( 414 ) 
that a molecule belongs to a certain group, may be represented by: 
A, 4E dp, dpg . «+ dpy dq, dag... dg. 
In this A; and A are constants, 4, the energy of the intramole- 
cular motion, pj - - « pu the coordinates, which determine that motion 
and gj « « « gu the momenta corresponding to those coordinates. 
From this would follow, that the chance that the amplitude en 
of the vibration of a molecule is contained within certain limits, 
is represented by: 
However we cannot accept this result without further proof. The 
motion, which we are considering, and which is the cause of radi- 
ation, is necessarily damped, so that between two collisions a mo- 
lecule has lost part of its intramolecular energy; moreover the 
molecule has absorbed energy from the field. For such a motion the 
proof of Prof. BOLTZMANN does no longer hold. 
In order to find the distribution of the amplitudes we shall have 
to take into consideration two causes of change: the collisions and 
the electric forces. 
First I shall examine the influence cf the electric forces, and then 
inquire whether the collisions of the molecules will modify the 
distribution brought about by the electric forces. I shall make the 
same assumptions about the construction of a molecule as Prof. 
Lorentz did!), i.e: 
a. I assume every molecule to contain an ion charged with 
electricity. 
b. That ion has a position of equilibrium in the molecule, from 
which it can move in all directions, and to which it is driven back 
with a force, proportional to the deviation. 
c. The mass of the ion is so small compared to that of the rest 
of the molecule, that when the molecule is vibrating, the ion alone 
may be considered to move. 
d. The remaining part of the molecule is charged opposite to 
the charge of the ion and that in such a way that, when the ion 
is in its position of equilibrium, the electric forces, exercised by 
1) Arch. Neerl, XXV, 5, 1892. 
