Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 1930"

A Theory of Electrons and Protons

Abstract: The relativity quantum theory of an electron moving in a given electro­magnetic field, although successful in predicting the spin properties of the electron, yet involves one serious difficulty which shows that some fundamental alteration is necessary before we can regard it as an accurate description of nature. This difficulty is connected with the fact that the wave equation, which is of the form [W/ c + e / c A + ρ1 (σ, p + e / c A) + ρ3 mc ] Ψ = 0, (1) has, in addition to the wanted solutions for which the kinetic energy of the electron is positive, an equal number of unwanted solutions with negative kinetic energy for the electron, which appear to have no physical meaning. Thus if we take the case of a steady electromagnetic field, equation (1) will admit of periodic solutions of the form Ψ = u e - i E t / h , (2) where u is independent of t , representing stationary states, E being the total energy of the state, including the relativity term mc 2. There will then exist solutions (2) with negative values for E as well as those with positive values ; in fact, if we take a matrix representation of the operators ρ1σ1, ρ1σ2, ρ1σ3, ρ3 with the matrix elements all real, then the conjugate complex of any solution of (1) will be a solution of the wave equation obtained from (1) by reversal of the sign of the potentials A, and either the original wave function or its con­jugate complex must refer to a negative E.

The splitting strength of mica

Abstract: Two well-ground and polished plane glass plates if put together, adhere. This phenomenon is called optical contact and is very much used in the manu­facture of optical instruments, since the boundary between the two glass surfaces shows practically no reflection of light, when the gap between the two glass surfaces is exceedingly small in comparison with the wave-length of visible light. An analogous phenomenon can be easily observed in mica. Two freshly split mica foils if put together adhere again with an appreciable force. It is interesting to see if the restoration is perfect, i. e ., if we need to apply the same force to split two mica sheets placed in optical contact as to split a fresh one. In the present work it will be shown that the splitting strength is a constant for mica ; that we can determine a surface energy of mica which is independent of the shape of the mica sheets chosen and that mica placed in optical contact is totally restored. A description will also be given of some electrical phenomena obtained by splitting mica in a high vacuum. It appears that the cleavage surface of mica is covered with electrical charges ; further, that the strength of mica in a high vacuum is more than in air and is also a fairly well-defined constant. The present observations are connected with the well-known work of A. Joffe on the tensile strength of rock salt. In the case of rock salt the surface was either dissolved to avoid the effect of imperfections of the surface or the surface action was avoided altogether as in the experiment with the rock salt sphere.

Mass Defect Curve and Nuclear Constitution

Abstract: In the discussion before the Royal Society on the constitution of the atomic nucleus held on February 7, 1929,* I proposed a simple model of a nucleus built from α-particles in a way very similar to a water-drop held together by surface tension. A certain number of protons (not more than three) and electrons can be bound to such an α-aggregate without forming a new α-particle. † Such additional units of nuclear constitution, usually bound less strongly than those involved in the α-particles, we shall term free nuclear protons and electrons. Their presence will, of course, affect the form of the nuclear energy curve (mass defect curve), not changing, however, its general shape. In the present paper I shall attempt to treat the problem more closely, analysing from the theoretical point of view the experimental facts concerning the nuclear energy.

Flow through Pipe Orifices at Low Reynolds Numbers

Abstract: Most of the experimental work in connection with the flow of fluids through diaphragm orifices in pipe lines has been directed to the establishment of the orifice as a flow meter, and has been carried out at the velocities of flow commonly encountered in commercial practice. As a result of such research the coefficients relating the volumetric discharge of incompressible fluids to the differential head across an orifice are well known over a large range of high Reynolds numbers. For a particular diameter ratio ( i. e., orifice diameter ÷ diameter of pipe line) the discharge coefficient is nearly constant under conditions of turbulent flow. Over the range from steady to turbulent flow, however, very appreciable variations occur in the value of the discharge coefficient, suggest­ing that the accompanying variations in the nature of the flow through and beyond the orifice will be no less marked. As regards the turbulent flow pattern, an investigation, in which the author collaborated, of the airflow downstream of a flat plate suggests that an orifice in a pipe will in general give rise to a vortex system, probably having some points of resemblance to the well-known Karman street which is a feature of the two-dimensional flow past a bluff obstacle, but doubtless exhibiting interesting differences arising from the symmetrical and three-dimensional character of the flow through an orifice. At sufficiently low Reynolds numbers, on the other hand, perfect flow free from periodic vorticity will occur. The stages connecting these two extreme conditions present many points of interest not only as regards the nature of the vortex system downstream of the orifice and the conditions of flow covering its inception, but also as regards the accom­panying pressure-velocity relation during the transition.

