144 KENNELLY— THE LINEAR RESISTANCE [April 24. 



such that cr=:i unit, in which case the depth of the slab is 

 cosh~^c? units and the breadth of the slab is 27r units. 

 The quantity Y defined by the relation 



Y = cosh-^{d/a) numeric (3) 



may be called the distance factor of the plane-cylinder system ; 



because the distance between electrodes in the equivalent slab of 

 Fig. 2 is 



L^=Y(T cm. 



When the radius a- of the cylinder is very small with respect 

 to the distance d; so that d/a is a large number, we have 



2d 

 F= log^ — numeric (4) 



so that for such cylinders the linear resistance 



p p 2d 



r = — Y = — log — absohm-cm. fs) 



p 27r 27r ^' a ^•'^ 



The accompanying table gives for successive values of d/a in 

 column I., the corresponding value of Y in column II. Column III. 

 gives the resistance factor Y /2i? which, when multiplied by the 

 resistivity p of the medium, gives the linear resistance of the plane- 

 cylinder system considered. 



Thus, if a conducting cylinder with a radius of 2 cm. is sup- 

 ported at an axial distance of 10 cm. from an infinite conducting 

 plane, in a medium of resistivity /d = 3Xio^° absohm-cms., we 

 have fl?/CT=5. The table gives for this ratio the value of Y as 

 2.2924, and the value of the resistance factor y/27r = 0.3649; so 

 that the linear resistance of the system will be 3 X 10^" X 0-3649 

 = 1.0947 X io^° absohm-cms. ; or 10.947 ohms in a linear cm. 



Linear Conductance. — The linear conductance, or conductance 

 per linear cm. of the plane-cylinder system will be by (i) 



s: = -. — , , , , , = -7, = 7 • ^ry abmhos per cm. (6) 



^p p cosh-^ (d/a-) pY ' Y ^ ^ ^ 



where y is the uniform conductivity of the medium in abmhos per 



