The letter which Mr Small has sent to the Royal Society, and which, at the request of the Council, I have the honour of bringing under the notice of the meeting, was acquired by the University in 1861, at the sale of the MSS. of the late Very Rev. Principal Lee. It is by no means destitute of historical importance, though its main value for us may rest on the consideration that it was written directly from the scene of the convulsion which it describes, by Professor Dugald Stewart to the Reverend Archibald Alison. As a zealous student of political philosophy, Mr Stewart took a lively interest in the early stages of the French Revolution. He accordingly visited Paris both in 1788 and in 1789; and while there he maintained an active correspondence on the subject which engrossed him, with his friend Mr Alison.

The author, preparatory to stating the experiments which he has made on the freezing of the egg of the common fowl, referred to the early ones of Mr Hunter on the same subject, and to the later ones of Mr Paget, both these inquirers agreeing as to the results, but differing in their conclusions, Hunter attributing the resistance which the egg offers to freezing to a supposed vital principle, Mr Paget attributing it to the peculiar viscid state of the albumen.

In this communication the author proceeds to show that when dense bodies, whether liquids or solids, are regarded as consisting of certain molecules, the volumes of these molecules are either equals, halves, or doubles, &c, as in aëriforms.

This he proves by showing that the densities of bodies in general, as determined by the balance, are proportional to the numbers which express the weights of their molecules.

This paper was divided into four parts. In the first part it was shown :—

1. That the actual, not the relative, fertility of our female population, as a whole, at different ages, increases from the commencement of the child-bearing period of life until the age of 30 is reached, and then declines to its extinction with the child-bearing faculty.

2. That the actual fertility is much greater before the climax, 30 years, is reached, than after it is passed.

The subject of this paper, is of a nature to find favour with all those chemists who are disposed to recognise in the fast accumulating evidence of a new and remarkable order of chemical phenomena rich and valuable materials for the construction of a sounder and more comprehensive chemical theory. This new order of phenomena appears to me, nevertheless, but imperfectly appreciated and understood, even on the part of our most distinguished experimentalists. Thus, for instance, Monsieur Pasteur, the illustrious French philosopher, and with him a host of other eminent thinkers, is of opinion, that matter is indebted for its chemical and physical properties mainly and exclusively to the peculiar manner in which the atoms are grouped together. In alluding to the probable cause of circular polarisation, Monsieur Pasteur considers, that this singular property ought to be referred to the unsymmetrical disposition of the constituents, and that the restoration of the chemical symmetry must at the same time obliterate every trace of circularly polarising power.

In this paper only those bodies are considered which are “absolutely isomeric,” that is, which have not only the same composition per cent, and the same molecular weight, but also the same constitutional formula. As the constitutional formula of comparatively few substances is known, this class is as yet a small one.

The science of Crystallography has for its object the classification of crystalline forms.

The principles which must guide us in attempting to arrive at a natural classification of crystals are the same as those which have been so successfully applied to the formation of a natural classification of plants by Ray and Jussieu, and of animals by Cuvier.

By the application of these principles it has been found that crystals are formed on six different types or plans of structure, and in consequence crystals have been arranged in six primary classes, termed crystallographic systems. They are named the cubic, pyramidal, rhombohedral, prismatic, oblique, and anorthic systems.

1. It is the object of this note to give an account of the results of investigations, which have had for their object the discovery of the connection between the form and optical properties of crystals. It is believed that in the results here given, some of the principal difficulties of this important problem have been overcome.

2. The first step towards the solution of this problem was made by Sir David Brewster in 1818. He discovered that crystals belonging to the prismatic, oblique, and anorthic systems, are biaxal; those belonging to the pyramidal and rhombohedral systems uniaxal, while crystals of the cubic system do not possess double refraction (a fact which had been previously stated by Hauy).

It is known that oxides of manganese, when ignited in air, either absorb or lose oxygen, until they attain the composition expressed by the formula Mn3 O4. Schneider found that when they are heated in pure oxygen, they leave the oxide Mn2 O3.

