I3i M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 



this ditt'erence 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 tempera- 

 ture varies very rapidly round the vertical : it is shown that in these 

 cases of exce25tion 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 formulae 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 I'adius, but whrch exceeds 

 however all accessible depths. These formulte 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 

 Obsei-vatory, 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 de- 

 gree for about 38 metres of increase in depth. 



As to the cause of this phaenomenon, 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. 



