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The dipolar broadened nuclear resonance spectrum of a solid shows a remarkable transformation when the solid rotates rapidly about an axis inclined to the magnetic field, especially when the angle of inclination is 54.7°. In this case the spectrum is very sensitive to the frequency of rotation when this is of the same order as the line width of the stationary sample, changing from a broad, usually featureless, line at low rotation speeds to a narrow central line flanked by sidebands spaced at the rotation frequency, at high rotation speeds.

A theory which shows all the features of this transformation is developed for a model in which each spin is supposed to interact to a small degree with a large number of other spins. In this case a single parameter, the second moment of the resonance, line serves to describe the dipolar interactions of the spins. The statistical time-dependent properties of the local field are obtained by a consideration of the time dependence imposed by the rotation and the effect of the changing orientation of the spins relative to the magnetic field. The rate at which this last effect proceeds, itself dependent on the rate of rotation, is obtained by a perturbation calculation. Line shapes are calculable for any combination of the basic data: (i) the motionally invariant second moment; (ii) the angle between magnetic field and rotation axis; (iii) the frequency of rotation.

The relevance of the theory to experiment is discussed.

The spin-Hamiltonian coefficients for Fe³⁺ in sapphire have been redetermined by the classical paramagnetic resonance method. The value of g is 2.0026±0.0005 and is independent of temperature. The other coefficients, in units of 10^-4 cm^-1, and for temperatures of 4, 80 and 299 °K respectively, are: D = +1719.2, 1718.2, 1678.5; a = +229.4, 236.4, 229.1; F = -112.1, 101.3, 100.8 (D and a,±1 unit; F,±2 units). The paramagnetic resonance lines are consistent with the spin Hamiltonian to within the experimental error of 2 gauss. The zero-field splitting frequencies, measured directly, are, for 4, 80 and 299 °K respectively: ν(5/2, 3/2) = 19 281, 19 288, 18 850; ν(3/2, 1/2) = 12 037, 12 029, 11 741 Mc/s (all±0.05%). These frequencies are consistent with the spin Hamiltonian using the above coefficients. It is concluded that the spin Hamiltonian is valid within the above limits of error for fields from zero to 10 000 gauss.

The dispersion law for spin waves in hexagonal cobalt is calculated by the method of Holstein and Primakoff. As this crystal contains two atoms per unit cell an optical branch in the spectrum is found. The cross sections for inelastic neutron scattering by spin waves in cobalt are evaluated and discussed.

The dispersion relations for phonons have been measured for symmetry directions in a crystal of iron by means of neutron spectrometry. The time-of-flight technique was employed, the experiment being carried out on the twin-rotor spectrometer at PLUTO. The dispersion curves obtained have been fitted in each case by a cosine series expansion in which the coefficients are interplanar force constants of the crystal. Interatomic force constants consistent with the experimental data have also been derived.

The decoherence curve of meson showers underground has been studied at depths of 37 and 61 metres water equivalent below sea level at separations from 0.4 m to 10 m, sufficient to overlap earlier measurements at 61 m.w.e. depth which extended to 320 m.

The events recorded may be satisfactorily apportioned between events produced locally by energetic mesons, and the penetrating component of extensive air showers. The measurements are consistent with the interpretation that the multiple penetrating particles observed in cloud chambers underground represent the high particle density region of extensive showers of μ-mesons.

The cross section for the production of penetrating showers by μ-mesons at 61 m.w.e. depth is (4 ± 2) × 10^-31 cm² nucleon^-1, for an energy transfer of 8 GeV, in agreement with earlier measurements.

The experimental data are analysed with the following conclusions. The molecular decay time τ0 of a thin anthracene crystal lamina at room temperature is 10 nsec. The thick crystal values are increased by self-absorption to 31.6 nsec (volume excitation, e.g. by γ-rays), 24.1 nsec (surface excitation, e.g. by ultra-violet or α-rays, and emission observed by transmission) and 19.4 nsec (surface excitation, and observation by reflection). Surface oxidation or reduction in crystal thickness yields lower values. For microcrystals of dimensions comparable with the exciton mean free path (similar 0.1 γ), the decay time is reduced below τ0 due to premature conversion of excitons into photons at the crystal surface.

