88 C. E. VAN ORSTRAND * 
type, the reciprocal gradients increase with depth, whereas in curves 
of the convex type just the reverse condition exists. Thus in the latter 
case, the reciprocal gradients diminish from 116.3 to 67.8; in the 
former, they increase from 38.8 to 56.0 feet per degree Fahrenheit. 
In some fields, the predominating curve is a combination of curves 
of the concave and convex type. 
TABULATIONS OF DATA 
The gradients (6) in Table I are tabulated for different groups 
of depths, namely, roo to 1,000 feet; 100 to 2,000 feet; and so on. 
This means that the constants in the straight line equation, y=a+6z, 
have been computed for each group of observations. In the first 
group, only those curves are included which reach a depth of 1,000 
feet or more. Curves of depth less than 1,000 feet are included in 
the column designated “roo—Total Depth.” The columns marked 
““t00-2,000 feet”’ include all curves that reach a depth of 2,000 feet 
or more, and so on for the 3,o00- and 4,o00-foot columns. 
The gradients tabulated in the column, “‘too—Total Depth,” are 
obtained by making a least-square adjustment of a straight line 
(dd or ff) through all of the points on the curve. In the following 
column, the values of 1/6, the reciprocal gradient, are given in feet 
per degree Fahrenheit. In the last column, the gradients have been 
computed from the annual mean temperature of the air (g, Fig. 2) 
and the single observation at the greatest depth in the well. As the 
annual mean temperature of the soil just beneath the surface of the 
ground must exceed the annual mean temperature of the air just 
above the surface of the ground, the constant value, 1°F., was added 
to the annual mean temperature of the air as interpolated from the 
volume on Climatological Data of the United States Weather Bureau. 
This value of the excess of soil temperature over air temperature was 
adopted by the Committee on Underground Temperatures of the 
British Association for the Advancement of Science in its report for 
the year 1882. The excess varies somewhat from place to place. An 
average value of 1.54°F. has been deduced from 514 tests in the 
United States (3). The values of the gradient in the last column are 
subject therefore to revision when the values of the excess of soil 
temperature over air temperature and the annual mean temperature 
of the air at the station are known more accurately; but the re- 
maining tabulations of the gradients, being obtained from least- 
square adjustments of the original observations, are not subject to 
revision. 
748 
