192 THE MATHEMATICAL THEORIES OF THE EARTH. 



quent distribntioii of heat and Ibe resulting? inecbanical effects. But no 

 great amount of reflection is necessary to conviiu^e one that tlie analysis 

 can not pi0(;ee(l without making a lew more assumi)tions. The assump- 

 tions which involve the least dilhculty, and which for this reason, partly, 

 have met with most favor, are that the conductivity and thermal capacity 

 of the entire mass remain constant, and that the heat conducted to the 

 surface of the earth passes ott" by the combined process of radiation, 

 convection, and conduction, without producing any sensible effect on 

 surrounding space. These or similar assumptions must be made before 

 the application of theory can begin. In addition, two data are essen- 

 tial to numerical calculations, namely, the dift'usivity, or ratio of the 

 conductivity of the mass to its thermal capacity, and the initial uniform 

 temperature. The first of these can be observed, approximately, at 

 least; the second can only be estimated at present. With respect to 

 these important points which must be considered after the adoption of 

 the conHistentlor status, the writings of Fourier afford little light. He 

 was content perhaps to invent and develop the exquisite analysis requi- 

 site to the treatment of such problems. 



Poisson wrote much on the w'hole subject of terrestrial temi)eratures 

 and carefully considered most of the troublesome details which lay be- 

 tween his theory and its application. While he admitted the nebular 

 hypothesis and an initial fluid state of the Earth, he rejected the notion 

 that the observed increase of underground temperature is due to a prim- 

 itive store of heat. If the Earth was originally fluid by reason of its 

 heat, a supposition which Poisson regarded quite gratuitous, he con- 

 ceived that it must cool and consolidate from the center outwards ; * so 

 that according to this view^ the crust of our planet arrived at a condi- 

 tion of stability only after the supply of heat had been exhausted. ]5ut 

 Poisson was not at a loss to account for the observed temperature gra- 

 dient in the earth's crust. Always fertile in hypotheses, he advanced 

 the idea that there exists bj' reason of interstellar radiations, great 

 variations in the temperature of space, some vast regions being com- 

 paratively cool and others intensely hot, and that the present store of 

 terrestrial heat was acquired by a journey of the solar system through 

 one of the hotter regions. " Such is," he says, " in my opinion, the true 

 cause of the augmentation of temperature which occurs as we descend 

 below the surface of the globe."t This hypotheisis was the result of 

 Poissou's mature reflection, and as such is well worthy of attention. 

 The notion that there exist hot foci in si)ace was advanced also in an- 

 other form in 1852 by Rankine, in his interesting speculation on the 

 re-concentration of energy. But whatever we may think of the hypoth- 

 esis as a whole it does not appear to be adequate to the case of the 



*77«forie Mathcmatiqne dr la Chalrur, Hiippli^moiit de, I'aris, ^^!!?7. 



t" Telle est, dans inon ojtiiiioii, la cause v(^rital)lo <lo I'anfxtiioiitatioii do tenip6ratnre 

 qui a lieu siir clia<|ue vcrtiralo a inesure que I'lm H'attaisso au-ilessoiw de la surface du 

 globe." — Thcorie Matln'matiquc dc la Chaleur, yupiilemout de, p. 15. 



