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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.

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 .

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.)

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.

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.

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.

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).

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.

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.

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.

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.

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.

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 greater part of this communication is concerned with obtaining the volumes and densities of the ions and ionic nuclei of three salts (KCl, NaCl, LiCl) from conductivity, viscosity, and freezing-point data, a process which is of limited interest and is therefore reserved for the later sections of this communication. The deductions which are drawn from the values so obtained, in conjunction with other data already available, lead to certain conclusions as to the beats of Formation both in the solid and ionic state which are of much wider interest and are dealt with in the next section. In two former communications there was developed a theory with reference to the ascertainment of the relative size of ions which was based upon a consideration of various Physical data relating to KCI and NaCl. In the present paper the necessary data are given for extending the results to LiCl. In the Former papers an empirical linear relationship was Found between the solution volumes calculated from density measurements and the ionic volumes deduced from conductivity and viscosity measurements, which is now extended to LiCl. In the present paper a new empirical relation will be found between the ionic volumes and the reciprocals of the effective molecular freezing-point depressions of the three salts in question. these two sots of empirical relations are found to do capable of simple theoretical interpretations, and to yield in combination interesting information as to the relative volumes and densities of the ions and of the ionic nuclei.

It has long been recognised that the dielectric constant of a substance gives an important indication of its constitution, and the classical papers of Nernst and Drude giving methods for the determination of dielectric constants, have been followed by a long series of papers giving the dielectric constants of several hundreds of pure liquids and solutions. Since the publication of Debye’s dipole theory in 1912, the literature of the subject has become even more voluminous than before. In surveying the mass of data one is struck by the very large discrepancies which exist in the values obtained by different observers for any one substance, and it is very difficult to decide whether they are due to the difficulty of pre­paring and purifying the substance, differences in experimental conditions such as frequency of the applied E. M. F., or errors in the methods of measure­ment. In order to make it possible to compare the results of different observers, and to provide a fundamental basis for new measurements, it is important that the value of at least one standard liquid should be known with unquestion­able accuracy. The object of the present investigation was to provide such a value. Benzene was chosen as the standard liquid since it has been very widely used in the past, and it is used as a standard in the measurement of other physical properties.

Rudorf, in a paper on the rare gases and the equation of state, has drawn attention to the high value found by Ramsay and Travers for the density of liquid xenon at its boiling point. As is well known the atomic volume in any group of elements in the periodic table either increases regularly with rise of atomic weight or remains approximately constant, so that it is to be expected that the atomic volume of xenon would be greater than of krypton, since the value for krypton exceeds that of argon. If Rudorf's calculated value for the density of neon is taken into account, this anomaly becomes more striking, as is shown from the following table taken from his paper

In a previous paper the writer has outlined the crystal structure of a number of long-chain compounds. One of the main results of this work was to show that the crystal molecules (chains) in all these substances can be represented as rods of definite cross section, the crystals being built up of bundles of these rods packed close together. A closer examination of the X-ray photographs of stearic acid gave the clue to the chain structure, and led to a general formula for the structure factor. It was then announced that a more detailed investigation of stearic acid was to follow. The choice of stearic acid was dictated entirely by practical reasons, no other well developed crystals of other similar substances being available at that time. But as it was obviously more desirable to study first the prototype of the long chain compounds, namely, the normal hydrocarbon, efforts were first made to find single crystals of these substances. The search was unexpectedly successful, and the present paper describes an attempt to interpret the results of the X-ray examination of a single crystal of the hydrocarbon C 29 H 60 .

Within the last few years papers dealing with the volatilisation of radioactive substances have been published by various authors. The principal aims of the experiments described in these papers may be classified under three heads:— ( a ) To determine the temperatures of volatilisation of the various members of the active deposits of radium, thorium, and actinium; in some cases with a view to the classification of these substances in the periodic system. ( b ) To prove that these extremely small quantities of matter form definite chemical compounds in a manner similar to that of the commoner elements. ( c ) To separate the various members of the series from one another. Other interesting results, which throw light on the phenomena of volatilisation, have also been reported, but these have always formed a subsidiary part of the researches described. Makower determined the temperatures of volatilisation of radium A, radium B, and radium C, in air, and showed that the effects observed depended to some extent on the nature of the surface on which these substances were deposited.

