Last summer I began an investigation of the Müllerian duct of Amphibians at the suggestion of Professor Wiedersheim, to whom I am indebted for most kind advice during the progress of my work, as well as for all the material that I have made use of in the course of it.

I have been able to examine stages in the development of the duct in Rana esculenta, Triton alpestris, Salamandra atra and S. maculosa, Siredon pisciformis (Axolotl), and Desmognathus; but I have paid special attention to Salamandra atra and Axolotl, which have not yet been studied in this connection. The Urodeles are easier to work with than the Anura, owing to the comparatively early formation of the Anlage of the Müllerian duct; and I have found Axolotl to be particularly instructive, as the pronephros and segmental duct persist during the early stages of the formation of the Müllerian duct.

I propose in this paper to describe what I have observed in various stages of the development of these two forms, and to compare the results thus arrived at with the appearances described in the published works on the subject.

The following general description of the capsule, trabeculæ, and sheaths of the splenic vessels is based on the examination of the spleen of the Kitten.

The Tunica serosa consists of a single layer of somewhat thick endothelial cells, which is continuous with the peritoneal lining of the body cavity, and in addition of a thin layer of very finely fibrillated connective tissue that lies immediately subjacent to the endothelial layer.

The Tunica propria differs from a true capsule in that it blends along its whole under surface with the splenic parenchyma, from which it cannot be detached without tearing the splenic substance.

1. Since I had the honour of showing the phonograph to the Royal Society of Edinburgh, at a special meeting in November 1894, the instrument has occupied a good deal of my time and attention, and I now venture to give the general results of the investigation.

2. The instrument chiefly studied has been the machine used in this country known as the “Commercial Phonograph.” Any records taken by myself have been obtained with the ordinary apparatus forming part of the “commercial” speaker arm, but I have always reproduced these with the aid of the so-called “musical” arm. The commercial machine, or, to give it a better name, the English model, is so geared that the wax cylinder, inch (197 mm.) in circumference, makes two revolutions in one second, while the spiral grooves described on the cylinder are inch (⅛ mm.) apart. A spiral line about 136 yards in length may be described on the cylinder, and the recording or reproducing point travels over this distance in about six minutes.

3. I have also used the American model, which resembles in all essential particulars the one just described, except that the grooves on the cylinder are inch (¼ mm.) instead of .

The first two parts of this paper—Physical Geography and Salinity—were communicated to the Society on May 18th, 1891, and published in the Transactions, Vol. XXXVI, Part III., No. 23, pp. 641–729.

Various circumstances have prevented me from sooner presenting the concluding part of the discussion. I postponed publication again and again, in the hope that it might be possible to discuss the results more thoroughly, and deduce from them more clearly than I have been able to do the laws which regulate the heat-transactions of sea-water of varying salinity, contained in basins of differing degrees of isolation from the circulation of the ocean. At length the conclusion has been arrived at that the observations are not sufficiently uniform, regular, and close to warrant the expenditure of the time devoted to their discussion. Many months of work have been occupied in proving that some special manner of classifying and treating the data led to no definite result. Thus, it is unnecessary to describe several series of voluminous calculations, or to bring forward a great number of maps and sections on which the distribution of temperature was plotted in different ways. It is difficult to establish theoretical conclusions of a general and far-reaching kind from my work, and I have not attempted to compare it with the many memoirs published in continental journals, on the temperature of lakes, fjords, and enclosed seas.

