where \(Q\) is the thermal effect per gram-molecule, and \(N\) is the number of atoms in a mole; it also provides experimental foundations for the views expressed earlier by Stark concerning the nature of the action of sensitizers in photochemical reactions.

Finally, in the phenomenon of electron emission by incandescent bodies, collisions of the 2nd kind may also play a role; in this case the observed Maxwellian distribution of velocities of the emitted thermions is explained by the fact that the liberation of electrons from the atoms of the substance occurs as a result of thermal dissociation, and does not presuppose free electrons, whose existence, especially in metal oxides, is, as is known, very doubtful.

Tr. Landsberg.

On the Luminescence of Atoms.

K. Försterling. Über das Leuchten der Atome. Zs. f. Ph., X, 6, p. 387, 1922.

Försterling’s work attempts to find experimental grounds for deciding the question whether the bond between the radiating electron and the radiation is broken instantaneously (Sommerfeld), or whether there exists between them a continuous bond of a differential character (Mie). First of all, there is no doubt that radiation issuing from a moving electron, even if Sommerfeld’s assumption is admitted, cannot be regarded as propagating from a fixed center, from the point at which the electron was at the moment the bond was broken. For, owing to the duration of the luminescence (W. Wien’s experiments and the older experiments of Lummer and Gehrcke on interference), an observer connected with the electron but facing it with his back would see light issuing from this center and overtaking the observer (since \(c > v\)). Thus, the possibility of “seeing” an electron located behind the observer’s back would serve as proof of the motion of the observer and the electron, i.e. would contradict the principle of relativity in its most acute form.

Having established the spatial proximity of the radiating electron and the center of the emitted wave, Försterling argues as follows. An electromagnetic field cannot act upon free radiation, but only upon the radiating electron. Therefore the influence of the field on the radiation of a moving electron can decide the question whether the radiation exists independently of the electron, or is bound to it throughout the whole time of emission. In Stark’s apparatus the luminescence of canal rays began, at least in part, before their emergence into the region where a high electric voltage prevailed. The velocity of the canal rays (\(10^7\) cm/sec), the duration of the luminescence (\(10^{-8}\) sec), and the length of the free path in the region described (about 3 mm) are such that the canal rays, during the time of luminescence, should not experience collisions with other atoms. Thus, if the radiation that follows the atom into the region of the electric voltage has already lost its connection with the atom, then it should not experience any action from the electric field, and alongside the lines that have undergone the Stark effect there should be lines that have not undergone splitting. However, Stark’s observations never revealed such unsplit lines. Consequently, it must be recognized that the connection between the radiation and the electron is preserved throughout the whole time of emission.

Tr. Landsberg.

On True Absorption of Light.

Günter Cario. Über Entstehung wahrer Lichtabsorption und scheinbare Koppelung von Quantensprüngen. Zs. f. Ph., 10, 3. p. 185, 1922.

Applying the terminology proposed by Klein and Rosseland, the author calls collisions of the 1st kind those collisions (with fast electrons and atoms) as a result of which the outer electron of an atom is removed to one of the higher quantum orbits, i.e. the atom passes into an “excited” state. Collisions of the 2nd kind are those in which the excited atom again passes into the normal

state, but the excess energy contained in it is not radiated, and is instead distributed among the other atoms participating in the collision.

By such collisions of the second kind, Cario attempts to explain, first, the weakening of the resonance radiation of mercury vapor as a result of adding neutral gases (observed for the first time by Wood), and, second, the phenomenon he discovered of the sensitization of metal vapors.

First part. The explanation of the indicated phenomenon is based on the assumption that every collision of an excited atom with an unexcited one is a collision of the second kind, i.e., that in each such collision one of the atoms capable of becoming a center of radiation loses this possibility. Calculating what diameter the excited atom must have in order that the corresponding number of its collisions (according to the kinetic theory of gases) could, under the assumption made, explain the observed weakening of the resonance radiation upon addition of gases, the author finds for the diameter of the excited mercury atom a value from 3 to 5.5 times greater than the diameter calculated from experiments on internal friction. The nonconstancy of the value of the diameter (the apparent increase in the case of admixture of light gases, \(He\)) proves that the assumption made is fulfilled only approximately (with light admixtures, evidently, not all collisions take away the energy of the excited atom); nevertheless, the mean value obtained for the diameter of the excited mercury atom, in agreement with the foundations of Bohr’s model and confirmed by the measurements of Füchtbauer and Joos (Ph. Zs, 23, p. 73, 1922) on line broadenings upon addition of neutral gases, compels one to consider that, in general, collisions of excited molecules with unexcited ones are almost 100% collisions of the second kind.

In Wood’s experiments (Ph. Zs., 13, p. 353, 1912) air served as the admixture. Cario, in his experiments, added noble gases (\(Ar\), \(Ne\)—\(He\)) in order to exclude the possibility of chemical interactions between mercury and the admixture. In addition, in his measurements the excitation of mercury vapor was produced not by means of a second mercury lamp (as in Wood’s), but by means of a stream of electrons of suitable velocity (Franck’s method). By this device it was possible greatly to increase the intensity of the glow. The first portions of the gas being mixed in even somewhat intensified the glow, evidently by creating more favorable conditions for collisions of the electrons with mercury atoms (elastic reflection of electrons from atoms of \(Ar\) and \(He\) in all directions).

