THE MATHEMATICAL THEORIES OF THE EARTH. 189 



Suppose, however, that we reject the idea of origiual tiiiidity. 

 Would uot a rotating mass of the size of the earth assume finally the 

 same aspects and properties presented by our planet"? Would not 

 pressure and centrifugal force suffice to bring about a central condensa- 

 tion and a symmetrical arrangement of strata similar at least to that 

 required by the Laplaciau hypothesis ? Categorical answers to these 

 questions can not be given at present. But, whatever may have been 

 the antecedent condition of the earth's mass, the conclusion seems una. 

 voidable that at no great depth the pressure is sufficient to breakdown 

 the structural characteristics of all known substances, and hence to 

 produce viscous flow whenever and wherever the stress difference ex- 

 ceeds a certain limit, which can not be large in comparison with the 

 pressure. Purely observational evidence, also, of a highly affirmative 

 kind in support of this conclusion, is afforded by the remarkable results 

 of Tresca's experiments on the flow of solids and by the abumlant 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 Lai>lace, does uot appear necessary to the evolution of a planet, even 

 if it reach the extreme refinement of a close fulfillment of some such 

 mathematical law as that of his hypothesis,. 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 existence of great pressures within the earth's mass, and 

 the notion of an approach to continuity in the distribution of density. 

 As representing this side of the question the views of the late M. Eoche, 

 who wrote much on the constitution of the earth, are worthy of consid- 

 eration. 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.* According to his conception, the strata of the 

 earth from the center outwards are substantially self-supporting aiul 

 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 materials of which we have any knowledge would sustain the 

 stress in such shells or domes. If the crust of the earth were self-sup- 

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

 of the best cast steel, or five hundred to one thousand times that of 

 granite. The views of Eoche on the distribution of the terrestrial 

 densities appear equally extreme.t He prefers to consider the mass as 



* Memoirc snr Vvtat iiitcriciir du t/Iohc terrcsire, parM. TCdoiiard Roche ; Wonioires de 

 liisection des sciences de I'Aciidcniio dcs Sciences et Lettres de M on tpoliier, 1880-1884 

 Tome X. 



t Ibid. 



