Although the action of potassium persulphate on silver nitrate solution was one of the first persulphate reactions observed (vol. xviii. p. 64), I had not until lately paid any special attention to the behaviour of the ammonium salt in this respect. It appears, however, that in the latter case there are additional actions of great interest, not possible with the potassium salt. A general description of these will be given now, but there are still some points deserving of further investigation.

It is well known that quaternions are intimately connected with spherical trigonometry, and in fact they reduce that subject to a branch of algebra. The question is suggested whether there is not a system of quaternions complementary to that of Hamilton, which is capable of expressing trigonometry on the surface of the equilateral hyperboloids. The rules of vector-analysts are approximately complementary to those of quaternions. In this paper I propose to show how they can be made completely complementary, and that, when so rectified, they yield the hyperbolic counterpart of the spherical quaternions.

Sets of equations of the form

where the coefficient of xr in the sth equation differs only in sign from the coefficient of xs in the rth equation, had often made their appearance in analytical investigations before the determinant of such a set came to be considered. An instance is to be found in a memoir of Poisson's, read before the Institute in October 1809, and printed in the Journal de l'École Polytechnique, viii., pp. 266 — 344; and similar instances of an earlier date in writings of Lagrange and Laplace therein referred to. The mathematician who first referred definitely to the determinant appears to have been Jacobi.

The title of the present communication describes a pure problem of abstract mathematical dynamics, without indication of any idea of a physical application. For a merely mathematical journal it might be suitable, because the dynamical subject is certainly interesting both in itself and in its relation to waves and vibrations. My reason for occupying myself with it, and for offering it to the Royal Society of Edinburgh, is that it suggests a conceivable explanation of the greatest difficulty hitherto presented by the undulatory theory of light; the motion of ponderable bodies through infinite space occupied by an elastic solid.

The Scottish Expedition to observe the Total Solar Eclipse of May 28 consisted of Professor Copeland and Mr J. B. M'Pherson, Engineer to the Royal Observatory, Edinburgh, who were sent out by the Joint Eclipse Committee of the Royal and Royal Astronomical Societies; Mr Franklin-Adams, who joined the party as a volunteer observer; and myself, who had the honour of being sent out by this Society. The special object which we had set before ourselves was, of course, the attempt, if possible, to add something, however little it might be, to the sum of known facts concerning the constitution of the solar corona.

It is easily seen that each of the equations of the set

remains unaltered for each of the three interchanges

and that the set as a whole is not altered by the simultaneous performance of the cyclical substitutions

In Dr Muir's Paper on a Peculiar Set of Linear Equations (communicated December 3, 1900) there occur two Determinants of the nth order, the expansions of which are given by Dr Muir, As the paper in question has so much to do with Symmetric Functions, the following simple method of obtaining their expansions may not prove uninteresting, based, as it is, upon the elementary theory of Symmetric Functions and the so-called Principle of Indeterminate Coefficients.

The solution of the problem of finding such pairs of integers is not a thing of yesterday, as may be seen by consulting Hutton's translation of Ozanam's Recreations, i. pp. 46–8 (1814).

For a number of years a very serious nuisance has arisen from the ‘sloblands’ of the upper reaches of Belfast Lough during the summer and early autumn—the stench at low tide being often quite overpowering, and the air heavily charged with sulphuretted hydrogen.

At a recent meeting of the Society, Dr Buchan read a paper based on certain observations of the temperature of the waters of the Mediterranean, which had been made by the staff of the Austrian ship Pola. These indicated that the direct effect of solar Tadiation was felt to a depth of over 150 feet. At any rate, the facts were that the temperature of the upper stratum of water of this thickness was perceptibly higher at about 4 p.m. than at 8 a.m., and that the difference was about 1°·5 Fahr. or 0°·8 Cent, at the surface, diminishing fairly steadily to value zero at a depth of fully 150 feet or 50 metres. It may easily be calculated that this excess of temperature at the afternoon hour means the accumulation of an amount of heat equal to 1460 units in every column of water 1 square centimetre in section; and this is accomplished within the eight hours from 8 a.m. to 4 p.m. It must be noted that this accumulation of heat is a daily occurrence.

