The paper began by stating, that although the hymns of the Rigveda exhibit a simpler and less developed stage of religious belief and conception than we find in the works of the earliest Greek poets, and a system of ideas wildly diverse, both from the mythological forms and the theosophic opinions, of the later Indian pantheon, and of subsequent speculation; and although many of the customs and practices of that early age are different from those of later times, we are not to suppose that in the former period the condition of society was of a very primitive description.

In 1866 the indefatigable Dr Livingstone is again in Africa, with the determination of filling up the great gaps in our knowledge of the lake region from Nyassa to Tanganyika, beginning the great journey from which he has not yet returned.

News arrived in England, in September 1866, that the traveller had, for a third time, entered the Rovuma river, and had succeeded in penetrating for 130 miles from its mouth, where he had found a friendly chief, whose residence he intended to make the starting-point of his expedition to the northern end of Nyassa, and the south of Tanganyika.

While discussing some of Mr Smith's applications of Maxwell's ingenious idea of representing galvanic currents by the motions of an imaginary fluid (ante, p. 79), I was led to the present investigation. I have since found that, as was only to be expected, I had been anticipated in a great many of the results I obtained — especially by Stokes, in the Trans. of the Cambridge Phil. Soc. 1843. Still it appears to me that I have a few novel results to communicate.

This is a quaternion investigation into the circumstances of fluid motion, especially with reference to the case of vortices. The method employed is very similar to that which I gave to the Society in 1862 (Proc. R.S.E. April 28).

A few words in explanation are needed. In my summer course of lectures on Medical Psychology and Mental Diseases delivered in the University, I have to investigate the human mind in its practical relations to the body, and especially I have to teach how each influences the other, so that the physician, or any intelligent person, may be able to modify these relations beneficially. The starting-point in these inquiries is the fundamental fact of experience, that no changes in the mind or the consciousness of whatever kind can or do arise, or continue, without a corresponding series of changes somewhere in the brain-tissue.

I discovered the peculiarity of chromatic vision, which is the subject of this paper, in the month of January, when conducting some experiments upon the perfection of definition at diflferent parts of the retina; and I may introduce the subject by first referring to these experiments.

That theory of capillary action, which seems to have satisfied the greater number of physicists, is founded on the assumption that the particles of a fluid are separated by distances immensely great in comparison with their magnitudes, and that these particles attract each other,—the sphere, however, of their attraction extending to a distance infinitesimally small in comparison with the observed disturbances of the fluid-level.

In his early investigations on the principles of construction of the Great Pyramid, the author was forcibly struck with the following fact—viz., that if a perpendicular be drawn through the apex of the Pyramid to its base, and the unit angle with the horizontal thrown up from the base on each side of this perpendicular, the angle comes out on the faces of the Pyramid at the openings of the north and south ventilating air-channels; at the same time he was led to the conclusion that one-tenth of the base line, and the same tenths also applied to the faces of the Pyramid, ruled the entire structure.

The paper consisted of a detailed account of the external form; the arrangement of the body-cavity and its walls; the perivisceral space and corpuscles; the digestive, circulatory, and generative systems.

It was specially mentioned, in regard to the perivisceral corpuscles, that the author was not at all inclined to think that they originated from the glandular fatty coating of the digestive tract and the dorsal blood-vessel. The corpuscles seem rather to be the product of the perivisceral cavity itself and its special (free) contents. This view requires no stretch of ordinary physiological principles, and is quite in keeping with what is found in other groups. In the Nemerteans, for instance, a complex corpusculated fluid is produced within a closed chamber with smooth walls.

In this communication an attempt was made to express by means of formulae the various modifications presented by the life series of the Hydroida. It was also shown that there existed among the Hydroida both centripetal and centrifugal forms of development. These were compared with one another, and numerous analogies between the hydroid gonosome and the inflorescence of plants were demonstrated.

In this paper the author adverted to the limited attention that was paid in this country to comparative philology, and noticed the principles it had developed and the progress it had made elsewhere of late years.

In illustration of the results thus attained in the Aryan or Indo-Germanic languages, he took as familiar examples the affinities that could be traced between the Latin and the Old English tongues, viewing the Latin as a type of the earlier branches of the family, including the Greek and Indian; and the English as a type of a later branch, consisting chiefly of the Low German dialects. The affinities referred to were not those which connected Latin with English through the romance languages, but those which subsisted between Latin and vernacular English, and which must have arisen from a prehistoric identity or connection.

In this paper an attempt is made to supply, at least in part, what the author has long felt as a want in the beautiful system of quaternions, so far as it has yet been developed. To apply it to general inquiries connected with electricity, fluid motion, &c, we require to have means of comparing quaternion-integrals taken over a closed surface with others extended through the enclosed space—and of comparing integrals taken over a non-closed surface with others extended round its boundary.

A friend informed me some time ago that the late Principal J. D. Forbes had often noticed that a long continuance of rain resulted in a track of cold weather. Principal Forbes attributed this fact to the rain having a lower temperature than the atmosphere through which it fell. It does not appear, however, that he made any observations to determine the truth of his hypothesis, and as the subject is of considerable importance in other meteorological questions, it occurred to me that a simple instrument could be made for ascertaining the temperature of falling rain.

Sir,—As Mr Clerk Maxwell, in a paper lately published in the Transactions of this Society, has done me the honour to refer to me as having been the first to show how to combine in one diagram a system of lines representing the directions and magnitudes of all the forces acting in a given frame, I wish to put on record, in the Proceedings of the Society, the time and manner of my first publication of the method in question. It was in the year 1856, in a lithographed synopsis of lectures which I delivered in the University of Glasgow, entitled “Mechanical Laws, Formulaæ, and Tables.” Copies of that synopsis were distributed to the students of my class, and to a few men of science.

The instrument used in the experiments forming the subject of this paper was a spectrum microscope, to which a polarising apparatus is attached, consisting of two Nicol's prisms, each of which is capable of being turned through any required number of degrees.

The first part of the paper relates to the spectra obtained when one or more thin films of mica or selenite are interposed between the polariser and the dispersion prisms, the light being subsequently analysed.

The method employed was, having first determined the axes of the films, to place them on the stage of the instrument which is rotatory, and to adjust them at various angles to the plane of polarisation.

In the beginning of this paper the author recapitulates the five fundamental laws of the heat of combination, which he had deduced from his previous researches, and which form the subject of several memoirs published in the Transactions of the Royal Irish Academy and of the Royal Society of London, from 1841 to 1848.

In a paper communicated to this Society last session, I pointed out that the proof of Euc. I. 5, given by Mr Mill, is unsound; endeavouring, at the same time, to show that this is no mere accident, but that it is impossible to give a mathematically correct analysis of the processes of Synthetic Geometry on any theory that holds figures to be merely illustrative, and does not admit that intuition in the Kantian sense—i.e., actual looking at a single engraved or imaginary figure—may be a necessary and sufficient step in a demonstration perfectly general.

The fundamental phenomenon or fact of the science of optics is vision, that is, the perception we have of distant objects through the eye, or by the sense of sight. That vision is an effect transmitted to the mind by the object seen, is a necessary truth, involved in the definition of the term, and independent of all theoretical views beyond the consciousness of that perception.