JR. S. Woodward — Mathematical Theories of the Earth. 347 



subsequent distribution of heat and the resulting mechanical 

 effects. But no great amount of reflection is necessary to con- 

 vince one that the analysis cannot proceed without making a 

 few more assumptions. The assumptions which involve the 

 least difficulty, and which for this reason, partly, have met 

 with most favor, are that the conductivity and thermal ca- 

 pacity of the entire mass remain constant, and that the heat 

 conducted to the surface of the earth passes off by the com- 

 bined 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 essential to nu- 

 merical calculations ; namely, the diffusivity, or the ratio of 

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

 initial uniform temperature. The first of these can be ob- 

 served, approximately, at least ; the second can only be esti- 

 mated at present. With respect to these important points, 

 which must be considered after the adoption of the consisten- 

 tior status, the writings of Fourier afford little light. He was 

 content, perhaps, to invent and develop the exquisite analysis 

 requisite to the treatment of such problems. 



Poisson wrote much on the whole subject of terrestrial tem- 

 peratures and carefully considered most of the troublesome 

 details which lay between 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 in- 

 crease of underground temperature is due to a primitive 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 out- 

 ward ;* so that according to this view the crust of our planet 

 arrived at a condition of stability only after the supply of heat 

 had been exhausted. But Poisson was not at a loss to account 

 for the observed temperature gradient in the earth's crust. 

 Always fertile in hypotheses, he advanced the idea that there 

 exist by reason of interstellar radiations, great variations in 

 the temperature of space, some vast regions being compara- 

 tively cool and others intensely hot, and that the present store 

 of terrestrial heat was acquired ■ by a journey of the solar sys- 

 tem through one of the hotter regions. " Such is," he says, 

 " in my opinion, the true cause of the augmentation of temper- 

 ature which occurs as we descend below the surface of the 

 globe."f This hypothesis was the result of Poisson's mature 

 reflection, and as such is well worthy of attention. The no- 



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



f '• Telle est, dous mon opinion, la cause veritable de l'augraentation de tem- 

 perature qui a lieu sur chaque verticale a mesure que l'on s'abaisse au dessous 

 de la surface du globe." — ibid., p. 15. 



