142 SOME APPLICATIONS OF 
Owing to the less density of the surface strata these reductions may be 
considerably too great, so that itis advisable to regard 32 x 10" as essen- 
tially a lower limit to the value of E. As stated above, the numerical 
result for the value of E would be but little altered if we supposed 7 
slightly less than 0-5; but unless 0-57 be very small, the terms inde- 
pendent of the eccentricity become of importance in estimating the 
maximum stress difference and greatest strain. 
The conclusion to which the previous investigations leads is that none 
of the principles at present recognized in the biconstant theory of 
isotropy are opposed to the hypothesis that the earth possesses in its 
interior an isotropic elastic solid structure with a linear stress strain 
relation, provided its material be very nearly incompressible. But the 
hypothesis that the material in the interior shows an isotropic, elastic 
structure, such as that of the ordinary metals under the ordinary con- 
ditions, to which they are exposed on the earth’s surface, can be main- 
tained only by those who are prepared to reject the usual theories of 
the rupture, the limitation (C) in the size of the strains, and the argu- 
ment introduced here from the theory of intermolecular forces. This 
raises no presumption against the hypothesis that the interior 1s in a 
perfectly solid state, and possessed of such a chemical constitution, 
Say, as iron, if it be admitted thatit is of a material in which the lin- 
earity of the stress-strain relation ceases when the compression becomes 
large. 
The results obtained raise no presumption for or against the theory 
that the earth isin a liquid or plastic state. They merely show that 
any argument against the possibility of an elastic solid structure in a 
body of the earth’s form is without foundation; and that any argument 
based on the destructive tendency of the enormous gravitational forces 
in a solid of its mass is inconclusive, even as directed against such 
structures as are compassed by the ordinary mathematical theory. It 
has not been shown that an exolotropic solid structure of some kind, or 
of a variety of kinds, may not satisfy all the conditions as well as or 
even better than a nearly incompressible isotropic material. The pre- 
sumption is, in fact, that the conditions may be satisfied in an infinite 
number of ways. 
It must be borne in mind that there may be fatal objections to an 
elastic solid structure which do not arise immediately from the theory 
of elasticity. Such an objection may arise from the rapid increase with 
the depth shown by the temperature near the earth’s surface. My 
principal reason for referring to this is to point out that the common 
argument against the production of fluidity by the high internal tem- 
perature (viz, an assumed raising of the melting point by pressure) has 
just as much weight for a nearly incompressible solid earth as for any 
other, because while the stress difference in such an earth is small the 
internal pressures are very large. 
Before passing to the second part of the paper, I have to confess that 
