Black radiation is frequently said to consist of a large number of regular periodic vibrations. This method of expression is perfectly justified, inasmuch as it refers to the resolution of the total vibration in a Fourier's series, according to equation [eqn:(149)] (149), and often is exceedingly well adapted for convenience and clearness of discussion. It should, however, not mislead us into believing that such a "regularity" is caused by a special physical property of the elementary processes of vibration. For the resolvability into a Fourier's series is mathematically self-evident and hence, in a physical sense, tells us nothing new. In fact, it is even always possible to regard a vibration which is damped to an arbitrary extent as consisting of a sum of regular periodic partial vibrations with constant amplitudes and constant phases. On the contrary, it may just as correctly be said that in all nature there is no process more complicated than the vibrations of black
radiation. In particular, these vibrations do not depend in any characteristic manner on the special processes that take place in the centers of emission of the rays, say on the period or the damping of the emitting particles; for the normal spectrum is distinguished from all other spectra by the very fact that all individual differences caused by the special nature of the emitting substances are perfectly equalized and effaced. Therefore to attempt to draw conclusions concerning the special properties of the particles emitting the rays from the elementary vibrations in the rays of the normal spectrum would be a hopeless undertaking.
In fact, black radiation may just as well be regarded as consisting, not of regular periodic vibrations, but of absolutely irregular separate impulses. The special regularities, which we observe in monochromatic light resolved spectrally, are caused merely by the special properties of the spectral apparatus used, e.g., the dispersing prism (natural periods of the molecules), or the diffraction grating (width of the slits). Hence it is also incorrect to find a characteristic difference between light rays and Roentgen rays (the latter assumed as an electromagnetic process in a vacuum) in the circumstance that in the former the vibrations take place with greater regularity. Roentgen rays may, under certain conditions, possess more selective properties than light rays. The resolvability into a Fourier's series of partial vibrations with constant amplitudes and constant phases exists for both kinds of rays in precisely the same manner. What especially distinguishes light vibrations from Roentgen vibrations is the much smaller frequency of the partial vibrations of the former. To this is due the possibility of their spectral resolution, and probably also the far greater regularity of the changes of the radiation intensity in every region of the spectrum in the course of time, which, however, is not caused by a special property of the elementary processes of vibration, but merely by the constancy of the mean values.