The collision between two electrons

Abstract: It is well-known that the problem of the collision between two particles interacting according to the inverse square law is exactly soluble on the wave mechanics, and that the solution yields the same scattering laws as the classical theory. If, however, the two particles are identical, e.g. , two electrons or two α-particles, this is not necessarily the case; for the wave functions used must be antisymmetrical or symmetrical in the co-ordinates of the two particles; and this may affect the scattering laws. In this paper we shall discuss the collision between two particles possessing spin, such as electrons, and also between two particles without spin, such as α-particles. Assuming an inverse square law force between the particles, and neglecting the actual spin forces, we shall deduce from the symmetry properties of the wave functions a scatter­ing law differing considerably from the classical. We shall also mention the various methods by which the effect could be observed, and give some experi­mental evidence in its favour. The application of the exclusion principle to collision problems has been discussed by the author in a previous paper. Suppose we wish to describe the motion of two particles interacting in any field of force. We obtain a solution w (r1 r2) of the wave equation, where r1 refers to the position of the first particle, and r2 to that of the second. If we did not use antisymmetrical wave functions, we should argue that the probability that the first particle should be at r1 and the second at r 2 would be | w (r1 r2)|2, and therefore the probability that one particle should be at r1 and the other at r2 would be | w (r1 r2)|2 + | w (r2 r1)|

The Moments of the Distribution for Normal Samples of Measures of Departure from Normality

Abstract: If x 1... x n are the values of a variate observed in a sample of n , from any population, we may evaluate a series of statistics ( K ) such that the mean value of k p will be the p th cumulative moment function of the sampled population; the first three of these are defined by the equations; k 1 = 1/ n S ( x ), k 2 = 1/ n -1 S ( x - k 1)2, k 3 = n /( n -1) ( n -2) S ( x - k 1)3; then it has been shown (fisher, 1929) that the cumulative moment functions of the simultaneous distribution, in samples, of k 1, k 2, k 3,..., may be obtained by the direct application of a very simple combination procedure. The simplest measure of departure from normality will the be γ = k 3 k 2-3/2, a quantity which is evidently independent of the units of measurements, and in samples from a symmetrical distribution will have a distribution symmetrical about the value zero. In testing the evidence provided by a sample, of departure from normality, the distribution of this quantity in normal samples is required.

The Spread of Vorticity in the Wake Behind a Cylinder

Abstract: This paper is an attempt to investigate the effect on the configuration of vortices in the wake behind a cylinder of an allowance for the thickness of the vortices. The vortices themselves are assumed to be initially rectilinear and of equal circular section, and we assume also that they arrange themselves in an “unsymmetrical double row.” We therefore find a relationship between the “stability ratio” of the double row—that is, the ratio of the distance between the rows to the distance between consecutive vortices on the same row, in the stable configuration—and the diameters of the vortices. The problem in its initial stages can no longer be treated as one in two dimensions, for the “self-induction” of a vortex only enters when we deal with a three-dimensional disturbance, and it is the self-induction that produces the differ­ence between this and the original treatment of the subject. By the “self-induction” of a vortex we mean the effect of the vortex on itself. The isolated rectilinear vortex is treated separately and the results obtained from it are extended to meet the case of the double row of rectilinear vortices. The three-dimensional stability of the Benard-Karman street has already been discussed, but the present treatment introduces various simplifications which, while not altering the general nature of the problem, make the expressions more amenable to treatment and yield results that appear to have been masked by the complexities of the algebra in the previous investigation. I would like to express my thanks to Dr. H. Jeffreys for many helpful criticisms which have had the effect of altering entirely certain sections of this paper.

Perturbation problems in quantum mechanics

Abstract: One of the great achievements of the Schrodinger wave-mechanics is the elegance of its perturbation theory, which has brought many problems, formerly considered intractable, within the range of a highly-developed mathematical technique. It is not necessary at this stage to review the numerous applications which have been made of this perturbation theory or to dwell upon its many advantages. The important advance towards an understanding of chemical forces which it has made possible is in itself a considerable achievement. There are, however, certain disadvantages in the perturbation theory in its present form, which limit the extent of its applications to complex problems of atomic and molecular structure. If the interaction of atoms, for instance, is to be calculated, as it most desirable, improved methods will have to be found.

