56 Art. 9.-T. Terada: 



in the earth, especially for a simple case convenient for mathe- 

 matical treatment, i.e. the case when the current is arranged 

 in an infinite train of ivaves, either stationary or progressive ^ 



Take the surface of the earth, considered plane as usual, 

 as :f?/-plane and the positive direction of z downward. For 

 the positive value of z, the space is considered to he filled with 

 a conducting medium with the uniform specific conductivity h 

 and the magnetic permeability ix, while the negative side of z is 

 regarded as a vacuum. Assuming the electric and magnetic force 

 independent of y and denoting their components respectively by 

 ^x> ©2. âa:. -Ös» the usual fundamental equations for the slow 

 variations reduce to 



-f^ 



It Iz 



"ht 2>X ' '^X 'èz 



(1) 



since ©^=©^=0, §^=0. Next, assume that the electromagnetic 

 field varies periodically with the frequency nl'Irr and the distri- 

 bution of the fields represents a two-dimensional wave with the 

 wave length 



a 



in the case of stationary waves, we may assume 



e^=:e'«^-(? + '-^)~'sin ax, (2) 



where ß and T are considered real. From 



M Tax- S^' 



we obtain 



ATZfikin = — «- + [ß + iy)' 

 or 



ß- — 'r=a-, '2ß}'=:4z/jik}i, (4) 



1) The mathematical solution of the case Avas kindly carried out by Prof. S. Sano, to 

 -whom the best thanks of the author are due. 



