1267 
and (14.5) in the form to be used here. 
15. On the other hand, the conditions A-3 are equi- 
valent to the following equations: 
P- Po the (15.1 
s = Up +; Vo (2 Pol i 
1/2 
Wi= Uy [(p - Po) (vy - v)] / (15.2 
Payee Oy a (15.3 
where s is the shock velocity (s = slope of D) and y is 
the specific volume. The variables in these equations are, 
of course, to be evaluated on D. Variables with and without 
subscript refer to the regions My and M respectively of 
the x,t-plane. The first two equations, (15.1) and (15.2), 
again express the conservation of mass and of momentum, 
respectively. The third equation supposes no entropy change 
in crossing D. It is convenient to rewrite (15.1) and 
(15.2) with the aid of (15.3) and (14.8) in terms of these 
five variables: c, u, Cos Up, and Se 
2 1/2 
= -1 
s =u, +—2 (crt Kilmer (15.4 
\¥ c - 4 
1 ue Yui 
f=) 
i 
2 5 ie 
u. + 2xOuil [fue yr a =\72G) ¢ y-T 
ie) VY cs ) ) " Ge ) ) 
a (15.5 
The equations (15.4) and (15.5) may be simplified if the 
a Ws 
