325 
a 
which is a physical approximation of that one underlying (15). Indeed, 
the system (25) is that one of the equations of motion of an ordinary (point) 
mechanical system with the coordinates .., 
and with the total energy 
Sent olga ae = 
(26) 2 2 (S3*) ee Grae 
at 
a a 
This is a system of mass points Nos. ..., -2,-/, 0, |, 2 .++ the point 
No. @ having the coordinate Ney jhe mass by and any two neighbors X,., 
and ie being connected by a "spring" which has the potential energy 
We = U, (Wy) when is Leneth 2s) Va Y= 
Now this system of "beads on a line, connected by springs" is 
clearly a reasonable physical approximation of the substance which the hydro- 
dynamical equation (15) describes. It corresponds to a quasi-molecular de- 
scription of this substance, where the mass ascribed to one "bead" (i.e. the 
one elementary volume) is the mass of a "molecule". We chose to treat this 
as the unit mass, but it may nevertheless correspond to any desired real mass. 
Clearly this is not the "true'' molecular description of the substance: For 
any workable computing scheme the number of these "molecules", i.e. of ele- 
mentary volumes, will be much smaller than the actual number of molecules. 
Thus if a gram-mol of a real substance is considered, the true number of 
molecules in it is Loschmidt's number N ~ 6 . | 07? while fora 
practical computing scheme some number of "molecules" JV between 1!0O and 
{ © Owill be appropriate. However, the actual value of Loschmidt's nun- 
ber N_ never figures in hydrodynamics; all that is required for the validity 
of (15) is that N should be a great number. The actual N ~ 6: /0 - 
is certainly great, but much smaller numbers NV may already be sufficiently 
great. Thus there is a chance that Nw~ (0* will suffice. 
