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.

The first part of this paper was communicated to the Society on June 1, 1896, and published in the Transactions (vol. xxxviii. part iii., No. 20, pp. 681–755), the data there discussed being mean values of the climatic elements for each day in the year.

In the present paper an attempt will be made to focus the results deduced from an examination and reduction of the various meteorological registers kept in Edinburgh from 1731 to 1736 and from 1764 to the present time, with special reference to secular and other weather changes.

The condensed results of a number of minor papers dealing with subjects which have, in many cases, formed part of the daily routine of observation during the last ten years have also been included. Attention may also be called to the list of remarkable atmospheric occurrences, such as phenomenal gales, snow-storms, auroras, etc., which is contained in the appendix. In presenting this paper my warm thanks must be expressed to Dr Buchan, from whom I received invaluable advice when points of difficulty arose in the reduction of the observations.

This paper is in continuation of two others, on the same subject, previously communicated to the Society. In the First Paper (Philosophical Magazine, July 1894) it was shown that the formula

where n, a, and b are constants in any one experiment, represents with accuracy the relation between y, the range of oscillation, and x, the number of oscillations which have taken place since torsion was first applied and the wire was left to itself, so that the oscillations gradually diminished. The apparatus employed, and the method of observation used, were identical with those described in the Second Paper above referred to. The wire which was experimented upon was the same as that used on the previous occasions. Its length, as given in the First and Second Papers, was 89·1 cm. A measurement made on the date 19.10.1897, in the course of the last series of experiments described in the present paper, showed that the length had become 89*3 cm. This increase was doubtless due to the fact that the heavy lead oscillator had been left attached to the wire during the whole of the intervening period. On the date given, it was also found that, with the same oscillator as was used in the experiments first described, ten oscillations were performed in 81 seconds, when the range was large, while 79 seconds were occupied when the range was small. This observation verified the result stated in the First Paper, that the period slightly increases as the range increases. It also showed that the wire was practically in the same condition as it was at first, in so far as elastic qualities are concerned; for the corresponding periods were only slightly less in earlier experiments, the difference being largely accounted for by the slight increase of length of the wire.

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) It is well known that Cayley effected the transformation of

by introducing an intermediary set of variables

connected with each of the other sets by means of a linear substitution of a peculiar type. The substitutions in fact were

and

where the determinant of the first substitution is unit-axial and skew, and the determinant of the second substitution is got from the preceding determinant by changing rows into columns, and where, therefore, the number of arbitrary quantities introduced by the two substitutions is only ½n(n−1).

The remarkable changes produced by magnetization in the internal volumes of hollow cylinders of iron, steel, and nickel have been described in Part I. (see Trans. R.S.E., vol. xxxviii. pp. 531–555). As pointed out in the closing paragraph, a complete discussion of these changes had to be “deferred until direct measurements of elongation had been obtained with the various tubes under the same magnetic influences.” It was not possible, of course, to measure the elongations of all the tubes that had been experimented with; for of these, eighteen (Nos. I. to VI. of each inclusive) were no longer in existence, having been the successive stages through which No. VII. was brought from the condition of small bore and thick walls to that of wide bore and thin walls.

The first instalment of this paper was devoted in great part to the general subject involved in its title, but many of the illustrations were derived from the special case of the flight of a golf-ball. Since it was read I have endeavoured, alike by observation and by experiment, to improve my numerical data for this interesting application, particularly as regards the important question of the coefficient of resistance of the air. As will be seen, I now find a value intermediate to those derived (by taking average estimates of the mass and diameter of a golf-ball) from the results of Robins and of Bashforth. This has been obtained indirectly by means of a considerable improvement in the apparatus by which I had attempted to measure the initial speed of a golf-ball. I have, still, little doubt that the speed may, occasionally, amount to the 300, or perhaps even the 350, foot-seconds which I assumed provisionally in my former paper:—but even the first of these is a somewhat extravagant estimate; and I am now of opinion that, even with very good driving, an initial speed of about 240 is not often an underestimate, at least in careful play. From this, and the fact that six seconds at least are required for a long carry (say 180 yards), I reckon the “terminal velocity” at about 108, giving v2/360 as the resistance-acceleration.

(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.

Since the Organ of Jacobson was first described in 1811, a large amount of study has been given to its structure, development, and morphology; and as a result of these investigations, we have now a very good idea of the distribution of the organ in the animal kingdom, of its relations in many typical forms, and of its minute anatomy in a few representative types. With the exception, however, of Seydel's work among the Amphibia, very little has been done to the study of the comparative anatomy of the organ, and it is hoped that the present contribution will assist towards a clearer understanding of its comparative anatomy in the Mammalia.

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.