Proposition I.—All spoken language is a growth, subject, like the creature who uses it, to a constant course of mutation; it is a living organism, developed according to certain laws, partly inherent, partly superinduced; and, though it is liable to decay, disintegration, and death, this disintegration, except in special cases of extermination, becomes the soil of a new growth, and this death the cradle of a new life. The historical action of this process of mutation is to produce either new varieties or dialects of one language, or new species of one family of languages.

Sir Charles Lyell, in the 3d edition of his “ Antiquity of Man,” published in 1863, makes the following statement:—

“Until lately, it was confidently assumed, that no alteration had. occurred in the relative levels of land and sea, in the central district of Scotland, since the construction of the Roman or Pictish wall (the wall of Antonine), which reached from the Firth of Forth to that of the Clyde.”

In preparing solutions of various salts with a view to determine their electrical conductivity, we found it of importance to know both the amount of salt in each solution, and its density. We prepared the solutions by mixing known weights of the salt under examination with known volumes of distilled water, and then measured their densities as soon as solution was complete by weighing a glass bulb in the liquid. We employed a balance which weighed to a milligramme with a kilogramme in each pan, and to give the results as great accuracy as possible we corrected for the upward pressure of the air displaced by the weights. The weight of the bulb itself was about eighty grammes. When not in use it was kept immersed in distilled water, in order to prevent change in its weight or volume being caused by impurities adhering to it. The temperature at which the densities were taken was 10° centigrade.

Comparative Anatomists have long been desirous to obtain detailed information on the Placentation of the Sloths. The only observations on this subject which appear to have been made up to this time have been recorded by Professor Rudolphi of Berlin, and Dr C. G. Carus of Dresden. Rudolphi in the course of some remarks on the structure of the umbilical cord in Bradypus tridactylus incidentally mentions that the placenta was cotyledonary as in the Ruminants. Carus figures the placenta and an almost mature fœtus of a B. tridactylus which came into his possession in 1830. He gives no description, however, of the specimen, but contents himself with a brief explanation of his engraved figures; in the course of which he says, that the specimen seemed to him important on account of the length of the umbilical cord, and the form of the cotyledons, which did not project, as is usual, outwards, but towards the inner face of the ovum, a peculiarity which had not yet been observed and described.

The following pages contain, in a comparatively compact form, part of the substance of a voluminous paper read to the Society six years ago. Of that paper, which employed ordinary analysis alone, only a few pages had been put in type when I succeeded in overcoming a formidable difficulty which had presented itself in my quaternion treatment of the subject. I therefore withdrew the paper in order that it might have the benefit of the simplification which quaternions always give; but it is only of late that I have found time to complete part of the translation into the new language. From the circumstances under which the paper has thus been produced, i, j , k come forward with undue prominence, a thing to be regarded (in Hamilton's words) “ as an inelegance and imperfection in this calculus, or rather in the state to which it has hitherto been unfolded.” Immense as is the simplification already attained, it is clear that in many places still more is attainable. But I have not postponed my paper till it should receive this final polish, partly because the time I can devote to such inquiries is extremely limited, and partly because I think that several of the results obtained, and of the modes of obtaining them, are new and remarkable. Besides, a question of this order of difficulty is admirably adapted to show in what respects quaternion methods require improvement. There must be some simple mode of deducing (13) and (21) below from (7) without the explicit use of i, j , k, but I have not yet been fortunate enough to discover it.

In the Session of 1867-8 I communicated to this Society a paper on the Dissipation of Energy, of which only a very brief abstract was published in the Proceedings. The main feature of that paper was the suggestion, as at least a valuable working hypothesis, that even in cases of the steady motion of heat, electricity, &c., the unexhausted energy is probably as small as possible, consistently with the conditions of each form of experiment.

Sensory nerves are divided into two classes, those of general sensibility and those of special sense. The nerves of general sensibility are distributed to the skin, muscles, or viscera, and convey influences to the brain which give rise to sensations of touch, heat, &c., or to those vague sensations, not definitely localised, which we include under the name of the muscular sense. The nerves of special sense are endowed with special and individual physiological properties. When a nerve of this order is irritated in any way, either by mechanical, chemical, or electrical stimuli, an influence is conveyed to the brain which gives rise to the same kind of sensation as that produced by the normal stimulus on the terminal organ. For example, pressure on the eyeball, as shown by Newton and Young, electrical stimulation by a continuous current, as demonstrated by Pfaff, Helmholtz Ritter, Purkinje, Du Bois-Reymond, and Schelske, produce many of the phenomena of vision, including not only the perception of light, but the perception of various colours and tints. But while this is the case, it is equally certain that each terminal organ responds to its normal stimulus. Thus the retina, though capable of stimulation by pressure or electricity, is specially fitted by its histological structure for the reception of those minute vibrations of the ether which constitute light. But while the terminal organ is capable of receiving a most delicate action of the normal stimulus, the nerve in connection with it is not so affected. For example, although the retina is affected by light, the optic nerve is not so, as may be proved by Marriotte's well-known experiment, by which it may be demonstrated that when the image of an external object falls on the entrance of the optic nerve, there is no corresponding sensation. The nerve is thus insensible to the normal stimulus of the sense organ, the retina.

In March 1869 I communicated to the Society a paper entitled “Motion of a Palladium Plate during the Formation of Graham's Hydrogenium,” which appears in the Proceedings for Session 1868-69. When engaged with this subject many points of interest regarding the behaviour of palladium containing occluded hydrogen, suggested themselves for investigation, and in concluding the paper I remarked “ that careful determinations must be made of the electromotive force, latent heat, &c., of hydrogenium ” before we could arrive at any conclusion regarding the condition of the absorbed hydrogen. Subsequently Professor Tait made a series of determinations on the “ Electrolytic Polarisation of Palladium Electrodes,” devising a new and ingenious method for the purpose. Although at different times subsequent to my first communication, the problem of determining the physical constants of hydrogenium recurred, as my attention was in the meantime directed to the specific heat of carbon at high temperatures, no progress was made with the investigation until September 1872, when the results of my preliminary experiments were communicated to the “ Philosophical Magazine,” under the title, “ Note on the Specific Heat of Hydrogenium.” In that note it is stated that by means of a specially constructed calorimeter the specific heat of hydrogen in palladium is found to be 3.1 per atomic weight, nearly identical with that of gaseous hydrogen. The present paper deals with some of the physical constants of hydrogenium, more especially with the specific gravity, specific heat, and co-efficient of expansion.