Measurement of Small Capacities and Inductances. 505 



be called A, and let it be positively charged, and the other be 

 B, and negatively charged. Let V A and Vb be the potentials 

 of these wires, and let the charge on each be q electrostatic 

 units per centimetre of length, then their capacity per unit 

 of length (<?) is equal to <7/(V A — Vb). 



Now from the expression for the potential of the electrified 

 filament we see that 



V A = ( - 2q log r + Ct) - ( - 2q log D + CO, 



Y B= -(-2qlogr + Qt) + (-2qlogT> + Ct), 



V A — V B = 4r_/(log D — log r) -— <Lq log D/r. 



The capacity per unit of length is therefore given by 



1 



41ogD/, 



in electrostatic units). 



If we employ ordinary logarithms and express the capacity 

 per unit of length in micro-microfarads {c') this becomes 



10 6 



4x2-303xyxl0 5 log 10 D/? 

 0-1208 



log 10 iD/d' 



where d is the diameter of either wire, and D their distance 

 from centre to centre. The formula for the capacity per 

 unit of length of the single telegraph-wire of diameter d 

 supported at a height h above the earth, is easily deduced 

 from the above. For since the ground-surface must be a 

 zero-potential surface, the capacity c in electrostatic units 

 of the single wire per unit of length under these conditions 

 must be 



4 log e 2D/d 2 log e U/d 



and the capacity c' per unit of length in micro-microfarads 

 will be 



10 6 



° 2x2-303x9xl0 5 log 10 4/i d 



(in M.M.lAbO. 



logic ±hld 

 Accordingly the capacity C of a telegraph wire / centimetre- 