Systems of ordinary linear differential equations are of great importance, both from a practical and from a theoretical point of view. They figure largely in dynamical problems; and Jacobi has shown that the general problem of determining the order of any system of ordinary differential equations whatever can be reduced to the problem of determining the order of a linear system with constant coefficients. Nevertheless, the present state of the theory of such a system still leaves something to be desired. It is true that a logical and systematic process for the solution was given by Cauchy. This consists in first replacing the system by another in which only first differential coefficients occur, by introducing as auxiliary variables the successive differential coefficients of the various dependent variables up to the highest but one, and then reducing this system to the “normal form” by calculating the differential coefficients as linear functions of the dependent variables. It happens, however, when we attempt to do this, that we are led to a system consisting partly of differential equations of the form

where fr, denotes a linear function of x1, …., xs, partly of a number of non-differential equations connecting the remainder of the variables with x1, …., xs. The order of the system—that is to say, the number of independent arbitrary constants required for its complete solution—is the number of differential equations in the normal form; but no rule is readily deducible from the method for determining beforehand how many of the equations in the normal system will be differential equations, so that we cannot predict the order of the system without actually going through the labour of reduction. Moreover, the normal form is in practice often not the most convenient for the purposes of solution.

On July 20th, 1891, I communicated to the Society a short note on the effect of longitudinal magnetisation on the interior volume of iron and nickel tubes (see Proceedings, 1890–91, pp. 315–7). These earliest results of observation of a new and interesting phenomenon in magnetic strains were obtained during my last few months' residence in Japan. In following out the lines of research therein suggested, I have been fortunate in having had placed at my disposal by Professor Tait the resources of the Physical Laboratory of Edinburgh University. I desire here to record my great indebtedness to him for the interest he has taken in the work, and for his many helpful suggestions. In surmounting the many experimental difficulties met with at every turn, I had the invaluable co-operation of Mr A. Shand, a senior student in the Physical Laboratory. Various results obtained since 1892 have been communicated in short notes from time to time (see Proceedings, 1891–2, pp. 85–88, 249–252; 1893–4, pp. 295–7; 1894–5, pp. 334–5; see also B. A. Reports, 1892 and 1893); but it was not possible to regard these as altogether satisfactory. It was only in May of last year (1895) that the many sources of error were finally got rid of, and the apparatus perfected. The present paper deals entirely with the results obtained since then. In these later experiments I was ably assisted by Mr A. C. Smith, a student in the Physical Laboratory.

In the report on Oceanic Circulation, based on the observations made on board H.M.S. “Challenger,” and other observations, which was published in the beginning of 1895 as an Appendix in the Summary of Results, Second Part Challenger Reports, the specific gravities dealt with were all at the standard temperature of 60° Fahr., the standard density being that of distilled water at 39°·2 (4° C). By this method of treatment the question of the salinity or saltness of the water is approximately stated, unquestionably one of the most important questions affecting the physics of the ocean. But the movement of the water, or oceanic circulation, as resulting from different densities, can only be represented by stating, not the specific gravity reduced to the uniform temperature of 60°, but the specific gravity at the observed temperature at all points in the ocean at which observations are made. In this paper these specific gravities are viewed in their relations to the circulation of the waters of the ocean.

The genus Anaspides was founded in 1894 by Mr G. M. Thomson of Dunedin, New Zealand, for the reception of a very remarkable Schizopod Crustacean which he had discovered in a fresh-water pool at an altitude of 4000 feet on Mount Wellington in Tasmania. The very striking peculiarities of the animal, the absence of a carapace, the presence of plate-like gills attached to the bases of the thoracic legs, and the possession of an auditory organ in the peduncle of the antennules, led its discoverer to regard it as the type of a new family of Schizopods, the Anaspidæ, while suggesting that it might be entitled to “even higher specific rank.” I have had an opportunity of examining three specimens of Anaspides presented to the Museum of University College, Dundee, by Dr Chas. Chilton of New Zealand, and from the dissection of one of these I have been able to supplement, in some important points, Mr Thomson's account of the external anatomy of the animal. I wish also to call attention to the remarkable resemblance, indicative I believe of close affinity, which Anaspides bears to certain Palaeozoic Crustacea belonging to a group hitherto supposed to be unrepresented among living forms. The present paper has been prepared under the direction of Prof. D'Arcy W. Thompson.

