168.

There is, however, also a method, applicable to the case of long waves, for the direct theoretical determination of the electric conductivity and, with it, of the absorbing power, $A$, as well as the emissive power, $E$, of metals. This is based on the ideas of the electron theory, as they have been developed for the thermal and electrical processes in metals by E. RieckeE. Riecke, Wied. Ann. 66, p. 353, 1898. and especially by P. Drude.P. Drude, Ann. d. Phys. 1, p. 566, 1900. According to these, all such processes are based on the rapid irregular motions of the negative electrons, which fly back and forth between the positively charged molecules of matter (here of the metal) and rebound on impact with them as well as with one another, like gas molecules when they strike a rigid obstacle or one another. The velocity of the heat motions of the material molecules may be neglected compared with that of the electrons, since in the stationary state the mean kinetic energy of motion of a material molecule is equal to that of an electron, and since the mass of a material molecule is more than a thousand times as large as that of an electron. Now, if there is an electric field in the interior of the metal, the oppositely charged particles are driven in opposite directions with average velocities depending on the mean free path, among other factors, and this explains the conductivity of the metal for the electric current. On the other hand, the emissive power of the metal for the radiant heat follows from the calculation of the impacts of the electrons. For,

so long as an electron flies with constant speed in a constant direction, its kinetic energy remains constant and there is no radiation of energy; but, whenever it suffers by impact a change of its velocity components, a certain amount of energy, which may be calculated from electrodynamics and which may always be represented in the form of a Fourier's series, is radiated into the surrounding space, just as we think of Roentgen rays as being caused by the impact on the anticathode of the electrons ejected from the cathode. From the standpoint of the hypothesis of quanta this calculation cannot, for the present, be carried out without ambiguity except under the assumption that, during the time of a partial vibration of the Fourier series, a large number of impacts of electrons occurs, i.e., for comparatively long waves, for then the fundamental law of impact does not essentially matter.

Now this method may evidently be used to derive the laws of black radiation in a new way, entirely independent of that previously employed. For if the emissive power, $E$, of the metal, thus calculated, is divided by the absorbing power, $A$, of the same metal, determined by means of its electric conductivity, then, according to Kirchhoff's law [eqn:(48)] (48), the result must be the emissive power of a black body, irrespective of the special substance used in the determination. In this manner H. A. LorentzH. A. Lorentz, Proc. Kon. Akad. v. Wet. Amsterdam, 1903, p. 666. has, in a profound investigation, derived the law of radiation of a black body and has obtained a result the contents of which agree exactly with equation [eqn:(283)] (283), and where also the constant $k$ is related to the gas constant $R$ by equation [eqn:(193)] (193). It is true that this method of establishing the laws of radiation is, as already said, restricted to the range of long waves, but it affords a deeper and very important insight into the mechanism of the motions of the electrons and the radiation phenomena in metals caused by them. At the same time the point of view described above in [sect:111.] Sec. 111, according to which the normal spectrum may be regarded as consisting of a large number of quite irregular processes as elements, is expressly confirmed.