The portions of sheet-lead above mentioned had attracted my attention on the days following the 4th of February, when engaged in repairing some damage which had then occurred to the electric wires connecting the Nelson Monument and the Observatory; and finding that plumbers (employed by the Town-Council) were removing the old lead and substituting new in its place, and being also encouraged by Professor P. G. Tait, who with me visited the spot, to believe that the markings which had been discovered were electrically of unusual interest, I lost no time in applying to Mr J. D. Marwick, town-clerk, for those portions of the leaden covering which contained the marks in question, with the View of presenting them to the Royal Society.

In two previous communications made by the author to the Royal Society of London, it had been endeavoured to show that earth currents and auroræ, which occur simultaneously with magnetic storms, are secondary currents due to the small but abrupt changes in the magnetism of the earth which such storms denote. Earth-currents also occur during periods of magnetic calm, but they can then be rendered visible only by means of a delicate galvanometer.

In the course of investigations which the author had been led to make in connection with a Treatise on Natural Philosophy which he and Professor Tait are about to publish, he met with some remarkable theorems, which appear to be new and of considerable importance. As the details of the investigations will soon be published, a very brief sketch only is given here.

The following paper gives an idea of the nature of the physical applications of quaternions to which I referred in a previous note (Proceedings, April 1862), but which other avocations have, as yet, prevented me from developing into a form and bulk suitable for publication in the Society's Transactions. The equations I now give form the basis of the investigations in question, which I hope to present to the Society in detail on some future occasion.

What Matter or Force may be, we have not as yet the slightest idea. Matter is only known to us by the forces it exerts or resists. It is possible that there may be but one species of ultimate parts (molecules or atoms?) of matter; but in the present state of chemical science, it is more philosophical to reason as if the ultimate parts of the various elementary bodies are distinct. However this may be, a particle of hydrogen, oxygen, sodium, or gold, exerts certain definite forces upon other particles; which forces, we have every reason to believe, will remain for ever unchanged, unless the so-called element should at some future time be decomposed.

We, the President and Fellows of the Royal Society of Edinburgh, desire humbly to approach your Royal Highness with the expression of our dutiful and heartfelt congratulations on your Royal Highness's marriage.

Ever ready to rejoice at whatever affords a prospect of increased happiness to your Royal Highness, and a further security for the continued sway of a Royal House which has conferred on this realm so many benefits and blessings, we hail with especial interest and gratification the union of your Royal Highness with a daughter of an ancient nation, distinguished at all times for noble and generous qualities, and which holds a high place among the countries of Europe in literature and science; and above all, we regard it as an unspeakable boon that the Royal Lady whom we now welcome to our shores is endowed with all those virtues and attractions which are best calculated to bless and adorn domestic life, to assist in cheering the widowed solitude of our beloved Sovereign, and to sustain in unsullied lustre the honour and dignity of the British Court.

Gentlemen,—The opening of our Session requires that I should lay before you the state and prospects of our Society, which I hope may to some extent be considered the criteria of the state and prospects of the sciences which it cultivates.

The Society has lost since the commencement of last Session by death, six Fellows, viz.,—Robert Allan, Esq., Beriah Botfield, Esq., Dr James Keith, Dr David Boswell Reid, Professor Connell of St Andrews, Professor Mitscherlich of Berlin; and by resignation, two, the Rev. G. V. Faithfull and D. E. Hay, Esq.

The Author has in this paper traced to its consequences the assumption, as if it were an axiom, of the proposition “That the angles of a triangle are together less than two right angles.” The results as regards the theory of parallels are such as to imply that such lines would have most of the properties of equal circles exterior to one another.

Professor Tait reminded the Society that, at the close of last session, he and Balfour Stewart, F.R.S., of the Kew Observatory, had deposited with the Secretary a sealed packet containing the coincident results of certain investigations which they had separately carried on from totally distinct points of view, and which appeared to lead to a new principle in Natural Philosophy.

These beds, as examined by the author, lie in the Torlin or Kilmorie Burn basin, in the Scoradale or Slidry Water basin (more strictly in the first north or north-west tributary of each, reckoning upwards from the sea), and in the Clachan Glen,—all in the southwest of Arran. They are of great extent and depth; at certain points they contain boreal shells in considerable numbers. They are divisible into two classes, (1.) underlying fine dark sands and clays; and, (2.) overlying coarse red clay with striated stones, probably boulder clay.

The author described the contents of the small tubular appendages, named Nematophores by Busk, which are developed upon certain definite points of the hydrosome in the Plumularidœ. These contents were shown to consist of a granular protoplasm, with occasionally a cluster of large thread-cells embedded in it.

The protoplasm has the property of emitting pseudopodia, which are very extensile and mutable in shape, and exactly resemble the pseudopodial prolongations, whose occurrence among the Rhizopoda is so eminently characteristic of this group of Protozoa. The contents of the nematophores, indeed, except alone in the presence of thread-cells, are indistinguishable in structure, and in the phenomena presented by them from the sarcode or protoplasm, which forms the substance of an amœba, a difflugia, or an arcella.

In the year 1835, Principal Forbes very carefully observed the temperatures of certain springs in the Pyrenees, with the view of ascertaining to what extent changes of temperature occur in them. Observations previously made were, for several reasons, of uncertain worth, and Principal Forbes was desirous of then fixing “data for future observers with a degree of accuracy hitherto unattempted.”

The author having determined to spend his autumn holidays in the Pyrenees, believed that a careful repetition of such observations, after the lapse of twenty-eight years, would afford results of some interest. He furnished himself with accurate thermometers made for the purpose, and, during the month of August, carefully observed the temperatures of several of the springs visited by Principal Forbes in 1835.

The Author compared the above crania with various human skulls which had come under his observation. He exhibited a skull brought by Mr Henry Duckworth, F.G.S., from St Acheul near Amiens, which in its general contour presented a striking resemblance to the Engis skull. The St Acheul skull was somewhat smaller, being probably that of a female. It might almost have been regarded as a reduced copy of the Engis skull. There was no evidence that the skull from St Acheul was of an earlier date than the Gallo-Roman period of French history. The Neanderthal skull was compared with several modern crania, mostly British, especially with reference to the projection of the supra-orbital ridges, the retreating forehead, and the slight convexity of the occipital region. He exhibited several skulls which were closely allied to it in one or other of these features.