During her famous circumnavigation of the world, H.M.S. Challenger left the Cape of Good Hope on the 17th December 1873, and, proceeding in a south-easterly direction, visited in succession Prince Edward and Marion Islands, the Crozet Islands, Kerguelen Island, and Heard Island. From Heard Island the Expedition sailed southward, and on the 16th February 1874 passed ten miles beyond the Antarctic Circle in longitude 78° 22′ E., the ship being at this time surrounded by a large number of huge tabular icebergs, some of them four miles in length, and all with perpendicular sides rising about 200 feet above the sea-level. From this most southerly point the Challenger took a north-easterly course towards Melbourne in Australia, where she arrived on the 17th March 1874.

The following essay, except for one or two slight corrections and additions which I have since interpolated, was read before the Eoyal Society of Edinburgh in June 1894. Very shortly thereafter, M. Jean Svoronos published in the Bulletin de Correspondance Hellénique (Janv.–Juillet, 1894) a learned paper “Sur la signification des types monétaires des anciens,” in which he demonstrated with an elaborate wealth of illustration the astronomic significance of many coin-types, the precise point that the greater part of this essay of mine was written to prove. Beginning with coins on which a beast- or bird-emblem is figured together with the symbol of a star, and passing on to others where the star-symbol is omitted, M. Svoronos shows clearly that in a very varied series of coin-types, the Lion, the Bull, the Eagle, the Horse, and so forth, represent not merely these creatures themselves, but their stellar namesakes: in short, that, in more or less obscure and occult shapes, astronomic emblems are imprinted on a vast range of ancient coins, just as in open and acknowledged forms they are visible, for instance, on the coins of Antoninus Pius. So clearly is all this put forward by M. Svoronos that my paper might well have remained unpublished were it not that I think I take the case somewhat further than he does. For, whereas M. Svoronos is content to demonstrate the symbols of individual constellations, I have attempted also in certain cases to show that the associated emblems correspond to the positions relative to one another of the heavenly bodies, in some cases to the configuration of the sky at critical periods of the year or at the festival seasons of the cities to which the coins belong. In some other respects, also, I have attempted to carry to a further issue the general considerations suggested by the astronomic hypothesis.

The main features of the scope of this paper are indicated by its title, from which it will be seen that I do not regard the current descriptions, which appear in textbooks of human anatomy, as providing an adequate conception either of the attachments or of the functions of the muscles at present named “Dorsal and Palmar Interosseous.” It may seem strange, in connection with such an exact (and, according to some, exhausted) science as human anatomy, that it should be possible to doubt the accuracy of modern text-books concerning such an apparently elementary consideration as the description of a group of muscles in the human hand; but we must bear in mind, first, the ease with which a statement is handed on from author to author without renewed investigation, if only, in the first instance, it has been stamped with the approval of a recognised authority, and second, that these descriptions were originally constructed with little or no reference to the facts of comparative anatomy. It is only by a series of careful comparisons that we can arrive at a proper understanding of the homologies of individual muscles or of groups of muscles in the human subject.

The group of questions which are connected with the Glacial Age seem to me to be among the most interesting and the most difficult in the whole science of geology. They include the question of Time—since, perhaps, the only hope we have of even reaching any unit of time in geological changes lies in the phenomena of the Glacial Age, The question of the comparative slowness or suddenness of great physical changes is not less directly involved. Bound up with this again is the question of the sudden or slow destruction of the extinct forms of life, and the introduction of new forms to replace them. The connection between Cosmical and Terrestrial causes of change comes directly into our view, and then the nature and operation of the terrestrial forces which were brought into play. I am very sceptical as to many of the solutions which have been proposed for most of these questions, and still more for the theories which profess to answer them as a whole. There is nothing to be done but to accumulate evidence in detail—to observe facts well, that is, completely—and avoid looking only at such of them as tell in favour of some preconceived hypothesis.

