Table of contents

Methods are described for the design of two aspheric surfaces for any given centred system, so as to achieve exact aplanatism. The practical application of the methods is illustrated by the design of a reflecting microscope.

In view of mis-statements made in the literature, the origin of the refractive index in electron optics is discussed in some detail, and the uniqueness of an expression previously given is demonstrated. On this basis, some general properties of electron optics are investigated.

A relation between ray direction and wave normal is obtained. Whereas the refractive index is unique in terms of the magnetic vector potential A, this itself is arbitrary to some extent. It is shown that A must, for purposes of electron optics, be chosen so as to satisfy Stokes' theorem and that, if it does, no observable effects result from the arbitrariness of A. An expression for the optical path difference is given in terms of the magnetic flux enclosed. The results are applied to a number of questions, viz. the differential equations for trajectories, the focusing properties of an axially symmetric field and the interference pattern produced by two converging bundles of rays which enclose a magnetic flux.

Lommel's problem, the disturbance near the focus of waves of uniform amplitude, is generalized to consider waves of radially non-uniform amplitude. Lommel's numerical results are extended, and his U and V functions, tabulated on a new basis, together with some new related functions, are employed to provide extensive intensity distribution curves for the diffracting patterns associated with waves of both uniform and non-uniform amplitude.

The results of a spectroscopic study of the white or coloured flames from typical pyrotechnic compositions are reported. Most of the visible light from these sources comes from a limited number of atomic or diatomic emitters. The effects of secondary emitters on the dominant wavelength, colorimetric purity and relative intensity are considered in general terms and some suggestions for improving the quality of the flames are put forward.

From an investigation of the discharge spread in Geiger counters filled with hydrogen, neon, argon or helium, it is possible to show that in certain circumstances the discharge spread is due almost entirely to photo-ionization in the gaseous counter filling. The results enable the absorption coefficients of the operative radiations to be found.

The paper describes a study of the excitation temperature in certain spark discharges of accurately known current characteristics. The excitation temperatures are found by measuring intensity ratios for certain spectral lines where the relevant transition probabilities are known, and are comparable with earlier work by Ornstein and his collaborators on arc discharges.

The excitation temperatures are, as would be expected, higher than those generally found for arc conditions.

Certain peculiarities relating to the evaporation of electrode metal are described. In particular the presence of discontinuous evaporation was noticed, and it was found that different electrode metals showed considerable variations in their behaviour in this respect.

The sound velocities ν have been measured, at frequencies f between about 700 and 3,000 kc/s., and at temperatures between about +15° and -80° C., of the following liquids: geraniol, di-dihydrocitronellyl ether, castor oil and iso-butyl alcohol. There is evidence of a positive dispersion (partial differentialν/partial differentialf>0) in the first three liquids at low temperatures. A negative dispersion has been observed in geraniol and di-dihydrocitronellyl ether at higher temperatures, and in iso-butyl alcohol over the whole temperature range.

The positive dispersions are discussed on the basis of the classical hydrodynamic theory, and the implications of a complex viscosity are examined.