970 Dr. G. Breit on the Effective Capacity of 



because it approaches zero as GrjH approaches zero. The' 



K e Grjl dY iii i j i fc e ~dY 



expression -r- ^rrr -j- has here been replaced by ; — =— 



F 4?r AB dy r J 47r Bw 



C TT 



because ~r~ = cos (GjHG) = cos (yn). Thus, to sum- 

 marize, if V is the average potential in the coil, if V is 

 the potential outside which becomes equal to Y at the 

 contour of the cross section, then the charges are dis- 

 tributed as if the volume density were 



p = _ S df ■ (1) 



and the surface density were 



where 



-*o BV K e ~dY , 9 . 



4-7T ^n 4-7T ^n 



8*989 x 10 u k = K = specific inductive capacity of the 

 medium outside the cross section ; 



8*989 x 10 n A: e = K e = effective specific inductive capacity 

 in the direction oy of the medium 

 inside the cross section ; 



^- is the directional derivative along the outward 

 drawn normal to the contour at the 

 point where a is taken. 



These results will now be used in deriving expressions 

 for the effective capacity of a coil with a circular section, 

 and later will also be applied to coils with square sections. 



Coil with Circular Section. 



Through the point (fig. 1) two rectangular axes are 

 now drawn. The axis parallel to the layers is called OX ; 

 the axis perpendicular to the layers is called OY. Consider 

 a point P inside the cross section. Its coordinates referred 

 to the axes are (#, y). It was shown that the potential 

 of P exceeds the potential of by an amount proportional 

 to the area LGMN. This area is 



LGMN = a'Tsin-^+^A/l-^l. 

 L a a V a 2 J 



The area of the whole section is 