The theory of the singular solutions of differential equations of the first order, even in the interesting and suggestive form due to Professor Cayley (Mess. Math., ii., 1872), as given in English text-books, is defective, inasmuch as it gives no indication as to what are normal and what are abnormal phenomena. Moreover, Cayley added an appendix to his theory regarding the circumstances under which a singular solution exists, which is misleading so far as the theory of differential equations is concerned, if not altogether erroneous.

The main purpose of the following notes is to throw light on the point last mentioned by means of a number of examples. I have also taken the opportunity to furnish simple demonstrations of several well-known theorems regarding the p-discriminant which do not find a place in the current English text-books.

1. Relation to Magnetic Survey.—After being engaged for sometime, in conjunction with Professor Thorpe, upon the Magnetic Survey of the United Kingdom, Professor A. W. Rücker, F.R.S., put forward his theory of Terrestrial Magnetism.

In connection with this theory, it was desirable to determine the permeabilities of various rocks, both at ordinary and at high temperatures.

2. The investigation which forms the subject of the present paper is an instalment in this direction. Professor Rücker proposed this undertaking and indicated the plan to be followed. It was then carried out under his supervision at the Royal College of Science, London.

The case under consideration was brought to my notice while I was attempting to arrange a colour match by the well-known disc method. The colour was somewhat like lilac, though rather more red. A number of onlookers—including the gentleman whom I afterwards found to be colour-blind, and whom I shall in this paper denote as Mr A.—pronounced the match fairly satisfactory. Mr A. subsequently remarked to me that he sometimes had a difficulty in distinguishing greens and blues. He said, also, that he had, though much less frequently, a difficulty with reds. This condition is so abnormal that I at once handed him a direct vision spectroscope and asked him to name the colours which he saw in succession from one end of the spectrum to the other. He said that red was the first. “And after the red?” I asked; “green,” he said: “and after the green?”; “blue.” And when asked what followed the blue, he said that the rest of the spectrum was blue throughout the whole extent. When asked if he saw white light between the red and green colours, he was very undecided, but said that he did not think he would call it white—it might be yellow.

In the following pages I have attempted to analyse various groups of figures derived from the records of the Royal Infirmary. When appointed Medical Registrar to the Infirmary in October 1891, it occurred to me that it might lead to interesting results if the admissions into the Medical Wards were contrasted with the varying states of the atmosphere, a sufficiently long time being taken to avoid the fallacies attendant on statistical generalisations from insufficient data. At first my intention had been to investigate the influence of the weather on the diseases of the principal systems, but as the work progressed I found that the repeated attacks of Epidemic Influenza so modified the results that I had perforce to take up the study of that disease in addition. The Infirmary year begins on the 1st of October; and, although the figures might have been calculated with some trouble for the year from the 1st of January, they have been left for the most part in their original form. The period to which most of the figures relate comprises the seven years from 1st October 1888 to 30th September 1895. Each case is noted as on admission, and each death as it occurred. Most of the figures are given as weekly totals. The year 1888–89 is included because no epidemic of Influenza occurred during it. In each of the other years epidemics were present.

For many years the Fossil Flora of the Yorkshire Coal Field has been engaging my attention, and among the species occurring in that district are many of considerable interest. This Coal Field supplied Artis with the specimens which he figured and described in his Antediluvian Phytology.

In 1888, at the Annual Meeting of the Yorkshire Naturalists' Union, held at Malton, a committee was formed for the investigation of the Fossil Flora of Yorkshire, and since that date four Reports have been prepared and published based upon specimens submitted to me for examination by private collectors, and from collections contained in public museums. These Reports only contain lists of the species found, and the localities and horizons from which the specimens were derived, with any occasional short notes that might have been thought necessary. All detailed descriptions or critical remarks were deferred, and the present paper is the first of what I hope may be several, dealing more in detail with the Fossil Flora of the Yorkshire Coal Field.