In a paper a “The Crystalline Structure of Metals,” Prof. J. A. Ewing, F. R. S., and one of the present authors described observations which led to the conclusion that the internal structure of metals is truly crystalline and that plastic deformation takes place either by mechanical twinning or by means of a series of minutes slips which occur on the gliding or cleavage planes of the metallic crystals. This conclusion, with slight modifications, has since been supported by one of the present authors in paper on “The Plastic Yielding of Iron and Steel,” and on Deformation and Fracture in Iron and Steel.” In another direction the generalisation quoted above has received further support from the explanation which it has afforded for the failure of metals under alternating stresses and fatigue. In these investigations, however, strain was applied to the metal at the ordinary temperature; the present authors desired to extended the experiments to the study of the modes of deformation of metals at such temperature changes of shape are applied to heated metals, as for instance, in such familiar operations as forgoing and hot-rolling. Further, iron and steel are known to undergo marked changes of constitution when heated above certain temperatures known as their “critical” points, and the study of the behaviour of these metals under strain at high temperatures promised to throw fresh light upon their true constitution. Finally, special interest attaches to the manner in which iron behaves under strain at high temperatures, owing to the peculiar character of the slip-bands which appear on a previously polished specimen of iron or very mild steel when subjected to plastic strain at the ordinary temperature; while the slip-bands seen in such circumstances in copper, lead, and most ductile metals are rectilinear and regular in character, in iron they are usually more or less curved and irregular. It is thus a matter of interest to determine whether, if deformation by slip occurs at high temperatures, the slip-bands then formed would retain the irregular nature of those, formed in the cold, or whether the heated iron would behave in a manner similar to other metals.

In a previous paper on "Chemical Equilibrium in a Mixture of Paraffins" the composition of the mixture in equilibrium at any temperature and pressure was calculated on the assumption that only paraffins C n H 2n+2 were present. The condition for equilibrium among the members of any homologous series in the vapour was shown to be p n = p 1 f n-1 , where p n denotes the partial pressure of the n th member of the series and f is a quantity less than unity which is approximately independent of n . In the present paper unsaturated hydrocarbons containing one or more double bonds as well as paraffins will be supposed present in the mixture. The homologous series to be considered are therefore the paraffins C n H 2n+2 , the olefines C n H 2n with one double bond, the diolefines C n H 2n-2 with two double bonds, and other series C n H 2n-4 , C n H 2n-6 , C n H 2n-8 , ..., containing 3, 4, 5,... double bonds.

In two earlier papers, which we shall refer to as Part I and II in the sequel, we described a very detailed investigation of the electron emission phenomena which occur when the liquid alloy of sodium and potassium reacts with phos-gene, COGl 2 , at very low pressures. In Part II we also gave a brief account of some of our principal conclusions from the results of experiments in which 22 gases were examined. In a third paper, Part III, we gave a detailed description of the corresponding phenomena observed with a variety of gases, namely, Cl 2 , NOCl, HCl, Br 2 , I 2 , COS, N 2 O, and H 2 O. A comparison of the data obtained with Cl 2 , COCl 2 , and NOCl disclosed a linear relation between the dissociation energy involved in the reaction and the maximum energy of the emitted electrons. A theory of the way in which we supposed this connection to originate had already been given in Part II. With the particular purpose of testing further the generality of this relation, as well as of widening the basis of our information as to the details of the energy distribution among the electrons emitted in different reactions, we selected for our next experiments a group of gases containing chlorine. The gases chosen were SOCl 2 , S 2 Cl 2 , SO 2 Cl 2 , HgCl 2 , and S 2 G 4 . We expected that one of the immediate results of the reaction of these gases with the liquid alloy would be, as in the case of Cl 2 , COCl 2 , and NOCl, the adsorption of a Cl¯ ion on the surface of the alloy; consequently the same theory should apply to all of them. The parts of this paper which follow immediately are concerned with a description of the results of the experiments with these five additional gases containing chlorine. We next describe experiments which, we made with mixtures of COCl 2 with COS, and with S 2 Cl 2 , and of SOCl 2 with S 2 Cl 2 . The object of these was to test the additive property of the chemical electron emission. We then go on to describe a new method of determining the contact potential difference between the alloy drop and the surrounding platinum electrode in presence of the different gases. We regard the results given by this method as of great importance in establishing the interpretation of the experimental data on a firm basis. This is followed by an analysis of the electronic spectra of the gases to be described in this paper. The primary object of the analysis consists in identifying the different groups in a composite electronic spectrum with the corresponding mechanisms of the reaction; the analysis is conducted in the light of our previous experience with the reactions involving halogens and also in the light of some new general considerations of the kinetics and of the electronic yield of the chemical reactions. The electronic spectra, having been thus analysed, are then applied to test the fundamental relation between the dissociation energy, involved in a certain reaction, and the maximum energy of the emitted electrons of the group originating from the reaction with the corresponding mechanism. Finally we present the energy distribution functions obtained with the gases under consideration.

