3909.] BETWEEN PARALLEL CONDUCTING CYLINDERS. 155 



After having established the position of the zero-potential plane 

 Z'OZ, the linear resistance between the cylinders may be found by 

 iising formula (i) on each side of the plane and adding the two 

 parts. The linear conductance will then be the reciprocal of this 

 result. 



The linear capacity of each cylinder to zero-potential plane is 

 to be found by formula (7). The linear capacity per loop cm. may 

 be found from the linear resistance per loop cm. by the formula : 



^ty _)_ Y^ statfarads per cm. (39) 



For example, if two conducting cylinders of radii 0-1 = 2 and 

 o-i = I cm., respectively, are separated in air by an interaxial dis- 

 tance of 8 cm., the zero-potential plane is displaced through a dis- 

 tance of ts cm., so that (/i = 4tB, ^2 = 3^^ cm. The ratio dja^ is 

 thus 2.094, and dja^_ is 3.815. The distance factor Y^ is 1.37, and 

 Y o is 2.014. The linear capacity of C^ is 0.365 statfarads per cm. 

 and of Co 0.248 statfarads per cm., each to zero-potential plane. 

 The linear capacity of the pair by (39) is 0.1477 statfarad per 

 loop cm. 



The potential distribution in the unequal cylinder system may be 

 obtained as easily as when the cylinders are equal, since the polar 

 points A-^An, Fig. 4, lie at equal distances from the zero-potential 

 plane Z'OZ. 



ExcENTRic Cylinders. 



Let the two parallel very thin conducting cylinders be hollow, 

 with radii a^ and a^. Let one be placed excentrically within the 

 other, as shown in Fig. 6, at an interaxial distance D. Let the line 

 CjCo joining their centers be prolonged as indicated in the figure. 

 The infinite zero-potential plane will perpendicularly intersect this 

 line at an inferred distance of 2A/2D cm. from the middle point of 

 D ; so that : 



2A D 

 ^i=2Z?+ 2 ^"'^ ('^°) 



and 



2A D 



