The former paper (5) on the Anatomy of Cephalodiscus was incomplete in certain particulars, which I am now in a position to add. These are mainly in regard to the alimentary canal, the nervous system, and the reproductive organs. To the present description of these will be appended an account of the budding processes, which are a very conspicuous feature of the species.

The immediate purpose of the present research was the investigation of the temperature at different pressures of boiling mixtures of steam and salts, analogous to the well-known freezing mixtures of ice and salt.

When steam is blown through common salt in coarse powder, it condenses to water, which dissolves some of the salt, and the resulting brine is kept boiling by the arrival of more steam. The temperature of this boiling mixture is quite constant so long as there is an abundant supply both of steam and of salt, and as the atmospheric pressure does not change, it is about 8·5° C. above the temperature of boiling water when the barometric pressure is the normal of 760 mm. When the barometric pressure is 560 mm. this excess has fallen to 8·0° C. Most other salts behave in a similar way.

In 1892 I communicated to this Society an account of a collection of Eurypterids from the Upper Silurian rocks of the Pentland Hills, in which I described new species and a new genus. Since that time I have had the opportunity of examining two other collections from the same locality. One of these was formed with the aid of a grant from the British Association. The fossiliferous bed—for these remains occur in a single thin bed of rock—was laid bare, and a considerable amount of it removed and split up. In this latter work I was fortunate to get the assistance of Mr John Henderson, the original discoverer of the locality, and I am glad to have this opportunity of recording my indebtedness to him. A fair number of specimens was thus procured, which not only threw considerable light on the structure of some of the already described forms, but gave evidence of some species as yet undescribed. More important than this collection, however, was the one formed by the late Mr Hardie of Bavelaw Castle, who had for many years collected among the Pentland Silurians. His collection was, on his death, acquired by the Edinburgh Museum of Science and Art, and Dr Traquair kindly put the collection in my hands for examination. From the size of the collection I expected some new and interesting results, and have been far from being disappointed. Seven new species of Eurypterids have come to light and one Scorpion.

In the autumn of last year Sir Archibald Geikie, F.R.S., Director-General of the Geological Survey of the United Kingdom, Kindly placed in my hands for determination a number of specimens of Cephalaspis, collected by his officers in the Lower Old Red Sandstone of the neighbourhood of Oban. On examining them, I found that they all belonged to one species, which was, however, new to science.

Accordingly I drew up a brief diagnosis of this new form, which was included by Sir Archibald in his Summary of Progress of the Geological Survey for 1897, and it is now my privilege, with his sanction, to offer to this Society a more detailed description of the species, accompanied with figures.

The remarkable fossil fish which forms the subject of the present communication belonged originally to the late Mr Powrie of Reswallie, and was acquired, along with the rest of his collection, by the Edinburgh Museum in 1892.

The specimen was obtained by Mr Powrie in a quarry of the Lower Old Red Sandstone at Turin Hill, near Forfar.

In his monograph on the Fossil Cephalaspidœ of Great Britain, published in 1870, (p. 41), Professor E. Ray Lankester refers in the following terms to the specimen in question:—

“A very remarkable specimen of shagreen-like structure has been discovered by Mr Powrie in Forfarshire, in beds which have furnished Cephalaspis. As I have not been able to assign it to Cephalaspidian fishes, though it may possibly, be connected with them, I only allude to it here. It consists of a surface covered with minute spinous tubercles, the whole having the appearance of a fossilised piece of shagreen, and its shape is more or less that of a Cephalaspid, with head and body.

This paper deals with a leisure-time study of mine, from which I once before drew the subject of an essay for this Society. The representations of animal form in Ancient Art interest me chiefly in so far as they present to us a problem involving an unsolved question as to the whole spirit and motive with which such representations were designed. We may see expressed in them merely a tendency to portray familiar objects in appropriate associations, to use the fish, or the crab, or the cuttle-fish as the device of an habitation of fishermen or resort of mariners, or to employ those creatures and others—the ox, the sheep, and the goat, the lion, the wolf, and the eagle—as the more fanciful appanage of divinities whose imaginary attributes were the attributes of the sea, the plain, the mountain or the sky. But we err, in my opinion, if we fail to recognise in this antiquated symbolism a deeper intention, whose spirit is rather Oriental than Western, archaic than modern. I believe these representations for the most part to have been associated with specific notions or beliefs of astronomical or astrological science, of religion or superstition.

We have already accounts of the development of the Müllerian ducts of reptiles from Braun (1), Mihalkovics (2), Hoffmann (3), and Wiedersheim (4). All of these writers agree in saying that the Müllerian ducts arise quite independently of the segmental ducts; but in view of recent attempts to show that in the other groups of vertebrates there are forms in which the Müllerian ducts are derived from the segmental ducts, it seemed expedient to reconsider this conclusion, and I have accordingly examined the development of the ducts in Crocodilus biporcatus, Chelone viridis, and Lacerta agilis.

As regards the derivation of the Müllerian ducts from cœlomic epithelium, I can only confirm the above-mentioned authorities; but I am able to supplement what they say as to the first foundation and the formation of the anterior end. I find that the anterior end is formed in reptiles, very much as in amphibians, by a modification of the cœlomic epithelium in the region of the pronephros. Backward growth proceeds independently alike of the segmental duct and of the epithelium of the body-cavity posterior to the ostium abdominale.

(1) The theorem in question concerns the finding of an expression for a determinant of composite order in terms of compound determinants or permanents of lower order; or, more definitely, the expression of a determinant of the mnth order as an aggregate of determinants or permanents of the mth order, each of whose elements is a determinant of the nth order.

