R. H. Fowler and L. Nordheim have presented a theory which seems to offer a satisfactory explanation of the phenomenon commonly known as the auto-electronic discharge, in which electrons are extracted from cold metallic cathodes by intense electric fields. Their theory considers the passage of electrons through a potential “hill” of the type shown in Fig. 1, where V is the potential energy of an electron at a point distant x units from the surface.

A modification of the alternating field method of measuring ionic mobility in a gas gives an experimental curve showing upper and lower limits to k. From this a distribution curve is derived, which has a calculable resolving power.

The mobility of negative ions in dry air shows a continuous distribution between the limits 2·15 and 1·45, with a peak value about 1·8.

At low pressures the current is resolved into ions and free electrons. From the relative numbers reaching the electrometer it is found that the electron makes an average number 9·4. 104 collisions before capture, independent of field strength and pressure, and therefore independent of the electron speed over a range W = 2×105 to W = 7×105.

The object of this paper is to make certain calculations which will be required in the estimation of the quantum defect. Hartree has defined certain solutions Gi(σ, ζ), Hi(σ, ζ) of the wave equation for an electron in a Coulomb field, viz.

An attempt has been made in the work described in the present paper to use the method initiated by Hartree, for the numerical solution of the Schrödinger wave equation for an atom with a non-Coulomb field of force, to estimate the number of dispersion electrons (hereinafter denoted by “ƒ” for brevity), corresponding to the lines of the principal series of the optical spectrum of lithium, and also to the continuous spectrum at the head of the series. Various attempts have been made to do this for hydrogen and other atoms by an application of the Correspondence Principle, but the first successful attempt at a complete description was made by Sugiura†, who has calculated ƒ for the Lyman, Balmer, and Paschen series and the corresponding continuous spectra, by using the known analytical solutions of the wave equation for an electron in a Coulomb field. The same author has also calculated ƒ for the first two lines of the principal series of sodium, by the utilisation of an empirical field of force in the atom calculated from the observed term-values by a method based on the old quantum theory. He has estimated the contribution to Σƒ (summed for the whole series) due to the continuous spectrum by the theorem that Σƒ = 1 in the one-electron problem§. This property provides a useful check on the work when ƒ for the continuous spectrum is also calculated. In the present paper ƒ for the continuous spectrum is actually calculated and it is found that Σƒ = 1 to a good approximation.

The equations of propagation of electromagnetic waves in a stratified medium (i.e. a medium in which the refractive index is a function of one Cartesian coordinate only—in practice the height) are obtained first from Maxwell's equations for a material medium, and secondly from the treatment of the refracted wave as the sum of the incident wave and the wavelets scattered by the particles of the medium. The equations for the propagation in the presence of an external magnetic field are also derived by a simple extension of the second method.

The significance of a reflection coefficient for a layer of stratified medium is discussed and a general formula for the reflection coefficient is found in terms of any two independent solutions of the equations of propagation in a given stratified medium.

Three special cases are worked out, for waves with the electric field in the plane of incidence, viz.

(1) A finite, sharply bounded, medium which is “totally reflecting” at the given angle of incidence.

(2) Two media of different refractive index with a transition layer in which μ2 varies linearly from the value in one to the value in the other.

(3) A layer in which μ2 is a minimum at a certain height and increases linearly to 1 above and below, at the same rate.

For cases (2) and (3) curves are drawn showing the variation of reflection coefficient with thickness of the stratified layer.

Case (3) may be of some importance as a first approximation to the conditions in the Heaviside layer.

The experiments described below were under-taken to follow up the observation, made independently by Dr Chadwick and one of us (M. L. O.), that the disintegration by sputtering of a plane cathode in a gas discharge was not uniform but showed a maximum at a small distance from the edge. By running the discharge for many hours under steady conditions it was possible to remove a narrow ring of metal at a distance of about a millimetre from the edge of a thin platinum cathode, the middle portion and the extreme edge remaining whole. A photograph of a cylindrical cathode taken by Kaye shows the same effect very clearly.

