As the immediate result of the ingestion of certain chemical compounds—chloral, camphor, benzol, phenol, &c.—substances make their appearance in the urine which have long been known to possess the power of reducing the oxides of some of the metals when in solution in the presence of an alkali, if that mixture be raised to the boiling point, but considerable confusion has resulted from the difficulty of finding a short process whereby many of these substances may be readily recognised as not belonging to that comprehensive group of conditions generally styled as glycosuria.

The principal phenomena connected with the great volcanic eruption at Bandaisan, in Japan, have been described by Professor S. Sekiya and Mr Y. Kikuchi in their “official report, but certain features, especially with reference to the effects of erosion on the ejected materials, seem worthy of more detailed description.

My aim in this paper will be to present as concisely as possible the problems involved in Man's Place in Nature, and to consider briefly how far an evolution theory contributes towards the solution of these problems.

Needful preliminaries can be disposed of briefly. We are agreed that evolution is “a change from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity, through continuous differentiations and integrations.” We are agreed that this process is to be taken as applicable in the history of matter and motion, and afterwards in the history of organised existence, raising the whole problem of biology. We do not require here to linger over the transition from the one to the other, as all requirements are met by accepting life and its laws as facts, and acquiescing in Darwin's hypothesis of one or more primordial germs.

The vast organic accumulations known as coral reefs are, undoubtedly, among the most striking ‘phenomena of tropical oceanic waters. The picturesque beauty of coral atolls and barrier reefs, with their shallow placid lagoons, and their wonderful submarine zoological and botanical gardens, fixed at once the attention of the early voyagers into the seas of equatorial regions of the ocean. Questions connected with the peculiar form, the structure, the origin, and the distribution of these great natural productions have, from the very outset, puzzled and interested all those who delight in the study of natural things. In this communication we propose to point out and discuss some of the more general phenomena of oceanic deposits, with special reference to the functions of corals and other lime-secreting organisms, and the accumulation of their dead shells and skeletons on the floor of the great oceans.

The following investigation was made in consequence of certain peculiarities in the earlier results of some recent measurements of ripples by Prof. Michie Smith, in my Laboratory, which will, I hope, soon be communicated to the Society. These seemed to suggest that viscosity might have some influence on the results, as might also the film of oxide, &c, which soon gathers on a free surface of mercury. I therefore took account of the density, as well as of possible rigidity, of this surface layer, in addition to the surface tension which, was the object of Prof. Smith's work. The later part of the paper, where Cartesian coordinates are employed, runs somewhat on the lines of an analogous investigation in Basset's Hydrodynamics. My original object, however, was different from his, as I sought the effects of viscosity on waves steadily maintained by means of a tuning-fork used as a current interruptor; not on waves once started and then left to themselves. Besides obtaining his boundary conditions in a singular manner, I think that in his § 521 Mr Basset has made an erroneous investigation of the effects of very great viscosity.

Professor Tait has shown that accurate determinations of surface-tensions would be obtained if we could measure the rate of propagation of ripples set up by the vibration of a tuning-fork of known pitch.

For the substances dealt with in this paper I have been indebted at various times, to the kindness of Mr David Hooper, Quinologist to the Madras Government. The observations have been made with several instruments, but have all been reduced to the scale of the direct vision spectroscope of the Chemical Laboratory of the Edinburgh University, kindly placed at my disposal for the most important part of the work. The illumination used with this instrument is a 10-candle power incandescent lamp; with the other instruments sun-light was used. I have thought it better for practical purposes to draw the spectra to the natural scale of the instrument than to reduce them to a scale of wave-lengths, but data are supplied for finding the wave-length corresponding to any part of the spectrum. To represent the varying shades of an absorption spectrum is extremely difficult, and the results usually obtained are, at best, far from satisfactory. The method I have employed is to draw the spectra on a large scale, shading the various parts by aid of a light curve, and then reduce this drawing to the required size by photography. The result, though not all that could be desired, is fairly satisfactory.

In a communication to the Royal Society of Edinburgh of 4th March 1889, I stated the problem of constructing a jointed model under gyrostatic domination, to fulfil the condition of having no rigidity against irrotational deformations, and of resisting rotation, or rotational deformation, with quasi-elastic forcive in simple proportion to rotation. I gave a solution, illustrated by a model, for the case of points all in one plane; but I did not then see any very simple three-dimensional solution. After many unavailing efforts I have recently found the following.

