a sustaining piston behind 
the shock. 
22. The equations (15.6), (15.7), (19.6), (19.7), and 
(20.1) lead to a differential equation for the shock fronte 
This equation is 
2syth;, 
B 2 
where f=4 +5 (Sy -5) 
At S22 
2 
j=2+8 (y+1)* 
The solution of this differential equation is 
3- 
= =r 5+ Hy] [ 1-(1+%5 active + 
. 2 
+ 7 F +z (44) ] t (22.1 
eRe 
