106 C. E. VAN ORSTRAND 
In the preceding summary, the values of 1/5 diminish uniformly 
with the depth. This is not the case in Tables I, II, and III. The dis- 
crepancies are the results of areal distribution of the wells. Table IV 
shows the results of attempting to eliminate these inconsistencies. 
In this table, the mean (m) of the ratios of the gradients for the differ- 
ent depths to the gradient computed for the first 1,000 feet has been 
tabulated. 
The first part of the table shows that the mean of 97 ratios of 
the gradients from 100 to 2,000 feet to the gradients from 100 to 
1,000 feet is 1.0523, the probable errors being represented as hereto- 
fore by r and 79, the latter being the probable error of the mean. 
Multiplying the mean ratio, 1.0523, by 0.01534, the value of 6 in 
the B group, Table I, we have for the mean gradient from roo to 
2,000 feet, the value, 0.01614, corresponding with the reciprocal gradi- 
ent 1°F. in 61.95 feet. The numbers in the remaining columns are com- 
puted in a similar manner. Two rejections occur in the first column 
of tabular results. The final sequence in the values of the reciprocal 
gradients, namely, 65.21, 62.58, 59.65, 54.65, shows that the normal 
curve is convex to the depth axis. The summary for Table III— 
62.14, 57-28, 55-97, 51.27—-shows a similar sequence, but the numer- 
ical values of the reciprocal gradients are greatly diminished, again 
showing the influence of the higher temperatures in the oil fields. 
The sequence for Table II—49.76, 50.57, 50.03, 47-40—Shows that 
an average of the depth-temperature curves on the crests of anticlines 
tends to approximate rather closely to a straight line. 
Summarizing the results of Table IV with reference to Tables II 
and III, we can say that the convexity of the depth-temperature 
curves increases as we pass from the crest to the flank of the structure. 
This experimental result is partly accidental, but it follows, also, 
from the geometry of the isogeotherms. Thus, for convenience, let 
it be assumed that a’’a’a and c’’c’c (Fig. 1) are isogeotherms. Then 
the gradients are determined by the constant difference in temperature 
between the two isogeotherms divided by the lengths ac, a’c’, a’’c’’. 
Since a’c’ is greater than ac, it follows that the gradient at a’c’ is 
less than at ac; but, since the temperatures must be the same at the 
depth at which the isogeotherms become parallel to a horizontal 
surface, it follows that the temperatures must increase much more 
rapidly along a’c’ extended than along ac extended. Hence the con- 
vexity of the depth-temperature curve a’c’ is greater than that of ac. 
Comparison of the B groups in Tables II and III shows that the 
reciprocals of the mean gradients vary from 49.76 on the crest to 
62.14 on the flank of the structure. As the tests were made mostly 
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