282 BELL SYSTEM TECHNICAL JOURNAL 



Yq. This circumstance would change the preceding formulas only to the 

 extent that 2ir would be replaced by 4. For a given eo, the resistance 

 would then be about 25% higher. 



The radius vq is not necessarily the same as the distance across which a 

 lightning stroke would arc to a cable in the vicinity. Streamers will extend 

 in various directions beyond ro so that ionization of the soil increases the 

 conductivity for a greater distance, r^ being the effective radius of an equiva- 

 lent hemisphere of infinite conductivity. 



The potential difference between the conducting sphere of radius ro and a 

 point at the distance ri is 



r„=^(l_L)=^a^" (74) 



2tt Vo ri/ It ri ro 



Let it be assumed that streamers extend beyond ro until the average 

 voltage gradient between ro and ri equals d . The potential difference is then : 



Foi = ei(ri - ro) (75) 



From (74) and (75): 



ri = ;^ = ro - (76) 



The latter expression applies when the field is assumed to have a radial 

 symmetry about the hghtning channel. When a buried cable is present, 

 however, this symmetry is disturbed. Calculations indicate that the po- 

 tential of the cable at the point nearest to the lightning stroke will be less 

 than 20% of the earth potential at the same point if the cable were absent. 

 As a first approximation the cable may, therefore, be considered to have 

 zero potential. The potential difference between the sphere considered 

 above and the cable is then: 



Fo2 = ^ - (77) 



27r ro 



If r2 is the distance from the channel to the cable, the potential difference 

 is also given by: 



Fo2 = e,{r2 - ro) (78) 



From (77) and (78): 



r, = ro (^1 + '^^ (79) 



The arcing distance calculated in this manner will be the maximum, while 

 that calculated from (76) will be the minimum distance. 



From measurements made of the effective corona radius of a conductor in 

 air,^^ it is found that the latter may be determined on the assumption that 



