134 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 
this difference may be determined from the observed merease, 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 tempera- 
ture 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. 
Cuarter XII. On the Motion of Heat in the Interior and upon the 
Surface of the Earth—It is shown that the formule 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 sur- 
face which is very small with regard to its radius, but which exceeds 
however all accessible depths. These formulz 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 ob- 
served at different known depths. 
Observation in harmony with theory shows that the diurnal inequali- 
ties 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 di- 
stance 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 119834. 
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 de- 
gree for about 38 metres of increase in depth. 
As to the cause of this phenomenon, 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. 
