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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:—

Dieke and Hopfield showed that the absorption bands of H 2 , which are located in the extreme ultra-violet (about 1000-1500 Å. U.) were due to transitions up from the ground level of H 2 , which they called A, to two higher electronic levels which they called B and C respectively. Two years ago I found the emission bands which go down to the B level and some of them were described and partially analysed in this journal. In a series of papers Dr. Davidson and I have been able to show that these bands comprise a large number of distinct band systems and contain a very large part of the total strength of the visible emission spectrum of H 2 . In previous papers I have called this B level of Dieke and Hopfield 2 1 S as it has an effective principal quantum number in the neighbourhood of 2 and its properties are those of an S level. In view of recently proposed changes in the nomenclature for band spectra I propose in this paper to denote this B or 2 1 S level by the symbol 2 p 1 ∑. In this notation 2 denotes the principal quantum number and p indicates that the azimuthal or equivalent quantum number of the excited electron is 1. ∑ means that the component of the total angular momentum (or equivalent quantized quantity) about the internuclear axis is 0 and the prefix 1 that the state is a singlet state. Various attempts have been made from time to time to discover bands in this spectrum which end on Dieke and Hopfield’s C level, but, until recently, nothing at all convincing has resulted from these efforts. I have now found a number of band systems which end on this C state.

In a paper published in the ‘Philosophical Transactions’ in 1908, the writer described some experiments on the X-rays emitted by a variety of metals when used as anticathodes in an X-ray bulb. Among the results established was the homogeneity of a large proportion of the X-rays when the bulb was very “soft.” The absorption curves of the several homogeneous radiations revealed their identities with the characteristic “secondary” radiations which Barkla and Sadler had then recently discovered. The experiments described in the present paper are an extension of the above, and were carried out partly at the Cavendish Laboratory in 1908 and partly at the National Physical Laboratory just prior to the war. The writer’s military duties have prevented the continuation of the work, and the results are now put on record in the hope that they may help to further the progress of the subject, to which the more precise method of the crystal-spectrometer has given a great impetus from a different point of view.

1. When reading a recent paper before the Royal Society, and also in the Press, Dr. Edridge Green has stated that he can find no connection between the luminosity and the colour sense of persons having either normal or abnormal colour sensations. Since I feel that to allow such a statement to go unchallenged might be interpreted as meaning that no such connection could be shown to exist, I propose in the following paper to place before the Society some of the evidence which indicated that there is in reality a very intimate relation between luminosity and colour sense. The results given include a small part of those which have been obtained in a series of experiments which have occupied the last two years and form part of investigation which is still in progress. The term “luminosity” as used in this paper has the following meaning: Suppose that light from some source, such as the electric arc, is admitted to a spectroscope by means of which a real pure spectrum is produced, and that a slide in the plane in which the spectrum is formed carries a slit of fixed width. Light of sensibly one wave-length, i. e. monochromatic light, will pass through this slit, and by means of a lens placed in the beam of this light an image of the first face of the prism which is used to from the spectrum can be formed on a screen. In this way a monochromatic patch of light is obtained, the brightness of which depends on the nature of the source of light, the width of the collimator slit, the width of the slit placed in the spectrum, which for short will be called the movable slit, and the dimensions of the lenses employed. Further, if alongside this coloured patch is formed a white patch of light produced by light which proceeds from the same source but has not undergone dispersion, and that by some means or other the intensity of this white light is altered till the coloured and white light, measured in any arbitrary units, measure the luminosity of the light of that colour which is passing through the movable slit. Since the unit in which the white light is measured is arbitrary, we are not concerned with the absolute intensity of illumination of the white patch, and may use any device we like to alter the quantity of white light which falls on the screen so long as we are able to measure the ratio of the quantity of light employed in different experiments. It will further be observed that for any given person the measurement of the luminosity of a given coloured light in the spectrum involves the comparsion of the brightness of the coloured patch as it appears to him with the brightness of the white patch as it appears to him.

I. Detonation in Acetylene and Pentane Mixtures .— Observations on detonation in acetylene and pentane mixtures at ordinary pressures with the object of finding the position of detonation in a tube under set conditions, were described in the previous paper. The present paper extends this work, but at higher initial pressures and temperatures. Apart from the study of detonations in engines, and experiments in explosion bombs where the pressure rise is observed, very little appears to have been done to extend the work of Le Chatelier and of Dixon on rate of propagation of combustion to regions of high pressure. The highest pressure at which explosions were photographed by Le Chatelier and by Dixon were about one and a half to two atmospheres. Woodbury, Canby and Lewis using a bomb of 12 inches length succeeded in photographing explosions in acetylene air mixtures at pressures up to 4 atmospheres. They also investigated the effect of initial temperature (up to 125° C.). The results are referred to by Brown, Leslie and Hunn who find that for any initial density or pressure there should be a certain maximum value of the initial temperature to provide a maximum rate of rise of pressure on exploding a given gaseous mixture; decrease in density of charge on rise of temperature overcomes the effects of increase in reaction velocity.

