Lord Neaves adverted to the peculiarity which had been observed in many Scotch airs, that they are composed on a pentatonic scale, and do not make use of the fourth or seventh of the gamut. It has been said that these airs can be played on the black notes of the pianoforte, which means that they can be played on the key of F# major, of which the fourth and seventh are represented by white notes, but are not needed. He also observed that this class of airs could be played on the white notes of the piano, both in the key of F and in that of G.

This paper commences with the following extract from the author's private journal, of date January 6, 1858:—

“Let be rectangular components of an impulsive force and an impulsive couple applied to a solid of invariable shape, with or without inertia of its own, in a perfect liquid, and let u, ν, ω, ѽ, ρ, σ, be the components of linear and angular velocity generated.

Messrs J. Murray and J. C. Young have been carrying out experimentally the idea mentioned in my former note on this subject. (Proc. Dec. 1870.) Their first sets of observations, of the results of which I subjoin a specimen, were made with an iron-silver and an iron-platinum, circuit working opposite ways on a differential galvanometer. The resistances (including the galvanometer coils) were in this particular experiment 53·1 and 25·9 B.A. units respectively, so that but very slight percentage changes could be produced in them by the elevation of temperature of the junctions.

I was recently led to consider this subject by Professor A. Dickson, who showed me some of his beautifully-mounted specimens, and explained to me the method he employs for the determination of the divergence, and of the successive leaves of the fundamental spiral or spirals. He referred me to two terribly elaborate papers by Bravais, and I have since met with another of a similar character by Naumann. These papers certainly cannot be supposed to present the subject from the simplest point of view.

In this paper the details were given of the computations made for extending the Table of Seven-Place Logarithms to 200,000 and of the precautions taken to ensure accuracy in the printed work.

The calculations were originally intended for a Nine-Place Table to One Million; and the manuscript shows the logarithms to fifteen places, with their first and second differences for all numbers from 100,000 to 200,000.

Professor Blackie then read a paper on “The Place and Power of Accent in Language.” On the subject of accent and quantity, he remarked, especially in relation to the learned languages, the greatest confusion had prevailed, and the existing practice was altogether unreasonable and anomalous. In articulate sound four things had to be distinguished—volume or bulk, force or emphasis, elevation and depression, and prolongation or duration.

Dr Dickson exhibited a number of specimens, chiefly Fir Cones and Cacti, illustrating the principal series of vegetable spirals. Almost all the cacti and many of the cones were from the Edinburgh Botanic Garden and the Museum of Economic Botany there. As the nomenclature of the cacti in the Edinburgh garden, as in many other botanic gardens, is in a state of considerable confusion, the specific names will not be referred to, and the generic ones, even, must in some cases be held as only approximately correct.

The author referred to the paper which he had read on the terraces of the Earn and Teith, and then described similar deposits which he had observed last autumn on the Spey, giving examples with drawings, from the neighbourhood of Kingussie, Dalvey, and Ballindalloch. The arguments formerly adduced were equally conclusive in the Spey to show that these terraces were not old sea beaches nor lake margins, but the fluviatile deposits of some former epoch when the floods rose to a greater height.

In this memoir the author described the dissection of the gravid uterus of an Orca gladiator, for which he was indebted to Mr James Gatherer of Lerwick. The paper contained an account of the uterus and appendages, the fœtal membranes, the position and general form of the fœtus, and a comparison of the placentation with that of other mammals possessing the diffused form of placenta. The structure of the uterine mucous membrane, its subdivision into a gland layer and a crypt layer, the relations of the glands to the crypts, their structure, the arrangement of their blood-vessels, and the much greater vascularity of the crypts than of the glands, were especially described.

A recent number of Poggendorff's “Annalen” contains a short but interesting paper by Christiansen, of Copenhagen, in which he states that a hollow prism filled with the alcoholic solution of fuchsine produces a highly anomalous spectrum, which, instead of proceeding regularly from the red to the violet like the ordinary solar spectrum, stops at a certain point, returns backward, then stops again and resumes a direct course to the end. This paper by Christiansen, kindly pointed out to me by Professor Tait, recalls to my memory an experiment which I formerly made more than thirty years ago, and which, with the permission of the Society, I will briefly describe, premising, however, that I write from memory, and without access at present to the original paper which I believe I have still preserved.

I have often felt the difficulty of illustrating, by means of Airy's Wave Machine, and various other complex instruments of a similar character, the composition of plane polarised rays into a single elliptically or circularly polarised one; the difficulty arising chiefly in showing separately, but in close succession, to the audience the two vibrations which are to be compounded, and their resultant. Lissajoux's apparatus would exactly answer the purpose if we had tuning-forks vibrating 10 or 15 times a second, its sole defect being the extreme rapidity with which differences of phase are run through; and, in fact, I have tried metronome pendulums with mirrors attached to them; but I have since found the following arrangement to be much more satisfactory. It consists simply in using plane mirrors rotating about axes very nearly perpendicular to their surfaces.

