16 L. J. PETERS AND J. BARDEEN 
where A 
2(rx? — k?)4/2(1 — coth k(A? — k?)*/2) 
(A) = [02 — ho?) 2-4 (A? — 2) 1/2] [(A2 — ho?) "2+ (A? — £2) "/2coth h(a? — 2) ¥/2] 
(48) 
and the change in magnetic intensity is: 
ik = 
(Hz)o — (H:)2 = = (A? — ho)*h(d)e~¥ ra)? cos Axdh. (49) 
Kw Jo 
The power flow through a horizontal plane in the air per centimeter of wire 
length is 
C.) kor ky 
pa f [Bo — Ba][(H=)o~ Ha] *dx = if | 6A) | #(o? — d2)1/20n. (50) 
When k?>>2,? this integral reduces to 

py gee Bye (51) 
= ——_—_— — 5 
4uw | Rk | = 
where R and JZ are real and 
; Par 
R-+ it = tanh bl &| (< ). (52) 
The normal power flow through the plane for a homogeneous earth is: 
rho! 
= (53) 
4a | k? | 
As the frequency approaches zero, the ratio ko*/w lk |? approaches zero, so 
that both the normal power flow and the power flow of the change in field 
due to the layer approach zero. The ratio, however, is 
P/P, = (1 —R)? +7 (54) 
where 
(1 + 4) 
(2)3/2 
u = h| k| = 0.0281 Ameter(of)!/. 

R+ aI = tanh u 
The ratio p/p, is shown graphically in Fig. 8. It is a maximum at zero fre- 
quency, and then drops off as the frequency increases, approaching zero at 
very high frequencies. In this case the optimum frequency depends primarily 
on the measuring apparatus. The frequency should be chosen as low as the 
apparatus permits the field quantities to be measured accurately. 
The curve in Fig. (8) shows the absorption‘of the surface layer. If the 
conductivity of the surface layer is 10-* ohms and the depth to the conducting 
layer is 100 meters, the effect of the layer at a frequency of 3000 cycles is only 
160 