The Crystal Structure of the Normal Paraffins at Temperatures Ranging from that of Liquid Air to the Melting Points

Abstract: The aim of this paper is to give a survey of the structures of the normal paraffins at temperatures ranging from that of liquid air to those in the neighbourhood of the melting points. The paper divides naturally into two parts, one dealing with the thermal expansion, i. e ., with the gradual and con­tinuous increase of the lattice dimensions with increasing temperature; the other with the discontinuous structural changes which occur under certain conditions when the substances are subjected to temperature changes.. Chemical Material . The chemical material was partly that already used in previous work and partly new material. Most of the substances were synthesised in the Davy-Faraday Laboratory. Some of the preparations such as hexane and pentane were bought and carefully purified. The writer is again very much indebted to his colleagues, Dr. H. S. Gilchrist and Mr. E. L. Holmes, who were kind enough to do all the chemical work for him.

Observations of the amount of ozone in the earth's atmosphere, and its relation to other geophysical conditions.—Part IV

Abstract: 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 Scattering of Electrons by Atoms

Abstract: The scattering of a stream of charged particles by a spherically symmetrical electrostatic field was first investigated, from the point of view of the wave mechanics, by Born. Various authors have developed his ideas and have applied them to the scattering of electrons by atoms, which for the purpose have been treated simply as fields of force. The purpose of the present note is to obtain formulae for the scattered intensity by methods similar to those used in calculating the scattering of X-rays by an atom. The formulae obtained have all been published elsewhere, either by the present author, or by others; it has, however, appeared worth while to publish the present method of obtaining them, partly because the analysis is particularly simple, secondly because the results are expressed in a form easy to compare with those for X-rays, and thirdly because the method makes it clear under what conditions the approximations used will lead to a sufficiently accurate result. Experiments on the scattering of streams of charged particles measure the “scattered intensity”; we shall first define just what we mean by this. Suppose we have a beam of particles of such intensity that one particle crosses unit area in unit time. Suppose that the beam fall on one scattering centre—that is to say, on one atom, at a point O. Suppose that a disc, of area R2 d ω be placed at a point P, distant R from O, and such that OP makes an angle θ with the original direction of motion of the particles. The disc is to be normal to OP, so that it subtends a solid angle d ω at O. Then if Iθ d ω be the number of particles striking the disc per unit time, Iθ is what we call the scattered intensity.

Characteristic Energy Losses of Electrons Scattered from Incandescent Solids

Abstract: The electron emission produced when solid conductors are bombarded with electrons of controlled speed has formed the subject of a great number of investigations. It is now generally recognized that this emission consists of three different parts: (1) Primary electrons, truly reflected without loss of energy; (2) electrons scattered back with reduced energy; and (3) secondary electrons proper, with very low velocities, which would seem to be produced from the atoms of the target by the same collision processes that give rise to the second group. In recent years considerable attention has been paid to the reflected electrons, the angular distribution of which reveals their wave character, if the target is a definitely orientated crystal of the substance in question. Some time ago I made some measurements on the velocity spectrum of the emission produced by electron bombardment, using a magnetic deflection apparatus of fairly high resolving power. The principal object of this investigation was to look for evidence of groups of electrons with character­istic velocities related to the soft X-ray levels of the substance. From certain theoretical considerations such electrons might be expected to be present in the emission. Targets of lithium, beryllium, boron, carbon and aluminium were tried, but in no case was there any evidence of electrons of the kind in question. These results are discussed in the paper mentioned. The distribu­tion curves obtained for different targets and bombarding voltages ranging from 40 to 900 volts were all similar in shape. The reflected electrons pro­duced a sharp and narrow peak, separated from the rest of the curve by a very deep minimum. The curve then rapidly rose to a maximum, corresponding to scattered electrons which had lost an energy equivalent to 25 volts in the collision. In addition to these, some experiments were made with targets of platinum and carbon, which could be kept at incandescence also when readings were taken. It was found that new maxima appear at high temperature, nearer to the reflected peak, and that the 25 volt maximum becomes very faint but reappears after some time on cooling. These changes were repeated several times. It was concluded that the 25 volt maximum was produced by an adsorbed layer formed on the cold target in the high vacuum, whilst the new maxima with hot targets should probably be regarded as characteristic of the target substance itself. Somewhat similar effects have been observed by Brown and Whiddington using a photographic method.

The Exchange of Energy between Gas Atoms and Solid Surfaces

Abstract: If gas molecules with average energy corresponding to a given temperature strike the surface of a solid at a different temperature, the average energy of the gas molecules leaving the surface does not in general correspond to the temperature of the solid but depends also on their average energy before staking it. In order to exclude complications due to the transfer of rotational energy we shall consider only monatomic gases. Let the average translational energy of the molecules before striking the surface at temperature T2 correspond to a temperature T1, and let the average translational energy of the molecules after leaving the surface correspond to a temperature T2' (see fig. 1). Modifying slightly a suggestion made by Maxwell* in a different connection, Smoluchowski assumed that the change in the temperature of the gas molecules brought about by striking the surface is proportional to the difference between the temperature of the surface and that of the gas molecules before striking it ; that is, that T2 - T1 = a , (T2 - T1). (1) The constant of proportionality a was later called the accommodation coefficient by Knudsen. Smoluchowski applied this idea to explain the so-called temperature jump at the surface of a solid.

