The magnetization curves of short tin, lead and tantalum cylinders were measured by the force method, and it was shown that although for tin there was no appreciable hysteresis in the transverse position, there was a very marked hysteresis in the longitudinal position, of the same form at different temperatures but depending on the sharpness of the cylinder rims. Lead and tantalum showed additional temperature dependent features which could be attributed to impurities.

The hysteresis due to shape in the longitudinal cylinder is analogous to the hysteresis of alloy ellipsoids, in that the magnetization for a given field always lies within a certain boundary curve and varies “classically” within this boundary. This analogy suggests that the mechanism of the shape hysteresis for a pure superconductor may be similar to the sponge mechanism proposed by Mendelssohn for alloys, but it is also possible that the hysteresis is due to the formation of macroscopic superconducting rings. The considerations which fix the boundary curve are probably similar to those in the superconducting ring, and in this connection some new measurements on a lead ring are reported. The paper concludes with a discussion of the time lag between magnetization and field, and it is suggested that this is not a primary phenomenon.

The vibrations of the particles which constitute a crystal can be represented in terms of normal vibrations subject to the condition that the energy of the crystal can be expressed as a homogeneous function of the second order in the displacements. This has been shown by Born and by Waller. It has been proved by Debye and, more generally by Born, that the density of the normal vibrations varies as ν2 when the frequency is very small. The spectrum has recently been worked out for a Born-v. Kármán lattice in the two- and three-dimensional cases. Otherwise practically nothing is known about the spectrum in individual cases, except perhaps in isolated cases where the frequency branches split up and the frequency spectrum shows certain gaps.

In a recent paper, the solubility of hydrogen in palladium was discussed. The statistical theory employed was essentially the same as that given by Fowler† for critical adsorption, the only modification necessary being to take into account the dissociation of the hydrogen molecules on absorption. In the present paper Peierls' theory‡ is applied to the same problem in order to enable a comparison to be made between the theories. According to both theories we must postulate that the absorbed (adsorbed) particles go into a definite number of potential energy holes and that the heat of absorption increases as the number of holes filled increases. Fowler uses the Bragg and Williams type of approximation to determine the energy of the particles in the holes; while Peierls supposes that there is an interaction energy V for each pair of neighbouring adsorbed particles and that all those arrangements of the particles in the holes having the same number of nearest neighbours have the same energy. The calculation of the dependence of the energy on the arrangements is approximated to by a method due to Bethe.

The theory of transport phenomena in metals depends upon the solution of an integral equation for the velocity distribution function f of the conduction electrons. This integral equation is formed by equating the rate of change in f due to external fields and temperature gradients to the rate of change in f due to the mechanism which produces the resistance. If this latter rate of change is denoted by [∂f/∂t]coll it happens with some mechanisms that

where f0 is the equilibrium distribution, and ℸ is the time of relaxation which does not depend on the external fields. When equation (1) is true, the problem is comparatively simple, but in general [∂/∂t]coll is an integral operator and it is not possible to define a time of relaxation and a free path. It is known that at high temperatures, such that (Θ/T)2 can be neglected, where Θ is the Debye temperature, a free path exists; but, in general, special methods have to be used to solve the integral equation.

A new method is developed for evaluating certain integrals occurring in molecular problems, where distances measured from three different centres of force are involved. The convergence of the results is discussed numerically and theoretically.

Bethe's method, used in the problem of order-disorder transitions in alloys, is applied formally to the problem of molecular rotations in solids. To apply this method, we assume that the solid is entirely homogeneous, and that the state of rotation is the same throughout the solid. Without this assumption, the application of this method is impossible.

A particular form of the mutual potential energy between two neighbouring molecules has been chosen, and classical statistics is employed throughout. The calculations are made entirely after the manner of Bethe, and the similarities of the two problems are pointed out. The result is that there is a critical temperature, and also a discontinuity in the specific heat of the magnitude of some ten times the Boltzmann constant per molecule, arising from the sudden setting in of the rotations as the temperature is increased beyond the critical point. Agreement with the experiments is bad, indicating that a more profound theory is necessary.

1. The reflexion of X-rays from an ideal crystal would be independent of temperature if the particles forming the crystal were at rest. Because of the motion of the particles a temperature effect does exist. It can easily be seen that only the component of the displacement at right angles to the reflecting plane is of importance, since it is the path difference between such planes which matters. The complete theory has been worked out by Debye and by Waller. The result is that, owing to the influence of the temperature, the intensity is multiplied by a factor e−2m, where

Here and μs is the mean square of the component of the displacement (in a direction at right angles to the reflecting planes) due to a normal mode π is the glancing angle of incidence of the X-rays on the reflecting planes, and λ is the wave-length.

Konopinski and Uhlenbeck have shown that the empirical β-ray spectra seem to require a modification of Fermi's original expression for the interaction leading to β decay‡. Their expression includes a derivative of the neutrino wave function. The purpose of the present paper is to investigate the most general type of such an interaction term and the possibility of introducing second-order derivatives. We have to deal with the transition§

neutron + neutrino → proton + electron

or proton + anti-neutrino → neutron + positron.

