The tow-nettings on which this survey is based were taken mostly from Keppel Pier. The tide as a rule runs down the channel strongly for several hours after high water, and the current is sufficiently strong to hold out the tow-nets more or less horizontal. Owing to some peculiarity in the configuration of the sea-floor at Keppel, the downward current is much the stronger and often begins an hour or several hours before high water. The flood-tide is never strong enough nor constant enough to hold out a tow-net for any length of time, and so most of the observations are based on tow-nettings taken on the ebb. Tow-nettings were taken almost every day and the tow-nets were usually left out for an hour.

The precipitation of sols by electrolytes naturally attracted the attention of the early investigators, and certain general relations were established. As these are to be found in any standard textbook on colloids, it is unnecessary to restate them here at length. They may be summarised as follows:— (i) A sol is precipitated by the ion of opposite electric charge, i.e. negative sols by kations, positive sols by anions; (ii) the precipitating power increases with the valency of the ion, the ratio for univalent, bivalent, trivalent being I: X:X2, the so-called valency rule; (iii) the other ion of the electrolyte tends to stabilisation of the sol; (iv) excess of the precipitating ion reverses the electric charge of the sol, which is then only precipitated by the ion of opposite electric charge; this occurs more readily with polyvalent ions.

The differential equation of the conduction of heat in ordinary three-dimensional space is generally written in the form

where v denotes the temperature of the medium at time t. For a medium in which the temperature varies only in one direction, e.g. an infinite cylinder with the temperature varying along the axis, the equation is

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 seasons at which the Atlantic salmon ascends rivers differ to a considerable extent in different countries.

In northern Norway and eastern Canada the severe winter conditions compel salmon to ascend from the sea only after the rivers have become free from ice. In one or two of the large rivers of northern Siberia it has been noticed that the salmon are well up into the upper reaches when the ice breaks up, from which it has been argued that they ascend under the ice.

Included in the area of distribution of Salmo salar are the western coasts of Europe as far south as the Franco-Spanish border as well as the British Isles and Iceland, and, in addition, the eastern coast of Canada and the United States down to the State of Maine. A very large number of investigations have been made in Great Britain and various European countries, both by marking the fish in order to trace their subsequent growth and movements, and by reading their age and history from the scales. Length calculations from scale measurements have also been made in Scotland, Norway, and Sweden.

In the Proceedings of the Royal Society of Edinburgh for 1921–22 Whittaker suggests an atomic model designed to absorb and emit radiation by quanta. This model consists essentially of a system of radial magnets, set as the spokes of a wheel with like poles (say south) at the centre. The electron approaching the wheel along the axis of symmetry will, according to the author, set the wheel into rotation, giving a “magnetic current.” The action of the approaching charge, giving a rotation to the North Pole and a “magnetic current,” is quite the analogue to the North Pole approaching a non-axial electric charge, setting it into rotation, and producing an “electric current.” The electron, with energy exceeding a definite value, succeeds in going through the atom, with the result that a definite amount of energy is permanently transferred from the electron to the atomic wheel, a result which resembles the absorption of electronic energy by the atom in spectrum excitation.

Unilateral ligation of the vas deferens in the mammal is a method now commonly employed in the surgical treatment of senility. The demonstrably beneficial results that follow the operation are explained on the assumptions that the testis is an endocrine gland; that if the gametogenic function is embarrassed, the interstitial tissue, regarded as the source of the sex-hormone, undergoes hyperplasia; and that associated with this increase in amount of tissue there is an increased elaboration of the internal secretion.

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.

The following pages deal with the simultaneous system of two general quadratic forms in n homogeneous variables. It is a special case of Gordan's Theorem which proves such systems to be finite, for the general projective group of linear transformations. While several works have dealt with the cases when n = 2, 3, or 4, nothing seems to have been written on the general case except a memoir in the year 1908. We continue, and simplify, the results there obtained, and now establish that

(1) All rational integral concomitants of two quadratic forms in n variables and any number of sets of linear variables may be expressed as rational integral functions of (3n + 1) concomitants, and forms derivable by polarisation.

(2) These (3n + 1) forms, called the H system, constitute a strictly irreducible system.

This system is exhibited in §7 as

together with polars.

The work is divided into three chapters: I §§ 1–4 is introductory notation, II §§ 5–17 provides a proof of these theorems, while III §§18–21 gives the non-symbolic and canonical forms of the results.

In order to examine the hypothesis, so ably enunciated by the Steinach school, that senility is a phase of life that is attended by, perhaps even caused by, the inefficient functioning of one or more of the components of the endocrine system, the writer set out upon a series of attempts to evoke rejuvenation in the aged fowl. In a previous communication (Crew, 1925) an account was given of an unsuccessful attempt to produce this result in the aged cock by means of unilateral vasoligation. In this paper the results of thyroid administration to aged birds of both sexes are reviewed.

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 following paper is ancillary to certain investigations in stellar photometry which are in progress at the Royal Observatory, Edinburgh, and require the establishment of data relating to the blackening of the plates employed. It describes the laboratory work carried out for this purpose, generally over the very restricted range of exposure times and densities used in the stellar work, but occasionally extended to cover a wider field. The conditions are chosen in order to give the maximum accuracy and range to the stellar work and not with a view to highly accurate laboratory work; on the other hand, the periodical change of emulsion which must occur in any lengthy investigation introduces an element which, though of considerable interest, is lacking in most of the published work on the subject.

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.

Il est fréquemment nécessaire de mesurer, avec la plus haute précision possible, les intervalles de temps compris entre des signaux inscrits sur un appareil enregistreur (signaux horaires, tops d'observations astronomiques, etc.). Lorsque l'intervalle de temps à mesurer est de courte durée, on peut utiliser divers procédés, par exemple un diapason entretenu électriquement sans contact au moyen d'un amplificateur à lampes et dont on inscrit le courant d'entretien sur le même enregistreur. Il est aisé d'évaluer l'intervalle à mesurer en nombre de vibrations et fraction de vibration. Si cet intervalle dépasse quelques secondes, le procédé devient impraticable et il est nécessaire de subdiviser l'intervalle à mesurer en fractions d'une seconde par exemple, de compter le nombre entier de secondes intercalées entre les deux signaux et de ne mesurer en vibrations du diapason que les résidus compris entre le premier signal et la lère seconde, le dernier signal et la seconde la plus voisine de lui.

The number of writings on compound determinants in the period 1900–1920 is almost identical with the number for the immediately preceding twenty-year period. The languages used by the writers are at least as numerous: but the contributions made by the various nationalities are relatively much altered in amount. The former strikingly high proportion of Magyar work is not at all maintained, and German has somewhat fallen off: on the other hand, English and Italian have increased. Although statements at variance with historical accuracy, and the publication of old results as new, are still more common than they ought to be, pleasing evidence is not awanting of improvement in these respects. There is nothing so glaring, for example, as the fact chronicled against the writers of the two preceding periods that they had unwittingly rediscovered ten times a theorem that had appeared in so well known a journal as Liouville's in 1851.