1333 
and Sk- yal fa SEE 
The other angles are then given by 
g,= =9f- cot -1 (eos =l) 
73in,, 
and p= wT = fy 3 
=-1 -cos 
and w= cot ( ) 
‘ sing, 
The solutions are surprising. Even though the one shock is 
very weak (F-1) the minimum resultant pressure Fmay be many 
times greater, 0-86 § = = 2.0234 for y = 1.40, §"= 3.3175 for 
4 = 2.00, and §” = 138. 67 for y = Wel (ef. figs Waes dye dey. 
In other words, 7a weaker resultant pressures & ‘ no three= 
shock configurations exist at all; they do exist, however, for 
an ideal gas with the same value of « It can be shown that 
this peculiarity is independent of y ‘ef. Appendix C). Thus we 
have another characteristic difference between water-like sub- 
stances and ideal gases! The configurations for limiting 
cases are shown in fig. l6a, b. 
Numerical results for y= 7.15 are shown graphically for 
given values of F; namely F ->1, F = 0.75 and 0.10; e.g., A(H) 
in fig. 17a, &(#) in fig. 17b, w(f) in fig. 1%, F (g~) in 
fig. 17dg, dg and w(/4) in fig. 17e. Here, too, for each value 
of Fis a minimum resultant pressure Finan. (0° © mare te0~2 for 
F = 0.75 and €"4,.748-1 for y= 0.10) in contrast to the three- 
shock solutions for the analogous ideal gas, where configurations 
with Fin the neighborhood of unity always exist. It is to be re- 
marked also how close the various curves are to the limiting one for 
f ~1, which is accordingly a good approximation for qualitative 
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