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



Equation (124) applies to any odd m. When m is even, ex- 

 change u and w, also u f and w' . in the with system we may write 



/. = 0«H BJ (125) 



the form of <f> being given in (124). The vorticity of the 

 impressed force is of course restricted to be of the proper kind 

 to suit the with zonal harmonic. Thus, any distribution of 

 vorticity whose lines are the lines of latitude on the spherical 

 surface may be expanded in the form 



2/.vQ«, (126) 



and it is the ?nth of these distributions which is involved in 

 the preceding. 



20. Both media being supposed to be identical, (/> reduces 

 to 1 



~~ &i u a (u a —ic a y ^ ) 



by using (114) in (124). This is with m odd ; if even, we 

 shall get 



In a non-dielectric conductor, k 1 =-i7rk, and q*=4irfikp; so 

 that, keeping to m odd, 



K w a {u a — w a )' 

 In a non-conducting dielectric, k Y = cp, and q=zpjv\ so 



**■ 55^=5 (130) 



In this case the complete differential equation is 



h.= 2^: «.{».-«■„)/„ .... (13 i) 



when there is any distribution of impressed force in space 

 whose vorticity is represented by (126). 

 Outside the sphere, consequently 



f 



(out) I 



-W*-*^l"W-vOfm • • (133) 



un ' 



derstanding that when no letter is affixed to u or w, the 

 value at distance r is meant. We see at once that u a = Q 

 makes the external Held vanish, i. e. the Held of the particular 