Experiments with high velocity positive ions

Abstract: It would appear to be very important to develop an additional line of attack on problems of the atomic nucleus The greater part of our information on the structure of the nucleus has come from experiments with α-particles and if we can supplement these with sources of positive ions accelerated by high potentials we should have an experimental weapon which would have many advantages over the α-particle It would, in the first place, be much greater in intensity than α-particle sources, since one microampere of positive ions is equivalent, so far as numbers of particles is concerned, to 180 grams of radium equivalent It would in addition have the advantage of being free from penetrating β and γ rays which are a complication in many experiments, whilst the velocity would be variable at will The main difficulty in obtaining such sources lies of course in the production and application of the very high potentials necessary to accelerate the particles if velocities approaching that of the α-particle are to be obtained For example, α-particle from polonium have an energy corresponding to 52 million electron volts and a potential of 26 million volts would be required to give a helium nucleus an equal amount of energy We have therefore to decide what is the minimum acceleration voltage at which we can usefully work, since the experimental difficulties increase very rapidly with increasing voltage In making this decision we are naturally guided by the recent theoretical work of Gamow on the “ Theory of Artificial Disintegration” On Gamow’s theory the probability of an α-particle of velocity v entering a nucleus of atomic number Z, after coming within the effective radius of the nucleus, is W = e -16π e 2Z/ hv Jk, Where Jk is a function varying slowly with v and Z It is clear, therefore, that for particles of equal energy the lighter particle has the greater chance of penetration into the nucleus, so that we should choose protons as our source of positive ions for this reason

The Swelling of Charcoal. Part I. Preliminary Experiments with Water Vapour, Carbon Dioxide, Ammonia, and Sulphur Dioxide

Abstract: The experiments of Meehan having shown that charcoal increases in volume when taking up carbon dioxide, it became an obvious step to correlate this expansion with the quantity of gas adsorbed. In this paper a form of extensometer is described which, while sufficiently sensitive and accurate for the measurement of the percentage linear expansion ( x ) of a rod of wood charcoal, was yet compact enough to permit its being sealed up in an all-glass apparatus, so that simultaneous determinations could be made of the weight ( s ) of gas taken up per unit weight of the absorbent. The graphs obtained by plotting the variables x and s have certain interesting characteristics which it will be convenient to describe before dealing with the detailed results. As fig. 1 shows, the coefficient dx/ds increases steadily with s ; thus far the charcoal behaves similarly to many of the common gels, which contract proportionately less in the later stages of drying, owing to the micellae coming in contact with each other. The swelling of charcoal, however, appears to follow a more regular course than that of the elastic gels, and in the case of ammonia, carbon dioxide, and sulphur dioxide is given within the limits of accuracy of our experiments by hyperbolic equations of the type x = k s /S— s ... where k and S are constants characteristic of each gas. In fig. 1 the experimental values of x have been plotted (for convenience of representation) against s /S. The smooth curves for ammonia of the above form, using appropriate values of the constants. An additional term (a small additive constant over the experimental range) is necessary to represent the behaviour of water vapour.

A Thermal Method of Measuring the Vapour Pressure of an Aqueous Solution

Abstract: The method described below of measuring the difference of vapour pressure between any two aqueous solutions, or between a solution and the solvent, arose from experiments on isolated surviving muscles, in which it was noticed that stimulation in nitrogen led to a large increase in the rate of resting heat-production. This increment in heat rate was traced finally to condensation of moisture on the muscle, due to the lowering of vapour pressure caused in the muscle by the accumulation of the products of activity. These experiments are described elsewhere. The unexpected sensitivity of the apparatus to a change of vapour pressure led to its trial with solutions of various concentrations held by strips of filter paper; the results were so promising that a special instrument was designed and constructed, which alone is referred to in the following pages. The method has various advantages: ( a ) it is direct and fairly exact, e. g ., the difference of vapour pressure between water and a not too dilute aqueous solution can be measured at any required temperature, within 1 to 2 per cent. ; ( b ) it is fairly rapid: a reading is obtained in 30 to 45 minutes and four or five measurements can be made at the same time, if desired, by a single observer; ( c ) it has a wide range, e. g ., one can measure, on the one hand, the difference of vapour pressure between 0⋅1 M. NaCl and 0⋅2 M. cane sugar, or, on the other, between 5 M. NaCl (5 g. molecules NaCl to 1000 g. H2O) and water, the latter difference being of the order of 500 times the former; ( d ) very small quantities of the solutions are required, enough namely to moisten 1 to 2 sq. cm. of filter paper, say 0⋅2 cc.