Dactylopterus volitans, the so-called “flying gurnard,” is not included by Günther in the genus Triglidæ, as its name might imply, but is assigned to the small allied family of Cataphracti.

Günther diagnoses it as follows :—“Dactylopterus, no lateral line, pectoral fins very large, an organ of flight, with the upper portion detached and shorter, granular teeth in the jaws, none on the palate, air bladder divided into two lateral halves, each with a large muscle.”

Before proceeding to describe in detail the swimming bladder and other anatomical peculiarities, it may be well to state, that the skull is provided with a superficial bony covering which projects backwards over the region of the “shoulder” in two flattened plates, each terminating in a spine (seen in fig. 2). Also that the first four vertebræ of the column have coalesced so as to form a rigid tube, the neural spines being united as a vertical plate, which for convenience I have termed the neural plate.

The equations considered are equations of the third and fourth degree in a single variable, and systems consisting of two equations in two variables. This is a comparatively small class; but if there be added systems consisting of a single equation of the third or fourth degree and a number of others all of the first degree, it will include all equations which admit, in general, of an algebraic solution.

The object of these notes is to point out the advantage of making greater use, than is generally the custom, of the discriminant in the solution of equations, and to emphasise the importance of looking for geometrical illustrations of analytical methods whenever this is possible. The usefulness of such illustrations is well known in considering, for example, limiting cases in the solution of equations, such as the cases of infinite roots and of equal roots, of the meaning of which it is almost impossible to form an adequate conception, without the use of such illustrations.

So much has been written on the zodiacal light that it may appear rather rash to say that a really accurate examination of this phenomenon has yet to be made. Still I have no hesitation in saying that neither its position, its shape, nor its spectrum has yet been determined with sufficient accuracy. In the hope of being able to add something to our knowledge of the last of these, I obtained, in 1882, a grant from the Government Grant Fund for the construction of a spectroscope specially designed for observing and, if possible, photographing the spectrum of the zodiacal light. The apparatus, which was made by Mr A. Hilger, consists of two interchangeable collimators of 36 inches and 8 inches focal length and 1½ inch aperture; an Iceland spar prism 1¼ inch high, 2¼ inches side, a camera with a lens of 8 inches focal length, and an observing telescope and a heavy glass prism which can be used for eye observations. The camera and telescope are fixed to a common base movable about a pivot concentric with the pillar carrying the prism, so that they are readily interchanged. The lenses are all of quartz, and the dark slide carrying the sensitive plate can be placed at such an angle that the whole or at least a considerable part of the spectrum is in focus at the same time.

The author gave an account of the microscopical appearances of striped muscle of the crab and lobster. The muscle of the crab and lobster is suitable for investigation because of the comparatively large size of the structural elements, and the readiness with which the sarcous matter can be fixed and otherwise prepared in different conditions. The author is entirely opposed to the opinions expressed by Melland, and more recently by Gehuchten, regarding the structure of the sarcous matter, and maintains, as he did at the International Medical Congress in 1881 (Transactions International Medical Congress, 1881, vol. i. p. 270), that the sarcous matter essentially consists of contractile fibrils, with an interstitial substance between them—an opinion previously expressed by Kölliker and others, and recently supported by Rollett.

The formulae established in a preceding paper are particular instances of some very general formulae to which I wish to draw the attention of mathematicians.

After the recent meeting of the British Association at Newcastle, Lord Armstrong, in showing me the appliances by which his house at Cragside is lighted electrically by water-power, told me of a very wonderful incident which he had recently experienced. A bar of steel, which he was holding in his hand, was allowed accidentally to come in contact with the two poles of a dynamo in action.

The circumstance that the oculomotor or third cranial nerve supplies no fewer than seven, muscles of the eye, two of them intrinsic and five extrinsic, and the fact that these muscles may be paralysed either singly or in groups as the result of central lesions, naturally suggest that each muscle is represented in the nucleus by a separate group of nerve cells. Hitherto, however, the anatomical text-books have been content with figuring the nucleus as a small indefinite group of cells lying in the anterior portion of the grey matter surrounding the aqueduct of Sylvius.

