My duty this evening is to give the usual Introductory Address at the opening of a new Session, this which commences this evening being the Society's 108th.

Before doing so, however, I must try to disburden myself of a weight which has hung heavy upon me for the last few days, and consists in the difficulty, which I find to be insuperable, how to select adequate terms in which to express my sense of the honour which you have conferred upon me, in placing me in the position of your President. In my wildest dreams it never occurred to me that such an event was possible, till a short while ago when certain members of the Council hinted to me that such a step was in contemplation; and I can assure you that it was not without considerable hesitation that I acceded to the request that I should allow myself to be put in nomination.

In the first section of the cruise of the “Challenger,” that from Tenerife to Sombrero, the existence was established of deep-sea muds, perfectly free from carbonate of lime, consisting mainly of silicates mixed with ochreous material, principally hydrated oxides of iron and manganese, and of local concentrations of these materials in the form of nodules and of coatings or incrustations on dead calcareous matter. The qualitative composition of these concentrations was carefully determined, and it was particularly noted that whether in the form of nodules or of incrustations they were aggregations of the general materials of the bottom, and not concretions or coatings of pure hydrous oxides.

It is now a year and a half since I communicated to this Society a description of a portable form of apparatus for enabling us to count the number of particles of dust in the atmosphere. The working of that instrument in my hands has been most satisfactory, and though it has occasionally given trouble, yet it has not given more than might have been expected. Though that apparatus has worked quite pleasantly with me, and enabled a beginning to be made of an investigation into the amount, and the effects, of dust in our atmosphere, yet very few have as yet followed up this line of inquiry. This has probably been owing to there being something in the complicated nature of the apparatus which has deterred others from joining in the work. I therefore determined to see if a simpler, and at the same time a reliable, form of the apparatus could not be devised.

It is well known that pseudomorphic changes take place with many minerals. These changes may be either by alteration or displacement. In the case of carbonate of lime they are generally of the former order.

Among other work conducted at the Marine Station, Granton, during the past year, a number of experiments were instituted with the view of showing how far carbonate of lime was influenced in this direction by metallic and other salts.

Corals, preferably the more porous and soft varieties, were selected for this purpose, and these were exposed to the action of solutions of the following salts:–Chloride of manganese, sulphate of iron, chloride of zinc, chloride of chromium, nitrate of nickel, nitrate of cobalt, nitrate of copper, nitrate of lead, chloride of mercury, chloride of tin, nitrate of silver, phosphate of ammonia.

Two theories have been put forward in order to explain the formation of manganese deposits in marine muds, and more particularly with regard to manganese nodules: one by Murray, in a paper read before this Society in 1876, the other by Buchanan in 1888. Murray assumes the gradual oxidation of carbonate of manganese resulting ultimately in the formation of hydrated peroxide of manganese.

In the “Challenger” Report on atmospherical circulation, the diurnal barometric curves at Gries and Klagenfurt in the Tyrol, and at Cordova in the Argentine Eepublic, are specially examined.

The most noticeable feature of these daily barometric oscillations is their very large amounts, those at Gries, for example, though in lat. 46° 30′ N., being quite tropical in amount; and the singular circumstance is that in no season does the morning minimum fall so low as the daily mean. Gries, Klagenfurt, and Cordova are each situated in a deep valley.

The fluctuation shown by the barographic record occurred immediately after 6 P.M., at the time of the passage of the tornado of Thursday, March 27, 1890, near Owensboro, Davies County, Kentucky. The distance of the barograph from the nearest point of the tornado can be approximated by the evidences of damage the tornado left, and did not exceed a mile and a quarter or a mile and a half. At this distance to the south-east of Owensboro there is a ridge 150 or 200 feet high, and a large brick house on top was unroofed and partially demolished. This is the first evidence of destruction in the vicinity of Owensboro, but previous to this the noise of the approaching tornado was plainly audible to persons on the streets of the town. Until reaching the ridge above mentioned, the tornado appears to have passed in the air, accompanied by a roaring sound, without doing any damage in its passage. From a point about twelve miles to the south-west a tornado passed over the latter city two hours later. The rate of progress of the cyclonic area of low pressure, as shown by the signal service map, was forty miles an hour. On the same day a parallel tornado passed about thirty miles to the south of Owensboro, near south Carrolton. There was none to the northwards.

Persulphuric anhydride and the corresponding acid have been known for some time. Berthelot obtained the former by subjecting a mixture of sulphurous anhydride and oxygen to the effluve électrique (as in the preparation of ozone), and a mixture of the latter with sulphuric acid, by adding the anhydride to water. He also prepared a similar mixture by the electrolysis of sulphuric acid solution in a cell where the electrodes were separated by a porous pot. Both substances he found to be very easily decomposed, spontaneously evolving oxygen. Up till now, however, the corresponding salts have not been prepared. In fact, Mendeléef, while commenting on Berthelot's results, expresses the opinion that persulphuric anhydride is not a true acid-forming oxide, but a peroxide similar to those of the metals barium, lead, &c, and that Berthelot's persulphuric acid is analogous to peroxide of hydrogen. Recently, however, I have obtained the potassium salt, and have since succeeded in preparing it in quantity.

The object of the present communication is to give the purport of the remainder of the letter referred to in the title, as well as that of other letters bearing on the same subject written by the late Mr Froude shortly afterwards, which were not at hand at the time the extract referred to was printed.

