Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 1909"

The Tension of Metallic Films Deposited by Electrolysis

Abstract: It is well known that metallic films deposited electrolytically are in many cases liable to peel off if deposited to any considerable thickness. This is the case with nickel which, when deposited over a certain thickness, will curl up into beautiful close rolls, especially if it does not adhere very tightly to the body on which it is deposited. For example, if a piece of glass is silvered by any of the usual silvering solutions, and then nickel is deposited on the silver, it is found that the nickel and silver peel off the glass in close tight rolls almost at once. In ‘Practical Electro-Chemistry,' by Bertram Blount, reference is made on pp. 114 and 272 to the tendency of nickel to peel off, and it is stated that it “will peel—spontaneously and without assignable cause” (p. 272), but that a thick coating can be obtained by keeping the solution at between 50° and 90°C. The late Earl of Rosse tried, about 1865, to make flat mirrors by coating glass with silver chemically, and then electroplating with copper; but he found that, owing to the “contraction” of the copper film, it became detached from the glass. I have had the' same experience in protecting silver 61ms in searchlight reflectors by a film of electro-deposited copper, it being found that if the film of copper is more than 0.01 mm. thick peeling is apt to take place.

Functions of positive and negative type, and their connection with the theory of integral equations

Abstract: This memoir is concerned with continuous symmetric functions k ( s, t ) for which the double integral ∫ a b ∫ a b k ( s, t ) θ ( s ) θ ( t ) dsdt is either not negative, or not positive, for each function θ( s ) which is continuous in the interval ( a, b ) ; in the former case the function k ( s, t ) is said to be of positive type, while in the latter it is said to be of negative type. The importance of these classes of functions in the theory of integral equations will be gathered from Part I. The greater portion of the second part is devoted to a proof of the theorem that the necessary and sufficient condition, under which a continuous symmetric function, k ( s, t ), is of positive type, is that the functions k ( s 1 , s 1 ), k ( s 1 , s 2 s 1 , s 2 ),....., k ( s 1 , s 2 ...., s n s 1 , s 2 , ......, s n ), ... should never be negative, when the variable s 1 , s 2 , ...., s n , .... are each confined to the closed interval ( a, b ). This leads to several interesting properties of such a function ; for instance, if k ( a 1 , a 1 ) = 0, the functions k ( s , a 1 ), k ( a 1 , t ) are identically zero.

The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light

Abstract: When a shaft of circular section is revolving uniformly, and is transmitting power uniformly, a row of particles originally in a line parallel to the axis will lie in a spiral of constant pitch, and the position of the shaft at any instant may be described by the position of this spiral. Let us suppose that the power is transmitted from left to right, and that as viewed from the left the revolution is clockwise. Then the spiral is a left-handed screw. Let it be on the surface, and there make an angle є with the axis. Let the radius of the shaft be a , and let one turn of the spiral have length λ along the axis. We may term λ the wave-length of the spiral. We have tan є = 2 πa / λ . If the orientation of the section at the origin at time t is given by θ = 2 π N t , where N is the number of revolutions per second, the orientation of the section at x .

On a Diffuse Reflection of the α -Particles

Abstract: When β -particles fall on a plate, a strong radiation emerges from the same side of the plate as that on which the β -particles fall. This radiation is regarded by many observers as a secondary radiation, but more recent experiments seem to show that it consists mainly of primary β -particles, which have been scattered inside the material to such an extent that they emerge again at the same side of the plate. For α -particles a similar effect has not previously been observed, and is perhaps not to be expected on account of the relatively small scattering which α -particles suffer in penetrating matter. In the following experiments, however, conclusive evidence was found of, the existence of a diffuse reflection of the α -particles. A small fraction of the α -particles falling upon a metal plate have their directions changed to such an extent that they emerge again at the side of incidence. To form an idea of the way in which this effect takes place, the following three points were investigated:— (I) The relative amount of reflection from different metals. (II) The relative amount of reflection from a metal of varying thickness. (Ill) The fraction of the incident α -particles which are reflected.

