52 SYLVAIN J. PIRSON 
precautions should be taken in order that the depth of penetration 
of the electrode stakes shall not exceed 1/5 of the electrode spacings. 
It is recommended that measurements be made for different values 
of the current, and of the commutating frequency. Since the value of 
the method depends greatly on the accuracy with which the resistivity 
of the top layer is known, too much precaution can not be taken in 
this determination. 
2. pi is plotted to scale on the resistivity axis and a line drawn 
from p; to meet tangentially the first part of the curve. 
3. Resistivities are read for several electrode spacings on the curve 
just drawn and Tagg’s method is applied to that first part of the 
curve. The process yields the resistivity of the second layer pe, the 
P2— Pi 

thickness of the first layer 4, and the resistivity factor Ki= zs 
p2T P1 
4. The depth to the third layer is estimated by Lancaster-Jones’ 
method. Thus 4,+/2,=3d where d is the distance to the inflection 
point comprised between the two lower maximum curvature points. 
5. The apparent or average resistivity p’; of the two layers of 
resistivities pi and pe in parallel is calculated by the formula: 
hy + he hy he 
+ 
p's Pi p2 

6. Tagg’s method is then applied to the bottom part of the curve. 
A more accurate depth h’, than the one previously estimated is then 
obtained by tracing the curve’s depth-resistivity factor. When they 
converge in a small area, the depth #,+h’2 and the resistivity factor 
P3— p2 
K,= 

are known with a fair degree of accuracy. From this 
pat pe 
expression of K», the value of the resistivity p3 of the lower medium 
supposedly of infinite vertical extent can be calculated. 
7. If the degree of accuracy with which 4,+h’2 is known is not 
sufficient, the process may be recalculated once more by using 41+A’2 
instead of $d in the calculation of the average resistivities of the 
two top layers. A value p’’; will be obtained and a more accurate 
value h,+h’’, will be found for the depth to the third layer. In other 
words, the mathematical process known as the “Successive Approxi- 
mation method” is proposed. 
A practical example worked from an actual resistivity curve is 
given here, 
The problem is one of water-table determination which was 
worked by Tattam (curve 26) in the Newman district (New Mexico). 
712 
