Societies and Academies

    Abstract

    LONDON. Royal Society, February 13.—Sir J. J. Thomson, president, in the chair.—L. Bairstow and A. Berry; Two-dimensional solutions of Poisson's and Laplace's equations. Starting from a theorem stated in Lamb's “Hydrodynamics,” problems involving solutions of Poisson's equation are interpreted in terms of the motion of the conventional inviscid fluid of hydrodynamics. The theorem states that the continuous acyclic motion of such a fluid inside or outside a rigid boundary can be reproduced by a system of sources round the boundary in all cases for which the fluid is at rest at infinity. The special point of the present paper is the formation and solution of an integral equation in order to find the strength of the sources. The answer appears as a series of integrals which is convergent in the four illustrations given; proof of convergency in the full mathematical sense is not attempted. The method of solution is applicable to boundaries of any shape and to more than one boundary. The integrals are easily obtained by graphical and mechanical methods.—Dr. G. H. Thomson: The cause of hierarchical order among the correlation coefficients of a number of variates taken in pairs. From the tendency towards “hierarchical” order among correlation coefficients in mental tests, the conclusion has in the past been drawn that all these correlations are due to the presence of a general factor, and that none of them are due to group-factors which run through two or more tests, but not through all. Although perfect hierarchical order can only be produced in this way, an approximation to perfection can be attained without any general factor by leaving the number and identity of the group and specific factors in each variate to chance. A card experiment is described in which this is done, and specimens of the resulting hierarchies are given. The proof depends on the formulæ of Pearson and Filon for the correlation of errors of correlation.—Dr. G. N. Watson: The transmission of electric waves round the earth. From Austin's experimental results it appears that the magnetic force due to a Hertzian oscillator varies as cosec ½θ exp. (-Aλ-½θ) at angular distance θ from the oscillator, where λ is the wave-length and, in the case of signals over the sea, the constant A has the value 9.6. It seems impossible to obtain any formula resembling this from a theory of pure diffraction, and it is therefore necessary to examine the hypothesis (put forward by Heavi-side and others, and submitted to some analytical treatment by Eccles) that the upper regions of the atmosphere act as a reflector of the waves. It is found that a formula of Austin's type is a consequence of this hypothesis, and that the numerical value of A given by Austin is obtained by assigning suitable values to the conductivity of the reflecting layer and its height above the surface of the earth. The problem of waves over dry land is also considered and the appropriate value of A determined.

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    Societies and Academies . Nature 102, 517–520 (1919). https://doi.org/10.1038/102517a0

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