346 i?. S. Woodioard — Mathematical Theories of the Earth. 



appeared to ns one of the grandest objects of cosmologicai 

 studies, and we Lave had it constantly in view in establishing 

 the mathematical theory of heat."" This ambition, however, 

 was only partly realized. Probably Fourier underestimated 

 the difficulties of his problem for his most ingenious and indus- 

 trious successors in the same field have made little progress 

 beyond the limits he attained. But the work he left is a per- 

 ennial index to his genius. Though quite inadequately appre- 

 ciated by his contemporaries, the Analytical Theory of Heat 

 which ap>peared in 1820 is now conceded to be one of the 

 epoch-making books. Indeed, to one who has caught the 

 spirit of the extraordinary analysis which Fourier developed 

 and illustrated by numerous applications in this treatise, it is 

 evident that he opened a tield whose resources are still far 

 from being exhausted. A little later Poisson took up the same 

 class of questions and published another great work on the 

 mathematical theory of heat.f Poisson narrowly missed being 

 the foremost mathematician of his day. In originality, in 

 wealth of mathematical resources, and in breadth of grasp of 

 physical principles he was the peer of the ablest of his contem- 

 poraries. In lucidity of exposition it would be enough to say 

 that he was a Frenchman, but he seems to have excelled in this 

 peculiarly national trait. His contributions to the theory of 

 heat have been somewhat overshadowed in recent times by the 

 earlier and perhaps more brilliant researches of Fourier, but 

 no student can afford to take up that enticing though difficult 

 theory without the aid of Poisson as well as Fourier, 



It is natural, therefore, that we should enquire what opinion 

 these great masters in the mathematics of heat diffusion held 

 concerning the earth's store of heat. I say opinions, for, 

 unhappily, this whole subject is still so largely a matter of 

 opinion that in discussing it one may not inappropriately adopt 

 the famous caution of Marcus Aurelius : " Remember that all 

 is opinion." It does not appear that Fourier reached any 

 definite conclusion on this question, though he seems to have 

 favored the view that the earth in cooling from an earlier state 

 of incandescence reached finally through convection, a condi- 

 tion in which there was a uniform distribution of heat through- 

 out its mass. This is the consistentior status of Leibnitz, and 

 it begins with the formation of the earth's crust, if not with 

 the consolidation of the entire mass. It thus affords an initial 

 distribution of heat and an epoch from which analysis may 

 start, and the problem for the mathematician is to assign the 



* La question des temperatures terrestres nous a toujours paru un des plus 

 grands objects des etudes cosmologiques, et nous l'avions principalement en vue 

 en etablissant la theorie rnaihematique de la chaleur. Annales de Chimie et de 

 Physique, 1824. Tome 27, p. 159. 



f Theorie Mathematique de la Chaleur. Paris, 1835. 



