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The measurements of compression and area on monomolecular films of fatty substances on water surfaces, described previously (1), were limited in accuracy by the disturbing effect of the jets of air necessary in the apparatus employed for measuring compression, for the purpose of preventing escape of the films past the barrier confining one end of the films. We think the error in measurements of compression with this apparatus may have been as large as half a dyne per centimetre in extreme cases, and as the apparatus was used under fairly accurately reproducible conditions, it was of the nature of a constant error. The reality of the lowest portion of the compression-area curves was therefore open to doubt. We have now designed an apparatus in which the gap at the ends of the floating barrier is completely closed by very thin strips of gold ribbon, placed vertically in the water, and soldered to the ends of the float and to brass pieces pressed tightly against the sides of the trough. This arrangement can be made leak-proof and very sensitive. In order to measure the force on this float, at a given position, fine silk fibres connect the float to (a) an optical lever system consisting of a mirror suitably damped with an oil bath, mounted on a light torsion wire, which is in effect a practically frictionless bearing, and (b) a fine torsion wire provided with an accurately graduated divided head, whose divisions can be calibrated in absolute measure by hanging weights on a small balance mounted on the wire. Full details of the apparatus are given at the end of the paper.

In this and the following paper a method will be described of obtaining good high order interference photographs of electron beams scattered by the vapour of any stable substance, organic or inorganic, whose vapour pressure exceeds 10cm at 1000°C, as well as an interpretation of the results achieved with this improved technique, using a simplified method of calculation. The apparatus has been so developed that it is now as easy to obtain electron interference patterns of vapours as it is to make measurements of the Raman effect, dipole moment, infra-red and ultra-violet absorption spectra; the results enable us to clear up a number of doubts that still exist concerning the spatial structure of certain compounds. Debye and Ehrenfest showed theoretically that if a beam of monochromatic X-rays was passed through a gas consisting of randomly oriented polyatomic molecules with fixed interatomic distances, then an interference effect might be expected. Later Debye worked out the general case for a molecule containing 1- i - j - n atoms each having a scattering factor F.

Introduction .—In a paper published some years ago, the amount of electricity liberated by exploding electrolytic gas (2H 2 + O 2 ) at certain pressures was measured and compared with the number of molecules of water formed by the explosion. It was found that about 10 7 molecules of water were formed for every pair of gaseous ions that reached the electrodes, and that the energy required to produce the observed quantity of electricity was an extremely small fraction of the energy set free by the explosion. The present investigation was undertaken to see whether these results would be substantially modified in the ease of the explosion of azoimide (HN 3 ). The explosion of this gas differs from that of electrolytic gas in two important particulars from the point of view of these experiments. In the first place it is disruptive, and secondly it is not productive of water-vapour, which with its well-known influence upon the motion of gaseous ions may, by promoting their re-combination, greatly obscure the electrical effects of the explosion.

There are very few reactions the rate of which can be measured both in the gaseous state and in solution. Several bimolecular reactions have been investigated in solution, and since the rate of a bimolecular gas reaction can be calculated from the equation Ink = In Z — E/RT, where E is heat of activation and Z the collision number, the rate of reaction in solution can be compared with that of the hypothetical corresponding gas reaction. The observed velocity constants in solution have usually been found to be smaller by several powers of 10 than the calculated values. On the other hand, as shown in the previous paper, in the one example where direct comparison has been possible, namely, the decomposition of chlorine monoxide, the rate in solution in carbon tetrachloride is the same as that in the gas phase. Thus it is evident that the retardation of reactions by certain solvents is a specific action and need not occur in an “ideal” solvent. The rates of unimolecular gas reactions cannot be calculated, and direct comparison has hitherto been possible only in two examples. The equation Ink = 31•69 — 24,710/RT has been found to represent the rate of decomposition of nitrogen pentoxide in the gaseous state and in a series of eight similar, chemically rather inert, solvents. In nitric acid or in propylene dichloride, however, In Z increases by several units and E becomes 28,300 calories. Daniels regards as “normal” those solvents which do not produce an alteration in E, and as “abnormal” those which cause a deviation from the value characteristic of the gaseous state. The solvents in which the decomposition of nitrogen pentoxide could be studied were naturally not very varied in character, since most liquids would be attacked chemically. Thus the impression which the results tend to convey, namely, that “normal” or "ideal" behaviour is more common with unimolecular reactions than with bimolecular reactions, may be an illusory one. In the only other known example, the isomerisation of pinene, the rate of reaction in the gas, in the liquid, and in carbon tetrachloride is the same.

Research on this subject originated in an attempt to discover in what way the structure of certain alloys is affected by undercooling at the first moment of solidification of the eutectic. The formation around the primary crystals of an alloy of what may be called a halo or envelope of the second constituent, separating the primary crystals from the banded eutectic, has been considered by some workerd to be the result of such superfusion. It has, however, been suggested by Desch that this effect is due to segregation of the eutectic in the immediate neighbourhood of the primary during solidification. At the same time it was suggested by him that, by preventing undercooling by means of inoculation, the influence of this phenomenon on the formation of such envelopes might be investigated.