Part II of this series of papers dealt with the compressibilities of hydrogen, helium, and mixtures of the two. The empirical result of that paper was to describe the effects of composition and of temperature upon the pressure- volume relationships in these mixtures. The chief theoretical results were (i) to show that the partial pressure law of Lennard-Jones quantitatively covers the facts; Dalton’s partial pressure law being inapplicable, as we had already proved in other cases in Part If; (ii) to measure the coefficients of the fields of attractive and repulsive force involved in an encounter between a pair of these molecules, by applying Lennard-Jones’ equations; (iii) to deter­mine the kinetic diameters of the molecules of helium and of hydrogen. The kinetic diameter of a molecule depends upon the temperature, being less at a high temperature than at a low. It appeared that at a given temperature, and especially when this is not a low one, a molecule of one of this pair of gases preserves the same diameter whether it is colliding with another of its own kind or with a molecule of the other kind. If this rule were generally applicable, the isotherms of a mixture could be predicted from those of the pure com­ponents. The case of helium and hydrogen was rather a special one, in that both gases deviate positively from Boyle’s law at all ordinary temperatures, and present no great range in the properties measured. Both kinds of molecule are light, small, and "hard," their behaviour in the mass is not necessarily typical, and the theoretical deductions from it might not be generally true. Accordingly, we have extended the work so as to study mixtures of each of those two gases in turn with argon .

With the figures in Table III of the preceding paper (p. 311) as a guide the problem of the spreading of one fluid over the surface of another may be approached with some sense of security. In an earlier paper the equation of a composite surface was found to be T S = T A + T AB -K g when T S is the tension of the composite surface, and K g a term depending upon gravity. Putting K g = 0, it is seen that spreading will occur only when T S > T A + T AB , and, at the limit, T S =T B that is to the tension of pure water in the experiments under consideration. Taking T B = 74, the tension of pure water, we have from the last paper That is to say a drop of any of these saturated substances should not spread upon a surface of pure water except octane, and in actual fact none of them do spread, except octane, a drop of which slowly expands on water to form a very thin plate. In the case of all the other substances examined the quantity (T A + T AB ), < T B , and they all flash over a water surface in characteristic fashion.

In an accompanying paper, secondary electron experiments on ordinary nickel are described. These were conducted mainly to study the conditions of secondary electron emission and to find how far the experimental results of Retry on a polycrystalline nickel target could be reproduced. It was found that a large number of inflections were obtained some of which coincided with Petry’s values. Most of these inflections had corresponding values in Thomas’s results for soft X-rays from nickel. In this paper, the results of experiments on total secondary electron emission from the 100 face of a nickel crystal are given.

