t-^o<w-W+^^+/V+wO 



Vortex Theory of Electromagnetic Action. 407 



The fourth term — ~ is, of course, that part of the electro- 

 motive force which arises from the electricity in the field. 

 Had we considered the case of a conductor, the terms which 

 we should have to add to equations (8) would he just the same 

 as those added above in (20) to equation (14). Thus, in a 

 conductor we should have 



dF 



dt p ' p dx 



& , +p--S • • w 



In the case considered by Mr. Hall, 



and f =°' ««'+^'+7/=0 ) 



d v/* 

 — -^- = impressed electromotive force in direction of x=~P t 



say; ,.p=p 1 - 8 ^ (7 ,_ / 3/; ) . . . . (22) 



Thus, if a current/ flow in a conductor in a field of strong 

 magnetic force 7, there will be produced an electromotive 

 force in the direction of y (perpendicular, that is, to the direc- 

 tions of/ and 7), whose value will be 



p u 



If we consider a wave travelling through the medium the 

 electromotive force parallel to x produced by electromagnetic 

 action will be rt 



d¥ 8wfiG, • • 



Substituting in the equations 



'«-/3A;}+V 2 F = 0; 



we get 



^ (cPF SirfiG d , 

 ^H-aW + ^~di^ 

 and from these Professor Eowland has calculated the magnetic 

 rotation of the vectors F, G-, H (Phil. Mag. April 1881). 



The equations satisfied by the magnetic force of, /3', 7', can be 

 found either from these by differentiation, or from the original 

 equations (19). We get, remembering that 



Ay dzy 



O 7 



J 4tt\, 



