PROPAGATION OF PERIODIC CURRENTS 531 



qhk being the Maxwell capacity coefficient given by (89). Further- 

 more, the systemic axial electric force Eutt occurring in (93) is expres- 

 sible in terms of the current Ik in wire k and the axial electric force fk 

 impressed on wire k, by the simple relation 



Ek^ = Zklk - fk, (94) 



Zk denoting the internal impedance of wire k, per unit length; for, 

 the resultant axial electric force at wire k must be equal to Zklk and 

 must also be equal to Ek^r + fk- Thus the axial gradients of the 

 charges can be expressed explicitly in terms of the currents and the 

 impressed axial electric forces at the wires, by substituting (94) in (93). 

 The axial gradients of the charges can be expressed still otherwise by 

 dififerentiating (88) with respect to x after substituting (91). 



Substituting into (85) and (87), the various foregoing expressions 

 for the charge Qh and its axial gradient dQn/dx, and in some cases trans- 

 forming and rearranging the results, gives the following formulas for 

 the potential Fjv and the axial electric force £jv produced at any 

 point X in the secondary wire j by the primary system t, when the 

 presence of the secondary ;' is entirely ignored in calculating the cur- 

 rents, charges, and potentials of the primary (in accordance with the 

 statement of the paragraph following equation (87)) : 



^;V = E PjhQk (95) 



= t TinVn. (96) 



ft=i 



= - E r 



A=l 



ih 



tw,k(^+tXkrFr) 



t=i \ ax r=l I , 



(97) 



where Tjh, which may be termed a 'potential transfer factor' or 'volt- 

 age transfer factor,' has the value 



n 



Tjh = L Pikqkh. (98) 



fc=i 



£,>=-EZ„A-^' (99) 



^ -t{zi,h + p/-^) (100) 



ft=l 



dx 



h=l 



= -Z(Z,J,+ T,.-j^) (101) 



