Chap. 10] 



ELECTRICAL METHODS 



747 



multiplied by the reciprocal of the ratio in eq. (10-42e). Hence, the correc- 

 tion factor is (r — h)/{r -f 6), and it is always less than and gradually 

 approaches 1 (for ratios figured in terms of Va/Vb) as the separation be- 

 comes smaller in comparison with distance. Ratios expressed in terms 

 of Vb/Va are reduced with the reciprocal of the above correction factor. 

 In stratified ground either a constant-spacing or an expanding-electrode 

 system is apphed. As shown in Fig. 10-776, the spacing 6 may be in- 

 creased in proportion to the center stake distance. A convenient electrode 

 separation is one-third of the center stake distance. Then, if 

 EA:EC:EB = 2:3:4, c equals x/3, so that eq. (10-42d) becomes 



(10^2/) 



|-^-/r^^-ir-| 



r -I 



Fig. 10-77b. Expanding electrode system. 



With the expanding system, the normal P.D.R. for homogeneous ground 

 (k = 0) is Va/Vb = 2. Hence, the correction factor is then constant and 

 equals ^. In comparison with the constant electrode system, the ex- 

 panding system has the advantage that the P.D.R.'s are larger and less 

 influenced by near-surface variations. 



For positive values of k, the series in eq. (10-42/) converge rapidly. 

 When a good conductor is underlain by a very poor conductor (k = 1), 

 the extreme ratio is about 1.3 for a constant electrode spacing of one half 

 the depth. This ratio occurs at a center stake distance of 1| times the 

 depth (see Fig. 10-77c). The same relation prevails for lesser resistivity 

 contrasts, although the curves become flatter and the peaks shift toward 

 values slightly greater than 1|. The simple relation between depth and 

 peak distance makes it possible to interpret measured P.D.R. values more 

 readily than resistivity values, provided that (1) a poor conductor occurs 

 beneath a good conductor, (2) only two layers are effpctive, (3) surface 

 interference is carefully eliminated, and (4) the observed ratios are reduced 

 for normal ratio. 



Curves like those illustrated in Fig. 10-77c may also be calculated for an 