The whole system has the equations of motion

where ψ1 and ψ2 are the wave functions of the initial and final states in configuration space, H1 and H2 are the Hamiltonians of the particles in the initial and final states, and A is a small interaction operator.

In an investigation of the disintegration of by protons, resulting in the emission of three α-particles, Dee and Gilbert* found that the observed distributions of ranges and angles of these particles could be explained by assuming that one α-particle is first ejected, leaving a short-lived, excited nucleus which then decomposes into two more α-particles. The half-life of this excited beryllium nucleus was estimated to be about 10–21 sec.

The criterion of maximum overlapping, as developed by Pauling and Slater, is shown to be true only under certain conditions, depending on the relative positions of three term values, and the relation of the true energy to these three subsidiary ones is discussed in some detail.

In his work on mercury, Benedicks (1) observed that the small temperature peak in the neighbourhood of the middle of the long tube containing the conductor was displaced in one direction or the other along the tube according to the direction of flow of the electric current by which the conductor was heated. Normally this effect increased with the cube of the current intensity, and was explained as due to Thomson heat. If the temperature was made as uniform as possible by means of controlled heaters at the ends of the tube, the effect became of opposite sign and increased linearly with the current. This was called the “electro-thermal effect” and was explained as due to an actual change of thermal equilibrium by the electric current, or the production of a temperature gradient by a flow of electricity.

It has been shown by Mott that it is legitimate in calculating the probability of excitation of an atom by close collision with a slow α-particle to treat the α-particle as a moving centre of force. This method gives for the probability P of excitation

where

and

During the course of a cloud chamber investigation of the occurrence of rare events accompanying the passage of fast β-particles through matter, it was found* that existing methods of introducing high-energy electrons into the chamber were unsatisfactory. Electrons of sufficiently high energy could only be obtained from sources which emit, in addition, a large amount of γ-radiation. Absorption of this γ-radiation in the walls and gas of the chamber resulted in the ejection of numbers of stray electrons, whose presence rendered the observation of the fast β-ray tracks a matter of some difficulty.

1. A familiar device in the study of statistical distributions is to form the moment-generating function

where the bar denotes averaging over all values of the statistical variate x. The moments μr of x are the coefficients of αr/r!, and the derived coefficients in the expansion of K ≡ log M are termed the semi-invariants kr. In particular,

and, for the normal (Gaussian) law,

we have the simple formula

A high-speed recording counter circuit is described which has proved very reliable. The basic circuit element employs two triodes in a symmetrical circuit which has two stable conditions. The circuit is triggered alternately from one stable state to the other by the applied impulses acting through a circuit comprising two “Westector” cuprous oxide rectifiers and an inductance.

It is easily possible to make a counter operate accurately at a speed of 20,000 random impulses a minute, provided that the associated recording meter operates in less than 1/100 sec.

A “watch-dog” thyratron recording circuit is also described. This is useful where the slow speed of the mechanical recording meter would introduce loss.

The paper describes calculations on the distribution in space of slow neutrons based on the application of diffusion laws to their motions. The effects of using spheres of different sizes, and of changing the composition of the hydrogenous slowing-down medium, are discussed. Curves are given which can be compared with the results of the experiments on the slowing down in different media carried out by the author in collaboration with Mr T. Bjerge, and a revision of the calculations based on these experiments leads to a value of 6 × 10−25 cm.2 for the total absorption cross-section of the water molecule, and indicates that most of this absorption must be attributed to the hydrogen atoms.

The author desires to acknowledge the receipt of a Senior Research Award from the Department of Scientific and Industrial Research.

In a study of the properties of hydrogen on tungsten by the method of contact potentials the following points have been established:

(1) The contact potential of a 92% covered surface of hydrogen on tungsten against bare tungsten is 1·04 V., and the Richardson constants for such a surface are, approximately,

A = 30, b = 5·60 V.

(2) A film of deuterium is 20 m V. positive relative to a similar hydrogen film.

(3) Over the range of temperatures and pressures used by Bryce in a study of the production of atomic hydrogen the films are nearly saturated, so that the production of atomic hydrogen is primarily due to a molecule striking a bare tungsten atom, one atom being adsorbed and the other going into the gas phase.

(4)The condensation coefficient for hydrogen molecules on cold tungsten is 0·01.

(5) The effective dipole moment of each hydrogen atom on the surface is −0·42 Debye unit and is independent of the fraction of the surface covered.

1. The cross-flow type of heat interchanger is shown diagrammatically in Fig. 1. One of the fluids involved is arranged to pass through a nest of small tubes, while the other streams past the tubes at right angles to them. To fix ideas we suppose that the tubes contain cooling water which enters at a temperature T1. The temperature of the water leaving a tube depends upon its position, but the water from all the tubes is mixed and is led to a single exit pipe in which the temperature is T2. In the same way the fluid to be cooled enters at a temperature t1 and leaves at a temperature t2. If the cooling water is not used again by being led through another nest of tubes also exposed to the fluid to be cooled, the arrangement is termed a single-pass heat interchanger.