ALL SYSTEMS HAVE THE SAME ENERGY.
119
From the last equation, with (298), we get
|
(375)
|
But by equations (288) and (289)
|
(376)
|
Therefore
|
(377)
|
Again, with the aid of equation (301), we get
|
(378)
|
if
. Therefore, by (289),
|
(379)
|
These results are interesting on account of the relations of the functions and to the notion of temperature in thermodynamics,—a subject to which we shall return hereafter. They are particular cases of a general relation easily deduced from equations (306), (374), (288) and (289). We have
|
|
The equation may be written
|
|
material points with this particular value of the energy as nearly as possible in statistical equilibrium, or if we ask: What is the probability that a point taken at random from an ensemble in statistical equilibrium with this value of the energy will be found in any specified part of the circle?