This memoir details a continuation of the author's investigations on the physiology of the Invertebrata. At this point we consider the physiological functions of the so-called “liver ” of the Brachyura.

Was it not M. Letourneau, in his La Biologie, who said, “Does the pancreas exist in the invertebrates? This is a question of comparative physiology which still waits for a reply. We have seen that we do not begin clearly to recognise the pancreas except in fishes, and then only in a rudimentary state.” From the recent researches of Krukenberg, Frederieq, Jousset de Bellesme, Plateau, Hoppe-Seyler, as well as those of the author, the problem now requiring solution is the following:-Does a true liver exist in the Invertebrata? The pancreas appears to be the chief digestive organ (other than a true stomach) of the earlier forms of animal life.

The influence of the air on the going of time-keepers has naturally been the subject of much discussion, particularly in reference to time-keepers used by astronomers. On pendulums the air acts in two ways :—by its buoyancy it lessens the downward tendency of the parts, and so lengthens the time of the oscillation; and it opposes resistance to the motion. On the chronometer balance, the latter action alone is felt; to this action we shall confine our remarks.

One of the chief biliary pigments is bilirubin. It has a red-orange colour, and is derived from the decomposition of haemoglobin. It can be oxidised first into a green, then into a blue, then into a red, and finally into a yellow-brown pigment. Between the blue and red a violet substance is produced, but it is uncertain whether or not this is only a mixture of the blue and red pigment. The formation of the green pigment, according to Städeler, is due to oxidation, together with the addition of a molecule of water.

In his well-known researches on the phosphines, Hofmann has shown (or believes that he has shown) that when an alkyl iodide (or other haloid derivative) is heated with phosphonium iodide and oxide of zinc, primary and secondary phosphines alone result; whereas, when an alcohol is heated with iodide of phosphonium, tertiary and quaternary phosphines are formed exclusively. Thus the two reactions are complementary to each other. Among the series to which he extended his investigations was that of benzyl, and in a paper published in the Berichte of the Berlin Chemical Society he describes the preparation of mono- and dibenzyl-phosphine, and gives their properties. Dibenzyl-phosphine he isolated as a crystalline substance perfectly tasteless and odourless, insoluble in ether, but soluble in alcohol. Its melting-point he found to be 205° C.

Nowhere, I think, does Hamilton, or any other author, attempt the very fundamental problem of finding the differential of qn where q is a quaternion and n any scalar. It was by noticing an oversight in Tait's Quaternions, § 182, where he considers d.q½, that I was led to a consideration of the subject.

There is, undoubtedly, an omission in § 182 of my Quaternions (2nd ed.), but it is by no means so serious as Mr M'Aulay asserts. In fact the solution there given is merely an unfinished one, not in any sense erroneous. I sketch briefly the completion of it, as prepared for the new edition of my book, which is now being printed.

In my paper, read Jan. 21, I stated that I would not “for the present, insist on this point [the value of β] further than to say that the main effect is merely to alter the value of the disposable quantity A, below.”

In Reiss we have an author who starts to his subject as if it were entirely new, the only preceding mathematician whom he mentions being Lagrange. Like Cauchy he opens by explaining a mode of forming functions more general than those of which he afterwards treats, the essence of it being that an expression involving several of the n.v quantities,

is taken, and each exponent (“exposant”) changed successively with all the other exponents, α, β, …, or each base changed with all the other bases, a, b,.… Only a line or two, however, is given to this, the special class known to us as determinants being taken up at once.

Let AB (fig. 1) be a piece of nerve interposed in the galvanometer circuit, and CD in the battery circuit. Then, as has long been known, on closing the battery circuit, one obtains a current in the galvanometer circuit, the direction of which in the nerve is the same as that of the polarising current. If, now, stimulation be made, say at I, this current undergoes a negative variation. Hermann, who investigated the subject, after Bernstein, was at first inclined to explain the negative variation by his law of “polarisation increment.”

In January of 1878, there was laid on the Society's table the Canon of Sines to each fifth minute of the decimal division of the quadrant, computed to thirty-three for thirty places; along with a detailed record of every step in the process. During the years 1880–81, this work was continued for each single minute, but only to eighteen- for fifteen places, and the record thereof to fifteen places is now submitted. When the rejected figures were from 497 to 503 a mark of interrogation is recorded, and it is believed that not a single error exists in the work. The arrangement of the sines with their first and second differences in position enables us instantly to detect an error.