Most of the theorems in question occur at the outset of a paper by Professor Cayley, entitled, “Chapters on the Analytical Geometry of n Dimensions” they constitute, in fact, Chapter I. The first theorem I should prefer, for the present, to enunciate as follows:-

If m determinants of the nthorder all have the same n − 1 columns in common, and all vanish, then every determinant of the nthorder whose n columns are chosen from the m + n − 1 different columns must vanish likewise.

The first step is to find an expression for the distances λ, μ, of the centre of the oval from the guides. These distances are to be found separately, beginning with λ.

For this purpose it is indifferent whether we consider the oval as moving in contact with the guides, or whether we consider the guides as variable tangents moving round the circumference of the oval. On the latter supposition, the extremity of λ is evidently the locus of the foot of the perpendicular on the tangent of the oval, whose equation is given in the title.

The question of the effect of wind on the readings of the barometer was first examined by Sir Henry James in a paper read to the Society on March 15, 1852. The observations were made during the succession of gales from the south-west which occurred in January and February of that year, at his house in Granton, with an aneroid barometer, laid horizontally in succession on the table of his room in the cottage, on the seat of the open summerhouse, and on the surface of the ground close to the summer-house, all at the same level. The anemometer employed was of a very simple construction, being on the same principle as the instrument used for weighing letters, the weight or pressure being indicated by the compression of a spiral spring in a tube. A table of results is added, giving the depression of the barometer in decimals of an inch for the velocity of the wind from 14 to 40 miles per hour. At 14 miles the barometric depression was 0.010 inch, and increased gradually to a depression of 0.045 inch at 40 miles per hour. Unfortunately, the number of observations on which the depression for each wind-velocity has been deduced are not given, and the observations in the cottage and those at the open summer-house are combined into one result.

In our previous communications to the Society (see Trans. xxxvi. 211) we described the behaviour of the ethyl potassium salts of normal dibasic acids on electrolysis. These we found always to yield the diethyl esters of normal acids of the same series. We have now extended our investigation to acids with side chains, and in this paper give an account of the electrolysis of ethylpotassium methylmalonate and ethylpotassium ethylmalonate.

It will, I think, be acknowledged that Quaternions, while providing for the physicist a machinery much more natural and graceful than the Cartesian, for all conceptions strictly geometrical, do not at present afford equal facilities for the consideration of questions involving differentiation. It is true that there is one well-known symbol of differentiation of great utility, which enables Quaternions to deal in a suitable manner with many such questions ; but there are left whole classes of differentiations in which the symbol is of no avail.

In a preliminary note communicated last July, I drew attention to what seemed a novel property of iron wire under the combined influence of circular and longitudinal magnetisations. Similar experiments were subsequently tried with nickel, and similar results obtained. It appeared, however, that in some respects nickel behaved oppositely to iron. The first series of observations brought out the fact that a current along the nickel wire seemed to assist the acquiring, under a longitudinal magnetising force, of a polarity oppositely directed to the direction of the current.

The muds, the analyses of which are reported in this paper, were collected in September 1879, during the laying of a cable between Marseilles and Algiers by the India Rubber, Gutta-Percha, and Telegraph Works Company, Limited, of Silvertown, the ship employed being the s.s. “Dacia.” The numbers of the samples are those which were affixed to them on board ship. Nos. 31 to 43 are all from localities lying near the African Coast; Nos. 45 and 46 are from positions between the African Coast and the Balearic Bank. Nos. 64 and 65 are from the Balearic Bank, and Nos. 86 to 89 are from the Gulf of Lyons. The positions and depths are collected in Table I.

The temperature observations recorded in this communication were all taken from the yacht “Medusa,” except those in Loch Morar, which were made from a small rowing-boat, but the sameinstruments and the same methods were used as in the other lochs.

All observations beneath the surface were made by means of Messrs Negretti & Zambra's reversing thermometer in the Scottish frame. The readings are published as they were observed, except that the instrumental correction is applied. The readings may, as a rule, be taken as exact to one-tenth of a degree when the sea was smooth, and when the temperature of water and air had a range less than six degrees. Experiments have shown that if a thermometer be reversed in water at 40°·0, and then brought to the temperature of 46°·0, it would change its indication slightly, and would read 40°·1. At first sight it would appear sufficient to subtract 0°·1 from the reading for each 6° of excess of air temperature over that registered by the instrument, and to add similarly in case the air temperature should be lower. This has not been done, because it was believed that, in summer at least, the cooling caused by evaporation from the wet instrument would reduce its temperature very considerably, and probably enough to make no correction necessary.

In a former jjaper to this Society, we pointed out the important role played by carbonic acid in modern seas, with special reference to the vast deposits of carbonate of lime now taking place in coral reefs and those other calcareous deposits known as Globigerina and Pteropod Oozes. It was pointed out that carbonic acid was the chief agent in the disintegration of felspars and other silicates of the earth's surface, that it was concerned in all the changes that result in the secretion of carbonate of lime by marine organisms from any of the lime salts in sea-water, that a vast amount of Carbonic acid was being locked up in the calcareous deposits now in process of formation on the sea-bed, and that there was an accumulation of these calcareous deposits chiefly towards the equatorial regions of the ocean basins. In the present paper we propose to deal with the great antagonistic power to carbonic acid, viz., silica, and with the siliceous organic remains in the ocean.