i4 L. J. PETERS AND J. BARDEEN 
The ratio of the power flow of the change in field to the normal power flow is: 
370 Mea 2.81 X 10-3 
PE ; DAL ela EO) er 80) (35) 
where 
(= Rte 1 
sy io 36 
g(u) = u Meer Nr Cy (36) 
u = h(pow)!'!? (37) 
L4i 
tanh wu —— = R+i7]. (38) 

Ge Ren ss 7 
Fig. 7. Power ratio curve for vertical electric dipole. 
Fig. 7 gives a graph of g(u) which shows a maximum at u=0.29. This gives 
the optimum frequency in terms of the depth of investigation and the con- 
ductivity of the upper beds. This frequency is 
10° u? (0. 29)?- 10° 107 
827° ho 817 hea hima 


if h is measured in meters. If ¢-=10-4 and h=100 meters, the best frequency 
to use is about 100 cycles. If h=300 meters the optimum is about 10 cycles. 
At higher frequencies the effect of the conducting layer on the field becomes 
smaller. Thus for o=10~4 and h=100 meters, the effect of the layer with a 
frequency of 2500 cycles is only about one tenth of the effect at 100 cycles. 
At very low frequencies only a small percentage of the power input enters 
the ground. At high frequencies, most of the power that enters the ground is 
absorbed by the surface layers. 
A similar investigation has been carried out to determine the effect of a 
highly conducting layer on the field of a long horizontal wire carrying an 
alternating current. As in the previous case, the earth is assumed homogene- 
ous with conductivity o to a depth h, below which the conductivity is infinite. 
158 
