1. It is well known that if hn denote the sum of the homogeneous products of a, b, c, … l of n dimensions, while h′n refers similarly to b, c, d, … l, then

The proof, which is very simple, may be stated thus :— We have

At this, the concluding meeting of the Session, some observations and information are expected from, the Chairman for the night, and which I now, at the request of the Council, proceed to offer.

The simplest form of the interlacing surfaces as spread upon a plane is illustrated in fig. 1. It will be seen that we have here three sheets, differently shaded so as to distinguish them to the eye, but otherwise quite similar.

During the course of an investigation on the cerite metals we found that peroxide of hydrogen, added to the precipitated hydrates in presence of excess of alkali, is a very delicate test for cerium, even in presence of Lanthanum and Didymium, owing to the formation of a dark yellow or brown compound, probably a peroxide, which differs from that produced by chlorine under the similar circumstances.

A very important inquiry—suggested by Mr Chamberlain when President of the Board of Trade—has just been concluded by the Trinity House of London into the relative merits of electricity, gas, and oil, as lighthouse illuminants, on which I think it advisable to make a few remarks, as the general results of the investigation ought to possess a certain amount of interest for this Society.

It is rather remarkable that the Decapoda should have yielded fewer new forms than the Octopoda, although judging by the number of genera contained in them, the former is a much more extensive group than the latter, and is furthermore represented by a larger number in the “Challenger” collection, as the following synopsis will show :–

The development of spermatozoa has been for the last twenty years the subject of prolonged research and controversy, which cannot yet be said to have resulted in satisfactory solution of the involved problems. In view of the intrinsic difficulties of the subject, and the discrepant results and nomenclature of different authorities, it is the object of the present paper to recapitulate the history of investigation, to collate the results and the nomenclature, and to propose a theory which will explain and rationalise the maze of apparently conflicting observations.

While I was communicating my Note on the Necessity for a Condensation Nucleus at the last meeting of the Society, an idea occurred to me which germinated (on my way home) to such an extent that I sent it off by letter to Professor J. Thomson that same night.

In my paper on “Chemical Affinity and Solution,” read before the Royal Society of Edinburgh on 16th February last, I gave some general proofs of the correctness of my theory of solution, taken from Thomson's researches on thermo-chemistry, as given in Muir and Wilson's book on that subject. In the present paper I propose to extend these proofs, and to show the laws of solution, so far at least as chlorides, bromides, and iodides are concerned. I have verified these laws in the case of many sulphates, and have no doubt they govern all cases of solution. My theory is simply this, “Solution is due to the chemical affinities of the constituent atoms or elements of the body dissolved for the constituent atoms of the solvent.” For instance, the solubility of BaCl2 in water is due mainly to the affinity of the Ba of the salt for the O of the water, and of the Cl of the salt for the H of the water, and the degree of solubility depends on the relation between these affinities.

It may be within the recollection of the Fellows of the Society, that in December 1883 I had the honour of reading, in this room, a paper on the Madi Tribe of Central Africa.