Larmor has shown that if the upper atmosphere contains electrons (charge ε, mass m, density ν) and if collisions between these electrons and molecules—and also the forces between the electrons themselves—are negligible, then electric waves are propagated as if the dielectric constant of the medium were reduced by , from which it appears that, so long as the approximations are valid, the velocity of propagation of the waves can be increased indefinitely by increasing either the electron density or the wave-length λ. Several later authors have attempted to take account of the collisions between electrons and molecules, assuming free paths or velocities according to Maxwell's laws for a uniform gas, and it appears that the above law holds only for short waves; but it is doubtful how far the properties of a uniform gas can be assumed when periodic forces are acting. In the first part of this paper an alternative method of solution is given by means of Boltzmann's integral equation for a non-uniform gas, the analysis being similar to that used by Lorentz in discussing the motion of free electrons in a metal. Only the case when ν is small is considered, i.e. the interactions of electrons with one another and with positive ions are neglected. How far it is possible to increase the velocity of propagation by increasing ν is a more difficult question, but it seems possible that the forces between the electrons and ions may impose a limit just as collisions with neutral molecules limit the effect of increasing the wave-length.

1. The formulae usually given for the scattering of electrons by atoms are calculated without taking into account the radiative forces. It has been suggested by the author in a former paper that in the case of the large-angle scattering of electrons with velocity comparable with that of light (for which case the scattering is entirely nuclear), these forces might influence the scattering by an appreciable amount, which would explain the divergence between the theoretical formula and the results of Chadwick and Mercier, which are some 40 per cent. greater. In this paper we shall show that for electrons–of any velocity the influence of these forces cannot be greater than 2 or 3 per cent., and so cannot be invoked to explain discrepancies between theory and experiment.

1. The method generally employed in investigating the angular scattering of electrons in gases consists essentially of firing a directed beam of electrons into a “field-free” enclosure, containing the gas to be investigated at a pressure of a few hundredths or thousandths of a millimetre. The electrons in the beam will be scattered, on colliding with the gas molecules, through various angles. Those which are scattered between θ and θ + dθ are selected by means of a pair of slits which can be set at any desired angle to the electron beam. The electrons selected by these slits are then resolved by means of retarding potentials or electric or magnetic fields into those which have been elastically scattered and those which, on being scattered by the molecule, have excited or ionised it. By plotting the final current received by the Faraday cylinder against θ, we can obtain the angular scattering curve for the elastically or inelastically reflected electrons.

The rate of recombination of ions in the copper arc is studied by means of the probe, the post-arc ion density being obtained directly as a function of time. Experimental results agreeing with the theory are obtained, and a coefficient of recombination, α = 5·7 × 10−9, is found. If the temperature of the gas in the path of the arc immediately after extinction is 2500°C., a comparison between the above value and that accepted for normal conditions shows that α varies approximately as the 2·5 power of the temperature, which is in agreement with the existing data.

The importance of experimental investigation of the intensity of scattering of X-rays by crystals has long been realized, since it affords valuable information regarding the charge distribution in the atoms of the crystal. Recently Debye has pointed out the importance of similar investigations of the scattering by gases. Here diffraction effects may be observed due to regularities in the structure of the gas molecules as distinct from crystal diffraction, where the regularities are due to the orderly arrangement of crystal atoms. This provides a means of obtaining important information as to the structure of molecules, and Debye and his collaborators have obtained interesting experimental results in this field. Debye has also introduced an approximate theory of the results obtained, but owing to the great complexity of the molecules considered it is at present impossible to proceed any further in the theoretical discussion. However, the case of molecular hydrogen may be worked out for short X-rays, since the charge distribution in the ground state of the molecule is fairly well known. It is the purpose of this paper to calculate the intensities of short X-rays scattered from hydrogen gas. The case of other diatomic molecules will not be very dissimilar.

If a receiving aerial is placed in the field of a wave produced by a distant transmitter, currents are induced in the receiving aerial and these dissipate energy in the ohmic resistances of the aerial. This energy may be thought of as being absorbed directly from the incident wave, but this viewpoint gives no insight into the mechanism by which the absorption takes place. In this paper the following alternative way of regarding the phenomenon is considered. The currents induced in the aerial cause it to re-radiate a secondary wave. The electric and magnetic fields of this secondary wave combine with those of the unabsorbed incident wave to give resultant fields which have, in general, a direction different from those of the incident wave. These resultant fields give rise to energy flows which are different from those in the incident wave, both in magnitude and direction. In this way a flow of energy into the aerial is produced, by the superposition of the incident and the re-radiated fields. It is important to notice that if this viewpoint is adopted we must add the secondary re-radiated wave to the unabsorbed main wave, the addition, in itself, producing the requisite absorption.

Experience has shown that simple absorption measurements lead to quite trustworthy estimates of the maximum energies represented in the continuous spectra of many β ray bodies. For the interpretation of these experiments the range-energy relation for homogeneous particles is apparently all that is necessary. In the present paper a detailed analysis is given of the various factors which conspire to this useful result. Analytical simplifications are possible when the energy distribution in question extends beyond about 7 × 105 electron volts energy. Under this limitation it is shown that the empirical result follows from the known form of the absorption curve for homogeneous particles and the most general considerations regarding the characteristics of such measuring instruments as are regularly employed. From the analysis in one case, however, it appears that, despite numerical agreement between the results of different methods of investigation, caution is still necessary in any statement concerning the absolute nature of the high energy limits of continuous β ray spectra.

