From the results obtained by Berzelius in his experiments with tungsten, the number 189·28 is calculated as the atomic weight of that metal. Many later investigations have been made, in which uniformly a lower figure was arrived at, in the majority of cases very nearly 184, which has therefore been regarded as the atomic weight.

The studies of which the results are here set forth were carried on at the Granton Marine Laboratory of the Scottish Meteorological Society, in the years 1886 and 1887. Our memoir is by no means a monograph, although our original aim was to investigate every species taxonomically, anatomically, and embryologically. Much further study would have been necessary to carry out this aim at all completely, but in August 1887, both of us, for different reasons, had to abandon our work at Granton and leave Scotland. We have thought it better to publish the notes and drawings we had made, because they will probably be of service to British naturalists interested in the Polychæta, no extensive work on these forms having appeared in English since Johnston's Catalogue of Non-Parasitical Worms in the British Museum, which was published 1865, and which is now a very inadequate guide to the study of the subject. The greater part of the work of collecting, and much the larger part of the drawings, were done by Mr Ramage. A discussion of some anatomical points has been published separately by Mr Cunningham (“Some Points in the Anatomy of Polychæta,” Quart. Jour. Micr. Sci., 1887).

In the present communication I have applied the results of my first paper to the question of the transference of momentum, of energy, and of matter, in a gas or gaseous mixture; still, however, on the hypothesis of hard spherical particles, exerting no mutual forces except those of impact. The conclusions of §§ 23, 24 of that paper form the indispensable preliminary to the majority of the following investigations. For, except in extreme cases, in which the causes tending to disturb the “special” state are at least nearly as rapid and persistent in their action as is the process of recovery, we are entitled to assume, from the result of § 24, that in every part of a gas or gaseous mixture a local special state is maintained.

The annexed tables are intended to facilitate the computation of the corrections for refraction which have to be applied to differential measures, such as are made with the micrometer or heliometer.

Differential measures are of two kinds :—(1) Direct measures of differences of right ascension and declination; and (2) measures of position angle and distance. In either case the observer only seeks to determine the relative positions of the objects under observation; and the correction for refraction consists in the applying to each reading a quantity representing the difference of the separate effects of refraction on the apparent places of the two stars, whose relative positions are to be determined.

The immense amount that has been written on the subject of dew renders it extremely difficult for one to state anything regarding it which has not been previously expressed in some form. It has been examined over and over by minds of every type, and from every point of view; so that every possible explanation of the different phenomena seems to have been given, and so many passing thoughts recorded, that from the literary point of view the whole subject seems exhausted. As a necessary result, these different treatises are in many respects contradictory; and it would be quite impossible to construct anything like a consistent explanation and account of our subject, from the very voluminous writings of those who have treated it from the purely literary point of view, and whose ideas have been evolved from their inner consciousness, according to what seemed to them the fitness of things, and without questioning nature as to the truth of their conclusions. On the scientific side of the subject, however, the writings are not so voluminous, and additions to it are still required to enable us to determine which of the many conflicting opinions are correct.

A glance at the expression

is sufficient to verify the fact that it is symmetric with respect to a, b, c, d, and also with respect to α, β, γ, δ. It is likewise, although not quite so evidently, an alternating function with respect to the interchange

that is to say, if a and α be interchanged, and at the same time b and β, c and γ, d and δ, the function is not altered in magnitude, but merely changes sign. With a little trouble, indeed, the expression can be transformed into

or say

The attempt to account for the behaviour of gases by attributing their apparently continuous pressure to exceedingly numerous, but nearly infinitesimal, impacts on the containing vessel is probably very old. It certainly occurs, with some little development, in Hooke's tract of 1676, Lectures de potentiâ restitutivâ, or of Spring; and, somewhat more fully developed, in the Hydrodynamica of D. Bernoulli, 1738. Traces of it are to be found in the writings of Le Sage and Prévost some 80 or 90 years ago. It was recalled to notice in 1847 by Herapath in his Mathematical Physics, and applied, in 1848, by Joule to the calculation of the average speed of the particles in a mass of hydrogen at various temperatures. Joule expressly states that his results are independent of the number of the particles, and of their directions of motion, as also of their mutual collisions.

