2S BELL SYSTEM TECHNICAL JOURNAL 



„ 2pMog[(l+p)/p] , .. c 



K = ?Ti /i 7 n //i ■ x = (radius of curvature 



21og(l+p)-p/(l+p) 



when = tt) (23) 



= 0, 1.564, oo at p=0, 1, oo, which checks the 

 sharp curvature of the curves which cross 

 the axis just to the left of the origin. 



Formulas for Figs. 4 and 5 

 s=AB/Aa, 



t =2[5log(s + \A 2 + l) + l-Vs 2 +l] (24) 



'2j 

 p 



N i= NSPr 



Aa Aa 



(25) 



= 2, [log 2,-1+1 -1-^-^+...] 

 = 2,lo g [f(l+l+^-i- i ^+.,.)] 



-'E 1 s+™+ ■-•■]■ (26) 



^^)(y)= 2 -vfe' (27) 



+2 1og(s 2 + l), (28) 



7V 2 (orA^) = i^g, ±2[log , (1 + vV + 1) _^ 2 + 1+5 + 1]> (29) 



iv 3 iv^,_n (5 -+1) (V2+iy 



-a-——, r2 log , 



Aa Aa |_ (i + V s 2 +2)« 



4-4(V^+2-v / ^+l -A/2+1)]. (30) 



Formulas for the Mutual Inductance Between Any Flows in Two Hori- 

 zontal Planes Grounded by Vertical Filaments 



Let the arbitrary flows be JC' and *' between points A', B' and a', b' 

 in the two horizontal planes, grounded by vertical filaments connect- 

 ing these four terminals with the points A, B, a, b on the surface of 

 the earth. In order to indicate briefly which of these eight points 

 are involved in each term of the result, we imagine a vertical line 

 which cuts the horizontal planes in the points P' , p\ P, p, where P 

 and p are the same point on the surface of the earth, since the non- 