The Liberation of Electrons from Metal Surfaces by Positive Ions. Part I. Experimental

Abstract: Modern theories of the glow and arc discharges require that electrons should be set free from the cathode surface as a result of the bombardment by positive ions. The conditions in the neighbourhood of the negative electrode are exceedingly complex, and it is only by systematic examination of each reaction which we believe to be present, isolated from the disturbing effects of the others, that we can hope for a complete understanding of this important region. This paper describes some experiments which have been carried out in an endeavour to explain the precise nature of the reaction between the positive ions and the surface of the conductor. The literature of this subject is fairly extensive, and many of the experiments have been very carefully thought out. It seems to be quite definitely estab­lished that ions of velocity greater than about 100 volts set free electrons from metal surfaces which are not rigorously freed from gas. Most of the experi­ments have been carried out with alkali ions from thermionic sources, and owing to the abnormally low ionisation potentials of the alkalis the results are scarcely applicable to the case of discharges in ordinary gas. We are not concerned with the liberation of electrons by very fast canal rays or alpha particles, but with the effect produced by positive ions of less than about 1000 volts energy. Penning has established by a series of experiments that neon ions of as little as 7 volts energy, drifting up against a metal surface, are able to set free electrons from it.

The n-Fatty Acids

Abstract: The normal fatty acids may unquestionably be regarded as one of the most interesting and important groups of chemical compounds. Many of them occur commonly in nature, and form the basis of valuable industrial products. The part which they and their derivatives play in life processes gives them a particular interest to the biologist. As compounds, which appear to be readily obtainable pure, and which form regular series including a comparatively large number of individuals, they furnish the chemist and physicist with material peculiarly adapted for the study of the relationship between constitution and properties. For these reasons they have been the subject of an almost endless number of investigations, in which the preparation and properties both of individual members or groups of individuals have been studied. At this stage, it might well have been assumed that every member of the series had long since been obtained pure, and its properties determined with so high a degree of accuracy, that only the exacting requirements of some new investigation would have demanded further study of the subject. Reference to the literature of the subject, however, showed that the real position was by no means satisfactory. While, on the one hand, the results of the determination of such a property as the melting point of certain members of the series, for instance, arachidic acid, obtained from various natural sources by chemists of established reputation, gave a constant value, and while the criteria of purity of the various samples were quite satisfactory, the material was certainly not identical with samples of the corresponding acid prepared synthetically. The difference was in some cases such as to justify the assumption that the natural and synthetic acids were differently constituted, but no theory could be found to account for the observed differences.

Vertical Electric Currents below Thunderstorms and Showers

Abstract: In a previous paper an account has been given of apparatus which was found to be suitable for studying the discharge of electricity from a raised metal point in the strong electric fields which occur at the surface of the ground during thunderstorms and showers. The two methods of observation which were employed consisted, first, in measuring the quantity of electricity of each sign which was discharged from the point in a definite period of time, usually the duration of a storm; and secondly, in obtaining a continuous record of the current from the point throughout a storm. Observations on a number of thunderstorms and showers over a period of several months, by the first method, showed that there was a considerable preponderance of upward discharges of positive electricity, indicating that negative gradients of potential predominated at the surface of the ground in such disturbed weather conditions. Some examples of records obtained by the second method were also given. In the present paper, results obtained by the first method over a period of two years are discussed, the observations including all occasions, during that time, on which intense electric fields existed at the observing station for a sufficiently long time to cause a measurable quantity of electricity to be discharged from the point. (The smallest quantity which would be detected by the integrating device is about 0·1 milli-coulomb.) The preponderance of negative potential gradients during periods of intense electric field has been confirmed over the longer period of time. Records obtained by the second method are also described, and their bearing on the question of the polarity of the clouds is discussed. For this purpose, the method of observation is simply a convenient way of obtaining an unambiguous continuous record of the sign of the potential gradient, and a rough estimate of its magnitude, throughout periods of heavy rain. Finally, the problem of the total interchange of electricity between the earth and the atmosphere from known causes is re-discussed, utilising the results already given.

