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.

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.

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.

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.

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.

The Arithmetical, or, as we should say, Algebraic, Problems of Diophantus involve a single unknown quantity, symbolised by ς′ or ς°′. The number for which this symbol stands is described as πλῆθος μονάδων ἄλογον, and is spoken of as ὁ ἀόριστος ἀριθμός, the undefined number, or simply as ὁ ἀριθμός, the number, par excellence, of the problem in question.

By all commentators, with but one exception so far as I know, the ς′ of Diophantus is taken as an abbreviation of ἀριθμός, and I find the same statement made unquestioningly in the standard Palæography of Gardthausen. The mathematicians, while expressing no doubt as to the fact, show, however, in some cases, a clear enough perception of the difficulty of accounting for such an abbreviation, and are not all agreed as to its more precise origin. Nesselmann, Cantor, and most others, treat the ς as the final letter of ἀριθμός: Heath, who devotes many pages to a discussion of the subject, puts forward, as an alternative and preferable hypothesis, a suggestion that the ς may be a corrupt cursive abbreviation of the two first letters αρ of the same word.

About two years ago I communicated to this Society a paper on the above subject, which was printed in the Philosophical Magazine (1894). The object of the investigations therein discussed was the determination of the law of decrease of torsional oscillations when the range of oscillation was large in comparison with the palpable limits of elasticity. An equation of the form

where y represents the range of oscillation, and x represents the number of oscillations which have taken place since the commencement of the observations in any one experiment, was found to give an exceedingly close representation of the results. The values of the quantities n, a, and b depend on the magnitude of the initial oscillation, and on the previous treatment of the wire. It was also found that, when the oscillations were allowed to die away to a sufficient extent, the value of n tended to diminish. The oscillations were practically isochronous.

This investigation first commenced in the examination of a few special points which had arisen in connection with Professor Ewart's investigations on the Cranial Nerves and Lateral Sense Organs of Elasmobranchs. As this examination revealed facts of more interest than was expected, it occurred to me to investigate very thoroughly the whole of the cranial nerves of this animal, and to publish the results as a continuation of the work already alluded to. The research turned out to be much easier and more interesting than I had anticipated, and, as regards its cranial nerves at any rate, Chimæra is unrivalled among vertebrates, first, for the ease with which its nerves may be dissected, and second, for the almost ideal results that are to be obtained. The endless perplexity and mystification produced by the study of the trigeminal and facial nerves of the cartilaginous fishes,—dispelled to a very great extent, it is true, by the researches of Marshall and Spencer,—would probably have never arisen if Stannius had made a careful examination of the roots of the 5th and 7th nerves of his Chimæra. This, however, he omitted to do in the very form—in fact, as far as we know, the only form—which would have repaid the investigation ; and hence the embryologist stepped in and made a discovery that the anatomist had just, and only just, failed to grasp. The more important facts, therefore, relating to the cranial nerves of the Holocephali are, it is claimed, here recorded for the first time.

Since the foundation of the Scottish Meteorological Society in 1856, a mass of information regarding the climate of Edinburgh has been reduced and published in the Society's Journal from time to time, the data being furnished to that body by its local observers. In addition, numerous unreduced manuscript books of meteorological observations which extend back to the year 1764 are further available for discussion. In 1861 the late Principal Forbes communicated to this Society a paper on the “Climate of Edinburgh,” two elements of climate being alone discussed, viz., temperature and rainfall, and for a period of but forty years. The reduction of the observations taken virtually without a break during the past 132 years was therefore desirable for the discussion of cyclical and other weather changes, for which records covering a long period are absolutely necessary. Through the kindness of the Councils of the Scottish Meteorological Society, the Royal Society of Edinburgh, and the Royal Meteorological Society, the loan of the manuscript registers kept in Edinburgh and its immediate vicinity was obtained.

By films of iron, nickel, and cobalt are here meant electrolytic deposits of these metals on platinised glass. The magnetic properties of such films are interesting in various ways. For example, when they are longitudinally magnetised, we have the case of a magnet where the ratio of length to breadth is very great, and where, consequently, the demagnetising force is very small, e.g., with a film of a 5000th part of a millimetre in thickness, and 5 mms. in length, we have a ratio in length to thickness of 25,000: 1; at the same time the film is so small that it can be tested in very high uniform fields.