It may well be thought that, in a field that has been so carefully reaped and garnered and gleaned by so many learned workers as have the works of the great Scottish poet, William Dunbar, there remained nothing still to be accomplished. Where such erudite students of Scottish literature as Laing, Small, Gregor, and Æneas Mackay, and such an illustrious scholar as Professor Schipper have laboured, and where even the poet's metrical forms have been the subject of careful investigation by Mr M'Neill, it might be thought alike vain and presumptuous to attempt to follow. Yet it so happens, nevertheless, that there has never been a thorough investigation made of Dunbar's rimes with a view of throwing light on the phonology or, in more popular phrase, the pronunciation of his day. And yet, perhaps, no more suitable, interesting, and instructive subject could be found for such treatment than just this same William Dunbar.

(1) The process of dialytic elimination was first applied to a set of general ternary quadrics by Sylvester in 1841, his method being to form from the three quadrics u1u2u3 ten cubics, viz.:—

and then eliminate dialytically the ten quantities

The actual work of obtaining the eliminant as a determinant of the 10th order he did not perform; and, indeed, with the notation which he used the labour would have been very irksome.

From the point of view of its function, a nerve fibre is a conductor of nervous impulses, and as such is the path of communication between two structures, the one situated in the central nervous system, and the other in the periphery. In the mixed nerve, such as the sciatic, the nerve fibres are distinguished as afferent or as efferent, according as they conduct impulses originating at the periphery, and received by a cell in the central nervous system, or vice versâ. It has long since been shown that nerve fibres are capable of conducting impulses in either direction, but normally, from their anatomical connections, the individual nerve fibres are conductors for impulses only in the one or in the other direction. This is proved by the Wallerian method of investigation, as on severance of the posterior spinal root distal to the ganglion only certain fibres degenerate and the conductivity of the nerve only for afferent impulses is lost, while the severance of the anterior root is followed by the degeneration of the remainder with loss of functions depending on efferent impulses.

For a number of years I have been collecting specimens and conducting an investigation into the craniological characters of the native inhabitants of our great Indian Empire, and several hundred skulls have now been under examination, and almost all have been measured. The sources to which I have been indebted for material are in part the collection of crania belonging to the Henderson Trustees, long known as the Edinburgh Phrenological Museum, and now deposited by the Trustees in the Anatomical Museum of the University; in part, a few specimens belonging to the University collected by my predecessors in office; in part, the valuable series of Indian crania belonging to the Indian Museum, Calcutta, which through the intercession of Dr John Anderson, F.R.S., the former Director, the Trustees of that Museum, with great liberality, most courteously permitted me to have the loan of for purposes of study; and lastly, a number of crania which have been forwarded to me by friends and former pupils, engaged in the public service in India, to whom I take this opportunity of expressing my indebtedness for the valuable material which I have received from them.

The various structures in the marsupial shoulder girdle are so unquestionably homologous with similar structures in the girdle of the human subject and of the Eutheria generally, that there has never been any difficulty in interpreting the parts in terms of human anatomy; but when the elements are compared with those in what we may consider to have been the ancestral condition, such as is exemplified in the shoulder girdle of the Monotremes, or of the Anomodonts, or in the more distantly related conditions met with in modern Reptiles and Amphibians, we are confronted with quite a number of difficulties, to which the most varied solutions have been applied by different morphologists. The chief difficulty in the way of comparing the typical mammalian girdle with that of the lower forms, is that in the girdle of the higher mammals certain structures are rudimentary, and, further, that the forms that have hitherto been examined have been so far removed from the ancestral stock that even a study of the early developmental conditions fails to give any clues that are more satisfactory than those afforded by comparative anatomy. Though it has been suspected that further results would be obtained from the study of the early condition in Marsupials and Monotremes, the embryos of these groups that have hitherto been studied have been too old to yield much further evidence than that obtained by a study of the adult forms.

1. The following paper is a contribution to the theory of non-alternate ± knots, together with a census of these knots for Order Ten; that is, all the knots are given which have in reduced form just ten crossings, and in which the thread does not proceed alternately over and under.

The census was begun in the fall of '93, and carried so far that the forms were drawn. The matter was then laid aside and taken up anew in the spring of '99.

2. Having postulated an endless one-dimensional continuum which may change its length and form in any way, subject only to the condition that it can never have a double point, and consequently no one portion can be made to break through another, I understand by a knot a continuum which can not be brought to a circular form.

The publication by the Royal Society of Edinburgh in 1890 of the hourly observations made at the observatory on the summit of Ben Nevis along with corresponding observations at five different hours at Fort-William at the sea level was an important contribution to meteorological science. As I held at the time the Lectureship in Geography at the University of Cambridge it furnished a welcome supply of facts for the illustration of important points in physical geography. What struck me most at the time in the study of this work was the unique character of the observatory of Ben Nevis itself, without reference to its companion at the sea level, as a first-class observatory in a locality where the atmosphere is for the greater part of the year completely saturated with moisture. Being also situated on a true peak, and that the highest point in the British Islands, the observations may fairly be taken to represent the meteorology of the clouds, or at least of such clouds as are in contact with mountain slopes, and in any case they must afford rich material for the study of the physics of the atmosphere.

In the autumn of last year (1897), Sir A. Geikie, F.R.S., Director-General of the Geological Survey, kindly placed in my hands for description an important collection of fossil fish-remains from the Silurian rocks of the Lesmahagow district, which had been made by Messrs Macconochie and Tait, collectors to the Survey. I accordingly prepared a brief report on these fishes, which was included by the Director-General in his Summary of Progress for that year.

The collection was, however, considerably increased by additional work on the part of Mr Tait in the spring of the present year (1898). Many better and more complete specimens were procured, and I was able to define one new genus and species, which had previously been represented only by undeterminable fragments. The results gained by the examination of the entire collection I now propose, with Sir Archibald Geikie's sanction, to lay before this Society in detailed form.