In the first section of this paper it is pointed out that one and the same metal may cause a great variety of different colours, just as the colour of gold vapour differs from the colour of the light reflected from gold as well as from the colour of the light transmitted by gold leaf. While the ultimate cause of the colour of a metalliferous medium is to be found in the structure of the metal molecule itself, the arrangement of these mole­cules, according to any fixed law, causes them to affect one another’s free periods in a definite manner, and thus gives rise to corresponding optical properties. The object of this paper is to discover, by means of these optical properties, the molecular arrangement (microstructure) of various metal glasses, of colloidal solutions of metal and of metallic films. Expressions giving the refractive index and the absorption coefficient (the optical constants) of a compound medium consisting of metal (1) in small spheres (granular), and (2) in discrete molecules (amorphous), diffused through an isotropic non-dispersive transparent medium (the solvent), are next investigated in terms of the corresponding optical constants of the normal metal.

The results recorded in this paper are an extension, with fresh substances, of those described in Parts II and III of this series of papers. No fresh principles have been introduced, and the experimental method and mode of recording results have been as before. The results are confirmatory of the theories developed in these papers. The α -Bromo Acids, CH 3 ( CH 2 ) n CHBr COOH . A series of six of these was available from the valuable collection of Dr. Le Sueur, and gave a very interesting series of films. In the condensed films, the most obvious point is the increase in the area of the heads of the molecules caused by the bromine atom; the next, a rather less agreeable one, is the property that these heads have of packing into several different arrangements of somewhat different areas, according to circumstances. These have not yet been fully worked out, but at least three distinct packings have been recognised. Possibly a greater number exist. As with the unsubstituted acids the packing is closer on water than on HCl. The phenomena on distilled water are complicated by some differences depending on the length of time the water has been in the trough, similar to those found with the simple fatty acids (Part II, p. 466).

The semi-graphical method about to do described enables solutions of many dynamical problems of a practical nature to do obtained with ease and rapidity. In particular, useful solutions can be found of problems relating to motion in a resisting medium in cases where the resistance is given as a function of the velocity which cannot be expressed by any simple algebraic form. In this paper the method is applied to the investigation of the motion of a projectile. Some of the curves obtained can be plotted directly from the ballistic table, but none of the curves are found in this way. They are derived by simple graphical processes from a primitive curve which represents the results of numerous experiments, reduced to give the resistance of a standard projectile, fired under standard conditions, as a function of the velocity. The curve, which is the basis of the diagrams given in the paper, is plotted from data given in the official 'Text-book of Small Arms,' 1909. From the educational point of view the method about to be described has the advantage that the essential scientific principles relating to the motion of a projectile can be taught rapidly, and without reference to the laborious methods of analysis by means of which the ballistic tables are derived from the experimental data. As will be seen, other functions, besides those given in the ballistic tables, can be plotted with ease, because elimination is done by mere projection with set-square and T-square. By the drawing of a ballistic diagram a student of gunnery becomes familiar with the general relations existing between the different functions involved; in fact the set of curves constituting the ballistic diagram will probably, when drawn by himself, persist as a permanent mental picture of reference which cannot but be useful to a gunnery officer.

It has been shown independently by Westgren and Phragmén, and by one of the present authors, that manganese is allotropic. Both investigations pointed to the existence of three crystalline modifications. The names given to the different forms of the metal were not the same in the two papers, and in order to avoid ambiguity we have adopted Westgren and Phragmén’s nomen­clature. This latter is preferable because the so-called electrolytic manganese, which we called α-manganese (their γ-manganese) is probably a hydride of the metal. It therefore seems better to give the names α-manganese and β-manganese to the two forms which are known to be metallic, as W. and P. have done. The present paper describes the structure of α-manganese, which is stable at room temperature and higher temperatures up to about 700°C. In the two investigations referred to above, the powder method of X-ray analysis alone was employed. In order that the results of any method of analysis may be trustworthy, the method must be capable of discriminating between all solutions which are theoretically possible, and it is not sufficient merely to indicate one solution which explains the observations. If the experimental data are not extensive, and the accuracy with which they can be tested is low, it is easy to get a spurious agreement between observation and calculation, which lies well within the limits of experimental error. This is especially the case with a structure such as that of α-manganese where the unit cell contains a large number of atoms, and the atomic positions depend upon a large number of parameters.

In a paper by one of us, the method of obtaining the relation between the range and velocity of recoil atoms has been described. In the work described in the following paper the same method has been used to extend the earlier results to greater ranges. Consider a forked track due to an elastic collision between an alpha particle of mass M and initial velocity V and a nucleus of mass m , initially at rest. If Φ and θ denote the angle of deflection of the alpha particle and the angle of projection of the struck nucleus, and if v a and v n are the velocities of the two particles after the collision, we have m /M = sin Φ /sin (2θ + Φ ), (1) v n /V = 2M/M+ m cos θ, (2) v n / v a = M/ m sin Φ /sin θ.

