326 
14 
So the replacement of (15) by (25) amounts to the introduction of 
a quasi-molecular description with a Loschmidt number N chosen for comput- 
ing purposes, and therefore much too low. Reality is not (15) either; it 
is molecular with the correct Nw~ 6: 107? . Hence (25) is an aecept- 
able approximation if this "scaling down" of NV from 6. tors to the 
value used, say lO* is acceptable. At this point two more remarks are 
) 
in order: 
First: This "scaling down" of N requires a corresponding "scal- 
ing up" of the "intramolecular forces", to produce the correct hydrodynamical 
forces. This has indeed been done: The potentials in (26), i.e. the forces 
in (25), were chosen so as to approximate just the correct forces in (15). 
Second: The actual intramolecular forces are of course much more 
complicated than those of the simple "beads and springs" model used in (25), 
(26). However, the classical derivations of hydrodynamics from molecular- 
kinetic models have established-that these more subtle details of the intra- 
molecular forces are immaterial for this part of hydrodynamics: It can be 
derived from the "beads and springs't model just as well as from one where 
those details are taken into consideration. 
§10. The above considerations make it plausible that the system 
(25) is a good approximation of the hydrodynamical equation (15), even for 
moderate values of the number of elementary volumes NM . The minimum size 
of N which will give acceptable approximations must, of course, be deter- 
mined by effective computation, and it may vary from problem to problem. We 
expressed above the surmise that values between IO and [00 will usualiy 
Suppace. 
All these considerations are, however, only plausible as long as 
(15) describes reality without any further complications, i.e. in a continu- 
