It was the opinion of Malus, and adopted by Arago, Biot, and other philosophers, that the surfaces of regularly crystallised bodies acted upon light in the very same manner as the surfaces of ordinary bodies, whether solid or fluid; or, in other words, that the reflecting forces extended beyond the limits of the forces that produced double refraction and polarisation. Having been led to question this opinion, I undertook an extensive series of experiments on crystalline reflexion, as exhibited in calcareous spar, a crystal peculiarly fitted for this purpose, from its perfect transparency and great double refraction; and I published the results of these experiments in the Philosophical Transactions for 1819.

Since the publication of my “Observations on the Polarisation of the Atmosphere,” a long and elaborate Memoir on the same subject, by Dr R. Rubenson, has appeared in the Acts of the Royal Society of Sciences of Upsal. The observations which it contains were made with the finest instruments, and with a degree of accuracy which had not been attempted by previous observers. They were begun at Upsal in 1859, and carried on at Rome between the 6th of June and the 5th of August 1861, at Segni in the Campagna, between the 6th and the 27th of August 1861, and at Rome from the 5th of October 1861 to the 27th of July 1862.

In a former paper I described the variation of the fecundity of women according to age, and arrived at the conclusion that the climax of fecundity in women was at or near the age of 25 years. Researches, completed since that paper was read, regarding the variations of length and weight of children according to the mother's age, and regarding the mortality of childbed as influenced by the mother's age, have been published in the “Edinburgh Medical Journal.” The results of these investigations seem to illustrate and confirm the statement made as to the age of the climax of fecundity, for I have found that, about that age, women produce the bulkiest children, as measured by length and weight; and about the same age of the mother there is the smallest mortality in childbed. As still further adorning the age of 25, I may add, that several sets of observations, including some made in St George's-in-the-East, London, and published in the eleventh volume of the “Journal of the Statistical Society,” show a greater amount of survival and rearing among children born of women about that age than at any other; and recently Dr Arthur Mitchell has published a collection of cases of idiocy, with the respective ages of the mothers at the time of the idiots' births, and these also show a smaller proportion born of women about the age of 25 years than at greater and lesser ages.

Before commencing the discussion of the subject, it is necessary to make some definitions, with a view to avoiding the confusion which extensively prevails, from the neglect of the all-important definition of terms. I might be even more exact than I shall be, and excuse myself from adopting such a seeming improvement, on the ground that further refinement of definition would itself cause confusion in the present stage of advancement of our knowledge.

Absolute sterility, I shall hold to mean the condition of a woman who, under ordinary favourable cirumstances for breeding, produces no living or dead child, nor any kind of abortion.

Sterility, I shall hold to mean the condition of a woman who, under ordinary favourable circumstances for breeding, adds not even one to the population, or produces no living and viable child.

Relative sterility, I shall hold to mean the condition of a woman who, while she may or may not be absolutely sterile, while she may or may not be sterile, is, under ordinary favourable circumstances for breeding, sterile in relation to the circumstance of time; or, in other words, in relation to her age, and the duration of her married life.

In a paper on Hemiopsy, published in the present volume of the Transactions (p. 15), I have mentioned the remarkable fact, that the parts of the retina which are insensible to visual, are sensible to luminous impressions, the light being occasioned by irradiation from the adjacent parts of the retina. The parts thus affected in hemiopsy extend irregularly from the foramen centrale to the margin of the retina; but the space which they occupy is so small, their distribution so irregular, and the time of their continuance so short, that it is difficult to make such observations upon them as would establish a general property of the retina.

The idea of chemical structure, as founded on that of atomicity (or the equivalence of atoms), enables us to divide any molecule, whose chemical structure is known, into radicals. The number of ways in which this may be done increases with the complexity of the molecule. Each of these modes of division corresponds to a series of conceivable reactions, some of which have been observed. Any one of these series may be made the basis of classification; but it is obviously most convenient to select for this purpose the most characteristic reactions, and those which are common to such substances as form natural groups. In studying these, we find that each series implies the presence of a particular radical, within which the reactions in question take place. We may call such series of reactions the Generic reactions, and the corresponding radicals Generic radicals. These are sometimes residues of double decomposition, but very frequently this is not the case, and this may account for the fact, that the importance of these generic radicals has been very much overlooked.

