ELECTRICAL METHODS 



475 



the current source. Let V\ and V2 be the values obtained at these two 

 points. From Equation 6 



Fx = ^^ and F2=^- 



2ir a 



2ir 2a 



In particular, if the source and the two points (a and 2a) lie in a straight 

 line, 



2Tr\_a 2a J A-n 



P_ 



Atra 



(7) 



or 



p = A-rra 



Vx-V. 



In practice the conditions of this problem are approximately satisfied by 

 placing the current or energizing electrodes at two widely spaced points 

 and measuring the potential difference Fi — V2 between two points which 

 are close to one of the energizing electrodes. This method is known as 

 the uni-electrode method for measuring resistivity, t 



Fig. 282. — Source and sink in a delimiting plane. 



Case III. — The conditions of Case II cannot be exactly satisfied in 

 practice, because it is impractical to separate the two energizing electrodes 

 by a sufficiently large distance. Practical measurements of resistivity, there- 

 fore, are based on the solution of a mathematical problem in which a source 



t F. W. Lee, J. W. Joyce and P. Boyer, "Some Earth Resistivity Measurements," U. S. Bur. 

 of Mines Inform. Circ. 6171 (1929). 



L. Gilchrist, "Measurements of Resistivity by the Central Electrode Method at the Abana 

 Mine, Northwestern Quebec, Canada," A.I.M.E. Geophysical Prospecting, Tech. Pub. 386 (1931). 



