In a recent paper published in these Transactions I gave an account of certain experiments upon the change of electric resistance of nickel due to magnetization at different temperature up to 100·C.

In the autumn of last year Sir Archibald Geikie, F.R.S., Director-General of the Geological Survey of the United Kingdom, Kindly placed in my hands for determination a number of specimens of Cephalaspis, collected by his officers in the Lower Old Red Sandstone of the neighbourhood of Oban. On examining them, I found that they all belonged to one species, which was, however, new to science.

Accordingly I drew up a brief diagnosis of this new form, which was included by Sir Archibald in his Summary of Progress of the Geological Survey for 1897, and it is now my privilege, with his sanction, to offer to this Society a more detailed description of the species, accompanied with figures.

In the years 1823 and 1826 I communicated to this Society two papers “On the Existence of Two New Fluids in the Cavities of Precious Stones and other Minerals.” These two fluids were generally found together in the same cavity, though sometimes the cavities were occupied only by one of them. They were perfectly transparent and immiscible. The denser of the two occupied the angles of the cavities, or the necks, or narrow passages, or canals which united two or more larger cavities; while the rarer fluid floated, as it were, on the other in deep cavities, or filled the body of shallower ones, with the exception of a circular vacuity, which diminished and disappeared with the slightest increase of temperature, or enlarged itself and disappeared in consequence of the fluid being converted into vapour.

Throughout the year 1884 the sun was seen over most countries under peculiar atmospheric circumstances; and these, instead of being confined to low altitudes, were never more conspicuous than during the summer of the year, and noon-tide of each day, and in the clear air on mountain heights of every country, whenever the sky was more or less free of actual clouds.

On such occasions then, the usual phenomenon to be noticed by the eye, was, that nothing like blue sky could be witnessed near the sun. But in place of that, there was a broad glare of whitish light extending for several degrees around the luminary; and beyond that range, or over 20 degrees distant from him, there spread a wide reddish haze, passing into purple, and at greater distances into blue, but nowhere a very decided and deep blue sky.

The experiments from which the following are extracted, make part of a course, instituted at the Royal Military Academy, for determining the resistance of the air to a surface of any form whatever, either plane or curved, moved through it with any degree of velocity. I was induced to undertake these experiments, both for the improvement of my students in the Academy, and with a view to apply the conclusions derived from them towards perfecting the theory and practice of military projectiles, as well as other branches of natural philosophy, in which the pressure or resistance of fluids is concerned: Circumstances, concerning the laws of which, authors on the theory have widely differed; some making the pressure or resistance equal to the weight of a column, whose altitude is equal to the whole height due to the velocity, while others make the altitude very different, either the half or the double of that.

If U, V, &c, are rational and integral functions (٭)(x, y, z)r, all of the same degree r, in regard to the co-ordinates (x, y, z), then √U + √V + &c. is a polyzome, and the curve √U + √V + &c. = 0 a polyzomal curve. Each of the curves √U = 0, √V = 0, &c. (or say the curves U = 0, V = 0, &c.) is, on account of its relation of circumscription to the curve √U + √V + &c. = 0, considered as a girdle thereto (ζῶμα) and we have thence the term “zome” and the derived expressions “polyzome,” “zomal,” &c. If the number of the zomes √U, √V, &c. be = ν, then we have a ν-zome, and corresponding thereto a ν-zomal curve; the curves U = 0, V = 0, &c., are the zomal curves or zomals thereof.

The questions which I propose to examine in the following paper, although not themselves dependent on chance, have arisen entirely from games in which it predominates. To determine some method of betting upon a number of successive events, (and the probability of each of which is either equal to, or less than one-half,) by which a profit shall be realised after a considerable number of them have been decided, is a problem which has occupied the attention, and exhausted the efforts, of one set of speculators, as completely as that of the quadrature of the circle has defeated the labours of another. The first and most simple plan, is that of doubling the stake whenever a loss occurs. This is well known, and has been so frequently practised, as to have acquired a peculiar name; it is technically called the martingal; it requires for its success, that the person who employs it have the power of leaving off whenever he please, and that he have the command of an unlimited capital. If the chance of the events happening is one-third instead of one-half, the stake must be tripled.

Man is formed to derive pleasure from a variety of different sources. Many of his pleasures are communicated by the channel of the external senses. Each of these has particular classes of objects that are suited to its gratification ; and these, being diffused in great abundance through the works of nature, or framed by the art and ingenuity of men, become to him a source of frequent and diversified enjoyment.

In former papers on the pharmacological action of Strophanthus, dating from 1869, I selected for description, from the considerable number of experiments that had been made, merely those experiments which sufficed to illustrate the general features of the action, and especially such effects as seemed likely to form a basis for the application of Strophanthus to the treatment of disease.

I had intended to have followed, at no distant date, these preliminary and somewhat fragmentary notices by a more complete description of the pharmacological action, for which, indeed, nearly all the required experimental data had several years ago been obtained; but unavoidable circumstances prevented this intention from being fulfilled. In this part of the present paper the fuller description will be given; and if any excuse were required for doing so, it may perhaps be found in the circumstance that the anticipation of the therapeutic value of Strophanthus has been amply confirmed by the important position now occupied by it as a therapeutic agent.

By the introduction of letters into algebra, to denote all the quantities, both known and unknown, involved in an equation, this very important advantage was gained, that the final equation exhibited both a general rule for the solution of all similar problems, and also the limitations within which such problems were possible.

