It is well known that, when examined with a modern high-power spectroscope, the bright lines in the spectra of the different elements exhibit an individual character. Some are diffuse, some are sharp, some are diffuse on the one side and sharp on the other, and some are accompanied by fainter lines in their neighbourhood. To the latter the name of satellites has been given. The most celebrated satellites are those of the green line of mercury, which have been investigated very often owing to the ease with which the mercury spectrum can be produced. They are much fainter than the main line, and at least six can be seen. But there are cases occurring in which a satellite is so strong that it is hardly possible to say which is the main line. Thus the red line of hydrogen is a close doublet with a separation of ·14 A.U., the two components of the doublet being of approximately equal brightness.

In a recent communication (Proc. Roy. Soc. Edin., 1914–15, vol. xxxv, p. 22) measurements of the optical rotation and cryoscopic behaviour of the following sugars, viz. β-l-arabinose, l-xylose, α-d-glucose, α-d-galactose, d-mannose, d-fructose, α- and β-lactose, dissolved in (α) formamide, (b) water, were described. The investigation has been carried a step further by the addition of β-d-ghicose, β-d-galactose and maltose to the above list. Thus the change in rotation or mutarotation in formamide solution has now been measured, starting from both the α and β-form of d-glucose, d-galactose and lactose. As in the case of the water solutions of these sugars, the constant rotation shown when there is equilibrium between the two modifications is found to be the same whether the startine-point be the α- or the β-modification.

The literature of the sugars would appear to show that no sugars have hitherto been observed to sublime with the exception of glycolose, CH2OH CHO, which is described as being “perceptibly volatile with water and alcohol vapour under diminished pressure, especially from a pure, concentrated solution” (Lippmann, Chemie der Zuckerarten, p. 4). This substance, being the first of the sugar series, might be expected to have properties somewhat different from the other members of the series, which are usually looked upon as non-volatile. Experiments with rhamnose and fructose appear to show that under diminished pressure they do sublime.

A new method for the mechanical analysis of soils and deposits has been developed. It consists in weighing, from time to time, on a specially constructed balance, the amount of sediment accumulated on a circular disc suspended from the balance near the bottom of a vessel containing an aqueous suspension of the sample. From the “accumulation-curve” thus obtained one finds by a series of mathematical operations a “distribution-curve,” i.e. a curve showing how the amount of particles of a certain size varies with the latter quantity.

This method has been applied to the study of some deep-sea deposits from the Challenger Office. The distribution-curves thus obtained show marked differences for the different samples, and reveal a surprising lack of very fine particles in the deposits from the largest depths, besides suggesting interesting problems for new research.

The following note presents in a simpler form the essence of Dr Sven Odén's mathematical discussion of the fall of small particles through a column of liquid, as given in his paper (immediately preceding) “On the Size of Particles in Deep-sea Deposits.”

It has the further advantage of solving the problem without taking account explicitly or implicitly of Stokes's law (or modification thereof) as to the relation connecting the time of fall with the size, form, and density of the particles considered. It is important, I think, to refrain as long as possible from making the assumptions involved in such a law of fall, and to recognise how far we may carry the investigation before introducing these assumptions.

In the course of a systematic inquiry, conducted in the Physiology Department of Edinburgh University, into the morphological and physiological changes produced in animals by thyroidectomy and thyroid-feeding—especially in rats—certain striking morphogenetic changes in the pancreas have come under observation. The full results of the investigations of which these observations form a part will be published subsequently, but it has been thought well to bring the effects herein described before the notice of this Society without waiting for the completion of every part of the investigation.

The value of the continued-fraction, as a means of representing an analytic function f(x), is now fully recognised. Other representations, such as power-series or Fourier series or Dirichlet series or series of inverse factorials, converge in general only over limited regions of the x-plane, and fail to converge over the rest of the plane, whereas the representation of the function by a continued-fraction converges (in a large class of cases at any rate) over the whole x-plane, with the exception of certain singular curves.

The earthquakes of Scotland, as compared with those of England and Wales, are notable on several accounts:—(i) They are more numerous. During the twenty-six years from 1889 to 1914, 357 earthquakes riginated within the area of Great Britain–51 in England, 27 in Wales, and 279 in Scotland. If area be taken into account, the inequality is still greater. For every shock occurring in England, there were during this period four in Wales and nine in Scotland, (ii) They are invariably simple earthquakes, twin earthquakes (which include the strongest of all British earthquakes) being confined to England and Wales, (iii) As simple earthquakes, they are due to movements along strike-faults, and, for the most part, along well-known faults, the majority of which belong to the Caledonian system, the only exceptions known to me being those connected with the Loch Broom earthquake of 1892 and the two Glasgow earthquakes of 1910.

The lavas of the Scottish Carboniferous are predominantly basaltic. True andesites and rhyolites are conspicuous by their absence, whilst trachytes and allied rocks are present in quite subordinate quantity. This association of basalt and trachyte is in accordance with the fact that the basalts have a slight alkaline cast, which is evidenced by an alkali content greater than that of the average basalt, and by the occasional presence of nepheline and analcite amongst their constituents. The transition from basalts to more acid types is accomplished, not by way of the andesites, but through the mugearites, volcanic rocks with chemical affinities to the essexites. All transitions from the more felspathic types of basalts, the Jedburgh and Markle types, can be traced through mugearites to trachytes or allied rocks.

§1. It is well known that Laplace's equation ∇2V = 0 possesses certain classes of solutions of the form V = F(X, Y) where F satisfies a partial differential equation with X and Y as independent variables and X and Y are real functions of x, y, and z. Such solutions have been called binary potentials. They are of some interest in the problem of finding cases in which the equations of motion of an electron in a steady magnetic field are readily integrable. There are also classes of solutions of the same type, except that X and Y are complex quantities and the coefficients in the partial differential equation for F may also be complex. In particular, there are solutions of the form V = Yƒ(X) where ƒ is an arbitrary function with continuous second derivative.

In July 1913, while collecting the larvæ of the large Pine Weevil (Hylobius abietis), I discovered a number of tiny larvæ feeding on some of them. These I succeeded in rearing, and they proved to be the larvæ of a Bracon which seemed to be B. hylobii. In July 1914 I recorded my experiments and observations.* In this record I stated that my identification of the species was based on Ratzeburg's description.† All the specimens I examined—and I have examined many—agree, for the most part, with his description of B. hylobii. In April 1914, specimens were sent for determination to Dr Szeplegeti, the authority for the family, in Budapest, but so far no reply has been received.