1. The problem of determining the possible modes of stationary oscillation for a compressible fluid, moving with a steady velocity which is not constant, usually presents great difficulties. One case which is to some extent amenable to analysis is that of uniform radial flow in two dimensions, where the undisturbed paths of the fluid particles are straight lines radiating from a common point or source. The term “source” is here used somewhat loosely, for in the solution which will be given it is found that the fluid density attains unreal values inside a certain circle having its centre at this common point. It is well known that in radial flow two systems of velocity are possible to a compressible fluid—namely, either (i) zero velocity at r = ∞, and an increasing but limited velocity as the radial distance from the source decreases ( i. e. , a modified “perfect fluid” motion); or (ii) the maximum possible velocity at infinity (corresponding with zero pressure and density), and a decreasing speed—also limited—as r decreases. This type of flow is peculiar to compressible fluids.

The method of analysing a beam of beta-particles by deflecting them with a magnetic field in a vacuum has long been known. The beta-rays of Radium B + C, examined by this magnetic focussing method give a ‘’continuous spectrum” of beta-particles over a wide range of velocities, on which are superposed lines which are ascribed to the conversion of gamma-rays into beta-rays in escaping from the radioactive atom. There has been considerable difference of opinion as to the origin of the continuous spectrum, whether it consists of the electrons ejected from the nucleus in its disintegration, or whether it is merely secondary in origin. For example, Pohlmeyer, after some experimental work, recently came to the conclusion that the continuous spectrum of Thorium B + C might be due merely to lack of resolution of the line spectrum. He argued that this was probably true also of the spectrum of Radium B + C, a view previously maintained by Meither. The relative velocity-distribution of the particles from Radium B + C was examined by Chadwick,! using an electrical counter, and by Chadwick and Ellis, using an ionisation-chamber. In the latter case it is necessary to know the law of the variation of ionising power with velocity of the particles, as well as to estimate the reflection from the walls of the ionisation-chamber it is difficult to determine these quantities with accuracy. In the measurements by W. Wilson the beta-particles were deflected by a magnetic field into a Faraday cylinder, and the rate of accumulation of charge was directly determined. In the course of experiments made in this laboratory last year, Mr. Curtiss showed that this method could be combined with good focussing if a sufficiently sensitive electrometer were used ; an account of the work has been given.

The object of the present investigation was to obtain some further evidence on the apparent production of neon and helium by electric discharges in vacuum tubes, which has been described by Collie and Patterson. Strutt has recently attempted to repeat these experiments, using methods somewhat different to those of Collie and Patterson, with negative results.

Taking the phenomena of light to be due to periodic displacements in a rotational ether, we shall investigate the exact character of these displacements in the case of reflection from an isotropic transparent substance. Two well-known vectors play the principal parts in any such optical discussion—the displacement of the medium and its curl; in the electro-magnetic theory the former is proportional to the magnetic force and the latter to the electric “displacement.” To give precision to the discussion we shall deal throughout with the displacement of the medium, there being no difficulty in dealing in a similar fashion with the curl. Let the displacement in the incident light be of unit amplitude and polarised in a plane making an angle θ with the plane of incidence. It can be resolved into two components ξ = cos θ cos pt in the plane of incidence, and η = sin θ cos pt perpendicular to this plane. The corresponding com­ponents in the reflected beam are then given by the formulæ ξ = -R' cos θ cos ( pt - ρ' ) and η = -R sin θ cos ( pt - ρ ).

In a previous paper by one of us it was shown that when an insulator of specific inductive capacity K rotates in a magnetic field there is an electro­motive force induced in it equal to that in a conductor multiplied by 1 — K -1 . The object of the experiments described below was to measure the induced electromotive force in a magnetic insulator rotating in a magnetic field parallel to the axis of rotation. According to the theory based on the “principle of relativity” this induced electromotive force should be equal to that in a conductor multiplied by 1 — ( μ K) -1 , where μ is the magnetic permeability of the insulator, whereas on the theory of H. A. Lorentz and Larmor the appropriate multiplier appears to be 1 — K -1 , as for a non-magnetic insulator.

The investigation to be described in the present paper was begun with the object of testing experimentally some suggestions made by Prof. D’Arcy Thompson in a letter addressed to “Nature,” published in the issue of August 8, and in private correspondence with the author. The substance of these suggestions is that many organic forms show symmetries corresponding closely to those of vibrating bodies of similar shape, and that many others recall very strikingly the shapes exhibited transitorily by splashes and by vortices. In the usual methods of producing vortices—causing drops of a coloured liquid to fall,* or jets of it to emerge, into another with which it is completely miscible—the various stages of the phenomenon succeed one another with great rapidity, so that either unusually acute observation, or instantaneous illumination and photography, is required to isolate any particular one. Even apart from this difficulty the procedure has a serious defect when viewed as a method of imitating organic forms, inasmuch as organisms cannot possibly consist of liquid alone, but are either colloidal solutions enclosed in membranes, or possess the physical properties of gels.

