ELECTRICAL METHODS 489 



The use of these tables is facilitated by noting that 



Whence 



00 



^ ^- =-alog(l-0'')-arF 



i=l -y/l+ -■ 



a 

 The left-hand member of this equation is identical with the expression 





appearing in Equation 14 provided one sets a = -r-p 



Zd 



For most calculations only the difference in potential between two points is used 

 and the logarithmic term will enter the equations as an additive constant independent 

 of r. Hence, the logarithmic term can always be dropped, because the potential is not 

 unique to an additive constant. 



The potential V at any point on the x axis is 



!00 00 ) 



1 L_ 4.0 V Q^" o V q-" L... 



X L-x ^ Zdl^-' + 4k'd']'^ Zi[(L-xr + 4kW]''^(^^^ 



k=l k=l ) 



where / = current leaving the source at So (Figure 292). 

 pi = resistivity of overburden. 

 P2 = resistivity of subsurface layer. 



P2 + P1 



X = distance between So and the point on the surface at which the potential is 



V. 

 L= separation of energizing electrodes (^o and — So), 

 d = thickness of overburden. 



Application to JVenncr Electrode ConHgnration. — The Wenner con- 

 figuration consists of four electrodes mounted in a straight line along the 

 surface of the ground at distances 0, a, 2a, and 3a respectively. If the 

 power is applied between the outer two electrodes, the expression for the 

 potential produced at either of the two inner electrodes may be obtained 

 from Equation 16 by replacing L by 3a. That is, 



V 



,00 oo 



27rUr 3a-x'^ Zi\x'" + 4k^d-]v^ Zi \(3a-xV 



27rUr 3a-x'^ Zi[x'" + 4k^d-]v^ Zi [(3a - x)^ + 4k~d^]'^ 



kz=l k=l 



The potential difference between the two inner potential electrodes is 

 found by substituting x = a and then x = 2a into the above formula and 



