The application of the quantum theory to the collision of electrons with atoms has now been worked out in some detail. For fast collisions the calculations present no difficulty, since Born's method may be applied and the probability of excitation of a given level of a simple atom can be worked out quite accurately. The corresponding problem for the case of slow collisions is much more difficult and requires a knowledge of the exact solution of the equation representing the motion of electrons in the static field of the atom considered. Using such solutions obtained by Faxén and Holtsmark's method, and allowing also for electron exchange, Massey and Mohr have been able to calculate excitation probabilities for low voltage impact in hydrogen and helium.

Measurements have been made of the positive ion currents emitted by tungsten at temperatures between 3000°K. and 3200°K. The results are in general accordance with the values calculated on the basis of the Saha equation from the rate of evaporation of neutral atoms, the electron work-function and the ionisation potential of tungsten. The “work-function” associated with the ionic evaporation appears to lie between 10 and 11 electron-volts.

1. The temperature variation of the paramagnetic susceptibility of most of the solids follows the generalised Curie law

as found first by Kamerlingh Onnes and Weiss. This gives a linear relation between 1/ψ and T. The value of C is a measure of the atomic magnetic moment, and if this moment is expressed in terms of the Weiss magneton-number p, then

where CM is the value of C when ψ refers to a gram-molecule. The experimental results for a paramagnetic substance are usually expressed in terms of p and θ. Weiss (1), Foex (2), Cabrera and others have found that in some substances there are discontinuities in the slope of the 1/ψ, T curve. Thus Weiss (3) finds that magnetite above its Curie point shows several sudden changes in the 1/ψ, T curve, which he has interpreted as corresponding to the magneton-numbers p = 4, 5, 6, 8,10. Similarly, for cupric chloride (anhydride) Weiss (4) gives p= 9.2 and 10, for the temperature ranges — 140° to 20° and 20° to 500° respectively. Nickel sulphate (5) has also been found to possess a transition point at about — 113°, where the p value on cooling changes from 14.6 to 18.2.

In an alternating current motor (of simplest type) the internal E.M.F. e, the terminal tension e, the useful electrical power transformed p and the rotor phase angle φ are connected by the known formula

in which

where r is the resistance and l the self-inductance of the armature and ω the angular velocity of the rotor.

Some general considerations regarding the design of hot cathode X-ray tubes for producing an accurately constant and repeatable beam of X-rays are first given. The construction of a tube in accordance with these considerations is then described. This tube has been used to show that except with small tube-currents the quality of the vacuum in such a tube has little influence on the steadiness of the beam if the electrical input to the tube can be satisfactorily controlled.

It is shown that the X-radiation associated with the fluorescence often observed in X-ray tubes has usually but not always a negligible effect on the steadiness of the beam.

Some factors limiting tube current when the filament is enclosed in a box containing a focussing slit are mentioned, and the mechanism of formation of the focus is discussed with reference to its size. The use of an auxiliary electrode to increase the tube current and improve the focussing is also discussed.

If an atom is excited by electrons incident upon it, the wave functions for the outgoing electrons must be calculated in the field of the excited atom. Such calculations have been made for helium excited to the singlet 2p state, and it is found that the outgoing waves differ more from plane waves than the incident waves.

An account is given of a simple experiment designed to illustrate quantitatively the phenomena of coupled oscillations. Two similar small magnets are suspended in the earth's magnetic field at a suitable distance apart so that there is appreciable magnetic interaction between the two oscillatory systems. Under the conditions employed, the equations of motion reduce to a simple form, and the experiment may be used as a method of measuring the intensity of the horizontal component of the earth's magnetic field.

(1)A beam of positive ions of mercury produced from an arc in mercury vapour and fired upon a surface of nickel produces an emission of electrons.

(2)For a fresh untreated nickel target the electron emission is of the order of 1·5 per cent. for ion energies less than about 600 electron-volts, and rises to about 15–20 per cent. at 2000 electron-volts.

(3)After degassing thoroughly at a red heat the secondary electron emission is found to fall to about half the value observed with a dirty target. Continued bombardment with mercury ions leads to a progressive decrease in the emission, which approaches a final steady state after some hours. In this steady state the ratio is about 2·3 per cent. at 2000 electron-volts. After degassing afresh, the same process is repeated.

(4)Tests were made to assure that the emission is in reality one of electrons from the struck target, and that it is due to the impact of the positive ions.

Here the notion of density is made more precise, by definition in terms of the fundamental orthoscheme. (The fact that reciprocal polytopes have the same density is a direct consequence of the precise definition.) A new criterion for regular polyhedra is given, superior to Petrie's in that it applies to degenerate, as well as to finite, polyhedra. The cases are examined in which the actual vertex figures of one polytope bound another; and this idea is developed into the process called alternation, which provides an alternative method for calculating density in four dimensions.

After a review of the magnetic and spectroscopic properties of compounds of the rare earth and of transitional elements of the first group, the types of bands in spectra of the latter are considered in detail. Reasons are advanced for the view that these are of “molecular” origin in ferric salts, but that the spectra of some transitional compounds contain lines which cannot be regarded in this way. Such lines are shown to be ionic, or quasi-ionic, and accord well with the suggestion of inter-combination transitions such as 4F—2G.

The theoretical intensity conditions, as a function of multiplet intervals, are in agreement with the observed appearance of intercombination transitions in Cr, and possibly also in Mn and Co. Similar considerations apply to the rare-earth spectra. As an example we have shown that the strong absorption in Pr and Nd compounds, and the much weaker lines found in Sa and Eu, are in perfect agreement with the theoretical prediction of intercombinations.

