this difference may be determined from the observed increase, and from a quantity depending on the nature of the ground. This remark and that of Laplace are not applicable to the localities where the temperature varies very rapidly round the vertical: it is shown that in these cases of exception the temperature varies even upon the vertical: and the law of this variation is determined from the variation which has taken place at the surface or in the exterior temperature. The mean temperature at a very small distance contains also a term which is not proportional to this depth, and which arises from the influence of the heat on the conductibility of the substance.
Chapter XII. On the Motion of Heat in the Interior and upon the Surface of the Earth.—It is shown that the formulæ of the preceding chapter, although relating to a homogeneous sphere the surface of which is everywhere in the same state, may notwithstanding serve to determine the temperatures of the points of the earth at a distance from the surface which is very small with regard to its radius, but which exceeds however all accessible depths. These formulæ contain two constants, depending on the nature of the soil, the numerical values of which may be determined in every point of the globe from the temperatures observed at different known depths.
Observation in harmony with theory shows that the diurnal inequalities of the temperature of the earth disappear at very small depths, and the annual inequalities at greater depths, in such a manner that at a distance from the surface of about 20 metres and beyond those two kinds of inequalities are entirely insensible. In this chapter are given tables of the temperatures, indicated by the thermometer, of the caves of the Observatory, at the depth of 28 metres. The mean of 352 observations, made from 1817 to the end of 1834, is 11°·834.
The increase of the mean temperature of the earth, in proportion as we descend below the surface, has long been established as a fact in all deep places, at different latitudes, and at different elevations of the soil above the level of the sea. The most adequate means to determine it is by sounding and boring. The results, still very few, which have hitherto been obtained are given. At Paris, this increase appears to be one degree for about 38 metres of increase in depth.
As to the cause of this phænomenon, the difficulties are stated which the explanation of Fourier presents, founded upon the original heat of the globe, still sensible at the present time near the surface; the new explanation alluded to at the beginning of this article is then proposed. The following reflections extracted from the work tend to prove that the solidification of the earth must have commenced by central strata, and that before reaching the surface the cooling of the globe must have been incomparably more rapid.
