( 890 ) 
fourth power of the wave-length, direct proportional to the density, 
to the average mass contained in the medium per scattering particle 
and to the square of the refraction constant. As the latter varies 
strongly in the neighbourhood of a proper frequency, also if the 
damping parameter is small or even approaches zero (Cf. Vorer, Le. 
p. 118), the coefficient of scattering will assume widely different, and 
relatively great values in such a region; it only vanishes for waves 
travelling in the medium with the same velocity as in the ether, i.e. 
in places of the spectrum where k=O, or n= 1. 
The effect of absorption and scattering may be considered from 
two points of view. First we may inquire into the influence of these 
two damping causes on the motion of the electrons, and, consequently, 
ou the optical properties of the medium (as characterized by n and z). 
The second point of view is that in which, the incident light being 
given, we desire to study the intensity and the composition of the 
light that leaves the absorbing medium. 
So far we have only considered the first question. We concluded that 
for waves, belonging to the nearest vicinity of those corresponding 
to the free vibrations of a gas, the damping parameter 4 must be 
the sum of two terms: 
2m 2 ve" 
IS PS ee es. a ERN 
7 er ata 
that in the middle part of that narrow region the first term is great 
compared with the second one; that very probably, however, the 
value of the first term sinks rapidly to zero at a short distance from 
each of the proper frequencies, so that in the rest of the spectrum 
it is only the effect of the second term which remains. 
The parameter /, therefore, is not a constant, even if we confine 
our attention to a part of the spectrum so small, that the variation 
of the factor »? may be neglected. Nevertheless, our fig. 1 (p. 884) 
gives the principal features of the index of refraction as a function 
of the frequency, with a fair degree of exactness, because the 
character of the dispersion curve is much the same for different” 
values of h. The relation, for instance, that the maximum and the 
minimum of 2 are found where w= + */, v', will continue to hold, if 
at these points of the spectrum the second (constant) term of / 
already prevails. But if at the points where pt passes the values + */, 9, 
the function pv’ (or h) increases rapidly with decreasing absolute 
value of uw, then the distance between the maximum and the minimum 
of 7 must be greater than 2. 
§ 5. Radiation through an extensive atmosphere. — We shall now 
