255 
Sec. 20 -}h Iq 132-157 
where ye Paw a1 4 exe 0% +@x° e PX, 
Also ap = BR (F-@xF') = oRz ; (132) 
aT a Vv Vv 
where Z = FPeQxF' ale ene ae xe Ox ww Bx 5 (132) 
Then Cy ae Tz with b = C,/nR. 
ax x (b= @ z) 
Ss 
e : ° int, = = dx ’ (153) 
T 1s) (8 be 
in which T' is a constant of integration and g = 1-(a z/»), 
From the general equation for Cy, we get in this case 
b=bp + @&(z-1) , (134) 
_where -—»j_= Cy; /URs ise. the ideal value of b. Also 
Y= 1+ (z2/y). (155) 
The pressure is obtained from the integral 
Mie: ate fe ode ae (136) 
12 I) yes 3 
while Gee ee MAGE yet Dm as (137) 
be M Xo ex 
in which t/t‘ is taken from the previous calculation. 
A rather exact treatment could be carried out using these equations, 
which enable the velocity U5 and the pressure Py of the expanded burnt 
gases to be tabulated as a function of x. From this Wu vs. B is plotted 
and compared with vs for the shock wave in air, taken from Table 
16-1. The intersection of the curves gives the solution for and ’ 
Bo that the shock velocity p* can be read from Table 16-1. At the present 
time, however, the above equations have not yet been applied rigorously. 
d. An approximate procedure. In the calculations so far carried out, 
certain simplifications have been used. First Tos Pos W and X5 were calcu- 
lated for the burnt gases directly back of the detonation front by the 
methods of Part II. Then the variation of heat capacity with temperature 
was ignored in applying Eq. (134) and (133). It was thus possible to 
