ON UNDERGROUND TEMPERATURE. 



Prepared for the Smithsonian Institution by Charles A. Schott, of the U. S. Coast 



Survey. 



The earth's solid crust being hotter than the mean temperature of the 

 lower atmosphere resting on its surface, heat is constantly and very 

 slowly- passing outward, and strata of equal depth would have very 

 nearly uniform temperatures but for the influence of the daily, the annual, 

 and the irregular variations of the atmospheric temperature, received by 

 conduction. The solar heat then acts as a disturbance of the thermal 

 equilibrium, and the depth of the stratum of the so-called "invariable 

 temperature," i. e., when the changes escape ordinary observation or 

 become less than 0°. 01 C, as generally defined, is found about 6 meters 

 below the surface in the tropics, and about 30 meters below the surface 

 in the middle latitudes. The corresponding depths at which the daily 

 variations become imperceptible are 0.3 meter and 1.3 meter very nearly. 

 These numbers, however, depend greatly on the kind of soil or rock, 

 and will differ considerably for loose soil of greater or less porosity 

 and for solid rock. Our records of observations are very scanty and 

 deficient in range, and barely afford the necessary data to form a basis 

 of calculation, on account of the many conditions which enter into the 

 problem. 



It would appear from experience that the mean temperature of the 

 air, as ordinarily observed, say at an elevation of 1 or 2 meters above 

 ground, is slightly higher than the mean temperature of the surface of 

 the soil. The mean temperature of the earth's crust increases from the 

 surface, with increasing depth, and with a nearly uniform rate for 

 moderate depths, with an average amount of about 28 meters for each 

 degree of the centigrade scale, and the temperature at the depth of in- 

 variable heat nearly equals the mean annual atmospheric temperature 

 of the place, but slightly exceeds it in amount. For greater depths the 

 descent to produce an increase of 1° C. is greater than the amount given 

 above. With increase of depth the amplitude of change is rapidly 

 diminishing, and for a depth increasing arithmetically the amplitudes 

 diminish in geometrical ratio; also the depth at which the daily and 

 annual variations, respectively, disappear is in proportion of the square 

 root of the length of these periods, or about 1 to 19. The amplitude Ai) 

 has been represented in the form, log J p = A — J^p, where A and B are 

 constants to be determined at the place, and j9 the depth. Observa- 

 tions by Quetelet at Brussels, for instance, give the following result: 

 log Ap = 1.15108 — 0.04119^9, (amplitude in degrees centigrade and jp in 