The Liberation of Electrons from Metal Surfaces by Positive Ions. Part II. Theoretical

Abstract: In this paper we propose to consider the process of electron capture by positive ions at a metal surface, and the emission of electrons which occurs as a secondary phenomenon. The discussion which we venture to give is admittedly crude, and it is to be hoped that an adequate theoretical treatment of the problem will not be long delayed. As a preliminary we shall discuss some aspects of present knowledge regarding electrical conditions near metal surfaces. Recent experiments of Compton and van Voorhis suggest that positive ions capture an electron from a metal before making thermal contact with the surface, so we require to know the nature of the electric field at some distance from the mechanical boundary. We shall proceed to some calculations on the probability of neutralisation, basing our work on the supposition that neutralisation is due to auto-electronic emission under the influence of the electrostatic field of the approaching positive ion. We shall then discuss the phenomenon from the viewpoint of the transition of an electron through a potential barrier between two states of equal energy, and attempt to apply the results obtained to an explanation of the mechanism of secondary electron emission.

The Theory of Flame Motion

Abstract: The motion of flame has been extensively investigated by experimental methods. The theoretical aspect of one mode of propagation has been studied by D. L. Chapman and by Jouguet. Their observations are limited to the phenomenon known as detonation. For the slower and more usual propagation of flame there is a well-known formula due to Mallard and Le Chatelier. It refers to the horizontal propagation of flame through a still mixture under such circumstances that the pressure produced by the combustion is freely vented into the atmosphere. That is to say, the explosive mixture is ignited at the open end of a horizontal tube, the tube being closed at the other end to shield the mixture from any external currents. This formula was intended as a tentative and general description, without detailed analysis, of the initial, uniform motion of the flame. It is based on the assumption that the trans­mission of flame depends on a balance between the conduction of heat from layer to layer and the cooling. In Mallard's original formula|| the velocity of the flame was held to be inversely proportional to the square root of the cooling due to the wall of the tube; but this relation disappears in the final, joint result of these authors, who wrote their formula V = K T - t / t -θƒ(T. t ), or, tentatively, V=K.L/ c .T - t / t -θ, which becomes V = K . L .Q/ c 2( t -θ),

On the Coefficient of Heat Transfer from the Internal Surface of Tube Walls

Abstract: The present work on the transfer of heat from a heated brass tube to water flowing through it was undertaken for the British Electrical and Allied Industries Research Association though the experimental methods pursued were left to the discretion of the experimenters. Two important innovations compared with the methods of previous experimenters were: First, the direct heating of the tube by a low tension alternating current; and secondly, the discarding of the use of thermocouples to obtain the temperature of the water, this being calculated for any cross-section from the amount of heat put into the water up to that cross-section. The temperature so calculated is what an engineer always understands as the temperature of the water. The only other way of getting a definite water temperature is to take the temperature at points in the axis—a quite unimportant temperature in practice. Naturally the value that is obtained for the coefficient of heat transfer depends con­siderably on what is taken as the water temperature. 2. Historical . Many experiments on the transfer of heat across condenser tubes have been made with the outside of the tube steam heated, the amount of heat transfer being obtained from the rise of temperature of the water flowing through the tube. None of this work has any scientific value, however, except in the few cases where the actual temperature of the tube was directly obtained by means of thermocouples. Here are included the experiments of Webster, Clement and Garland and McAdams and Frost. Also worthy of mention are some early experiments by Stanton in which the temperature of the tube was obtained from its increase in length.

The Mobility of Ions in Pure Gases

Abstract: Although determination of the mobility of ions in gases have been made Almost continuously during the last 30 years, the nature of the ions still remains obscure. The values obtained by different experiments, using a variety of methods, differ by amounts far in excess of those to be attributed to be observational errors and some methods yield results which are complicated and difficult to explain on any simple theory of the nature of the ion. The main facts which have emerged from the mass of experimental data are summarised in “Conduction of Electricity through Gases.”* It seems probable that in none of the experiments made hitherto has the gas under examination been spectroscopically pure. In many cases materials such as ebonite and sulphur have been in contact with the gas. In others the apparatus has been made gas-tight by means of waxed flanges or greased joints. In such conditions the purity of the gas leaves much to be desired. It is continually being contamined by impurities such as water vapour and carbon dioxide coming from the walls of the vessels and from the metals parts of the apparatus as well as by the vapours from the wax, ebonite, etc. Such impurities may have large affinities for electron and may unite with the positive ions to form groups. In such conditions, in a given gas, the ions may well consist of clusters of which the size and mass vary from one experiment to another. The reason why many observers have found the negative ions to be of molecular magnitude and not electrons in nitrogen, hydrogen, etc., becomes Obvious, and it is not surprising that the actual mobilities found are smaller than those calculated theoretically from the standpoint of the classical dynamical theory of gases, assuming the ions to be monomolecular. The present writers for example, found that in an experiments on nitrogen at a pressure of 600 mm, freshly introduced into an apparatus contained under a bell jar, the negative carries consisted of a mixture of ions and electrons. The effect of the contamination coming from the walls was clearly shown by the fact that the number of “normal” ions increased, and of electrons decreased, on leaving the gas in the apparatus overnight.

