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Since the Iast papers the research has been continued at intervals through the nine years. Lome numerical errors on pp. 325 and 327 in the last paper have been detested by the author, but nothing which in the least decree alters the main results of that paper, viz., that the number of revolutions per second which a disc having a white sector w , and a black sector 360° — w , must make in order that the flicker may just vanish, under an illumination I, is given by an equation of the form n = a+b log w (360- w ), a being a constant, and b of the form c+d log I, where c and d are constants. If the disc is considered to be under unit illumination when lighted by a standard stearins candle, burning 8·273 grm. of stearins per hour, at a distance of 4 metres; that is, if I is taken to be 1 under these conditions, then, from the combination of the series of observations described in papers I and II, with man others made since, it follows that the numerical value of n is determined with a very fair decree of accuracy to within at most threes revolutions per second, and generally within one, from the equations n = 10·7+12·57 log I, for discs half white, half black, and n = -27·83+(8·57+20·79 log I) log w (360 - w ), when tbs angle of the white sector is w °.

The second section of Chapter XVI of the Statutes of the Royal Society 'commences with these words: “A catalogue of the manuscripts in the archives shall be available for reference at the rooms of the Society.” Now a catalogue assigning a single number and title to a whole volume or collection of more or less independent documents does not afford much help to the inquirer. However, one detailed catalogue, dealing, item by item, with a large part of the correspondence of the Society, down to the year 1740, was compiled by Mr. W. E. Shuckard, the Librarian, and published in 1840. The arrangement adopted in cataloguing the documents preserved in the 48 “Letter-Books” of this series, was alphabetical for authors, and chronological in the sequence of the contributions of each writer. Parallel with these “Letter-Books,” there exists a set of guard-books, 39 in number, filled mainly with early classified MS. papers of the period 1606—1741. These documents, about 2500 in number, the production of some 800 authors, were catalogued in 1907, a manuscript Calendar being compiled, together with an Introduction and Index Nominum , both since printed. The titles and numbers attached to the several guard-books of this series are here given: it should be noted that the documents had been arranged mainly in accordance with their subjects, but in a few instances by authorship. There has been given to this set the designation- Although some notion of the character and range of these “Classified Papers” may be formed from the titles given to the several books, yet a reference to the MS. Calendar will be required should exact details of any particular paper be wanted. Here the printed Index of Authors’ names will be found useful. Still there are many papers which, being anonymous, cannot be reached in this way. In this connection may be mentioned two long lists of manuscripts in various libraries; these lists are Nos. 32 and 33 in vol. xvii. Of authors’ names in the Index which afford no clue to the subjects of their papers are those of a number of persons concerned in the farming of sea-coals and the trade therein, both at Newcastle and in Scotland. These papers are Nos. 29 to 55 in vol. xxv, and belong to the period 1610—1633. They, and many others dated long before the foundation of the Royal Society, scarcely belong to the Archives, but are interesting in themselves and afford material useful in tracing the antecedents, the scope, and the development of the Society.

Although dry paper is widely used as a supporting and insulating material in telephone cables, the published data with regard to its specific inductive capacity (or permittivity) appear to be very meagre. For this reason Mr. Gavey, C. B., Engineer-in-Chief of the Post Office, asked us to investigate the matter, and sent for test a large number of samples of paper obtained from four different cable manufacturers. All the samples consisted of what is known as “chemical wood paper,” presumably free from lignified fibre. This type of paper, according to the Society of Arts Report on the Durability of Papers, is better in lasting quality than “mechanical wood paper” or paper made from straw, jute or esparto grass. Mr. Gavey, in addition, has kindly supplied the results of some tests on actual cables and further data for some of the samples of paper. This information is embodied in Part II of the present paper. Part I.–Tests on dry paper. One of the main difficulties in the testing of paper lies in the fact that it absorbs moisture so readily; and the presence of moisture has a large effect on the specific inductive capacity and an enormous effect on the insulation-resistance. The nature of these effects is well illustrated by the curve in fig. 6 (Part II, p. 204), which shows how the capacity increases and the resistance decreases as a well-dried cable is allowed to absorb moisture from the atmosphere.

