Table of contents

The effective bulk and shear moduli are calculated by a self-consistent method due to Fröhlich and Sack. The bulk modulus k is determined by applying a hydrostatic pressure, and the shear modulus μ by applying a simple homogeneous shear stress, to a large sphere. Each hole is surrounded by a spherical shell of real material, and the reaction of the rest of the material is estimated by replacing it by equivalent homogeneous material For consistency, both the density and the displacement of the outer spherical boundary must be the same whether the hole and its surrounding shell are replaced by equivalent material or not. The effective elastic constants calculated from these conditions are 1/k = 1/k₀ρ + 3(1 - ρ)/4μ₀ρ + O[(1 - ρ)³], (μ₀ - μ)/μ₀ = 5(1 - ρ)(3k₀ + 4μ₀)/(9k₀ + 8μ₀) + O[(1 - ρ)²], where k₀ and μ₀ refer to the real material and ρ is the density of the actual material relative to that of the real material, in the next approximation k depends on the standard deviation of the volumes of the holes.

The dilatation due to a distribution of pressures in the holes is p(1/k - 1/k₀), where p is the mean obtained when the pressure in each hole has a weight proportional to the volume of the hole. By using the hydrodynamic analogue of the elastic problem, the theory is briefly applied to the theory of sintering, and used to discuss the effective viscosity of a liquid containing small air bubbles.

Ferromagnetic particles of diameter from 10^-3 to 10^-5 cm when exposed to light move along the lines of force of an inhomogeneous magnetic field It does not seem possible to explain the movement when only dipole properties of the particles are taken into account. Field strengths of 10^-2 gauss are sufficient to cause distinct movement The motions resemble those of electrically charged particles in electric fields

Experiments on Geiger counters are described in which localization of the ion sheath was brought about by reducing the wire potential immediately after each count. The effect on the dead time is discussed The dead time of a counter 30 cm. long was found to be 20 μsec and independent of the counting rate up to 1.8 × 10⁶ counts per minute The reduction of the dead time of short counters was also investigated.

When, in cold-cathode discharge tubes, electrode spacings and surface areas deviate from the ideal of infinite parallel planes, it is found that the breakdown voltage between electrodes increases. This is explained as a decrease in the effective η of the gas due to loss of electrons and positive ions by diffusion to the walls of the container The loss factor per unit potential difference is shown theoretically to be inversely proportional to the field strength and tube radius, although this is not fully verified by experiment

Paschen curves obtained experimentally for potassium and nickel cathodes in argon and in a neon-argon mixture at low pressures are shown and, from these, values of γ for the two cathode surfaces are obtained as a function of E/p₀. The apparatus used for measuring breakdown voltage is described.

Earlier theories of statistical and formative time delays are extended to cover the case of a rising overvoltage and also the case where the primary electrons appear in bursts as with ionization by α-particles. The shape of the statistical distribution curve is an indication of whether the primary electrons have been produced singly or in bursts. The overvoltage ΔV of breakdown due to formative lag and the rate of rise of the uniformly increasing applied voltage V are found to bear the relation ΔV ∝ (dV/dt)^1/2. This has been experimentally verified.

It is pointed out that the mechanism of operation of the multiple circuit magnetron oscillator in the region of minimum magnetic field and voltage, where the efficiency is commonly assumed to approach zero, should approach that of an oscillator of the travelling wave tube type, providing that a cathode of suitable size is used. Useful efficiencies should thus be obtainable under these conditions.

Details of experiments are given in which an electronic efficiency of 12% was obtained at a wavelength of 3 cm. at values of magnetic field and voltage several times lower than those used for high efficiency operation. The mode of operation was determined by the value of the magnetic field, a given mode being maintained over a range of magnetic field of the order of 8% The anode voltage was about 70% of the critical value.

The experimental results generally support the hypothesis and suggest that the minimum voltage regime should be of extreme importance for work at the highest radio frequencies.

An account is given of measurements (carried out in March 1947) of the reflection coefficient of water at a wavelength of 8.7 mm. over a range of angles of incidence.

The method employed is to measure the relative field strengths of the direct waves and waves reflected from a trough of water using free-space propagation and high-gain aerials.

The following electrical constants of water have been computed from the measured results (water temperature 11.1° C.): refractive index 4.40±0.24, dielectric constant 10.86±2.21, absorption coefficient 2.91±0.06, conductivity/frequency 12.82±0.42, Brewster angle 79°.

In this paper an approximate solution to the wave equation is given for propagation in an ionosphere in which the gradient of the density N is in the vertical, z, direction only, and in which account is taken of the earth's magnetic field. It corresponds exactly to the ray theory and expresses a quantity Z, which is the z derivative of the phase function S, by a quartic equation. Z can be represented as a function of ζ (which is proportional to N) on a four-sheeted Riemann surface, and the branch points are studied for the case of vertical incidence for which Z becomes the refractive index. By considering the branch points in the complex ζ plane, the amount of the coupling between the ordinary and the isolated extraordinary branches of the (Z, ζ) curves can be expressed as a function of the obliquity of the magnetic field. The triple splitting of rays reflected from the ionosphere, observable where the field is nearly vertical, can thus be explained, and the theory is substantiated by the observation that the polarizations of the echoes on the (P', f) records are ordinary, ordinary and extraordinary in order of increasing critical frequencies, as given by the branches of the (Z, ζ) curves.