and Resistance of Straight Conductors. 383 



It must, however, be remarked that in the derivation of 

 (22) Maxwell appears to have overlooked the effect of the 

 matter composing one conductor in disturbing the lines of 

 induction due to the current in the other. On this account 

 the formula is correct only when the permeabilities yu, are all 

 equal, and the results cannot be applied to iron wires without 

 reservation. It would seem, however, that the error is of 

 small importance when the wires are distant. The application 

 to wires in contact, contemplated in § 688, will hold good 

 only for the nominagnetic metals. 



If we write c 2 for (a 1 2 — a 2 2 ), so that c is the radius of the 

 solid cylinder of equal sectional area, we have in {'22), 



a 2 — Za 2 4a 2 4 -. «i 



^ log 

 «i — <V ( a i a 2j «2 



_ 3c 2 -2a 1 2 2(a 1 2 -c 2 y 



c 2 c 4 



2 



W(i-$) 



Sa 2 



+ terms in — r 



Hence, when the thickness of the cylinders is relatively small, 

 L , b 2 u c 2 u f c 12 



T= 2 ^ l0 S^7 + 3^ + 3< 



If b, c, d be given, the self-induction diminishes with 

 increase of a 1; %', especially when fi, \x' are much greater 

 than jx . 



When fju is constant throughout, the " geometric mean dis- 

 tance " (§§ 691, 692) may conveniently be introduced. If 

 A l3 A 2 be the areas occupied by the outgoing and return 

 currents, we have 



j = 4/^ [log R Al A 2 -i log B Al -i log R A J, 



where R Al , Ra 2 are to be understood as in (5), (6), (9) 

 § (692). 



For two circular areas, 



log R a x a 2 = log 6, log R A] = log «! - i, log Ra 2 = log a4 - J, 



if a 1} %' be the radii and & the distance between the centres ; 

 so that 



as before. 



In § 692 the value of Ra is given for rectangles and circular 



