The quantum theory of the heavy electron field is applied to calculate approximately the cross-sections for “photoelectric” absorption of heavy electrons by a bound nuclear particle and for emission of a heavy electron by a free nuclear particle on collision with a nucleus. The absorption cross-section per nuclear particle is of the order 10−26 cm.2 for heavy electrons with energies up to 108 e.V., but probably decreases rapidly at higher energies. Although the energy loss of a proton, of energy 108 e.V. or higher, due to heavy electron emission is found to be greater than that due to radiation, the cross-section is very small (⋍ 10−29 cm.2) and the phenomenon is unlikely to be observed in a cloud chamber. In the present state of theory it is impossible to decide whether radiative emission of heavy electrons by nuclear particles is capable of contributing appreciably to the heavy electrons observed at sea-level but, if so, the cross-section for the process must be very much greater at high energies than in the non-relativistic energy region which we have investigated.

It is shown that, if account is taken of the uncertainty of position and momentum of the reference origin with respect to which observations are made, the self-energy and transverse self-energy of the electron become finite and the quantum theory is considerably modified for high-energy electrons and quanta.

The object of this note is to extend the proof, for the general canonical varieties of any dimension k < d on a Vd whose existence was established by Dr Todd in a recent paper, of the property of adjunction given by the relation

where S is any non-singular variety of dimension d−1 lying on Vd, and Xk[S] denotes the canonical system of dimension k on S. This formula was proved by Todd in the case when Vd is a general non-singular variety, and S is non-singular and belongs to a sufficiently general linear system. Using this result, I show how to remove the latter restriction. (1·1) cannot be taken, without further proof, as defining canonical systems on virtual or isolated varieties, as is done by B. Segre, since the canonical systems on an effective isolated variety are already well defined.

It is well known that a single neutron may cause a nuclear reaction chain of considerable magnitude, if it moves in a medium in which the number of secondary neutrons which are produced by neutron impact is, on the average, greater than the number of absorbed neutrons. From recent experiments it would appear that this condition might be satisfied in the case of uranium.

It is shown that in a crystal there exist states in which the electron is bound to a surface of the crystal and has an energy lying within a forbidden band. The wave functions and energies of these states are calculated, on the nearly free electron approximation, in terms of the constants of the crystalline potential field, which is represented by a triple Fourier series having the periodicity of the lattice. The method is shown to be applicable to a general crystal having a surface parallel to any one of the crystal planes.

The exchange forces between two heavy particles (neutrons, protons) have been treated on the basis of the meson theory by Yukawa, Sakata and Taketani (5), and by Fröhilch, Heitler and Kemmer (2), assuming the existence of positive and negative mesons only. The calculations have been extended by Kemmer (3) for a meson field which includes in addition neutral particles (neutretto's). The first order approximation of the exchange potential, i.e. the potential due to the emission and subsequent absorption of one meson only, gives qualitatively the correct interaction between the unclear particles.

Experiments are described which show the effect of current on the transition of cylindrical superconductors to the normal state produced by increasing an external magnetic field. The transition curves were determined with an accuracy of 0·1%. Both longitudinal and transverse fields were used.

The following results were found.

(a) Transverse field

(i) The field strength at which the first traces of resistance appeared was independent of current strength for reasonably small currents (up to about 100 mA. for 0·010 cm. wire).

(ii) With increase of current the transition curve at first changed shape, becoming more and more nearly linear, and then was displaced parallel to itself toward smaller values of the applied field by an amount in accordance with Silsbee's hypothesis.

(iii) The change in shape of the transition curve was accurately reproducible and was identical for specimens of the same material and diameter.

(iv) The results for specimens of different diameter could be accurately correlated if the measured values of the resistance were plotted against the current divided by the specimen diameter raised to the power (l + R/Rn), i.e. I/(diam.)(1+R/Rn), where R/Rn is the ratio of the measured resistance to the resistance just above the transition point.

(b) Longitudinal field

(i) With increase of current, however slight, the transition curve was displaced parallel to itself, toward smaller values of the applied field, without showing any change in shape.

(ii) The displacement of critical field for a given change of current was completely independent of the diameter of the specimen.

(iii) The observed shift to smaller fields was much greater than could be accounted for by the additional field produced by the current at the surface of the wire.

(iv) If we denote the (extrapolated) value of the critical field for zero current by (Hc) and the difference between this and the observed value for a current (I) by (ΔHc) then I and Hc are connected by the empirical relation

where A and n are constants depending on the nature of the superconducting metal.

when Hc is expressed in gauss and I in milliamperes.

The problem of the conduction of heat in a solid sphere with a concentric core of a different material, the surface kept at a constant temperature, and the initial temperature of the whole zero, has already been solved in these Proceedings.

The wave functions and energies of both the normal and surface electronic states of a finite linear chain are determined in terms of the overlap integrals by the approximation of tight binding, it being assumed that the interaction of atomic s-states with p-states can be neglected. It is shown that the existence of surface states depends on the ratio of two overlap integrals being greater than unity, and reasons are given for expecting this to be so.