It is the aim of this series of papers to extend knowledge of the structure of molecules by work in the infra-red. There are three obvious lines of development. The first is the study of the spectra of diatomic gases and the deductions which follow according to the classical quantum theory ; this has already been done with success by Imes (Sleator, Astropys. J.,' vol. 48, p. 125 (1918); Imes, ibid ., vol. 50, p. 251 (1919)) for the hydrogen halides. Comparisons will be made of the molecular constants from the infra-red bands with those obtained from electronic band spectra. As a second development there is the use of the infra-red results in the light of the newer quantum theory. Dennison's prediction ( 'Phys. Rev.,' vol. 31, p. 503 (1928)) of the shape of absorption bands needs confirmation by experiment ; and, if absolute intensities of absorption bands can be measured, the wave-mechanics is ready with an interpretation. Thirdly, the problems offered by triatomic molecules will be attempted. papers on the subject. Their work has removed most of the uncertainty which hinders such researches as this; but sines they do not discuss the use of gratings, and since we have found by experience that it is impossible to make a technique too clear, it has seemed desirable that the construction and use of an instrument should be described.

Soon after the introduction of modern rifles, which give their projectiles a velocity much higher than that of sound, I noticed that when standing in a position in front of the gun and not far from the line of fire, the sound seemed to come, not from the firing point, but from some point considerably in advance of the gun. The natural explanation seemed to be that the sound thus heard was not that of the explosion itself, but was caused by the wave-surface, which is generated in the air by the projectile, moving at a velocity higher than sound. In 1898 I made some observations at the ranges at Broundown to see if the apparent directions agreed with this supposition. A large range like Broundown, however, at which many parties are firing at the same time, was not a very good place for such observations, but in the present year I have again made similar experiments under much more favourable circumstances. It is clear (if the source of the sound is due to the wave caused by the projectile) that the apparent direction of the sound will be the normal to the wave-surface, and that if the direction of this normal is known, the velocity of the projectile, at the time that that particular portion of the wave-surface was generated which ultimately reaches the observer, can be calculated. I now record these observations, not as giving a practical method of ascertaining the velocity of projectiles, but as showing that the ear can distinguish with considerable accuracy the direction of a sound which consists, not of a train of waves, but, at most, of two waves only. The figure gives the plan of the range and the stations at which the observations were made.

Introductory .—During the last ten years there has been much controversy as to the correct method of measuring the overvoltage of an electrode in an electrolytic cell. One body of workers considers that it should be measured during the passage of current through the cell, whereas another maintains that the current should be interrupted by means of a rotating commutator or similar device before the electrode in question is connected to the potentiometer or other measuring instrument. The question is one of considerable importance, as the results obtained by the two methods differ widely in magnitude and behaviour, and no theory of overvoltage can be generally accepted until this controversy is settled. The vital point at issue may be shortly stated thus:—( a ) Is the total oppo sition to the passage of current from electrode to electrolyte due to an active back electromotive force? or ( b ) Is a part of this opposition due to a passive resistance? In other words, is the whole of the fall of potential from electrode to electrolyte reversible, or is a part of it irreversible?

Using an electrical method, Prof. Rutherford and myself were recently able to determine accurately the number N of α-partieles which are expelled from a gramme of radium per second. The final value of N obtained as an average of a great number of observations was 3·4 × 10 10 α-particles per second from a gramme of radium itself, or four times this number if the radium is in equilibrium with its three α-ray products. In another paper the charge carried by an α-particle was measured by the same authors and found to correspond to 9·3 × 10 -10 E. S. unit. Since recent experiments have given conclusive evidence that an α-particle is identical with an helium atom carrying twice the ionic charge, it was necessary to take the ionic charge as 4·65 x 10 -10 E. S. unit. The values of N and e as found from the above experiments enable us to determine the number of ions which are produced by an α-particle along its whole path with a greater accuracy than hitherto. A determination of the number of ions produced by an α-particle emitted from radium itself was made in 1905 by Rutherford in the following way. The ionisation current due to a thin film of radium was measured at its minimum activity, and the total number of α-particles fired off from this film was calculated from the total charge which the α-particles carried with them. Taking the charge on an α-particle as equal to twice the ionic charge e , the number Z of ions produced by an α-particle from radium itself was found to be 1·72 × 10 5 . This number becomes 1·8 × 10 5 if for N and e the latest values, referred to above, are introduced.

In the previously published papers on this subject it has been shown that there is a marked relation between the amount of ozone in the upper atmosphere and the type of atmospheric pressure distribution. By means of simultaneous observations at six stations in N. W. Europe, a fair idea of the distribution of ozone with different pressure distributions was obtained. To get further insight into this relation it was necessary to know the distribution of ozone layer the world at different times of the year. The instruments were, therefore, redistributed to get observations in widely different latitudes, and a year’s observations have been taken at these stations. While the results for one year cannot establish the annual variations with great accuracy, they are enough to show the main features, and several years’ observations would be necessary to give a greatly improved accuracy. The places where the observations have been made are as follows :─ Place. Latitude. Longitude. Arosa (Switzerland) ......................... 46° 45’ N. 9° 40’ E. Table Mountain (California) ....... 34° 22’ N. 117° 41’ W. Helwan (Egypt) ........................... 29° 50’ N. 31° 10’ E. Kodaikanal (India) ...................... 10° 10’ N. 77° 30’ E. Christchurch (New Zealand) ...... 43° 30’ S. 172° 40’ E.