The argument of this paper map be regarded as centred round the ascertainment of two linear differential equations, those denoted by (P′ - p ) η -1 Ψ = 0, (Q′ — q ) η -1 Ψ = 0; these are, in fact, differential equations satisfied by a quotient of theta functions of several arguments when all of these arguments except one are taken constant, and the theory of the paper is in close connection with the classical method for approaching the definition of the theta function from the algebraical side. It would seem to be important to justify this assertion in precise terms, so as to make clear the general bearings of the results arrived at by the authors. The elementary algebraic method which they follow has in my opinion great interest, especially as it enables them to deal in part with the theory even when the curve has unknown multiple points; but one is not satisfied until the functions involved are defined by their behaviour and not by their algebraical form. I hope, therefore, that the writers will allow me to make the following remarks; and that I may be pardoned for explicit references to my own volume, ‘Abel’s Theorem,’ 1897. This was witten before the appearance of Weierstrass’ lectures (‘Werke,’ vol. 4, 1902; 600 quarto pages), and is very imperfect; but it is briefer in one respect than Weierstrass’ theory, by the use of the fundamental integral functions (Kronecker, Dedekind and Weber, Hensel). What there is of novelty in the following remarks relates mainly to these. The general ideas are expounded also in Clebsch and Gordan’s ‘Abelsche Functionen’ (1866)—to which, as to Weierstrass’ volumes, explicit references are given below. I consider in the first place a curve of which the multiple points are known and allowed for; but exemplify in examples how the theory can be applied when this is not so, the existence of a new multiple point being regarded as a particular case.

The authors have recently made a series of observations on some cases of inter-crystalline fracture in various metals, occurring as the result of the prolonged application of stress. In explanation of these phenomena they have formulated an hypothesis which appears to afford a satisfactory account of the present observations and to correlate them with other well-known phenomena whose exact nature has, however, hitherto remained obscure. In putting their observations and hypothesis on record at the present stage, the authors are well aware that much fuller experimental investigation of the whole subject is required, and they hope to carry this forward. The evidence now available, however, appears to them to justify preliminary publication, especially in view of the fundamental interest and great practical importance of the subject. The present paper relates to a group of phenomena some of which have long been known, in the case of brass, as “season cracking.” Brass articles which have been manufactured by a process of alternate cold-working and annealing—such, for instance, as cartridge-cases and other articles made by operations of cupping and drawing—sometimes exhibit a tendency, after a period which may vary from a few hours to several years, to undergo spontaneous cracking. The occurrence of this type of failure of brass has been a serious manufacturing difficulty and much study has been given to the subject; as a result, modifications of both the annealing and the drawing processes have been made, which, to a considerable extent, eliminate the trouble. A satisfactory explanation of “season cracking” has not, however, been put forward so far as the authors are aware. From the present point of view, perhaps the most interesting fact which has been observed about "season cracking” in brass is that the fracture—in those cases where its path can be traced clearly among the micro-constituents of the metal—markedly follows the inter-crystalline boundaries. An example of such a crack is illustrated, under a magnification of 100 diameters, in fig. 1, where the inter-crystalline character of the fracture can be clearly traced (Plate 1).

In a previous paper I investigated the problem of the formation of waves on deep water by wind, and found that the available data were consistent with the hypothesis that the growth of the waves is due principally to a systematic difference between the pressures of the air on the front and rear slopes. Lamb had already discussed the maintenance of waves against viscosity by an approximate method, but without obtaining numerical results. Being under the incorrect impression that Lamb’s approximation would not hold for the short waves I was chiefly considering, I proceeded on more elaborate lines. It now appears, however, that Lamb’s method is not only applicable to the problem of waves on deep water, but is readily extended to cover the case when the water is comparatively shallow, and to allow for surface tension. The fundamental approximations are first, the usual one that squares of the displacements from the steady state can be neglected, and second, that viscosity modifies the motion of the water to only a small extent. The motion of the water can then, to a first approximation, be considered as irrotational. With the previous notation, let ζ be the elevation of the free surface x, y, z the position co-ordinates, t the time, U the undisturbed velocity of the water, h the depth, and φ the velocity potential. Also let σ, p, q , and ϑ denote respectively ∂/∂ t , ∂/∂ x , ∂/∂ y , and ∂/∂ z , and write p 2 + q 2 = - r 2 .