1. In a recent paper Houston has proposed an explanation of the extraction of electrons from metals by intense electric fields, which is based upon Sommerfeld’s modification of the Lorentz electron theory of metals. The writer has also investigated this problem from the same standpoint, but reached the conclusion that such an explanation is inadequate, at least in its present form. Houston’s paper should, however, be regarded as a treatment of the Schottky effect for very intense fields, but, as will be shown, if the Sommerfeld electron theory is accepted the expression for the Schottky effect should be modified, and this modification becomes significant at high fields. The object of this paper then is (1) to derive an expression on the Sommerfeld theory for the thermionic current in the presence of an electric field, and (2) to point out the difficulties in the way of accepting this effect as the correct explanation of the “field currents” examined in detail by Millikan and Eyring, Gossling, del Rosario, and others. In the course of the paper it will be necessary to work out the volume distribution, i. e ., degree of penetration, of a surface electrical charge on the basis of the Sommerfeld electron theory.

Robertson and Fox in their fundamental memoir have published a comprehensive account of the precautions necessary for obtaining reliable results with a prism spectrometer in the infra-red between 1 and 17 μ. The authors feel, however, that some advantage to other workers may accrue if they in turn outline their own particular difficulties with the manner of their resolution. it may be stated at once that it is how possible to make scale readings to an accuracy of 1 mm. during the day , with a galvanometer sensitivity of 10 -10 to 10 -11 amp. per millimetre deflection at 1 metre distance. If it is realised that the work is carried out on the top floor of the Chemistry Department of this Institution, in a building which houses some dozen electrical generators and a large liquid air plant with a stream of heavy bus traffic 10 yards from the building and a tube railway at 100 yards, it will be seen that the usual experimental difficulties have been completely overcome. Preliminary experiments were made in a constant temperature room in the basement; the humidity was high and had a deleterious effect on the rocksalt portions of the apparatus, whilst the discomfort of night work in such a room was extreme. It has consequently decided to re-approach the problem from the beginning, but not before trials had shown that where the motion of the building as a whole is small, comparatively simple expedients serve to eliminate most of the mechanical disturbance. This was cut out by placing the galvanometer with its Paschen shields (total weight about 250 lb.) on a large block of wood supported by for pairs of inverted small porcelain crucibles placed at the corners. Eight of the thinnest available crucibles were selected; the two in a pair were placed one on top of the other and separated by a small piece of 5-ply wood and a few pieces of filter paper. If the galvanometer and shields are not too heavy, the replacement of the rubbershock absorber in the ordinary anti-vibration spider by a crucible and one or two layers of filter paper was found very efficient.

In a paper read on December 8, 1916, Lord Rayleigh makes an important contribution to the dynamics of revolving fluids, taking as “the starting point of part of his investigation,” the paper by Dr. Aitken on “The Dynamics of Cyclones and Anticyclones.” After setting out the general equations of motion of an inviscid fluid Lord Rayleigh says “for the present purpose we assume symmetry with respect to the axis of z so that u, v, w and P (assumed to be single valued) are independent of θ .” I take that to be the definition of a revolving fluid for the purpose of the subject under consideration, and it is that form of motion, that is to say, motion which is symmetrical with regard to a vertical axis, that Lord Rayleigh had in mind when he wrote the opening sentence of the paper: “So much of meteorology depends ultimately upon the dynamics of revolving fluid that it is desirable to formulate as clearly as possible such simple conclusions as are within our reach.” For most ordinary readers, meteorology in its dynamical aspect is quite rightly regarded merely as a useful synonym for “Cyclones and Anticyclones.” Dr. Aitken illustrates his view's of the nature of cyclones and anticyclones by many interesting experiments in the dynamics of revolving masses, and when Lord Rayleigh is moved by Dr. Aitken’s paper to set down clearly the conclusions that can be drawn from the theory of revolving fluids it is apparently with the hope that those conclusions may find their application in the phenomena exhibited by cyclones and anticyclones.

The present paper is a continuation of the work on the spectra of selenium, carried out by the authors partly in Professor Fowler’s Laboratory at the Imperial College and partly in Professor Siegbahn’s Laboratory at Uppsala. A detailed account of the experimental part of the investigation together with the analysis of Se IV and Se V has been given in a previous communication. As already reported in ‘Nature’ the experimental data there described have led to the identification of the system of energy levels characteristic of the spectrum of doubly-ionized selenium. It is the purpose of the present paper to give an account of the structure of this spectrum so far as it is revealed by a study of the spectrograms of selenium under different conditions of excitation. The lines of the spectrum in question appear when discharges, even of moderate intensity, are passed through selenium vapour contained in a capillary tube. In the ordinary spark in air, the spectrum is represented only by a very few of the stronger lines which could be ascribed to Se III, but with strong discharges through capillary tubes, the lines are considerably enhanced and the complete spectrum is easily photographed. In the region of very short wave-lengths, below λ 1500, the source found suitable for the excitation of the spectrum was the spark in vacuum between aluminium poles tipped with metallic selenium. With this source, excited by a 50 K. V. transformer, it was found necessary to include an inductance of about 0·5 m. h. to elicit lines of Se III and Se II. At the same time, a study of the spectra excited with and without inductance in series in the secondary circuit has greatly facilitated the assignment of the lines to the various stages of ionization of the element. Reference may be made to a reproduction of the spectra in the previous paper by the authors ( hoc . cit .), where the method of measurement and the instruments employed for photographing the various regions of the spectrum have also been described.

