Measuring Conductivity along a Glow Discharge. 353 



is not electrically connected to the Lecher wires the theory 

 can still be reduced to the case as shown in fig. 1, where a 



Fig. 1. 

 B A 



■o — - 



system B having a capacity C and resistance R in shunt is 

 connected to the Lecher wires BD. For when the body 

 is disconnected from the wires as in fig. 2 a, this system can 

 always electrically be replaced by that of fig. 2 b y i. e. by a 



Fig. 2 a. 



q=s= ?R, 



c, 



) 



c 2 



condenser C and resistance R directly connected to the 

 Lecher wires. If the capacities Ci, C 2 , C 3 and resistance R 3 

 of the loose system of fig. 2 a are given together with the 

 angular frequency oj, C and R of the equivalent fig. 2 b will 

 be uniquely determined by the conditions : 



1_ !_•(!_ 1 \ 



. 1 >\d + cJ' 



where j = V — 1. 



When the resistance in the Lecher wires is, for the time, 

 neglected and the distance from the inserted system B to the 

 first potential node A (fig. 1) is called I, the resonance value 

 of I will be given by * 



, 4ttZ 2b n . 



tan r=?rp3T' « 



where the numerical quantities a and b represent 



c 



b = 27rC _ wC 



" AC "~ cO ' 



* Drude, Wied. -4*i«. lxi. p, 466 (1897). 



