286 BELL SYSTEM TECtlNlCAL JOURNAL 



attenuation curves obtained in this manner, together with similar curves 

 for the vohage, between the sheath and the core conductor of an ordinary 

 cable, or between the copper shield and the lead sheath of the cable on 

 which these observations were made. 



1.3 Crest Values and Attenuation of Voltages 



The current along the copper shield produces a voltage between this 

 shield and the lead sheath, due to the resistance drop along the shield from 

 the stroke point to a point sufficiently remote for the current in the shield 

 to have become negligible. This voltage is proportional to the unit-length 

 resistance of the copper shield. From the considerations of the precedmg 

 section, it follows that the voltage will be proportional to the square root of 

 the earth resistivity and, if the wave-shape remains congruent but the 

 duration of the current is changed, that it will be proportional to the square 

 root of the duration or of the time to half -value. These two propositions 

 follow from the fact that the voltage is proportional to the distance traveled 

 by the current before it is attenuated to a given value. 



The crest voltage between the sheath and the cable conductors of an 

 ordinary cable, or between the copper shield and the insulated lead sheath 

 of a cable of the type on which these observations were made, is given by 

 the following expression for a current reaching its half-value in 65 micro- 

 seconds: 



V = 2.25 JRp'i^ (6) 



where F is in volts and / is the crest current in kiloamperes, R the resist- 

 ance per mile of the outer envelope (in this case the copper shield), and p 

 the earth resistivity in meter-ohms. This formula follows from expressions 

 given in the paper referred to previously, which also contains curves from 

 which the voltage attenuation along the cable shown in Fig. 5 may be 

 obtained. For a resistance of .7 ohm/mile, which is that of the copper 

 shield, and p = 1000 meter-ohms, the crest voltage for a current of 1 ka 

 would thus be 50 volts; and, for a crest current of 200 ka, 10,000 volts. 

 If the dielectric strength of the thermoplastic insulation exceeds 10 kv, 

 the liability of such cable to lightning damage would thus be small, unless 

 the time to half-value of the current substantially exceeds 65 microseconds. 



II. Experimental Installation 

 2.0 General 



From the preceding discussion it is seen that a lightning current dropping 

 to half-value in some 50 to 75 microseconds, which is of the wave-shape 

 ordmarily assumed, would attenuate to half its crest value in 500 to 1000 

 feet when the earth resistivity is from 1000 to 2000 meter-ohms. With 