In a previous paper by the writer an examination was made of the torsional vibrations occurring in a reciprocating engine shaft. The case studied was that of a shaft driven by a six-cylinder engine, all parts except the shaft being considered rigid. Certain interesting results, arising from the action of the reciprocating parts, appeared. On account of the importance of the subject of torsional vibrations in engineering practice, and on account of the unexpected nature of the analytical results, it was considered of some interest to examine in greater detail the effect of the reciprocating parts in producing or modifying the vibrations. For this purpose a model is proposed which, it is considered, is as simple as can be conceived, and which, at the same time, involves the characteristics of reciprocating motion. The model is described and the analytical results obtained in Part I of this paper. To verify the analysis, the model was set up in the laboratory and the vibrations observed. Further, to simplify the experimental work, it was thought sufficient for the purposes of verification to arrange it in the first place so as to give only a qualitative agreement with theory, and therefore a precise quantitative agreement was not aimed at, and should not be looked for. An experiment on a much more refined method is being proceeded with to examine minutely into the numerical accuracy of the theory. The details of the present experiment and the numerical results are given in Part II.

The light of the night sky has been discussed in previous papers more particularly with reference to the occurrence of the green auroral line. From a spectroscopic point of view this line is the most definite and interesting feature, and it is important to determine how its intensity varies with time, and whether any connection with the solar cycle of eleven years can be traced. It is also important to determine whether other regions in the spectrum the night sky undergo variations, and, if so, whether they are directly connected with the auroral line or not. In this paper methods are given which have been found practicable for attacking these questions, and systematic observations extending over more than a year are recorded. These establish the existence of a number of interesting variations, and seem to open up a wide field; but it will be necessary to pursue them for a good many years before the questions connected with the solar cycle can be answered. An individual worker cannot, of course, rely on being able to complete such a programme, and it seems desirable to record what has been done so far.

It is recognised as a result of numerous independent experiments that ionisation by X-rays is the result of corpuscular radiation liberated by the X-rays. In a recent paper it was shown by the author that, in the case of carbon and oxygen compounds, the corpuscular radiation liberated by a beam of X-radiation was an “atomic” phenomenon, i. e . that the number of corpuscles given out by an atom of carbon or oxygen in a beam of X-rays is the same whether the atom is in combination or not the resulting ionisation is not, however, “atomic”, the ionisation produced in different gases or vapours by a given amount of corpuscular radiation being dependent on the nature of the gas or vapour. In the present paper an attempt has been made to test whether this “atomic” law holds good for other elements of higher atomic weight. These, given much larger ionisations than the lighter elements, also allow of greater accuracy in the observation, although as the absorption is corresponding increased, large absorption corrections are rendered necessary in some cases.

In the ‘Proceedings’ of the Royal Society, A, vol. 84, p. 209, I gave an account of experiments with Potassium vapour, which had for their object the determination of the dispersion curve for the vapour. The effect of the first three pairs of lines of the principal series was quantitatively estimated, and it appeared that certain conclusions could be drawn as to the numbers of systems taking part in the absorption of light. The present communication deals with further experiments of the same kind with vapours of Sodium and Rubidium, and again with the vapour of potassium, as far as regards a temperature effect, which will be discussed later. The experiments were made possible by a grant from the Royal Society, which enabled me to obtain metallic rubidium, and I am glad to take this opportunity of thanking the Government Grant Committee. In a former paper I gave results of the measurements of wave-length of the principal series lines for rubidium obtained in the absorption spectrum. This spectrum was obtained by heating rubidium chloride with metallic potassium; enough vapour was formed to give an absorption spectrum showing 25 lines of the series. With metallic rubidium it is easier to get the absorption spectrum, and the list of lines has been extended to include 30 members. A better reading microscope has been available since the original measurements, so that the complete series of lines has been remeasured. The method adopted was the same as that described in the paper referred to, so that there is no need for further description.

The present paper is a continuation of previous work* on the thermal expansion of normal paraffins. It is confined to an investigation of the lattice changes which take place in the range between room temperature and the individual melting points. The observations are rather complex and certain difficulties in the interpretation of the X-ray photographs arise which make further investigations necessary. Such work is now in progress. There were, however, several unexplained points in the last paper which are now clear and dealt with in the present work. Range of Materials . The investigation was carried out with 15 specimens ranging from C 18 H 38 to C 44 H 90 . The method of their preparation has been described previously.

An account of experiments on detonation in gaseous mixtures of acetylene and pentane has already been published. Certain further observations are here recorded as an addendum to the former papers. (a) Influence of Pressure on Velocity of Detonation . It was mentioned on p. 157 of the second paper referred to, that further measurements of the velocities of the detonation waves set up in the explosive mixtures investigated were necessary to determine the precise extent of the increase in velocity occasioned by rise of initial pressure.

