This paper describes the remarkable changes which the glacier of La Brenva, on the south side of Mont Blanc, has undergone between the years 1842 and 1846.

It has increased to such an extent, that it has risen against the opposing wall of rock on the side of the valley nearly 200 feet vertically; it has covered a large additional surface of ground, and appears to be approaching the moraines of 1818. The author describes the measures which he took for comparing its size at any future period, and he cites some observations made by the Vicar of Courmayeur (M. Guicharda), which plainly establish its continued motion during winter.

The object of this memoir is to effect the solution of differential equations, and equations of differences, in which the index of differentiation is a simple fraction. The process employed is the calculus of operations in which symbols of operation are treated in the same way as symbols of quantity, provided the former are subject to the same laws as the latter.

“In the investigation of the vegetable alkalies which I have made for the new edition of my Hand-Book, I consider myself to have established, in a satisfactory manner, that the alkaline constituent of these substances is ammonia, coupled with a variety of different compounds, such as carbo-hydrogens, organic oxides, chlorides, oxychlorides, sulphurets, amides, and even saline compounds. The ammonia in these substances can be converted into amide, ammonium, or oxide of ammonium, under different circumstances. Although, however, I conceive we are now on the right road with the basic constituent of the alkaloids, we are still very much in the dark with regard to the substances which are coupled with the ammonia. The investigation of these will be a much more difficult problem, if, indeed, we ever succeed in solving it.

The author shewed, in the first place, that the successive radii of a circle forming equal angles with one another, are properly symbolized by the successive expressions, &c., where α is the arithmetical length of the radius, and the angle which the several radii make with one another. He proceeded to shew how this theory of symbols, first advanced by Mr Warren, is applicable to the problems of plane trigonometry.

The author began by adverting to the position of Edinburgh as favourable to the study of geology, from the proximity of the transition rocks, the old red sandstone, and the coal measures; and then stated, that the deposits belonging to the modern epoch were equally accessible and interesting.

In order to illustrate the character of the superficial strata, the author considered, in the first instance, the condition of the surfaces of the rocks, on which these loose deposits rest.

The author, having observed in Iceland some remarkable intermixtures of lava with volcanic tuff; and, more recently, on the coast of East Lothian, a somewhat similar intermixture of masses of greenstone in trap-tuff, conceived the idea that cavities existed underneath the crust of the earth, or deeply seated within it, containing water exposed to heat, and the agitation of which, occasioned by the production of steam, had reduced the materials of trap-tuff to the state in which we find them, which had been afterwards erupted at the bottom of the sea, or forced between the beds of superincumbent rocks.

In continuation of his former paper, Dr Alison proceeded to review the chief facts known in regard to the formation of the oils and the albuminous compounds in organized bodies, with the view of illustrating the modification given by vitality to chemical affinities. The formation of fat or oil in vegetables appears to be effected simply by the separation of oxygen from some of the varieties of starch; but in animals, where no oxygen is evolved, and where, nevertheless, oily compounds may certainly be formed from starch (as shewn by Liebig, Chevreul, and Milne-Edwards), this appears to be effected by an affinity of the greater part of the carbon and hydrogen of the starch, for a small part of the oxygen, to form fat, while a smaller part of the carbon and hydrogen, with the greater part of the oxygen of the starchy aided by additional oxygen absorbed from the air, passes off as carbonic acid and water. In both cases, the essential characters of that affinity, which appears to be peculiar to the state of life, lies apparently in the attraction of carbon for hydrogen, with a much smaller proportion of oxygen than exists in the compounds of these elements existing in the inorganic world; and as no such compound is formed from starch, under the same circumstances in other respects, without the presence of living cells, he regards the formation of oil in living bodies as an effect of vital affinity; although admitting that in the course of the decomposition of animal compounds, by various chemical agents, oily matters may be formed by simple chemical action, as in the well-known example of the formation of adipocere from fibrin.

In this communication, the author described some observations made by him in the autumn of 1845, by which he had ascertained that in the Common Green Polype, as had previously been observed in the Hydra fusca, generation takes place at the approach of winter by the development of impregnated ova.

Professor Thomson ascertained, that, at this season, while a number of the polypes bore the spermatic capsules near the base of the arms, a few animals were to seen, on which, besides these capsules, an ovum was developed from the exterior of the middle of the body.

The author, after referring to the views of former observers, stated, that though he had proceeded to Glen Roy under a strong impression that Mr Darwin's marine theory afforded a solution of the question, he had felt himself constrained, after an examination of the valleys, to abandon that theory, and that he had satisfied himself that the shelves had been formed by lakes of fresh water. He referred to the proofs still existing of the mode in which these lakes had been discharged, and he described particularly the unequivocal traces of an old river course running from the head of Glen Glaster to Loch Laggan, with a delta at the level of shelf 4 on Loch Laggan side, formed by this ancient but now extinct river.

This paper is a continuation of the Register of Observations already recorded at page 29 of this volume of the “Proceedings.”

Being at present chiefly taken up with the computation of his predecessor's observations, the author takes this opportunity of examining into what is going on in other Observatories; and then endeavours, from the results of such a survey, to select some unpursued branch of Astronomy, as the proper subject to which the Edinburgh Observatory should be devoted; and he dwells much on the great caution to be used, in the present multiplication of astronomical observatories, that several of them be not working against each other on the same subject; and urges the extreme importance of first selecting an appropriate object of research, and then following it up with a constancy enduring through ages, after the manner of the Greenwich Observatory, which has consequently produced results of such inestimable service to the promotion of the science.

The tables accompanying this letter include daily observations of three wells and one spring for the greater part of 1842 and 1843.

(1.) On a Fatty Substance derived from Animal Matter.

This substance, derived from a pig buried for fifteen years on the side of a hill, was found to consist of free fatty acids, with a mere trace of animal matter, and no appreciable trace of phosphate of lime. The bone earth appears to have been dissolved by the water percolating through the soil.

This paper the author considered as nothing else than an abstract of the thoughts he entertained on the subject. His object was to shew there was no analogy in nature, rendering a prospective law of progressive development from lower to higher types probable; and he brought forward various examples to prove that, in all cases in which variation took place among domestic animals and vegetable productions, the varieties, though they might be regarded as improved or new, were not permanent, but required selection and care to preserve them; so that new forms and qualities appearing, could not confirm the progressive hypothesis.

The author proceeded to shew that the lake theory of the Lochaber shelves was not inconsistent with any established geological truths, but was on the contrary supported by them.

He alluded to the occurrence in the Lochaber district, as well as in other parts of Scotland, in valleys far from the sea, not only of lakes at high level, but of beach lines on hill-sides precisely analogous to those of Glen Roy, and shewing depressions of water to nearly the same extent. One of the localities referred to is a valley near Inverournan, where three parallel roads are to be seen shewing a depression first, of about 197 feet, secondly, of 94 feet, and lastly, of 184 feet. The blockage required for this ancient lake, and of which a small remnant still exists, was nearly as extensive as that required for Glen Roy.