The Absolute Intensities and Internal Conversion Coefficients of the Formula-Rays of Radium B and Radium C

Abstract: It is well known that with many radioactive bodies the departure of the disintegration particle is followed by the emission of γ-rays. In addition to γ-rays of frequencies v1, v2, ..., it is observed that there is an electronic emission consisting of several homogeneous groups whose energies can be written The energies of these groups are identical with those that would be produced by photoelectric absorption in the parent atom of the γ-rays emitted from the nucleus, and this phenomenon is frequently described as the internal conversion of γ-rays. By this is meant that in every case when the nucleus emits energy E this occurs in the form of radiation of frequency E/ h , but that this does not always escape as such from the atom. In a fraction a of the cases the radiation is absorbed in the electronic structure and gives rise to a photoelectron, in the remaining fraction (1 — α) the γ-ray is emitted clear of the atom. The quantity a is termed the coefficient of internal conversion. Smekal* and others have pointed out that there is no need and even no justification to consider the γ-ray ever to be emitted in the case of those atoms which give photoelectrons. All that can be truly inferred from the experimental facts is that the atom as a whole is capable of emitting energy E, and this it may do either in the form of a quantum of radiation hv = E, or in the form of an electron of energy E — K, or E — L, etc., followed by the appropriate excited K-, L-, X-radiations. The greater portion of this energy E is certainly resident in the nucleus, so that this second standpoint implies some type of what may be termed collision interaction between the nucleus and the electronic structure of the atom.

The Tidal Oscillations in an Elliptic Basin of Variable Depth. II

Abstract: The problem of the "long" waves in a circular basin of uniform depth involves in its solution a transcendental function–the Bessel function, and the determination of the free periods requires a knowledge of the zeros of this function or an allied function. On the other hand, when the basin, still circular, has a certain variable depth, it was shown by Lamb that the solution is expressed in terms of simple algebraic polynomials and the free periods of oscillation are expressed by an extremely simple formula. In similar fashion, the solution of the problem of the "long" waves in an elliptic basin of uniform depth involves the use of elliptic cylinder functions, and the free periods are only obtained as the result of lengthy numerical approximations.

A new method of determining the distribution curve of polydisperse colloidal systems

Abstract: No quantitative method has been developed for the complete determination of the distribution curve of polydisperse systems containing all sizes of particles of colloidal dimensions. Certain of the methods used in the mechanical analysis of soils could, with sufficiently accurate temperature control and refine­ment of detail, enable the distribution curve to be constructed as far down as particles of equivalent diameter 200 mμ , but, owing to the slow rate of settling of such particles in water under gravity, the estimations would take several weeks to carry out. These methods are very ably discussed by F. V. von Hahn in a recent monograph. The special problems of the mechanical analysis of soils have been critically reviewed by M. Kohn. The force acting on particles in suspension can be enormously increased by the use of the centrifuge, which has been developed by Svedberg so successfully that even large molecules, such as those of the proteins, can be made to sediment with appreciable velocity. The range of forces available is therefore ample for the study of polydisperse systems.

A camera for electron diffraction

Abstract: The apparatus described in this paper, which will be called for shortness an electron camera, is intended to study the diffraction patterns formed by the reflection of cathode rays from crystalline surfaces. It differs from the original apparatus used by Davisson and Germer for this purpose in that the method of detection is photographic instead of electrical, and that the energy of the electrons is much greater, being at least 6000 volts (more usually 30,000) instead of about 300. In consequence of the much greater penetrating power of these fast rays it is not necessary to use an elaborate vacuum technique. The principle of the apparatus is that a narrow beam of cathode rays generated in a gas-filled discharge tube is selected by passing through two fine pin-holes and then strikes the crystalline target, where it is diffracted into divergent beams which ultimately strike a photographic plate.

An Experimental Determination of the Intensity of Friction on the Surface of an Aerofoil

