a) In water, the black circle in Fig. 1 denotes the nucleus of the oxygen atom, the black crosses—the nuclei of the hydrogen atoms, and the white circles—the electrons. Electrostatic forces have displaced four electrons from the vertex of the cube where they were located in the oxygen molecule.

b) A whole series of properties of nitrogen brings it closer to the noble gases; therefore the model of the nitrogen molecule, according to the author’s theory, must have the form shown in Fig. 2, where the black circles denote the nuclei of the nitrogen atoms that have combined into a molecule, and the white circles—the electrons.

Vas. Shuleikin.

The absorbing cross section of molecules with respect to slow electrons.

1) H. F. Mayer. Über das Verhalten von Molekülen gegenüber freien langsamen Elektronen. Ann. d. Phys. 64, p. 45, 1921.
2) C. Ramsauer. Über den Wirkungsquerschnitt der Gasmoleküle gegenüber langsamen Elektronen. Ann. d. Phys. 64, p. 513, 1921.

P. Lenard showed in 1903 that the absorption of free electrons in matter proceeds according to the usual absorptional, exponential law:

\[ J = J_0 e^{-apx} \qquad \ldots\ldots\ldots\ldots\ldots\ldots\ldots (1) \]

where \(J_0\) is the initial intensity of the electron stream, \(J\) is the intensity of the stream after passing through a layer of gas of thickness \(x\) and at pressure \(p\), and \(a\) is the specific absorptive capacity, evidently proportional to the cross section of the electron stream absorbed by a single molecule.

Lenard found that the magnitude \(a\) increases as the velocity of the electrons decreases, asymptotically approaching a constant value, beginning with velocities corresponding to approximately 10 volts. The phenomenon of the absorption of electrons in gases has for many years been carefully studied by Lenard’s pupils in all directions.

Both papers under review, which came from Lenard’s laboratory, are devoted to the question of the dependence of the magnitude \(a\) on the gas pressure and on the velocity of the electrons for various substances. The methods of the two authors are entirely different. Mayer, in order to obtain slow electrons, uses a cathode with a heated tungsten filament and, by applying additional opposing electric fields, selects cathode rays sufficiently homogeneous with respect to velocity. Ramsauer uses photo-electrons, attaining greater homogeneity of the electrons, but losing in the possibility of wide variation of the velocities.

When a parallel beam of electrons passes through a thickness of gases, the following cases are possible:

1) The electron undergoes no change whatever with respect to the direction and velocity of its motion.

2) The direction and velocity of the motion of the electrons change somewhat, while the velocity remains of the order of the electronic one, changing relative to the mean only within very narrow limits (diffusion).

3) The velocities and directions of the electrons after passing through the substance are distributed according to the ordinary Maxwell law; the absolute values of the velocities become of the order of molecular ones (absorption).

4) The velocities and directions are distributed according to the same Maxwell law; however, the maximum velocity remains of the order of the electronic one (reflection).

Ramsauer’s method was developed for the purpose of studying the total perturbation in the motion of electrons, consisting of diffusion, absorption, and reflection; in Mayer’s work it was possible to determine only the number of absorbed electrons. However, in the range of velocities in which both authors worked (1–10 volts), the number of absorbed electrons is so large in comparison with the number scattered or reflected that the quantities determined by both authors for the same substances practically coincide. In the table we give the results of Ramsauer’s measurements.

Table 1.

In the table \(v\) is the velocity of the electrons in volts, \(q\) is the cross-section of the flux of electrons absorbed by one molecule, where \(q\) is calculated on the basis of \(a\) (formula (1)), determined experimentally; \(r\) is the ratio of \(q\) to the cross-section of the molecule, calculated from the data of the kinetic theory of gases. The quantity \(q\) is entirely independent of the gas pressure and practically does not depend on the velocity of the electrons for small velocities. The only exception is argon, for which \(q\) increases strongly with even a small change in velocity. Exactly the same, but more complete, results were obtained by Mayer; they are shown in the drawing. Along the abscissa axis are plotted quantities proportional to the velocities in \(\sqrt{\mathrm{volt}}\), and along the ordinate axis the values of \(a\); the curves have been drawn exactly through the numerous points determined experimentally. We see that for all gases, with the exception of argon, the curves asymptotically

approach parallelism with the axis of abscissae, i.e. independence from velocity. For argon there exists, as is clear from the drawing, a sharp “selective” absorption with a maximum at about 12 volt. It should be noted that the electron beam in Mayer’s experiments was not sufficiently homogeneous; the author estimates its conventional “width” at 0.5 V. It must be thought that with electron beams more homogeneous the curve for argon would turn out still sharper. The authors do not draw final theoretical conclusions from the results found, proposing a further development of the phenomenon they have found of “selective absorption” of electrons. Let us note the extremely small value of \(q\) for argon at the base of the absorption band. The argon molecule is as it were “transparent” to electrons, in contradistinction to the molecules of the other gases studied, for which the “absorbing cross-section” is in all cases greater than the “kinetic cross-section.” The study of \(q\) for various substances constitutes an extremely promising method for determining the spatial configuration of molecular electro-magnetic fields.

S. Vavilov.

A New Determination of the Charge of the Atomic Nucleus.

J. Chadwick. The charge of the Atomic Nucleus and the Law of Force. Phil. Mag. 40, p. 734 (1920).

The charge of the atomic nucleus is one of the most important constants of an element, and therefore its exact determination is a problem of the highest importance. Already from the early observations of Geiger and Marsden ¹) on the scattering of \(\alpha\)-rays, Rutherford concluded that this charge is equal to \(\frac{1}{2}Ae\), where \(A\) is the atomic weight of the element, and \(e\) is the charge of the electron. Further experiments by the same Geiger and Marsden ²) confirmed this conclusion. However, experimental difficulties allowed them to make the determination of the nuclear charge only roughly, with an error within 20%.

Van den Broek ³) expressed the hypothesis that the nuclear charge is equal to the atomic number \(Z\) of the element. This hypothesis was brilliantly used by Moseley in his classic work on the X-ray spectra of the elements ⁴) to explain the fact he discovered of a linear dependence between the frequency of oscillations of the corresponding lines of one and the same series (for example, the \(K\)-series or \(L\)-series) and a certain whole number, changing by one in passing from element to element.

But the most direct method of determining the charge of the nucleus still remains the study of the scattering of \(\alpha\)-rays. The chief difficulty, which also caused the especially large error in the experiments of Geiger and Marsden, reduces to the fact that the intensities of the primary and of the scattered beam differ very greatly from one another, and therefore one has to resort to different methods for measuring it in the one and in the other case.—Following an idea of Rutherford, Chadwick carried out an arrangement which made it possible to count the number of \(\alpha\)-particles both in the primary and in the scattered beam on one and the same screen of zinc sulphide. The scattering sheet had, in his experiments, the form not of a small circle, as in Geiger and Marsden, but of a ring subtending a considerably larger solid angle. In the drawing \(R\) is the source of \(\alpha\)-rays,

¹) Geiger and Marsden. Phil. Mag., 25, p. 604 (1913).
²) Geiger and Marsden. Phil. Mag.
³) Van den Broek. Phys. ZS. 14, p. 32 (1913).
⁴) Moseley. Phil. Mag. 24, p. 1024 (1913); 29, p. 703 (1914).