NORMAL GEOTHERMAL GRADIENT 89 
ERRORS IN GRADIENTS 
A word of caution should be spoken in regard to errors in the 
observations. For example, the curves in Figure 2 are excellent 
examples of precise measurement; nevertheless, the resulting gradi- 
ents may be incorrect. The flattening of the Shumway curve as it 
enters the granite at a depth of about 2,700 feet is to be expected for 
the reason that granite is a better conductor of heat than sedimentary 
deposits. The extreme curvature, however, may be the result of 
swabbing oil from the well a few hours before the test was made. The 
extreme convexity of the Volcano well is due in part to surface 
topography. Unstable temperature equilibrium is a disturbing factor 
in a large number of the wells. As it is impossible to eliminate these 
errors and irregularities, it is necessary to bear in mind that our final 
determinations are to be regarded as rather rough approximations to 
the true values. Definitive determinations can not be obtained from 
existing data. 
FORMULAS FOR AVERAGING GRADIENTS 
It is impossible to correctly interpret the numerous averages of 
gradients that can be obtained without the assistance of mathematical 
analysis. In order, therefore, that we may properly interpret our 
results, let us consider the significance of the formulas by means of 
which the averages have been obtained. 
Let us put, 
yi = rise in temperature from a point just beneath 
surface of ground to depth x in well A, 
ye = same for depth x in well Ae 
Yn = same for depth x, in well A, 
Also, let us put for the residuals (v), 
%1 = yi — computed value of y; 
Ye = ye — computed value of Ye 
Un = Yn — computed value of y,. 
Then we have by definition: 
b = y:/x, = gradient in well A, 
b = yo/x, = gradient in well A» 
b = yn/%n = gradient in well A, 
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