Inductance of Two Parallel Wires. 2G1 



where the origin is in the axis o£ the wire, and 



P = — 4-7T flip/a. 

 It will be convenient to write 



a = K ' {ilia) J {ha) r J J Qca) K (ilia) . . (29 N ) 



where « depends entirely on the first wire. 



The corresponding function of the second wire will be 

 called yS, and its radius b. 



Thus -r, kE T , ., , 



B =^ J » ^ ( 3 °) 



Writing n = in (28), it appears that 

 K {ihr) =K (the) J (hp) + 2 2°V K s ( Jtc J s (A/3) cos s<£, (31) 



and if lib is small, as in all applications proposed in this 

 paper, this series is rapidly convergent in the neighbourhood 

 of the second wire. 

 We may write 



o = K o (i7w), &=2t'K<(«fc) *£0, . (32) 



and the vector potential H, which may be regarded as 

 incident on the second wire, becomes 



H = B<9 J (hp) + 2* B . & . J s {hp) cos j?<p. . (33) 

 1 



We neglect, in the present section, the terms dependent on 

 orientation. This will afterwards appear to be equivalent to 

 a neglect of terms of the order (a/c) 2 , so that the wires are 

 not close together. Thus 



K = B6 J (hp), (34) 



is incident on the second wire. A secondary disturbance 

 will be thrown off, of the form 



H=CK„0V), (35) 



zero at infinity, and inside the wire, a disturbance 



H=DJ (*», (36) 



finite at the origin, will be introduced, where 



k" 2 =—-iirvipja\ (37) 



v being the permeability of the second wire. 



Phil. Mag. S. 6. Vol. 17. No. 98. Feb. 1909. T 