Histologists have long ago demonstrated that a muscle is not a simple histological unit, and that it consists of innumerable muscle fibres associated together in fasciculi, each muscle fibre being brought into individual relationship with the central nervous system by its own fibre. Physiologists have been too apt to overlook this fact, and have regarded a muscle as a simple indivisible physiological unit. When a muscle or its nerve are stimulated by an instantaneous electrical shock all the fibres contract together, for they are all stimulated in the same way, and at the same time. This is not the case, according to the investigations of the author, when the muscle contracts reflexly or voluntarily, and especially during any prolonged contraction. The individual fibres are then never completely co-ordinated together, and vary constantly in their “pull.” They are like a body of men pulling on a rope where perfect and prolonged co-ordination is impossible. The proof of this is obtained by the use of very delicate levers attached to different parts (fasciculi) of the same muscle. Two levers attached in this way to a muscle always give slightly different curves, evidence of individuality being very apparent. Experiments were conducted both upon the human masseter muscle and upon the gastrocnemius of a frog, and in each case the curves obtained by the two levers corresponding in the main always differed in detail.

Kronecker, Hall, Schäfer, Horsley, and others have found, when stimulating the spinal cord with rapid induced currents (ten, twenty, thirty, forty times per second), that the muscles always responded by giving a curve showing oscillations of one invariable period, no matter what the period of the stimulation may have been. With rapid stimulation, the muscles in the hands of the first named observers gave oscillations of twenty a second, in the hands of the latter observers of ten a second. These results are to be explained in the following way. When the central nervous system is stimulated, the muscles contract but never smoothly, for local fascicular movement, as the author has elsewhere shown, always occurring. These cause the registering apparatus to oscillate at its own period, just as any swinging body may be kept in motion by occasional disturbances. We can thus explain how each observer obtained the same number of oscillations every time he stimulated the nervous system; it was because he used the same recording apparatus each time. We can also see that the different periods observed by different observers are due to the fact that they each used a different recording apparatus. The author finds that on changing the recording apparatus (lever or tambour) the tracing obtained can be changed at will, and is practically a tracing of the oscillating period of the instrument used.

Potassium ethyl adipate was prepared by adding the calculated quantity of alcoholic potash to an alcoholic solution of adipic ether, and boiling. After the alcohol had been driven off on the waterbath, the residue, when shaken up with water and ether, yielded an aqueous solution which after concentration was used for electrolysis.

The electrolysis was conducted in precisely the same manner as in our former syntheses. A colourless oil was observed to collect on the top of the solution. After completion of the electrolysis, the contents of the crucible used as cathode were extracted by ether, which was subsequently distilled off and the residual oil kept for some hours at 120°. When hot this oil smells of melted butter, but on cooling the fatty odour disappears, a very slight smell resembling melons being left.

It is obvious that the amount of the optical activity of a given compound containing an asymmetric atom of carbon depends upon the amount of difference in character among the four radicals united to the asymmetric carbon atom, so that if two of them are very nearly equal we come very near to a compound of a symmetric carbon atom, in which the optical activity is zero. The question suggests itself, How are we to measure this difference of character ? We shall assume that there is a function, capable of numerical representation, derivable from the composition and constitution of the radical and the temperature of the substance, and that it is the difference between the values of this function in the case of two radicals which gives us the difference of character referred to. For the sake of brevity, we may call this function the K of the radical. The object of this paper is to show that, if there be such a function, there are methods by means of which we may hope to ascertain its value in each case.

In a paper “On the Height of the Land and the Depth of the Ocean,” read to the Society on 19th December 1887, and published in the Scottish Geographical Magazine, vol. iv. pp. 1–41, Dr John Murray gives a very detailed estimate of the volumes of oceanic hollows and continental protuberances. I have recently had recourse to Dr Murray's calculations in order to determine the position of the contour-line which should separate the portions of the solid earth above the general level of the surface from those below that level. The results of this determination were published in the Scottish Geographical Magazine, vol. vi. pp. 182–187; but since then the theoretical importance of the particular contour-line in question has induced me to give further consideration to the subject.