ti-i L. Page — Fundamental Relations of Electrodynamics. 

 Applying I and reducing, we get 



s , e * ( l ~ "^-J (sin + - ~. sin ij 



F' 



F.'= "' "' (' ~ ° r ) C ° S * 

 r-(l -£-»•#)* 



Let F x and F z be the forces as measured in K (o) that must 

 be applied to the charge at B in order to produce the same 

 effect as F x ' and F/. Then 



F, = 



F,= 



e , e * (l - ~ir) (sin <£ - H s in 0J 

 r' (l - -Hi sin 2 tf\* 



e i e 2 ( l ~ -^r) cos 4> 



-' ( x - v »• ") ! 



Now replace e a by a current element (X^ + Xji*,,) <Zs. In 

 this current element there is at rest the positive electricity 

 (k— X,) <&, and the negative electricity (k—\) ds. Consider 

 the positive electricity \ 1 ds which is moving, and a portion 

 \ ds of the negative electricity which is at rest. Then the 

 components of the force due to e 2 on the negative electricity 

 Aj ds at rest will be 



— A.,6, U r J sin 4> ds 



r * A _ £_ sin 2 flV 



— A, e, [ 1 -5- ) cos <£ c ^ s 



F = - 



(l ~ f In- «)* 



But the components of the force due to <? 2 on the positive 

 electricity X : ds in motion is, as we have just found, 



