ELECTRICAL PROSPECTING 15 
The wire is on the z-axis of rectangular coordinates, the y-axis is vertical 
and the x-axis is horizontal and perpendicular to the wire. Maxwell’s equa- 
tions for the conducting medium reduce to: 
E,= E£, = H.=0 




0H, OH, } 
ax Oy ee a en 
aE aly (40) 
ay = wyH, 
OF, = 
Ox ae 
or 
V7E. + k?E, = 0. 
The equations for the air may be obtained by setting o=0 and p=». Let us 
take 
E, = Epo in the air 
(41) 
E, = E in the earth. 
The boundary conditions then are 
Eo = E 
aty = 0 (42) 
dE\/dy = aE/day 
E=0Oaty=—h (43) 
and 
Eo — ko log (x? + y?)/2 as x, y 0. (44) 
The solution of these equations for Ep is | 
© Qe-¥ ho")? Cos Xxdd 
Ey = ko I —— __ i —. (45) 
0 (02 — Ro?) 1? + (2 = [g) ille coth h(r? att k?)1/2 
The normal field for a homogeneous earth is 
9 Qe-¥ rk) ® Cos Nxdd 
aah if oe (46) 
0 (r2 25 ko?)1/2 + (2 pad 2) 1/2 
Thus the change in the field due to the conducting layer is 
Ey — E, = ko f b(d)e-¥ "= #0")"” cos Nadd (47) 
0 
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