This latter result is not what one might have expected, for we know of no positive action exerted on manganese oxides or on pure oxygen by nitrogen. Thus air should act like dilute oxygen, producing the same oxide.

The author referred to the paper on the Elie Glacial Clay, with Shells, read by him on the 2d of March 1863. During the succeeding summer he learned from Dr M'Bain, that shells had been found in a brickfield near Errol, but so badly preserved, that none of the species had been determined. During the autumn, while staying in the neighbourhood of Perth, he took occasion to visit the Errol brickfield, and found that the shells, which occur in considerable abundance, are precisely the same group with those at Elie.

In Greenock, excavations have lately been made for a new gasometer. The works are now completed, but the superintendent, a most intelligent man, took me to the place, and told me what they had found in the course of digging.

The site of the excavation is close to the shore, and very little above the tide-mark.

At the south-east corner of the works, i.e., most remote from the sea, the workmen reached the rock at a depth of 20 feet. It was a soft shale, and I could not ascertain that any striations were observed on it. Probably there were none preserved on such material. Its upper surface was flat. Towards the sea, or north and west, the rock sloped downwards very steeply, and this seaward face was covered by a great bed or bank of sand, that sloped up from the edge of the rock, and as it receded rose higher as a bank.

In opening this Session of the Royal Society of Edinburgh, at the close of my tenure of the Presidency, I must express my sincere regret on account of the small amount of attendance which it has been in my power to give. I can only assure you that, if I had had the opportunity, my attendance would have been far more regular; and that nothing but the impossibility of reconciling this with other duties has prevented my occupying this chair as often as the honour you have done me, and not less my own inclination, would have led me to do.

In taking the Chair, to which, by your kindness, I have been appointed, it may not be an inappropriate introduction to its duties if, in congratulating you on the prosperous state of the Society, I should refer to some facts in its history, not generally known, which have materially contributed to its prosperity and progress.

In the closing years of the last and in the first decade of the present century, the Society was in a very languid condition. In each of the years 1799, 1802, 1803, 1808, and 1809, only one of the papers read at its meetings was published in the Transactions; and in 1801 and 1806, not a single paper read in these years was published.

The author, after referring to variations in the external form of the body in different individuals, and to the relations between external form and internal structure, proceeded to discuss the subject of variability in the different organic systems. He showed that internal structural variations conferred upon the individual characters as distinctive as any peculiarities in external configuration. It was argued that in the development of the individual a morphological specialisation occurs, both in internal structure and external form, so that each man's structural individuality is an expression of the sum of the individual variations of all the constituent parts of his frame.

Professor Blackie read a paper on Onomatopoeia, or the influence of the imitative principle on the formation of language. Without denying that a number of words in the later development of language were purely notional, that is, intended to represent an idea, not to imitate a sound, he strongly contended, that the whole original stock of language was either direct imitations of natural sounds, or analogical representations of things visible and tangible by things audible. As proofs of this he adduced various illustrations from the Aryan and the Semitic languages.

When we consider that the Phlogistic Theory formed, as it were, the central point round which the facts of chemistry first crystallized into regular scientific form, and that for more than a hundred years it was recognised by all as the foundation of the science, we might reasonably suppose that it should contain at least some germ of truth.

I think I shall be able to show in the following note that not only is this the case, but that the theory itself, as stated by its founders, Beccher and Stahl, is, if not strictly true, a very close approximation to what we now recognise as truth.

On the 6th February 1843, or almost twenty-two years ago, I had the honour of laying before this Society an account of a topographical survey of the Mer de Glace of Chamouni and its neighbourhood, together with the detailed map founded upon it, being probably the first map of a glacier on such a scale ever constructed. Since that time I have never ceased to interest myself in the improvement and extension of this survey. Two subsequent editions of the map appeared, containing the results of my continued observations with the theodolite in 1843, 1844, 1846, and 1850. The last edition (on a reduced scale), in 1853, included the whole of the glacier of Bossons and the results of an extended triangulation, in which the Flegère and the Breven formed the extremities of a new base connected with the stations L, M, and I of my former survey.