( 882 ) 
absorption of light is not always accompanied by ionisation; in most 
cases the above-said critical value evidently is not exceeded, which 
means that some cause must exist by which the increase of the 
amplitude is limited. Such a cause is formally accounted for by 
introducing a “resistance”, which opposes the motion of the electron 
and is supposed to be proportional to its velocity. The equations of 
motion of an electron, moving under the influence of a (periodically 
changing) electric force (NVZ), therefore have the form 
dt de fs 
m We +h eats Wa R GES. es NN 
where m means the mass, ¢ the charge of the electron, while the 
magnitude of the quasi-elastic force is determined by %, that of the 
resistance by /. 
We propose to study in this paper the nature of the damping 
parameter /, and to inquire into the influence which the damping 
forces exert on the intensity of light propagated through very extensive 
gaseous media, like the atmospheres of the sun and the stars. 
§ 2. Recalling: some results of the dispersion theory. — We 
know that the dispersion theory answers the question, how a given 
periodically changing electric force is propagated through a medium 
containing a large number of electrons, the motion of which is 
represented by a set of equations of the above form '). 
Let the medium contain ® similar molecules per unit of volume, 
each of them furnished with a few differently connected electrons, 
so that there are a limited number of periods of free vibrations; 
then we only have to apply the general equations of the electro- 
magnetic field to this charged medium, and, using the notation 
introduced by W. Vorer *), which is well adapted to our purpose, 
we find the following solution: 
3 
C 
4am— 
2 2 . > wv m | yO Q >) 
u =S (1—iz) =H 7 si SEAN De (2) 
ln tl » Vo +wy—r 
ye 
mm 
In this equation « represents the complex index of refraction, 
1) The equations of motion of the electron with which Lorentz starts (The 
Theory of Electrons, p. 139) contain two additional terms, and, therefore, are 
more general than the set (1). In the problem of which we are going to treat, we 
may omit those terms, because 1st we need not account for an exterior magnetic 
field, and 2nd we only wish to apply our results to media of low density. 
2) W. Vorer, Magneto- und Electro-optik, (1908) p. 107. 
