134 LOUIS VESSOT KING 
radius than this limiting radius will be unstable and collapse in 
such a way as to form a number of smaller cavities each of which 
might be stable. 
§ 8. NOTE ON CONDITIONS OF STRESS IN THE EARTH’S CRUST 
The determination of conditions of stress existing in the earth’s 
crust constitutes one of the most difficult problems of geodynamics 
and one on which many recent investigations have been published. 
If the earth is considered as a perfect sphere in which the density 
is a function of the radius only, the problem can be solved without 
difficulty in terms of the elastic solid theory. The application 
of these results throughout the interior of the earth is not legitimate 
because an infinite number of laws of density can be formulated 
to represent the known distribution of mass throughout the earth. 
Near the surface considerations of surface inequalities vitiate the 
result. In this connection Love states,? “Apart from the difficulty 
concerning the initial stress in a gravitating body of the size of the 
earth, a difficulty which we seem unable to avoid without treating 
the material as incompressible, there is another difficulty in the 
application of such an analysis to problems concerning compressible 
gravitating bodies. In the analysis we take account of the attrac- 
tion of the inequality at the surface, but we neglect the inequalities 
of the internal attraction which arise from the changes of density 
in the interior; yet these inequalities of attraction are of the same 
order of magnitude as the attraction of the surface inequality.” 
In a recent work Love’ has attacked the problem of isostatic 
support of continents and mountains. ‘‘The problem admits of 
an infinite number of solutions even if the distribution of the mass 
1S) KANO Wallops The problem must remain indeterminate, and 
all we can do is to obtain explicitly one or more of the infinitely 
tLamé solves the problem for an isotropic elastic sphere under its own gravita- 
tion (Love, Elasticity, 2d ed., 140); the result can only be reconciled with fact by the 
assumption of incompressibility or by taking into account a state of initial stress. 
L. M. Hoskins in a paper “‘Flow and Fracture of Rocks as Related to Structure”’ 
(U.S. Geological Survey, 1894-95, Part I, 854), solves the problem throughout a com- 
pressible concentric crust of uniform density and small thickness; no account is taken, 
however, of surface inequalities or of considerations of isostasy. 
2 Love, Elasticity, 2d ed., 253. 
3 Love, Some Problems of Geodynamics (Adams Prize Essay, 1911), chaps. ii and 
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