1272 
disturbance in Mo remains progressive. One may verify that 
the error so introduced is negligible by comparing the analytic 
solution so obtained with the result of the Riemann type 
of numerical integration. Therefore, let the disturbance 
everywhere in M, be progressive so that 
a 
P (x,t) = “¥-I (19.1 
Then by (19.1), (19.2), (14.5), (14.6), and (14.7) it follows 
that 
aa _ 
24 - O34 (19.3 
The solution of (19.3) is 
Ot+x=w(4) (19.4 
where w is.a function to be determined by the boundary condi- 
tions. When these conditions are (17.1) and (17.2), then 
-Bx +B + 5 
a=——_t—,, rc1-t (19.5 
Bey a 
=) i}! 9 Pe 
The discontinuity in the derivatives of A along the line 
x+t=1 (see fig. 9) has its origin in the discontinuity 
at the tail of the initial pulse (equation (17.1)). ‘The 
straight line EF is the world line of the tail of the incident 
shock? and F represents its intersection with the head of 
= 90) = 
