VIII. Numerical results of the theory of the diffraction of a plane electromagnetic wave by a perfectly conducting sphere

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Abstract
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 for k 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 Y 1 , Y 2 , Z 1 , Z 2 could be constructed with some confidence, but such graphs were entirely impossible in the case of k 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.

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