Table of contents

The radiation field is quantized by introducing four types of photons - two transverse, one longitudinal, and one scalar. The scalar photons are treated by using an indefinite metric, and it is found necessary to modify the usual supplementary condition slightly. The present theory offers a justification for the symmetrical treatment of the four components of the electromagnetic potential, recently applied by a number of authors, and proves to be very convenient in applications. The results of physical interest, however, are the same as obtained from the ordinary formulation.

When the energy of α-particles emitted by radioactive nuclei is compared with the energy calculated from the usual semi-empirical formula for nuclear binding energies, systematic variations ranging from 4.5 MeV. to -1.0 MeV. are found, which exhibit in a very clear way the special importance of configurations containing 82 protons and/or 126 neutrons. The general features are readily explained in terms of the shell model. The analysis can be used to predict unknown α-energies. Calculated α-energies are tabulated for the heavy nuclei (Z ⩾ 78) and for nuclei in the rare-earth region.

Topics in the electronic theory of the colour of symmetrical cyanine dyes have been discussed by means of resonance formalism. Our conclusions for the formamidinium ion have been confirmed by use of the molecular orbital method. As a result of this analysis, certain modifications in the qualitative symbolism of colour theory have been put forward in the hope that the factors governing absorption may be more clearly understood.

Experimental arrangements are described by which clearly resolved spectra have been obtained of the luminescence, at the temperature of liquid air, of seven different phosphors of simple crystal structure (cubic) and of mixed crystals. The main peaks in each case may be arranged in a band series. The vibration frequency in the lower state is nearly the same for the same host lattice with different activators. The energy of the electronic transition is determined both by the activator and the host crystal and there is a progression of decreasing energy in the series of simple crystals MgO, CaO, SrO, CaS, and in the order CaO, CaO-SrO with mixed crystals. The most probable transitions are from the lowest level of the upper state. There is evidence that self-excitation occurs and for the view that the luminescent centres are large.

Kirkwood's formula for dielectric constant, , gives it in terms of a correlation coefficient which depends on the probability that any two dipolar molecules have a certain configuration.

The main object of this paper is to calculate the configurational probability of the dipole orientations; this is dealt with in the first part of the paper by considering two dipoles and replacing the rest by a homogeneous dielectric. The dipolar molecules are regarded as point dipoles and the effect of other forces on the orientation of the molecules is neglected.

In the second part of the paper the calculation of the correlation coefficient appearing in Kirkwood's dielectric constant formula is carried out. This correlation coefficient is evaluated for water, and the value of then obtained from Kirkwood's formula is in fair agreement with the observed value.

Agreement between the results of theoretical and experimental investigations of the absorption of hydrogen by palladium indicates that, at least at higher temperatures, the hydrogen is contained in solid solution. Apparatus for observing the changes in electrical resistance of palladium during absorption and evolution of hydrogen is described, with which resistance-pressure isotherms from 75° to 150° c. were obtained for pressures increasing and decreasing between zero and atmospheric. Factors affecting the resistance of the Pd-H system are discussed and an explanation of the form of the isotherms is given; a decrease in resistance which is observed, when hydrogen is added to the alloy in the β phase, is attributed to completion of the d shells of palladium.

An account is given of further experiments on the Barkhausen effect in cylindrical ferromagnetic specimens. The form of the decay of induction following a Barkhausen discontinuity has been investigated and there is reasonable agreement between the theory given and the experimental results. As a result of this investigation it has been possible to satisfy the different conditions which are necessary for the detection of the discontinuities so as to obtain (a) accurate reproduction of the form of the discontinuities and (b) maximum sensitivity in the counting experiments. The number and size of the discontinuities are measured, and an estimate is made of the contribution of the discontinuous processes to the total change in magnetization over the relevant part of the hysteresis curve. Discontinuous changes in magnetic moment greater than 0.3 × 10^-6 E.M.U. (corresponding to a minimum volume of 0.9 × 10^-10 cm³ for iron) account for from 47% to 86% of the total change in magnetization. This is considered in relation to associated work on reversible changes, and the nature of a Barkhausen discontinuity is briefly discussed with reference to other investigations on domain structure.

A single crystal of silicon-iron was shaped so as to encourage the formation of large ferromagnetic domains. Its magnetization curve was found to contain a large Barkhausen jump, indicating reversal of magnetization in a volume of the order of 1/10 cm³. The rate of change of magnetization was found to be proportional to the excess of the applied magnetic field over a certain critical field, and could be made very slow. It is suggested that the rate of change is controlled by the braking effect of eddy currents on the movement of domain walls.

From two earlier papers by the author it follows that eigenfunctions obtainable by Sommerfeld's polynomial method contain either a Riemann P-function or a degenerate form of it when the fundamental interval is either finite or infinite respectively. Comparing the differential equation for the P-function or its degenerate form with the differential equation which we get for P from the original differential equation of the eigenvalue problem, we obtain standard formulae for the constants determining the eigenvalues and eigenfunctions. The calculations necessary to give the complete solution of an eigenvalue problem, which can be treated by Sommerfeld's polynomial method, are thus reduced to a minimum of differentiations and simple algebraic operations. It is also possible using appropriately chosen P-functions to obtain the eigenfunctions directly in the required form. The method yields also eigenfunctions for eigenvalues in the continuous spectrum.

The spectrum emitted by a high voltage arc in CO₂ at atmospheric pressure has been investigated in the region 2000 Å to 9000 Å. It was found to consist, mainly, of a continuum and the `CO flame bands'. A study of the spectrum at different dispersions and on photographic plates of various kinds shows that although the Schumann-Runge O₂ bands do form a part of the spectrum they are relatively weak compared with the bands attributed to CO₂. The excitation of the Schumann-Runge O₂ system in flames is discussed.

Corrections to 1950 Proc. Phys. Soc. A 63 653.