336 
24 
(46) Pee Oheale eS Gao=2, aa a, , 
and to place rigid walls at the two ends: 
(47) For all C20 ae Oe Vin onthe 
This corresponds to (28). The initial state of the substance is as in (27), 
i.e. "normal" specific volume v= | and uniform motion to the left: 
For t=0 Xe =a, ee 
dt 
(48) | Forvall | ape ty Qa kan, ODA astt 
+ with a given te 2 (O) ¢ 
As the system of total differential equations (25) is replaced by 
the system of difference equations (34), the boundary conditions (47), (48) 
are to be replaced by 
(49) homeil) 20 (2)... Wer are: XS ae 
Renmei Oy = 42). Y. G52 al" Xqe ia. 
(50) 
x =) CR acare 
The following remarks are now in order: 
First: Of the Q,+ {| “molecules" Qz=v», |, Ds geen, 
Oe’ Gi. the first and the last, @-= 0, @,, represent the two 
walls. Hence the substance proper consists of the @,-{ molecules 
A= |, Tiny ek age | SOG OA MONE EN 
Second: The initial velocity -& points to the left (towards 
oO = 0, away from = 4, ), hence there will be a compression wave ori- 
ginating at the wall Q=0O, and an expansion wave at the wall Q=-=a,. 
I.e. the former will be a shock, and the latter a Riemann rarefaction wave. 
Third: In order to have a way to estimate the significance of a 
given initial velocity ® on an absolute scale, it is best to compare it 
with the "normal" sound velocity C, of (45). This gives as a measure 
