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APPENDIX C 
THREE “SHOCK CONFIGURATIONS FOR WEAK SHOCKS 
In the case of weak reflected shocks, F> 1, a quadratic 
equation has been derived for ideal gases in terms of the 
cosine of the limiting angle a. The analogous equation 
for water-like substances is 
a{o2(7-0) -(30+ vi} con’ 3, 4 Or (O*+ Cow, + {or (- o-®)- Ursr*stzo 
As is the case for ideal gases dp, approaches 97as a limit, 
and the limiting angles w,;, 5, are given by 
tan, = ———__T 
eseaA-r o cotA, 
and cot J, = cscQ@,- cot ,’ 
The distinction between ideal gases and water-like 
substances becomes apparent when one considers a value of F 
slightly less than one. Let this correspond to a value of 
@ =1-C¢, where € is a small positive quantity. The dis- 
criminant of the above quadratic equation is then given, in 
terms of a power series in @, by the expression 
16¢* [ep 2 ij + terms in ¢} 
which is negative for a sufficiently small value of ¢€ and 
y¥ > 1. Hence, for a value of F sufficiently near one there 
is always a region where no real three-shock solutions can be 
found in the case of water-like substances. 
For ideal gases on the other hand, the discriminant is 
