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21 
tial equation (15)) is a symptom of some inadequacy of the computing setup. 
It is therefore important to visualize that in the proposed setup this cri- 
terion must be abandoned: As soon as a shock has been crossed such oscilla- 
tions must develop, and they have a perfectly good physical significance. 
They represent the thermic agitation caused by the degradation of energy 
through the shock. 
Second: Since this important criterion for spotting errors or in- 
adequacy of the computing setup is lost, we must see what other criteria re- 
main. For errors there is always effective numerical checking, but it is 
practically difficult to get along without additional criteria of a more in- 
trinsic significance, and they are also necessary in order to judge the ade- 
quacy of the entire setup. 
The following criteria suggest themselves: 
(A) Any conspicuous feature which appears in the initial conditions 
or anywhere later in the solution, will be propagated by the computation ac- 
cording to (35), while hydrodynamics cause propagation according to (36). 
The signal of (35) is the numerical or false signal, while the signal of (36) 
is the hydrodynamical or true signal. According to (37) the false signal 
must always be ahead of the true signal. Hence an actual computation can 
only be significant if the false signal is very weak (it should become weaker 
than any specified amount for a sufficiently small "grain size"), and if the 
essential changes arrive with the true signal. 
(B) Since (25) conserves the total energy (26), therefore (34) 
should approximately conserve the equivalent of (26), i.e. 
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