The observations which I have now the honour to submit to the Society were made chiefly with the intent to endeavour to ascertain whether, in the instance of the egg of the common fowl, that which may be presumed to be vital action can for a while be arrested, and yet be capable of renewal. Whilst this was the main object kept in view in conducting the trials, a secondary one was to observe, however cursorily, the changes which take place in the contents of the egg when vital development has been prevented.

Having already published in the Transactions a detailed report on the Hourly Meteorological Register kept at Leith Fort, at the expense of the Society, during the years 1824 and 1825, it is unnecessary to enter into any recapitulation respecting the origin and history of this class of observations.

The singular and unexpected results obtained from these Registers, and the rapid approximation to general laws which some of these results exhibited, attached a great interest to the observations of future years; and it is satisfactory to find that the results for the two following years of 1826 and 1827 are almost perfectly coincident with those for 1824 and 1825, not only in their general relations, but even in their numerical laws.

The following communication is an attempt to eliminate the geological history of our Scottish Peat Mosses. So much, however, has already been done in this matter, that the reconsideration of phenomena, for the most part well known, may appear almost a superfluous task. But, notwithstanding the essays of Walker, Rennie, Anderson, and others, in this department of geological inquiry, there is still probably much to be gathered from the same source, which shall greatly increase our knowledge of the condition of these latitudes in the ages that followed upon the close of the glacial epoch. At present, I mean to give only an outline of the subject, reserving for some future occasion a fuller statement of the facts on which the conclusions arrived at are based.

Mr President and Gentlemen,—I beg to thank you for the favourable opportunity which you have kindly afforded, and the facilities you have granted, for enabling me now to try to lay before you some short and simple account of my chief employments last winter at the Great Pyramid of Jeezeh.

My object in going there, was not to excavate, nor to collect antiquities, but merely to inquire instrumentally, and by my own individual labour, into the very discrepant, and sometimes mutually contradictory, accounts which have been published of the form and detail of that ancient monument by writers of almost all nations; and as one chief source of their unfortunate variations seems to have been the usually short and hurried character of their visits, my first care was to apply for leave, from His Highness the Viceroy of Egypt, to occupy the ground at the Pyramid with a permanent establishment, and to stay there as long as might be necessary for the work in hand. His Highness, as I am extremely happy to confess, and with the best of my thanks to acknowledge, was most liberal in his condescensions; conveyed our party, at his own expense to the Pyramids; lent us tents for the period of our stay; and sent a force of twenty men for a month to clean out the interior of the Great Pyramid, or otherwise prepare its more than classic walls for the examination to be made, and which lasted from that time uninterruptedly for a period of four months.

In 1861, in a part of the province of Otago, New Zealand, not previously botanically explored, I made, among other botanical collections, one of Lichens and Fungi. The number of new species and varieties proved to be considerable, amounting to about 20 per cent. of the whole lichens, and 40 per cent. of the whole fungi, collected. Since my return home, I have submitted (with a view specially to the study of the minute anatomy of the reproductive organs and their contents) the new species (and varieties) in question—some of them repeatedly—to microscopical examination: the results whereof are contained in the notes which follow.

In the beginning of the year 1865, I received from the Rev. Alexander Robb, one of the missionaries of the United Presbyterian Church, residing at Creek Town, Old Calabar, Western Africa, a package containing some zoological specimens, preserved in spirits; and in a letter dated 28th October 1864, referring to its contents, he states, there “are also two or three small eel-like fishes.” Some time passed before I was able carefully to examine the package, and I was then at once attracted by these small fish, which I saw belonged to the very distinct and interesting Order of the Ganoid fishes, so abundant in a fossil state in the rocks of our earlier geological epochs, but of which so few representatives are now to be found as living inhabitants of the present waters of our globe.

1. Dr Matthews Duncan having requested me to point out to him some simple method of comparing the fertility of different races, I endeavoured, as a preliminary step, to represent by formulæ some of the chief results which he has obtained in his very lucid and elaborate papers recently read to this Society, and printed in their Transactions for 1863–4 and for the present session. Some of the formulæ which I have obtained are so simple, and accord so well with the tables, that I have thought them worth bringing before the Society.