190 THE MATHEMATICAL THEORIES OF THE EARTH. 



made up of two distinct parts, au outer shell or crust whose thickness 

 is about oue-sixtli of the earth's radius, and a solid nucleus haviugiittle 

 or no central condensation. The nucleus is conceived to be purely 

 metallic, and to have about the same density as iron. To account for 

 geological phenomena, be postulates a zone of fusion separating the 

 crust from the nucleus. The whole hypothesis is consistently worked 

 out in conformity with the requirements of the ellipticity, thesuperflciaE 

 density, the mean density, and jirecession ; so that to one who cais 

 divest his mind of the notion that pressure and continuity ar.» impor- 

 tant factors in the mechanics of such masses, the picture which Roche- 

 draws of the constitution of our planet will present nothing incongru- 

 ous. 



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 hypoth- 

 esis ; and although 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 tiud 

 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 diihcult one after two centuries of observation 

 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 ett'ects? Concerning iihenomena 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 geol- 

 ogists assign to the earth's ciust; 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 philos- 

 ophers was armed with 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 philosophers, 

 in ours, to undertake the drudgery of applying the machinery of analy- 

 sis to the details of an hypothesis. aSTearly a century elapsed before au 

 order of intellects capable of dealing with this class of questions ap- 

 peared. It was reserved for Joseph Fourier to lay the foundation and 



*Protoa:^e, on tie la formation et des r6volntion8 dn globe, par Leibnitz, onvrage 

 tradnite - - - avec uno jntrodiictioii et def^ notes parte Dr. Hertrand de Saint- 

 Grermaiu, Paris, 1859, 



