1524 
there appears in the damping-term a coefficient which represents 
the excess of the mean number of molecules in the small space con- 
sidered, if it is known that one molecule lies within that space. 
This number is 1 for a random distribution, but in our case it is, 
as will be seen easily, 1+ G. Thus this way also leads to the 
known formula for the extinction, according to which this quantity 
is inversely proportional to dp/dv. 
Thence it is clear that we must take into account the influence 
of the molecule considered on the density of its surroundings, even 
at distances comparable with the wave-length. To this end it will 
no longer be possible to use the developments in power-series, which 
Lorentz applies repeatedly. In order to make the calculation possible 
without that, I introduce the following simplification. 
The electrons which are brought into vibration in the molecules 
by the incident light, (for simplicity we imagine one electron in 
every molecule) will in reality perform a somewhat irregular vibra- 
tion, with an amplitude not always equal for everyone. I neglect 
these differences in calculating the resistance which the neighbouring 
oscillators exert on the electron particularly considered. Lorentz 
also makes use of this approximation at a later point. Of course this 
is much more acceptable, however, for a diluted gas than for the 
rather dense nearly critical state. 
First consider one molecule in the origin of coordinates, which 
bears a variable moment in the direction of ¢: 
PaP Sith ss ue ee ne ca a (6) 
With the aid of well-known formulae for the potentials g and a 
we then find for a point (x,y, 2) at a distance 7 
Op pp, | (#2?  v7—827) . rN, kr? —32? r 
nn enn 
a Pp, ke r 
SS En sink (1 _") 
c An cr c 
The sum of these two expressions with the negative sign gives 
the z-component of the electric force. Now if the incident light 
comes from the negative v-axis, the phase of the variable moment 
of a molecule in (a, y, 2) will be so much in advance of one for 
which # — 0, as corresponds to a difference of way ur, in which g 
is the refractive index of the material. Thus 
E LT 
Pz‚y‚z = Po sink (« — Ee) 
Y> 5 
The electric force which this moment exerts in the origin is evi- 