The problem of obtaining accurate measurements of the relative intensities of spectral lines or bands when these cover a considerable wave-length range is one of the most difficult in experimental spectroscopy. These difficulties have been enumerated by many writers, e. g ., in a recent paper by Read and L. W. Johnson, and it is not proposed to enter into a detailed discussion here. The problem is much simpler when a small spectral range only is being investigated, such as, for example, the fine structure of an individual band or the intensity within a line multiplet, and a large amount of experimental work has been done within these limits. The desirability of quantitative data on intensity distributions within band systems is apparent from the theoretical work of Condon published in 1926, explaining the general characteristics of such distributions. The cases to which Condon’s theory has been applied by way of illustration have been almost all naked-eye estimates of band intensities on an arbitrary scale (0-10). An exception to this is the α-system of BO on which Elliot has made accurate measurements. In the present paper we have made preliminary observations on the well-known “Swan” system of the C 2 molecule. This system has the advantage, from an experimental standpoint, of lying wholly within the visible region of the spectrum, and, further, that its intensity distribution is characteristic of a large class of band systems, and that it can be produced under a variety of experimental conditions.

The application of Dalton’s law of partial pressures to the osmotic pressures of mixtures of protein salts and diffusible salts has been discussed in a previous communication. The observed osmotic pressures of protein salts, measured with membranes permeable by water and other crystalloids but impermeable by the protein, are difficult to interpret until they have been analysed in terms of the partial osmotic pressures of protein ions and of diffusible ions. The partial osmotic pressure of the protein ions, symbolised p p , may be calculated from the observed osmotic pressure p by the formula p = p p + P i , in which P i represents the “ion pressure difference,” or the pressure due to the excess of diffusible ions inside the membrane. The provisional estimates of these partial pressures, p p and p i , published in the paper referred to above, depend upon a number of simplifying assumptions concerning the deviations from the ideal solution laws in mixtures of protein salts and diffusible salts, and the range of application of the approximate formulæ employed is restricted to mixtures in which the equivalent concentration of the protein salt is relatively small. In order to confirm the provisional results and to interpret the osmotic pressures of concentrated protein solutions, a more general method, based on Gibb’s fundamental equations, is developed in this paper.

In a previous paper the writer suggested a new mode of attack on some ionisation problems and described its application in experiments on mercury vapour. The object of the method is to give a direct means of studying the types of ion produced in a gas or vapour by electrons of known speed. The experimental principle involved is the combination of an ordinary ionising potential apparatus with an arrangement for positive-ray analysis. It does not seem necessary to repeat the general discussion of the advantages to be gained or the difficulties to be overcome in using such a method. Suffice it to say that at first it appeared impossible to deal with substances gaseous at ordinary temperatures, but that now the method has been extended to include them. The nature of the difficulty and the manner in which it can be overcome are best understood by passing directly to the experiments on nitrogen, which are the subject of the present paper.

Previous papers have dealt with the homogeneous catalysis of the decomposition of ethers and of acetaldehyde by iodine. The problem of the mechanism of these catalysed reactions can be approached in two ways: on the one hand, by seeking to obtain as complete a picture as possible of the types of chemical change which are susceptible to the action of a given catalyst, and, the catalysts which will promote a given chemical change; and, on the other hand, by investigating in detail the kinetics and molecular statistics of individual reactions. Experiments on the different kinds of reaction which iodine will catalyse are being published elsewhere. Most of the chemical changes have involved too many side reactions, or secondary reactions with the catalyst, to be suitable for complete kinetic analysis. Nevertheless, they show the chemical specificity of the action of iodine in the clearest manner, and this aspect of the problem is discussed from a general point of view in the last section of the present paper.

In this paper the results of the examination of mono-molecular surface films of numerous sterols, and of compounds simply related to them, are reported. The work is a continuation of Part XII of this series of papers, and was undertaken in the first place to provide results on a number of derivatives of sterols, whose constitution is known in its main features, for comparison with those obtained on surface films of various irradiation products of ergosterol. The results on irradiated ergosterol will be given in a separate paper. The results of this paper are of considerable interest, as showing how different substituents in the complex ring system of cholesterol affect the behaviour of the molecules on water surfaces. It has appeared that a very great, and unexpected, variety exists in the character of the surface films, although nearly all the substances studied have practically the same ring system; that is, the bulk of the molecules is the same in all cases. A change in the position of a substituent group may make a profound alteration in the compressibility of the films and their area; this is perhaps not surprising, as the water-soluble groups in the molecule will naturally be directed downwards, being anchored to the water, and the position of these will affect the tilt of the molecules and consequently their mode of packing. It is more surprising that quite a small change in the nature of one group only, such as the transformation of CHOH into CO, without change of position of the group, may also have a great effect on the structure of the film.

