If we are not yet very far advanced in the study of the mechanism of the production of the spectrum,[47] we are, on the other hand, well acquainted with its constitution.  The extreme confusion which the spectra of the lines of the gases seemed to present is now, in great part at least, cleared up.  Balmer gave some time since, in the case of the hydrogen spectrum, an empirical formula which enabled the rays discovered later by an eminent astronomer, M. Deslandres, to be represented; but since then, both in the cases of line and band spectra, the labours of Professor Rydberg, of M. Deslandres, of Professors Kayzer and Runge, and of M. Thiele, have enabled us to comprehend, in their smallest details, the laws of the distribution of lines and bands.

[Footnote 47:  Many theories as to the cause of the lines and bands of the spectrum have been put forward since this was written, among which that of Professor Stark (for which see Physikalische Zeitschrift for 1906, passim) is perhaps the most advanced.  That of M. Jean Becquerel, which would attribute it to the vibration within the atom of both negative and positive electrons, also deserves notice.  A popular account of this is given in the Athenaeum of 20th April 1907.—­ED.]

These laws are simple, but somewhat singular.  The radiations emitted by a gas cannot be compared to the notes to which a sonorous body gives birth, nor even to the most complicated vibrations of any elastic body.  The number of vibrations of the different rays are not the successive multiples of one and the same number, and it is not a question of a fundamental radiation and its harmonics, while—­and this is an essential difference—­the number of vibrations of the radiation tend towards a limit when the period diminishes infinitely instead of constantly increasing, as would be the case with the vibrations of sound.

Thus the assimilation of the luminous to the elastic vibration is not correct.  Once again we find that the ether does not behave like matter which obeys the ordinary laws of mechanics, and every theory must take full account of these curious peculiarities which experiment reveals.

Another difference, likewise very important, between the luminous and the sonorous vibrations, which also points out how little analogous can be the constitutions of the media which transmit the vibrations, appears in the phenomena of dispersion.  The speed of propagation, which, as we have seen when discussing the measurement of the velocity of sound, depends very little on the musical note, is not at all the same in the case of the various radiations which can be propagated in the same substance.  The index of refraction varies with the duration of the period, or, if you will, with the length of wave in vacuo which is proportioned to this duration, since in vacuo the speed of propagation is entirely the same for all vibrations.