In a former communication the æolotropy of iron, demagnetised by the method of decreasing reversals, was shown. During the early stages of induction the permeability is greater to the re-application of a magnetising force in the same direction—whether positive or negative—as that used in the immediately preceding demagnetising process, than to a transverse force. The demagnetisation is complete in the sense that there is no external polarity, and also in the sense that perfect symmetry exists to the subsequent application of the same positive or negative directional field. This symmetry being uni-directional, æolotropy immediately appears if the subsequent magnetising force contains a transverse component.

Of late years a great deal of experimental work has been carried out with the object of determining the effect upon various metals of a load applied and removed many times in quick succession. The chief object of such researches is to determine the maximum stress which can be applied and removed indefinitely without causing fracture of the piece. Little attention has been given to any change in the structure of the metal, except in cases where there has been well-marked permanent distortion. The writer accordingly undertook some simple preliminary experiments in order to ascertain the effect upon the structure of a few alloys of numerous small blows, each of insufficient force to cause a permanent deformation of the specimens.

No branch of dynamics or physics provides a more profitable or interesting subject of study to the student of physics or engineering than that which deals with the phenomena presented by spinning-tops. Within the last few years the most interesting form of top, namely the gyrostat, has advanced from being a piece of lecture-room apparatus, or a toy, to a position of great practical importance. In the dirigible torpedo, Brennan's monorail car, the Schlick device for rendering a ship steady at sea, and in the gyrostatic compass, the results are obtained by utilising the properties of the gyrostat. Undoubtedly, too, the gyrostat is destined to play an important part in many inventions still to be brought to light.

If a railway circular curve spring directly from the tangent, the curvature at the point of contact is discontinuous, since it is zero for the straight line, and finite for the circle. This causes shock whenever rolling stock enters the curve, and at high speeds this is a matter of danger. Further, the outer rail is elevated on the curve, while the rails are at the same level on the straight. This indicates a further discontinuity. The transition curve is introduced to give both a gradual change of curvature and a gradual cant or super-elevation of the outer rail.

The question of the elastic strength of flat plates, supported or fixed at the edges, and subjected to uniform or concentrated loads upon their areas, is, from an engineering standpoint, one of the most unsatisfactory parts of mechanics; for exact solutions, rigorously based upon the laws of elasticity, have been obtained in only a few cases, chiefly for circular and elliptical forms.

Amongst practical engineers the confusion that exists on the subject is remarkable, for the author has, in the course of his inquiries, elicited the most contrary results. As a case in point, there seems no real knowledge whether rectangular and square plates should be ribbed along the diagonals or across the diameters. Again, as an instance of the doubt existing concerning the stress values in these plates, it may be mentioned that, in reply to an inquiry asking for help in this connection, a correspondent in the American Machinist, under date August 7, 1909, deplores the fact that he can obtain no assistance from English or American text-books and states that there is an entire absence of experimental data. Although the latter statement is not quite accurate, yet it can be confidently asserted that there have been very few experimental results recorded, and these few, for the most part, are not available in English.

When Mr Crawford's paper (see pp. 348–389) was passing through the press, Professor Love drew our attention to a paper by Walther Ritz, whose early death robbed the world of science of one whose brilliancy gave promise of a great future. This paper was published in Crelle's Journal in 1908 under the title, “Ueber eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik.” In illustration of this new method Ritz showed how to solve, by a series of successive approximations, the problem of the clamped rectangular plate.

The thorium emanation is given off more or less freely from the compounds of thorium, the best source, according to Professor Soddy, being a preparation of radiothorium in a moist condition. The important members of this group from the medical point of view are mesothorium, thorium X and its emanation.

The presence of the emanation can by shown by the ionising effect in discharging an electroscope, by the phosphorescence it imparts to zinc sulphide, and by its behaviour as a gas. The ionising effect can be produced at a considerable distance, and in consequence after a certain lapse of time. At a distance of ten feet there is a delay of about half a minute before the leaves begin to fall; when once the fall has begun, it continues steadily until the leaves are discharged.

The subject of this paper is a consideration of the mathematics of some of the problems given by present-day developments of Mendelism. Breeding formulas are becoming more and more complex, and it seems probable that many others are yet more complex. Without a suitable mathematical analysis it will be nearly impossible to analyse some of these by direct experiment, while a suitable analysis must always render the method of experimental attack much less obscure. Some of the formulas in the present paper were calculated when I read my last paper* on this subject to this Society, but most of the developments seemed too remote from actual experimental work to render their publication useful. However, a paper published in the last number of the Journal of Genetics, by H. M. Leake, concerning the hybridisation of the cotton plant suggests that the time has come when they may prove of practical value.

In this paper are described some new spinning-tops, gyrostatic apparatus, and illustrations of gyrostatic action devised by the author in the course of the last nine months. The apparatus has been built in the workshops of the Natural Philosophy Institute of the University of Glasgow, and has been employed in illustrating the lectures on rotational motion delivered in the Natural Philosophy classes in the course of the session just closed.

Fig. 1 shows a model aeroplane fitted with a small gyrostat in the position of the propeller. The gyrostat is therefore fixed on the front of the aeroplane with the plane of its flywheel at right angles to the length of the machine. The flywheel of the gyrostat, so fitted, represents exactly the rotor of the engine and the propeller of an actual aeroplane.

In a communication to the Mineralogical Society, published in September 1910 (Min. Mag., vol. xv. p. 390), I suggested that the relation between the component structures of twin crystals was similar to that existing in combinations of crystals of different substances with definite relative orientation (Barker, Min. Mag., vol. xiv., 1907, p. 235), and was determined by equality of molecular distances in the two structures in the plane of contact or composition.

It has been my purpose in the present paper to determine what are the possible, geometrical relations between crystal structures in which such equality exists in all or some of the molecular rows in the plane of contact.

Some time ago, in a paper published by the Royal Anthropological Institute, I applied a Mendelian analysis to that part of the observations made by the late Dr Beddoe (1) which refers to the colour of the hair. In that paper (2) I showed that these observations obeyed in a highly remarkable degree the law referred to, and that this result held from the north of Scotland, through the whole of England, Ireland, France, and Germany, to the south of Italy. At that time I was unable to make any application to the observations on eye colour also published in the same work, but I have now succeeded in completing the analysis.