In this paper we use Dirac's relativity quantum mechanics to derive the well-known Kramers-Heisenberg dispersion formula for an atom with one electron. The treatment is not limited to the case of a central field, but is quite general. An expression is also obtained for the dipole moment to which is due the incoherent scattering. The formulae obtained are similar to those obtained by O. Klein for the case of a central field. We find in this way an explicit expression for f, the number of dispersion electrons for any line of the optical spectrum (being a measure of the intensity of the line), in terms of the solutions of the four wave equations of Dirac's theory. It is further shown that the sum of the number of dispersion electrons for any state of the atom is not exactly unity, but differs from it by an amount of the order of 10−4. The result Σf = 1 has been shown by London to hold exactly for the simple wave equation as originally given by Schrödinger. It is here shown that the exact relativity treatment has a very small effect.

Two alternative views have been expressed in regard to the configuration of quadrivalent atoms. On the one hand le Bel and van't Hoff assigned to quadrivalent carbon a tetrahedral configuration, which has since been confirmed by the X-ray analysis of the diamond. On the other hand, Werner in 1893 adopted an octahedral configuration for radicals of the type MA6, e.g. in

and then suggested that “the molecules [MA4]X2 are incomplete molecules [MA6]X2. The radicals [MA4] result from the octahedrally-conceived radicals [MA6] by loss of two groups A, but with no function-change of the acid residue…. They behave as if the bivalent metallic atom in the centre of the octahedron could no longer bind all six of the groups A and lost two of them leaving behind the fragment [MA4]” (p. 303).

The present paper contains an account of some work done in an attempt to produce high speed electrons, using an indirect method suggested by Sir Ernest Rutherford. Although it was not found possible to make the method work, yet a description of it may be of interest on account of the importance attached to any method of obtaining fast electrons.

A method of obtaining approximately the high-velocity limits of continuous β-ray spectra by electroscope measurements is established and used for the β-ray bodies of thorium active deposit.

The absence of thorium C γ-rays is confirmed and leads to some interesting results.

The work was carried out in the Cavendish Laboratory, Cambridge. Thanks and gratitude are due to Professor Sir Ernest Rutherford, P.R.S., for his interest in the problem; to Dr C. D. Ellis, F.R.S., who suggested the problem, for continual help and advice; to Mr G. A. R. Crowe for help in preparation of the sources; and to the Department of Scientific and Industrial Research for a Grant during the time the work was being carried out.

Recently Yovanovitch and d'Espine using a magnetic spectrum method of low resolving power have found a band of very fast β-rays in the spectrum of radium B + C, having energies up to 7·6 × 106 volts. As early as 1911 Danysz found some evidence of the existence of such high velocity β-rays but they have not been observed by other investigators. A moderate number of such rays, if spread over a considerable range of velocities, might escape detection in most experimental arrangements for the study of β-rays, on account of their low absorption and low ionizing power. As it is important to know how many of these fast β-rays there are on the average per disintegration, the following simple experiment was performed by the writer in an attempt to determine this.

In the measurement of small ionisations it is usual and desirable to employ an ionisation-chamber whose central collecting electrode serves also as an electroscope, of the gold-leaf or the quartz-fibre type. As an instrument for the measurement of quantity of electricity even the most sensitive of these is inferior, by a factor of about 100, to the combination of an ionisation-chamber and a Compton electrometer. The new type of ionisation electroscope here described combines a high voltage-sensitivity with a small capacity and has a sensitivity for quantity of electricity of the same order as the combination mentioned.

The approximation is made that in a many-electron atom each electron is in a stationary state in the field of the nucleus and the remaining electrons, and further that this field is central.

To this approximation it is known that, if the electrons obey Schrödinger's equation, then a complete n, l group of electrons [i. e. 2 (2l + 1) electrons with the same n, l] can be divided into two half-groups for each of which the distribution of charge is spherically symmetrical. To the same approximation it is shown that, if the electrons obey Dirac's equation, a complete Stoner sub-group [i. e. 2j + 1 electrons with the same n, l, j (j = l ± £)] can be divided into two halves, for each of which the distribution of charge is spherically symmetrical.

The distribution of current and the resultant magnetic moment for a solution of Dirac's equation in a central field are obtained, and it is shown that for a complete Stoner sub-group the net current and magnetic moment are zero. The Landé g-formula for one electron is derived from the formula for the magnetic moment by neglecting ‘relativity’ terms.

