Matheviatical Theories of the Earth,— Woodimrd- 275 
important factors in the mechanics of such masses, the picture which 
Roche draws of the constitution of our planet will present nothing 
incongruous. 
In a field so little explored and so inaccessible, though hedged about 
as we have seen by certain sharply limiting conditions, there is room 
for a wide range of opinion and for great freedom in the play of 
hypothesis ; and though the preponderance of evidence appears to be 
in favor of a terrestrial mass in which the reign of pressure is well- 
nigh absolute, we should not be surprised a few decades or centuries 
hence to find many of our notions on this subject radically defective. 
If the problem of the constitution and distribution of the earth's 
mass is yet an obscure and difficult one after two centuries of observa- 
tion and investigation, can we report any greater degree of success in 
the treatment of that still older problem of the earth's internal heat, 
of its origin and effects ? Concerning phenomena always so impressive 
and often so terribly destructive as those intimately connected with the 
terrestrial store of heat', it is natural that there should be a considera- 
ble variety of opinion. The consensus of such opinion, however, has 
long been in favor of the hypothesis that heat is the active cause of 
many and a potent factor in most of the grander phenomena which 
geologists assign to the earth's crust ; and the prevailing interpretation 
of these phenomena is based on the assumption that our planet is a 
cooling sphere whose outer shell or crust is constantly cracked and 
crumpled in adjusting itself to the shrinking nucleus. 
The conception that the earth was originally an intensely heated and 
molten mass appears to have first taken something like definite form 
in the minds of Leibnitz and Descartes. But neither of these philoso- 
phers was armed wdth the necessary mathematical equipment to sub- 
ject this conception to the test of numerical calculation. Indeed it 
was not fashionable in their day, any more than it is with some phil- 
osophers in ours, to undertake the drudgery of applying the machinery 
of analysis to the details of an hypothesis. Nearly a century elapsed 
before an order of intellects capable of dealing wath this class of ques- 
tions appeared. It was reserved for Joseph Fourier to lay the founda- 
tion and build a great part of the superstructure of our modern theory 
of heat diftusion, his avowed desire being to solve the great problem 
of terrestrial heat. "The question of terrestrial temperatures," he 
says, "has always appeared to us one of the grandest objects of cosmo- 
logical studies, and we have had it constantly in view in establishing 
the mathematical theory of heat." This ambition, however, was only 
partly realized. Probal)ly Fourier underestimated the difficulties of 
his problem, for his most ingenious and 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 The- 
ory of Heat," which appeared in 1829, is now conceded to be one of 
the epoch-making books. Indeed, to one who has caught the spirit 
