324 BELL SYSTEM TECHNICAL JOURNAL 



and the other a temporary line of insulated wire laid along the surface 

 of the ground. 



For the purpose of analysis, each of the lines may be replaced by 

 its input impedance. This simplification is shown in Fig. 6c, where 



„, _ K tanh 75 + Z' 

 1 + ^ tanh 75 



The impedance between terminals 1 and 3 is: 



S, = 5/ + G. (4) 



The impedance between terminals 2 and 3 is: 



52 = 52' + G. (5) 



The impedance measured between terminals 1 and 2 in parallel and 

 terminal 3 is: 



5 'S ' 

 Sq= G -\- ^ , Y ^^ ' (6) 



Eliminating S\ and Si! fiom equations (4), (5), and (6) and solving 

 forG: 



G = 5o - ^^ [(5i - S,r + (52 - 5o)2 - (5: - 52)2]. (7) 



By building out either line 1 or line 2 with added series impedances 

 until 



5i = 52 = 5i2 (8) 



the expression for the ground-connection impedance simplifies greatly, 

 and incidentally the precision of the determination becomes greater 

 because the number of measurements involved is less. Under this 

 condition 



G = 25o - 5i2. (9) 



This latter case is the one that was actually used in measuring the 

 ground impedances. 



Since the distribution of ground currents about the buried ground 

 may be different under each of the three conditions that are measured, 

 there is undoubtedly some error in measuring the ground-connection 

 impedance by this method. This error is a second-order effect, how- 

 ever, so that the values determined are reliable within the precision 



