PROPAGATION OF PERIODIC CURRENTS 545 



where, in accordance with equations (7) in Section I, 



Y,,k = ghk -{■ iuiqhk- (20) 



It should here be remarked that Yhk depends not only on the geometry 

 of the system and on the conductivity of the medium but also on any 

 direct leakage admittance existing between the wires themselves and 

 also on any between the wires and ground. The direct leakage 

 admittance between wires // and k, per unit length, will be denoted by 

 Y'hk and that between wire h and ground, by Y'hh\ these are regarded 

 as being uniformly distributed along the system. 



When there is present an impressed potential, the existence of the 

 direct leakage admittances gives rise to the following supplementary 

 terms for the right side of equation (19) : 



where 



FhY\u + E (/^. - F,)Y',u = Z XnuFu, 



Xhk = — Y'hk for k 9^ Ji, 



" , (21) 



^hi, = ^ Y hk- 

 t=i 



It is seen that Yhk and Xhk are of the nature of admittances (per 

 unit length), although they are not 'direct admittances.' Their pre- 

 cise meanings are readily deducible from equations (90). 



When the medium itself is of zero conductivity, ghk reduces to Xhk- 



