L. Page — Fundamental Relations of Electrodynamics. 65 

 A, e, ( 1 -J ( sin <f> l T sin \ ds 



F. = 



F, 



r 2 (l - ~ sin 2 fl\* 



^iM 1 _ -^r) cos «A <& 

 /■ 2 /l _^l s in a ^ 



Combining, we have left the force 



A,<v<, v I y 2 \ . 



' — I 1 ) sin d 



c 2 \ c . / 



r * ^ _ 2L S in 2 tf)l 



in the X direction. 



Proceeding in the same manner, we find the total force on 

 the current element at B due to the moving charge at A is 



— - — - sin 6 



F,= 



(-£) 



(l-?- *.■•)• 



where *', is the current in electromagnetic units. As the drift 

 velocity of the charges constituting a conduction current in a 

 wire is certainly small compared with the velocity of light, we 

 can place the factor 



(,-i-drf.#)i 



equal to unity. 



If we replace 2 by a current element, we will find for the 

 total force exerted by the current element i„ ds 2 at A on the 

 current element i 1 ds 1 at B, as measured on the earth (system 

 K. (o) ), the expression 



i, i„ sin 6 dads, 

 F _ LJ L_L 



where i 1 and i 7 are measured in electromagnetic units. 



Am. Jour. Sci.— Fourth Series, Vol. XXXIV, No. 199.— July, 1912. 

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