1374 WILLIAM M. BARRET 
Denoting the permeability of the media surrounding the casing by 
nu, we have by Coulomb’s law 
m m 
7 ee AC ae) 
m m 
pb eP’ Be (@ + 2?) 
As the triangles Pcn and fOP are similar, we may write 
cn Of b 
i n = eeneNbe 
° = (b? + x2)+ 
Substituting the value of Pn and reducing, we have 
bm 
~ pw (bt + xi G) 
cn 
Similarly, it is seen that 
kr Oe a 
Pr-a 
and kr @ pp! 
ch ee iI Ss (4) 
bm (a? + x)8 
Combining expressions (3) and (4) we find the vertical component 
of the anomalous field at the point P to be 
bm am 
dZ = = ———_, — ———"_,, 
pe Ee ow (+ xh 
(5) 
In like manner it may be shown that the horizontal component of 
the anomalous field at the point P is 
xm xm 
iH) Ss 2) 3. Se SS 
e+e p@ +a 
(6) 
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