1323 
Inasmuch as V is intrinsically negative for 0< i. a ro) 
such angle exists for 7 >7‘; hence the limiting condition is 
given by T'= 7 , for which @ = 0. It is seen that the magni- 
tude of &, varies in general not only with the value of x 7 
as is the case for ideal gases 1,3) 
» but also with the strength 
F of the incident shock. The situation is shown qualitatively 
in fige 11 where aw (8) is plotted against ‘T(€) and - v( F) 
against T(§) for y= 1.40, 2.00 and 7.15. It is to be 
noted that for Y<5 the curves intersect at a point T's oVealts 
= « vu only for weak shocks,1.6.e, T~T~1. Furthermore, 
in this Pi range 7’>7 so that the angle a, exists for all 
strengths F - On the other hand, for y¥ 75 (lenge, y= 7215.) 
the curves start out in a reversed position so that 7’ is 
initially less than 7 ; in other words, there is no such angle 
GQ, - At some lower value F.0° however, the curves cross over 
so that then 7'>7 and Q@ exists. For example, for y= 7215 
the weakest shock for which @ =Q’is €.= 8.481 (10)+4, i.e., 
Poo/Po = 3.538 (10)1& outside the domain of interest. Finally, 
it is seen that for y = 5 the curves form a vertical cusp in 
the neighborhood of weak shocks. Let F771. Then 
and ia neat a (1- F) 
a(- Vv) i = 
hence ae As » Which becomes infinite for y= 35. 
For angles of incidence greater than Q or 0, if a, 
does not exist, the reflected pressure actually exceeds the 
= Se 