The change in the intensity of the glow was determined by means of successive photographs of the spectrum; photometric measurement of the plates was carried out with Hartmann’s microphotometer.

Second part. As an admixture to mercury vapor there is chosen a substance satisfying the following requirements: its excitation potential is less than the excitation potential of mercury (corresponding to the line \(2536.7 A^\circ\)), but close to it; its ionization potential is greater than the excitation potential of mercury; the line \(2536.7 A^\circ\) lies outside the region of absorption of the admixture. In such a case one may hope that the excitation energy of the mercury atom, passing in collisions to the atoms of the added substance, will be capable of exciting (but not ionizing) them and will cause the glow of the admixture. A suitable substance is thallium vapor (\(Tl\)). Indeed, heating in one end of a sealed quartz vessel \(Hg\) (to \(100^\circ\)), and in the other \(Tl\) (to \(800^\circ\)), Cario succeeded in obtaining a mixture of \(Hg\) and \(Tl\) vapors which revealed the expected phenomenon: illuminating the mixture with the line \(2536.7 A^\circ\) and photographing the resonance radiation, he, with an exposure of one hour, obtained simultaneously with the mercury lines the following thallium lines:

Control experiments: elimination or weakening of the line 2536.7 correspondingly eliminates or weakens the indicated lines; pure Tl vapor, despite intense illumination, gives no traces of the aforementioned lines.

The lines that appear are in good agreement with the serial scheme and the selection principle (azimuthal and inner quantum numbers). The appearance of the line \(4d_1—2p_1\), when a direct transition from the basic orbit \(2p_2\) to the orbit \(4d_1\) is impossible (for this would require more energy than is present in the excited mercury atom), compels one to suppose that, in the collision, the electron is transferred from the orbit \(2p_2\) to \(2p_1\), where it becomes trapped, since the reverse transition to \(2p_2\) is impossible by the selection principle. The next collision throws it onto the orbit \(4d_1\), and thus the indicated line appears. Therefore the orbit \(2p_1\) must be regarded as a metastable basic orbit, the existence of which is confirmed, incidentally, by the absorption line \(5351 A^0\) \((2p_1 — 1,5s)\), observed at a temperature of \(500^\circ\).

Experiments with Ag serve as a supplement to the experiments with Tl. In a mixture of Hg, Tl, Ag, the Ag lines appear.

\[ \lambda = 3281 A^0 \ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ 2p_1 — 1,5s \]
\[ 3383 A^0 \qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad 2p_2 — 1,5s \]

In the absence of Tl the Ag lines are greatly weakened. In exactly the same way, the relative intensity of the Tl lines changes appreciably in the presence of Ag. This phenomenon is explained by the assumption that the most favorable conditions for the transfer of energy occur when the energy of the exciting atom does not differ greatly from the energy of the atom being excited. (Hence, for Tl, jumps to \(2,5s\), \(3d_1\), \(3d_2\) are more probable than to \(1,5s\).) Excitation of Ag proceeds better not directly from Hg, but through the mediation of Tl. Conversely, some Tl lines (the \(3776 A^0\) line of the series \(1,5s — 2p_2\)) are more intense in the presence of Ag, since the energy of the excited Ag is closer to the energy required for its excitation than is the energy of Hg.

The work reviewed, which served as a dissertation by Cario, carried out under Franck in Göttingen, is of very great interest, for on the experimental side it approaches the question of the possibility of distributing energy, absorbed in the form of a quantum of a definite frequency, among different atoms by means of collision. The absence of unquestionable facts of this kind has considerably hampered, among other things, a rational explanation of deviations from Einstein’s photochemical law of equivalence.

Gr. Landsberg.

On One Remarkable Case of Quantization.

P. Ehrenfest und G. Breit. Ein bemerkenswerter Fall von Quantisierung. Zeitschr. für Physik. 1922. B. 9. Heft. 4.

In recent years the theory of quanta has been moving irresistibly forward; to a considerable extent the reason for this is Bohr’s “principle of analogy.” Mystical in its basis, in all examples in which it was in one way or another possible to apply it, it led to correct results. In the paradoxical example, from the point of view of the methodology of quantization, to which Ehrenfest and Breit point, the principle of analogy gives an exhaustive answer.

Let us imagine a plane system of rectangular coordinate axes \((xy)\), whose origin coincides with the center of a rigid disk. Let this disk rotate about its center in the coordinate plane. Simple quantization of this circular motion leads to the following formula for the angular momentum:

\[ p = n \cdot \frac{h}{2\pi} \ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ (1) \]

where \(n\) is an integer; \(h\) is Planck’s constant; we see that the angular momentum changes by steps; the magnitude of the step is

\[ \frac{h}{2\pi}. \]