The PRESIDENT, on opening the Session, said—During the past Session 62 papers have been read. Of these, 14 belong to the department of Physics, 10 to Mathematics, 6 to Chemistry, 4 to Oceanography, 1 to Geology, 5 to Natural History, 4 to Comparative Anatomy, 3 to Anatomy, 6 to Physiology, 6 to Meteorology, and 1 to Literature.

In 1849 William Swan, subsequently Professor of Natural Philosophy in the University of St Andrews, read a paper on the “Gradual Production of Luminous Impressions on the Eye and other Phenomena of Vision” before the Royal Society of Edinburgh (see Transactions, Vol. XVI.). This paper contains some results of high interest, but I have no recollection of ever having seen it referred to in modern literature on the subject.

By means of a large quantity of solid carbonic acid, obtained from the University Chemical Laboratory, it was found possible to solidify, and maintain in the solid form for a considerable time, a large mass of mercury. Preliminary experiments made about a year ago, in the usual manner, by means of a triple circuit (iron, german silver, mercury), did not give results of a satisfactory kind. This was apparently due to the difficulty of maintaining steady, or steadily varying, temperatures.

This paper gave details of a series of experiments made on the same iron wire as was used in experiments described in previous papers. This series was made on the wire after it had been heated to redness and allowed to cool. A linear relation was again found to hold between log. b and n, where b and n are the quantities (constant in any one experiment) symbolised in. the equation yn(x + a) = b, y being range of oscillation and x being number of oscillations of the wire which have taken place since the commencement of the experiment. It was further found that the line representing that relation passed (as did all other such lines previously obtained with this wire) through the point log. b = 2·3, n = 1. Thus the quantity provisionally called the Oscillation Constant in the preceding paper, and regarded as characteristic of the material of the wire, retains its old value even after the wire has been heated to redness.

It is only within a few months that my attention has been (at first accidentally) called to this matter. For, though I owe to the kindness of Prof. Klein a copy of his and Sommerfeld's Theorie des Kreisels, I had passed over, in reading the work, the “Digression on Quaternions” which it contains. But Prof. C. N. Little, in the course of correspondence about his remarkable paper on Knots (whose passage through the press I was looking after), referred me for a numerical detail to an article by Prof. Klein on the progress of publication of Gauss' Gesammelte Werke. Shortly afterwards Prof. Joly called my attention to the same article from another point of view. These references have led me to write the present paper; whose somewhat puzzling title is explained in the first section below.

In the first part of Klein and Sommerfeld's treatise “Ueber die Theorie des Kreisels,” there is a section entitled, Excurs über die Quaterionentheorie. In the preceding paper, Professor Tait has discussed the main conclusion contained in this digression; and I here propose to sketch the line of argument by which Klein and Sommerfeld have arrived at their curious mis-interpretation of Hamilton's Quaternion.

In a paper communicated to the Royal Society, Mr E. T. Günther and the author gave an account of the results obtained from the examination of two samples of water taken from Lake Urmi, and amongst other determinations of a chemical and physical nature, were those of the refractive indices, which were performed with the aid of the Royal Society's large quartz prism and spectrometer, the latter reading by means of micrometers to 2″ of arc. On comparing the values obtained for the refractive indices of the two samples of water with those obtained for the relative densities, it was at once apparent that the former differentiated the two samples quite as distinctly as the latter.

In the “Report on Investigations into the Life-History of the Salmon in Fresh Water,” published in 1898, the changes which the fish undergoes between the months of May and November were dealt with, but there was no material available to enable the observations to be extended throughout the remaining five months of the year, from December to April.

The so–called rectal gland of Elasmobranch fishes claimed notice early in the history of scientific research, as might indeed be expected from the obviousness of its appearance and the invariability of its occurrence. But, in spite of this fact, the rectal gland remains one of those organs the knowledge of the structure of which is unsatisfactory, and the conjecture as to the function of which is consequently hazy.

In connection with some investigations dealing with the velocity of muscular contraction under different conditions, I found it necessary to design a special apparatus for certain experiments. It subsequently occurred to me that, with some modification, this instrument could with advantage be used for various myographic purposes. I was thus induced to make the necessary additions and alterations—adapting the instrument for some special, as well as for most of the ordinary experiments in which a myograph is used.

