THE MATHEMATICAL THEORIES OF THE EARTH. 101 



build a great part of the super-structure of our modern tbeory of heat 

 dittusioD, his avowed desire being to solve the great problem of terres- 

 trial heat. "The question of terrestrial temperatures," he says, "has 

 always appeared to us one of the grandest objects of cosmological 

 studies, and we have had it princii)ally in view in establishing the 

 mathematical theory of heat."* This ambition however was only 

 l)artly realized. Probably Fourier underestimated the dihiculties of 

 his problem, for his most ingenious aud industrious successors in the 

 same field have made little progress beyond the limits he attained. 

 But the work he left is a perennial index to his genius. Though quite 

 inadequately appreciated by his contemporaries, the Analytical Theory 

 of Heat, which appeared in 1820, is now conceded to be one of the epoch- 

 making books. Indeed, to one who has caught the spirit of the extraor- 

 dinary analysis which Fourier developed and illustrated by numerous 

 applications in this treatise, it is evident that he opened a field 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, t Poisson narrowly missed being the fore- 

 most mathematician of his day. In originality, in wealth of mathe- 

 matical resources, and in breadth of grasp of physical princii)les he was 

 the peer of the ablest of his contemporaries. 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 with- 

 out the aid of Poisson as well as Fourier. 



It is natural, therefore, that we should inquire what opinions these 

 great masters in the mathematics of heat dift'usion held concerning the 

 earth's store of heat. I say opinions, for, unhapi>ily, 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, " Ee- 

 member 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 condition in which there was a 

 uniform distribution of heat throughout its mass. This is the amsisten- 

 tior status of Leibnitz, and it begins with the formation of the eartli's 

 crust, if not with the consolidation of the entire mass. It thus atfords 

 an initial distribution of heat and an epoch from which analysis may 

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



* "La question ties temperatures terrestres nous a toujours paru un des plus <i;randsj 

 objets des 6tude8 cosrnolo^iques, et nous I'avions principalement en vue en ^tablissant 

 la th^orie niathduiatiquo de la clialenr." Annalcs de Chimie et de Physique, 1824, tome 

 XXVII, p. 1.59. 



t Theorie MuthnnatUjtn' de la Chohiu-j PiU'is, 1^3.'). 