On pressure perpendicular to the shear planes in finite pure shears , and on the lengthening of loaded wires when twisted

Abstract: In the ‘ Philosophical Magazine,' vol. 9, 1905, p. 397, I gave an analysis of the stresses in a pure shear which appeared to show that if e is the angle of shear and if n is the rigidity, then a pressure n e2 exists perpendicular to the planes of shear. That analysis is, I believe, faulty in that the diagonals of the rhombus into which a square is sheared are not the lines of greatest elongation and contraction, and are not at right angles after the shear, when second order quantities are taken into account, i . e ., quantities of the order of e2; I think the following analysis is more correct, and though it does not give a definite result, it leaves the existence of a longitudinal pressure an open question. The question appears to be answered in the affirmative by some experiments, described in the second part of the paper, in which loaded wires were found to lengthen when twisted by a small amount proportional to the square of the twist. I.— Stresses in a Pure Shear . Let a square ABCD (fig. 1) of side a be sheared into EFCD by motion through AE = d , the volume being constant. The angle of shear is ADE = e, and tan e = d / a exactly ; neglecting e3, we may put e = d / a .

The yielding of the earth to disturbing forces

Abstract: 1 Any estimate of the rigidity of the Earth must be based partly on some observations from which a deformation of the Earth’s surface can be inferred, and partly on some hypothesis as to the internal constitution of the Earth The observations may be concerned with tides of long period, variations of the vertical, variations of latitude, and so on The hypothesis must relate to the arrangement of the matter as regards density in different parts, and to the state of the parts in respect of solidity, compressibility, and so on In the simplest hypothesis, the one on which Lord Kelvin’s well-known, estimate was based, the Earth is treated as absolutely incompressible and of uniform density and rigidity This hypothesis was adopted to simplify the problem, not because it is a true one No matter is absolutely incompressible, and, the Earth is not a body of uniform density It cannot be held to be probable that it is a body of uniform rigidity But when any part of the hypothesis, e g , the assumption of uniform density, is discarded, the estimate of rigidity is affected Different estimates are obtained when different laws of density are assumed Again, whatever hypothesis we adopt as regards the arrangement of the matter, so long as we consider the Earth to be absolutely incompressible and of uniform rigidity, different estimates of this rigidity are obtained by using observations of different phenomena Variations of the vertical may give one value, variations of latitude a notably different value It follows that “the rigidity of the Earth” is not a definite physical constant But there are two determinate constant numbers related to the methods that have been used for obtaining estimates of the rigidity of the Earth One of these numbers specifies the amount by which the surface of the Earth yields to forces of the type of the tide-generating attractions of the Sun and Moon The other number specifies the amount by which the potential of the Earth is altered through the rearrangement of the matter within it when this matter is displaced by the deforming influence of the Sun and Moon If we adopt the ordinarily-accepted theory of the Figure of the Earth, the so-called theory of “fluid equilibrium,” and if we make the very probable assumption that the physical constants of the matter within the Earth, such as the density or the incompressibility, are nearly uniform over any spherical surface having its centre at the Earth’s centre, we can determine both these numbers without introducing any additional hypothesis as to the law of density or the state of the matter We shall find, in fact, that observations of variations of latitude lead to a determination of the number related to the inequality of potential, and that, when this number is known, observations of variations of the vertical lead to a determination of the number related to the inequality of figure [ Note added , December 15, 1908—This statement needs, perhaps, some additional qualification It is assumed that, in calculating the two numbers from the two kinds of observations, we may adopt an equilibrium theory of the deformations produced in the Earth by the corresponding forces If the constitution of the Earth is really such that an equilibrium theory of the effects produced in it by these forces is inadequate, we should expect a marked discordance of phase between the inequality of figure produced and the force producing it Now Hecker’s observations, cited in § 6 below, show that, in the case of the semidiurnal term in the variation of the vertical due to the lunar deflexion of gravity, the agreement of phase is close If, however, an equilibrium theory is adequate, as it appears to be, for the semidiurnal corporeal tide, a similar theory must be adequate for the corporeal tides of long period and for the variations of latitude]

Syntonic wireless telegraphy; with specimens of large-scale measurements

Abstract: The absence of effective tuning is one of the marked features of wireless telegraphy as at present usually conducted in practice. In many cases messages are disentangled from a crowd of superposed disturbances, i. e . from other messages, largely by the skill of the receiving telegraphic operator, who, by the exercise of selective attention, manages to interpret and read what is intended for him ; the process being identical with the ordinary human faculty whereby a conversation can be listened to amid general talking and a crowd of other noises at a dinner table.

