1181 
Ee, 
Werd 4 BT en 
Ti A GAG ter). <4 «505 oi ae 0) 
If it is possible to find such a form for the function g (which 
represents a function of all variables g and p) that the following 
formula is satisfied : 
1 1 
ee ge Dp? 
3 Benares 
Jie eet te Mdqd iia? 
167. p(q--.p) gdp 9 ma 
Pe ces a 
oa eu g an pee 
fe 6 p(q...p) Hdgdp 
then the average energy in the ensemble for every degree of freedom 
has the value which is indicated for it by the spectral formula of 
PrLaNck. The function of y must of course have such a form that 
an equation of the form (5) is satisfied for every variable, not only 
for the q’s, but also for the p’s. The function y may moreover 
contain the-frequeneies p, but it must be independent of 4, for else 
the equations of motion of the system would depend on 4, whereas 
the conception “equation of motion” involves, that they are perfectly 
determined by the condition of the system at a given instant (the 
qs and p's and constants), and that they do not contain a quantity 
as 6, which is not characteristic of the individual system, but of 
the ensemble. If the condition that p must be independent of 6 did 
not exist, then it would be easy to find several solutions for the 
integral equations (5). With this condition it seems to offer rather 
great difficulties *). 
1) The integral equation can in general be brought into the following form : 
1 
vh 
C 2 
e p(q...p) F er Hdqdp = 0. 
Pa gas 
It is possible that 7 may be split up into a product of functions f(q,v) each of 
which contains only one variable and the number of vibrations belonging to it. 
In this case the equation for the determination of f(g,v) may be written: 
