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LXXII. On the Mutual Induction between two Circular 

 Currents. By Dr. D. N. Mallik, F.R.S.E*. 



1. rilHE mutual induction (M) between two circular cur- 

 JL rents i, i' in any relative position to each other is 



where c l5 c 2 are radii of the concentric spheres of which the 

 circles are the cross- sections, Ci<c 2 and # = the inclination 

 between the normals to the two circles. 



2. If the circles are coplanar, then //,=0, /// = 0, = 0. 

 Also 



dF 2m+1 (^) ^ 3. 5.7.(2^+ 1)^ 



dp (/m=o) 2.4 .6... 2m 



If M is the value of M in this case (i = l = i') } then 



— +-S^-(1)M:4©^)"+} 



But if V = gravitational potential" of a wire of radius c 2 

 at a distance c x from the centre in the plane of the wire 

 (density =1), 



27TC 





^). .... a) 



Now V=f— — ?***- . - 



J vcy-rCi 2 — 2c x c 2 cos 



4c 2 p # 



C l + ^2 J o \/l ~~ ^ Sm 



4 / I 2 1 2 3 2 \ 



1 i». 1. 

 2 2 "1.2 



where & 2 = 



4cy 



(c,+c 2 ) 2 

 * Communicated by the Author. 



and k' — - - (assumed to be small). 



Ci + Co 



