The extraordinary richness of the littoral region and the deeper water surrounding Guernsey and Herm, as well as the marked southern character of many of the Annelidan types, formed, for instance, an excellent comparison with the ample series of specimens which the dredgings of Mr Jeffreys in the Shetland seas had lately brought before us; or, again, with the valuable collections procured during the expeditions of the “Porcupine,” in 1869 and 1870, the former chiefly from the Atlantic, the latter from the same region and the Mediterranean.

During the earlier part of the middle ages, or until the middle of the eleventh century, students of logic had a very incomplete knowledge of the logical works of Aristotle. They knew the translations which Boethius had made of Porphyry's Εἰσαγωγὴ of Aristotle's περὶ κατεγορίων, and of his περὶ ἑρμηνείας, and they knew little else. Their labours did not go beyond the reproduction of, and commenting on, these old Greek writings.

Towards the beginning of the twelfth century, however, the gradual diffusion of knowledge had brought with it acquaintance with the remaining treatises of Aristotle's Organon. The old translations of Boethius were recovered, and new translations were made. We are told that “Jacobus Clericus of Venetia translated from Greek into Latin certain books of Aristotle, and commented on them, namely, the Topica, the Analytics Prior and Posterior, and the Elenchi, although,” adds the chronicler, “an earlier translation of these same books may be had.”

In their celebrated essay, “Sur la disposition des feuilles curviseriées,” the brothers Bravais describe a cone of Pinus Pinaster (Pin maritime), where the lower part of the cone exhibited secondary spirals 7S, 12 D (series ), while towards the apex the arrangement, in consequence of the disappearance of one of the spirals by 12, changed to 7S, 11D (series ). They describe another cone of the same species, in which the lower four-fifths exhibited secondary spirals 9 S, 13 D (series ), changing at the upper fifth to 8S, 13 D (ordinary series ) by suppression of one of the spirals by 9. Such cases, along with some others chiefly in the capitula of Dipsacus sylvestris, lead these authors into a discussion of the general question of the possible transition from one discussion of the general question of the possible transition from one arrangement to another by change in the number of secondary spirals.

I should not have thought of appearing before you to-night to lecture on so hackneyed a subject, had I not been assured by several members of the Council that such an address was really desired by many Fellows of the Society. It is a subject to which I have not paid very special attention, partly because it is in so many and such good hands, and partly because (except from the point of view of theory) it requires for its extension, especially to astronomy, very costly instrumental appliances and a great sacrifice of time.

Newton, in his observations on the spectrum, appears never to have used a narrow aperture. In fact there was nothing, in the existing state of knowledge in his day, to lead him to suppose that this would alter the phenomena.

Wollaston was the first who observed some obscure bands in the spectrum, by viewing with a prism the aperture left by the shutters of his room when nearly closed. It is surprising that this acute philosopher did not follow up the hint thus accidentally presented to him, but contented himself with the rude observation above mentioned.

The attention of the scientific world has been for some years past fully awakened to the importance of observing the spectra exhibited during the combustion of chemical substances. But in making an extensive series of such experiments, it must often happen that the observer has to test substances of which he only possesses a very minute quantity. In that case, before he has viewed the spectrum long enough to feel fully satisfied of its nature, his stock of the substance is exhausted, and he is obliged to leave his observation imperfect. He might perhaps be testing some mineral in his cabinet, of which the native locality was unknown, and he might surmise it to contain a new metal, from its yielding a ray not before seen in the spectrum, yet after a short time his observations on it would come to an end, and he would have no means of showing this ray to other observers.

Many years ago, when this beautiful and useful optical instrument; was new and very little known, I wrote a paper in a scientific journal calling attention to its merits, and recommending its use. It was first described by its inventor in Jameson's Journal for 1828, p. 83. The title of the paper being “On a Method of so far increasing the Divergency of the two Rays in Calcareous Spar that only one Image may be seen at a time.” This paper was reviewed in Poggendorff's Annalen for 1833, p. 182, who says—That he perused Mr Nicol's account of his invention with very little hope of its proving successful, but that having constructed the instrument, he found that nothing could answer more perfectly than it did. Having read this testimony to its merits, I had one made by a London optician; which proved very successful.

It is generally known that this country is extremely deficient in well-marked chalybeate waters. Plenty natural waters, containing small proportions of iron, are to be met with in the United Kingdom; but, with the exception of those of Tunbridge Wells, Harrogate, Sandrock (Isle of Wight), Heartfell, near Moffat, and Vicarsbridge, in the vicinity of Dollar, they contrast very unfavourably with those of the numerous spas of the continent of Europe. If we restrict ourselves to an examination of the chemical characters of the above-mentioned Scotch chalybeates, we observe that the iron is present in large quantities in the form of sulphate, along with sulphate of alumina, on which account they are more nauseous to invalids, and are at the present time rather unpopular.

After a brief notice of the seven bi-vertebral segments of the cranium in man:—

1. The hypo-cranial, or the axis and atlas vertebræ, which is adopted as a key to the cranial segments;

2. Para-cranial, or occipital;

3. Wormi-epiotic parietal, or meta-cranial;

4. Sphenoidal, or meso-cranial;

5. Ethmo-frontal—pro-cranial;

6. Nasal, or apo-cranial.

7. Rhino-nasal.

Professor Macdonald gave a short outline of the osteology of the human cranium, in order to trace the homologous osteology of the osseous fishes, or ichthyia.

