LIGHTNIXG PROTECTIOX OF BiKIED TOLL CABLE 



261 



With a = .013-10', b == .5-10', a current of the wave shape used m the 

 measurements referred to above is obtained. This current reaches its 

 crest in 10 microseconds and deca}-s to its half-value in 65 microseconds, 

 and is fairly representative of the average wave shape of lightning stroke 

 currents. In the following, the voltages are for convenience referred to a 

 crest value of 1000 amperes, which is obtained when / = 1150 amperes, 

 the latter current being the initial value of each of the two exponential 

 component currents included in (19). 



/ 



"L h(u) = c-"' 



Table I 



t 



f''" dr = 



H when u < .1 

 1 



le erf (hi) 



2u 



when II > 10 



A more complete table for the range between u = and ii = A\?> published in Bericht- 

 everhandliingen Akademie der Wissenschaften. Leipzig, Malh-Phys. Klasse, Vol. 80, 1928, 

 pages 217 to 223. 



In Fig. 3, the dashed curve shows the measured voltage and curves 1 and 

 2 that calculated for the above surge current for two conditions. In cal- 

 culating curve 1, S'{i) was taken as curve 3 of Fig. 2, the voltage being 

 obtained by numerical integration in accordance with (1); in calculating 

 curve 2, z is taken as the direct-current resistance of the sheath and the 

 velocities of propagation are assumed to be intinite, so that S'(t) is given 

 by (18). In the latter case the following e.xpression is obtained for the 

 voltage by solution of (1): 



Vit) = ^^f^ ^,^ [a-'^h{Vat) - b-''h{Vbt)] (20) 



where the function Jiin), u = -x/ at or \^bt, is defined as before. 



