This investigation into the nature of the clay substance contained in the fireclay from Glenboig was undertaken at the suggestion of Professor J. W. Gregory. Professor Gregory thought that the fine material might be halloysite, and the results obtained tend to confirm this view.

The very finest material was separated by repeated washing from a sample of the best clay, and used for the analyses. Although apparently white when suspended in water, the material when dry had a decided buff colour. As the colour indicated the presence of some impurity, efforts were made by further washing to remove it; but with no good result. The sample was dried in the steam oven and analysed.

In his Theory of Infinite Series, Dr Bromwich gives an account of the recently developed theory of non-convergent and asymptotic series, so far as the arithmetical side of the theory is concerned. The connection between Borel's integral “sum” and Euler's well-known transformation

is discussed. Now, if we apply this transformation to such series, for example, as

which are of great interest in the theory of Elliptic Functions, we obtain results which may be described as formless, or at least of such complexity, owing to the mixture of q-factorials (1 − qn)! with ordinary factorials n!, that the resulting series are practically useless so far as the possibility of applying further transformations is concerned.

For many important meteorological purposes it would be an advantage to be able to keep separate records of the components of the wind in two fixed rectangular directions, the north-southerly and east-westerly directions being those that would naturally be chosen. At present the registering Robinson anemometer records merely the total amount of wind that has passed any spot; a separate pen gives the direction; and a somewhat laborious process of calculation is needed in order to obtain even an approximate estimate of the wind-components. The object of the instrument described below is to resolve the wind into northerly and easterly components and to record their absolute values with two separate pens. The instrument is so arranged that the distance of the one pen from its zero line at any instant will be a measure of the excess of north wind over south wind which has flowed past up to that instant, and the curve traced by that pen will show all the variations of this north-southerly component.

As we have already pointed out (Hist., i. p. 487), bigradients were first brought to light by Sylvester in 1840 in the paper in which he made known his so-called “dialytic“ method of eliminating the unknown from two equations of the same or different degrees. Shortly afterwards Richelot and Cauchy recalled attention to Euler's and Bezout's method of 1764, as giving substantially the same result as Sylvester's, the fact being that the determinant obtained by Sylvester differs from that obtainable in the other case merely by being its conjugate. The details of these papers and of others related to them have already been given.

As has already been pointed out (Hist., i. pp. 485–487), the special form of determinant named “persymmetric” in 1853 by Sylvester came first to light in 1835 in a paper of Jacobi's on the elimination of the unknown from two equations of the nth degree, the fact being that the adjugate of Bezout's condensed eliminant—in other words, the adjugate of the determinant resulting from Bezout's “abridged method“ of elimination—is there shown to be such that the elements of it whose place-numbers have the same sum are equal.

A method for determining the boiling-points of solids as well as liquids, such that little material is required, and only constant, easily reproducible conditions are involved, is much needed. None of these qualities is possessed by the distilling flask method.

The apparatus suggested consists of a bulblet with a bent capillary not less than 1 mm. in diameter. This is attached to a thermometer and suspended in a beaker (fig. 1). The latter contains water (for substances boiling below 100°), sulphuric acid (up to 200°), melted paraffin (up to 280°), or a mixture of sodium and potassium nitrates (45·5, 54·5 parts) for use from 220° upwards. A stirrer is provided.

When the bulb of a thermometer is enclosed in an evacuated vessel, the dilatation of the bulb introduces a considerable error in the temperature readings. This fact may be well known, but in the literature of boiling-point and vapour-pressure determinations we have observed no reference to it, and no corrections on account of it. Yet, except in the roughest work, this effect cannot be ignored. Thus, a test carried out with eleven thermometers showed that when the pressure round the bulb was lowered from 748 mm. to 20 mm. and thermal equilibrium with the bath had been recovered, the readings were from 0·10° to 0·17° lower. In all but one case, when there was a slight permanent dilatation, the change was constant and was a linear function of the change in pressure. The change bore no relation to the sizes of the bulbs. The thickness of the glass varied considerably, but could not, of course, be measured.

