ANISOTROPY IN APPARENT RESISTIVITY CURVES 41 
where 2, 7 and & are unit vectors taken along the axes ox, oy, and oz. 
Since we must have conservation of the vector current, we find that 
the divergence of J is zero: 
oy ( 1 Oza TOs Va I —) 
Sy ore, (iy (frst fax toh Sih 
pin Ox? pir Oy? fin OF 



Thus Laplace’s equation in the anisotropic medium considered 
becomes: 



I (— —) I 07V;, 
pin \ Ox? Oy? Piy O22 
If we substitute in this equation 
we obtain the equation: 
OVinn OV Oz Va 
=F aF 
of On? 0c? 

which is the ordinary Laplace’s equation. We have thus reduced the 
space xyz into a space &, 7, £ in which Laplace’s equation is satisfied 
but where the dimensions are expanded by the factor /py, in the 
horizontal directions and 1/p, in the vertical direction. 
If we leave the vertical dimensions unchanged, the horizontal 
dimensions of the space x, y, z, are then expanded by a factor 
Pir sale 
4/ — = Va 
Plv 
in order to obtain a medium £, 7, ¢ in which Laplace’s equation is 
satisfied. Thus we have the transformation: 
E = xa/o 
I. n= yor 
G¢=2. 
701 
