Minding has proved a remarkable theorem concerning a variable system of forces defined as follows:—the points of application of the different forces and their magnitudes are given, while the directions are such that a pencil of rays through any given point parallel to them moves as a rigid body.

Muscovite is so easily recognised by its optical properties that the only cases which seemed to me to call for analysis were those which, from being possessed of characteristic colour, were of special interest. Of these the most singular is a variety found rarely in the great vein of Ben Capval, Harris; it occurs in crystals of a peculiar green tint, the crystals are small and have somewhat of a pearly lustre.

In the “Journal für praktische Chemie,” [2] 6, 99, Pfankuch states that “when one adds chloroform to an alcoholic solution of sulphide of potassium a reaction takes place often with explosive violence, and by repeated extraction of the mass with absolute alcohol one obtains a compound which crystallises from alcohol in long prisms, and may be considered as a double salt of sulphide of potassium and sulphoform.”

The rows of a determinant of the nth order having been separated into two sets, one containing the first p rows and the other the rest, if each minor of the pth degree formed from the first set be multiplied by a minor, called its complementary, formed from the second set, and the result have its sign chosen in accordance with a certain law, it is well known as an elementary theorem that the aggregate of the products thus obtained is equal to the original determinant.

I. If be a rational equation of the nth degree, Newton's rule for a superior limit to the number of its imaginary roots depends upon the changes of sign in the series of functions—called, by Sylvester, Quadratic Elements—

n + 1 in number.

It is a matter of some interest to know the relations in which the quadratic elements stand to the roots of the equation. The following method exhibits this relationship, and leads to others of a higher class.

There is no department of natural science which is so defective in its general scheme of arrangement as mineralogy; and its sectional grouping is, if possible, still more defective.

Such correlations as are expressed by the terms, “the Micas,”—“the Felspars,”—“ the Garnets,” &c., are only admissible if the substances united in such groups are included under one general formula, and function in a more or less similar manner as rock-formers.

In the autumn of 1877 I found on stones in a sea-water aquarium in Professor Huxley's laboratory at South Kensington, the curious little Alga which forms the subject of the present paper. I have ever since kept specimens growing, carried them with me to various places in Britain and on the Continent, and subjected them to frequent examination at all seasons of the year. Dr Bornet has kindly identified it for me as a species of Enteromorpha.

While trying to verify by actual statistics some of the “ Laws of Population” first enunciated by Malthus, a curious fact was observed, viz., that some seasons of the year are more prolific in the number of births than others.

This led to the further investigation of the subject, the results of which are before the Society.

Since the liver is an organ whose due activity is indispensable for the maintenance of health; since it is frequently the subject of disorder, and consequently receives a large share of attention from the physician, it is obviously of great importance that he should possess precise knowledge of the manner in which it is affected by medicinal agents.

The following experiments, in continuation of our research on the discharge of electricity, were made in Professor Tait's Laboratory during the College Session 1878–79, and papers briefly describing the results were read before the Society on 6th January 1879 and 19th July 1880.

In the course of a series of experiments upon fusion point, as determined by the mercurial thermometer, I had occasion to investigate several of the properties of that instrument. In the hope that the results of that investigation may economise the labour of other experimenters, and aid in its accuracy, I have ventured to submit them to the consideration of the Society. The memoir comprises the following sections:—

I. Calibration and the calibration unit.

II. The exposure correction.

III. The movement of the zero with (α) time, and (β) temperature.

IV. Poggendorff's correction.

V. Comparison of the mercurial with the air thermometer.

VI. Effect of compression.

In a former paper read before the Society, and published in the Society's “ Transactions,” on ” Some New Bases of the CnH2n—11N series,” obtained from the “ vitriol-tar,” from the distillation of shale, evidence was given of the isolation of three bases of this series, in addition to the Leucoline, Iridoline, and Cryptidine of G. Williams.

