The Memoir now submitted to the Society, while it details the chief events in the life of a man who occupied a distinguished place in the literature of Scotland, at a period when it had attained a high reputation, cannot claim to be so complete as might be desired. His life was prolonged for several years after nearly all of his early friends had passed away; and since his death many papers have been destroyed or have fallen aside, which would now be of the greatest interest.

Whilst in this way much has been lost that might have given greater completeness to these pages, still, the recent publication of the Diary of his friend Dr Carlyle of Inveresk, has furnished many additional details, and afforded further evidence of the estimation in which he was held by his literary associates.

Several letters selected from the lives of his distinguished friends, and from the Manuscript Collection of the University, in addition to information derived from the short notices of his life already printed, have afforded the materials for preparing this sketch of one, whose career was more varied, while his public labours and literary connections were not less important and extensive, than those of any of his contemporaries.

1. The object of the present paper is to draw a comparison between the results of the mechanical theory of heat, and those of the recent experiments of Messrs Fairbairn and Tate on the density of steam, published in the “Philosophical Transactions” for 1860.

In the year 1859, a book of remarkable power and originality was published by Mr John Taylor, of London, entitled “The Great Pyramid, why was it built?”

On first looking into it, I was unfortunately inclined to fear that its results were unlikely to be very sound; though merely because they seemed to bear, in a hitherto nearly barren, or difficult, and certainly most mysterious field, such a remarkably large crop of rich and promising-looking fruit. But considering afterwards, that that was not the proper frame of mind to be indulged in connection with, and certainly not in place of, strict scientific investigation into the merits of the case,—I read the book carefully, and then searched for the data required to test it, both in the original authors appealed to, and in some others.

1. For eighteen years it has pressed on my mind, that essential principles of Thermo-dynamics have been overlooked by those geologists who uncompromisingly oppose all paroxysmal hypotheses, and maintain not only that we have examples now before us, on the earth, of all the different actions by which its crust has been modified in geological history, but that these actions have never, or have not on the whole, been more violent in past time than they are at present.

In the following remarks I intend to confine myself to the consideration of those compounds which have not only the same composition per cent., and the same molecular weight, but also the same constitutional formula. Such compounds may be termed absolutely isomeric. As the constitutional formula of few substances is fully known, this class is of course a small one, or rather there are few substances of which we can certainly say that they belong to this class.

The general proposition in the theory of commensurables is to determine the conditions under which lines, surfaces, or solidities, connected with prescribed figures or forms, may have their ratios expressible by integer numbers.

The attention of geometers must have been drawn to this subject by the contemplation of incommensurable lines: the altitude of an equilateral trigon is incommensurable with the base; the diagonal of a square incommensurable with the side, and so on. And, when the two sides of a right angle are expressed by two numbers, the hypotenuse is, in the great multitude of cases, incommensurable with the sides: thus, if the sides be 5 and 7 inches respectively, the length of the subtense cannot be accurately expressed either in integers or fractions. However, when the sides are 3 and 4 units, the hypotenuse is exactly 5 of the same units.

The rapid advances made of late in the diagnosis of cardiac and other diseases affecting the organs of circulation, render the present inquiry into the normal or healthy condition of the valves of the vascular system, not more important anatomically, than medically. As the nature and composition of the parts in which valves are found in some instances materially influence their action, I have deemed it necessary to advert briefly to the properties and structure of the veins and arteries, when describing the venous and arterial or semilunar valves; and to the arrangement of the muscular fibres in the ventricles, when pointing out the peculiarities of the auriculo-ventricular ones. As, moreover, much information is to be obtained by comparing analogous structures, I have, in the present instance, not confined my observations to any particular form of valve, but have examined in succession the entire valvular arrangements of the fish, the reptile, the bird, and the mammal; my object being to arrive, if possible, at a correct knowledge of the more elaborate varieties as they exist in man, and in the higher mammalia.