1. In the paper recently communicated to this Society, Dr. Duffield has described a promising method of determining gravity at sea, but a somewhat fuller discussion on the theoretical side is required before an opinion of its capabilities and limitations can be formed. For this purpose it is more especially necessary to investigate the effects of the forced vibrations which may be imposed on the mercury in the apparatus by the vertical acceleration of the ship. 2. The problem of determining the period of free oscillation in a barometer tube is very simple, but in the present case three tubes are connected with each other, and at least two of the tubes are not of uniform section, but contain a portion with a narrow bore introduced to damp the oscillations.

Criticism of Dr. Chapman was not the primary object of my paper, and it would seem that I have studied brevity too much in referring to differences which to myself were conspicuous. That fault I shall hope to repair now. But first I should make it clear that there are certain points about which there is, I think, no difference of opinion. Our knowledge of magnetic storm phenomena in high latitudes is very limited, but in low and moderate latitudes the following phenomena in the variations of H (horizontal force) during storms having Sc’s (sudden commencements) have been, I think, generally recognised for many years. The result of the Sc movement or movements is almost invariably to enhance H, and a marked fall does not as a rule set in immediately. This rule is not absolutely without exception. For instance, on the occasion of the very large storm on August 11-12 of the present year, a large reverse movement set in so soon after the Sc that the mean values alike for the first hour, the first half hour, and even the first quarter hour of “storm time” are much below the pre-storm value. Still exceptions are rare, and the mean value of H for the first hour or half hour after the Sc is nearly always in excess of the pre-storm value.

The apparatus used by Mr. Merton in the above-mentioned paper was very kindly handed over to the author. The following experiments were made with it:—Five grammes of metallic uranium were finely powdered in a steel mortar and then heated to redness in a water-pump vacuum for half an hour. The metal was then transferred to a small bulb in which the metal could be bombarded with the cathode discharge, and this tube sealed on to the Merton apparatus. A small bulb containing charcoal, a hard glass tube containing copper and copper oxide, and a small bulb with phosphorus pentoxide were also sealed on to the apparatus. The whole was then pumped out and washed out several times with oxygen till the spark would not pass in the tube containing the uranium. The tube was then heated as strongly as possible and the gases pumped off and examined; carbon gases and hydrogen were present, but only just enough helium and neon to detect them in the ordinary was using a capillary tube. The tube was again washed out with oxygen and pumped till the spark would not pass through the tube containing the uranium. The palladium tube was then heated for about 20-30 seconds as as to admit hydrogen and allow the spark to pass. The bombardment of the uranium lasted about two hours. During all this time carbon gases and hydrogen were evolved from the metal. These were absorbed by keeping the charcoal bulb cooled in liquid air and heating the copper oxide. At the end of Experiment 1 enough helium and neon at about 2 mm. pressure remained to fill the capillary examining tube and also a small space below. Experiment 2.—Bombardment for one and a-half hours. Rather less helium and neon. (The helium lines–red, yellow, and green–not so strong as in Experiment 1.)

In a paper read before the Society on February 28, 1905, I drew attention to the fact that all thorium minerals, so far as could be ascertained, appeared to contain uranium and radium. Since then, I have examined a number of additional minerals, in order to test the induction further. The result has been quite confirmatory of the original conclusion. I have, in this further investigation, contented myself with determining the thorium and radium, for it may now be considered proved that radium is a product of uranium, and it is much easier to establish the presence of radium by its emanation than to detect uranium by chemical analysis. The experimental methods explained in the former paper were employed. The results are as follows:—

Frenkel's derivation of the electromagnetic mass and the equations of motions of the electron are very suggestive and simple. But we cannot admit that our method of reasoning is unjustified. There are two points: (1) We have proved exactly that the two variation principles using the Lagrangian and the Hamiltonian are entirely equivalent, both leading to the same results (p. 436). The reason why we have to use the Hamiltonian, not the Lagrangian, for the derivation of the equations of motion is the additivity of the p kl (D, H) and not of the f kl (E, B) in accordance with Frenkel's statement; we regret that we have stated this important point only in a footnote (p. 449).

