1180 
p may be considered to be the momenta corresponding to the coor- 
dinates g. As however we must assume that the equations of HAMILTON 
do not apply, this observation is of no consequence for the equations 
of motion of the system. 
Now if no vibrator occurred in the space, every partition of energy 
would remain unchanged, and there would be no oceasion to speak 
of an equilibrium partition. If a vibrator occurred which had the 
property to be able to transform radiation of every wavelength into 
every other wavelength and whose motion was determined by the 
equations of HamiLron, then the energy partition would approach to 
that indicated by the formula of Rarrein. In this case we might 
represent the condition of the system by means of an ensemble for 
which the probability of phase would be represented by ') : 
Pp. 
1 
Lael er 
Hr nat te wei 
Pe ô WE NE 
I wel 
where wy and 4 are constants and TE =g + En Xp? is the energy of 
o 
the system, the summation being extended over all quantities g and p, 
also over those provided with accents. 
Properly speaking this expression for the energy is incomplete. 
In the first place the energy of the proper coordinate of the vibrator 
has been neglected, but moreover we have neglected the energy of 
the vibrator, which it has in consequence of its foreed vibrations. 
If we imagine the volume sufficiently large these approximations 
will meet with no serious objections. More risky is another simpli- 
fication which I will introduce; I will namely represent an’ element 
of extension-in-phase*) by Mdpdg and here also I will neglect the 
proper coordinate (or coordinates if the electron has more degrees 
of freedom). I think I may suppose that this simplification also will 
not affect our conclusions greatly. Perhaps it is even perfectly 
justified. It is namely possible that we must assume, that the motion 
of the vibrator is entirely determined by the electromagnetic field, 
and that therefore there is no reason to introduce a “proper” 
coordinate. 
As the spectral formula of RayLuicn is not satisfied by the expe- 
riments, the formula (3) cannot give the right expression for the 
probability of phase. I shall therefore put: 
') Comp. Graas. Elementary principles in statistical mechanics p. 16, 
2) Comp. G1BBs, le. p. 6. 
