1294 
In terms of the variable 5 equation (1) can be written 
a al 
M= U-Vo = | (¥+l)¥ + (¥ -21) (19 
ie 2 
where Coz ¥(Po+ 7) Yo 
Vo-b 
Likewise from equation (2a) we obtain 
ge UN. fOr’ + yn (2a! 
c 
where c 
fl 
p+ 77) ve 
Ve 
The functions fy and c represent the speed of sound in front 
of the shock and behind it, respectively. It is to be noved 
that the equations (1'), (2a'), and (3') are identical with 
those for an ideal gas having the same value of Xy e 
If the change in entropy across the shock-front 
is small, the pressure-volume relation is expressed approxi- 
mately by the static adiabatic, viz., 
n° $F ie 
In this instance equations (1) and (2a) become respectively: 
= +1 
M a == rae on (1" 
© ¥(¢ ¥ -1) 
nd Cc iic\ igs tint (2a" 
a 5 Fae a 
For values of 5 slightly less than unity equations (3') 
and (3") both reduce to 
dik yh (om 
yx 
- 6 = 