1. In a previous paper the writers showed that a considerable number of discontinuities which had been detected in the excitation of the soft X-rays from these elements by the photo-electric method could be arranged on the assumption that they were due to transitions from two levels not far from the M I and M II III , as these had been deduced from hard X-ray emission data, and a series of virtual levels falling, with a close approximation into a Rydberg series. The present paper is an attempt to arrange the remaining discontinuities which have been observed into the same scheme. Although the identity of a level formerly referred to as A with the hard X-ray M I level and of the higher level with M II III seems probable ultimately, it is not certain, and we do not wish to be dogmatic about it, so that for the present we shall refer to these levels provisionally as X 1 and X 2 respectively.

In a paper called “The Chemical Constant of Hydrogen Vapour, and the Entropy of Crystalline Hydrogen,” the writer has investigated the vapour pressure of crystalline hydrogen at very low temperatures. He used the Einstein-Bose statistics for the hydrogen gas, and obtained results slightly different from those of Fowler, who had used the classical statistics for the vapour phase. The result found by the writer for the chemical constant i ' was in slightly better agreement with experiment than Fowler’s result, being larger than Fowler’s by log 10 1·04 = 0·02 at the temperatures of Eucken’s experiments. Also, the writer found that when hydrogen gas was condensed to the solid phase at these very low temperatures, the ratio of the number of ortho-hydrogen molecules to the number of para-hydrogen molecules in the crystalline phase, provided that most of the molecules were in the gaseous phase, was not 3 : 1 but instead about 3 ⅙ : 1. However, there was a mistake in the writer’s calculations. He carelessly omitted, from equations (5) and (5') of his paper on hydrogen, the factors involving the work of evaporation χ at the absolute zero, per molecule.

It has been shown in the previous paper that, where there are four refractive centres arranged dissymmetrically in a molecule, there is a definite rotatory power depending on the dimensions of the molecule. In the simple active molecule of four different radicals we seem to have been provided directly with four different refractive centres. It is, however, necessary to examine if a chemical radical fulfils all the properties which were assigned to the hypothetical particle in the general calculation; but, if this true, we can substitute dimensions of such a molecule in the general formula to device a simpler formula for the rotation. If the radical is to have the same properties as the polarizable particle, it will have a definite refractivity for a fixed wave-length and its electric field in the polarized state must approximate to that of a dipole of equal value situated at its centre. A chemical radical has a definite refractivity for a given frequency, but it is only if the radical is small and fairly compact that its ield in the polarised state may be taken as that of a dipole concentrated at a single point. Consequently this paper will be limited to the calculation for molecules containing radicals of only a few atoms in length. The refractive properties will be regarded as concentrated at the geometric centre of these small radicals.

The present paper includes some experiments suggested by criticisms of Part III of the research, and describes work upon the effect of depth of im­mersion on the corrosion of zinc in potassium chloride solutions. Some of the factors which influence the distribution of corrosion over the metallic surface are discussed with particular reference to the effect of differential aeration. Curves are given showing the effect of concentration of potassium chloride and potassium sulphate on the initial corrosion rate of zinc in tranquil conditions. The experimental methods used are those described in previous papers, supple­mented by micrographic work and a few potential measurements. The criticism has been made that the tranquil conditions in which the present series of experiments is being conducted cause abnormally slow rates of oxygen supply which dictate the corrosion rates; these, therefore, are not considered characteristic of the metal under test, but merely of the rate of penetration of oxygen through the liquid and any corrosion products which cover the metal. It has also been suggested that much faster rates of oxygen supply would be required to bring out the true corrosion characteristics of a metal or even to differentiate between two fairly reactive metals.

