42 SYLVAIN J. PIRSON 
The medium £, n, ¢ obtained by the preceding transformation of 
codrdinates will be rendered homogeneous by making the following 
substitutions for the horizontal and vertical resistivities. 
I 
Pih see 
a/ at 
p’ 1» = Piv Joy 
‘ 
Pik 

where p’, and p’;, are the resistivities parallel with, and perpendicular 
to, the bedding surface in the medium &, 7, ¢. 
Similarly the medium 2 will be reduced to homogeneous con- 
ditions by the following transformation: 

E! = ay/on 
n! = yor 
, =g 
II. - 
pes = pa — 
V/ a2 
p'20 = P2v Jon 
In order that the points at infinity in medium 2 shall correspond 
with the points at infinity in medium 1, it is necessary to expand 
: ay : ° 
the medium £’, n’, ¢’ by the factor —, horizontal and vertical 
ae 
dimensions as well. The transformation II becomes: 

£ = a/ay 
n = n/a 
¢ en 
— Zz —— 
II. a2 
DR a5 
P 2k = P2h 
ae 
p' 2» = Pov Jay 
We have thus reduced media 1 and 2 to a single system of co- 
ordinates £, 7, § in which we have homogeneous and isotropic con- 
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