In the first paper read before this Society “ On some New Bases of the Leucoline Series,” and published in the Society's “ Transactions,” it was stated that amongst other methods proposed for separating the members of the series and identifying the higher bases, was the process of converting the mixed bases into methyl-iodide compounds by digesting them with the iodide at a high temperature, and separating by fractional crystallisation the bodies so produced. It was found, however, that repeated crystallisation of these bodies could not be effected without great risk of their decomposition. This process was, therefore, abandoned in favour of fractional distillation.

The following experiments were undertaken with a view to determine by actual observation the effect produced on solids by hydraulic pressure.

The instrument was constructed according to my directions by Mr Milne of Milton House, about two years ago, but it is only now that I have been able to devote myself to its application to the purposes for which it was designed. It consists of a hydraulic pump, which communicates with a steel receiver capable of holding instruments of considerable size, and also with a second receiver of peculiar form. This receiver consists essentially of a steel tube, terminated at each end by thick glass tubes fitted tightly. It is tapped at the centre with two holes, the one to establish connection with the pump, and the other to admit a pressure gauge or manometer. The steel tube may be of any length, being limited only by the extent of laboratory accommodation at disposal. The tube which I am using at present has a length of a little over six feet, and an internal diameter of about three-tenths of an inch. The solid to be experimented on must be in the form of a rod or wire, and must, at the ends at least, be sufficiently small to be able to enter the terminal glass tubes, which have a bore of 0·08″ and an external diameter of 0·42″. The length of the solid is such that when it rests in the steel tube its ends are visible in the glass terminations.

In a paper published in the Transactions of this Society for Session 1877–78, I described an experiment which showed, that if a moderately strong current, such as that from four or five Bunsen cells, be led through two jam-pots filled with fragments of carbon, and if any sound be uttered strongly in the one jampot it will be reproduced distinctly, although faintly, in the other. In this experiment it has been found that the fragments of carbon may be replaced by any kind of loose contact, such as microphones, or a handful of screw-nails put into each jam-pot, or vibrating springs beating against metallic stops, or nails laid across each other in log-hut fashion, and that in each case an effect similar in kind, although it may be differing greatly in degree, is produced. Hence it may be almost laid down as a general experimental result, that if an electric circuit conveying a tolerably strong current contain two places of loose contact, A and B, and if any sound be produced loud enough at A a similar sound will be heard proceeding from B.

The alloys which we used in the following experiments were in the form of very thin hard-drawn wires,—the same as those whose thermo-electric properties we described in a paper published in the Transactions of this Society in 1877. They were prepared by Messrs. Johnson and Matthey of Hatton Garden, London. In giving their constitution we rely upon the authority of the manufacturers, as the quantities we had were too small to admit of our having them analysed.

Although the Spectrum whose linear record is now presented to the Royal Society, Edinburgh, is unfortunately not so perfect as it might have been with better apparatus (but which I did not possess)—yet it represents the labour and expense connected with two voyages in 1877–1878 to Portugal; and many weeks work there in both years, with the sun in a more favourable position for observing really solar, and not telluric, or atmospheric, phenomena, than is ever, at any time, obtainable in Great Britain.

Some time before the telephone was invented, I had occasion to consider very closely the problem of the opposition offered to the passage of the electric current by an electrolyte, and to seek for new methods of dealing with it. It was not difficult to see that the telephone afforded advantages in this kind of electrical measurement. As far as regards the measurement of what is usually called Electrolytic Polarisation, these advantages are perhaps even greater than they might at first sight appear. In the case of what is generally called Electrolytic Resistance, they are, however, less than they appear.

On the 26th of last month the full year appointed by Government Contract for the testing of the new Rock-Thermometers having expired, and they having approved themselves at all points, been accepted, and set fairly afloat on a new course of observation,—I hasten to announce the event to the Royal Society, Edinburgh, who have long had a lively interest both in these instruments and in the problems they have been employed upon.

The genera, which I at present include under the family term Platysomidæ, are the following:—

1. Eurynotus, Agassiz.

2. Benedenius, Traquair.

3. Mesolepis, Young.

4. Eurysomus, Young.

5. Wardichthys, Traquair.

6. Cheirodus, M'Coy.

7. Platysomus, Agassiz.