1909.] BETWEEN PARALLEL CONDUCTING CYLINDERS. 145 



cm. The quantity 2it/Y may be called the conductance-factor of 

 the plane-cylinder system. It appears in column V. of the table. 



Thus, if a conducting cylinder of radius a = 0.5 cm. be sup- 

 ported at an axial distance of d = 7.S cm. from an infinite con- 

 ducting plane, in a medium of conductivity y=io"^° abmhos per 

 cm., the ratio d/a in column L is 15, and the conductance factor 

 for this ratio appears in column V. as 1.848. The linear conduct- 

 ance of the system is thus 1.848 X iO"^° abmhos per cm. The 

 distance-factor of the system is given in column II. as 3.4001 ; so 

 that the depth of the equivalent rectangular slab of medium is 

 1.700 cm., the breadth being 3.142 cm. 



Linear Electrostatic Capacity. — The linear capacity Cp of a 

 plane-cylinder system in a dielectric medium of specific inductive 

 capacity k, is numerically the same as the linear conductance of the 

 same system in a medium of conductivity k/Att or resistivity ^tt/k ; 

 so that, in C.G.S. electrostatic units : 



K I 



<r„ = -. — , , ,. ■ = K ■ — ,- statfarads per cm. (7) 



^ 2 cosh-^ {^1^) 2 V ^ ^' ^ 



The values of the capacity factor i/(2F) appear in column VI. of 

 the table for each selected value of d/a. 



Thus, a cylinder of radius o- = o.4 cm. is supported at an axial 

 distance of i cm. from an infinite conducting plane in a medium of 

 K^i. Here c?/o- = 2. 5, and i/(2F)= 0.3 192. The linear capacity 

 of the system is therefore 0.3192 statfarad per cm. 



In order to convert the linear capacity Cp statfarads per cm. into 

 microfarads per km., expressed by Cp', we have: 



9 9 



r ' = -^ = - • ,; microfarads per km. (8) 

 Q Q 2Y ^ ^ ^ 



Similarly, to express the linear capacity in microfarads per mile 



/* /c I 



= X — vr microfarads per mile (9) 



" 5-591 5-591 2F 



That is, we must divide the capacity-factor of the table by 9 to obtain 

 microfarads per km. or by 5.591 to obtain microfarads per mile. 



PROG. AMER. PHIL. SOC. , XLVHI. I92 K, PRINTED SEPTEMBER 2, I909. 