Abstract: 1. The principal part of the present investigation* is concerned with an experimental determination of the intensity of friction on the surface of an aerofoil from the well known relation f = (∂V/∂ z ) z - 0, where f is the intensity of friction, μ. the coefficient of viscosity, and V the velocity parallel to the surface at a normal distance z from the surface. In general, the velocity changes rapidly near the surface, so that the velocity gradient (∂V/∂ z ) z = 0 can only be predicted reliably when the velocity observations are taken very close to the surface. A review of the instruments available for the measurement of the velocity very close to a surface led to the conclusion that the most suitable device would be a surface tube of the type designed by Sir Thomas Stanton, and used to examine the conditions at the boundary of a fluid in turbulent motion. The special feature of this tube is that the inner wall of the tube is formed by the surface itself. Three surface tubes were used in the present experiments, the widths of the openings being 0·0020, 0·0032 and 0·0044 inch respectively. These tubes were calibrated in the known laminar flow in a pipe with a rectangular cross-section, and with them it was possible to measure the velocity at points situated about 2 to 3 thousandths of an inch from the surface. The observations taken with the three tubes were found to be mutually compatible and allowed predictions to be made of the velocity gradients at the surface, and so of the frictional intensities. A check on the general accuracy of these values of frictional intensity was obtained from a comparison of the resultant frictional drag of the aerofoil predicted from them, with that obtained when the form drag due to the normal pressures on the surface was subtracted from the total drag deduced from the total head losses in the wake. In addition, explorations of total head in the boundary layer, that is, the thin layer adjacent to the surface throughout which the retarding influence extends, were made with small tubes. It was found that the velocities measured near the surface with these tubes were compatible with those measured still closer to the surface with the surface tubes. The frictional drag of the aerofoil was also determined from the changes of momentum along the boundary layer.* 2. The experiments were made on a large model aerofoil mounted horizontally with very small clearances, between the vertical walls of a 7-foot wind tunnel. The observations were taken midway between the walls, where the flow was closely two-dimensional. To obtain a smooth surface in this region, the middle part (6-inch span) of the model was formed from a hollow gunmetal casting accurately milled to shape and polished. The remainder of the model was a light but stiff wooden framework built up of two longitudinal spars, nose and tail pieces, and transverse ribs, with a hand-finished surface covering of three-ply wood.

Investigation of the passage of "fast" β - particles through gases

Abstract: 1. The Wilson cloud method affords considerable scope for the investigation of the phenomena exhibited by electric particles traversing matter. its possibilities in this connection were abundantly shown by Wilson in his experiments, in which he applied the method to the investigation of such phenomena as ranges, primary and secondary ionisation, frequency of pro­duction of “branch” tracks, nuclear scattering, and the momentum relations in branch collisions. Since Wilson’s work the method has been used by several workers for the investigation of the passage of α-particles through matter, but has been little used for investigating the phenomena connected with the loss of energy by β-particles. In his experiments Wilson did not aim at a high degree of accuracy and this especially applies to the observations he made on “fast” β-particles. His observations were also confined to β-particles traversing air. In the present work the cloud method is applied to a further investigation of phenomena representing loss of energy by fast β-particles in oxygen, and methods are adopted to enable quantitative measurements to be made. The observations are also extended to hydrogen, which is of considerable importance for comparison wit theory. In the experiments a radioactive source of high-speed β-particles is used, β-particles with energy up to a million and a half volts being thus available. Though for several other methods such sources are too weak, they are of sufficient intensity for the purpose of investigation by the cloud method which deals with individual particles. The phenomena investigated here are the primary ionisation, the frequency of production of “branches” and the momentum relations in "branch” collisions. The primary ionisation gives information about the frequency of collisions in which the β-particle loses energy of the order of the ionisation potential for the outer electrons in the atoms traversed, whilst the frequency of branches refers to collisions in which the losses of energy are of the order of 5000 volts or greater.

The Analysis of Surface Layers by Electron Diffraction

Abstract: The very close correspondence which has been shown to exist between the diffraction patterns formed by cathode rays passing through thin solid films,* and the crystal structure of these films, suggests the possibility of using electron diffraction to investigate surface layers of unknown composition. This possibility was indeed indicated in Davisson and Germer’s original paper and has since been further applied. These experiments have all been made with slow electrons, of energies of the order of 300 volts. With such electrons the experiments do not agree well with theory even in the case of known structures, so their application to the investigation of unknown structures involves considerable uncertainty. Further, slow electrons can only be detected photographically with very long exposures, while the electric method of detection is very cumbrous if it is desired to survey the complete diffraction pattern. For these reasons I decided to use the apparatus described in the previous paper to investigate the diffraction patterns obtained by the reflection of cathode rays from the surfaces of various solids. The discharge was generally produced by an induction coil and the energy of the rays was of the order of 30,000 volts. In a few cases, an Evershed and Vignolles direct-current generator was used giving about 6,000 volts. In the course of the investigations, it appeared that these fast rays are uninfluenced by the thin layers of gas which are normally present on surfaces in a vacuum, or, possibly, that they temporally remove the layers by bombardment. From one point of view this is an advantage, as it is therefore unnecessary to take special precautions to degas the surfaces used, or to keep a very high vacuum. On the other hand, it limits the range of the method to the investigation of solid layers.