STUDIES ON MAGNETIC DISTEIBUTION 93 



E the element of length dy. Now, if we take all the elements of the 

 rod in the same way and consider the effect at H F, the total magnetic 

 potential at this point will, by hypothesis No. 1, be equal to the sum 

 of the potentials due to all the elements dy. 



Let 4Q' be the number of lines of force produced in the bar at the 

 point E due to the elementary difference of potential at 

 that point, Qdy, 

 AQ" be the number o* lines of force arriving at the point F due 



to the same element, 



Q" be the number of lines passing from bar along length JL, 

 /> be the sum of the resistances of the bar in both directions 



from E, 



/> z be resistance at F in direction of D, 

 y be the distance D E, 

 x be the distance D F, 

 6 be the distance C D, 

 s" and s' be the resistance of the bar, &c., respectively at C in 



the direction of A, and at D in direction of B, 

 be the magnetizing-force of helix in its interior. 

 Let 



At y jt^t -r * AH *v jm, T * 



** ~ * ^ 9 " ' j---,^ ^>^ 7i 9 



f>* = 



ft 



4- e 



_ 



~ 2R'r A'A"-1 



This gives the positive part of Q"- To find the negative part, 

 change x into & a;, A' into A", and A" into A', and then change the 

 sign of the whole. 



When the helix is symmetrically placed on the bar, we have s' = s", 

 A'=A"; whence, adding the positive and negative parts together, we 

 have 