Among many geological questions which wait solution, there is probably none more interesting or perplexing than the agency by which Boulders or “blocs erratiques,” as the French term them, have come to their present sites. I allude, of course, not to blocks lying at the foot of some mountain crag from which they have fallen by the decay or weathering of the overhanging rocks, but to blocks which have manifestly been transported great distances, after being detached from the rocks of which they originally formed part.

The magneto-electric machine, which I am about to describe, approximates in its general arrangements to Ladd's hand machine. In it Mr Ladd makes use of a compound Siemens' armature, consisting of two separate armatures placed in length, and revolving round the same axis, with their coils at right angles to each other. The armature revolves between the poles of an electro-magnet, of the description introduced by Mr Wilde. The electro-magnet, in the present instance, is made of a rectangular piece of boiler-plate, three-quarters of an inch in thickness, bent so as to form three sides at right angles to each other, as shown (in section) in fig. 1. The upright sides (P P' P) are nearly 9 inches high and 11 inches in length, and the top of the same length is 6 inches broad. Pieces of cast-iron (N and S) are put in the open end to form the poles of the magnet.

In the course of an investigation connected with the free rotation of a rigid body I was led to the remark that, if ξ and η be two vectors related to one another so that

where φ is a self-conjugate linear and vector function, we have also

(so that the relation is reciprocal) provided which implies also the corresponding equation

Two projectiles are anyhow projected simultaneously from a point, what is the relation between their vertical heights at any instant?

This simple inquiry, which was instituted in consequence of some results recently obtained from thermo-electric experiments (see ante p. 311) carried on at high temperatures, where the indications given by two separate circuits, immersed in the same hot and cold bodies. were used as ordinate and abscissa, leads to a very curious consequence.

Let

and

be any two parabolas whose axes are vertical, and which pass through the origin.

Since the algebraic operator

when applied to any function of x, simply changes x into x + h, it is obvious that if σ be a vector not acted on by

we have

whatever function f may be.

If Δ bear to the constituents of σ the same relation as ∇ bears to those of ρ, and if f and F be any two functions which satisfy the commutative law in multiplication, this theorem takes the curious form

of which a particular case is

The modifications which the general expression undergoes, when fand F are not commutative, are easily seen and need not be indicated in this abstract.

If ρ be the vector of the element ds, where the surface density is fρ, the potential at σ is

F being the potential function, which may have any form whatever.

By the preceding Note this may be transformed into

or, far more conveniently for the integration, into

where Δ depends on the constituents of σ in the same manner as ∇ depends on those of ρ.

In a Preliminary Note, read before this Society on the 31st of May 1869 (see Proceedings), a number of experiments were described, which proved that the lethal action of certain doses of physostigma can be prevented by the administration of atropia. Further, it was pointed out, that antagonism between any two substances, in the sense of the lethal action of the one being preventible by the physiological action of the other, had not previously been shown to exist by any certain and satisfactory evidence. In the various instances where experiment seemed to indicate the existence of such an antagonism, sufficient proof was not given that the dose of the substance whose action appeared to be antagonised was certainly a lethal one. The conflicting opinions and doubts this fallacy has given origin to, have induced the author to follow a plan whereby it may be completely avoided.

In this communication an Actinozoon (Actinia) was compared with a Hydrozoon (Hydra), and the various Sub-orders of the Hydrozoa were compared with one another.

The author agreed with Agassiz in regarding the radiating chambers of an Actinia as the homologues of the radiating canals of a medusa, but he differed from him as to the true homologies of the differentiated stomach-sac of Actinia; for while Agassiz regards this as represented by the proboscis or hypostome of the Hydra inverted into its body cavity, Professor Allman maintains that it is impossible on this supposition to conceive of the structure of Actinia; and on comparing a Hydra with an Actinia, he imagines the tentacle to become connate for a greater or less extent with the sides of the hypostome and with one another, so that the hypostome of the hydra, while retaining its normal position, will thus become the stomach of the Actinia, and will at the same time become connected with the outer walls by a series of radiating lamellæ—the connate tentacle walls—separated from one another by radiating chambers, the cavities of the tentacles; while such portions of the tentacles of Hydra as still continue free will be represented by a single circle of the tentacles of Actinia.

Although the Bust was only placed in the Hall at this time, the offer of it to the Society was made by Sir Eoderick I. Murchison in June 1871, in the following letter to the President:—MY DEAR PROFESSOR,—As it is very improbable, indeed—nay, almost a certainty—that I shall not be able to attend the meeting of the British Association at Edinburgh this year, I wish to send, as my representative, a marble bust of myself, executed by Mr Henry Weekes, R.A., and which is on the point of completion.

At the commencement of this, the 89th session of the Royal Society of Edinburgh, I beg to congratulate you on the successful issue of that which has just come to an end. The number of our members has increased, in consequence both of a low proportion of deaths among us, and likewise of an increase of new members beyond the average; so that, from 326 at the same period last year, the Society has grown to 331 at the present time.

We may appeal with equal, and even more, satisfaction to the success of our late meetings; which, in the first place, were carried on a full month longer than usual before exhausting the list of communications approved by your Council as worthy of being read before you; and which, in the second place, attracted from first to last unusual attendance and interest, on the part both of ourselves and of our visitors, by reason of the variety and value of the inquiries communicated at them.