The unorganised ferments or enzymes which are present in the digestive juices have for many years occupied the attention of physiologists. Although their chemical nature is still doubtful, yet most of their physical and chemical characters are known, and there are methods by which they may be extracted from the tissues and digestive juices. They are generally believed to play the most important part in the digestive process, and within recent years physiologists and pathologists have speculated as to the existence of similar substances in other tissues, and so have endeavoured in many instances to offer a hypothetical explanation of some of the changes that occur in tissue cells themselves. During the last eighteen months I have endeavoured to ascertain the presence or absence of these enzymes in normal and pathological tissues generally. Before describing the method adopted in carrying out this research, with the enumeration of the tissues examined and the results obtained, I shall briefly refer to our present knowledge of the existence of these enzymes in tissues other than those of the digestive tract, as well as to their presence in plants.

In this paper a discussion of the mode of description of the linear paths in the (log b, n) diagram—described in previous papers—was given. It was shown that the assumption that fatigue was induced by oscillation of a wire enabled one, in almost all cases, to predict accurately the mode of description of these paths. In a few cases, however, when the condition of the wire was such that the critical angle fell within the range of experimentally observed angles of oscillation, the mode of description of the linear paths agreed with the supposition that oscillation diminished fatigue. The truth of this supposition seemed also to be confirmed by the observed rate of decrease of oscillations in these cases; but further experimental evidence is required to fully test the point.

The Nemerteans which form the subject of this communication were collected by Messrs F. P. Bedford and W. F. Lauchester during a year's stay in and near Singapore. The number of species procured is ten, nine of which have not hitherto been described. These are Eupolia pholidota, Cerebratulus natans, C. brunneus, C. robustus, C. insignis, C. erythrus, C. sordidus, C. ulatiformius and C. bedfordii. The species previously known is Eupolia quinquelineata (Bürger), but for reasons given it has been considered desirable to change the name to E. melanogramma.

The first traces of the special functions now known as alternating functions are said by Cauchy to be discernible in certain work of Vandermonde's; and if we view the functions as originating in the study of the number of values which a function can assume through permutation of its variables, such an early date may in a certain sense be justifiable. To all intents and purposes, however, the theory is a creation of Cauchy's, and it is almost absolutely certain that its connection with determinants was never thought of until his time.

The character of Jacobi's expansion of this form of alternant will be more readily understood if the two simplest special cases be first considered.

Two curious identities have been established regarding certain aggregates of minors of special determinants; the first, which concerns axisymmetric determinants, having been discovered by Kronecker in 1882, and the second, which concerns centrosymmetric determinants, having been published by me in 1888, When we come to think of the possibility of generalising these identities, it is readily seen that there are at least two lines of attack which suggest, themselves on reading the mere description of the kind of identity; for, in saying that the identities deal with “an aggregate of minor determinants of a special determinant,” we are conscious of two points of limitation in the description, the one signalised by the word “minor” and the other by the word “special.” If, therefore, an identity were obtained regarding an aggregate of which the terms were determinantsunrestricted by a family relationship, we might have one form of generalisation; and if, while retaining the family relationship, we succeeded in removing the restriction as to the form of the parent, a generalisation of a different type might be the result.

The investigation was undertaken to find out in what way the activity of the salivary ferment varied in different diseased conditions of the body.

In my report on the Entozoa, brought home by the “Challenger” expedition, I described two new species as Tetrabothrium torulosum (from Diomedea brachyura) and Tetrabothrium auriculatum (from Thalassœca glacialis and Daption capensis) My descriptions have recently been subjected to adverse criticism by Fuhrmann, who maintains that these two species do not belong to the genus Tetrabothrium, but to the genus Prosthecocotyle; that Tetrabothrium auriculatum is identical with Tetrabothrium (Amphoterocotyle) elegans-heteroclitum, Diesing; that these two Cestodes are not Tetrabothria but typical Tœnice; that my drawing of the scolex of Tetrdbothrium torulosum does not correspond with the actual relations; and that my representation of the masculine genital organs of Tetrabothrium auriculatum is inaccurate.

This part of my memoir on the crania of the people of India is especially occupied with a description of the hill tribes in the Lower provinces of Bengal and the Central provinces. It is based on an examination of a number of crania, the majority of which were placed at my disposal by the authorities of the Indian Museum, Calcutta. Some belonged to tribes speaking dialects of the Kolarian group of languages; others of the Dravidian group.