WAVE PROPAGATION 545 



where 



p"-^V{hx-Vh,Y+x' 



hV = h2Va 

 x' = x'\/a. 



From the preceding the series self impedance of the ground return 

 circuit may be conveniently written as 



Z = Z'+Z' (25) 



and the mutual impedance as 



Zi2 = Z?o+ZJo (26) 



where Z^, Z\i are the self and mutual impedances respectively, on the 

 assumption of a perfectly conducting ground, and 



Z'-4a; r"(ViuM^-M)e~'''''^M, (27) 



Jo 



Z(o =4co r (VfJ^-fJi)e~^'"'^''-^'' cos x'fi dfji. (28) 



»/o 



The calculation of the circuit constants and the electromagnetic 

 field in the dielectric depends, therefore, on the evaluation of an 

 infinite integral of the form 



J(p,q)=J= / (Vm-+*'-m)c-^^. cos qfjL dfx. (29) 



In terms of this integral 



Z' = 4co./(2/z'.0) (30) 



Z'i2-4co.J(/;/+//,',.V). (31) 



To the solution of the infinite integral J{p,q) we now proceed. 



Ill 



The solution of equation (29), that is, the evaluation of J(p,g) 

 can be made to depend on the solution of the infinite integral 



VpH^^.e-^^dfji 



