1106 
ments can more sufficiently be represented by applymg the formula 
not of Erxstrm, but of NeRNsT-LINDEMANN for the specifie heat; the 
equation (18) leads for the specific heat to the formula of Einstein. For 
solid matter Born and Van Karman have given a theory leading to a 
formula which seems to represent the experiments on s. h. as well as the 
formula of Nurnst-Linpeman. They start from the conception that there 
cannot be attributed one definite frequency to the atoms of solid 
matter, but that, because of the coupling a great number of 
frequencies occur, which accumulate infinitely at one or more 
definite frequencies. The fact that the formula of Nernst is the 
more appropriate also for gases, makes it acceptable that also in 
gases, through the mutual influence of molecules, there cannot be 
spoken of a finite number of definite frequencies. 
I may still observe, that for the given consideration the way 
in which the system at length comes into the most frequently 
occurring state, is of no importance. That it will get into it, 
may be regarded to be sure, as well from the point of view of 
statistical mechanics as from that of the theory of energy-quanta. 
I will still consider now in what way we can, in liquid states, 
come to the condition of equilibrium. We must for a moment return 
to equation 3), then. There we could divide into parts relating to 
each of the molecules, the general integral which, according to the 
definition of GiBBs, denotes the number of systems of given state. 
However, in the case now considered we cannot proceed likewise, 
because of the mutual influence of the molecules. The number of 
systems of specified state is in general given by 
Te 
tf 
Ne dateen dlja MR, BR mM, deens da 
where «,,.--@ represent the coordinates of the centres of gravity, 
n,, the velocities, and where dà relates to the internal coordinates 
and moments of all molecules. Now considering a system with 
n, molecules x, built up of specified atoms, and allowing all values 
for the coordinates of the centres of gravity, the total number of 
systems obtained in this way 2” may be represented by 
k ai 
~ 
3 
k Soa = Il, == <= 
zl (20 m, 6) 1 IE Oe das. 
The value of the integral can always be represented by 
k 
ii, 
1 
V Ff (Vin, m+. ©) 
