1353 
Fo EE Ee Htro-sre tHe +fesne-g” BPP 
Taking the square root of each side we obtain 
fcr ps & eH} > tre prg Es Les oes DY 
which is what we set out to prove. 
Hence 
Ve Proof of (8e') 
This relation may be seen to be true by considering three 
points on a forwerd rarefaction wave %1<%; <*, with effective 
pressures Py» Py» and P, and material velocities Vy, Vis and Vi. 
The theorem simply states that 
(V,, - V,) = (Vv; - ley + (Vv). - V5). 
