1909.1 BETWEEN PARALLEL CONDUCTING CYLLXDERS. 153 



Linear Conductance of Double-Cylinder Systems. — The linear 

 conductance of a double cylinder system will be half that of a plane- 

 cylinder system of equal d/tr ; so that : 



TT TT 77r 



S'm = u-i / ji \ = ~T/ = ^y abmhos per cm. (33) 



"" /> cosh [a/cr) pY Y ^ ^-^-^^ 



where y is the conductivity of the medium. The conductance- 

 factor of the double-cylinder systern is therefore half of that given 

 in column V. of the table. 



Linear Electrostatic Capacity of Double-Cylinder Systems. — The 

 linear capacity C^q of a double-cylinder system in a dielectric me- 

 dium of specific capacity k is half the capacity of a plane-cylinder 

 system of equal d/a; so that: 



'^ = 4cosh-(^/cr) = '''4V '^^^^^'^^' P^' 1°°P ^"^- (34) 



The linear capacity of each cylinder to the zero-potential plane, 

 or the capacity of the system per cylinder-cm., is given by formula 

 (7). The capacity factors of a double-cylinder system of given 

 d/(T are thus half of the values given in column VI. of the table; 

 but the capacity factors of the system per " wire " cm. to zero 

 potential midplane are those recorded in column VI. 



At interaxial distances large with respect to the cylinder-radii, 

 Y = loge D/u, and we obtain the well known formula 



"1 / T-,1 s statfarads per cm. f^;) 



The linear capacity of a double-cylinder system expressed in 

 microfarads per km. is 



'00 



""9 9 



Similarly, 



K I 



C.J =-- = -• ~—^ microfarads per cm. (36) 



'00 



'00 



<r„„ K I 



= X — T> microfarads per mile (^7) 



5.591 5.591 4F ^ ^-^^^ 



Potential Distribution in Double Cylinder System. — All of the 

 formulas (10) to (31) inclusive referring to the potential distri- 

 bution in a plane-cylinder system apply immediately to a double- 



