192 THE MATHEMATICAL THEORIES OF THE EARTH. 



quent distribution of heat and the resulting mecbanical effects. But no 

 great amount of reflection is necessary to convince one tbat the analysis 

 can not proceed without making a few more assumptions. The assump- 

 tions which involve the least difiQculty, and which for this reason, j)artly, 

 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 oft" by the combined process of radiation, 

 convection, and conduction, without producing any sensible eft'ect 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, namelj-, the diffusivity, 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 consistentior 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 whole subject of terrestrial temperatures 

 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 supplj- of heat had been exhausted. But 

 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 by 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 jiresent 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 

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

 The notion that there exist hot foci in space was advanced also in an- 

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

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

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



* Theorie MatMmatique de la Chaleur, Supplement de, Paris, 1837. 



t" Telle est, dans nion opinion, la cause v<5ritable del'augmontatiou de temperature 

 qui a lieu sur chaque vtirticale a mesure quo Ton .s'abaisseau-de.ssoiis de la surface du 

 globe." — Theorie Mathematiquc de la Vhaleur, yupplement de, p. 15; 