In a previous communication to the Society, an account was given of an investigation of the magnetic shielding of a large space, by the use of a series of spherical iron shells. The basis of this investigation, which is still in progress, is strictly quantitative, and the work has been retarded, to a great extent, by the fact that several processes adopted commonly by various investigators of magnetic phenomena have never been examined accurately on the theoretical side, and in several cases even on the experimental side, to an order of precision which is sufficient for delicate measurements. One of the main objects ultimately in view, in the work described already, is the production, throughout the volume of a large iron specimen, of a magnetic field so small, in comparison with that of the earth, for example, as to render possible some accurate conclusions regarding the behaviour of iron under indefinitely small magnetic forces. This behaviour is at present a matter of doubt, and it remains to be shown that the indications of its real nature, obtained in earlier papers by one of us, continue to point in the same direction when the force is decreased below any values which have been employed hitherto. In the experiments described in the former paper, a field so low as 0·0033 C. G. S. unit was obtained in a spherical space of radius 32·5 cm. by the use of four concentric shells. It was accompanied, however, by a leakage field of 0·006 C. G. S. unit, and the shells still showed some traces of permanent polarisation after continued treatment with many reversals of a slowly decreasing current. This method of demagnetisation is used extensively, and in its application coils have sometimes been wound somewhat loosely on the iron to be demagnetised, and the constant field given by Maxwell’s formula for a spherical internal space surrounded by a very closely wound coil assumed to exist. But if a thin shell is wound in this manner, although the more internal parts may be subject to this field, the results must be widely different in the outer material of the shell. Further experimental work on the improvement of magnetic shielding beyond the order obtained already— in fact by such methods as the employment of a very small magnetising current to remove, in the internal space, the small part of the earth’s field which may remain after the operation of the shielding effect of a set of shells —requires a precise knowledge of the value of the magnetic induction in a shell, or one member of a set of shells, wound by a spherical helical coil. For the condition of indefinitely close packing is found to be essential to the success of Maxwell’s formula, which—but only from this particular point of view—does not appear, either from an a priori theoretical consideration, or from the experimental results described in the present paper, to have the large range of validity which has been assumed for it hitherto by practical workers on magnetic phenomena.

In a recent paper Raman and Krishnan have shown how the phenomenon of birefringence exhibited by liquids in a magnetic field can be utilised to determine the degree of magnetic anisotropy of the molecules concerned. Since magnetic double refraction is an effect arising from the molecules being both magnetically and optically anisotropic, and the optical anisotropy is known from studies on light scattering, the magnetic anisotropy can be evaluated from the known value of the Cotton-Mouton constant. In this way, they showed that the benzene molecule has a high degree of magnetic anisotropy, the susceptibility in a direction perpendicular to the benzene ring being about twice as great as that in any direction parallel to the ring. In another papers they showed how this magnetic anisotropy may reasonably be explained in terms of the special structure of the benzene molecule. Considerations of the same kind suggest that the higher members of the aromatic series ( e. g. , naphthalene and anthracene) should exhibit an even more striking degree of anisotropy. Some calculations, as yet unpublished, by Krishnan indicate that the naphthalene molecule should have, in directions perpendicular to the ring, a susceptibility about four times as large as in directions parallel to the ring. It is known that diamagnetism of crystal is in general anisotropic. In a recent paper Raman and Krishnan have discussed the case of nitrates and carbonates and shown how the anisotropy of the crystals is in each case connected with the structure of the individual ions. If, as stated above, the naphthalene molecule possesses a large magnetic anisotropy in the liquid state, it is reasonable to expect that naphthalene crystals in the solid state should also exhibit a very pronounced magnetic anisotropy. In fact, Bragg and Oxley have made some qualitative observations on the magnetic behaviour of naphthalene crystals which support this inference, but no quantitative results are available. The present work was undertaken with a view to obtain some measurements of the susceptibility of the crystals in different directions and with the hope that such data would be of assistance in determining the orientation of the molecules in the crystal lattice.

Measurements of the number of particles emitted with different velocities in the beta-ray spectra of Radium B and Radium C have been recently described by the writer. In the present paper the measurements have been extended to the spectra of Thorium B and Thorium (C + D). As before, portions of the magnetic spectrum were focussed into a Faraday cylinder, and the number of electrons determined in absolute magnitude. The conclusion reached in the previous paper was that in the case of both Radium B and Radium C there is, underlying the beta-ray lines, a continuous spectrum similar to that of Radium E, and of the same magnitude—that is, containing one electron per atom breaking up. This leaves little doubt that in these three bodies it is the nuclear electrons ejected in the disintegration with varying velocities which form the continuous spectra. If this is true of other bodies we expect to find in the Thorium series also large continuous spectra containing one electron from every disintegrating atom. Ike measurements of the spectrum of Thorium (B + C+ D) by Pohlmeyer showed, however, that the continuous spectrum was feeble in comparison with the beta-ray line Hρ 1398. But since an ionisation method was used, no determination of the absolute number of particles was possible.

During the last few years there have been improvements in this branch of metrology. In 1905, as pointed out by the writer, the best gauges were greatly defective as to their end faces and the machines for their measurement were faulty in principle. Since then Johanson has, by a secret process, produced gauges incomparably superior to anything previously on the market, with the result that other gauge-makers have been stimulated to improve their standards. The ordinary bar gauge has flat ends. This paper deals with this form only. The ideal gauge would satisfy two conditions: (1) The ends to be absolutely plane and parallel, though they need not be truly normal to the length of the bar; (2) the distance between the planes to be exactly the length for which the gauge stands. In this paper only condition (1) is considered.

