46 C. E. VAN ORSTRAND 
heights. In making this comparison, I have attempted not to underestimate 
the computed heights. For example, the assumed elevations of the top of the 
hill above the level of the plain, namely 360 and 320 feet, instead of 296 feet 
given by Dr. Carlson, gives a rise of isothermal surface which is too high. 
Likewise, the substitution of a long ridge for a hill tends to make the com- 
-_puted values too high. An important possible exception, however, should be 
noted. Let us assume that the gradient beneath the plain is the steepest in 
the field corresponding to a rate of 1°F in 48.5 feet instead 1°F in 53.86 feet 
as used in constructing Table I. Hence we have 
a = 0.000 375 811 c, = 0.866 954 
and substituting in Eq. (9), putting c.=0 in order to represent the 0°F iso- 
therm, we find 299 feet instead of 293 feet as recorded in Table I. This dif- 
ference of 6 feet is rather insignificant in comparison with the large difference 
of more than 100 feet for which we require an explanation. Using the value 
a’ =0.00006 instead of a’ =0.00005, the corresponding rise is 288 feet instead 
of 299 feet. This shows that the value of a’ is of importance in determining 
the computed heights. Taken as a whole, however, the evidence substantiates 
the conclusion that the differences in elevation between the highest and low- 
_est points on the observed isotherms are abnormally large. 
COMMENTS ON THE Data OF OBSERVATION 
The tests in the Salt Creek field were made under conditions such that a 
close approximation to true rock temperatures is to be expected. Values of 
a in the equation 
y=a+ bx 
in which y=temperature at depth x; a=annual mean temperature just be- 
neath the surface of the ground; )=gradient, vary from 46.9 to 52.3°F. The 
mean from 19 wells is 49.8+0.2°F. The probable error r of an observation of 
weight unity is 1.0°F. Values of the.excess of soil temperature over air tem- 
perature (a—b, Figs. 1 and 6) range from 0.2 to 5.6°F. The mean is 
3.10+0.2°F. r= +1.0°F. 
At Long Beach, the temperatures just beneath the surface of the ground 
from 42 wells fall between the limits 68.4 and 77.2 with a mean value of 
71.640.2°F. r= +1.4°F. The maximum value of the excess of soil tempera- 
ture over air temperature is 14.6, the minimum, 5.8°F. The mean is 9.0 
+0.2°F. r= +1.4°F. 
The large range in the preceding values suggests the possibility that the 
temperatures in some of the wells that had been pumped are too high. The 
resulting error is a maximum at or near the surface of the ground and gradu- 
ally diminishes with more or less regularity to zero at the source of the rising 
column of oil or water. An obvious effect of this abnormality is to elevate the 
isotherms in amount roughly proportional to their elevation above the fluid 
bearing sand, and diminish the gradients or increase the reciprocal gradients 
in the same relative proportion. To ascertain the possible magnitude of this 
190 