When I first saw Le Roux's account of his very singular discovery of the abnormal refraction of iodine vapour, I was inclined to attribute the phenomenon to something similar to over-correction of an achromatic combination. In fact, if a hollow prism be filled with a mixture of two gases or vapours, one of which is more refractive than air, the other less refractive; while the second body is more dispersive than the first; it is easy to see that Le Roux's result might be obtained, although each of the substances employed is free from anomalous refractive properties. In a recent conversation with Mr Talbot, I happened to mention the subject, and I learned from him his remarkable observation just laid before the Society.

It is very singular to notice how small a matter makes the difference between the intelligibility and unintelligibility of a demonstration to an audience as a whole not mathematical. In no part of Physics have I found this so marked as in the most elementary portions of geometrical optics. Such a formula as

when interpreted directly as signifying that “the sum of the reciprocals of the distances of the object and image from the surface of a concave spherical mirror, is equal to double the reciprocal of the radius of the mirror,”. if understood at all, is understood as a sort of memoria technica which enables the student to make calculations; but unless he have some knowledge of mathematics it suggests absolutely no higher meaning.

The best known living representatives of the Echinoderm Class CRINOIDEA are the genera Antedon and Pentacrinus—the former the feather stars, tolerably common in all seas; the latter the stalked sea lilies, whose only ascertained habitat, until lately, was the deeper portion of the sea of the Antilles, whence they were rarely recovered by being accidentally entangled on fishing lines. Within the last few years Mr Robert Damon, the well-known dealer in natural history objects in Weymouth, has procured a considerable number of specimens of the two West-indian Pentacrini, and Dr Carpenter and the author had an opportunity of making very detailed observations both on the hard and the soft parts. These observations will shortly be published.

1. On the Rate of the Action of a Large Excess of Water on Monochloracetic Acid at 100° C.—When monochloracetic acid is heated with water, double decomposition takes place, glycollic and hydrochloric acids being formed; and conversely, when glycollic acid is heated with hydrochloric acid, it is converted into monochloracetic acid and water. A similar reaction takes place with the two monochloropropionic and corresponding lactic acids, and probably with all their homologues.

In considering the authority for the division of the sacred cubit into 25 inches, we have, first, the architectural fact that the Queen's chamber, containing the visible expression of that cubit, stands in or upon the 25th course of masonry, comprising the whole Pyramid. And here, though not strictly bearing on the case, may be mentioned a connection between the lengths of the two passages (the first ascending, and the horizontal passages) leading to that chamber, remarkable when expressed in inches, of which 25 make a cubit.

In this communication, the author offers remarks on journals kept by Dr Carlyle, in the city of Carlisle, from 1757 to 1783 inclusive; by the Rev. Joseph Golding, at Aikbank, near Wigton, Cumberland, from 1792 to 1810 inclusive; and by himself at Bunkers Hill, two and a half miles west of Carlisle, which is situate 184 feet above the sea-level. The author gave tables showing the quantity of rain of each month and year included in these periods. From the averages, it appears that about twice as much rain falls in each of the latter months of the table as in the month of April; and about one-third less rain falls in the first six months of the year than in the last six months, and that April is the driest month of the year.

This communication was chiefly directed to the question whether the idea of distance be obtained from the adjustment of the eyes to distinct vision, or from the convergence of their axes. The case of the chameleon was cited as one in point, since that lizard directs its eyes each to a separate object, but habitually, when about to strike its prey, brings both eyes to bear upon it. Several experiments, mostly suggested by Wheatsone's inquiries, were cited, and the conclusion was arrived at, that, although the adjustment for direct vision concur in the formation of the estimate of distance, the convergence of the eyes plays the principal part.

A problem proposed to me lately by my friend T. Stevenson, C.E., for constructing what he calls a Differential Mirror, when attacked directly led to the equation

where a is a unit-vector, perpendicular to β.

By another mode of solution it was easy to see that the integral must be of the form

It may be instructive to consider this question somewhat closely, as the form of the unintegrated expression is certainly (to say the least) at first sight unpromising.

The following results were obtained lately while I was considering how most simply to describe by working sections surfaces analogous to that treated in the preceding note. They are so elementary that it is not likely that they can be new, but as they are novel to myself, and to several mathematicians whom I have consulted, I bring them before the Society:—

Let two coplanar circles be described, with centres A and B. Take any point, C, in the line of centres, and draw a line CPQ, cutting the circles in P and Q. Find the locus of R, the intersection of AP and BQ.