The present paper contains an account of an investigation of the effects of electron collisions with neon atoms by a method similar to that used with helium and with argon. The apparatus employed is practically the same as that described in the account of the experiments with argon, the only difference being that one of the lower gauzes (C) was removed and that two small platinum plate electrodes were sealed into the ionisation chamber, so as to provide an electric field at right angles to the direction of the electron stream. The arrangement will be understood by reference to fig. 1, in which the lettering corresponds to that used in the earlier paper. The object of introducing the side electrodes, G and H, was to enable a second test of the production of ionisation to be made by means of a delicate galvanometer included in a subsidiary circuit. The usual precautions for ridding the glass and the electrodes from occluded gases were taken, and in all the observations recorded in the paper a magnetic field parallel to the axis of the discharge tube was used to prevent the electron stream from spreading laterally.

The methods of determining intermolecular fields, which have been used in former papers,* apply only to molecules of the same kind. This paper considers the more general problem of determining the forces between molecules of different kinds. It shows that this information can be derived from a study of the equation of state of binary mixtures, provided that the experimental work covers a sufficiently wide range of temperature and deals with mixtures of sufficiently varied proportions. The experimental information available at present is somewhat scanty and needs considerable extension. Apart from the earlier measurements of Amagat, the only available work on gaseous mixtures appears to be that of Holborn and Olto on a mixture of helium and neon, that of Verschoyle on a mixture of hydrogen and nitrogen, and that of Masson and Dolley on binary mixtures of ethylene, argon and oxygen. The former carried out experiments on a mixture of one proportion only, but have supplemented the results with further work on helium alone and neon alone, in each case covering the range of temperature 0 to 400° C. This work provides just enough data for the purpose of this paper, and from it the field between a helium atom and a neon atom, as well as the fields between two helium atoms and two neon atoms, can be deduced.

In recent years it has been shown by X-ray methods that the structures of a large number of crystals are based on frameworks of linked tetrahedral groups of oxygen atoms. The individual tetrahedra contain silicon or aluminium atoms, and other atoms (such as sodium or potassium) and water molecules or molecular groups (such as CO 3 and SO 4 ) are located in the interstices of the oxygen atom arrangement. Some of the structure determinations are incomplete and lack direct experimental proof, but in others it has been possible to discover the details of the atomic arrangement. The present writer has been associated with several of these detailed investigations, and in this paper presents some general conclusions which may be drawn from an examination of the available data. Experimental details and evidence for the correctness of individual structures have been published elsewhere. For the purpose of the present paper a framework structure is defined as one in which every tetrahedron SiO 4 or AlO 4 shares all its corners with other tetrahedra, thus accounting for all the silicon aluminium and oxygen atoms in the structure; such a crystal has a chemical formula in which the ratio (Si + Al) to O is 1 to 2. Framework structures include the forms of silica, the felspars, the zeolites, the ultramarines, nepheline and kaliophilite, and related compounds which will be mentioned later; also danburite if boron may be supposed to take the place of aluminium in our definition, and probably leucite.

As soon as we found that the glow of radium bromide consisted mainly of light from nitrogen stimulated into luminosity by the radium, and giving the negative pole spectrum, we formed the intention of photographing the spectrum of the glow when the radium bromide was placed in an atmosphere of hydrogen, primarily in the hope of finding an answer to the question raised in our first paper, “Have we to do with occluded or with atmospheric nitrogen?”, and, in the second place, to determine whether the radium is able to render hydrogen luminous. In these experiments some unexpected results came out, which made it desirable to repeat them many times. This circumstance, together with the long exposures necessary—from 10 to 14 days—and the slow changes which we found to take place in the radium when allowed to remain in the hydrogen for long periods, reckoned in months, have necessarily delayed the publication of this paper. The investigation is still in progress, but it seems desirable not to delay any longer the publication of the results which have been already obtained.

