122 C. A. HEILAND 
Bardeen (ref. list No. II;), and Ehrenburg and Watson (ref. list No. 
TI). 
Very little is available on the theory of interpretation of results 
obtained by the single-probe method. It seems, however, that the re- 
sults obtained by this method are generally not nearly as difficult to 
interpret as those obtained by the 4-terminal Gish-Rooney method. 
For the single-probe method in its application, illustrated in Figure 
7, IIa, the thumb rule that the depth of discontinuities of resistivity 
is approximately equal to the arithmetic means of the two potential 
probe distances at which a marked change in resistivity is observed 
generally works well. This holds in particular if the distance PR is 
much smaller than E,P; otherwise, the rule that k=/2bc should be 
applied. Thus, if £,P is used equal to PR (method II), the depth of 
the geologic body becomes equal to the electrode separation at which 
its influence is noticed, or h=a. 
It is beyond the scope of this paper to go deeply into the details 
of the theory of interpretation. However, several diagrams are given 
which represent the results of theoretical computations of the effect 
of vertical changes in resistivity on the 4-terminal method. 
Figure 16 illustrates curves of apparent resistivity for the 2-layer 
case, and for various ratios of the resistivity of the lower layer di- 
vided by the resistivity of the upper layer. The corresponding values 
4 
of & mean the ratio: f 2 
p +p 
as ordinates, the abscissas being electrode separations; for the pur- 
poses of interpretation, however, it is more instructive to make the 
depth axis the ordinate and plot the observed resistivity values as 
abscissas, in accordance with the statement previously made that, in 
a general way, marked changes in resistivities occur at electrode sepa- 
rations a which are equal to the depth / of the resistivity discontinuity 
underneath. (Or else, this depth / is by a constant ratio greater or 
smaller than a, which is taken into consideration in the diagrams, as 

. The observed resistivities may be plotted 
not k, but is plotted.) 
Thus, we see from Figure 16 that for all resistivity ratios the 
interface between surface layer and bottom layer coincides approxi- 
mately with the inflection point in the curve. The abscissas, by the 
way, do not represent the observed apparent resistivities directly, 
but the ratio of the observed resistivities to the resistivity of the 
upper layer. For the reason just stated, the ordinates likewise do not 
452 
