of Lightning-Conductors. 223 



The second term has to do with the magnetization of the 

 conductor, and is, for high frequencies, very small. It is 

 interesting as showing that of the two terms in the quantity 

 " impedance*" 



or, as it becomes for condenser discharges, 



\/{* E,2 4'}> 



the second is always the larger; because, by (7), 



?iL' = R' + ?i/x/m 2 . 



Practically the second term is so much the larger that it is 

 the only one that matters, and so 



impedance = ?iL' = nL = n/juhu 2 = — j — = ij^ = a / ^ . . (8) 



impedance = 60, a /(21og 1 J ohms. . . (8') 



The total impedance, therefore, to a condenser discharge 

 is half the critical resistance which determines whether the 

 discharge shall be oscillatory or not ; it has no important 

 connexion with the ordinary resistance of the conductor; 

 neither does it depend appreciably on the magnetic permea- 

 bility of its substance. 



Hence, so long as the specific resistance of the conductor 

 does not rise above a certain limit, its impedance depends 

 almost entirely upon the amount of space magnetized round 

 it and upon the capacity of the discharging condenser, and is 

 barely at all affected either by the magnetic permeability, or 

 the specific resistance, or even the thickness, of the conductor. 

 The one thino- that does matter is its length. True the dia- 

 meter of the conductor does appear in the expression for 

 impedance, but only under a logarithm ; hence the effect of 

 varying the thickness is only slightly felt. 



The fact that impedance to a condenser-discharge is equal 

 to half the critical resistance, or ^/(L/S), and depends not at 

 all upon the ordinary resistance of the discharging circuit 

 (provided this keeps well below the critical resistance for which 

 the discharge ceases to be oscillatory), is manifest also from 

 equation (3'). 



Thus , then, we find that a lightning-conductor offers an 

 obstruc tion to a discharge as great as what a resistance of 



