Open AccessVIII. Numerical results of the theory of the diffraction of a plane electromagnetic wave by a perfectly conducting sphere
Publication year - 1918
Publication title -
philosophical transactions of the royal society of london. series a, containing papers of a mathematical or physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9258
pISSN - 0264-3952
DOI - 10.1098/rsta.1918.0008
Subject(s) - bessel function , mathematics , order (exchange) , diffraction , computation , rayleigh scattering , plane (geometry) , plane wave , mathematical analysis , combinatorics , geometry , physics , optics , algorithm , finance , economics
1. At the suggestion of Dr. Bromwich, I began the computations leading to this paper nearly three years ago. Using tables constructed by Lord Rayleigh and Prof. A. Lodge, I obtained results fork a= 1, 2, 10 and θ = 0°, 180°; 90°; 45°, 135°; 20°,160°; 70°, 110°; in this order. From the results for 1 and 2, graphs of Y1 , Y2 , Z1 , Z2 could be constructed with some confidence, but such graphs were entirely impossible in the case ofk a= 10, owing to the large number of their undulations. (For the graphs of these functions, as finally drawn, see figs. 1, 3, 18, 20, 22, 24.) I then handed over the work to Messrs. Doodson and Kennedy, and the whole of the results as they now appear are due to them. Mr. Doodson first constructed tables for Bessel’s functions of half-integral orders, and Mr. Kennedy constructed tables for the derivatives of Legendre's functions. These two sets of tables, together with those of Lodge already quoted, are what have been used in all the subsequent work.