Table of contents

The Hartmann test and the " knife-edge " method for the determination of lens constants are described as applied to the investigation of electrostatic " unipotential " lenses. The results of measurements on a number of such lenses are presented graphically.

It is shown that the curvature of the principal surfaces plays an important part and that it is, therefore, necessary to distinguish between longitudinal spherical aberration and difference of zonal focal lengths. Up to about half the lens diameter, primary spherical aberration only is noticeable in most cases. The dimensionless spherical aberration constant S can be approximately represented, over a wide range of modifications of lens design or lens potentials, by the formula S=K₁(f/D)², f being the focal length and D the internal diameter of the centre electrode of the lens. K₁ is a constant of the order of 10 for the lenses investigated without stops limiting the axial length of the field, and of the order of 20 for lenses incorporating such stops. In the case of one specially constructed lens, good agreement is found with calculations by Ramberg. In an experimental unipotential lens from which the diverging parts of the electrostatic field were removed, the spherical aberration is as low as in magnetic lenses of comparable dimensions.

The change on "aging" in the electrical properties of cold worked iron-carbon alloys of low concentration is investigated theoretically. During the process of "aging", the carbon atoms diffuse into the dislocations, thus forming rows of atoms. The electrical resistance due to scattering of electrons by these rows of carbon atoms is expressed in terms of the scattering power of a single carbon atom dissolved in the iron lattice, and hence in terms of the resistance of the same number of randomly distributed carbon atoms. It is found that this change depends on the wavelength of the electrons at the Fermi surface. This wavelength is determined by the effective number of free electrons, and with a reasonable value of about 0.6 electrons per atom for iron, the agreement with the observed diminution in resistance is satisfactory.

Alternatively, one can use the calculations to determine both the number of free electrons in iron and the number of dislocations in the specimen at different degrees of hardening, from the observed changes in the electrical resistance and thermoelectric power of the specimen.

A calculation is made of the change in the energy of a monovalent metal when one of its atoms is replaced by an atom of a different monovalent metal, not necessarily of the same atomic volume. From a knowledge of this energy the heat of solution can be determined and thereby, through the usual thermodynamic relations, also the solubility limits. Numerical calculations have been carried out for the copper-silver system and the theory shows in this case the existence of narrow solubility limits, in agreement with the known phase diagram. The theoretical values of the heats of solution are compared with those required to give the observed solubility limits.

A study of fractures in a well-sintered polycrystalline aggregate of corundum crystals has shown that the strengths of the crystals and the crystal-boundaries are approximately equal. Reflected light microscopy was employed and the usefulness of this method of examination has been established.

A torsion device is described in which a small and decreasing stress is exerted on the visco-plastic substance by means of a blade attached to a torsion wire. A modification of the Scott Blair-Nutting equation is suggested to account for the variation of both stress and strain with time and a "firmness intensity factor" of the substance is calculated, by means of the modified equation, from the observed relation between blade deflection and time. The apparatus has been used to study the properties of milk curds.

Four methods of conditioning a sample of material to a prescribed liquid or vapour content are examined mathematically. The "two-stage method" of conditioning leads to considerably shorter conditioning times than the other methods provided it is carried out in a certain way, and information presented in graphical form in this paper shows how to obtain the maximum advantage in practice. The necessary equations are developed for both a plane sheet and a cylinder, and the corresponding problem in heat flow is mentioned.