1317 
Now 7 and Uare both functions of F: 7 and 
v‘are both functions of e. Hence equations (9a) and 
(9b) are sufficient to determine the strength F of the re- 
flected shock and its angle of reflection oO in terms of the 
known strength f of the incident shock and its angle of in- 
cidence &. For computational purposes it is convenient to 
combine these equations in a single quadratic equation as 
follows: 
LX°+MX+N=0 (9 
X = cos 2a 
Lev’ {(7'2 -6'2) - (72 -62)} 
Mev’ § (7r2 -2) +o'@fB- vf (7'2 -'2) +02} 
Nev'2? (¢2 - o'2) 
The graphical representations of typical numerical 
solutions are shown here for LS 7.15 and 2.00; @ (cq) for 
given F ( or P/P,) in fig. 8a, b and €(@) for given F in 
13) 
fig. 9a, b. As in the case of ideal gases there are, in 
general, two solutions e & for given F »@& 3: one with 
large F ‘and large ': the other with relatively small §& me 
and small a. For certain "extreme" values, however, 
the two solutions merge into one, while for still higher 
values of Ono solutions at all exist. The "extreme" values 
¢ 
are determined by the condition that the derivative 2 or 
ae 
4 
= becomesinfinite (cf. fig. 9a, b). Subject to this 
¢ 
condition equations @a), (9b) give for %,....( F ) 
a 
extr. 
=- 29 « 
