I was led to the following investigations while seeking an elementary, and at the same time instructive, application of Hamilton's General Method in Optics. They were completed in all but a few of their numerical details before I met with the remarkable paper by Wollaston, in which the subject of multiple atmospheric images seems first to have been treated by a sound physical method. Wollaston's experiment with a long bar of iron raised to a high temperature suggests undoubtedly the true explanation of at least many of the curious phenomena seen by Vince, Scoresby, and others. But he seems to have thought that sufficient temperature-differences for the natural production of the phenomena could not exist in the atmosphere; and thus the latter part of his paper, in which he tries to explain them by the agency of aqueous vapour, presents a singular contrast to the strength and correctness of the earlier part. A good deal of what follows is implied, if not directly stated, in Wollaston's paper; but I think there is sufficient novelty in what remains to justify my bringing it before the Society.

If Sn be a rational integral function of x of the nth degree, and Sn-1 Sn-2… S1 S0 a series of such functions of the n — 1th, n—2th, &c., degrees, so related to Sn that, when any one of the whole series S0 S1…. Sn vanishes, the two on opposite sides have opposite signs, and farther Sn-1 and Sn have always opposite signs when x is just less than any real root of Sn = 0, then S0 S1… Sn-1 may be called a set of Sturmians to Sn. It is obvious that the problem of finding such a set of functions admit of an infinite number of solutions. The first discovery of such a set was made by Sturm, and the researches of Sylvester, Hermite, and others have shown how other solutions of the problem may be obtained.

In a paper by Mr E. W. Binney on the Fossil Fishes of the Pendleton Coal Field, published in 1841, the dentary bone of Rhizodopsis is figured as the “upper jaw of a new species of Holoptychius,” to which, however, he did not attach any specific name. In the same paper its scales are also figured and referred to the same genus. Scales belonging to the same fish were afterwards figured by Professor Williamson under the name of Holoptychius sauroides, and again by Mr Salter, as those of Rhizodus granulatus. Both of these specific names occur under Holoptychius in Agassiz's general list of Ganoids published in 1843, but as they were unaccompanied either by figures or descriptions, it is really immaterial which of them, if indeed either, was applied by him to the fish in question. The authority for the term “sauroides” as applied to the common species of Rhizodopsis, the only species of the genus which is as yet known with certainty, must therefore remain with Professor Williamson. Holoptychius sauroides of Binney and of Messrs Kirkby and Atthey is quite another fish, now also distinguished generically as Strepsodus, and for it the specific name “sauroides” is therefore equally valid.

The area lying between the north of Britain and the Faeröe Islands is classical in the annals of Marine Zoology, not only from the fact that the first systematic deep-sea investigations undertaken by this country were carried out there, but also from the number of new and remarkable types of animal life which have been first found in that region. Speaking only of the Echinoderm fauna, in justification of these remarks, it will suffice to mention the discovery of such forms as Phormosoma and Porocidaris amongst Echinoids, and of Hymenaster, Korethraster and Zoroaster amongst Asteroids.

In the present paper I propose extending my previous observations “On the Structure and Division of the Vegetable Cell.” I have shown that a nucleolus and nucleolo-nucleus (at Professor Rutherford's suggestion I now propose terming this the endonucleolus) are essential, and in most cases evident, parts of every growing vegetable cell, and that the division of the endonucleolus very probably precedes that of the nucleolus, just as division of the latter undoubtedly precedes that of the nucleus, in all the cases investigated.

The phosphines, or substances derived from phosphuretted hydrogen by the partial or complete replacement of its hydrogen by hydrocarbon radicals, have formed the subject of many valuable researches; but although their discovery was anterior to that of the compound ammonias, their study has made comparatively little progress. This is no doubt mainly due to the difficulty attending their preparation, a fact which is immediately forced upon the notice of any one who wishes to investigate them.

In this paper I give an account of observations made during a visit in 1879 to the Færöe Islands in company with my friend Mr Amund Helland of Christiania. The principal object of our journey was to examine the glacial phenomena of the islands, but we studied so far as we could the various rockmasses of which the group is composed, and constructed a geological sketchmap to show the line of outcrop of coal, the disposition of the strata, the direction of dykes, and the trend of the glaciation. I have only to add, that all the observations recorded in the following pages were made in concert with my friend, and I am glad to say that we were quite at one in our general conclusions.

At the surface of separation of any two different substances in contact, there exists in general an electromotive force tending to maintain a certain difference of potential between them. This principle, established for metals by Volta in 1796, has been extended by later investigators to other substances, including liquids and gases. From these early researches of Volta, and the later more elaborate inquiries of Kohlrausch, Hankel, and Gerland, there have been deduced certain fundamental laws, which have been fully corroborated by the recent work of Clifton, and Ayrton and Perry. If, of a number of conductors set serially in contact, the difference of potential between each successive pair is quantitatively estimated and reckoned positive or negative, according as the first member of the pair is at a higher or lower potential than its successor, then the difference of potential between the first and last members of the chain is equal to the algebraic sum of the potential differences between the successive contiguous pairs.

In a paper by Professor Crum Brown and the author on Dimethyl- Thetine and its Derivatives, attention was drawn to the analogies which frequently exist between elements which have different atomicities, and which are usually considered as belonging to different families. The most striking examples of such elements are boron and carbon, gold and platinum, and phosphorus and sulphur.

Water is perhaps the most abundant and most universally distributed form of matter on the earth. It has to perform more varied functions and more important duties than any other kind of matter with which we are acquainted. From its close connection with all forms of life, it has been the subject of deepest interest in all ages. It is constantly changing from one of its states to another. At one time it is solid, now liquid, and then gaseous. These changes take place in regular succession, with every return of day and night, and every successive season; and these changes are constantly repeating themselves with every returning cycle. Of these changes, the one which perhaps has the greatest interest for us, and which has for long ages been the subject of special observation, is the change of water from its vaporous state, to its condensation into clouds, and descent as rain. Ever since man first “observed the winds “and “regarded the clouds,” and discovered that “fair weather cometh out of the north,” this has been the subject of intensest human interest, and at present forms one of the most important parts of the science of meteorology, a science in which perhaps more observations have been made and recorded than in all the other sciences together.

The object of this investigation was to obtain information as to the change of specific resistance produced in wires of various metals by different amounts of elongation. The present paper refers to experiments on copper, iron, and German silver wires.