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



electric force at the origin. Comparing with (233) we see 

 that the solution of (258) maybe derived, when / is constant, 

 starting when £=0. Take g = 0, making p = o-=47r&/2c. 

 Then 



H=j^ (47r^ + cp)| 6 --^( i 9 + o-)J [^ 2 -^V] + X r },(259) 



where X y is what the X a of (237) becomes on changing a to 

 r ; and 



'K =vkr~ 2 x vol. integral of/, . . . (260) 



supposing the impressed force to be confined to the infinitely 

 small sphere, so that its volume-integral is the "electric 

 moment," by analogy with magnetism. The solution (259) 

 begins at r as soon as t = r/v. It is true from infinitely near 

 the origin to infinitely near the front ; but no account is 

 given of the state of things at the front itself. H is the 

 final value of H. We may also write X, thus, 



(261) 



and (259) may also be written 



H =;&^+^( 1 -4K • • W 



When c = 0, (259) or (262) reduce to 



H = H [@V^ + l-g) 4 {,- | ^ + | ^/-...}] ) (263) 



where y — (Sir/juk^/i)*. 



42. Conducting sphere in nonconducting dielectric. Circular 

 vorticity of e. Complex reflexion. Special very simple case. — 

 At distance r from the origin, outside the sphere of radius a, 

 which is the seat of vorticity of e, represented by fv, we have 



R = (j>^(W/W a )fya/r. . . . (264) 



The operator (f> will vary according to the nature of things 

 on both sides of r = a. When it is a uniform conducting 

 medium inside, and nonconducting outside, to infinity, we 

 shall have 



= 0! + (/> 2? 



where </> 15 depending upon the inner medium, is given by 



_. gi {l + (q l a)- 2 }smhq 1 a-(qia)- 1 coshq l a 



^ 47r& 1 + c 1 p coah q 1 a—(q 1 a)~hmhq 1 a ' ^ ' 



