344 JR. S. Woodward — Mathematical Theories of the Earth. 



viscous flow whenever and wherever the stress difference exceeds 

 a certain limit, which cannot 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 abundant proofs in geology of the plastic move- 

 ments 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 ques- 

 tion 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 pressure 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. 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.* According to his conception, 

 the strata of the earth from the center outward are substan- 

 tially 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 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 thou- 

 sand times that of granite. The views of Roche on the distri- 

 bution of terrestrial densities appear equally extremef. 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 cen- 

 tral 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 hy- 

 pothesis is consistently worked out in conformity with the 

 requirements of the ellipticity, the superficial density, the mean 



* Memoire sur l'Etat Interieur du Globe Terrestre, par M. Edouard Roche. 

 Memoires de la section des Sciences de l'Academie des Sciences et Lettres de 

 Montpellier. Montpellier, 1880-1884. Tome x. _ \ Ibid. 