On the Change in Hue of Spectrum Colours by Dilution with White Light

Abstract: That a change takes place in the hue of the spectrum colours when white is added to them has been noticed, but I am not aware that any measurement of the extent of the change has been made. The need of a quantitative investigation has been forced upon me by the fact that in a research on the colour of fluorescence in various bodies the value of the dominant colours obtained by a photographic method did not correspond exactly with that obtained from visual observations. The photographic results also showed that mixed with the dominant colour of the fluorescence was more or less white light, and it occurred to me that this added white might account for the difference. The colour-measuring apparatus, which has been described in various papers and most recently in the paper “On a Modified Apparatus for the Measurement of Colour,” was employed in the investigation, a slight modification in the method of obtaining the two similar spectra being carried out. In the apparatus described in that paper a portion of the beam of light which had traversed the collimator, the prisms, and the lens which brought the spectrum to a focus was diverted by means of a partially silvered mirror placed in the path of the beam. In that used in the present instance only the lower half of the beam was deflected at right angles to the axis of the beam, and again deflected nearly parallel to its original direction. Both deflections were made by silvered mirrors. The two spectra were of approximately the same intensity. Two colour patches could now be formed side by side on a white surface when slits were inserted in each spectrum. The beam of whie light reflected from the first surface of the first prism could be thrown on either of the patches. In the investigations here given the white was thrown on the right-hand patch which was produced by the spectrum formed the diverted beam.

On the depression of the filament of maximum velocity in a stream flowing through an open channel

Abstract: When water flows with sinuous motion through a circular pipe the resistance introduced by the solid boundaries reduces the velocity of axial flow as the sides are approached, this velocity being greatest at the centre and least at the sides, as indicated by the transverse velocity curve of fig. 1. When flow takes place through a closed rectangular pipe, the same effect is noticed, the transverse velocity curves and the curves joining points of equal velocity, or the contours of equal velocity in a cross-section, being much as shown in fig. 2. Here, again, the maximum velocity is found at the centre of the pipe. From analogy with this latter case it might be expected that when flow takes place through an open rectangular flume such as would be obtained by taking the portion of the rectangular pipe of fig. 2 below the level AA', or indeed through an open channel of any ordinary section, the filament of maximum velocity would be found in the water surface and in the centre of the stream.

The isothermal layer of the atmosphere and atmospheric radiation

Abstract: The investigation of the upper air by means of balloons carrying self-recording instruments, which have furnished values for the atmospheric temperature up to heights between 15 and 20 kilometres, has revealed the existence of an abnormal change in the vertical temperature gradient. After a fairly uniform fall, with increasing altitude, of about 6° C. per kilometre, a height is reached above which the temperature changes very little, sometimes increasing, sometimes diminishing slowly. The phenomenon was first noticed by M. Teisserenc de Bort in a communication to the Societe de Physique in June, 1899. He improved his apparatus and made further investigations, in many cases sending up the balloons by night to eliminate any possible insolation effects. He found the average height, at which the change began, to be about 11 kilometres. He discovered also that the height was greater near the centre of high pressure areas than in low pressure areas, the average heights for the two cases being 12-5 and 10 kilometres respectively. More recently he found that the height increased with approach towards the equator and that near the equator, ballons-sondes , ascending to 15 kilometres, had failed to reach this layer if it existed there. He proposed to call this layer, in which little temperature change occurred, the “Isothermal Layer of the Atmosphere,” and the name has been generally accepted.

The coefficients of capacity and the mutual attractions or repulsions of two electrified spherical conductors when close together

Abstract: In connection with spark systems of wireless telegraphy, a knowledge of the electrostatic energy stored between spherical electrodes at the instant of the disruptive discharge is of great value to the engineer. In order to increase this energy, without unduly increasing the applied potential difference, the electrodes have been placed in compressed or highly rarefied gases and in oils or other liquid dielectrics having great electric strength. In these cases the least distance between the electrodes may only be a small fraction of the radius of either, and so the computation of the electrostatic energy by the ordinary formulae is so laborious that it is practically prohibitive. By extending a mathematical theorem first given by Schlomilch, the author has succeeded in greatly simplifying the computation of this energy. The formulae given below are very easily evaluated when the spheres are close together, and hence, in conjunction with Kirchhoffs final modification of his own formulae, they give the complete practical solution of this important historical problem.