The formula for the magnetic moment suggests the question whether it is ever possible to specify the direction of the spin axis of the electron (as distinct from the magnetic moment of the whole atom). This is investigated, and it seems justifiable to specify the direction of the spin axis for states for which the magnetic quantum number m has its extreme values ±j, but not otherwise.

Generally, when an alternating voltage is applied to a cumulative grid rectifier no grid current flows at mean grid potential. The behaviour of a rectifier working under these conditions is examined. An expression is derived for calculating rectified current for any applied voltage. As this equation is rather cumbersome to apply, a very simply empirical formula is given which is applicable for any value of applied potential whatever.

An expression is derived for the power absorbed by the rectifier. It is shown that as the applied voltage increases, the apparent resistance of the rectifier decreases and approaches half the value of the grid leak resistance.

Further, it is shown that rectified current depends on the peak value of the applied potential and that it is almost independent of ordinary wave-form variations, even when the applied voltage is small.

By slightly modifying the expression for rectified current we find that, in an amplifier, the grid current is a measure of V and, in an oscillator, the grid current is a measure of the output. The only condition is that V > 2b in both cases.

In conclusion I wish to express my indebtedness to Professor C. E. Inglis for placing at my disposal the facilities of the Cambridge University Engineering Laboratory, and to Mr E. B. Moullin for the interest he has taken in the work.

A considerable amount of experimental work has been done in recent years on the properties of the electrons which leave a metal surface when it is bombarded by an incident beam of electrons. Farnsworth, who first studied the energy distribution of the secondary beam systematically, showed that it is made up of two groups. The first has the same energy as the primary beam and may be regarded as consisting of reflected primary electrons; and the second has for the most part a very small energy, of the order of a few volts, and contains the true secondaries derived from the metal. The present writer in a preliminary note has described some measurements of the differential energy distribution by means of the magnetic spectrum method. Owing to an inadequate technique those experiments are considered to be valid only in the upper half of the energy range, where the form of the distribution has several features of particular interest when the mechanism of secondary emission and of electron reflection are considered. In this note, the author called attention to the peculiar depression in the curve immediately preceding the “reflected” peak. It was impossible then to insist on the reality of such an effect, owing to the probable presence of an instrumental cause (which was given there as the explanation). That it is real, however, has been demonstrated in a striking manner by Whiddington and Brown, who have succeeded in recording electrons as slow as 100 volts photographically on a specially sensitised film.

During my visit to Cambridge last year I was given the opportunity of carrying out in the Cavendish Laboratory some experiments with a view to studying the reflection of atoms from a solid surface. For this purpose the atoms of radioactive substances offer the advantage of extreme sensitivity and also the possibility of quantitative measurements by means of their radiations. While the main object of the experiments could not be achieved, some phenomena have been observed which seem to deserve brief mention.

This paper is concerned with the electric and magnetic field close to conductors which carry an alternating current. Hertz's famous solution of Maxwell's equations gave the field at a great distance from a magnetic or electric dipole whose moment was alternating harmonically: but from its very character it could not describe the field at points which were insufficiently remote from the origin for the source to appear as a dipole. The great development of radio communication has made important certain problems about the field in the vicinity of wires which are carrying an alternating current. Thus imagine that an aerial of some thousand feet in height and very many acres in extent has been erected. Before the designer of this vast and costly structure can calculate the rate of energy output, he must suppose himself so far removed that the aerial has dwindled to a mere speck in the aether. Such a process must seem both unsatisfactory and unsatisfying to those who take the responsibility of obtaining radio communication. It is already known that the field at any point can be expressed formally when the distribution of current and charge in the source is postulated: it is shown in this paper that the field at all points very near to the source can be expressed by simple formulae. Of course it is not an exact solution for the field due to a conductor of specified shape, because the postulated distribution of current and charge is incorrect.

While investigating the effect of a caesium film on the auto-electronic emission from a tungsten surface I noticed certain phenomena which seemed worth further investigation. Langmuir and Kingdon have shown that the emission from a tungsten filament in caesium vapour varies with the temperature of the filament in the manner shown in Fig. 1. The initial rise in the emission at low temperatures is due to the existence of a caesium layer on the filament. At higher temperatures the caesium evaporates and the emission drops until eventually the temperature becomes high enough to produce a thermionic emission from the clean tungsten surface.