1269 
integration. As already seen (cf. par. 9) the two methods 
lead to nearly the same results. 
16. Only the condition A-1 remains to be formulated. 
As stated above (cf. par. 2), three types of incident pulse 
are considered in this report. Incident pulses of type (a) 
and (b) were treated numerically and the results were 
given in Table I, par. 9. We now consider an incident 
shock of type (c), in which the velocity pulse is linear, 
and the pressure distribution is determined by the condi- 
tion that the wave is progressive. From equations (14.4) 
and (14.5) the progressive condition follows. For according 
to these equations, P and Q travel in opposite directions 
with the velocities c + u and c = u respectively. The condi- 
tion, therefore, for a progressive wave is that either P 
or Q be constant; and in this case, it must be P, since 
the pulse is travelling in the direction of - @0. Ths 
boundary conditions A-1l on the velocity, Uy (x,t), and on 
the Riemann function, B (x,t), are then 
u, (x,0) =- B+Ax, KEB/A (16.1 
uy (x,0) = 0 > X>B/A ,B>0 
Bai( mg) c= a a. (16.2 
Here B is the peak velocity and B/A is the length of the 
incident pulse. The velocity, a, is the value of c in un- 
disturbed fluid (p =™). Equation (16.2), together with 
(14.3) and (14.8), determines the pressure as the following 
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