of vibrators, when their vibration is influenced by their interaction 
(collisions). 
I shall start from the first supposition. In the first place because 
it is simpler. But it seems to me also to be more plausible. For we 
cannot doubt that the equations of motion are not linear. A vibrator 
iherefore, when set into vibration by a perfectly homogeneous ray 
of light, will not execute perfectly harmonic vibrations. The radia- 
tion, emitted by it will therefore contain vibrations of other period 
than the incident ray. If therefore it is inclosed in a space with 
perfectly reflecting walls it will change the partition of energy of 
radiation which is also inclosed in that space. If now the spectrum 
which originates in this manner was not the normal spectrum (be- 
cause this latter was only brought about by a great many inter- 
acting vibrators) it wonld be astonishing, that even the most rarified 
gases, in which relatively only a few collisions occur, always give 
rise to the normal spectrum, and not to a spectrum whose partition 
of energy lies between the normal spectrum and that of one vibrator. 
1 will therefore imagine one single vibrator. If its motion was 
determined by the equation: 
Ee 
dt? ‘ Td 
in which the coefficients m,f,g,e were constants, then it would 
necessarily give rise to a partition of energy agreeing with the 
spectral formula of RAYLEIGH °). 
Therefore we shall assume from the outset that the equation (1) 
is not satisfied. The vibrator will then not be able to execute per- 
fectly harmonic vibrations, but its vibrations, when analysed in a 
series of Fourier, will consist of several, in general of an infinite 
number of harmonic vibrations. This seems not to agree with the 
fact, that undisturbed vibrating vibrators as they occur in gases, 
emit very sharp spectral lines. We must, however, bear in mind, 
apart from the fact that no element exists whose spectrum consists 
in one single line, — that according to the electron-theory the 
mass is not perfectly constant and the light of a vibrator therefore 
not perfectly monochromatic. It is true that light of a period 7, 
differing from the fundamental period 7’, of a vibrator, often occurs 
only to an imperceptibly small amount in its radiation. But it 
cannot be totally: wanting. Now it is well known that the intensity 
of radiation of a certain period in the normal spectrum does not 
depend upon the emission alone, but upon the ratio between emis- 
m 
OEE 3." ot oe eee 
1) Comp. H. A. Lorentz, Nuovo Cimento V, 16, Anno 1908. 
