330 
18 
Assuming harmonicity 
( ye ST ee 
Vose + RN inne ‘ 
So the left-hand side (29) should be replaced by 
(31) V Om i eeu cee IM 
ae 
wr 
§13. In the mathematical terminology the surmise of §12 means 
that the quasi-molecular kinetic solution ((25)) converges to the hydrodynam- 
ical one ((15) with (10), (14)), but in the weak sense. I.e. that only the 
averages converge numerically. (Even this requires a slight qualification 
due to what was observed above concerning the We -averages, but there is no 
need to consider such details already here.) 
A mathematical proof of this surmise would be most important, but 
it seems to be very difficult, even in the simplest special cases, The 
procedure to be followed here will therefore be a different one: We shall 
test the surmise experimentally by carrying out the necessary computations 
for certain moderate values of N (cf. §§9, 10), on problems where the rigor- 
ous hydrodynamical solution ((15) with (10), (14)) is known, and produces 
shocks. The comparison of the computed, approximate motion with the rigor- 
ous, hydrodynamical one will then be the test. 
§14. It is worth while to state once more what we propose to do: 
The system (25) is a computational approximation of (15). (15) describes 
continuous hydrodynamical motions, but not shocks. It is nevertheless ex- 
pected that the approximation (25) will prove itself better than its original 
