Our first investigation of Scottish plankton in 1901–2, although only tentative and somewhat meagre, was sufficient to show that, as regards the phytoplankton, the lochs of the west and north-west of Scotland were probably richer than any lakes previously examined. Owing to the extraordinary richness of the few collections then examined, it was considered eminently desirable that the investigation should be further extended. This we have been enabled to do by means of a third successive grant from the Royal Society, and the present paper is one of the results of a visit to the north-west of Scotland in July, August, and September, 1903.

In this paper some properties of the functions J[n](x, λ), P[n](x, λ), Q[n](x, λ) will be investigated. These functions are generalised forms of Bessel's and Legendre's Functions.

In the determination of the effects of stress upon different materials, the investigator has several methods of attack open to him, each of which has its own particular advantages. In the great majority of cases the material under investigation obeys the generalised Hooke's law, and the effects of a stress are therefore most easily followed and measured by observations of the strains produced. The strains being usually exceedingly minute, it is necessary to magnify them sufficiently to allow of accurate measurement. To this end many instruments have been devised for measuring the strains obtained by the action of different stresses, and in fact the great majority of our experimental knowledge has been obtained in this way. The application of polarised light to the determination of stress was first suggested by Brewster, and he applied it to many problems, particularly the determination of the neutral axis of a glass beam. Neumann, with a full knowledge of the work of Brewster, developed a theory of the analysis of strain by polarised light, and Maxwell also independently developed a theory. A third method, which has assumed great prominence in recent years, is the microscopic examination of metals under stress, as developed by Ewing, and Rosenhain, and others.

The spectrum of the new star in Perseus, which Dr Anderson, of Edinburgh, discovered 1901 February 21, was photographed at the Glasgow Observatory from 1901 March 3 till 1903 January. From the early photographs one gains the impression that the spectrum consists of a number of bright bands of different lengths, fading towards the ends, and overlapping each other, thus producing a series of maxima and minima of brightness. Near wave-length 5000 the intensity rapidly falls off towards the less refrangible side, and the bands appear detached. The middle of each of the three most intense maxima approximately coincide with the hydrogen lines Hβ, Hγ, Hδ, and on two photo-plates, March 18 to 20 and March 25, each of the bands is crossed by a sharp Fraunhofer line. On the photo-plates taken after 1901 August 1 the bands are all detached; some, including the two bands whose middles approximately coincide with the principal nebular lines, have almost the same lengths, and suggest a line spectrum in which the lines have been broadened into bands, others are considerably longer and have pronounced maxima.

The nudibranchs collected by the Scottish National Antarctic Expedition comprise only six species, but these include two new and interesting genera.

The species are—

1. Notaeolidia gigas, gen. et spec. nov.

2. N. purpurea, sp. nov.

3. Tritonia appendiculata, sp. nov.

4. T. pallida, Stimpson.

5. Tritoniopsis brucei, gen. et sp. nov.

6. Scyllaea pelagica, L.

The Scyllaea was caught on the return voyage, in the Atlantic, 32° N., 33° W.; Tritonia pallida, off Dassen Island, forty miles north of Cape Town; Tritoniopsis brucei, off Gough Island, 40° 20′ S., 9° 56′ W.; and the three remaining species in Antarctic waters.

Consider a sequence of elements p1, p2, p3,.......... then (mr) will denote the sum of the first mr elements of the sequence. The simplest connection between the terms of the sequence is equality.

Before giving a description of the specimen which forms the subject of this communication, it seems desirable that a brief summary of the literature dealing with the internal structure of Sigillaria, and some general remarks on the classification of the genus, should be given.

More for the purpose of convenience than on scientific grounds, the genus Sigillaria is usually divided into four groups. These groups were originally supposed by their founders to be of generic value, but experience has shown that the characters on which they were founded are more or less common to all four divisions, and in some cases the distinctive divisional characters even occur on the same specimen.

The material for the observations recorded in this paper has been kindly lent to me by Mr Graham Kerr, Professor of Zoology in the University of Glasgow. It consisted of some of his beautiful series of cut embryos, and of some freshly-sectioned material which I stained specially for the purposes of the research.

The blood corpuscles of the embryo Lepidosiren are exceptionally favourable objects for the study not only of the morphology of the blood, but also of cell structure. The karyokinesis in the red corpuscles presents features of considerable interest—and the phenomena are presented to the observer on such a scale as to render them almost diagrammatic.

In the present paper I shall deal with the structure of the corpuscles and the mitotic phases in the erythrocytes, reserving for a future communication the results of studies on the origin and histogenesis of the elements.

In a recent paper published in these Transactions I gave an account of certain experiments upon the change of electric resistance of nickel due to magnetization at different temperature up to 100·C.

In a preliminary note read before the Society on July 4, 1904, I drew attention to the fact that a number of line-series, forming a group which includes the first series of Hydrogen, can be represented by an equation of the form

where v denotes the wave-frequency of any line of the series, v∞ that of the so-called “tail” of the series (m = ∞), and a1, b1 constants depending on the nature of the emitting substance; the frequencies of successive lines being obtained by substituting successive integers for m. We see at once that this equation is a generalisation of Balmek's formula, into which it is transformed by equating b1 to zero. In the same note I also pointed out the existence of another group represented by an equation of the same form, if (m + ½) is substituted for m. As a special case (b1 = 0) this group contains the second Hydrogen series discovered by Professor Pickering in the spectrum of ζ Puppis. Subsequent investigations convinced me, however, that, although a considerable number of line-series may be classified into these two groups, there are numerous instances where the more general formula

must be employed, in which μ represents various fractional numbers.

