IIo C. E. VAN ORSTRAND 
tions in the present records preclude the possibility of using this 
method of evaluating the constants for very many of the curves. 
Another method consists in computing the derivatives from a 
truncated power series that has been properly adjusted. In some of the 
fields, Salt Creek, for example, the depth-temperature curves possess 
a double curvature somewhat resembling a letter S. In these fields, 
the computation of the gradients from a truncated power series would 
lead to a misrepresentation of the facts. 
Scientists use the term ‘‘normal gradient” without realizing, per- 
haps, that the term can be defined in a great number of different ways, 
and that some of the mathematical definitions can not be realized 
experimentally. The definitions in common use, equations 7 and 8, 
imply an average of a great number of gradients distributed uni- 
formly or at random throughout a large area. This definition is 
theoretically correct but impossible of practical realization because 
of the very great number of observations required to determine an 
average that approaches a constant value. This is the method used 
by the Committee on Underground Temperatures of the British 
Association for the Advancement of Science in obtaining the com- 
monly accepted value of 1°F. in 60 feet. 
In the absence of complete evidence in the areas surrounding 
domes and anticlines, it is impossible to do other than to infer 
possibilities. About the only approach to a definite conclusion that 
can be made at present in regard to these areas is the possibility that 
the values of 1/b in Table II should be multiplied by factors which 
vary uniformly from a little more than unity for 1/5=150 feet per 
degree Fahrenheit to 3 or 4 times the tabular values as the lower limit 
of about 20 feet per degree Fahrenheit is reached. A closely related 
statement is the following: in oil-bearing areas, free from intrusives, 
the probability that a location is on a dome or the crest of an anticline 
increases from about o.5 to practically a certainty (1.0) as the values 
of the reciprocal gradients decrease from about 50 to approximately 
20 feet per degree Fahrenheit. 
Koenigsberger (8) has grouped geothermal data for different 
geologic and topographic features into 10 groups and concludes that 
the averages for the different groups differ from one another—that 
for the bituminous group, particularly petroleum, being higher than 
the others, except for areas of recent intrusives. 
Classification of the gradients in accordance with the sequence of 
geological epochs may provide a means of establishing a normal 
gradient for each epoch. The last gradient in the series would repre- 
sent a normal gradient for an undisturbed earth. 
770 