1. According to the ionisation theory, both the depression of the freezing point and the conductivity of a solution of an electrolyte are connected with the ionisation of the solute, and conclusions as to the degree of ionisation in dilute solutions may be drawn from both phenomena, on certain assumptions. The experiments on the depression of the freezing point of very dilute solutions, described in the paper, were planned in connexion with measurements of the conductivity of similar solutions which were made by Mr. W. C. D. Whetham, F. R. S., and have been described in papers communicated to the Royal Society in 1900 and 1902. It was intended to compare the conclusions, drawn from the results of the associated researches, as to the degree of ionisation of the solutions, especially at great dilution. If it be assumed that each molecule which dissociates in solution yields i ions, and that the osmotic pressure is equal to the pressure, according to the simple laws of gases, existing in a gas having the same number of molecules per unit volume as there are molecules and ions in unit volume of the solution, then the coefficient of ionisation (the proportion of molecules ionised in the solution) is given by α = ∆δ/δ( i -1).

Of the three related reactions 2N 2 O = 2N 2 + O 2 ............ [1] 2H 2 + O 2 = 2H 2 O ..............[2] N 2 O + H 2 = N 2 + H 2 O ................[3] only the first two have hitherto been studied. The investigation of the kinetic relation of the third to the first two is the object of this paper. In the preceding paper it has been shown that the thermal decomposition of nitrous oxide into its elements is a homogeneous reaction in which practically every pair of nicrous oxide molecules react which collide under the condition that their joint energy exceeds about 58,000 cals, (for 2 gram molecules). This decomposition is uncatalysed by platinum or by rhodium. The combination of hydrogen and oxygen is, on the other hand, a reaction very dependent on catalytic influences. Bodenstein (‘Z. Physikal. Chem.,’ vol. 29, p. 665 (1899)) found that between 482° C. and about 600° C. the combination proceeds exclusively on the walls of a porcelain containing-vessel. Platinum, rhodium, and other metals have long been known to have a very pronounced catalytic action on a mixture of hydrogen and oxygen. Langmuir (‘Trans. Faraday Soc.,’ vol. 17, p. 621 (1922)) has studied the kinetics of the interaction of hydrogen and oxygen on the surface of a platinum wire, and finds that between 300° and 600° abs. the rate of combination is approximately proportional to the pressure of the oxygen and inversely to that of the hydrogen. There is now abundant evidence that catalytic reactions occur within a layer of adsorbed gas not more than a molecule or so deep, in immediate contact with the surface, and the interpretation of Langmuir’s results is that between 300° and 600° abs. the surface of the platinum is nearly completely covered with a layer of hydrogen and that reaction occurs when oxygen molecules enter gaps in this layer, the number of free spaces being easily shown to be inversely proportional to the pressure of the hydrogen. Turning now from the reactions [1] and [2] to the related reaction [3], the following questions present themselves, namely:— ( a ) whether nitrous oxide and hydrogen undergo a homogeneous bimolecular interaction at temperatures below that at which [1] takes place; ( b ) whether hydrogen and nitrous oxide interact catalytically on the surface of platinum. On the one hand, platinum becomes covered with a film of hydrogen which is activated for reaction [2], while on the other hand, platinum has no activating effect on nitrous oxide for reaction [1].

Chemical changes in which molecules of complex structure take part have recently assumed a particular importance in the theory of the mechanism of reaction velocity. Decompositions of organic compounds in the gaseous state provide excellent examples of such reactions. It is often necessary, in these, to suppose the intermediate formation of unstable radicles which undergo rapid subsequent transformations; and whenever each stage of a reaction is not expressed by conventional chemical equations, involving known substances only, there may always remain a slight doubt whether the course of the reaction has been truly represented. Although this does not prevent the drawing of perfectly valid conclusions about the kinetics of a given reaction, nevertheless an example in which every stage can be represented by a simple chemical equation has undoubted advantages. The decomposition of dimethyl ether, with which this paper deals, provides such an example. CH 3 .O.CH 3 → [CH 4 + HCHO] → CH 4 + H 2 + CO. The complexity of the dimethyl ether molecule is only moderate, and in the light of the discussion in the papers referred to above it is interesting to note that the reaction is an almost perfect example of the transition from the unimolecular to the bimolecular type.