The ultra-violet and visible components of the thermal glow of KCl(Tl) phosphors were recorded separately for the study of the distribution of traps with respect to depth. The experimental results obtained help one to understand the correlation between the two principal glow peaks and the two main emission bands of the phosphor. It is suggested that the electrons released from traps corresponding to the 200 °K glow peak favour emission in the visible and those released from traps connected with the 300 °K glow peak prefer emission in the ultra-violet.

A.C. field effect measurements on fast surface states on Si are not possible because the minimum of conductance cannot be observed. The pulsed field effect measurements and the flattening of the a.c. field effect curve are utilized in attempting to interpret the a.c. field effect curve and deduce the density and energy of the surface states.

The mechanism by which molecular momentum and energy in a liquid are dissipated is found to be linear, with friction constant β, if a time τ exists which is long enough for the mean square increment of momentum to be proportional to τ, but short enough for βτ<<1. This is distinguished from earlier, formally identical, results in that τ is less, not greater, than the autocorrelation time of the force.

From the success of calculations based on the assumption of a linear dissipative process, and from the experimental value of the friction constant, it is concluded that the mechanism of self-diffusion is one in which the typical molecule executes a quasirandom walk within the region bounded by its nearest neighbour shell for periods much longer than β^-1.

Results for the frictional force of 64-denier undrawn nylon monofilaments running against rigid cylinders showed an increase in the coefficient of friction with increasing load, i.e. in the formula F = αWⁿ relating friction and normal load, n is greater than one. This can be explained by a large increase in the number of asperities making contact as the load is increased, as is shown by experiments with rubber models and theoretical considerations.

A partial analysis has been made of the effects of fluctuations in a plasma on the data obtained by conventional use of Langmuir probes. Consideration has been given to effects of periodic fluctuations of electron temperature, random current and space-potential, supposed independent of probe potential. For a wide range of conditions, the values of electron temperature obtained will be correct, but values of electron concentration underestimated. Experiments are described to check part of the theory, and the bearing of the experimental and theoretical results obtained on the probe analysis of discharges in which there are plasma electron oscillations is discussed briefly.

A scale model of a marine echo-sounder is described, in which acoustic waves are scattered by fish. The parameters are considered for a model immersed in a tank of fresh water in the laboratory.

A frequency of 1.48 Mc/s was chosen. Many measurements were made on standard targets, supports for small obstacles, the sensibly plane-wave region, the variation of velocity of sound in water after refilling the tank and the signals received from a target of known acoustic back-scattering cross section at various ranges.

As the experimental results show close agreement with calculations from theory, the validity of the model is established.

Two methods of measurement of the acoustic reflectivities of solids immersed in water were adapted to specimens in which either two or all three of the dimensions were small (e.g. one to ten times the incident wavelength). These methods are particularly relevant to materials which cannot be obtained in sufficient bulk or which are of a flabby nature. The latter can be largely overcome by using small samples.

At a frequency of 1.48 Mc/s determinations were made of the reflectivities of wet fish bone (26%), damp fish tissue (4.6%), plasticine (44%), soft rubber (11%) and `pc' rubber (3%), and of their respective densities, whence the velocities of sound in these materials are calculated. The acoustic absorption of plasticine was also measured (19 dB cm^-1).

The merits of some of these materials for scale-model experiments are considered.

A method is described for finding changes in the penetration depth from changes in the resonant frequency of a helix having a core of the superconductor. Some results have been obtained for pure and impure aluminium samples. At the lowest temperatures that could be reached, there was no significant deviation from a linear variation of the penetration depth λ with z = (1 -t⁴)^-1/2. The value of dλ/dz in the range 1.1 ⩽ z ⩽ 1.7 was found to be 5.3 × 10^-6 cm.