The purpose of this memoir is (1) to make known a number of drawings and descriptions of the eggs, embryos, and larvæ of the species of Teleosteans which I have been able to study at the Scottish Marine Station; (2) to review as comprehensively as possible what is known at the present time concerning the structure of the embryos and larvæ of the species of Teleosteans, and to discover what features are common to each family or each order; (3) to discuss the changes which take place in the protoplasm and nucleus of the mature ovum immediately after it is shed, both when fertilised and when unfertilised. The ova of the following species were taken directly from the parent fish, and artificially fertilised. The necessary operations were carried out, in some cases by myself, on board fishing boats—usually steam trawlers from Granton. In many instances I did not myself go out in the boats, but the ova were obtained and brought to me at the laboratory by Alexander Turbyne, keeper of the station. But in every case there is no uncertainty as to the species of the fish from which the ova were taken; if there was any doubt, specimens of the parent fish were brought with the ova.

The expansion of ϕ(x) in terms of Go(x), G1(x), G2(x), &c., connected by a given law. being of great importance in mathematico-physical investigation, every method of effecting this expansion must have some interest for scientists.

I therefore proceed to propose what I think to be a new method, in the hope that it may prove to be useful.

Many special expansions of this nature have been effected by Fourier, Legendre, and others.

In the course of some remarks on the scheme proposed for the Forth Bridge, which remarks are published in the eleventh volume of the Transactions of the Royal Scottish Society of Arts, I was led to enunciate, among other theorems, one of a somewhat unexpected character, to the effect that any symmetric structure built on a rectangular basis, having no redundant parts, and depending on longitudinal strain alone, is necessarily unstable. This theorem was established by arguments restricted to the single matter under consideration; it is one of an extensive class, and I now propose to discuss the subject from a general abstract point of view.

In a Review of Dr Stur's Zur Morphologie und Systematik der Culmund Carbonfarne, I pointed out that he appears to have included two types of fern fructifications in his genus Calymmatotheca.

The first type includes those forms originally placed in Calymmatotheca and consists of a number of exannulate sporangia arranged around a common point of attachment; the second type, which was first described in Zur. Morph., u. Syst. d. Culm- u. Carbonfarne, is there represented by C. Avoldensis and C. Frenzli. The fruit of these two species is apparently surrounded by an involucre or indusium, and it is only with this part of the fructification that we are at present acquainted. I also further indicated that in Calymmatotheca, as I proposed to restrict the genus, the fruiting portions of the frond are entirely deprived of foliage pinnules, whereas in the other type (C. Avoldensis and C. Frenzli) only a very slight modification takes place in the fertile portion of the fronds—the sporangia being borne on the ordinary foliage pinnules.

My attention for the last few years having been specially directed to the vertical distribution of the Carboniferous Fossil Flora, it is my intention to publish a series of papers dealing with this subject.

While carrying on these investigations it has been necessary, in addition to visiting public and private collections, to visit several of the coal fields for the purpose of collecting specimens, as in almost no case have the smaller and less attractive species been secured, and, as a rule, only what strikes the ordinary collector as being “a fine specimen” is preserved, to the exclusion of many less striking but often more valuable examples. Hence our public collections, and, with few exceptions, also our private collections, give a very imperfect idea of the richness of the flora of the Carboniferous Formation of Britain.

The first impression upon the mind of the reader of the above title will probably be, that the subject has long since been exhausted. The explanation of these colours, as due to interference, was one of the first triumphs of the wave-theory of light; and what Young left undone was completed by Poisson, Fresnel, Arago, and Stokes. And yet it would be hardly an exaggeration to say that the colours of thin plates have never been explained at all. The theory set forth so completely in our treatises tells us indeed how the composition of the light reflected depends upon the thickness of the plate, but what will be its colour cannot, in most cases, be foretold without information of an entirely different kind, dealing with the chromatic relations of the spectral colours themselves.

In the following paper I desire to place on record the results of certain experiments which have lately engaged my attention. The facts established are, so far as I am aware, novel and in themselves interesting.

Many of the physical properties of hydrogenised palladium or hydrogenium have been carefully studied by Graham, Dewar, and others; but no one seems to have called attention to its thermoelectric peculiarities, or to have made a special study of its electrical resistance. These two inquiries form the subject of this paper. Throughout I shall use, for brevity's sake, the name Hydrogenium, which was applied by Graham to the fully-saturated form.