The work to be here considered is a continuation of a previous investigation by Prof. Laby and the present author, in which the existence of fluctuations in the ionisation due to γ-rays from radium was demonstrated. In the present paper the quantitative measurement of this fluctuation is described, and its relation to the theory of γ-rays investigated. At the present time two theories exist for the explanation of the Röntgen and γ-rays (the two radiations exhibit so many properties in common that they are regarded as phenomena differing only in degree), viz., the pulse and entity theories. According to the former, the rays are conceived as propagated from the source, with a continuous wave front, while the latter theory includes the corpuscular form of Bragg, the pulse in a tube of force, or bundle, theory of Sir J. J. Thomson, and the quantum form postulated by Planck and Stark. In any of these last theories the disturbance has a discontinuous wave front and is propagated from the source along a straight line.

In this paper, the effect of alkalinity of the underlying solution on substances with end groups other than carboxyl is studied. Surface pressure measurements only were made. Fig. 1, curves I to III, show the pressure-area relations found with three members of the series on twice normal caustic soda. The acid with n = 32 is condensed at 20°, tending to an area at no compression of about 30 sq. A.; this figure is not very accurate, owing to collapse of the films; the area is nearly the same as with the films of monobasic acids on this solution. The condensed films of these dibasic substances, with a polar group at each end of chain, were shown in Part IX to be oriented upright with one soluble group only in the water. On 2N soda, the acids with n = 24 and 20 are both gaseous at the lowest temperature attainable (3°), the acid ( n = 20) being the naturally the more perfectly gaseous film.

When electrons lose energy by colliding with gas atoms, they may do so either in definite amounts by exciting the atom to a discrete level, or by ionizing the atom, in which case the electrons may lose any amount of their energy over and above the minimum required for ionization. The first process has now been studied in several aspects by a number of investigators ; in particular, the authors have dealt with the angular distribution of the scattered electrons. The study of ionizing collisions, however, has so far been confined largely to the measurements of collision cross-sections, while only slight attention has been paid to the angular distribution and the energy distribution of the scattered electrons. The most valuable information concerning the collision process is to be derived from a detailed study of the angular distribution of the scattered electrons, and such an investigation is described in the present paper.

The purpose of this communication is to announce certain results relative to the expansion of a symmetrisable function k ( s , t ) in terms of a complete biorthogonal system of fundamental functions, which belong to k ( s , t ) regarded as the kernel of a linear integral equation. An indication of the method by which the results have been obtained is given, but no attempt is made to supply detailed proofs. Preliminary Explanations . 1. Let k ( s , t ) be a function defined in the square a ≤ s ≤ b , a ≤ t ≤ b . If a function ϒ ( s , t ) can be found which is of positive type in the square a ≤ s ≤ b , a ≤ t ≤ b and such that ∫ a b ϒ ( s , x ) k ( x , t ) dx is a symmetric function of s and t , k ( s , t ) is said to be symmetrisable on the left by ϒ ( s , t ) is the square. Similarly, if a function ϒ' ( s, t ) of positive type can be found such that ∫ a b k ( s , x ) ϒ' ( x , t ) dx is a symmetric function of s and t , k ( s , t ) is said to be symmetrisable on the right by ϒ' ( s , t ).

The study of gaseous reactions has recently acquired additional interest, since it has been found that a considerable number of reactions can be explained on the basis of a chain hypothesis. In 1923 Christiansen and Kramers studied the kinetics of a unimolecular reaction and found that explosion is possible if the total change of energy resulting from the reaction is greater than the energy of activation. Since that time the mechanism of chain reactions has been carefully investigated and some of the conditions for the continued propagation of the reaction have been ascertained. Thus, if we have two gases mixed together without any chemical change taking place, a reaction may commence when even a very small quantity of a third molecule is added, or if one of the original molecules receives energy of activation (from whatever cause). Designating the original molecules for simplicity by A and B and the new molecule by C, which we will suppose reacts with A, giving a fourth molecule D (and possibly other molecules also), we have A + C → D.

1. It has already been shown that the observed variations with temperature of the intensity of reflexion of X-rays from crystals of rock-salt and sylvine agree closely with those predicted by the theory of Debye as modified by Waller, from the lowest temperature at which experiments have been made, that of liquid air, up to about 500° abs. Moreover, the absolute intensities of reflexion agree closely with those calculated theoretically, if the atomic scattering factors, F, are calculated from the Schrödinger charge-distributions for the atoms, obtained by the method due to Hartree. To obtain agreement, it is necessary to assume the existence of zero-point energy of an amount half a quantum for each degree of freedom, and the experiments may perhaps do considered as furnishing direct confirmation of such energy, since the differences between the intensities calculated with and without it are considerable. The work to do described in this paper was undertaken with a view to extending the investigations to a crystal of a metallic element. Aluminium at ones suggested itself as suitable for this purpose, since it can do obtained in largo single crystals, and since its coefficient of adsorption for the X-rays employed in the experiments, Mo K a , is small.