The object of this paper is to examine and extend a method frequently applied by Lord Rayleigh to the calculation of the frequency of the gravest mode of a vibrating system. In this method no attempt is made to obtain an accurate solution of the differential equations of vibration in any normal mode, but any fairly simple function satisfying the boundary conditions is adopted as an approximate solution. This solution will involve the time only through a harmonic factor such as sin 2 π vt , so that the mean value of the kinetic and potential energies of the system may be calculated—always on the supposition that frictionless constraints are applied so that the displacements of the system follow the law of the approximate solution adopted. By equating these mean values of the kinetic and potential energies there is obtained an expression for v , the frequency of the constrained motion. According to Rayleigh’s principle, this value of the frequency is always in excess of the natural frequency of the gravest mode of vibration. Moreover, it is usually found that almost any differentiable function satisfying the boundary conditions of the problem may be made the basis of a calculation yielding a close approximation to the fundamental frequency. Although these results follow easily enough from the Lagrangian method of treating the oscillations of a system possessing only a finite number of degrees of freedom, they do not appear to have been investigated in the far more important case of a continuous system. In this paper a closer examination of Rayleigh’s principle is made by considering a series of successive approximations to the accurate solutions of the problems proposed, and a method is devised for obtaining an upper bound to the error involved in the approximate values of the frequency. Rayleigh’s method is also extended to the calculation of the frequency of the first overtone, and analogous methods are given for more general problems of the computation of “characteristic numbers.”

In Part II of this series of papers (1) it was shown that (with suitable substances) films 1 molecule thick could be obtained on the surface of water, in which the molecules were packed with much the same degree of closeness as in other condensed forms of matter such as solids or liquids. Moreover, under proper conditions, it was shown that the molecules packed themselves, so as to give, for the measurement of the cross-section, some-times that of the hydrocarbon chain, sometimes that of the polar end group, called the "head." Concordant measures were obtained on different substances for the area of cross-section of a saturated normal chain of CH 2 groups, and for some common end groupings such as COOH, COOC 2 H 5 , etc. No check was, however, possible at that time on the measures of the dimensions of the groupings made by this method, as no other method had been applied to the measurement of these groups in condensed forms of matter. Sir W. H. Bragg's measurements of the dimensions of the naphthalene and anthracene molecule within the crystal have made and attempt to measure monomolecular films of substances containing an aromatic nucleus near the head of the molecule very desirable. The present paper describes the results of such and attempt carried out on benzene derivatives.

There are two fairly distinct problems involved in a treatment of the stability of the benzene ring. The first is to explain why of all the single-ring structures C n H n , that of benzene ( n = 6) is by far the most stable. The second is to examine the different models proposed by the chemists for the benzene ring in the light of quantum mechanics and to show in fact that they are all represented with varying probabilities in the complete model. Attempts have been made at both problems, but only the second has been worked out satisfactorily. In the present paper we attempt a more accurate solution than has hitherto been given of the first problem. Before commencing this it is necessary to give a description of previous work, since otherwise it is very difficult to see what is already certain and what remains to be done. In a series of papers Hückel has discussed at great length both of the problems mentioned above, not only for the simple benzene ring, but also for many of its substitution products. He evaluates the energy of the plane ring compound in two ways, one of which virtually amounts to the method of generalized electron pairs and the other to that of molecular orbitals. The chief weakness in his theory is that he considers only what he calls the p r electrons, viz., the n 2 p -electrons whose wave functions are odd for reflection in the plane of the ring. As we shall show, the three remaining bonding electrons on each carbon nucleus have a most important influence on the best value of n . Nevertheless, Hückel's work is quite satisfactory as regards the resonance between the p r electrons.

In previous papers we have given an account of the effect produced on the light of the Nernst filament by passing it through the vapour of the elements of the sulphur, phosphorus and mercury groups and have shown the bearing of the phenomena observed upon the constitution of the vapour in each case. In the present paper we propose to deal with chlorine, bromine, and iodine, the only other elements which lend themselves readily to this method of investigation. Ten years ago the absorption spectra of bromine and iodine were investigated by Evans by a method similar to that which we employ. He showed that the absorption varies with the temperature and pressure and drew from his results the conclusion that at sufficiently high temperatures the vapour of these elements is diactinic. This he explained by assuming that the monatomic molecules into which the more complex molecules are gradually resolved as the temperature is raised are colourless and without absorbent action on light at any rate within the limits λ 3500 to λ 6800. In most of his experiments the pressure was kept constant by connecting the observation tube in which the vapour was heated with a reservoir of the element maintained at a constant and lower temperature. The mass of the vapour at different temperatures was, therefore, variable. Our experiments were designed to show the effect produced by a constant mass of vapour on the absorption when the temperature was varied over as wide a range as possible. For this purpose a known quantity of the element under examination was enclosed in a sealed vacuous tube and the temperature gradually raised, observations upon the absorption being made at intervals. Under these conditions while the mass of the vapour remains the same throughout, the pressure increases both with the rise of temperature and as a consequence of the dissociation of the molecules. As, however, the tubes were evacuated with the Sprengel pump and the initial pressures were, therefore, low, it is improbable that the changes of pressure had any great influence upon the phenomena. This view is confirmed by the fact that observations made upon different quantities of the element showed only such differences of spectra as might be expected from the variation in the mass of the substance employed. In no case, so far as we observed, was the temperature of maximum absorption altered.

