Abstract
LONDON. Royal Society, November 17.—Prof. C. S. Sherrington, president, in the chair.—P. A. MacMahon and W. P. D. MacMahon: The design of repeating patterns. The study and classification of repeating patterns in space of two dimensions is founded upon the simplest geometrical forms which happen to be repeats. These are employed as bases and are subjected to specified transformations which depend upon certain contact systems between the sides which are in contact in the assemblage. Repeats are of three varieties: the block, the “stencil,” and the “archipelago.” There is a further broad division into normal and abnormal repeats. A theory of “complementary repeats” is established. A contour can be drawn around every normal repeat in an infinite number of ways, such that the area within the contour, which does not belong to the repeat, is itself a repeat. The contour under specified conditions is itself the boundary of a repeat, which is therefore a combination of the original repeat and its complementary. Mr. G. T. Bennett finds that “every quadrilateral figure” is a repeat.—J. W. Nicholson: A problem in the theory of heat conduction. The temperature at any point in the external medium, and the rate of loss of heat from a cylinder, the surface of which is maintained, from some specified instant, at a constant temperature for all subsequent time, is found for any instant by the use of a generalised form of the Bessel-Fourier double integral. A solution can be obtained in a similar way when the temperature maintained on the cylindrical surface is not constant.—C. H. Lees: The thermal stresses in spherical shells concentrically heated. Thermal stresses in the material of a furnace of approximate spherical form due to differences of temperature, and the stresses due to pressures on the inside and outside surfaces, may be expressed in terms of the volume of the spherical surface through any Point or of its reciprocal. The whole problem can be treated graphically. The increase of stress due to sudden changes of temperature of the inside surface is discussed.—R. A. Fisher: The mathematical foundations of theoretical statistics. The most efficient statistic has the least standard deviation; the efficiency of any other statistic is the ratio of number of observations required by the most efficient to that required by statistic under consideration in order to obtain a value of the same accuracy. The criterion of consistency applied to a method of estimation is a special case of criterion of sufficiency, which requires that the sufficient statistic shall include the whole relevant information provided by sample. Statistics obtained by the method of maximum likelihood are always sufficient statistics. Their standard deviation being easily calculated, the efficiency of any other statistic of known probable error may be found. F. P. White: The diffraction of plane electromagnetic waves by a perfectly reflecting sphere. The series solution is transformed into a contour integral along a path of “steepest descents,” and the value of this integral is determined approximately. The results obtained are in agreement with those obtained by other workers.—C. V. Raman and G. A. Sutherland: The Whispering Gallery phenomenon. Observations made in the Whispering Gallery at St. Paul's Cathedral and in laboratory experiments show that Rayleigh's theory of the phenomenon does not offer a complete explanation. The single belt of maximum intensity close to the wall contemplated by Rayleigh is obtained only in the limiting case when the radius of the reflecting circle is practically infinite in comparison with the wave-length. For more moderate values of the radius of curvature there is a succession of belts of alternately great and small intensity. The slight deviation from the condition of strictly circumferential wave-propagation postulated by Rayleigh gives rise to such effects.
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Societies and Academies. Nature 108, 421–422 (1921). https://doi.org/10.1038/108421a0
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DOI: https://doi.org/10.1038/108421a0