360 Mr. 0. Heaviside on Electromagnetic Waves, and the 

 and therefore 



/*(0=-KV-«*+<kl (14) 



= -i(k a -i a y+c a J 





where C a , C^ are constants such that 



XXXIX. On Electromagnetic Waves, especially in relation to 

 the Vorticity of the Impressed Forces ; and the Forced Vibra- 

 tions of Electromagnetic Systems. By Olivek Heaviside. 



[Continued from vol. xxv. p. 405.] 



31. SPHERICAL Waves (ivith diffusion) in a Conducting 

 Dielectric. — In an infinitely extended homogeneous 

 isotropic conducting dielectric, let the surface r=abe a sheet 

 of vorticity of impressed electric force ; for simplicity, let it 

 be of the first order, so that the surface-density is represented 

 by fv. By (127), § 20, the differential equation of H, the 

 intensity of magnetic force is, at distance r from the origin, 

 outside the surface of/ (v meaning sin 0), 



where / may be any function of the time. Here, in the 

 general case, including the unreal " magnetic conductivity "#,* 

 we have 



g=[(47T^ + Cp)(47T^ + ^)]^ = V- 1 [(^ + p) 2 -0- 2 ]^| ^ (20?) 



k x = 4:7rk + cp ; J 



if, for subsequent convenience, 



Pl =47rk/2c, p 2 =47r#/2/*, <;=(»-§ ;-> 

 P=Pi + P2, <r=Pi—p2- ) 



The speed is v, and p l9 p 2 are the coefficients of attenuation of 

 the parts transmitted of elementary disturbances due to the 

 real electric conductivity h and the unreal g ; that is, e~ pt 

 is the factor of attenuation due to conductivity. On the 



* Owing to the lapse of time, I should mention that the physical and 

 other meanings of the coefficient g are explained in the first part of this 

 Paper, Phil. Mag. Feb. 1888. Also k = electric conductivity ; /x = magnetic 

 inductivity ; and c/4tt = electric permittivity. All the problems in this 

 paper, except in § 43, relate to spherical waves j the geometrical coordinates 

 are r and Q. Unless otherwise mentioned, p always signifies the operator 

 d/dt, t being the time, 



