Darwin's Theory.–During the voyage of the “Beagle” and subsequently, Mr Darwin made a profound study of coral reefs, and has given a theory of their mode of formation which has since been universally accepted by scientific men.

Darwin's theory may be said to rest on two facts—the one physiological, and the other physical—the former, that those species of corals whose skeletons chiefly make up reefs cannot live in depths greater than from 20 to 30 fathoms; the latter, that the surface of the earth is continually undergoing slow elevation or subsidence.

Comparatively little has yet been done in the way of precise measurement of the rate at which the exposed surfaces of different kinds of rock are removed in the processes of weathering. A few years ago, some experiments were instituted by Professor Pfaff of Erlangen to obtain more definite information on this subject. He exposed to ordinary atmospheric influences carefully measured and weighed pieces of Solenhofen limestone, syenite, granite (both rough and polished), and bone.

A sulphurous acid steam-pressure thermometer, on the plan described in my communication on the subject to the Royal Society of March 1, has been actually constructed, with range up to 25° C., but not yet in a permanent form.

Water flows from a little cistern or reservoir R through a wide vertical tube S, about two metres long, thence through a horizontal capillary tube C', 50 or 100 centimetres long; thence through a wide horizontal metal tube T, 20 or 30 centimetres long; thence through a second horizontal capillary C; and lastly, out by a little constant-level overflow cup L. A vertical glass manometric tube M, a metre and a half long, standing up above the end of T next C to measure the pressure in T by a water column; and a means of giving any uniform temperature to the outsides of S and C, and any other uniform temperature, to the outsides of T and C; complete the instrument.

This thermoscope is founded on the change produced in the magnetic moment of a steel magnet by change of temperature. Several different forms suggest themselves: the one which seems best adapted to give good results is to be made as follows:—

(1.) Prepare an approximately astatic system of two thin, hardened steel wires, r b, r′ b′, each 1 cm. long, one of them, r, b, hung by a single silk fibre, and the other hung bifilarly from it, by fibres about 3 cms. long, so attached that the projections of the two, on a horizontal plane, shall be inclined at an angle of about ·01 of a radian (or ·57°) to one another.

In the article on “Heat” published in the eleventh volume of the Encyclopœdia Britannica, referred to in my previous communications to the Royal Society on Steam Pressure Thermometers, it is shown that the Constant Pressure Air Thermometer is the proper form of expansional thermometer to give temperature on the absolute thermodynamic scale, with no other data as to physical properties of the fluid than the thermal effect which it experiences in being forced through a porous plug, as in the experiment of Joule and myself on this subject; and the thermal capacity of the fluid under constant pressure. These data for air, hydrogen, and nitrogen have all been obtained with considerable accuracy, and thererfore it becomes an important object towards promoting accurate thermometry, to make a practical working thermometer directly adapted to show temperature on the absolute thermodynamic scale through the whole range of temperature, from the lowest attainable by any means, to the highest for which glass remains solid.

An occultation of a star, though not appealing to ordinary observation with the same force, is intrinsically an event as striking as an eclipse of the sun. It establishes the fact of the moon's proximity. Were it not that the moon's brightness overpowers the light of the small stars, occultations would be commonplace phenomena. As things are, we can watch, with the eye unaided, the eclipses of the planets and larger stars, not down, perhaps, to below the third magnitude; and the rarity of such conspicuous objects makes the occultations correspondingly rare.

The physical activity going on in the Sun is still increasing, and worthy of all admiration. There was a very large spot had come round on the North-following limb on March 29; and was after that the subject of observation from day to day as it approached the central Solar meridian. But when it arrived there, on April 3, behold two less large but still most notable spots had burst out clear and full within the previous twenty-four hours between the great spot and the preceding limb. And on this day, April 4, there are two more notable ones very close to the greatest spot, making in all five remarkable spots not only all visible at once, but working and seething positively before our eyes.

In former papers laid before this Society, I showed that when any two metals are rubbed against each other, a current of electricity is produced; and that this current agrees in direction with the thermo-electric current for the same two metals, and is neater approximately at least, in proportion as the metals rubbed are far apart on the thermo-electric scale,—the greatest current, as far as I have yet observed, being got from antimony and bismuth.

I have made the following observations in the Natural Philosophy classroom of the United College, St Andrews, with the view of ascertaining whether the electromotive force required to cause a spark to pass between a small globe and a plate, or between a point and a plate, differs for the two kinds of electricity. Sir William Thomson suggested that I should apply to this question the method of measuring the electromotive force required to produce sparks, which I have described in papers already contributed to the Society (Trans. Roy. Soc. Edin. vol. xxviii. p. 633). It is a problem to which Faraday attached great importance. He says at sect. 1523, vol. 1, of his Experimental Researches in Electricity: “The results connected with the different conditions of positive and negative discharge will have a far greater influence on the philosophy of electrical science than we at present imagine, especially if, as I believe, they depend on the peculiarity and degree of polarised condition which the molecules of the dielectrics concerned acquire.” He records a great number of experiments on this subject in sections 1465–1525. He took sparks between a ball 0·25 inch in diameter and a ball 2 inches in diameter. When the large one was connected with a discharging train, the small one charged positively gave a much longer spark than when charged negatively; also the small ball charged negatively gave a brush more readily than When charged positively in relation to the effect produced by increasing the distance between tho two balls (sect. 1489).