In a recent paper published in these Transactions I gave an account of certain experiments upon the change of electric resistance of nickel due to magnetization at different temperature up to 100·C.

The original design of this research was to determine whether the extract of suprarenal medulla (or its active principle) has the power of antagonising the effects of an overdose of chloroform upon the heart and arterial system. Incidentally the research became extended so as to cover the action of certain other antagonising agents. It further appeared necessary, as the investigation proceeded, to subject the action of chloroform upon the vascular system to renewed study. For although, as the result of numerous recent researches, physiologists are in agreement regarding the general effect of the drug upon the heart, there yet remain various points requiring elucidation both as regards its effect on the heart and on the arteries.

§ 1. The variations of the surface-level of lakes due to the direct action of wind and rain, and the smaller disturbances caused by surface waves, of small or moderate length, due to the action of the wind and the movement of boats and animals, must have been familiar phenomena at all times. The first accurately recorded observation, that lake-levels are subject to a rhythmic variation, similar in some respects to the ocean tides, seems to have been made at Geneva in 1730 by Fatio de Duillier, a well-known Swiss engineer. Owing to the peculiar configuration of the Geneva end of Lake Léman, these variations occasionally reach a magnitude of 5 or even 6 feet; and Duillier mentions that they were known in his time by the local name of “Seiches,” which has now been applied to rhythmic alterations of the level of lakes in general.

(1) It is known that a continuant whose three diagonals are formed of certain equidifferent progressions is resolvable into linear factors, the earliest specimens placed on record being those of Sylvester and Painvin. The object of the present paper is to show that there are continuants of quite a different type which are also so resolvable, and to expound a general mode of investigating the subject.

The Bathgate and Linlithgow Hills occupy a well-defined belt of rising ground stretching S.S.W.–N.N.E. from Bathgate to Bo'ness, and included in the marginal portions of sheets 31 and 32 of the 1-in. maps of the Ordnance and Geological Surveys. Throughout the range the steeper slopes face the west, while the eastern flanks are deeply buried in drift. The glaciated contours are well seen from the east, and the sky-line is in several places deeply indented by glacial grooves. The physical geography is throughout intimately dependent upon the geological structure, but the latter is simplicity itself when contrasted with the complicated structure of the shale-fields to the east. Alternating zones of volcanic and sedimentary rocks strike parallel with the direction of elongation of the range from Bathgate to Bonnytoun Hill, and these are cut by a later connected series of dykes and sills of intrusive igneous rock. The latter, as a rule, are more resistant than the lavas, and form the more prominent features of the landscape, while the sedimentary intercalations may frequently be traced, even where no rock is visible, by the trough-like depressions which have been hollowed out of them between the zones of lava.

It is readily seen that the two differential equations

which play an important rôle in Professor Chrystal's mathematical theory of the Seiches, are special cases of the more general type

With regard to the first, the Seiche-equation, this becomes at once apparent by writing a= − ½. Equation (2), on the other hand, which we may briefly call the Stokes equation [see Professor Chrystal's paper on “Some further Results in the Mathematical Theory of Seiches,” Proc. Roy. Soc. Edin., vol. xxv.] will be recognised as a special case (a = + 1) of the equation

which is transformed into (3) by the substitution .

The area embraced in this paper consists of that part of Pembrokeshire which lies to the north and north-east of St Bride's Bay. Bounded on the west by St George's Channel and on the north by Cardigan Bay, it extends to the north-east as far as the mouth of the river Teifi, near Cardigan.

That part of the country which lies in the immediate neighbourhood of St David's has, through the laborious researches of the late Dr Hicks and others, become well-known to geologists, and may now be regarded as classic ground. The solid geology of this promontory has given rise to much discussion, and has, perhaps, attracted more attention than that of any other part of the Principality. The reason for this great interest is to be sought in the facts that the rocks of this area are of a very great antiquity, and that the sedimentary series contain the remains of some of the earliest organic forms yet found in the earth's crust, whilst the igneous rocks are also displayed in great abundance and variety, and present us, in the words of Sir Archibald Geikie, with “the oldest well-preserved record of volcanic action in Britain.”

Although they are thoroughly aquatic animals, the Tardigrada. are not very abundant in permanent waters. They are most thoroughly at home in situations where the supply of moisture is intermittent, and are therefore conspicuous members of that numerous community of animals known as moss-dwellers. They share with the Bdelloid Rotifera the power of withstanding dessication.

Although they have their headquarters in land mosses, many species are quite at home in ponds, rivers, and lakes.

As lacustrine animals they belong entirely to the littoral region, into which they no doubt continually migrate from the adjoining mosses. A favourite habitat is that strip of shore between the highest and lowest levels of the lake, the ‘grève inondable’. of Forel. Into this often mossy margin they may migrate in the ordinary way, when the loch is low. The next step may be involuntary—the loch rises during floods, and the bears, in common with many other animals, find themselves, willy-nilly, converted into lake-dwellers. It appears to be certain that of the water-bears introduced into lakes, by whatever means, some have found the conditions very congenial. Several species have hitherto been found nowhere but in lakes.

The causes of the peculiarities of the solar rotation exhibited by the superficial layers of the sun's body must still be considered unknown, notwithstanding recent interesting attempts at explanation. This is no doubt partly due to the difficulties of the hydrodynamical problem placed before the mathematician in an investigation of such complexity as the movements of particles in a rotating fluid subject to energetic convection. But it must also be conceded that the observational data available for a basis of mathematical, or even speculative, research are still so scanty, that for this reason alone we may perhaps not feel surprised at the failure so far of theoretical attempts.