SKIN EFFECT 71 



Values of R' for both 25 and 60 cycles are tabulated in 

 Part III. . When taking the resistance of a conductor from 

 the tables, R' should always be used for alternating current, 

 and R should be used only when the conductor carries 

 direct current. 



The total drop in quadrature with the current is 



p 2 48 8640 



24 4320 



The series i -- m 2 H -- m* 



24 43 20 



is thus a correction factor for the term J or 80.47 in the 

 ordinary formula for reactance. Its effect is too small, 

 however, to make any appreciable change in the tabulated 

 values of reactance. 



Proof by Infinite Series. The above formulas for the 

 resistance and inductance of a wire carrying alternating 

 current are sufficiently accurate for transmission line calcu- 

 lations with ordinary frequencies. They may also be ex- 

 tended to include more terms without undue labor. How- 

 ever, as skin effect formulas are generally obtained and 

 expressed by means of infinite series which can be carried 

 out to any degree of accuracy for high-frequency work, a 

 short outline of the derivation of the infinite series will be 

 given. It will prove a check upon the correctness of the 

 formulas given above, but it will probably not give as 

 clear an idea as they do of the actual distribution of 

 current in the wire. 



Let an alternating current, 7, of sine wave form and of 

 steady value, flow in a round wire of radius p. (See Fig. 14, 



