HJTM7VT7-1 \ 



T H E 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AKD 



JOUENAL OF SCIENCE. 



4- 



r 0- ^^ 



[SIXTH SERIES.] 



MARCH 1911. 



XXXIV. On the Bending of Electric Waves round a Large 

 Sphere.— -IV. By J. W. Nicholson, M.A., D.Sc* 



The evaluation of a type of integral. 



THE analysis necessary for the determination of a second 

 approximation valid for points within the region of 

 brightness, is somewhat involved, and it is convenient, in the 

 first place, to collect certain formulae from earlier sections 

 for ready reference. 



In the previous notation, the value of the magnetic force 

 is given by 



7p = 'igj^f m(R»BJ*(l+ &x*)&*-*^ d J±. (110) 



By the use of the Mehler Dirichlet integral for the zonal 

 harmonic, if g(0) is an operation defined by 



,,. 2isin»fl d C 9 __ wty 

 ^> = -^T ^J VlVc Ts^cos"^ ' (111) 

 then by (39) 



<YP=g{0) X m(E ft R n r) i (l + ^») ^ l ~^cos m<£ 

 =?Wi<« l H^' 3 ), ....... (us) 



where 



w=im(R„R n ,)*(l + « 2 'X») 



(v l5 r 2 ) = <£„ — 0„. r Hh m<£. 



* Communicated by the Author. 

 Phil. Mag. S. 0. Vol, 21. No. 123. AforcA 1911. fr 



