The extraordinary processes developed in connection with the base of the suspensor in the common Indian Cress (Tropæolum majus) have long excited the interest of vegetable embryologists, and have led to the publication of numerous observations on the embryogeny of that plant. As the following remarks are interesting chiefly in regard to the peculiar features in which the germs in two other species of the genus differ from that in the common Indian Cress, it will not be out of place for me briefly to recapitulate the principal facts connected with the development in that plant.

The mode of growth and increase amongst the Coralligenous Actinozoa in general has been more or less fully treated of by various observers, including such distinguished naturalists as Milne-Edwards, and Haime, Dana, Martin Duncan, Fromentel, Agassiz, and others. I do not, therefore, in the present communication propose to pass the whole of this subject in review, but rather to consider the general and special peculiarities of growth and non-sexual reproduction exhibited by the corals of the Palæozoic Period alone. Many of these peculiarities are of great interest, both from the stand-point of the palæontologist, and also as concerns the systematic zoologist, and they have not yet met with all the attention they deserve. To carry out this inquiry, it will be necessary first to consider the general phenomena exhibited by the Palæozoic corals, as regards their mode of growth and increase. We may then examine the bearing of these phenomena upon various points connected with the classification of these ancient corals, and more especially upon their generic and specific affinities and differences. Finally, we may briefly consider the relations which exist between different parts of a compound corallum as regards their growth, and their influence upon the ultimate form of the colony.

The proposed scalars represent the differentials of the three functions, X, Y, Z, of the co-ordinates x, y, z, put under the form

where ◁ represents the operator

and where

.

These functions, equated respectively to constants, are intended to represent a system of orthogonal surfaces.

Observations on the form of the Placenta and on the arrangement of the Fœtal membranes in the Seals have been recorded by more than one anatomist. Alessandrini of Bologna obtained a specimen of the Monk Seal (Phoca bicolor) Monachus albiventer, in the gravid condition, in which the uterus contained a single fœtus.

The method of solution which I have the honour to lay before the Society is founded upon an old and well-known arithmetical process called “ casting out the nines.” It consists in substituting for any number the remainder which that number leaves when divided by nine. As this remainder contains only a single figure, whereas the original number may contain any number of figures, it is obvious that if the remainder can be employed instead of the number itself, a great saving of time and trouble must follow.

Although the subject of the following communication has of late years attracted a great deal of attention among the public generally, it may, nevertheless, be well for me to preface my statements by a few elementary remarks.

It is well known that organic substances, when left exposed under ordinary circumstances, undergo alterations in their qualities. For example, an infusion of malt experiences the alcoholic fermentation; a basin of paste prepared from wheaten flour becomes mouldy; or, again, a piece of meat putrefies when so treated. The microscope shows that each of these changes is attended by the development of minute organisms. In the fermenting sweet-wort the yeast which falls to the bottom of the containing vessel is found to consist of budding cells, constituting the yeast-plant, Torula Cerevisiæ, represented in Plate XXII. fig 2. In the mouldy paste the blue crust which is the most frequent appearance, owes its colour to the spores of a species of filamentous fungus, Penicillium Glaucum, the commonest of all moulds, of which fig. 1 in Plate XXII. represents a pencil of fructifying threads; and the putrid flesh will be probably found teeming with bodies which, in the most typical form, consist of two little rods, connected endways as by a joint, such as are seen at a, fig. 3, Plate XXII., characterised by astonishing powers of locomotion, and, from their rod-like form, termed Bacteria.

In the month of August 1872, Professor Turner suggested as a subject of investigation the structure of the ovary, and development of the ova, more especially with reference to the recently published observations of Waldeyer.

In the month of April 1874, I handed in to the Medical Faculty of the University of Edinburgh, as my graduation thesis for the degree of M.D., an essay entitled “Contributions to the Normal and Pathological Anatomy of the Ovary and Parovarium.”

Concerning the affinities and systematic position of this very remarkable Devonian fish, there has hitherto prevailed very great uncertainty. The two original specimens, discovered by Mr C. W. Peach, in the Old Red Sandstone of John O’Groat’s, Caithness, and described by Sir Philip Egerton, left us in complete ignorance as to the osteology of the head and the dentition, while the evidence they afforded as to the structure of the pectoral fins was by no means so clear as might have been wished for. To quote from Sir Philip's description:—“ The bones of the head, with the exception of a small fragment of the operculum, are wanting, but the impressions left upon the matrix show that they were sculptured in rather a bold pattern, not unlike the ornament on some of the cranial bones of some of the Holoptychii, and consequently differing in this respect from the corresponding parts in Dipterus. The pectoral fins are very indistinctly seen. They appear to have had a short obtuse lobe forming the base, and extending therefrom a set of numerous fin-rays more elongated than those forming the pectoral fin in Dipterus.” To Dipterus, however, in Sir Philip Egerton's opinion, its affinities pointed, as far as could be gathered from the structure of the body as displayed in the specimens, his description concluding as follows:—“ The absence of all evidence as to the dental apparatus of Tristichopterus is much to be regretted. On other points the affinities between this genus and Dipterus are so striking that they cannot be classified in separate families. Accordingly he assigned to Tristichopterus a place along with Dipterus in the family of “Cœlacanthi,” the term being used in its former extended sense, not as now restricted to the peculiar genera Cœlacanthus, Undina, Holophagus, and Macropoma.

Of the periodical variations of atmospheric pressure the best marked are the diurnal oscillations which in tropical and sub-tropical regions are among the most regular of recurring phenomena. In higher latitudes these oscillations become from day to day gradually more and more masked, owing to the frequent fluctuations to which atmospheric pressure is there subjected. If, however, hourly observations continue to be regularly made for some time, the diurnal oscillation becomes apparent in the averages deduced from them.

At the meetings of the Society on February 1 and 15, 1875, I exhibited a number of photographs which had been executed for me in my laboratory by Mr A. Matheson, one of my students who has acquired great skill in working with very sensitive films of collodion. My object in advising him to undertake this work was to discover, if possible, the cause of the peculiar zig-zag form which electric sparks, and specially those of a Holtz machine, always show in ordinary air. At the desire of the Council, a selection of a few of the more interesting of these photographs has been printed (by Mr Dallas, F.R.S.E.) for the Transactions from the original glass negatives, by what is commonly called the carbon process.