In this the centenary year of Lord Kelvin's birth it is fitting that the Society should call to remembrance one who was for long its most distinguished Fellow, who first became its President at the age of thirty-nine, and was repeatedly re-elected to the office, which he held for twenty-one years in all, and who used the Society as a medium for the publication of many of his most brilliant discoveries. In the long list of his published papers there are at least one hundred and twenty items communicated to the Royal Society of Edinburgh. No other contributor has done so much to give to our Proceedings and Transactions a world-wide and lasting fame. It was to this Society that he brought, in 1849, his account of Carnot's Theory, which marks the beginning of his study of Thermodynamics, and it was in our Transactions that he published his epochmaking series of papers on the “Dynamical Theory of Heat” from 1851 to 1854. It was here in 1852 that he propounded the doctrine of the Dissipation of Energy. It was here that his investigations of underground temperature and the secular cooling of the Earth appeared in 1860 and 1862. It was here in 1865 that he “briefly refuted” the doctrine of Uniformity in Geology. Here, too, were published his long series of papers on Vortex Motion and Vortex Atoms, from 1867 to 1881, and much of his work on the molecular constitution of matter. Here he first showed, in germ, his mariner's compass, in 1874.

Little is known of the details of systems of concomitants belonging to double binary forms. The cases of the single ground form of orders (1, 1), (2, 1), (2, 2) respectively, together with the simultaneous system of any number of (1, 1) forms, are the only four cases, which have been published. The following pages establish the simultaneous system of two (2, 1) forms.

This system is fundamental for the geometrical treatment of two twisted cubics lying upon a quadric surface and having four common points.

The object of this paper is to communicate a general formula for elementary symmetric functions of any assigned degree of a given number of the roots, in ascending order of magnitude, of an algebraic or transcendental equation with complex coefficients. In virtue of the simple relations that exist between these symmetric functions, the formula gives a literal expression in terms of infinite series for all the roots of an equation. In practice it is generally desirable to transform the equation first into one with roots widely separated in value (e.g. by the root-squaring process) in order to make the convergence of the series sufficiently rapid for satisfactory numerical computation.

Four compounds have been electrolysed and the nature of the resulting compounds investigated. These are:—

(a) Potassium ethyl ethoxymalonate, which gave ethyl diethoxyacetate, the alcoholate of ethyl glyoxylate, a little ethyl diethoxysuccinate, ethyl alcohol, oxalic acid, formaldehyde, and acetaldehyde.

(b) Potassium ethyl diethoxysuccinate, which gave ethyl formylethoxyacetate, oxalic acid, ethyl oxalate, ethyl alcohol, formaldehyde, and formic acid.

(c) Potassium ethoxyacetate, which gave formaldehyde, alcohol, and formaldehyde diethylacetal.

(d) Sodium amyloxyacetate, which gave amyl amyloxyacetate, formaldehyde diamylacetal, formaldehyde, and iso-valeric aldehyde.

The author wishes to acknowledge his indebtedness to Professor Sir James Walker, F.R.S., for his helpful suggestions and advice in the course of this research.

The ionisation of iodine vapour by light has been sought by several investigators with negative results. Nevertheless, the application of the quantum theory, which has proved so fruitful with respect to the relation between electron impact on gaseous molecules and the emission of light, leads to the expectation that the ionisation of a gas should be affected by light of sufficiently short wave-length. This ionisation was first observed by Lenard, who investigated the effect of light in the extreme ultra-violet on air and other gases.

Balanus nubilis, one of the sessile Cirripedes, grows to a considerable size, a large specimen measuring some 10 to 11 cm. across the base and an equal distance in height. During a visit to Nanaimo Biological Station an opportunity was taken to study in this giant form a few features pertaining to the mechanism of movement of the operculum, which is attached within the cup of the shell by the opercular membrane. Peripherally the membrane is attached close to the downwardly directed sharp edge of an overhanging shelf formed by the inner wall of the shell; centrally it is attached to the free edge of the operculum on its basal aspect.

The first experiments on this subject were suggested by the absorption effects associated with the “J” phenomenon. In a comparison of the absorbability in aluminium and in copper of the radiation emitted in one direction from an X-ray tube, it is found that in many cases, as the tube is hardened and a certain value of the mass-absorption coefficient reached, there is a sudden increase in the absorption by aluminium. Since the radiation is not strictly homogeneous, and since the above effect does not invariably take place, it is evident that the phenomenon is not to be explained simply in terms of a “J” series characteristic radiation similar to K and L characteristic radiations as regards the manner of its excitation. It is evident that certain critical conditions must obtain before the phenomenon occurs, and on account of the abruptness of the change it appears as though the whole wave-length range of the radiation were affected in respect of absorption by aluminium. This seems to be further substantiated by the fact that the discontinuous character of the change in absorption is preserved with a beam which is much more heterogeneous.

1. The rates of sedimentation of a kaolin suspension in presence of varying concentrations of a salt (sodium chloride, potassium chloride, sodium sulphate, di-sodium hydrogen phosphate, sodium citrate, calcium chloride, calcium sulphate, monocalcium phosphate, “superphosphate”, aluminium chloride, ferric chloride or lanthanum chloride) have been compared at various pH values. Abnormal results are obtained with sodium chloride, monocalcium phosphate, aluminium, ferric and lanthanum chlorides.

2. Sodium chloride increases the rate of sedimentation in alkaline solution, but actually inhibits it in acid solution.

3. In concentrations of monocalcium phosphate above 0·06 per cent, abnormal sedimentation in alkaline solution takes place, with the result that it is much more complete than at the corresponding concentrations in acid solution.

4. In acid solution the tervalent ions, aluminium, ferric and lanthanum have little effect, but a zone of very marked flocculation occurs at pH 7–8. This zone separates a region within which the unsedimented particles are negatively charged from a region within which they are positively charged.

1. The properties of a colloidal sol of cholesterol have been investigated, more particularly in relation to the effect of pH in the presence of protein (gelatin) of various concentrations.

2. The cataphoretic P.D. between the particles of the sol and the medium has been determined in the presence of gelatin at various concentrations and at various pH values.

3. The effect of the presence of gelatin in preventing the precipitation of a cholesterol sol by sodium chloride at various pH values has been investigated. It has been shown that the amount of gelatin required to protect is approximately that required to cover the particles with a layer of gelatin from one to two atoms thick.

4. The mechanisms of precipitation and protection are discussed in the light of these results.

It has been pointed out in a previous paper (Wright and Kermack, 1923), that whereas the precipitation of colloidal gum benzoin by salts containing a uni- or bi-valent cation commences at a given concentration and continues to take place with increasing concentration, in the case of ferric chloride, there occurs with continuously increasing concentrations of this salt, first non-precipitation, second precipitation, then a range of concentrations where no precipitation occurs, and lastly precipitation again. Such a series of changes has been observed with other sols under the action of tervalent ions (cf. Burton, 1916).

In this paper it is proposed to study the problem of the vibrations of a uniformly-stretched membrane whose superficial density σ depends upon the distance r from a fixed point in the membrane in accordance with the law

in which C and a are constants. The constant a will be known as the critical radius and the circle r = a as the critical circle.