MUTUAL IMPEDANCE OF GROUNDED WIRES 



285 



the earth, extending up to the height //, and of width 2a. We can 

 now allow pi to become infinite, corresponding to the assumptions of 

 our problem, since this circuit is completed through the earth. Upon 

 allowing a to approach zero, such that 2a = dS, we find the field 

 corresponding to a rectangle of infinitesimal width. We then take the 



4 5 6 



VALUES OF r' 



Fig. 12 — Real and imaginary parts of 





integral of this expression around a similar circuit consisting of a 

 horizontal element of wire of length ds at the height h, grounded by 

 wires at its end-points. Upon making various algebraic simplifica- 

 tions, we finally obtain the mutual impedance as given by formula {A). 

 It is perhaps more convenient to derive this formula from results 

 obtained by H. von Hoerschelmann,' again following the method 



' H. von Hoerschelmann, "Uber die Wirkungsweise des geknickten Marconischen 

 Senders der drahtiosen Telegraphie," Jahrbuch der drahtlosen Telegraphic und 

 Telephonie, 5, 14-34, 188-211 (September, November, 1911). 



