The General Statutory Meeting of the Royal Society of Edinburgh was held in 24 George Street on Monday, 27th October 1913, at 4.30 p.m.

Principal Sir William Turner, K.C.B., President, in the chair.

Before the transaction of the usual business, the bust of Lord Kelvin (see frontispiece), which had been gifted to the Royal Society of Edinburgh by Lady Kelvin, was presented by Professor Crum Brown, acting for Lady Kelvin, and received by the President for the Society.

Gentlemen,—For the high honour you have done me in electing me to the Presidency of this, the premier scientific Society of Scotland, I offer you my grateful thanks. I am proud indeed that you should have deemed me not unworthy to succeed the eminent men who have heretofore occupied this chair. My complacency, however, is tempered, if not subdued, by the consciousness of my own limitations. But if I cannot, like my predecessors, add lustre to the office I hold, I can at least endeavour to devote all my energies to the performance of its duties.

Early in September of this year I received from the Falkland Islands a box, dispatched by Mr G. Millen Coughtrey, a former student of the University, now an employé in the New Zealand Whaling Company. It contained a number of specimens which illustrated the anatomy of the auditory apparatus in the Cetacea. The whales were caught in the South Atlantic, mostly at South Shetland, though some were from Graham's Land, at which place he had been whaling last season.

The specimen was presented to me by Mr G. Millen Coughtrey, who obtained it in Admiralty Bay, South Shetland, lat. 62° S., and long. 58° W., in 1912. It was procured in about 20 fathoms, and was brought to the surface when the ship's anchor was weighed. It consisted of white, delicate, thread-like spicules collected into two tufts or bundles. At the first glance the threads might easily have been mistaken for white hair, but they would not burn; neither were they calcareous, for they were not acted on by mineral acids. From their vitreous appearance they were obviously siliceous and indeed were not unlike spunglass. Their aspect and composition led me to regard them as belonging to a siliceous sponge, but the body of the sponge was wanting. In its absence one had to rely on the characters of the tufts and spicules in attempting to determine the genus of the sponge.

If we start with a determinant A of order n, and, using exclusive umbral notation, take the minor of the (n — k)th compound of A, Sylvester has shown that

My last communication in reference to the history of bigradients (Proc. Roy. Soc. Edin., XXX. pp. 396–406) brought the record up to the year 1859. The present paper continues it to the year 1880.

In the stream-line flow of a viscous fluid through a circular pipe of radius a, the velocity of flow at any radius x is given by

where

In a communication to the Royal Society of Edinburgh, Mr J. D. Hamilton Dickson has examined with great care the valuable results of Professors Dewar and Fleming on the thermoelectromotive forces of various couples, and has come to the conclusion that the curve representing the thermo E.M.F. is in every case a parabola whose axis is, not vertical as had always been assumed, but inclined a definite though very small angle to the E.M.F.-axis.

This remarkable result has led me to go back to some experiments which I made a few years ago on the thermoelectric properties of longitudinally strained metal wires, to see if by any chance the same phenomenon might be detected there, and in one instance (only) I have been able to establish its existence unmistakably. The experiments in question, which I have described elsewhere,† were made on couples consisting each entirely of one and the same pure metal; but one wire of the couple might be subjected to any desired longitudinal tension while the other remained unstrained. The temperatures of the junctions were the same in all the experiments, one junction being steam-heated, the other water-cooled.

The path of a ray of light in irrotationally moving media was first investigated mathematically by Fresnel, who showed that to account for the observed phenomena it is necessary to suppose that, the æther being fixed, the medium imparts of the amount of its own motion, resolved in the line of the refracted ray, to the advancing disturbance. This conclusion is also a necessary consequence of the modern Theory of Relativity, which, while holding that, with reference to axes with regard to which the medium is stationary at any point, the speed of light depends only on the refractive index, for any other system leads to the above result.

Every science has two aspects or two stages in its development. In the first, the inductive stage, observations are made and compiled, and axioms or laws are laid down. In the second or deductive stage the laws are applied by syllogistic reasoning, mathematical or otherwise, to elicit conclusions which either disclose new facts or show the inevitable connection between facts already known, and, in either case, complete the claim of the study to the rank of a science.

In the study which has been the subject of the foregoing pages we have always considered the motion of the air to be regulated by a distribution of pressure balanced by the rotation of the earth, except in regard to the surface layer and one other suggested exception when the momentum of the general westerly circulation was invoked. It should here be noted that by this limitation to what may perhaps be called “great circle motion,” we are considering almost exclusively the circulation above that half of the earth's surface which is north of the northern tropic and south of the southern one.

In a previous paper (Proc. Roy. Soc. Edin., vol. xxxi. p. 342) a method was described for measuring small degrees of enzymatic peptolysis, and in a subsequent paper (Proc. Roy. Soc. Edin., vol. xxxii. p. 251) the conditions were dealt with under which such experiments could be carried out with the greatest possible guarantee of sterility combined with the least interference with the reaction.

The intention was to employ these methods for the purpose of pursuing the main object of research—the activation of zymogens in germinating seeds—and it was accordingly decided to carry through a series of experiments on germinating barley. This material was selected on account of the readiness with which it may be obtained.

The extinction of the Tasmanian aboriginal in 1876 closed, for all practical purposes, the further scientific study of this ancient and highly interesting race, and it appeared almost certain that our knowledge of this people would remain dependent on the earlier works of those who were fortunate enough to have studied them during life, and on the few remains housed in such fortunate centres as London, Paris, Edinburgh, Oxford, and Cambridge.