Having had occasion in the course of my work to investigate some of the properties of the mercurial thermometer, I have obtained a series of results which are comprised in a memoir now submitted to the Society. A brief summary of these is given in the following abstract.

1. After describing a simple method of calibrating a thermometer, I give a detailed proof (following Pierre) that the calibration unit gradually undergoes a slight diminution in value. In the course of five years this may amount, in a new thermometer, to as much as ·21 per cent. The 0°–100° interval, therefore, requires periodic verification.

The subject of these investigations, some of the results of which are before the Society to-night, was suggested to me by Professor Carl Ludwig, and was carried out in his laboratory at Leipzig, where I worked with the help of his assistant, Dr Drechsel, to whose kindness and large knowledge of the subject I was much indebted.

In this paper I shall give simply an account of the method of analysis, leaving for the future a record of the facts which it has enabled me to obtain.

In the course of an examination of some of the “Challenger” deep-sea thermometers, I have recently had occasion for measurements, accurate to one or two per cent., of pressures such as five or six tons weight per square inch. The ordinary gauges showed themselves to be quite untrustworthy, and it was necessary to devise come plan of whose accuracy the experimenter can feel assured. The following process has proved completely successful, and is capable of any desired degree of accuracy.

The materials for this Report have been obtained from the Convener, Professor Forster Heddle of St Andrews University, William Jolly, Esq., H.M. Inspector of Schools, Inverness, and William Wallace, Esq., High School, Inverness.

To make the descriptions of the boulders more intelligible, it has been found necessary, as in former Reports, to annex a few diagrams, which will be found at the close of the Report.

These specimens have recently been presented to the Anatomical Museum of the University, by J. Wharton Cox, Esq., who had received them from his father, Dr Cox of Sydney, the well-known Australian naturalist.

The masks had been procured by Dr Cox from missionaries, and were either from the island of New Ireland or New Britain, in proximity to the north coast of New Guinea. They were both formed of the frontal and facial bones, on which a face had been modelled in a composition, formed of a mixture of a resinous substance with earth or clay. This artificial face had then been painted with red, black, and white pigments. The larger mask was hollowed out behind, by the removal of the sphenoid and ethmoid bones, so that it could be adapted to the face of a wearer, and a bar of wood was fastened transversely across the hollow, which the wearer had evidently used for holding the mask between his teeth; as the mask had both the eyelids and lips separated from each other, the wearer could both see and breathe through these openings.

In continuation of researches communicated to the Royal Society of Edinburgh, 1880 (February 16), in which I gave the probable position of an ultra-Neptunian planet, I have now to inform the Society that I have detected the existence of perturbations in the motion of Uranus, agreeing remarkably in character and period with those which would be produced by the new planet. These results are obtained from observations of Uranus extending over more than a century. The position of the planet, from this point of view, is found, from the first rough examination, to be the same as that given by me in my former memoir. This gives a means of determining the mass of the new planet.

Professor Jenkin has contributed several valuable papers to our Transactions.

In 1869 we had “The Practical Application of Reciprocal Figures to the Calculation of Strains on Framework,” in which he exemplified in a very clear manner the mode of applying to important statical questions a beautiful principle, due in part to Rankine but mainly to Clerk-Maxwell.

The paper for which the award of the Keith Prize is now made is more thoroughly original, and may be roughly described as an extension of Maxwell's principle to the kinetics of machinery, where all parts move in one plane. It is entitled “The Application of Graphic Methods to the Determination of the Efficiency of Machinery.” The first part was read to the Society in 1877, and the second in the following year. All three of these papers are in our Transactions.

When I had the honour of being asked by the Council of the Royal Society to give the following address, I chose the subject partly because it had been brought under the notice of the fellows by my predecessor, Professor Kelland. His memoir was written comparatively early in the history of the subject; and he seems to have been but little acquainted with what others had done even up to the time at which he wrote. Accordingly, although the subject is treated very ably in his paper, it is treated from only one point of view; and, indeed, one side of it is left out of sight altogether. The relation of the whole theory to the question of the origin and mutual independence of the axioms of geometry has been made much clearer of late, and I believed that some account of the more modern views might be of interest.

[After this note had been laid before the Council, the new number (vol. ii. No. 4) of the “American Journal of Mathematics” reached us. In it there are exhaustive papers by Messrs Johnston and Story on the subject of this American invention. The principles they give differ only in form of statement from those at which I had independently arrived. I have, therefore, cut down my paper to the smallest dimensions consistent with intelligibility.—P. G. T.]

The essential feature of this puzzle is that the circulation of the pieces is necessarily in rectangular channels. Whether these form four-sided figures, or have any greater (even) number of sides, the number of squares in the channel itself is always even. (This is the same thing as saying that a rook's re-entrant path always contains an even number of squares. This follows immediately from the fact that a rook always passes through black and white squares alternately. The same thing is true of a bishop's re-entering path, for it is a rook's upon a new chess-board formed by the alternate diagonals of the squares on the original board.) That there may be circulation in the channel, one of its squares must be the blank one.