SsfTEMSER 6, 1 8^9.] 



SCIENCE. 



cient to break down the structural charadteristlcs of all known 

 substances, and hence to produce viscous flow whenever and 

 wherever the stress difference exceeds a certain limit, which can- 

 not be large in comparison with the pressure. Purely observa- 

 tional evidence also of a highly affirmative kind in support of this 

 conclusion, is afforded by the remarkable results of Tresca's exper- 

 iments on the flow of solids and by the abundant proofs in geology 

 of the plastic movements and viscous flow of rocks. With such 

 views and facts in mind, the fluid stage, considered indispensable 

 by Laplace, does not appear necessary to the evolution of a planet, 

 even if it reach the extreme refinement of a close fulfilment of some 

 such mathematical law as that of his hypotheses. If, as is here 

 assumed, pressure be the dominant factor in such large masses, 

 the attainment of a stable distribution would be simply a question 

 of time. The fluid mass might take on its normal form in a few 

 days or a few months, whereas the viscous mass might require a 

 few thousand or a few million years. 



Some physicists and mathematicians, on the other hand, reject 

 both the idea of the existence of great pressures within the earth's 

 mass, and the notion of an approach to continuity in the distribu- 

 tion of density. As representing this side of the question, the 

 views ot the late M. Roche, who wrote much on the constitution of 

 the earth, are worthy of consideration. He tells us that the very 

 magnitude of the central pressure computed on the hypothesis of 

 fluidity is itself a peremptory objection to that hypothesis. Ac- 

 cording to his conception, the strata of the earth from the centre 

 outwards are substantially self-supporting and unyielding. It does 

 not appear, however, that he had submitted this conception to the 

 test of numbers, for a simple calculation will show that no materi- 

 als of which we have any knowledge would sustain the stress in 

 such shells or domes. If the crust of the earth were self-support- 

 ing, its crushing strength would have to be about thirty times that 

 of the best cast steel or five to one thousand times that of granite. 

 The views of Roche on the distribution of terrestrial densities ap- 

 pear equally extreme. He prefers to consider the mass as made 

 up of two distinct parts, an outer shell or crust whose thickness is 

 about one-sixth of the earth's radius, and a solid nucleus having 

 little 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, he postulates a zone of fusion 

 separating the crust from the nucleus. The whole hypothesis is 

 consistently worked out in conformity with the requirements of 

 ellipticity, the superficial density, the mean density, and precession ; 

 so that to one who can divest his mind of the notion that pressure 

 and continuity are 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 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 find many of our notions on this sub- 

 ject 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 ob- 

 servation 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 in- 

 timately connected with the terrestrial store of heat, it is natural 

 that there should be a considerable variety of opinion. The con- 

 sensus of such opinion, however, has long been in favor of the 

 hypothesis that heat is the active cause of many and a potent fac- 

 tor in most of the grander phenomena which geologists assign to 

 the earth's crust ; and the prevailing interpretation of these phe- 

 nomena 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 defi- 

 nite form in the minds of Leibnitz and Descartes. But neither of 



these philosophefs Wds armed With the necessary mathematical 

 equipment to subject this conception to the test of numerical cal- 

 culation. 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 analysis to the details of an 

 hypothesis. Nearly a century elapsed before an order of intellects 

 capable of dealing with this class of questions appeared. It was 

 reserved for Joseph Fourier to lay the foundation and build a great 

 part of the superstructure of our modern theory of heat diffusion, 

 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 cosmological 

 studies, and we have 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 industrious successors in 

 the same field have made little progress beyond the limits he at- 

 tained. 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 con- 

 ceded 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 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 mathe- 

 matical theory of heat. Poisson narrowly missed being the fore- 

 niost mathematician of his day. In originality, in wealth of math- 

 ematical resources, and in breadth of grasp of physical principles, 

 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 overshad- 

 owed in recent times by the earlier and perhaps more brilliant re- 

 searches of Fourier, but no student can afford to take up that en- 

 ticing though difficult theory without 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 diffusion held con- 

 cerning the earth's store of heat. I say " opinions," for, unhappily, 

 this whole subject is still so largely a matter of opinion that in dis- 

 cussing 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 condition in which there was a uniform dis- 

 tribution of heat throughout 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 af- 

 fords an initial distribution of heat and an epoch from which analy- 

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

 the subsequent distribution of heat and the resulting mechanical 

 effects. But no great amount of reflection is necessary to convince 

 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 capacity of the entire mass remain 

 constant, and that the heat conducted to the surface of the earth 

 passes off by the combined process of radiation, convection, and 

 conduction, without producing any sensible effect on surrounding 

 space. These or similar assumptions must be made before the ap- 

 plication of theory can begin. In addition, two data are essential 

 to numerical 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 observed, approx- 

 imately at least ; the second can only be estimated at present. 

 With respect to these important points which must be considered 

 after the adoption of the consistentior status, the writings of Four- 

 ier afford little light. He was content, perhaps, to invent and de- 

 velop the exquisite analysis requisite to the treatment of such 

 problems. 



Poisson wrote much on the whole subject of terrestrial temper- 



