Forms of the Lines of Electric Force. 305 



Confining our attention to points in the plane of the wires 

 we thus obtain for points between the wires the values 



Z=Dlbg^, i 



R=-D^( 1 + r ^) ! (6) 



H=-D^(- 1 + J-)\ 



pr \r b — rj } 







per \r 



b — rj 1 



and for 



point; 



3 not between 



i the wires 





Z = 



Dlog r , 



j 





R = 



- D ^- 



1 N ' 

 b+.r)' ," 





H = 



-D^Yi- 



-^ 



(7) 



The further discussion of phase-differences and lines of 

 force is a good deal simplified by the fact that the constant 



2i 



— , which appears in " Z n for a single wire, goes out in the 



present case. 



An application of the surface conditions leads to the equation 

 for c 2 



C log - = ? T 7 — ' (b) 



° a h' 2 ao i{h: 2 a) 



§ 3. The Relative Phases of the Components. 



We shall now investigate the phase-differences existing 

 between the periodic magnitudes ZRH in the dielectric at 

 the surface of a wire. As the expression for Z is real, the 

 arguments of the complex quantities occurring in R and H 

 will give their phase-differences in advance of Z. Let a and 

 /3 represent these quantities for R H respectivelv, so that if 

 at a given point of the wire we have 



Z = Z sin pt, 



we shall have R = R sin (jit + a), 



K = E i) >m( 1 ,t + ;3). 