The effect of interstellar matter on the sun's radiation is considered with a view to explaining changes in terrestrial climate. It appears that a star in passing through a nebulous cloud will capture an amount of material which by the energy of its fall to the solar surface can bring about considerable changes in the quantity of radiation emitted. The quantity of matter gathered in by the star depends directly on the density of the cloud and inversely on the cube of its velocity relative to the cloud. Thus vastly different effects on the solar radiation can be brought about under fairly narrow ranges of density and relative velocity (ranges that are in accordance with astronomical evidence). In this way the process is able to explain the small changes in the solar radiation that are necessary to produce an ice age and, under conditions less likely to have taken place frequently, the high increase in radiation required for the Carboniferous Epoch. Despite the large effects that the mechanism can bring about, it is shown that the mass of the sun does not undergo appreciable change and hence reverts to its former luminosity once the cloud has been traversed.

Although the existence of an electromotive force in apparently homogeneous circuits under asymmetrical temperature distributions has been questioned by only a minority of workers in this field, all attempts at explaining the effect have been little more than speculations. These speculations may be divided roughly into two types, first(2), those which agree with the contention of Benedicks that the E.M.F. is an essentially new effect not explicable in terms of the classical theory of Kelvin, and secondly(3), those which contend that the effect is essentially spurious, to be explained away as due either to hidden sources of error, or to unsuspected heterogeneities in the circuit. The somewhat fantastic claim of Benedicks' school that the effect was an inverse of the Thomson effect, which proved entirely false upon examination in the light of Sommerfeld's work(4), did much to increase scepticism. Benedicks' later claim to have found yet another inverse of his original effect(5), the “electro-thermal” effect, has also been refuted(6), and this does not inspire confidence in the genuine nature of the original effect.

The fine structure of the Al L23 and Zn M23-absorption edges has been determined using the experimental methods described in an earlier paper(1).

A table containing numerical data for the Al and Zn edges, together with revised data for the edges of Li, Mg, Ni and Cu is included.

The method of the previous paper is extended to determine the surface states of a simple cubic crystal on the approximation of tight binding. It is also applied to the case of a semi-infinite linear chain when the atomic s- and p-states are to be regarded as degenerate, the existence of surface states being again predicted.

For the purpose of the present discussion the magnetron will be defined as a diode thermionic tube, having concentric cylinders as electrodes, in which there is a uniform magnetic field parallel to the axis of the electrodes. An electron emitted from the cathode travels towards the anode in a path which is bent by the action of the magnetic field. If the anode has radius a and is at potential V with respect to the cathode of radius b, then it is well known that electrons emitted without velocity from the cathode will just graze the anode when the uniform and axial magnetic field has a value H such that

It has been found by one of the authors (1) in collaboration with Dr H. Jones that a flow of heat in liquid He ii is accompanied by what seems to be a transfer of momentum. The effect can be seen when the channel through which the heat and liquid flow consists of a smooth-walled glass capillary, such as shown in Fig. 1a. Due to the high thermal conductivity of He ii, a considerable part of the heat put into the reservoir is carried down through the capillary to the bath. When a steady heat flow exists, a flow of liquid takes place in the opposite direction, and the level of the liquid in the reservoir is seen to be higher than that in the bath. Smooth capillaries, however, produce a rise in level of only 1 or 2 cm. at most, since the viscosity of the liquid is small and hydrostatic pressure pulls the accumulated liquid in the reservoir back through the capillary. When the heat flow is large, violent surging is observed in the reservoir, but there is no further rise in level.

In mathematical theories the question of notation, while not of primary importance, is yet worthy of careful consideration, since a good notation can be of great value in helping the development of a theory, by making it easy to write down those quantities or combinations of quantities that are important, and difficult or impossible to write down those that are unimportant. The summation convention in tensor analysis is an example, illustrating how specially appropriate a notation can be.

In this paper the usual theory of quantum electrodynamics is outlined and an alternative method of quantization is introduced. Some of the difficulties of this theory are discussed and a modification is introduced to meet them. The theory is developed so as to satisfy the principle of relativity, but is not quantized. In the following paper an extension of the theory is given which removes this restriction.

By means of purely qualitative arguments which do not depend on any particular model, the general scheme of stable nuclei and the isotopic breadth of nuclei with odd charge number are explained.

The breadth of the isobaric region can be obtained if the numerical values of certain energies are known. Though these can be estimated only very roughly, the values for the breadth of the isobaric region obtained in this way are in good agreement with the experimental values. The increase in the breadth of the isobaric region from light nuclei to heavier nuclei can be explained, but no plausible explanation has been found for the fact that the breadth decreases again for the heaviest nuclei.

1. In a note published recently in the Proceedings* Goldstein suggests the truth of the following theorem.