Abstract
LONDON. Royal Society, March 5.—Sir Arthur Schuster: On the life statistics of fellows of the Royal Society. A revision and extension of a statistical inquiry made by Lieut.-Gen. R. Strachey towards the end of last century. Its principal results are: (i) The average age at election remained fairly constant between the years 1848, when the nominations for election were placed into the hands of the Council, and the end of the century, the average being 44-4 years. There has been a decided increase since then, more especially in the last ten years, but some of this may have been due to war conditions. (2) The average age of fellows on January i, 1923, was 60-9 years. (3) Their expectation of life is about 6 years greater than that recorded in the tables published in "Whitaker's Almanac "as applying to the entire population of England.-G. I. Taylor and Miss C. F. Elam: The plastic extension and fracture of aluminium crystals. In the early stages of the tests under direct tension the previous results are confirmed, and the nature of the distortion in the later stages is now proved to be due to slipping on the two crystal planes previously indicated. After double slipping has begun, the rate of slip on the original slip-plane is usually greater than that on the new one. The geometrical conditions with a shearing-stress parallel to the slip plane are such that the crystal is quite stable while the slip occurs on one plane, but as soon as double slipping occurs, it be'comes far less stable, or even unstable. Therefore the specimen usually breaks before it has slipped far on the second plane, but never before the double slipping begins.-A. Page: An experimental study of the vibrations in the blades and shaft of an airscrew. The sounds emitted were analysed with 4 Tucker hot-wire microphones used in conjunction with a four-valve amplifier. The sounds of rotation which arise from the rotation of the source-and-sink system associated with the pressure differences on the blades are composed of a large number of harmonics, having as fundamental a note of frequency equal to the product of the number of blades and the rotational speed. The natural frequencies of flexural vibration were measured for four-blade shapes, the variables of design being width and geometrical pitch. The measured frequencies of the shaft vibrations agree very closely with the calculated results, except for a discrepancy of 8 per cent, obtained on the heaviest airscrew.-J. H. Vincent and A. L. Beak: Experiments on the effects of resistance in the oscillating circuit of a triode. The circuit employed is that previously used by Eccles and Vincent. In this the main oscillator consists of a condenser and coil in series, the coil being variably coupled to the grid coil which is in conductive connexion with a point between the condenser and main coil, the opposite point being joined to the negative end of the plate battery; these two points divide the main oscillating circuit into two branches, inductive and capacitive. With this apparatus the conditions were studied under which oscillations could be started and maintained, and the changes in frequency of oscillations and the simultaneous changes in the oscillating and mean plate currents, due to altering resistances in the inductive and capacitive branches of the oscillating circuit. The chief results support Eccles's control equation, but disagree with his formula for changes in frequency. G. H. Hardy: The lattice points of a circle. Proof of the fundamental identity in the problem of the circle by means of a singular integral the kernel of which is a theta-function, with an application to a theorem of J. E. Littlewood and A. Walfisz, published recently in the Proceedings.-H. M. Macdonald: The transmission of electric waves around the earth's surface. The transmission of wireless signals to great distances and other phenomena associated with wireless telegraphy have been ascribed to the presence of a conducting layer in the upper atmosphere. Such a layer, if it were conducting in the ordinary sense, would act as a screen in respect of electrical effects having their origin external to the layer, and electrical disturbances set up in the space between the earth's surface and the conducting layer would subside very slowly, ft appears natural, therefore, to assume that, if there is reflection from the upper atmosphere, there must also be radiation through it, to allow a steady state to be attained in a comparatively short time. The simplest hypothesis consistent with this is that the upper atmosphere differs from the lower atmosphere in respect of the constants involved in the propagation of electrical effects, namely, the specific inductive capacity and the magnetic permeability. On this hypothesis the condition that a steady state of electrical oscillation can be set up in the lower' atmosphere in a comparatively short time is investigated. Taking an ideal case, the condition is that the ratio of specific inductive capacities is approximately equal to the ratio of-magnetic permeabilities.-R. M. Wilmotte: On the field of force near the neutral point produced by two equal coaxial coils with special reference to the Campbell standard of mutual inductance. The accuracy of any apparatus depending on the mutual inductance between two coils and another coil situated at the neutral circle formed by the magnetic field of the first two coils depends largely on the variation of the magnetic force near the neutral circle. An expression in terms of the magnetic forces produced by a circular current is obtained for the variation of the mutual inductance due to a small displacement from the neutral circle of a single turn of wire acting as the secondary to two co-axial single-layer coils.-W. R. Dean: On the theory of elastic atability: After Hooke's Law has been extended, two methods are available. The three conditions for the equilibrium of an elementary volume may be written down, correctly to the second order, by considering the forces acting upon it, or the strain energy may be calculated to the third order, and the equations obtained by variation. With a cylindrical shell the energy method is shorter. The equations refer in the first instance to the displacements of any point of the shell. To reduce them to equations connecting the displacements of points of the middle surface only, the displacements of any point are expanded in series of the distance of this point from the middle surface, and the boundary conditions at the faces are used.-R. A. Frazer: On the motion of circular cylinders in a viscous fluid. The paper is restricted to two-dimensional flow, and deals primarily with the motion of circular cylinders in fluids of great viscosity, inertia terms being neglected. The flow due to a stationary cylinder immersed in a uniform infinite river is treated as the limiting case of flow between two concentric boundaries, the stream being uniform over the outer, and stationary over the inner. The essential elements for a solution are obtained with arbitrary velocity distributions specified over any two mutually external circular cylinders. The stream-function is completed for the case where the cylinders are in steady "rotation. Another type of motion investigated is where two spinning cylinders are rotated as a "planetary"system about a particular "focus."The cases examjned include "planetary "systems, problems of contact, and the combined rotation and translation of a cylinder in proximity to a wall.
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Societies and Academies. Nature 115, 400–403 (1925). https://doi.org/10.1038/115400b0
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DOI: https://doi.org/10.1038/115400b0