3 Ee, 
Pe ee | | 
(2am,0) vf e hig a Diggin Ker TEEN 
in which the integration must be extended over the above mentioned 
space. Now the number of the systems considered z’ may be repre- 
sented by 
Ls k 
7) 5 
ze Ne OE iced EE 
] 
Now we have to determine the number of systems in which the 
atoms are combined so as to give 2, molecules of the x" kind, ete. 
We must bear in mind that the total number of atoms of each kind 
is fixed; so that when x, is the number of atoms of the at kind, 
we have p equations of the form 
Nia de Ny YE eo OE Ui ey EN 
Now, in order to get the number of combinations possible, we 
must in the first place consider that #- atoms are to be combined 
into groups of 1,4,» .-- particles in 
Ur ! 
ae FN ASR 
CEN Lee CE (1) 
different ways. 
Further, that the number of different ways, in which 2,4,» particles 
are to be combined into ”, groups of 4,» particles, is given by 
(2, Vr) ! 
(adm! DE rc 
In order finally to obtain the total number of cases possible, we still 
ought to consider in how many ways the n, groups of y,,…. Yiz Yip 
particles may be combined into molecules «‚y,, +. &z4r … + ay: 
Suppose 3, of the quantities 7,, to differ from zero, then the wanted 
number of the combinations in question will be 
(nha A 
For the total number of eombinations we find, bearing in mind: 
that (n,/)* ete. oeeurs in the denominator 
TN NII Sh a ee 
yl se Mads oe L(Y, oe Vire oe Yap) eee Genes Wer Ur) EAS ig IN ee (ED 
By uniting into a constant C the quantities not depending on 
n‚, we get for the total number of systems, in which m.... 
molecules x are present (z) 