The fundamental form of the Volume and Surface Integral is

Apply it to a space consisting of a very thin transverse slice of a cylinder. Let t be the thickness of the slice, A the area of one end, and a a unit-vector perpendicular to the plane of the end.

After giving a summary of recent literature on the subject, the author then proceeded to state the nature of the material which he had employed in the present investigation.

The bird selected was the common fowl (Gallus domest.), and he had examined a series of microscopic sections through the limbs from the fourth day of incubation to the day of hatching.

The mammalian embryos examined were mice and rabbits, and the fingers of the human fœtus from an embryo approaching the full period of uterogestation.

In continuation of experiments on the electricity of air within doors, which I made twenty-seven years ago, and which are described in §§ 296–300 of my Electrostatics and Magnetism, a series of observations was commenced under my instructions at the end of April last, within the Natural Philosophy Class Room and Laboratory, the Bute Hall, the University Tower, and other places inside and outside the buildings of Glasgow University, by Mr Magnus Maclean, official assistant to the Professor of Natural Philosophy, and Mr Goto of Tokio, Japan, for the purpose of endeavouring to find a relation between the electrification of air within a building and the atmospheric potential in its neighbourhood outside; and of finding causes which produced or changed the electrification of any given mass of air.

The only observations hitherto recorded on the placentation of the Dugong are by Paul Harting, of Utrecht, in 1878, who examined the foetal membranes of a foetus 27.8 cent. long. He stated that the placenta was diffused and non-deciduate.

The gravid uterus described in this communication was presented to the author by C. W. de Vis, Esq., M.A., curator of the Queensland Museum, Brisbane, through Professor Anderson Stuart of the University of Sydney.

The uterus was bicornuate, and contained a single fœtus, 5 feet 4 inches long. The fœtus and its membranes occupied the left cornu, and there was no extension of the membranes into the right cornu.

The chorion was an elongated sac, upwards of 5 feet long from pole to pole.

The subject of the present paper has occupied my attention for some years, but I may state that what follows is the outcome of notes prepared for lectures to my students and is only a preliminary attempt to focus our present knowledge of the geographical distribution of some tropical diseases, and to indicate as far as possible the knowledge which we at present possess of those physical phenomena which influence the production of these diseases and the area of their distribution. Why, for instance, some diseases are confined to limited areas of distribution, whereas others are endemic in extensive districts, and others again periodically extend their ravages throughout clearly defined, though widespreading, regions.

The problem referred to is that of inscribing in a sphere a closed n-sided polygon, whose sides shall pass respectively through n given points which are not on the surface. Hamilton evidently regarded his solution of this question as a very tough piece of mathematics (see his Life, vol. iii. pp. 88, 426). In preparing a new edition of my Quaternions, I was led to a mode of treating this question which enables us to dispense with the brilliant feats of analysis which seem to be required in Hamilton's method.

At Dr Murray's request, I have during the past winter continued the investigation of Messrs Irvine and Young on the solubility of carbonate of lime in its different forms in sea water (the results of which they submitted to this Society in May 1888); and the following notes of the work done and the results obtained by me, under Mr Irvine's guidance, in the laboratory of the Marine Station, Granton, may be of interest.

In a paper read before this Society, on May 7, 1888, on the “Secretion of Carbonate of Lime by Animals,” we gave the result of experiments made upon domestic fowls, which established the fact that they could elaborate carbonate from sulphate of lime in the formation of the calcareous covering of their eggs.

About thirteen years ago, when officer of a vessel trading from London to Australia, and in the daily practice of verifying the error of the compass by azimuth's declination, the idea first occurred to me of projecting the sun's path on the plane of the horizon; and during the voyage I succeeded in solving the problem, and constructed a diagram which I used daily while at sea for several years, until I gave up long voyages, and had no further occasion to trouble about azimuths.

[As Sir W. Thomson was unable personally to communicate Capt. Weir's paper to the Society, he asked me to add to it a Note on the principle of the new method.]