=< oo di “es “=< 
= PHYSICS AND MATHEMATICS TO GEOLOGY. 135 
show clearly that the high authority of Thomson and Tait is on my 
side. The example considered raises however what seems to me at 
least an equally strong argument against the theories from the side of 
the principle (B). For we must remember that the stresses inside the 
material are determined by the intermolecular forces. Now whatever 
molecules may be, and however they may act on one another, it seems 
incredible that the molecular forces should lead to one and the same 
stress-strain relation, however much the mean molecular distance may 
be reduced. The fact that Sir W. Thomson regards the existence of 
an irreducible minimum volume as possible may, I think, be taken as 
proof that he is opposed to the view that it is possible for the stress- 
strain relation to remain linear under such circumstances. It thus 
seems to me, on various grounds, that the inevitable conclusion is that 
while one or other of the two theories may, under ordinary circum- 
stances, be sufficient to define the limits of the mathematical theory, 
the result must always be checked by reference to the condition (C), 
or, what comes to the same thing, we must give up the mathematical 
theory when the strains it indicates are such as would markedly alter 
the mean molecular distance. 
I next proceed to discuss the possibility of the earth’s possessing an 
elastic solid structure, deriving the necessary data from three papers 
published in the Transactions of the Cambridge Philosophical Society. 
For brevity these will be referred to as (a),* ( b),t and (c).f 
The strains due to the action of the sun and moon being compara- 
tively insignificant, we need consider only the “centrifugal” forces due 
to the earth’s diurnal rotation, and the gravitational forces due to the 
mutual attraction of its parts. 
The data supplied by geology do not enable us to formulate any likely 
theory as to a probable distribution of density and elasticity through- 
out the earth regarded as an elastic solid. All we know with certainty 
is that the surface strata are on an average considerably below the 
mean density, that they differ widely in character, many being markedly 
weolotropic, and that frequently they are far from horizontal. Thus, 
as our object is merely to consider what are the possibilities on the 
hypothesis of solidity, it will be best to make the hypothesis as simple 
as possible. Now, if the deviations from the earth’s mean density and 
from an isotropic elastic structure were limited to the surface strata, 
where alone we are certain of their existence, the effect of the “ centrif- 
ugal” forces would be nearly the same as if these deviations did not 
exist; but the effect of the eravitational forces on the eccentricity of 
the surface may depend largely on the nature of the deviations. I thus 
propose to treat the problem in stages. 
The first stage neglects entirely the gravitational forees and regards 
the earth as a slightly spheroidal body—which has departed from the 
spherical form in consequence of its rotation—of uniform density and 
*Vol. X1v, pp. 250-369. _—‘t Vol. Xv, pp. 467-483. t Vol. xv, pp. 1-36. 