On the absorption of homogeneous β-rays by matter, and on the variation of the absorption of the rays with velocity

Abstract: The present work was undertaken with a view to establishing, if possible, the connection between the absorption and velocity of the β-rays. So far, no actual experiments have been performed on this subject, but Schmidt has determined the velocity of the rays emitted by radium E and uranium X. These have absorption constants of 40 cm.-1 and 14 cm.-1, and their velocities, assuming the Lorentz formula for the variation of e/m with velocity of an electron, are 2.31 and 2.76 x 1010 cm. per sec. respectively. The matter has been attacked theoretically by Sir J. J. Thomson. He deduces a formula connecting the "diffusion" coefficient of absorption with the velocity, and finds that the variation takes place inversely as the fourth power of the velocity. Seitz has made a series of experiments on the number of cathode particles passing through thin sheets of matter, and finds the coefficient of absorption to vary inversely as av 6– bv 4, where a and b are constants and v the velocity of the electrons.

The relation of the earth's free precessional nutation to its resistance against tidal deformation

Abstract: The modern investigation of the wandering of the Earth’s axis of rotation, considered as a physical problem relating to the actual non-rigid Earth, may be said to have been initiated in Lord Kelvin’s address to the Physical Section of the British Association in 1876. After referring to the scrutiny of the recorded observations of change of latitudes, conducted by Peters in 1841 and independently by Maxwell in 1851, in search of the regular Eulerian free period of 306 days which would belong to a rigid Earth, with negative results, he insisted that the irregular motions brought out in these analyses are not merely due to instrumental imperfections but represent true motions of the Pole, due to displacement of terrestrial material. For example, he estimates that existing shifts of material, of meteorological type, are competent to produce displacements of the axis of rotation ranging from ½ to 1/20 of a second of arc. A sudden shift of material on the Earth will not at once affect the axis of rotation, but will start it into motion round the altered axis of inertia, with a period of 306 days if the Earth were rigid, which will go on displacing the Pole until it is damped out by the frictional effects of the tidal motions thus originated. A radius of rotation of 1 second of arc would raise an ocean tide of the same period as the rotation, having as much as 11 cm. of maximum rise and fall. Thus the motion of the Pole is to be considered as continually renewed by meteorological and other displacements, as it is damped off by tidal and elastic friction; it was therefore, perhaps, not to be expected that it would show much periodicity, though the movements were eminently worthy of close investigation. Their nature was examined more closely by Newcomb at Kelvin’s request; but not much more had been done regarding their cause when Chandler announced that the records of changes of latitude did actually indicate a period of precession—of 427 days, however, instead of the Eulerian period of 306 days, which, if any, had previously been taken for granted. Soon after, in 1890, observations were organised systematically by the International Geodetic Union on the motion of Prof. Foerster, of Berlin; and already, in 1891, he was able to inform Lord Kelvin that a comparison of European observations with synchronous ones made at Honolulu gave direct proof of his conclusion of 1876 ( supra ), “ that irregular movements of the Earth’s axis to the extent of half a second may be produced by the temporary changes of sea level due to meteorological causes.” In the following year the synchronous observations had already indicated periodicity, apparently in about 385 days, considerably less than Chandler’s estimate, which, however, longer observation has since confirmed substantially. Lord Kelvin remarks in his next annual address as follows:—“ Newcomb, in a letter which I received from him last December, gave what seems to me undoubtedly the true explanation of this apparent discrepance from dynamical theory, attributing it to elastic yielding of the Earth as a whole. He added a suggestion, especially interesting to myself, that investigation of the periodic variations of latitude may prove to be the best means of determining approximately the rigidity of the Earth. As it is, we have now for the first time what seems to be a quite decisive demonstration of elastic yielding of the Earth as a whole, under the influence of a deforming force, whether of centrifugal force round a varying axis, as in the present case, or of tide-generating influences of the Sun and Moon, with reference to which I first raised the question of elastic yielding of the Earth’s material many years ago.” But “when we consider how much water falls on Europe and Asia during a month or two of rainy season, and how many weeks or months must pass before it gets to the sea, and where it has been in the interval, and what has become of the air from which it fell, we need not wonder” that the amplitudes of the polar wanderings “should often vary by 5 or 10 metres in the course of a few weeks or months.”

