616 Mr. J. R. Carson on 



similarly derived from the Bessel function of zero order 

 and complex argument bivi. From (19) the proximity 



effect correction factor C is given by 



G = l + l/2ilA,l 2 ^~^ n (20) 



»=i' ' u o v —u v 



By aid of formulas (19) and (20) the a.c. resistance of the 

 wire is calculable, once the coefficients h x . . . lt n or A, ... A„ 

 are determined; to this determination we now proceed. 



As stated and discussed above, the harmonic coefficients 

 are determined by the continuity of the tangential magnetic 

 force and the normal magnetic induction at the surfaces of 

 the wires ; that is, by the continuity of H i and /jJ3. r i at 

 r 1 = a, and of H e2 and fiK r2 at r 2 = a. From considerations 

 or! symmetry, however, these boundary conditions need be 

 formulated at the surface of one wire only, and their satis- 

 faction at the surface of either wire insures their satisfaction 

 at the surface of the other. To formulate these conditions 

 at the surface of wire #1, we require that the tangential and 

 normal components of the magnetic force at the surface of 

 this wire be expressed in terms of i\ and X only, whereas 

 H x and H y of formulas (12) and (13) are expressed in terms 

 of both r 1? #i and r 2 , 6 2 . As a preliminary, we therefore 

 require the expansion of H 2 and H,,, as given by equations (12) 

 and (13) in terms of r x and l alone. This is effected by the 

 following transformations : — 



e ! ( 1 - n ov c ) cos *> + ( -^tr- } M? cos 2e i 



cos s 



\ - 



3! 



(r^c) 8 cos 3^..., (21) 



sin s6<. 



i r ij(n/«)«ntf 1 -^±^_(r 1 /«) , «dn2tfi 

 ~iv" = ? I + (£H£±i}(£±2) (Vc)3sin Wl ... . .' (21a) 



(It may be remarked in passing that these transformations 

 may be very advantageously employed in calculating the 

 capacity coefficients of a system of parallel cylinders.) 



It" these transformations are substituted in (12) and (13), 

 H x and H y in the dielectric are expressed entirely in terms 

 of r and & u or, omitting subscripts, in terms of r and 6. If 

 we now employ the relations 



H r = H^cos^ + Hysin^, 



H e = H^ cos 6 — H x sin 0, 



