The equation

may be put in the very simple form

if we write

and

The author in this paper details the results of a series of experiments, commenced three years ago, on the oxidation of the pyridine series of bases. These bodies are readily attacked by permanganate of potash; and the oxidation products of picoline thus obtained are ammonia, carbonic, nitric, oxalic, acetic, and dicarbopyridenic acids, along with a very small quantity of some solid base, possibly a condensed base.

The experiments, of which the results are recorded in the present communication, were undertaken in order to determine the rate at which blood flows through tubes of moderately small diameter, with a view to the study of the mechanical theory of dysmenorrhœa; they were afterwards extended to blood-clot, serum, milk, and urine, &c.

With the exception of the physical characters of this rare chemical substance, which is only known as an abnormal constituent of the human body, we know so very little, that even a few facts with regard to its behaviour with reagents may not be altogether uninteresting.

Cystine has the composition C3H7NO2S; and crystallises in the form of six-sided plates. It forms with hydrochloric, nitric, and phosphoric acids, definite crystalline compounds.

After passing through the usual routine work of acquiring skill in the fundamental operations, several of my students have remained long enough in the laboratory to make investigations in various branches of Physics. A great many of these inquiries related to matters already thoroughly known; but some have claims to notice as dealing with subjects on which our information is as yet incomplete. These I propose, from time to time, to lay before the Society. Their value as scientific results must depend on the skill and care of the experimenters.

Gentlemen, Fellowsof the Royal Society of Edinburgh,—In compliance with a special request of the Council, I come before you this evening to deliver the Address usually given at the opening of our Winter Session.

This practice of annually taking stock to ascertain what business we are doing, and how we are doing it, seems to me very right and expedient. The whole Society is thus made aware whether it is retrograding or advancing,—whether it is or is not, carrying out the objects of its institution.

In a paper presented to the Society in 1867–8 I deduced from certain hypothetical considerations regarding Dissipation of Energy results connected with the thermal and electric conductivity of bodies, the electric convection of heat, &c. As these were all of a confessedly somewhat speculative character, I printed at the time only that connected with thermal conductivity, which I had the means of comparing with experiment, and which seemed to accord fairly with Forbes' experimental results. But the assumption on which this was based was essentially involved in all the other portions of the paper.

The generally non-commutative character of quaternion multiplication introduces into the solution even of linear differential equations with constant (quaternion) coefficients, difficulties of a somewhat novel character. To some of these which have presented themselves to me in many investigations, I wish to draw attention in the following note, but want of leisure prevents my attempting at present either to classify the numerous curious forms which may be met with in physical inquiries, even when these lead to mere physical interest, inasmuch as they include the problem of finding two homogeneous strains, such that the vector-sum of their effects on any vector shall represent the effect of one given strain on that vector, while the effect of their successive performance in a given order on any vector shall be equivalent to that of another given strain.

In my paper on “Green's and other allied theorems” (Trans. R. S. E. 1869–70), I showed that

where P is any scalar function of ρ, and the single integral is extended round any closed curve, while the double integral extends over any surface bounded by the curve, ν being its normal vector.

Writing

this gives at once

of which the scalar and vector parts respectively were, in the paper referred to, shown to be equal.

The principal upon which this calorimeter is founded is, that a contraction of a definite amount takes place on the conversion of ice at 0° C. into water at 0° C., and that a definite amount of heat is required for this conversion. Early in the year 1866 I sent a description and drawing of the instrument to Messrs Kemp & Co., instrument-makers here, with an order to have it constructed. Some mechanical difficulties occurred which prevented its completion at the time.

Mr President And Gentlemen,—If I were addressing almost any other assembly, I should probably begin by saying that the subject of the educational system of Prussia possesses a peculiar interest at the present moment for two reasons—1st, Because the wonderful successes of Prussia make one curious to know all the methods which have been applied to bring that nation to its present state; 2dly, Because public instruction is just now one of the chief questions of the day for the inhabitants of G-reat Britain and Ireland.

In the present memoir the author enters very fully into the figure-of-8 wave movements, described by the wing in space, to which he first directed attention in March 1867. He has adduced the experiments with natural and artificial wings, on which his description was originally based, and has shown, by the aid of original models and a large number of diagrams and drawings, that artificial wings can be made to approach indefinitely near to natural ones, not only in their structure, but also in their movements.

Nearly a century after Julius Cæsar had landed in this island the conquest of Britain was begun in earnest.

In the year 79 Agricola planted the Eagles of Rome on the banks of the Tyne, and during the next campaign carried his conquests as far as the Tay. Before he gave up his command, he had raised the Roman standard in the Orkney Islands.

When Rome planted her foot she usually planted it firmly, and thus she retained in her grasp all the best portions of the island for more than 300 years. Some of the legions which landed in the time of Claudius remained in the island until the close of the Roman domination.

Mr Archer exhibited two interesting Foraminifers, one being Saccammina Carteri, which forms a large proportion of the Carboniferous limestone at Elfhills, Northumberland; the other, a gigantic species of the Arenaceous group brought from Persia by the late Mr Loftus, and named after him, Loftusia persica. The latter specimen was that to which Mr Archer especially called the attention of the Society, as it was similar to a class of fossils which had previonsly been found in the Upper Greensand formation in England, and believed to be sponges.

The theory of vision has been the subject of much more scientific study than that of any of our other senses, but notwithstanding this, the subject is still encumbered with some difficulties and contradictions, the solution of which is essential to our having a true and complete theory. Such are the questions,—first,—regarding single and double vision, as depending on the excitement of corresponding, or, as they are generally called, identical points of the retinæ; second,—the question whether perception is in the retinæ or in the brain; and lastly, the question regarding the decussation and ultimate course of the fibres of the optic nerves.

In the course of physical inquiries we meet with many problems having the appearance of great simplicity, and yet presenting to the analyst difficulties of the highest order. The law of the motion of a heavy body along the circumference of a circle is one of these.

One particular case of this motion, viz., the case of the swinging of a clock-pendulum, is of paramount importance, and has been investigated with very great care. In this case our attention is directed principally to the computation of the time of an entire oscillation, since it is this which determines the beating of the clock.

In the autumn of last year, whilst spending a few days in the neighbourhood of Oban, I visited Dunstaffnage, and in the courtyard of the Castle saw the two halves of the lower jaw-bone of a sperm-whale. On inquiry, I learned that they were the relics of a whale captured some years ago in the neighbouring sea. From some of the older inhabitants of Oban I gleaned some particulars respecting this animal; and as no record of its capture has as yet found a place in zoological literature, I am induced, as the sperm-whale so very seldom visits our shores, to communicate a brief notice to the Society.

There can be no doubt that, among the numerous matters at present occupying the attention of obstetricians, none is more important than the subject of this paper. So evident is the correctness of this statement that one cannot but wonder why attempts to arrive at the truth have been, so far as we know, delayed till the present day. It is long since excellent researches of an analogous kind in regard to the force of the circulation of the blood, the power of the ventricles of the heart, were published; yet such researches do not seem naturally so attractive, nor do they give promise of so valuable practical results as those into the power of labour.