1356 
and to region r by a forward wave, 4, If we draw a Bue curve 
(cf. fig. 28) through 1 and a YW, curve through r, m! will be 
determined by the intersection of these two curves. We wish to 
show that m' is on the shock branch of W., but on the rarefaction- 
wave portion of : 
Since m was connected to r by a snock the curve W,, passes 
through the point m. From the dispositionof the point 1 and 
the slope of Wy it is evident that m' is on the shock branch of 
tne Hence the forward wave connecting m' with the region r will 
be a shock. We will now draw 3m through 1 and m. It follows 
from relations (8e) that Sm Will lie on the left of W,, for values 
of p> Pin’ Hence m' will lie on the rarefaction branch of JW;. 
Let us consider a forward shock overtaken by a forward 
rarefaction-wave. The inequalities (A) and (A') yield the fol- 
lowing relations for the effective pressures and material 
velocities in regions l, m, and r: P< Diam PL and Vi< Maas 
The points 1 and r will lie on the R, and 3. curves, respectively 
(cf. fig. 29a). Now for p<P,, filB)< YP) (cf. 8a'). 
Hence the curve $, will lie above Ry. It may be shown that 
WW, Will also lie above R, for values of p below p,. It follows 
that the point m! will fall on the 3, branch of the qi curve, 
resulting in a weak reflected shock. On the other hand, m! 
may fall either on the or or R, branch of i. curve depending 
on the original position of 1 on the BR, curve (cf. fig. 29b). 
= 650— 