In the above paper it is pointed out that before we may use the usual wave equation for the propagation of current along a straight wire in free space it is necessary that (a) the inductance L and capacity C per unit length of the wire are independent of the current distribution and (b) that the product LC = 1/c2. This has been shown to be the case.

The inductance and capacity of an element of a conductor are defined generally in the way suggested by Moullin and it is shown that the radiation resistance term, which is a function of the current distribution, is small compared with the corresponding terms involving inductance and capacity. The usual wave equation is derived from Maxwell's equations for the case of a tubular conductor in which the current is a function of the distance z along the conductor only. If the curl of the current is not equal to zero this will not represent the true state of affairs.

It is pointed out in the earlier part of the paper that a complete solution of the problem, taking into account the radiation resistance, and the skin effect, involves the solution of an integral equation which is given.

The field about a tubular current, with a current distribution J0 sin kz along it, is examined. It is found that, for a long wire, the electric force is perpendicular to the surface at every point since we neglect the contribution from the ends. The magnetic force is in circles about the axis as would be expected.

A small component parallel to the current, and in phase with it, is introduced by the charges upon the ends of the tubular conductor, and this component determines the radiation resistance. From this it follows that the radiation resistance could be increased by placing a capacity on the ends—thus increasing the charges there.

The upper portion of the β-ray spectrum of thorium C″ has been investigated by measuring the tracks produced in a Wilson chamber. No trace of a “tail“ is found, no tracks of Hρ greater than 10,800 being observed in some 600 to 800 disintegrations. The end-point is placed at 9400 Hρ, somewhat higher than the value obtained by other workers.

It is pointed out that there is some confusion concerning the meaning of the sign of a mutual inductance. The question is examined from first principles and it is shown that since the sign of a mutual inductance depends upon conventions as to sign of current directions, these, as well as the sign of the mutual inductance, must be given in order to specify what is really required—the relation between the directions of winding of the primary and secondary coils. It is also shown that in many cases it is possible to replace mutual inductance by a quantity which is numerically equal to the mutual inductance but which is independent of current directions. The two methods applied to a Wheatstone network yield consistent results.

A high-tension supply suitable for all types of Geiger counter must supply up to 5000 volts, free from A.C. ripple and other electrical disturbances, and it must be possible to rely on the voltage remaining constant to within one or two parts in a thousand over considerable intervals of time. With the apparatus here described these requirements have been fulfilled sufficiently well for satisfactory operation of Geiger-Müller tube-counters from ordinary A.C. mains, and since the method of keeping the voltage constant does not appear to have previously been used for this purpose, it seemed desirable to record it briefly.

The electron theory of metals, established in its present form mainly by Pauli, Sommerfeld and Bloch, makes it possible to classify the phenomena connected with metals into two main divisions, which may be called first order effects and second order effects, according to whether the effect depends on the first or second approximation to the energy of a degenerate electron gas at a given temperature. Examples of the first group are the constant paramagnetism of the alkalis and Volta contact potentials. Examples of the second group are the specific heat of the electrons and all thermoelectric effects. The temperature dependence of the electrical conductivity should be included in the group of first order effects, since here the temperature is introduced through the lattice wave motion. The limits of the existing theory are now easily described. First order effects are accounted for with success, second order effects are in the main far from being adequately covered by the theory. To see clearly the reason for this, one must examine briefly the basis of the existing theory. In the first approximation the metal is regarded as composed of two independent systems; a system of lattice vibrations, and a system of electrons free to move in a given space periodic field of potential. In this way by dealing with the two systems quite independently one can reproduce many properties of metals, for example, Debye's theory of specific heats. The theory of pure lattice heat conductivity is concerned only with the former system, while the constant paramagnetism of the alkalis, and the fact that the electrons contribute only a very small amount to the total specific heat of the metal can be accounted for by considering the latter system only.

This paper describes a repetition of J. B. Johnson's determination of Boltzmann's constant by observing the thermal agitation of electrons in a conductor. The principle of the measurement is described and the various sources of error are examined separately. The attenuator system of the calibrating circuit is discussed in detail and mutual agreement established between the three different attenuating systems. The valve amplifier had a maximum response which could be arranged to occur at any frequency between 1000 and 4000 cycles/sec. The mean value of 52 determinations of Boltzmann's constant (with the amplifier set to respond to one of four frequencies within the range 1 to 4 k.c./s.) was found to be 1·361 × 10−16 ergs per degree, with a probable error of 1·42%: this value is 0·8% less than the accepted value of 1·372 × 10−16 ergs per degree. The investigation developed out of a research initiated with a directly practical objective; we desire to express our thanks to the Hebdomadal Council of the University of Oxford, who by a grant to one of us have enabled this section of the work to be completed.

The spontaneous disappearance of an electron and proton in the form of radiation has often been suggested as a possible source of energy to maintain the emission of radiation from hot stars. It can be calculated that the energy of a single quantum formed in this way should be about 1000 million electron-volts. In order to account for the absorption of the ultra-penetrating radiation observed by Regener in deep lakes, and interpreted on the basis of the Klein-Nishina formula, a quantum of still higher energy is required. Sir James Jeans has recently calculated that the transformation of a helium atom into a single quantum would provide a radiation of about the required penetrating power.

With the aid of experimental results on the absorption of homogeneous β-rays in aluminium, a method is developed for calculating the absorption curve of β-rays forming a continuous spectrum. When applied to certain known spectral distributions reasonable agreement is obtained with the experimental absorption curves of these heterogeneous β-rays. Distribution curves with momentum of the β-rays from actinium C″, uranium X2, thorium C and thorium C″ are found, which lead to similar agreement.

The distribution curves with energy and with momentum for eight β-ray bodies and a table of average energies emitted in thése spectra are shown.