262 



BELL SYSTEM TECHNICAL JOURNAL 



Comparison of curves 1 and 2 of Fig. 3 shows that (20) is accurate enough 

 for practical purposes, so that the voltage may be taken proportional to the 

 direct -current resistance of the sheath. Since /3" is only 2.5 per cent of 

 a\ propagation in the core-sheath circuit may be neglected in comparison 

 with propagation along the sheath-earth circuit, so that it is permissible 

 to take the voltage proportional to the square root of the earth resistivity. 



12 5 10 20 50 100 



t - Microseconds 



Figure 2 — Approximate solution for S'ii). 

 1 : Calculated from formula for small times. 

 2 : Calculated from formula for large times. 

 3: Transition curve giving approximate solution for S'{i). 

 Earth resistivity, p = 400 meter-ohms. 

 Radius of cable, a = 1.75 cm. 

 Sheath thickness, h = 2.4 mm. 

 Sheath resistance, R = .92 ■ 10~^ ohms meter. 

 Core-sheath cap. Co = .96- 10^^ fd meter. 

 Core-sheath resist. Ro = R ^ .92 •lO"^ ohm meter. 

 Velocity I'o = 2-10* meter 'sec. 

 Velocity!' = 1 • 10^ meter sec. 



Furthermore, from (20) it is seen that when a and b are divided by the same 

 factor k, so that the wave shape of the current remains the same but the 

 duration of the current is increased k times, the voltage is increased -x/k 

 times. Thus, if the surge current had reached its crest value in 20 micro- 

 seconds and its half-value in 130 microseconds, the voltage would be in- 

 creased by s/l, and the crest voltage would have been reached after 120 

 rather than 60 microseconds. 



