3i2 BELL SySTHM TECHNICAL JOURNAL 



;i = permeability of conductor in electromagnetic c.g.s. units, 

 co = 2ir times frequency in cycles per second, 

 t = \/^ 

 X = ay/ AirKiii 



y = a\/4irXa) 



i = yiVi 

 X.,= -y„+.(f)/ii:„+i(f) 



/«(?) =Un-\-iVn 



= Bessel function of first kind of cirdiT /; .uui ari;uiiiL'nt xiy/i, 



ii„'-\-iv„' = 



dk 



dJni^) 



dx 



K (^) = Bessel function of second kind of order ;/ and argument xi\/i, 

 dK„{^) 



i? = resistancc per unit length of tubular conductor with parallel 

 return, 



^0 = resistance per unit icngtli of tubular conductor with con- 

 centric return in electromagnetic c.g.s. units, 



C = proximity effect correction factor, 



R = CRo. (I) 



The auxiliary functions invoKed are: 



M Uollo'+Vc 



,;?„^j;;,„(l-^ "°"»+''t ) (20^ 



\ m UoVo — Uo Vol 



wlH-rc 



/?-= 1 IJl»ot'o'-"o't'o (21) 



a \ ttX Wi^+i'i" 

 = resistance of solid wire with (■(inccntric return, 



'" + '"= i+x„/c„'(«)/yo'(«)" ^^^^ 



,.l, g[«l(»o-fo)+t'l(t<o+t'o)l ^ fcyos 



«=«^r"p[«.("o+t,)-t,(«„-t-„)ii' ^2^) 



' The ratio R„/ R'. oscillates about unity which it approaches more and more 

 closely as the frec|Uency increases. It is clue to the fact that the phase of the current 

 in the inner portion of the solid conductor may be such as to oppose the current 

 in the outer portion, that the resistance of the solid conductor may be grcilcr than 

 that of the tube even though the heating effect in the latter is the greater. 