In December 1910 we published, in conjunction with Dr K. Stuart Cross, in the Proceedings of the Royal Society of Edinburgh (1, 2, 3, 4) a series of four papers dealing with the relations of the Tasmanian aboriginal to Pithecanthropus erectus and to primitive man generally. In an earlier publication, published in the Transactions of the Royal Society of Victoria (5), we also made available the material upon which our Tasmanian work was based. In the present publication we propose to deal with the question of the relationship of the Tasmanian aboriginal to the Australian, with a view to deciding, if possible, the vexed questions as to whether the Tasmanian and the Australian are one and the same race, or, if not, if the Australian is a homogeneous or a heterogeneous race.

Investigations into the nature of the organic matter in oil-shales began at the time of the famous Torbanehill case in 1854, when experts attempted to settle the question as to whether the substance known as “ Torbanite ” or “ Boghead Mineral” was a coal or an oil-shale. Several witnesses at the trial (Gillespie v. Russel, Session Papers, 1854) maintained that the oilproducing material in the Mineral was of organic origin, while others pronounced it to be bituminous and produced by subaqueous eruptions. T. S. Traill, M.D., proposed for the Boghead Mineral the name “ Bitumenite,” as it seemed to him to “ consist of much bitumen, mingled with earthy matter” (Trans. Roy. 8oc. Edin., 1857, xxi. p. 7). Dr Redfern (Quart. Jonrn. Micros. Soc, 1855, x. pp. 118-119), on the other hand, supposed the round orange-yellow bodies which occur in torbanite to have had their origin in "“ a mass of vegetable cells and tissues which have been disintegrated and otherwise changed by maceration, pressure, and chemical action, and subsequently solidified."” C. E. Bertrand and B. Renault (Bull. Soc. Hist. Nat. Autun, 1892-3) on microscopic examination have classed these bodies as the remains of gelatinous algae which have been altered by bacterial action.

The general effect of products of combustion would be to cause a transformation of the small ions of the air into large ions, which, acting alone, would tend to decrease the air conductivity. Ionisation by flames, however, adds to the number of ions in the air, so that the size of the ions might be increased without the conductivity of the air diminishing. In the case of the fresh smoke direct from the forge or colliery chimneystalks or railway engines of our experiments, it is suggested that combustion in the furnaces would result in an ionisation producing more positive than negative ions. It is only where similar conditions obtain that we should expect such large increases in the positive potential Gradient, due to smoke, as we have recorded.

Of the more recent researches on the subject of this paper, mention may be made of the work of H. Zahn* on the galvanomagnetic and thermomagnetic effects in various metals. Zahn has measured these effects in many different metals, and has used his results to test the electron theory of the properties of metals as developed by P. Drude. He has also determined in some cases the temperature variation of the effects.

The author of the present paper has confined his attention to the thermomagnetic transverse effects and the Hall effect. These have been measured in magnetic fields of various strengths and at temperatures varying over a range of about 100 Centigrade degrees.

The experiments were carried out with a view to obtaining some light on the electron theory, and the ratios of the effects are discussed in relation to this theory.

1. In the Transactions of the South African Philosophical Society for January 1905, Dr Thomas Muir gives the most general continuant resolvable into factors by means of a given set of line-multipliers. He starts with the multipliers and determines the continuant resolvable by them. At the end of his paper he gives another continuant and its factors, but not the line-multipliers, which he says “is equally interesting in itself and equally full of promise as a base for investigation.” Throughout his paper Muir is dealing with one of the two determinant factors of order n into which every centro-symmetric continuant of order 2n can be broken up. Starting with the larger continuant of which Muir's is a factor, one of the objects of this paper is to determine a set of row and column multipliers that will cause the continuant to break up into quadratic factors and thence into linear factors. Other and more general types of continuants are given which these same multipliers reduce to quadratic factors. Another and more convenient way to determine the factors of these determinants is obtained in the form of reduction formulas It is also shown how, for the two parts of order n into which the larger continuant of order 2n breaks up, the linear factors come out by reduction.

In the new and rapidly developing experimental science known as “Experimentelle Pädagogik” in Germany, “Pédagogie expérimentale” in France, and “Experimental Pedagogy” or “Experimental Education” in this country and in America, two well-marked and not entirely consistent tendencies have been hitherto manifest. On the one hand, there has been a tendency, more particularly in Germany, to develop the work in the new field on the lines of experimental psychology, and to employ almost exclusively the apparatus and methods of that science. On the other hand, there has been a tendency, to a very marked extent in this country and in America, to endeavour to carry on experimental work entirely without the aid of exact and elaborate apparatus, eschewing, even regarding as “tabu,” the methods of the psychological laboratory. Both tendencies are perhaps more or less inevitable, and both to a certain extent may be said to have been justified by results. Nevertheless, there are certain obvious dangers and defects inherent in both, and the whole situation is itself dangerous for the new science.

“Echini are a particularly good group in which to study questions of variation, because here variations can usually be expressed in very definite terms of numerical or other equally positive character.” On this account, and because, in spite of much description, the variants liable to occur in sea urchins have not yet been exhausted, the three specimens described below are recorded. Each of these exhibits a pronounced abnormality in the major symmetries. Two of them resemble another abnormal echinoid in the same collections, already discussed in Proc. Zool. Soc., in lacking part of a definite ambulacrum; but the means by which the tests have accommodated themselves to changed conditions of growth differ markedly in each of the three cases. The third specimen exhibits, in place of the normal five-radiate arrangement, almost perfect hexamery—a type of abnormality very different from that of the first two specimens. For in these the distortion is due to incomplete development caused, by interference with the processes of growth, while there the hexamery is a fundamental change in symmetry, is congenital in origin, and probably represents the type of variation known as duplication of parts.