CORRELATION OF ISOGEOTHERMAL SURFACES 45 
(9) gives the elevation beneath the apex of the hill of that particular isotherm 
which is asymptotic to c2. The difference between z and cz is equal to the rise 
of the isothermal surface above its asymptotic plane. Thus in Fig. 8, oa rep- 
resents the rise of that isothermal surface which is just beneath the surface 
of the plain, (¢:=0), and which has ox extended for an asymptote; bb’ repre- 
sents the rise of that surface whose asymptote is perpendicular to the axis 
of the hill at 6’; and so on. These values are tabulated in Table I. The table 
applies to any other hill of the same cross-section and the same geothermal 
gradients (a and a@’) beneath the plain and along the mountain slope. To 
determine the temperature represented by any isotherm, it is merely neces- 
sary to add the tabular value in the table, or Fig. 8, to the annual mean 
temperature of the ground just beneath the surface of the plain. 
In order to compare the theoretical rise of the isogeothermal surfaces 
with the observed, the gradient beneath the plain was assumed to be, a 
=0.000,338,412, corresponding to a rate of temperature increase of 1°C in 
29.55 meters, or 1°F in 53.86 feet. This value is an approximate average of 
the gradients for 42 wells in the Long Beach field. From the same wells, the 
average annual mean temperature just beneath the surface of the ground was 
found to be, vo=71.6+0.2°F. Hence, the 80°F isotherm corresponds to a 
temperature difference in Table I of 8.4°F. Interpolating, we find the rise of 
the isotherm to be 215 feet. The last two columns of Table II were obtained 
by a repetition of this process, using for the last column a table similar to 
Table I. In column 4, the level of the plain was assumed to coincide with sea 
level; in the last column of the table, it is taken to be 40 feet above sea level. 
The data for the transverse section of the hill, Fig. 8, were kindly forwarded 
to me by Dr. A. J. Carlson. The observed differences in elevation of the sur- 
face of the ground and the isotherms, column 3, Table II, are taken from 
his paper on “Geothermal variation in the oil fields of Los Angeles Basin, 
California.”* 
Comparison of column 3 of Table II with the last two columns shows 
that the observed heights are somewhat more than twice the computed 
TABLE II. Rise of tsogeotherms. 
Differences in elevation 
Depth 
Isogeotherms beneath Assumed Assumed 
F bin Chee computed Computed 
ee ee ee 
296 360 320 
80 453 492 215 189 
90 991 348 166 144 
100 1530 274 136 118 
110 2068 223 116 100 
120 2607 182 100 86 
130 3146 200 89 76 
140 3684. 141 80 68 
150 4223 — did 62 
Lower Brown 
ne —_ 1100 — — 
189 