In a previous communication, the writer discussed the double refraction of a medium composed of similar particles arranged in rectangular order, the results being applied especially to the effects produced in colloidal solutions by mechanical stress and by a magnetic field; the present paper is the discussion of a similar problem, using a simpler method of procedure suggested by Professor Larmor. The object is to investigate to what extent it is possible to consider double refraction, whether produced artificially or occurring in natural crystals, as due simply to an æolotropic distribution of similar particles; the questions which arise when one considers whether the æolotropy occurs naturally or is produced by the action of mechanical, electric, or magnetic force are not specially considered, but the various cases are classified in the first section. In the next sections we consider a medium composed of a homogeneous assemblage of optically isotropic molecules and obtain an expression giving the dispersion of the double refraction. This is applied first to artificial double refraction produced by mechanical stress and by an electric field; then on the same basis the dispersion in quartz is examined. Certain divergences in natural crystals and especially such anomalous cases as apophylite and vesuvian lead to an extension of the theory. This is, briefly, an æolotropic distribution of optically æolotropic molecules, each of which disperses regularly; it is examined first in relation to uniaxal crystals and finally in general for biaxal crystals, and is found to contain the possibility of all the varieties of dispersion of double refraction which occur in natural crystals.

For the purposes of navigation tidal currents may be more important than the rise and fall of the surface, and in fact navigation may be impossible except near times of slack water. In British waters the currents have fairly close connection as regards time and speed with the surface movements, though in some straits in Canadian waters the currents may be largely diurnal in character, whereas the rise and fall of the surface may be semidiurnal in general character. Therefore, the currents cannot be satisfactorily inferred from the tables of high and low water times and heights, and this is probably true in general. The measurement of tidal currents is not easily effected, but if hourly values are available then the ordinary methods of tidal analysis can be used, though such is rarely the case. The usual method of observation is to determine the time of slack water if the currents are constant in direction.

The purpose of this memoir is to discover an optical appliance which shall correct in a practical manner the faults in the field of a Cassegrain reflector, while leaving unimpaired its achromatism and the characteristic features of its design, which gives a focal length much greater than the length of the instrument, combined with a convenient position of the observer. The question touches an investigation by Schwarzschild as to what can be done with two curved mirrors the figures of which are not necessarily spherical. With these be corrects spherical aberration and coma, but in order to secure a flat field he is led to a construction in which the second mirror, which is between the great mirror and its principal focus, is concave, and therefore shortens the effective focal length, in place of increasing it. The deformations from spherical figures are also so great, especially for the great mirror, as to leave it doubtful whether the construction discussed could ever be the model for practicable instruments. If we keep to the Cassegrain form, spherical aberration and coma may equally be corrected by deformations of the mirrors which through large, are less extreme, but there remains a pronounced curvature of the field. For this reason I am led, in the present memoir, to consider more complicated systems produced by the interposition of systems of lenses, achromatism can be preserved completely for a single focus if there are three lenses of focal length determined when their position are given, and if all are made of the same glass. One of these lenses, which I call the reverser, is silvered at the back and replaces the convex mirror; the other two are placed close together in the way of the outcoming beam, about one third of the distance from the great mirror to the reverser; the members of this pair, which I call the corrector, are of nearly equal but opposite focal lengths, introducing very little deviation in the ray but an arbitrary amount of aberration, according to the distribution of curvatures between the two faces of each lens. All the surfaces are supposed spherical except that of the great mirror, The essential problem is to bring the necessary work into a form that will allow unknown quantities which express the distribution of curvature between the faces of each lens to be carried forward algebraically. The methods employed are those of a recent memoir by the author,* and a part of the paper is occupied in working out expressions to which this theory leads, for thin lenses, systems of thin lenses, mirrors, reversers and the like, and it may be regarded as an expansion and working illustration of that memoir. Ibis part does not lend itself to summary, When the expressions are obtained the solution proceeds in a straightforward manner, by approximation, which is somewhat complicated owing to the number of considerations which it is necessary to keep in view, but is not otherwise difficult. The solution is completed at the stage where the unextinguished aberrations are considered negligible.

Since Lord Rayleigh’s experimental study of the polarisation of light scattered by gases, the subject has been examined theoretically from various points of view; in particular by the late Lord Rayleigh, M. Born, Sir J. J. Thomson, and R. Gans. The object of the following paper is to connect the polarisation of light scattered by a simple homogeneous medium with the constants of the dispersion formula for that medium. The result of the calculation gives the ratio of the intensities of the two polarised components for all wave-lengths for which the dispersion formula is valid. Although the expressions can be generalised, they, are given in the first instance in their simplest form. Assuming the medium to be a gas whose approximate dispersion formula contains only one natural frequency in the ultra-violet, this is generalised by supposing the molecules to be anisotropic; the single natural frequency is then replaced by a triplet, or by a doublet for molecules with axial symmetry. In the latter case the dispersion formula is, in the usual notation n 2 - 1 = ⅓ C {( p 1 2 - p 2 ) -1 + 2 ( p 2 2 - p 2 ) -1 }.

