M. E. Edlund on the Nature of Electricity. 95 



from m if the latter is at rest, we have for 



case 2 : — 



+ '^[l + 0(+^.cos^)+t(7[l~cos2^])]. 



For case 3, in which m approaches the space occupied by mJj 

 we obtain : — 



In the last place, we have for No, 4 :— 



mm' 



Subtracting now the sum of the last two expressions from the 

 sum of the first two, we obtain the definitive result ; — 



+ ^^(^( + A.cos(9)+<jE,(-^.cos(9)+2^;r^^[l-cos^l9]^1.(3) 



This result is the theoretic expression of the reciprocal influ- 

 ence of two current-elements which move in the same direction 

 in parallel lines. 



By making, in formula (3), cos^ = (that is to say, by sup- 

 posing the line of junction between the two current-elements to 

 form a right angle with the lines of direction of the currents), 

 the function <^ will become, as we have seen, =0. We shall 

 therefore have for this case : — 



+"?.<;) (4) 



Now, according to the preceding reasoning, the value of the 

 function ijr is always positive. It hence follows that in this po- 

 sition the current- elements attract each other — a fact already 

 demonstrated by experiment. 



We will now compare the theoretic result with experiment, in 

 order to determine the functions (/> and ^/r. 



Ampere, as is known, has determined experimentally the mu- 

 tual action of two current- elements; and W. Weber has proved 

 by very accurate experiments the correctness of the results ob- 

 tained by the French physicist. For the case in which the cir- 

 cuit-elements are parallel, r being their distance, and 6 the angle 

 made by one of them with their line of junction, Ampere^s for- 

 mula is 



-!-^Vl-|cos^6>V5 6/s', . .... (5) 



in which i and V denote the intensities of the two currents, ds 

 and ds^ the two circuit-elements, and k a constant. As long as 

 this expression is positive, there is attraction between the circuit- 



