Table of contents

The two-fluid model of liquid helium II is applied to the problem of predicting the behaviour of waves and pulses of second sound of finite amplitude. It is found that equations quite analogous to the Riemann and Rankine-Hugoniot equations for ordinary sound waves and shock fronts can be established. These equations predict the `overtaking effect' with the establishment of a `temperature-shock' for pulses of second sound of finite amplitude The temperature-shocks should be of `front-edge' type (propagation of an abrupt rise in temperature) if the liquid helium is at a temperature below 1.96° K., but should become `back-edge', corresponding to an abrupt fall in temperature, between 1.96° K and the λ-point. There is experimental evidence in support of both these predictions. It is shown that, just as for ordinary shock fronts, the irreversible effects due to the passage of a temperature shock should be proportional to the cube of the height of the shock.

A pulse technique for the propagation of second sound is described and the expected shape of the received pulse is discussed. In this connection, experimental evidence has been obtained for a temperature discontinuity at the interface between liquid helium II and a solid medium at second sound frequencies. The pulse method has been used to study the attenuation of second sound with distance and the formation of shock waves. The observations on the latter are shown to be in agreement with the predictions of the equations of motion of liquid helium II if second order terms are not neglected.

Measurements of the magnetic susceptibility of copper sulphate pentahydrate have been made at temperatures between 20° K. and 1° K. on a single crystal specimen. It is found that the susceptibilities measured in different directions with respect to the crystallographic axes follow a Curie-Weiss law, with different Curie constants but a fixed Weiss constant of -0.6°. The discrepancy between this result and that of Krishnan and Mookherji is attributed to temperature-independent paramagnetism.

It has previously been shown by the author that the interaction between free electrons and the lattice vibrational field (if strong enough) leads at the absolute zero to the formation of a new state The London equations are now derived in the sense conjectured by F. London.

An expression is derived for the photoelectric current excited at the surface of a metal by radiation of frequency below the threshold frequency of the first order photoelectric effect A physical interpretation of the formal results is given and the possibility of detecting this current experimentally is briefly discussed.

A model for plastic deformation in soft metals, i.e. metals which are not age-hardened or severely cold-worked, is given. It is based on the assumption that in real crystals there is always a number of regions present which, by an unknown process, act as sources of dislocations. Furthermore, it is assumed that in soft metals dislocations are very mobile except in a limited number of regions which act as obstacles. The model is applied to explain a number of facts connected with plastic deformation.

The work of Peierls and Nabarro is extended to a family of edge dislocations of greater widths. The weaker the shearing forces between adjacent atoms in the slip plane, the wider is the dislocation. The external shear stress required to move the dislocations is extremely sensitive to the width, becoming vanishingly small at widths of the order of three atomic spacings. The theory is applied to bubble raft dislocations, and satisfactory agreement is found with experiment.

A β-spectrometer is described which focuses a conical sheaf of rays emitted at about 80° to the axis of a prolate spheroidal magnetic field. In agreement with a previous theoretical prediction, the trajectories cross over at two sites in the rotating meridional plane. The field behaves in some ways like a magnetic mirror and can be arranged to form an aberration-free image of a point on the axis of symmetry. It cannot, however, give a clear image of an area because the Abbe sine condition is not fulfilled.

The wide-angle focusing action is compared with that recently found by Slätis and Siegbahn, for which a different optical analogue is suggested, based on the isolation of a meridional focal line between two refractions

The adjustment of the spectrometer and measurements of its resolving power and solid angle of collection are described, an example being 1.4% of 4π with a line-width of 1/113 at half-height. By working at less than unit magnification it is possible to focus rays emitted at less than 80° to the axis.

The exposure was made at the Jungfraujoch, altitude 3,457 m., using Ilford type C2 nuclear research emulsions. The frequency of stars under thicknesses of carbon up to 220 gm/cm² was measured, the experimental value of the absorption length of the radiation causing them being 166±8 gm/cm². The proportion of the stars due to fast π-mesons has been evaluated and, on subtracting this proportion, the absorption length of the radiation responsible for the remainder is found to be 143±10 gm/cm². The energy distribution of the stars having from 3 to 20 tracks is found to be of the form dE/E^2.6, with no apparent discontinuity. The frequencies of slow π- and π-mesons at various depths is reported. The π-mesons exhibit a transition effect which is interpreted in terms of their production in stars occurring in the carbon absorber. The ratio of negative to positive π-mesons is found to be 3.1 to 1.

The `prong distribution' for the disintegrations produced by the σ-mesons of the cosmic radiation in photographic emulsions exposed below ground is found to be different from that observed in emulsions exposed above ground. The underground distribution contains relatively more `stars' consisting of one prong. The observations are consistent with the hypothesis that most of the σ-mesons below ground are in fact negative μ-mesons and not negative π-mesons. It is concluded that 8.7 ± 1.7% of the negative μ-mesons captured in the emulsion lead to disintegrations accompanied by the emission of charged particles. The average number of prongs per disintegration produced by the capture of negative μ-mesons is 0.10 ± 0.02 The mean number of prongs and the associated prong distribution suggest that a nuclear excitation of about 15 MeV is produced by the capture of a μ-meson

The energy of the photo-protons from deuterium, measured in an ionization chamber, has been used to determine the energy of gamma-rays produced by the proton bombardment of several light elements. The results are expressed in the following Table:

Isotope	Target thickness (keV.)	Proton energy (keV.)	Gamma-ray energy (MeV.)
9Be	2	1000	7.39±0.15
11B	200	950	12.50±0.21
13C	20	570	8.14±0.08
5.81±0.25
19F	thick	740	12.09±0.28
7L1	thick	500	14.4 ±0.4
15N	unknown	900	4.45±0.04

The absence of certain well-known lines from the above table merely means that their energy was not determined in this investigation.