92 C. E. VAN ORSTRAND 
from which the values of a and 6 can be obtained by algebraic meth- 
ods. The weights of a and 6 are respectively: 


(2x)? (2x)? 
fo =n’ — =a po = Zx* — ae (12) 
In these equations, 
Da = x x2 + + + a, 
Ly =n t+ y+: - yn’ 
Ley = xy + xeye- > - Xn' Yn’ 
Ba ia pn 
Equation 12 shows that the weight of 6 is dependent on n’, the 
number of observed points in the well, and also on the distribution 
of these points in the well. 
AVERAGES DEDUCED FROM TABLE I 
The summary at the end of Table I shows that it is based on a 
total of 658 wells. The total number of fields and single locations rep- 
resented is 155. Out of this total of 155 wells, 139 wells reached a 
depth of 1,000 feet; 102 wells reached a depth of 2,000 feet; and so on 
for the other depths. The average depth (m) of the 155 wells is 2,781 
feet. In fields in which there are more than one well, that well has been 
selected in which the gradient is a minimum or the reciprocal gradient 
is a maximum. When there is precise correlation of temperature with 
structure, the well thus selected is, of course, the lowest on the struc- 
ture. 
Comparison of the values of 1/0 in the last column of the summary 
with the tabulations in the third from the last column shows without 
exception that the smaller values are always found in the last column. 
The reciprocal of the mean of 6 average values of the gradient in 
the second from the last column is 61.60; in the last, 59.16, leaving 
a difference of 2.44 feet per degree Fahrenheit. This difference is 
readily explained. Referring to Figure 2, it will be seen that a straight 
line drawn from g, or, more accurately, from a point 1°F. above g, 
to the 4,400-foot point on curve BB’, makes a greater angle with the 
depth-axis than the straight line ff which is adjusted by the method of 
least squares to all of the points on the curve BB’. The reverse con- 
dition exists for the concave curves AA’, but the convex curves out- 
number the concave curves about 2 to 1; consequently, the average 
for a number of curves reflects the more rapid rise of the convex curves. 
752 
