Abstract
LONDON. Royal Society, January 26.—Sir Archibald Geikie, K.C.B., president, in the chair.—Major P. A. MacMahon: Memoir on the theory of the partitions of numbers. Part v.: Partitions in two-dimensional space.—Arthur Schuster: The origin of magnetic storms. The paper contains a critical examination of the theory that magnetic storms are caused by streams of electrified corpuscles ejected from the sun. If the electro-kinetic energy of such storms be calculated, it is found that, when the magnetic field produced is comparable with that observed in magnetic storms, the energy is enormously great compared with that obtained by mere addition of the energies of the separate corpuscles. Even if during violent storms, when the magnetic force may be of the order 0.004 C.G.S., the corpuscles had an initial velocity nearly equal to that of light, the energy required to establish the magnetic field would be sufficient to reduce the speed to less than 4 kilometres a second before the swarm reaches the earth, the passage between the sun and the earth taking about a year. In this calculation the cross-section of the swarm is assumed to be determined by the effective duration of the magnetic disturbances which it is supposed to produce. If the swarm be reduced in cross-section the energy belonging to it would be diminished, but for a given magnetic force the density of the corpuscles in the swarm must then be correspondingly greater. This leads to the consideration of the effects of electrostatic repulsion between the particles. It appears that if H be the magnetic effect, the electrostatic acceleration at the edge of a swarm of electrons must be greater than 5×1017. This acceleration would be sufficient to drive a corpuscle in the first second through a distance equal to more than the diameter of the earth. It follows that, even taking account of electromagnetic attractions between the corpuscles, a swarm of corpuscles, when sent out from the sun in a definite direction, would soon be dissipated to such an extent that no sensible magnetic disturbance could be produced. Finally, the electrostatic effects, which would be observed on the surface of the earth in each magnetic storm, are discussed, and here the calculation also leads to the conclusion that the theory criticised is untenable. If magnetic disturbances are produced by rays emanating from the sun, it can therefore only be in an indirect manner. We may imagine that the injection of corpuscles ionises the upper portions of the earth's atmosphere, and consequently renders the already existing electromotive forces more effective, or we may imagine that the approach o towards the earth's magnetic field of highly conducting material containing ions of both kinds acts by induction. The effect of such induction would primarily be an increase in the horizontal and a diminution of the vertical forces, while the currents induced in the earth, tending to diminish the horizontal forces, would, owing to their inertia, die out more slowly, so that a semi-permanent effect would be left after the storm. This agrees with observation, but there are at present not enough data available to test the sufficiency of the explanation. Arthur Schuster: The periodicity of sun-spots. In this communication, the sun-spot records of the last ten years are discussed in so far as they have a bearing on the results previously submitted to the society. It appears that the period of 4.79 years discovered by the author is confirmed, but that the evidence does not support the periodicity of 4.38 years, which had been previously described as doubtful, nor that of 8.36 years, which during the first half of last century seemed active. Attention is directed to the independent discovery of the period of 4.79 years in the declination range of the magnetic needle at Munich by Mr. Oppen-heim.—Dr. G. C. Simpson and C. S. Wright: Atmospheric electricity over the ocean. This paper contains the results of observations made on the voyage from England to New Zealand on Captain Scott's Antarctic ship the Terra Nova. The investigation is divided into four parts. The first part deals with the electrical potential-gradient over the ocean. It is found that the gradient has its chief maximum in the evening and its chief minimum soon after midday. The afternoon minimum is remarkable because, though observed at many stations on land, it has often been ascribed to the disturbing effect of dust. In view of the present results, this explanation does not seem correct. The minimum, which is observed at 4 a.m., and which has been considered the principal one in observations taken on land, is only feebly developed at sea. The numerical value of the potential-gradient was found, on the average, to be about 80 volts per metre, and is therefore approximately the same as that observed on land. The second part of the investigation deals with the quantity of radio-active products which are found in the air. The observations show that these products are decidedly fewer at sea than on land, and a specially low value, both north and south of the equator, is found in latitudes from 30° to 40°. This is ascribed to the fact that the air in these latitudes is supplied by pure air descending from the upper parts of the atmosphere, while it is mainly the air which has passed over land which carries radio-active products with it. In the third part of the investigation, the number of free ions in the air are measured, and here again it is found that the ionisation over the sea is smaller than that over land. In the concluding part of the paper the spontaneous ionisation in a closed vessel is measured. Though part of the effect is ascribed to a real effect of air becoming conducting by itself, some of the results obtained indicate clearly that when the ship near land was exposed to radio-active emanation, the observed ionisation showed an increase for several hours afterwards.—Dr. W. H. Young: The Fourier constants of a function. In this paper the possibility of treating the Fourier series of a function f(x) in various circumstances, as if it were convergent and integrable term by term, when multiplied by another function, is illustrated by the application of this fact to the determination of expressions for Sannand 5.bmv, an and bn denoting the Fourier coefficients of f(x), and q having a non-negative value. The formulas are shown to be valid for any function that has bounded variation in an interval containing the origin, and is elsewhere sum-mable, provided only that q is greater than zero.—J. A. Crowther: The energy and distribution of scattered Rontgen radiation. Experiments have been made to determine what fraction of the incident radiant energy is scattered per unit mass of a radiator when primary Rontgen rays fall upon it. From the numbers obtained a value has been deduced for the number of electrons per atom of the radiating substance. The value obtained agrees closely with that previously deduced from experiments on the scattering of homogeneous /3 rays, being very nearly three times the atomic weight of the substance. The distribution of the scattered radiation has been measured. It reaches a maximum forwards and backwards along the line of the primary beam, and falls to a minimum at right angles to this direction. At any given angle with the primary beam there is always a preponderance of scattered radiation in the forward direction. This preponderance increases the more nearly we approach the line of the primary beam.—Mrs. Hertha Ayrton: Some new facts connected with the motion of oscillating water. The author's explanation of the origin of ripple-forming vortices having been contested, she has made further experiments to prove the two propositions on which it rests, viz. that when water oscillates over a submerged obstacle:—(1) during the whole of any single swing a diminution of pressure is established close to the upper part of the lee side of the barrier; (2) while the water is falling below the mean level, in the half of the trough where the obstacle is, there is a back pressure against the flow on its lee side below the area of diminished pressure. Experimental proof of these pressure conditions is given by means of an obstacle in the form of a hollow watertight box, of which the top and one side are covered with thin guttapercha tissue diaphragms, the air being expelled and the box partly filled with water. These pressure conditions cause a jet to flow down close to the lee side of an obstacle during the first part of a swing, and a vortex to form during the second by upsetting the equilibrium of water, in the lee of the obstacle, that would otherwise remain at rest. The back pressure extends only to the limits of this slack water, i.e. to the line where the lowest water flowing over the obstacle strikes the bottom. A trough with an artificial end fitted with diaphragms is used to show that such pressure conditions are not confined to submerged obstacles, but come into existence close to any solid where water, in oscillating, is moving away from it, and wherever two masses of water are flowing away from one another, as at the node of a stationary wave. These variations of pressure give rise to jets and vortices near the surface of oscillating water wherever it meets the end of a vessel, and at every node; it is these jets and vortices, and the streams that feed them, that cause the residual whirls previously found by the author in oscillating water. The most important proof of this is that when the trough is rocked, so that there is much bottom motion but very little rise and fall, and, consequently, only feeble jets and vortices, the author's residual whirls are insignificant, while Lord Rayleigh's, beneath, develop to their full length and height even in deep water.
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Societies and Academies . Nature 85, 461–464 (1911). https://doi.org/10.1038/085461a0
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DOI: https://doi.org/10.1038/085461a0