100:>. I Mcctric Waves round a Conducting Obstacle. 59 



" The Bending of Electric Waves round a Conducting Obstacle : 

 Amended Kesult." By H. M. MACDONALD, M.A., F.E.a 

 Deceived May 12, Read June 11, 1903. 



I have recently (May 3) received an intimation from the Secretaries 

 of the Royal Society that Lord Rayleigh has questioned the validity 

 of my analysis* of the problem of bending of electric waves round a 

 conducting obstacle, the ground of the criticism being that the short- 

 ness of the wave-length involves that the important harmonics in the 

 expansion are of high order comparable with the ratio of the circum- 

 ference of the sphere to the wave-length, and that for them the 

 approximations in the paper are not valid. Subsequently I have 

 learned that M. Poincare has made a similar objection. 



I have at once to admit the validity of the objection thus raised. As 

 it appears that it is still to some degree uncertain what phenomena 

 would be indicated by theory, I venture to submit the following correc- 

 tion and development of my analysis, which gives a solution of the 

 problem agreeing with Lord Rayleigh's anticipation (p. 40, supra). 



Starting from the expression for 8f/^ti r , given on p. 254, 







ca 



it may be written 



3^ 3 



that is 



fy 3 



m) + 



(7/V=a O/*L IK 



where 



Writing 



Koy. Soc. Proc.,' vol. 71, p. 251. 



