1055 
the extension considered up to now. We can, namely, write for this: 
(vn)k (kv) pr \k iV _ 4 ‚ RN 
ZE or ——. We take, therefore, now the function 
(ne NI N! 
je instead of »*, and have retained the property (3). 
We arrive at the same result, when we do not take into account 
the interchanges between the molecules of the different parts v, 
but also disregard the individuality of the molecules of each part 
in itself, so that the number of generic phases instead of the number 
of specific phases has become decisive. *) 
The remark might be made that a consideration as the above is 
more of a mathematical than of a physical nature. It should, how- 
ever, not be overlooked that no physical reason is given either why 
the entropy should have to be S=k log P or &k log extension. 
These functions have been taken tor the entropy because they 
showed analogy with the thermodynamic entropy. It is, therefore, 
natural to make changes in these functions which render the analogy 
more perfect, when it is seen that the analogy is not perfect yet. 
We may also call the division by .V! such a change, through which 
we get a mathematically determined quantity, which satisfies the 
three or four conditions mentioned in § 1. 
§ 4. We will now discuss for a moment the quantity for the 
entropy which GrBBs puts most in the foreground, viz. —%j= —| ndt, 
D 
in which 4 = /og P and Fs when JD is the density of the 
system points in the element dr of the Ispace, and NV the total 
p-E 
number of system points. For a canonic ensemble P = es, in 
which attention is drawn to the fact that P has the dimensions of 
1 
“phase extension’ 
But then » has logarithmic dimensions, hence also — 7; as was 
observed above, this is no quantity in the strict sense of the word.” 
E and 9& being of mutually equal dimension, also y must have 
logarithmic dimensions; y and £ have therefore different dimensions, 
are therefore dissimilar quantities. Yet G1BBs speaks of w as of the 
energy, for which the coefficient of probability (P) = 1. 
1) Cf. also: H. Terrope, “Theoretical Determination of the entropy constant 
of gases and liquids”. These Proc. XVII p. 1167. 
2) Cf. Graas, Statistical Mechanics, p. 19. 