Sensitive Micro-Balances and a New Method of Weighing Minute Quantities

Abstract: In the course of experiments undertaken by the authors with a view to establishing a possible relation between the amount of ionisation produced at the surface of certain heated metals and the amount of oxidation of the metal, it became necessary to be able to measure changes of weight of the order of one-thousandth of a milligramme (1 X 10 -6gramme). A micro-balance of the Nernst type was accordingly constructed which possessed the requisite sensitiveness, but considerable difficulty was experienced in obtaining consistent readings with it, owing chiefly to the inconstancy of zero and the great variation of sensibility with load. This latter defect is an inevitable consequence of the fact that a restoring couple due to gravity, the magnitude of which varies, as in the ordinary balance, with the position of the centre of gravity of the system relative to its point of suspension, is superposed on the restoring torque of the quartz fibre. Attempts to minimise this trouble led finally to the conclusion that for the purpose in view better results were to be expected from a gravity balance of the ordinary type in which the required degree of sensitiveness should be attained by making the beam very light. As the maximum load which it was intended to use on the balance was less than half a gramme, this could be done without loss of proportionate rigidity.

The Wave-Making Resistance of Ships: A Theoretical and Practical Analysis

Abstract: The theoretical investigation of the total resistance to the forward motion of a ship is usually simplified by regarding it as the sum of certain independent terms such as the frictional, wave-makings and eddy-making resistances. The experimental study of frictional resistance leads to a formula of the type. R s =ƒSV m , (1) where S is the wetted surface, V the speed,ƒ a frictional coefficient, and m an index whose value is about 1.83. After deducting from the total resistance the frictional part calculated from a suitable formula of this kind, the remainder is called the residuary resistance. Of this the wave-making resistance is the most important part; the present paper is limited to the study of wave-making resistance, and chiefly its variation with the speed of the ship. The hydrodynamical theory as it stands at present may be stated briefly.

On the Influence of Their State in Solution on the Absorption Spectra of Dissolved Dyes

Abstract: In a previous investigation of the absorption spectra and sensitising properties of some iso cyanine dyes,* the influence of the solvent was examined and it was found that the absorption maximum was shifted toward the red as the refractive index of the solvent increased. This is in accordance with Kundt’s law. The absorption in water, however, differs markedly from that in organic solvents. In the latter the spectrum consists of a prominent band in the orange and a half-shade nearer the blue. In water this half-shade has become a separate band comparable in intensity with the orange. Absorption curves in alcohol and water are shown. It is convenient to term the band near the red the β-(organic) band, the one nearer the blue the α -(water) band. It appeared desirable to investigate this difference further.

The Elastic Limits of Iron and Steel under Cyclical Variations of Stress

Abstract: An explanation of fatigue is developed in the paper which is in accordance with all the researches on the fracture of materials by the cyclical repetition of stress. The theory was put forward by Bauschinger in 1886, when he suggested that the necessary condition of safety was that the repeated stresses applied should be within the limits of elasticity of the specimen, and that the least variation from this condition introduces fatigue and ultimately fracture occurs. In order for this to be true for Wohler’s well-known experiments, the elastic limits must be variable within very wide limits, and the present paper describes observations made during the adjustment of the limits of elasticity to any particular condition of experiment.

"Dynamic" Osmotic Pressures

Abstract: 1. The following paper is a preliminary account of what is apparently a new method of measuring osmotic pressures. The account is published now because during the course of the experiments we have unfortunately damaged the only two good semi-permeable membranes that we possess, and it will be some months before the damage can be repaired. 2. A word of explanation as to the use of “ dynamic ” to distinguish the osmotic phenomena we are about to describe seems necessary. In all discussions of osmotic pressures (except those involving diffusion) the locution “ osmotic pressure ” connotes some form of equilibrium between a solution and its solvent; in the experiments about to be recorded we have measured the rate at which the solvent flows into the solution, and the essence of the observations lies in the fact that there should be no approach to equilibrium. Thus the osmotic pressure here involved is substantially that assumed to act in Nernst’s theory of diffusion.

On the Physical Properties of Gold Leaf at High Temperatures

Abstract: In a paper by Prof. T. Turner * some experiments were described which show that gold leaf becomes transparent when heated in contact wild glass. The following experiments, suggested by Prof. H. A. Wilson, were undertaken to see if this effect takes place when the gold leaf is heated by itself. Hie apparatus in which the leak was heated consisted of a double walled fused quartz crucible. The outside of the crucible was 6 cm. deep and 5 cm. wide, and the inner chamber was 4·5 cm. deep and 3·5 cm. wide. Both chambers were fitted with lids. Inside the inner chamber, as near to the leaf as possible, a thermocouple, composed of platinum and nickel wires, was placed. The other ends of the couple dipped into mercury cups immersed in melting ice, from which wires led through a reversing key to a dead-beat galvanometer, with lamp and seals, a resistance of 800 ohms being included in the circuit.