1. The Council of the Royal Society of Edinburgh having, on my application in 1832, entrusted me with Hansteen's Magnetic Intensity Apparatus, in their possession, I feel it to be my duty to communicate to the Society the results then and subsequently obtained with it.

2. The instrument consists of a mahogany box 5 inches long, 4 broad, and 2 deep, with sides and top of glass, having also a wooden tube, screwing into the top, for containing a silk-worm's fibre about 5 inches long, by which the magnetic needle is suspended so as to place itself horizontally, and after being caused to deviate from its point of rest, the time of any given number of oscillations in a horizontal plane is measured,—whilst a graduated circle in the bottom of the box indicates its arc of vibration.

Although the amount of active research that has been carried on during the past few years on the question of chromosome reduction and relative problems has been very great, the nuclear activities here concerned are still far from being understood. We are not yet in a position to draw general conclusions in regard to meiotic phenomena. It therefore seems to me desirable that all observations of fact and rational interpretations should be placed on record, so that when it becomes possible to generalise, all lines of evidence may be available.

The analogy between certain properties of the co-ordinates of elliptic and hyperbolic sectors, which forms the subject of this memoir, was observed by the early writers on the fluxional or differential calculus, and employed by them in its improvement. But, independently of this important application, the propositions in question are some of the most elegant theorems in geometry, and highly interesting as abstract truths.

Maclaurin, in the third chapter of the second book of his Treatise of Fluxions, has proved the truth of this theorem: “Supposing n to be any number, let E and n × E be elliptic sectors, which stand on arcs that begin at a vertex of either axis, and H and n × H hyperbolic sectors, which stand on arcs that begin at the extremity of the transverse axis: the algebraic equation which expresses the relation between x and z, ordinates drawn to the other axis from the extremities of the arcs, must be the very same in the two curves.”

Forty years ago Kolbe showed that a strong aqueous solution of potassium acetate, when subjected to the influence of the electric current, is decomposed with formation of the following products. At the anode a gaseous mixture is evolved which consists chiefly of carbonic acid and ethan; while at the cathode hydrogen escapes, and potassium hydrate is formed in the solution. When dilute solutions of the same substance are electrolysed under similar conditions, the decomposition products at the cathode are the same as in the previous case, but at the anode the gas evolved is now oxygen, and free acetic acid makes its appearance in the solution. The difference between the two cases must, on modern views of electrolysis, be attributed to the occurrence of secondary reactions. The primary process is in all cases the transference of the electrically-charged submolecules or ions to the corresponding poles, where they lose their charges, and thereby become capable of reacting with one another or with neighbouring molecules. As a general rule they are, when discharged, themselves incapable of independent existence.

Though the genus Lepidophloios, in regard to species, is a comparatively small one, yet it derives considerable importance from its occurring throughout the whole of the Carboniferous Formation, as well as in the peculiar characteristics of the plants comprised in it.

The fragmentary condition in which the specimens are usually found has given rise to the creation of several genera, which can all be shown to merely represent different conditions of growth and preservation of one generic type. There are, also, other points in the structure of Lepidophloios which require further investigation, and the object of the present paper is to attempt to clear up some of these, about which much confusion still exists.

During the summer of the present year (1820), while navigating with the ship Baffin, the icy sea in the immediate neighbourhood of West Greenland (the east side), several extremely curious appearances of distant objects, produced by the reflective and refractive properties of the atmosphere, were observed.

This paper examines the astronomical theory of ice ages of James Croll (1821–1890), its influence on contemporaries John Tyndall, Charles Lyell, and Charles Darwin, and the subsequent development of climate change science, giving special attention to the work of Svante Arrhenius, Nils Ekholm, and G. S. Callendar (for the carbon dioxide theory), and Milutin Milanković (for the astronomical theory). Croll's insight that the orbital elements triggered feedbacks leading to complex changes – in seasonality, ocean currents, ice sheets, radiative forcing, plant and animal life, and climate in general – placed his theory of the Glacial Epoch at the nexus of astronomy, terrestrial physics, and geology. He referred to climate change as the most important problem in terrestrial physics, and the one which will ultimately prove the most far reaching in its consequences. He was an autodidact deeply involved in philosophy and an early proponent of what came to be called ‘cosmic physics’ – later known as ‘Earth-system science.’ Croll opened up new dimensions of the ‘climate controversy’ that continue today in the interplay of geological and human influences on climate.

Groundwater is widely used in the semi-arid region of Remila plain (Khenchela, Algeria) for urban and agricultural supplies. An integrated statistical and hydro-geochemical approach was performed with 70 water samples in order to identify the main processes and the origin of water salinisation. The results have suggested the dominance of three chemical facies: Sulphato cloruro calcic (SO4–Cl–Ca) in the northeastern part, Sulphato cloruro calci magnisian (SO–4Cl–Ca–Mg) in most of the waters andalkali-earth bicarbonate (HCO3–Ca–Mg) in the southeastern part. Although based on principal component analysis and hierarchical clustering analysis, the statistical approach identified three water groups: (1) saline water (17 %; total dissolved solids >1000 mg l−1 with the dominance of Sulphate (SO42−)); (2) moderately saline water (17 %) with a dominance of bicarbonate (HCO3−); and (3) moderately saline water (66 %) with mixed facies. The binary diagrams confirmed the predominance of three processes: evaporite dissolution and/or precipitation, combined by ionic exchange. In the northeastern part of the area, however, another process was detected – the saline intrusion of Sabkha water, favoured by extensive groundwater use.