331 
(15), and give adequate approximate descriptions of shocks. 
In order to evaluate the system (25) by effective computation it is 
now necessary to carry out the second step mentioned at the beginning of §8, 
i.e. to make the remaining independent variable t discrete too. Choosing 
for t a sequence of equidistant values 
(2h. sta See), G 4 fixedyand -5.0. | San See Sa 
a certain care in choosing T is necessary. 
First, we amplify (24) by writing 
(33) MeL Jeane) = Xa 
Second, the system of total difterential equations (25) must now be replaced 
by the system of difference equations 
Stl S Sau 
Wea tok a, Ss 
ai Po (x? =x5)| — Po ant 3) : 
(34) 
Third, it is clear that in the recursion of (34) ee is determined by 
$ Ss s-! s $-! s= Ss: $-2 
cS anyas Sa een Vet i.e. Karey Moc: 1 ese Meer jum emnreamme 
So yS is determined by a family of x*,'s with 
(Quel S baesh . 
Ike. x (a,t) is determined by a family of x(a¢')'s with 
(35) Ja'-al ot |t-t]. 
On the other hand the underlying hyperbolic partial differential equation 
(15) has a definite way to propagate influences: along the characteristic 
lines. The equation of those lines is 
(da)” = ~ (de) .(at)® 
i.e. the area in which a change made at q, t makes itself felt is given by 
[dal < j= 28 | at | 