The spectrum of the nitrogen afterglow, as ordinarily obtained, consists of three groups of bands, which we designated as the α, β , and γ groups. The α -group is in the visual region, and consists of a selection of the first positive bands of nitrogen. The β -group is chiefly in the ultra-violet, but extends into the violet. It can be observed in the discharge, but is much better developed in the afterglow. The γ -group is wholly in the ultra-violet, and identical with Deslandres’ third positive nitrogen group. I have not much to add to the results of the former paper as regards the measurement and classification of these various groups of bands. The circumstances under which they appear have, however, been reinvestigated, and the conclusions of the earlier paper modified in some important respects.

1. Summary of Paper .—The main object of this paper is to apply Nordheim’s theory of the emission coefficient of electrons from metals so as to explain the remarkable relation between the constants A and X of the thermionic emission formula, first recorded by O. W. Richardson and recently reformulated by Du Bridge. This theory regards the emission as due to the passage of electrons through simple surface potential steps and double layers, to be calculated according to the wave mechanics. We conclude that the theory gives a completely satisfactory account of the facts whenever it can be properly applied. The necessary conditions for its proper application are formulated. Certain apparent discrepancies in absolute magnitude between the observed and theoretical values of A are left outstanding and it is necessary to discuss possible explanations of these in some detail. It is concluded that though their precise cause cannot yet be specified they can certainly be explained and their existence is in no way antagonistic to the main theory. 2. The Experimental Facts .—Much attention has been devoted recently to the values of the constant A in the formula for the saturated thermionic (electronic) current I, namely, I = AT 2 e - x/k T , where T is the absolute temperature, X the work function and k Boltzmann’s constant. Particularly interesting measurements of A (and X ) have been recorded by Du Bridge for platinum when very severely outgassed. Du Bridge seems definitely to have established that for really clean platinum the photoelectric threshold and the thermionic work function agree at or near 6·35 volts, and that the corresponding values of A for various specimens range from 10,000 to 20,000 amp./cm. 2 .

In a previous paper entitled “Structure in the Secondary Hydrogen Spectrum,” Part IV, it was shown that there were a number of bands associated with Fulcher’s bands. It now appears that these and other related bands form a set of band systems whose null lines are connected by a Rydberg-Ritz formula. This formula has the normal value of the Rydberg constant, as is the case with the formula found by Fowler to connect the heads of some of the helium bands. This discovery makes it possible to apportion the effects observed as between electron jumps and vibration jumps, a matter which had to be left open in the previous paper (p. 740). The present paper deals only with the Q branches which are the most strongly developed and have been investigated most fully. A preliminary account of some of the results has been published a letter to ‘Nature,’ but the numbering of the vibrational states of the H α bands proposed therein has since been abandoned. It will be shown that all the lines of Fulcher’s red bands arise as a result of transitions in which the total quantum number (electron jump) changes from 3 to 2 and the vibrational quantum number is unchanged. In the part of the band denoted by A in “Structure,” Part IV, the vibrational state has the lowest possible quantum number both before and after the transition. I shall indicate this state of affairs by the symbol 0 → 0. The corresponding vibrational states in the parts denoted by B, C, D, E and F are, both initially and finally, 1, 2, 3, 4 and 5, and I shall denote these transitions by 1 →1, 2 → 2 , 3 → 3 , 4 → 4 and 5 → 5 respectively. The different lines in part A all have the same electron jump (3 → 2) and the same vibration state (0 → 0) but have different rotational jumps either of the molecule as a whole or of the emitting electron or of both. This statement will be equally true if the letter A is replaced by any of the letters B, C, D, E or F, except that the vibrational jump 0 0 is replaced by 1 → 1, 2 → 2, etc. In the present paper I shall confine my attention to the Q branches so that all the rotational transitions here dealt with are of the type m + ½ → m + ½ , m = 1, 2, 3, 4, 5, etc. (see Part IV, p. 749). Fulcher’s green bands also have the same electron jumps (3 → 2), but in these bands the vibrational quantum number is higher by unity in the initial than in the final states. Thus for the various green bands denoted by the letters A, B, C, D, E and F the vibrational transitions are 1 → 0, 2 → 1, 3 → 2, 4 → 3, 5 → 4 and 6 → 5 respectively. In addition to these, bands with the same electron jump (3 → 2) can be found in the infra-red with the vibrational jumps 0 → 1, 1 → 2, 2 → 3, 3 → 4 and 4 → 5 and others on the side of the green towards the violet which correspond to the vibration jumps 2 → 0, 3 → 1, 4 → 2, 5 → 3 and 6 → 4, and a few lines which may correspond to the vibration jumps 3 → 0 and 5 → 2. All these lines have the electron jump 3 → 2 and are the band analogue of the single line H α in the line spectrum of the hydrogen atom. For this reason it is convenient to refer to this system of bands as the H α bands.

