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.

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.

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.

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.

§ 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.

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 .

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 following paper deals with an investigation of the successive zones of plant remains contained in the deeper peat deposits covering areas in the Scottish Southern Uplands. The field work was carried on during the summer and early autumn of 1904, and the detailed examination of the peat in the laboratory during part of the winter. No attempt has been made to work out the detailed flora of the different zones, but attention has chiefly been directed to the dominant plant remains found at different horizons in the mosses. Whilst the list of plants from each zone is small, the general facies of the flora of any layer can be gauged from the abundant presence of a few characteristic plants such as Salix reticulata and Empetrum, or Sphagnum and Eriophorum. Thus, while the investigation is incomplete as regards any addition to the history of the British Flora, it will, I hope, throw some light upon the succession of vegetation over the older peat mosses since their origin.

§ 1. The networks considered in the following paper are those networks of the plane whose meshes are regular polygons with the same length of side.

When the polygons are all of the same kind the network is called regular, otherwise it is semi-regular.

The regular networks have been investigated for the three geometries from various standpoints, the chief of which may be noted.

1. The three geometries can be treated separately. For Euclidean geometry we have then to find what regular polygons will exactly fill up the space round a point. For elliptic geometry we have to find the regular divisions of the sphere, or, what is the same thing, the regular polyhedra in ordinary space. The regular networks which do not belong to either of these classes are then those of the hyperbolic plane.

The present work was commenced in the summer of 1902, with the object of writing a complete monograph of the morphology of Myxine. It had previously been undertaken by the late Professor G. B. Howes, F.R.S., but, owing to the pressure of other work, and the first indications of the illness which subsequently proved fatal, he handed the work over to me. During the earlier stages, however, he exhibited a characteristic interest in the research, and most generously placed his material and the late Dr Pollard's sections at my disposal. His death has removed a kindly and a stimulating figure from our midst; a man whose life was devoted to the service of his friends and the advancement of his favourite study, and whose generous and sympathetic nature was the wonder and the delight of all who knew him.

The present communication is intended to be the first of a series dealing with observations on the life-history of the Anura Aglossa and their anatomy at different stages of development. Xenopus lævis, with its small ova and protracted larval free-swimming stages, must necessarily form a basis for the study of the development of that other remarkable Aglossan, Pipa americana. Although the adult Aglossan is an aberrant and specialised Anuran, there are Urodele features in the development of Xenopas which make its embryology of great general interest. These primitive features, combined with others peculiar to the genus, impress a character upon the early life-history of this frog which is widely divergent from that of the Phaneroglossa with small ova.

§ 1. In a paper published in the present volume of the Transactions of the Society (p. 659, 3rd July 1905), one of the authors of this communication has given a Hydrodynamical Theory of Seiches, and deduced formulae with a view to particular applications. The object of the present paper is to give some account of a series of calculations on which we have been occupied for some time, with a view to work out, a priori, from the Bathymetric Data of the Lake Survey, the Seiche Constants for the three seiches of lowest nodality in Lochs Earn and Treig.

§ 2. As this is the first time that any attempt has been made to solve completely a problem of the kind, we naturally selected lakes having as simple a configuration as possible. A general idea of the shape of the two lakes, and also of the nature of the data from which we have worked, will be obtained from the 3-in. maps reproduced in figures (3) and (4).

The Aleyonarians collected by Mr W. S. Bruce on the Scotia voyage represent nine species—six of which are new, namely:—

Primnoisis ramosa, n. sp.

Thonarella brucci, n. sp.

Amphilaphis regularis, Wright and Studer.

Primnoella scotiæ, n. sp.

Primnoella magellanica, Studer.

Paramuricea robusta, n. sp.

Gorgonia wrighti, n. sp.

Gorgonia studeri, n. sp.

Umbellula durissima, Kölliker.

Apart from the six new species, the collection is of interest in extending our knowledge of the geographical distribution of previously recorded forms. Thus Amphilaphis regularis, Wright and Studer, previously collected off Inaccessible Island, Tristan da Cunha, and off Nightingale Island, was got in abundance off St Helena; Primnoella magellanica, Studer, previously collected off Monte Video and in the Magellan Straits, was obtained at Burdwood Bank 54° 25′ S., 57° 32′ W.; while Umbellula durissima, Wright and Studer, previously obtained by the Challenger from the North Pacific Ocean, south of Yeddo, was found by the Scotia at 48° 06′ S., 10° 5′ W.