1909.] BETWEEiN PARALLEL CONDUCTING CYLINDERS. 151 



an expression for the potential of a point in the medium in terms 

 of its polar ratio m, and the distance j'^ of the conducting cylinder 

 from the plane. 



The current density 8 at any point whose polar distances are 

 r and r' will be perpendicular to the equipotential cylinder passing 

 through the point and will be equal to 



S = 7 — • -^ absamperes per cm.^ (3 i^) 



The preceding formulas for potential distribution have been de- 

 veloped with reference to a conducting medium between the infinite 

 plane and cylinder. They are, however, applicable to the case of a 

 dielectric medium, if the electric flux <f> replace the electric current 

 /, and the dielectric constant k be substituted for y or i/p. No 

 substitution will be needed in formulas (13), (16), (18), (19) and 

 (2^) to (31), inclusive, which apply either to an insulating or to a 

 conducting medium. 



Two Equal and Parallel Conducting Cylinders. 



If, instead of an infinite conducting plane and a parallel conduct- 

 ing cylinder, as in Figs, i and 3, we have two indefinitely long par- 

 allel conducting cylinders of equal diameter, as in. Fig. 4, at an 

 interaxial distance CC of D cm., then each cylinder may be regarded 

 as forming an independent plane-cylinder system with a fictitious 

 infinite conducting midplane Z'OZ, axially distant d = D/2 cm. 

 from each. This midplane will be perpendicular to the central line 

 CC The double-cylinder system will have two polar lines equi- 

 distant from the system center 0, and represented in Fig. 4 by the 

 polar points AA'. The potential of the midplane Z'OZ will be 

 midway between the potentials of the two cylinders; so that if these 

 have equal and opposite potentials, the potential of the midplane 

 will be zero. All of the preceding formulas for plane-cylinder sys- 

 tems may, therefore, be applied, in duplicate, to the double-cylinder 

 system of Fig. 4. 



Linear Resistance of Double Cylinder Systems. — The linear 

 resistance from either cylinder to the midplane is given in formula 