The experiments described in the present paper were made in connection with the investigation of sulphur spectra developed by the nitrogen afterglow, in continuation of previous observations by Profs. Strutt and Fowler. A result of considerable interest is the detection of a series of ultra-violet bands which appear to be characteristic of a compound of sulphur and carbon. This band system extends from λ 2436-2837 approximately. It is, however, quite distinct from that developed, in the same region, by carbon disulphide in the afterglow, which is described in the paper to which the reference is given. Further photographs were taken, and it was found that the two sets of bands had nothing whatever in common.

In a previous paper, it was shown that the β -rays of radium E excited ϒ-rays in different materials, the amount increasing with the atomic weight of the substance used. It was found that the ϒ -radiation was largely increased when the β -rays fell on a lead screen suitably placed, and as the active material, radium (D + E + F), was mixed with lead sulphate confined in a small space, it was obvious that some, if not all, of the ϒ -radiation issuing from the mixture was due to ϒ -rays excited by β -rays in the lead impurity. It thus seemed possible that no primary ϒ -rays were emitted by radium E. By using a more suitable source, in which the active material was spread in a thin layer over biter paper, it has been found that a primary ϒ -radiation is emitted from the active matter. This radiation, however, is much sorter than that excited by the β -rays in lead. more detailed account of these primary rays will be given later.

In a former paper I gave an account of experiments on the presence of helium in a variety of the common minerals of the earth’s crust. The conclusion arrived at was that the quantity of helium is, in general, determined by the traces of radio-active elements present. The minerals investigated were mostly of palæozoic age, and little attention was paid to the effect of geological age on helium content. If, however, the accepted theory of the progressive accumulation of helium in minerals by radio-active change is correct, it is evident that geological age must be all-important. In the present paper, the subject is considered from that point of view. There is some difficulty in finding suitable material for comparing the helium content of minerals with their geological age. To make such a comparison advantageously, it is necessary to obtain minerals from a very great range of geological horizons, so that the oldest minerals considered shall be many times older than the youngest. Thus it becomes imperative to get material from the secondary and tertiary strata. Most of the constituents of these strata are unsuitable. For instance, derivative materials like clay and sand must be rejected, because they have presumably been accumulating helium long before they were laid down in their present stratigraphical position. The chemical precipitates like rocksalt and gypsum are so free from radio-active constituents that accurate measurements of the helium in them are very difficult; while limestones are, in a lesser degree, open to the same objection.

Band spectra of the alkaline earth halides were familiar to the earliest spectroscopic workers. Most of these spectra can be produced in both the flame and arc. The fluorides of calcium, strontium and barium all give interesting groups of bands which present obvious regularities, and these have been measured under high dispersion by several observers. The chlorides, bromides, and iodides have not been measured with such precision, although from time to time low dispersion measurements seem to have been made. In 1921 Datta made a systematic study of the fluorides of calcium, strontium and barium, and, added to these, data of the bands of magnesium fluoride. He gives an excellent plate of photographs of all these spectra and it has, therefore, not been considered necessary to reproduce any spectrograms in the present paper. Constant reference will, however, be made to this plate. Datta’s work was principally directed to the discovery of numerical relationships between the molecular weights and corresponding band spectra of these similar compounds. With this in view he labelled the band groups in each spectrum A1, A2, A3, ..., B1 B2, B3, ..., C1, C2, C3, etc., so that analogous groups in the spectra of the various molecules should have the same designation. His selection of analogous spectra was largely based on their general appearance, and Datta gives several numerical relationships of an empirical character on the basis of this assignment. This work was completed before the applica­tion of the quantum theory to band spectra became prevalent, and it, therefore, needs revision in the light of our present knowledge. For convenience, how­ ever, Datta’s designation of the spectra by these letters will be used in referring to them. Mecke has recently made a quantum analysis of many of these bands and recognised distinct band systems in the fluorides of all the alkaline earths. He has expressed these systems by formulae of the usual type, and discussed the band structure, the doublet separation, and the vibration frequency shown by this series of similar molecules. The present paper is a continuation and extension of Mecke’s work on the analysis of these spectra. The whole of the known band spectra of the fluorides of Mg, Ca, Sr, and Ba have been completely analysed and ordered in regard to their gross structure.

The lack of a simple and fairly complete theoretical treatment of the moving boundary method has been felt in this laboratory in the course of transport number measurements in dye solutions. The results of these measurements are shortly to be published by Dr. C. Robinson and one of us (J. L. M.). In the present paper we shall attempt to develop a theory of the method, of necessity including some previous work, and to explain experimental results in the literature and the aforementioned work on dye solutions. Doubts have been expressed as to the validity of the method, in spite of the convincing experimental work of MacInnes, Smith, Longsworth, and co-workers, to whom we shall frequently have occasion to refer. These attacks on the method, we believe, have arisen from a misunderstanding of the fundamental principles involved, and we shall endeavour to answer them in this paper. In order to avoid confusion, we shall first explain the terminology to be used, which we hope will be adhered to in future communications from ourselves and coworkers. In this paper we confine ourselves to electrolytes (including colloidal electrolytes). The application of the method to colloids will be the subject of a future communication from this laboratory.