Vapour Pressures.—The submerged bulblet apparatus described in a preceding paper may readily be adapted to determining vapour pressures. The apparatus is unchanged, excepting that the lower part of the thermometer is enclosed in a test-tube containing a portion of the bath-liquid (fig. 1). The interior of the test-tube communicates, through the L-tube, with a gauge, with a pump, and with the atmosphere. The bath is brought to constancy at the required temperature with the pressure in the apparatus above the vapour pressure of the substance. The pressure is next lowered gradually until a continuous stream of bubbles issues from the capillary. Then the pressure is allowed to rise until the stream ceases. The details of manipulation and correction may be understood from the former paper without special description.

During the electrolysis of a solution of potassium ethyl di-propyl-malonate it was discovered by Crichton that when a concentrated aqueous solution of the salt was shaken up with a concentrated aqueous solution of potassium carbonate two distinct layers were formed. The peculiarity of this case lies in the fact that both substances are salts of the same metal, though cases of the non-miscibility of aqueous solutions of two totally different substances are common, as, for example, that of potassium carbonate and alcohol.

Some time ago the author commenced an investigation of the Zeeman effect in the spark spectrum of certain rare elements. The research promised results of considerable interest, as the properties and relationships of these substances are as yet very imperfectly known, and certain of the elements show indication of high magnetic quality. The following elements were examined: uranium, rubidium, gadolinium, samarium, scandium, dysprosium, neo-ytterbium, and lutecium. The author is greatly indebted to Sir William Crookes for his kindness in supplying the scandium, and to Professor Urbain of the University of Paris for the samples of the three last-mentioned elements.

The object of this paper is to derive two relations in magnetism. In substance they are not new, but in method of statement they are, and the derivation presented here is shorter and simpler than other methods.

Consider a ferro-magnetic wire hanging vertically inside a vertical solenoid with heating jacket, a pan being attached to the lower end of the wire for holding weights. Then, if hysteresis be neglected, the state of the wire may be regarded at any time as a function of the three independent variables T, F, and H,—temperature, stretching force, and magnetic field intensity.

The portable gold-leaf electrometer designed by C. T. R. Wilson gives a means of measuring the charge upon and current through a conductor exposed to the earth's field and maintained at zero potential. Further, Wilson has shown (1) that the dissipation factor (the ratio of current per minute to the corresponding charge) is approximately the same for a surface of turf and the metal test-plate; and (2) how to deduce the corresponding charge and current per square centimetre on the neighbouring ground-level. Wilson's measurements were made chiefly in a country atmosphere (near Peebles), and we have made observations with a similar instrument in town air, in and near Edinburgh, to find out whether the dissipation factor is notably affected by the purity of the atmosphere as regards smoke, etc.

1. The three physical states of a substance, solid, liquid, and gaseous, are representable, as is well known, by means of three functions of pressure, volume, and temperature; say

f1(p, v, t), f2(p, v, t), f3(p, v, t).

In the case of water-substance, James Thomson represented these functions as surfaces of his geometrical (p, v, t) model.

No attempt has been made to group these three functions in a single form F(p, v, t), though various equations combining f2 and f3, either empirically or as deductions from theory, have been given; first, and notably, that of Van der Waals. In Thomson's model the process of gradual isothermal and isopiestic passage from one state to another is indicated by motion of the representative point along a line parallel to the axis of volume.

1. At the present moment there is much discussion regarding the means by which properties are hereditarily transmitted from a parent organism to its offspring, and of the extent to which the Mendelian theory is capable of accounting for the facts. In this note it is not proposed to discuss the general question but to investigate the conditions under which the theory of correlation may be applied to Mendelian groupings. Two important papers on this subject have already been published: one by Professor Pearson, entitled “A Generalized Theory of Mendelian Inheritance”; the other, which is largely a criticism of this, by Professor Udny Yule. In Professor Pearson's paper the results produced when two organisms with any number of pairs of different zygotes mate indiscriminately are fully considered. He finds that such a population once established is stable, and he then deduces the parental and fraternal correlation coefficients.

