332 
20 
or, using (30), by 
(36) [dal 2 & |dtl. 
Note that c was the velocity of sound in the physical space Ket , While £ 
is the velocity of sound in the label space Cee Equivalently, . ats 
the flow of mass across the sound wave. 
Now as hk. Courant pointed out first for a more general class of 
problems, the computation cannot give significant results unless the depend- 
ences (35) which it permits contain the dependences (36) which the underlying 
problem demands. Consequently it is necessary that 
LE ELS 
Th me 
ees) whee 
Vv 
(37) (Sa 
Practically even a certain "factor of safety" in (37) will be advisable. 
§15. The system of difference equations (34) is well suited to 
mechanization. Specifically, it can be solved with punch-card equipment, 
with g being the number of each one of the successive stacks of cards pro- 
duced, and a the current number of each card within its stack. However, 
the following points must be emphasized: 
First: We expect that after crossing the equivalent of a shock, a 
"molecule" qa will develop an oscillation of A, , Which represents thermic 
agitation. The period of this oscillation will be of the order { in a 
i.e, of the "grain size" introduced by the numerical approximation, by the 
operation of making the continuous a discrete. 
Now by the usual standards of numerical computing, the appearance 
of such oscillations (of a period which is imposed by the "grain size" of the 
approximation, and not by some quantity derived from the underlying differen- 