It has been shown by Ratcliffe and White that the effective specific inductive capacity (ε) and the effective conductivity (σ) of soil placed, as dielectric, in a simple condenser vary in a marked manner with frequency. The range of frequency used was from 0·1 × 106 cycles per second to 10 × 106 cycles per second. It was found that at 6·1 × 106 cycles per second the specific inductive capacity was very large (about 40 e.s.u.) and that it decreased to a value of about 12 e.s.u. at 10 × 106 cycles per second. This latter value agrees with the value found in experiments on the propagation of short radio waves over the surface of the earth. The effective conductivity of the soil had a low value at 0·1 × 106 cycles per second but increased rapidly to a constant value for frequencies above 3 × 106 cycles per second.

A development of the “echo” method of observation of the height of the Kennelly-Heaviside layer is described. Short wave-trains of radiation lasting sec. are transmitted at regular sec. intervals, and observed stroboscopically, together with their echoes, by means of a cathode ray oscillograph. Details of the transmitting and receiving apparatus are given. The rapid fluctuation in amplitude of the echoes is easily studied by this method.

The β-ray spectrum of radium C is remarkable for the large number of faint lines of about equal intensity which occur above Hρ 4900. These lines were first measured by Rutherford and Robinson and many of them were found again by Ellis in a reinvestigation of this spectrum. It was then stated that no attempt was made to check the existence of each faint line and that Rutherford and Robinson's measurements of the faint lines were taken over directly, with certain necessary adjustments to the absolute energies. Subsequently the intensities of the β-ray lines in this spectrum were measured by Ellis and Wooster and by Ellis and Aston and the faint lines were again treated in much the same way.

1. In a recent paper Landau has shown that, when electrons are moving freely in a magnetic field, they exhibit, in addition to the paramagnetic effect of their spin, a diamagnetic effect due to their motion. This result is rather unexpected, since it is quite contrary to the classical case. There it might appear as though the circles described by the electrons must produce a magnetic moment, but the error was long ago pointed out by Bohr. The motion of the electrons must be confined to some region by means of a boundary wall, and the electrons near the wall describe a succession of circular arcs, repeatedly bouncing on the wall, and slowly creeping round it in the direction opposite to that of the uninterrupted circles; when the moment of these electrons is taken into account, it exactly cancels out that due to the free circles. In Landau's work it is of course necessary to consider the boundary, but he shows how allowance is to be made for it by an appropriate process. The complete justification is rather subtle, and so it may be worth considering a special case, admitting of exact solution, which takes the boundary into account, and so makes it possible to follow more closely the analogy between the classical and quantum problems. With regard to the general case with a boundary wall of any type, we shall only observe that the different results arise, because in the wave problem ψ must vanish at the bounding “potential wall,” and so will be small near it; this upsets the balance of the electric current near the wall, and yields the magnetic moment.

The rotation of a dielectric covered body, suspended between the poles of a Wimshurst machine, is investigated and found to be due to the accumulation of charge on the surface of the body, under the action of the brush discharge, and to the subsequent electrostatic repulsion of this charge. It is shown theoretically, in an appendix, that the rate of rotation is governed by the rate of decay of the surface charge, and is a maximum for a certain value of this rate of decay. The rotation of a chain hanging from an electrical machine into the dielectric layer of a Leyden jar (the inner conducting coating being removed) and similar electrostatic experiments are described, and shown to be due also to the superficial charging of a dielectric body, body, and depends upon the rate of decay of this surface charge. A similar explanation is shown to account for some other electrostatic phenomena.

The advent of quantum mechanics has provided a means of treating the interaction of atoms and the formation of molecules and has had very many successes in this field. In particular the phenomenon of the saturation of valence forces appears as a natural consequence of the theory. Nevertheless there are very many difficulties still to be overcome.

The purpose of this note is to amplify the discussion and conclusions of a recent paper by one of us. It has recently been shown by Webster, drawing largely from the work of Weiss and Forrer, that in single crystals of both iron and nickel there is a family of natural directions of micromagnetization defined by the observed directions of easy holomagnetization. The evidence presented by Webster is completely convincing, and we therefore may refine our picture of micromagnetization by asserting that the micro-elements are all (holo)magnetized in one or other of the directions of easy holomagnetization. These directions are the family of six directions (± 1, 0, 0) (0, ± 1, 0) (0, 0, ± 1) for iron and the family of eight directions (± 1, ± 1, ± 1) for nickel. We wish to comment on Webster's theory later in connection with the properties of cobalt.

In a previous paper the nature of the phenomena occurring when electrons are ejected from metal surfaces by the impact of metastable atoms and positive ions was discussed. It was shown that electrons may be ejected by excited atoms at considerable distances from the surface, and by considering the case of an excited hydrogen atom at the centre of a spherical cavity in the metal the order of magnitude of the effects to be expected and the velocity distribution of the ejected electrons was determined. In this paper the theory will be extended in two directions.

No satisfactory formula has so far been derived theoretically for the photoelectric absorption of X-rays and γ-rays. The empirical law

has hitherto been generally accepted as giving approximately the variation of the photoelectric absorption coefficient per electron, with atomic number Z and wave length λ for X-rays of wave length greater than 100 X.U., and the validity of this law has often been assumed for γ-rays also.