(881 ) 
Physics. — “Selective absorption and anomalous scattering of light 
in extensive masses of gas.” By Prof. W. H. Juus. 
(Communicated in the meeting of January 28, 1911). 
§ 1. Resonance and damping. — The dispersion of light is at 
present generally explained by supposing the molecules of the medium 
to contain electrons, bound to positions of equilibrium by quasi- 
elastic forces. Such electrons have their own period of vibration 7’; 
their motion will continually increase by resonance, if in the incident 
beam of light there are waves of the same period. As light, some- 
where in the visible spectrum, may give impulses at the rate of 500 
billion a second to a resonant electron, one conceives that in a very 
short time the amplitude of the electron will considerably increase, 
even though the impulses may be weak. 
Waves of a slightly different period 7” are also able to set the 
same electrons moving; they force the period 7” upon them; but 
the resulting amplitude of the forced vibration is the smaller, the 
greater the value of + (7— 7”). The absorption. spectra of gases will 
appear, however, to be only slightly affected by this phenomenon. 
We may refer to a general result obtained by HELMHOLTZ") as to 
how the intensity of the forced vibrations of a system is determined 
by the rate of extinction of the free vibrations, and the difference 
of the periods, 7—7”’. If the extinction is slow, sensible amplitudes 
are not reached unless 7” differs very little from 7. Now we know 
from the phenomena of interference with great differences of path, 
that the free vibrations of electrons are so little subject to damping, 
as to have more than */,, of their energy left after 300.000 vibrations 
have been accomplished. Applying HermuHoLtz’s formula to the case, 
we find, that the energy of the forced vibrations of period 7” will 
be smaller than */,, of the energy of the exactly resonant vibrations 
of period 7, if the wave-lengths corresponding to those two periods 
differ as little as 0,01 A. So the width of the region of sensible 
co-vibrating scarcely exceeds some 0,02 A. 
The amplitude of a resonant electron cannot, of course, go on 
increasing infinitely, and no doubt the quasi-elastic force will cease 
from being proportional to the displacement when the latter has 
become very great. As soon as the amplitude surpasses a certain 
value, the electron will be strained out of the molecule and set to 
moving independently: then radiation has led to ionisation. But 
1) Hetmnorrz, Die Lehre von den Tonempfindungen (1877), 5. 233 und 642, 
