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BELL SYSTEM TECHNICAL JOURNAL 



or 



log \p{u) = log ux-'^ + log 



1 - exp - 



ttXx^ 



Thus Figure 3 may be used to indicate the range of applicability of 

 the limiting form, which is quite large; in this range the unit step 

 voltage is simplified as shown above. 



VALUES OF 



1TAu2 



Fig. 4 — The function ^iu), for collinear straight wires; for values below the range 

 1 , ttXh- 



shown f (?<) 



+ 



The function '^{u), for the case of collinear straight wires, is shown 

 on Fig. 4 for values of the argument //(ttXm^) fi-om 0.1 to 1000; for 

 small values of the argument, the function is approximately 



, , 1 , ttXm" 



xXm^ 



< 0.4 



These curves may be employed to obtain voltages due to other 

 forms of disturbing currents by numerical or mechanical integration 

 of the following integral : ^ 



£12(0 





/(r)Fi2(/ - r)dT 





r) T''i2(r)f/r, 



where I{t) is the disturbing current as a function of time. 

 'J. R. Carson: loc. cit., p. 16, eq. (20) and (20a). 