Like the manganese group, the cadmium group of hexahydrated double selenates consists of only three salts, those containing rubidium, caesium, and ammonium, the potassium salt being incapable of preparation and apparently of existence. A potassium cadmium selenate with two molecules of water is obtained instead, and was described by Yon Hauer in the year 1866, and by Topsøe in 1870. Indeed, so near in this group is even the rubidium salt to the limit of existence that it has only been obtained at all after many and prolonged attempts. Moreover, it was only formed then in small quantity in the very coldest weather, the great majority of crystals even in these few crops having been those of the salt just referred to with other than six molecules of water. Almost as great difficulty has also been found in preparing the cæsium salt, and the crystals of both these alkali metallic salts of the hexahydrated group have always been white and opaque, so that no optical investigation has been possible. These salts, indeed, would appear never to have been previously obtained at all. Moreover, the ammonium salt, which was obtained by Yon Hauer and measured by Topsøe, affords crystals which are for the most part opaque, and are described by Topsøe as being porcelain-like. No optical investigation of them has ever previously been attempted; they were not included by Topsøe and Christiansen in their great work. The author has succeeded, however, in obtaining a very few crystals of ammonium cadmium selenate hexahydrate, which remained sufficiently transparent for the few hours, after their removal from the mother liquor, necessary to enable them to be subjected to a fairly complete optical investigation. The method followed was the rapid one used in the even more difficult case of potassium ferrous selenate. The cadmium selenate used in preparing the double salts was obtained by precipitating a solution of cadmium sulphate with a just adequate quantity of sodium hydrate, and dissolving the thoroughly washed precipitate in selenic acid. Equal molecular quantities of solutions of cadmium selenate and of the alkali selenate were then mixed, and the liquid at once filtered and set out for spontaneous evaporation and crystallisation, with the results just specified.

The probability of the simultaneous of a positron and an electron, with the emission of two quanta of radiation, has been calculated by Dirac and several other authors. From considerations of energy and momentum it follows that an electron and positron can only annihilate one another with the emission of one quantum of radiation in the presence of a third body. An electron bound in an atom could, therefore, annihilate a positron, represented by a hole on the Dirac theory, by jumping into a state of negative energy which happens to be free, the nucleus taking up the extra momentum. The process is now mathematically analogous to the photoelectric transitions to states of negative energy in the sense that the matrix elements concerned are the same, and we might expect that the effect would be most important for the electrons in the K-shell. Fermi and Uhlenbeck have calculated the process approximately, for the condition where the kinetic energy of the positron is of the order of magnitude of the ionization energy of the K-shell. The result they obtained was very small compared with the two quantum process, which is to be explained by the fact that for these small energies, the positron does not get near the nucleus. In view of the fact that positrons of energies of the order 100 mc 2 occur in considerable quantities in the showers produced by cosmic radiation, and that the primary cosmic radiation itself may consist, in part, of positrons, it becomes of interest to calculate the cross-section for the annihilation of positrons of high energy by electrons in the K-shell, and their absorption in matter, and also to compare this process with the two quantum process for high energies. In the photoelectric effect for hard γ -rays, the electron the electron leaves the atom in states of different angular momentum (described by the azimuthal quantum number l ), and the terms which give the largest contribution are roughly those for which l is of the order of the energy of the γ -ray in terms of mc 2 . For high energies, therefore, a calculation by the method of Hulme, in which the last step is carried out numerically, is out of the question, and we must find some approximate method of effecting a summation. We shall use an adaptation of Sauter's method, in which we shall treat as small the product of the fine structure constant and the nuclear charge. This method may be expected to give a good approximation for small nuclear charge. Our method has the further restriction that it is valid only when the kinetic energy of the positron is not small compared with mc 2 .

An analysis of the mechanism of the thermal hydrogen-nitrous oxide reaction in silica vessels by the kinetic method has shown that it is a chain process. The experiments were confined to a comparatively narrow pressure range and the evidence for chain propagation, although quite definite, required confirmation. The present paper is therefore concerned with the kinetics under a much wider variety of conditions. First, the experiments have been extended to pressures below 30 mm; second, photochemical methods have been employed to she more light on the individual steps of the reaction and to demonstrate unequivocally its chain character; third, in view of the close similarity of the hydrogen-nitrous oxide and hydrogen-oxygen reactions, a detailed study has been made of the effect of small amounts of oxygen on the former reaction. The results of these experiments all lend additional strong support to the chain hypothesis. Small alterations to the apparatus were made. A glass spring gauge was employed for measuring low pressures. One end of the furnace was provided with quartz lens in order to focus the light from the mercury lamp on the reaction bulb; the cathode of the lamp was water cooled. Arrangements were also made for inserting a hollow silica cell between the lamp and the lens so that filters could be used for controlling the intensity and wave-length of the light reaching the bulb. Direct photo dissociation of the nitrous oxide molecule was not attempted since ( a ) absorption of photochemically active light at low pressures in small bulbs is not complete, ( b ) the intensity of the lines of the mercury arc in the absorption region of nitrous oxide is weak. Recourse was therefore made to mercury sensitization in spite of a little additional complication.