Studies of the intermediate state of tin and lead films, 2000 Å thick, in a transverse magnetic field have been made using a Hall-effect probe with a resolution of ¼ mm. The magnetization patterns showed structure comparable with the resolution at fields much smaller than the bulk critical field; it is likely that this was not the true domain structure but rather the coarse modulation of a much finer domain spacing due to lack of uniformity in the film. Except when flux trapping occurred, there was no sign of any structure much coarser than the resolution. The magnetization patterns were reproducible under similar conditions with identical magnetic history. As far as their magnetic properties were concerned, the films seemed to be completely normal at fields well below that at which resistance appeared, indicating the persistence of continuous superconducting threads. Hysteresis effects associated with flux trappings were observed, the pattern of the trapped flux being disturbed by the passage of a current. It was also found that a current could generate trapped flux in a virgin film. Measurements of the magnetic field configuration due to a current in a lead strip 2000 Å thick and 1.5 mm wide showed the current to be concentrated at the edges.

In an attempt to find anisotropy of the penetration depth in super-conducting aluminium, such as would confirm a non-local relation between field and current, high-frequency measurements have been made on single-crystal wires of different orientations. No strong evidence for anisotropy has appeared, and there is some evidence from the measurements of surface resistance that the crystals used may not have had the best orientations to reveal any effect. The behaviour of the surface resistance and reactance has been carefully studied very near the transition temperature, and the latter has been found to show a maximum just below T_c. There is qualitative but not quantitative agreement with the predictions of theory.

In 1946 Bloch has shown that with the aid of ideal transformers the dual networks can be constructed for any given non-planar networks. In this article it is shown that dual networks can also be given by introducing elements with infinite impedances (admittances).

A law is postulated which describes the asymmetry of probability distributions under time reversal. Briefly, it states that influences coming from infinity in different directions are statistically independent; a precise statement of the law is provided. This irreversible statistical law supplements the reversible dynamical laws of classical relativistic fields and particles, and from it the time direction of irreversible physical processes can be derived. This is illustrated by deriving the time direction of (i) electromagnetic waves radiated from a dipole, (ii) the scattering of beams of particles, and (iii) recording processes. A restricted law of increasing entropy is also obtained, and some cosmological implications of the theory are indicated. No attempt is made to derive detailed kinetic equations for the irreversible processes in many-particle systems. To ensure that all temporal asymmetries in the theory derive from the postulated law, a symmetric definition of probability is provided.

A new vector potential W(Q, P; t) is associated with a general scalar wave field U(P, t) of any prescribed time dependence. This potential has the property that the normal component of its curl, taken with respect to the coordinates of any point Q on a closed surface S surrounding an observing point P, is equal to the integrand of the generalized Helmholtz-Kirchhoff integral provided.

The closed expression of the vector potential is derived. This general formula is applied to non-monochromatic plane and spherical waves.

These theorems provide the possibility of the transformation of the Kirchhoff diffraction integral (two-dimensional integral) to the line integral and may be regarded as a generalization of Maggi-Rubinowicz's diffraction wave to the general cases.

Electron wave functions in a one-dimensional chain of δ-function potential wells, which have no long-range order or which have short-range disorder, are considered. By considering the `pulling' of the wave function, conditions are found for its locking to the same near-periodicity as the chain. When the disorder is small enough and/or the wells strong enough, there is an energy gap in which there are no states. When the condition is nearly satisfied, or just outside such a gap, the density of states is very small and the corresponding wave functions are shown to have in general a single-peaked localization. Examination of computations of wave functions and eigenvalues in chains of length a thousand wells and upward supports the conclusions reached and shows the features predicted, in particular the strong localization.

Luminescence from columnar electron-ion recombination following α-particle and fission fragment ionization of an argon-nitrogen gas mixture is detected and an estimate of the period for recombination made. In the presence of an electric field, a decrease in particle scintillation pulse-height from a photomultiplier tube is attributed to a loss of recombination luminescence by ion collection. The relative variation in the magnitude of this decrease with photomultiplier clipping time constant indicates that recombination occurs within 10^-7 sec for α-particles in A + 6% N₂ at two atmospheres pressure.