274 Mathematical Theories of the Earth. — Woodward. 
tion and a symmetrical arrangement of strata similar at least to that 
required by the Laplacian hypothesis? Categorical answers to these 
questions can not be given. But whatever may have been the ante- 
cedent condition of the earth's mass, the conclusion seems unavoida- 
ble that at no great depth the pressure is sufficient to break down the 
structional characteristics of all known, substances, and hence to pro- 
duce viscous flow whenever and wherever the stress difference exceeds 
a certain limit, which can not be large in comparison with the pres- 
sure. 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 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 reflnement 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 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 an 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 and unyielding. It does not appear, however, that he had 
submitted this conception to the test of numbers, for a simple calcula- 
tion 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-supporting, 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 ter- 
restrial densities appear 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 sep- 
arating the crust from the nucleus. The whole hypothesis is consist- 
ently 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 