One of the most striking dissimilarities between the hydrogen-oxygen and hydrogen-nitrous oxide reactions is the absence in the latter of sharp explosion limits, a feature characteristic of the former. Another important difference is that propagation of chains in the H 2 -N 2 O mixtures is rather less easy than in H 2 -O 2 , for the photochemical chain length is smaller for H 2 -N 2 O than for H 2 -O 2 at the same temperatures and pressures (see below). It has, however been postulated that the carriers in the two reactions are identical and that at least one step, viz., OH+H 2 →H 2 O+H, is common to both reactions. The differences in the propagation factors would therefore be due to these reactions H+N 2 O=OH+N 2 and H+H 2 +O 2 = OH+H 2 O, or H+O 2 = HO 2 HO 2 +H 2 = OH + H 2 O. It may be anticipated that termination processes will be somewhat similar, and consequently the observed differences in the thermal reactions will also be partly due to initiation reactions.

Recent experiments by Roberts have shown, not only that the accommodation coefficients of helium and neon atoms impinging on a clean heated tungsten surface are extraordinarily low, but also that these values increase with time after cleaning the surface. To explain this increase he suggests the gradual formation of adsorbed films on the surface of the tungsten due to residual impurities in the gas. The primary object in starting the investigations to be described in this paper was to gain some information as to the nature of these films, the existence of which has also been postulated by Blodgett and Langmuir. For this purpose experiments have been carried out in which the emission of energy from electrically heated wires of platinum, a metal relatively resistant to contamination, has been investigated under varied conditions. Apparatus A pure platinum wire about 20 cm long and 0·025 mm diameter was silver-soldered to platinum leads of 0·4 mm diameter and mounted loosely in a vertical glass tube of approximately 5 cm diameter. The wire was connected, by double leads, to a Thomson bridge, by means of which the resistance could be determined and also controlled by suitable adjustment of the current. The potential drop along the wire was measured by means of a Siemens and Halske potentiometer. The mean temperature of, and the heat developed in, the wire could thus be determined.

The International Temperature Scale, which has been in force since 1927, is based on certain values assigned to the boiling and freezing points of pure substances and on specified means of interpolation between, or extrapolation beyond, these points. The highest basic point of the scale is the freezing point of gold, defined as 1063·0° C, while for extrapolation from this temperature use is made of the Wien law of radiation, with a certain value of the constant C 2 . Though any temperature above 1063° C is thus completely defined without reference to further fixed points, determinations of such points are of considerable value. In particular, they serve to indicate the degree of reproducibility of the scale by the various users of it, and, when well authenticated, to provide secondary standards for its realization. Of such fixed points the most important has been the freezing point of palladium (1555° C), but the latest developments in furnace technique and refractory materials should now enable the freezing point of platinum to be used with equal, if not greater, advantage. The qualities of platinum which render it especially valuable in this connection are as follows: its freedom from oxidation; its high standard of purity, for which a convenient electrical test is available; its high freezing point (about 1775° C) which approaches the important zone of temperature covered by the electric fighting industry These qualities also make the platinum point especially suitable as the basis for a standard of fight, as has been proposed by a number of experimenters. It is with the two objects indicated above that the National Physical Laboratory has undertaken an investigation concerning the freezing point of platinum the precise scope of which may be defined as follows:— (1) To determine the value of the freezing point in terms of the International Temperature Scale.

The present work was undertaken with the object of testing the fine structure intensity formulæ deduced by Hill. Up to the present very few intensity measurements have been made on the fine structures arising from nuclear spin. The principal difficulty in such measurements arises from the smallness of the structures which are usually incompletely resolved by the interferometers employed. The use of the interferometer in any event necessitates careful corrections for the instrumental intensity distribution. Schüler and Keyston have made photometric determinations of the intensity ratios in the fine structures of two Cdl lines and have verified the intensity rules for these lines. An inherent difficulty in the examination with a FabryPerot interferometer of Cdl structures lies in the presence of an intense evei isotope line within the pattern due to the nuclear spin of the odd isotopes The even isotope component contributes 77% of the intensity of the line and the remaining 23% is distributed amongst the members of the nuclear spin multiplet. The authors do not describe their method of coping with this difficulty which, judging from the experience of the present writers, must have been serious.

The action of light on N 2 O was studied by Leifson and continued in recent years by Wulf and Melvin, Dutta, and the present authors from experiments on its absorption spectra. The experimental data so far known indicate that under the action of light quanta of suitable wave-length N 2 O dissociates into a normal NO and N which may be in different excited metastable states as shown below. N 2 O + hv 1 = NO + N ( 4 S) (1) N 2 O + hv 2 = NO + N ( 2 D) (2) N 2 O + hv 3 = NO + N ( 2 P) (3) These processes are inferred from the various starting points of continuous absorptions from a long wave-length limit, and with retransmitted patches of light occurring between these beginnings. The energies corresponding to hv 1 , hv 2 , hv 3 are given by the different long wave beginnings of absorption at λ 2750, λ 1850, and λ 1580; the differences of energy between of these light quanta are respectively the values of 4 S - 2 D 2 D - 2 P of N.

