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VIIL Numerical Results of the Theory of the Diffraction of a Plane 
Electromagnetic Wave by a Perfectly Conducting Sphere. 
By J. Proitdman, A. T. Doodson, and G. Kennedy. 
Communicated by T. J. I’A. Bromwich, Sc.D ., F.P.S. 
Received April 13,—Read November 23, 1916. 
« 
Introduction. 
(By J. Proudman.) 
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 <a = 1, 2, 101 and 6 — 0°, 180°; 90°; 45°, 
135°; 20°, 160°; 70°, 110°: in this order. From the results for kci = 1 and 2, graphs 
of Y l5 Y 2 , Z,, Z 2 could be constructed with some confidence, but such graphs were 
entirely impossible in the case of kci = 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. 
Mr. Doodson computed quite independently the cases of/ca = 1,2, for all the values 
of 6 that I had taken together with 6 = 10°, 170°; 30°, 150°; 60°, 120°; 80°, 100°. 
His results were in agreement with mine, except for a number of small differences 
* Rayleigh, “ On the Acoustic Shadow of a Sphere, with an Appendix giving the Values of 
Legendre’s Functions, . . ., by Prof. A. Lodge,” ‘Phil. Trans. Roy. Soc.,’ A, vol. cciii., p. 87 (1904); 
[‘ Sc. Papers,’ vol. v., p. 149]. 
Rayleigh, “ Incidence of Light upon a Transparent Sphere of Dimensions comparable with a Wave¬ 
length,” ‘Roy. Soc. Proc.,’ A, vol. Ixxxiv., p. 25 (1910); [‘Sc. Papers,’ vol. v., p. 547]. 
t The notation is explained in the next section. 
J These have been published by the British Association; ‘ Report’ for 1914, p. 87. 
§ These are to be presented shortly to the British Association. 
vol. ccxvii.— a 556. 2 r 
[Published August 15, 1917. 