Bunsen's classical experiments on the absorption of gases by liquids show that the coefficient of absorption in water and alcohol between 0° and 20° diminishes as the temperature rises. Bohr and Bock found that at higher temperatures the coefficients of some gases (hydrogen and probably nitrogen) pass through a minimum, hydrogen in water at 60° C, nitrogen not far from 100° C. These results were not confirmed by Winkler, who concluded from his experiments that the coefficient approaches a smallest value asymptotically. Recently Estreicher, working with Professor Ramsay, found a minimum in the solubility for helium in water at 25° C.

About a year ago, while writing a Text-book on Heat in which the use of higher mathematics had to be avoided, it appeared tome that the phase-rule could be rigorously proved by a process which does not involve the deduction of the somewhat difficult thermodynamical equations used by Gibbs, Planck and others; Quite lately, however, I discovered that proofs somewhat similar to mine had been previously given by Nernst and Bancroft, and I must therefore not be understood to claim originality in thispaper. Seeing, however, that modern thermodynamics do not yet command in this country the interest they deserve, it will not be superfluous to draw the attention of the Society to the subject.

In the case of any harmful insect of economic importance, in order to war against it, or apply remedial measures at all intelligently, a knowledge of the life-history of the pest is necessary. This proposition will, I think, meet with such ready acceptance as to render proof unnecessary, but I might in illustration mention two cases which came under my own observation, where in the one case a knowledge of the round of life of the attacking insect saved a whole forest, and in the other proved of great importance.

The Scolytidse is a family of small roundish tetramerous beetles characterised by the fact that the female beetle enters bodily the tree or plant for her egg-laying, the eggs being generally laid in little notches cut out in the sides of the mothergallery. With some species, however, the eggs are laid all together in a bunch. The grubs are whitish, wrinkled and legless, and have, brown scaly heads. The close resemblance to each other of the grubs of the various species renders the determination of the species from larval characters extremely difficult, if not impossible, but the figures or patterns presented by the mother gallery and the larval galleries in relation to it are in general so highly characteristic, that with these and the name of the host plant one can generally determine the species.

We are again indebted to Dr T. D. Anderson of this city for the announcement of the discovery of a new star, which was first seen by him at 2h 40m a.m., G.M.T., on Friday, the 22nd February.

The history of research in this planet is briefly as follows:—In 1879 Professor Newton enunciated the proposition that if the elliptic orbits of comets have been changed from parabolas by planetary perturbations, then the probabilities are in favour of the comet's position at the time becoming the aphelion position of the new orbit. This explains why the aphelion distances of so many comets agree with the mean distances of Jupiter and Neptune respectively.

The taxonomic value of hair has long been recognised. The different types of human hair have been made use of as a basis for classification of the varieties of Man by Primer Bey and many others, while Waldeyer in his Atlas has described briefly the hair characters of well known members of the Mammalian orders. In the present paper it is proposed to deal with hair within the limits of a single family, that of the Equidæ, and to describe certain peculiarities in the hairs of members of that group, which the author is of opinion are probably of specific value. But before dealing with the hair characters by which the species may be distinguished from one another, something must be said about those of the group as a whole.

The habits and mode of existence of Foraminifera are always interesting subjects to students of the Protozoa, and this fact alone might perhaps justify the following notes, even were they not accompanied by the valuable drawings prepared by Mr G. West, from pencil sketches and microscopic slides made by Sir John Murray from the living Foraminifera collected during the voyage of H.M.S. ‘Challenger.’

In June of last year I had the honour of reading before this Society a preliminary account of the Scottish expedition for the observation of the Total Solar Eclipse of May 28th, 1900, at Santa Pola, on the south-east coast of Spain (long. 0° 30′ W., lat. 38° 13′ N.). I have now to lay before the Society the results of the part of the expedition specially assigned to me, which was to obtain photographs of the Corona. I succeeded in securing four, that being the largest number I considered it advisable to attempt in the very short total phase of eclipse, only 75 seconds being available for the exposures and necessai'y manipulation of the camera backs.

The simplest and most common form of reproduction amongst the Ciliata is binary fission. In this ordinary, possibly vegetative, method of reproduction the plane of division is generally perpendicular to the long axis of the creature, To this generalisation the Vorticellidse form an apparent exception, but on the view that their evident long axis really corresponds to the dorso-ventral axis of other ciliates their case falls into line with that of the rest of the sub-class. Formerly many instances of fission in the direction of the long axis were described; they may safely be considered to have been mere instances of conjugation.