Thermal Conductivity of Air and Other Gases

Abstract: Although there has been a number of experimental determinations of the thermal conductivity of air, its value even to two figures is still uncertain. It is true that the values hitherto obtained are of the same order as that deduced from the kinetic theory by Clausius, Maxwell, and others, but they differ among themselves to the extent of 20 per cent. There have been only two methods of experiment. Stefan, Kundt and Warburg, and Winkelmann observed the rate of cooling of a thermometer in an envelope of rarefied air, the outer surface of which was kept at a constant temperature. Schleier-macher and Schwarze measured the rate at which heat passed from an electrically heated wire stretched along the axis to the surface of a cylinder maintained at a lower constant temperature. Repetitions of these two methods have not cleared away the uncertainty as to what is the correct value of the thermal conductivity of air. Under these circumstances it might be interesting to give an account of another method for determining this quantity. It will be noticed that in this method, which was suggested by Prof. Poynting, the conductivity is measured at ordinary pressures, there being no need to take precautions against convection currents by the reduction of the pressure as is necessary in the other methods.

The Ionisation produced by an α-particle.—Part I

Abstract: 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 × 1010 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 × 105. This number becomes 1·8 × 105 if for N and e the latest values, referred to above, are introduced.

On Flapping Flight

Abstract: This paper is supplementary to one by the same author published in the 'Proceedings of the Royal Society' in 1899, "On Flapping Flight of Aeroplanes," communicated by the late Prof. George F. FitzGerald, F. R. S. Towards the end of that paper, the author refers to the subject of hovering, and points out that the method of his paper does not apply, in any satisfactory way, to that case. The paper of 1899, in fact, considered the force supporting an aeroplane as due to its motion with nearly constant speed in a nearly horizontal, but slightly waved path, to which its plane was inclined at a small variable angle.

An Approximate Determination of the Boiling Points of Metals

Abstract: Despite the facility with which high temperatures can be reached and maintained constant by means of electric heating, no general investigation of the boiling points of the metals has yet been carried out, and such information as is available has in many cases been obtained by considerable extrapolation. Moreover, the published data are remarkably discordant, as will be seen from the individual results quoted below. In the course of an extended experimental investigation, H. Moissan has made observations on the vaporisation of metals at high temperatures by observing the loss of weight of a considerable mass of metal heated for definite periods of time in his arc furnace. O. P. Watts has attempted to deduce from these experiments approximate values for the boiling points of the metals. In addition to the uncertainty due to the fact that many metals possess a high vapour tension at temperatures much below their actual boiling points, considerable errors are caused by the fact that Moissan does not appear to have measured the expenditure of energy in the furnace, which varies widely according to the conductivity of the vapours surrounding the arc. Also, in many of his experiments the temperature of ebullition must have been altogether modified by carburisation.

Bakerian Lecture. On the Statistical and Thermodynamical Relations of Radiant Energy

Abstract: It was surmised by a prominent school of thought in ancient times, it become absorbed into the mechanical philosophy of Newton, and it was at length established by the experiments and reasonings of Dalton and his contemporaries, that matter is not divisible without limit, but is constituted of an aggregate of discrete entities, all alike for the same homogeneous substance, and naturally extremely minute compared with our powers of direct perception. The smallest portion of matter which we can manipulate (at any rate until very recently) consists of a vast assemblage of molecules, of independent self-existing systems which exert dynamical influences on each other. The direct knowledge of matter that mankind can acquire is a knowledge of the average behaviour and relations of the crowd of molecules. The sentient intelligence with perceptions of space and time minute enough to examine the individual molecules, each of them -would probably appear as a cosmos in itself, influencing and influenced by others,—not unlike stars in a firmament. The observed laws of nature are thus laws of averages—are statistical relations. Yet they are for practical purposes exact. To illustrate this in a way that will presently be of use let us imagine a row of urns whose apertures are of different areas, and let us consider how N objects will be distributed at random among them, assuming that the chance of an object getting into an urn is proportional to the area of its aperture, and is otherwise indifferent as regards them all. If the number of objects is not very large in comparison with the number of urns, no direct law of numbers emerges in this random distribution: though by the doctrine of probabilities we may calculate definitely the relative numbers of times that the various distributions will occur in a vast total number of cases, and this will represent the chances of recurrence of these distributions, the most likely arrangements are those ranging close around the equable distribution, in which the contents of the urns are proportional to their apertures. Those far removed therefrom are much less likely. "When the number N is very great, a relatively small deviation from the equable distribution has an almost negligible chance of occurring. Equable distribution then assumes the aspect of a rigid law; nevertheless occasionally in an soon it will he widely departed from. The abstract laws governing the extent and distribution of the various kinds of deviations from the mean distribution constitute an important part of the theory of statistics, first explored and developed by J. Bernoulli.

