( 709 ) 
YW is a constant corresponding with the free energy, & represents 
the potential energy, which is here only chemical energy, as we 
shall leave van per Waats’ attraction forces out of consideration. 
Now to find 8 we must sum 6" with respect to the coordinates 
and conic openings for all cases in which n, atoms are free and the 
others bound to definite pairs. On account of the applied simplification 
the coordinates of the , free atoms and of n, of the bound atoms 
can traverse the whole volume WV, the available space for dà for 
each of them amounting to 47. If we caleulate this sum we find 
for the contribution of all the considered systems to the number ¢': 
i = ene 
2 
© (22 Om) (4a V)nitns ene den, + No +1 - ‚den Day, trg+l1l--- dA, 
Then the remaining #, atoms must be ce so that EU are 
bound to those of the #, atoms which have been pointed out; if 
we take all the configurations into account for whichöthis is the case, 
we see easily that: 
3 
YP 
2 = Dik dad 
el as N e® (2zr Om) (4-7) n V mna (== aw ° 
is found for ¢’. 
For constant do the integral in the second member must be extended 
over A (p. 708), while further we must ascribe all positions of the 
region w to dw. We shall denote this integral by 4. As y,, and 
© have the dimension of an energy, 4,, has that of a volume. 
9. To find the total number of the systems that contain n, free atoms 
and #, molecules, we must consider that from ” atoms groups of #, 
and 27, atoms can be formed in 
ni 
n, ! (2n,)! 
ways, and that further the 27, atoms can be joined to pairs in 
2n,)/ 
ei. 3.9 pe 
2nan, ! 
ways. 
So the total number of the considered systems in the ensemble 
amounts to: 
WY 3 
— sl / 
© ¢ 2 
S= Ne~ (22 Om) (420)" Vite k, te, 
nt n,! 2 
where n, + 2n, =m. This number will be maximum, when : 
Slog — 90 
if 
46 
Proceedings Royal Acad. Amsterdam. Vol. XIII. 