In July 1909 I communicated to the Society a description of the skeleton of Sowerby's whale, and discussed the morphology of the Manus in the Ziphioids, Mesoplodon and Hyperoodon, and in the Delphinidæ. In this paper I propose to consider the morphology of the manus in the pentadactylous Gangetic dolphin, the type example of the Platanistidæ.

The most complete account of the anatomy of Platanista is contained in the chapter on the Cetacea in the important “Anatomical and Zoological Researches” by the late Dr John Anderson. As director of the Indian Museum, Calcutta, he collected and studied both the soft parts and the skeleton in a number of specimens of both sexes. He analysed the constitution of the manus, and assigned to the carpal bones names corresponding with those used in descriptive human anatomy.

During the investigation of the viscosities of aqueous solutions of tetrapropyl-ammonium chloride, Taylor and Moore noticed that the density of a concentrated solution was less than that of a dilute solution at the same temperature. The following investigation, undertaken at the suggestion of Dr W. W. Taylor, shows how the density depends on the concentration and temperature of the solution.

Tetra-propyl-ammonium chloride was prepared from tetra-propylammonium iodide. Silver chloride was added to an aqueous solution of the iodide and the mixture allowed to stand in the dark for some time. The tetra-propyl-ammonium chloride solution which was formed was then filtered off from the solid silver iodide and evaporated to dryness in a vacuum desiccator. The solid so obtained was a white crystalline substance which was very deliquescent. It was tested and found to be free from iodide.

An examination of the existing data of the vapour pressures of mercury shows that at the higher temperatures a most astonishing lack of precision characterises all the measurements. The existing tables, especially above 300°, are therefore completely untrustworthy, a fact which might be guessed from the disagreement between the values they give (see table below). Regnault made his measurements with the thermometer bulb completely immersed in 50 kilos of the violently “bumping” metal. Hence his results are much too high. Ramsay and Young's well-known values were based on observations at four points. The two lowest of these were original: one was the boiling-point, taken from discordant data of Regnault's; and one was a measurement of the pressure at the boiling-point of sulphur.

The apparatus to be described was developed from the submerged bulblet apparatus, a description of which was recently published in these Proceedings (vol. xxx. p. 487).

The Isoteniscope, Bath, and Stirrer.—The substance is placed in the spherical bulb (20 mm. in diameter). The confining fluid, which, when a liquid is being investigated, is the same material as the substance, occupies the lower part of the ∪-tube (fig. 1). The whole instrument, which we have called the Static Isoteniscope, is 24 cm. long. It is suspended, along with the thermometer and mechanical stirrer, in a tall 2-litre beaker, containing a suitable bath liquid. When the substance is a solid, then the ∪-tube is charged with mercury, melted paraffin, a fusible alloy, or a molten salt or mixture of salts. To secure steadiness and equal distribution of temperature, a cylindrical glass screen (cut from a broken beaker) surrounds the bath, and a very active stirring arrangement is used.

The return of Halley's Comet in May of this year gave rise to much speculation as to its possible effects on the earth. As it was expected that the earth would pass through the tail of the comet when the comet passed between us and the sun, many observations were arranged for in order to see if the tail, whatever it was composed of, had any effect on the earth or on its atmosphere. If the tail was composed of matter in any form, gaseous, or fine solid or liquid particles, then it seemed possible to get some evidence of its presence in the atmosphere; or if the tail was composed of electrons, then these would disturb the electrical condition of the atmosphere, and also the magnetic condition of the earth.

If the finger be held vertically in front of the eyes and a distant object be looked at, it is well known that two images of the finger will be seen, quite transparent if the two images do not overlap, and opaque only at overlapping parts. In place of the finger, use a thin rod at a distance of some 6 or more feet, and focus on another vertical rod at a distance of 30 feet or more, so that the second rod is seen between the two images of the first. The apparent position of the second rod will be found to be distinctly nearer than its real position.