1. No systematic investigation on this subject has yet been attempted. The efforts made to group these materials in a series according to the charges generated when they are rubbed two at a time are of uncertain value because of (1) impurities of substance and surface, (2) indeterminate initial surface strains. Moreover, the general practice has been to rub the solids when held, one in each hand. A more reliable method is to mount the bodies in a mechanism which ensures that the same parts of them come into contact at each fresh stroke. In the present research, the elements, mostly metals, are those specified in the preceding paper. The textiles are made and cleansed as described in an earlier paper. Silk, cotton and linen in our experience behave reliably when fully cleaned. The other great textile material, wool, is more oily and cannot be readily cleansed; so is less trustworthy. We therefore at present confine ourselves to one animal and one vegetable textile, choosing the pure samples of silk and cotton specified in the above paper. Also filter paper, another convenient fabric, is used after being boiled in several lots of distilled water. As the silk and cotton are treated with boiling chloroform, we tried exhausting the filter paper in this solvent to see if such treatment affected the cellulose in any way; but no effect on the properties of the paper could be found.

The difficulties attending continuous registration of electrical potential gradient of the atmosphere are very great; but it is not my intention in this paper to discuss these. My object is to call attention to the measuring part of an electrograph, and more especially to experiments made with an instrument that promises to be of considerable service in work of this kind. A recording voltmeter ought to have a uniform scale value over the range for which it is intended to be used, it must possess a high degree of insulation, and it ought to be capable of acting efficiently for long periods without having to be taken to pieces for cleaning. The general excellence of the Dolezalek electrometer and its high degree of mechanical symmetry suggested to me its use as a recorder, although I do not know that it has been tried before. The instrument was designed to measure very small differences of potential between the quadrants with a potential of, say, 100 volts on the needle. The first thing to ascertain was whether, with a fixed difference due to a single Weston cell, the sensitiveness could be reduced so that the movement of the needle would record, on a suitable scale, the potential applied to it. A trial suspension made of phosphor bronze proved successful, and a scale value of about 200 volts per centimetre was obtained on the photographic paper, which is carried on a drum 1 metre from the mirror attached to the needle Up to 500 or 600 volts the behaviour was excellent, but for higher potentials the needle began to tilt, and if a sudden change was made the needle generally discharged to the quadrants. Experience showed that it would have frequently to carry over 1000 volts. The needle was therefore loaded by prolonging the vertical axis to about 3 cms. beneath the needle, and adding at the end a small brass nut of about 1½ grm. It now carries 1100 volts with perfect safety and stability.

This paper embodies the results of experimental investigations, carried out during the past five years in the Fuel Laboratories of the Imperial College of Science and Technology, South Kensington, into the resinic constituents of bituminous coals and their supposed determining influence upon the coking propensities thereof. The property of “coking,” when carbonised at 900°-1000°C., is not inherent in all “black” coals, but varies from zero up to a high degree. Although, to some extent, it appears to be connected with the amount of volatile matter yielded by the dry ashless coal substance at such temperatures, the connection is by no means so direct as is sometimes supposed. Thus, whilst it may be said to be generally non-existent in coals yielding below 15 or above 45 per cent, of “volatiles,” and to be at its maximum in those yielding between 15 and 30 per cent., and whereas also it gradually diminishes as the yield of “ volatiles” rises above 30 per cent., yet there is no corresponding gradual diminution as the yield falls below 20 per cent. Indeed, in the region of 15-20 per cent, of “volatiles” there is an abrupt failure of coking properties; for in this region—and particularly at about 15 per cent. —are to be found not only some exceptionally strongly-coking coals, but also many that are quite devoid of the property. The reason for such an apparently sudden disappearance of coking properties in the said region remains one of the unsolved questions in the chemistry of coal.

I. This experiment was undertaken to elucidate the real character of such statistics as those of eye-colour, hair-colour, temper, health, etc., which have been given, e. g ., by Mr. Galton and by Professor Pearson. The statistics are, it should be noted, not merely statistics of qualities , but of ill-defined qualities , the only guidance to the use of the terms of classification being—with some exceptions—common usage. Strictly speaking we must remember that data so collected are statistics, not of qualities themselves, but of names assigned thereto. It was desired to determine how far the distinction is of importance (1) as regards the naming of single samples: (2) as regards the naming of pairs, two samples of a quality being named more or less together, by themselves, for forming a contingency-table. A matt-surfaced photographic paper was printed by successive exposure to 16 depths of tint, from a slightly impure white to a deep blackish-brown. Small scraps of about ⅜-inch square were cut from each tint, and mounted on cards, two scraps being placed on each card, combined in such a way that every possible combination occurred, making 16 x 16 = 256 cards. Observers were then asked to name the tints on each card under one or more of the following schemes of classification, each observer naming the whole pack:—