The Passage of Electricity through Gaseous Mixtures

Abstract: According to the current theory with regard to the production of ions in a gas subjected to the action of Rontgen rays, the act of ionisation consists in the expulsion of one or more corpuscles ( i. e . negatively charged units of electricity) from each of a certain number of molecules constituting the gas. The residual portion of each of these molecules is then said to be positively charged, although the nature of this charge is not in any way specified. There are thus present in the gas negatively charged nuclei ( i. e . the expelled corpuscles) and positively charged nuclei (the residual portions of the ionised molecules); owing to the forces due to electrostatic induction these nuclei attract several of the gas molecules, and the resulting molecular aggregates constitute the gaseous ions, both negative and positive. Suppose, now, that a mixture of two gases, e. g ., sulphur dioxide and oxygen, is subjected to the action of Rontgen rays; the positive nucleus would be of greater volume and mass in the case of sulphur dioxide than of oxygen, and in consequence it is quite possible that the resulting ions should show similar differences. Accordingly, if the two groups of positive ions move in the same electric field, a difference in velocities might thus reasonably be expected.

On the Electricity of Rain and Its Origin in Thunderstorms

Abstract: During 1907-08 an investigation was undertaken at the Meteorological Office of the Government of India, Simla, into the electrical phenomena which accompany rain and thunderstorms. Two lines of research were adopted :— (a) A systematic record was obtained by means of self-registering instruments of the electricity brought down by the rain throughout one rainy season. (b) Laboratory experiments were made with the object of determining the source of the electricity of thunderstorms.

On the Effect of Previous Magnetic History on Magnetisation

Abstract: It is well known that if a piece of iron be subjected to a considerable magnetising force and then be tested for permeability correnponding to a lower force, the permeability so obtained may differ widely from the permeability which would have been obtained had the material been previously demagnetised. The effects of previous history have been studied by a good many experimenters, notably by Searle. The object of this part of the present paper is to examine the effect of previous history upon the dissipation of energy by magnetic hysteresis. Suppose in fig. 1 that a piece of iron is carefully demagnetised and that the hysteresis loop No. 1 corresponding to a force H is obtained. This loop is symmetrical about the origin in all respects and its area gives the loss usually referred to in testing work. Suppose that the last value of the force H is positive and that it be increased to a value H1, reversed a few times, and reduced to zero from its positive value. After re-applying the force H and reversing it a sufficient number of times to produce stability, a loop such as No. 2 will be obtained. As is well known, this loop shows a reduced change of magnetic induction and, consequently, a reduced permeability. Suppose, now, that the iron is carefully demagnetised and that a magnetising force supplied by an independent source is applied very gradually, so that when added to the original force H it gives a force H3 such that the change of magnetic induction corresponding to a change of the force H is exactly equal to the change observed with loop 2 for the same change of H. The loop obtained will appear as No. 3 in fig. 1. We have now obtained two loops, Nos. 2 and 3, each having the same change of magnetic induction, and each having the same net change of force H. The change from loop 1 to loop 2 has been brought about by inter-molecular force, whereas the change from loop 1 and loop 3 has been brought about by the application of an externally applied constant force H3 - H. If the effect of inter-molecular force were capable of being exactly equivalent to the externally applied constant force, one would expect to find that the energy required to perform a complete cycle would be the same in each case; that is, the area of loop 2 would be equal to the area of loop 3.

On the Resolving Power of Photographic Plates

Abstract: Introduction .—The convenience of the photographic plate as a recording instrument, in that it not only makes a record but also integrates impressions which are individually too faint to be observed, is so manifest that to a continually greater extent physicists are designing instruments for use solely or chiefly by photographic methods. It is curious to note that while the resolving power of physical instruments generally has been completely investigated, very little indeed has been published upon the resolving power of the plates used as recording instruments.