48 C. E. VAN ORSTRA ND 
surface of the hill must be taken into account. Thus, the value of a@ for six 
wells on the south side of the hill is 73.0+0.8; the same for 15 wells on the 
north side is 71.4+0.3, making a possible temperature difference on the two 
slopes of 1.6+0.9°F. Other observers have likewise found maximum tem- 
peratures on southern slopes.’ 
As a further explanation of the slight increment in the observed values 
of (1/b) as the crest of the hill is approached, a comparison must be made 
between the assumed gradient (a) beneath the plain and the theoretical 
gradient (a@,) beneath the summit of the hill. Using the value of H/d given 
in Table I and Fig. 8, and making the appropriate substitution in the equa- 
tion 
a,=a— H(a —a’)/d 
we obtain the values of a, tabulated in the first part of Table IV. In the sec- 
ond part of the table, (@,) is given for H=320 feet, H/d=0.245 240. 
Interpolating for our assumed reciprocal gradient beneath the plain, 
1°F in 53.86 feet, we find the value 1°F in 68.3 feet at the summit of the hill. 
That is, the computed variation from the plain to the summit of the hill is 
four or five times the differences, 3.1 and 2.3, shown between the highest and 
lowest groups on the structure in the last set of values in Table III. In one 
way only does it seem possible to bring theory and observation into agree- 
ment. Substitution in the equation, 
ov Hd 
SSG SCS) SS (10) 
0z (zg + H+ d)? 
which represents the gradient at any elevation (z) beneath the apex of the 
hill, we find for 
a = 0.00033 8412(1° F in 53.86 feet), a’ = 0.00005, H = 360 feet, 
the values, 
1/b=1°F in 62.5 feet z=0 meters 
=” S529? z=500 { 
=” 54:8) >? z=1000 < 
At z=o, 360 feet beneath the top of the hill, the theoretical difference of 
8.6 feet between the assumed and computed values of (1/6) greatly exceeds 
the observed differences, 3.1 and 2.3 feet, Table III; but at z=500 meters, 
corresponding to a depth of 2000 feet beneath the top of the hill, the observed 
differences slightly exceed the computed value of 2.0 feet. At greater depths, 
Eq. (10) shows that the gradients beneath the plain and the hill approach 
coincidence. 
To sum up the evidence at Long Beach, the elevation of the isotherms 
with reference to the topographic surface, and the small variation of gradient 
over the structure in comparison with the theoretical variation proves con- 
7 Edith M. Fitton, Soil temperatures in the United States. Monthly Weather Review 59. 
9 (1931). 
192 