Recent studies of many chemical gas reactions which involve the production and behaviour of atoms, have shown that the effect of the surface of the reaction vessel on the atom concentration can seldom be regarded as a small disturbing factor to be allowed for by a semi-empirical correction, but must be adequately considered in relation to the other processes determining the velocity of reaction. In this connection, therefore, alteration in the pressure of any one reactant must involve an effect depending on the diffusion coefficient of the atom concerned, with regard to the expected from the mass action principles of the chemical kinetics. Examples of this simple diffusion effect are well known. The results to be expected on these lines are sometimes complicated by the existence of other factors consequent on increase in pressure in the reacting system. In the photosynthesis of hydrogen bromide, where bromine atoms are involved, it has been shown that increase in total pressure, by the introduction of an otherwise inert gas, produces a relative decrease in reaction velocity, where the application of the simple diffusion theory as above would lead one to expect an increase in velocity by prevention of the removal of bromine atoms by the walls. This decrease has been attributed to the stabilization of the bromine “quasi-molecule” by the added gas molecule, the removal of bromine atoms being thus facilitated by what is virtually a triple collision. Similar considerations apply to the photochemical formation of posgene.

The thermal decomposition of ozone has been generally regarded as essentially a bimolecular reaction. The exact determination of the nature of the mechanism has, however, been attended by the discovery of several conflicting influences, the interpretations of which have been matters of no small difficulty and interest. It can scarcely be said that the mechanism of decomposition has been definitely established. General discussion has centred round that calculation of the absolute rate of reaction from the experimentally determined energy of activation, from which it appears that the velocity coefficient, calculated in the usual way, is much less than the experimentally determined value when the decomposition is regarded as bimolecular. Thus Riesenfeld and Wassmuth inclined to the idea of an energy chain reaction, the length of the chains being sufficient to explain the discrepancy, while Schmacher and Sprenger considered that the energy of activation cannot adequately be considered on the “two squared terms” basis, but that allowance must be made for the possible other degrees of freedom of the ozone molecule. This view is regarded as supported by recent work of Glissmann and Schumacher.

Although both the physical properties of penetrating X-rays and gamma rays and their biological effects have been carefully studied, the mechanism of the action of the rays is little known. The question of the relative effects of the same absorbed energy per cubic centimetre of tissues when different wave-lengths are used is a particularly important and obscure one. The present paper is attempt to apply recent theories of high-speed electron production to this problem. Radiations, such a high voltage X-rays or gamma rays, on suffering real absorption give rise to high speed negative electrons, either in photoelectric absorption whereby nearly the whole of the quantum is transferred to the electron, or in a Compton recoil process in which only part of the energy is transferred. The mean fraction given to the electrons rises gradually as the radiations become more penetrating. The relative importance of these two types of process varies in a complex manner with the wave-length and absorbing materials, but in this paper it is proposed to confine discussion to the absorption of “hard” radiations in light elements, of which living materials are mostly constructed.

The collision of a slow moving electron with an atom is known to be a very complicated phenomenon involving a number of processes which are themselves complex. To obtain even an approximate description of such phenomena the only method of attack is to consider the effects of the different individual processes separately in order of estimate the nature and magnitude of their contributions to the resultant scattering. In both elastic and inelastic scattering the principal processes occurring may be stated as follows:- 1-Scattering by the field of the atom considered electron as undisturbed by the incident electron, the latter being also thought of as only slightly affected by the collision. 2-The distortion of the incident and scattered electron waves by the potential field of the atom, the latter field being taken as the undisturbed atomic field. 3-The exchange of electrons between the incident and scattered electron waves and the atom. 4-The disturbance of the atomic field by the incident electron waves.

Following a previous investigation of the afterglow of carbon dioxide it was decided to examine sulpur dioxide under similar conditions of experiment. An afterglow of considerable intensity and duration had, in fact, already been noted by Professors Sir J. J. and G. P. Thomson as occurring when sulphur dioxide was excited in a ring discharge, but no observations on its spectrum appear to have been recorded. Strutt has recorded an afterglow when ozone is passed over sulphur, but no glow was recorded with sulphur dioxide. The spectrum yielded by SO 2 in vacuum tubes varies greatly according to the conditions of excitation. With sufficiently powerful condensed discharges and a rather low pressure of the gas the molecules are dissociated into atoms and the spectrum consists of lines of oxygen and sulphur. With uncondensed discharges of moderate intensity and a suitable pressure of gas, the spectrum shows a strong system of bands degraded to the red which have been analysed by Henry and Wolff and attributed to the diatomic molecule SO; these bands are most intense in the region λ 2442 to λ 3941. Still weaker excitation yields an entirely different system of bands extending from the blue to about λ 2000, and there is evidence that these bands are due to undissociated molecules of SO 2 . The absorption of SO 2 is characterized by a large number of bands, which are most intense in the region λ 2800 to 3150. Owing to the continuous spectrum emitted by the gas during electrical excitation, this absorption may appear superposed on the emission spectrum in some forms of discharge tube. Recently Lotmar has reported on a band system excited in SO 2 by fluorescence.