Table of contents

In experimental work with nuclear research emulsions, one sometimes makes scattering measurements to determine the energy distribution of a beam of particles incident on the emulsion. To do this, one selects particles which leave tracks longer than a certain minimum length. This sample is a biased sample, and a correction for this bias has been calculated, considering both single and multiple scattering.

Alpha particle and α + ³H tracks have been measured at angles of dip between 0 and 90° in Ilford C2 emulsions. No significant variation in the length with angle of dip has been found except in measurements made with a microscope. A fault in the depth measuring mechanism is shown to account for this effect.

While in most observations on the helium II film, transport at the critical velocity has been studied, the present paper describes observations of film transfer at velocities less than the critical. Three different methods of investigation have been employed. The first is an analogue of an electrical circuit embodying a current-potential measurement on a superconductor. The second method uses as indicator the formation of bulk liquid out of a film which passes over a surface of varying perimeter. In these two methods film transfer occurs from a higher to a lower meniscus of bulk liquid. In the third method film transfer is initiated by the introduction of a thermal gradient and transfer rates under varying heat input are studied. The experiments show conclusively that, similar to the phenomenon of superconductivity, below a critical velocity, flow of helium through the film is completely free of dissipation. The third method has been used to determine the heat of transport for the film, and these experiments are described and discussed in an Appendix.

The effect of a uniform magnetic field on the conduction band of metal is investigated, using as model the tight-binding approximation for a simple cubic crystal. The normally discrete magnetic levels pertaining to free electrons are shown to be non-uniformly spaced and broadened as a result of the lattice forces.

Using translational properties of the Hamiltonian, a standard form is derived for the wave functions describing conduction electrons moving in a uniform magnetic field. This is used to obtain a solution of the Schrödinger equation in order to examine the magnetic energy levels. For non-overlapping bands the notion of effective mass is shown adequate (neglecting level broadening) but in an overlap region neighbouring bands interact strongly and distort the single band levels. A brief application to the diamagnetism of metals is considered.

It is shown that the positive partial correlation which exists between the meson intensity at sea level and the stratospheric temperature can be interpreted as being due to the μ-e decay. Two `second-order' effects of the μ-e decay contribute to the positive temperature effect which is observed at sea level. One is due to the fact that neither of the standard pressure levels (the 100 mb and 50 mb levels) which have been used as reference levels in the analysis of experimental data is a sufficiently good approximation to the mean level of meson production. The other is due to the fact that the survival probability of a μ-meson depends on the way in which its energy loss is distributed over the distance which the meson has to traverse. The theoretically predicted values of the positive temperature effect associated with the μ-e decay are in reasonable agreement with the available experimental results. The observed dependence of the effect on the choice of reference level is also explained.

A theoretical expression is derived for the Kerr constant of a gas at low pressures using a general expression for the energy of a molecule in a strong electric field. It is shown that the temperature independent part is closely related to the change of molecular polarizability with field strength. For spherically symmetric systems, the measured Kerr constant can be used to find the magnitude of this hyperpolarizability.

A statistical-mechanical theory of the Kerr constant is presented, and expressions are derived which are applicable at any density. For anisotropic molecules without permanent dipole moments, the Kerr constant is expanded, powers of the polarizability and the leading non-vanishing terms retained. To this order of accuracy, the molecular Kerr constant of molecules of this type is unaffected by pressure changes provided the forces acting between the molecule are independent of orientation. Experimental data for some compressed non-polar gases support this conclusion. For orientationally dependent intermolecular forces, the Kerr constant is expanded in powers of the density and the leading term representing a departure from ideal behaviour is discussed in some detail for both polar and non-polar molecules.