Physics and Mathematics to Geology. 251 



surface, can be maintained 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 argument introduced here 

 from the theory of intermolecular forces. This raises no 

 presumption against the hypothesis that the interior is in a 

 perfectly solid state, and possessed of such a chemical consti- 

 tution, say, as iron, if it be admitted that it is of a material 

 in which the linearity 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 is in 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 seolotropic solid structure of some 

 kind, or of a variety of kinds, may not satisfy all the con- 

 ditions as well as or even better than a nearly incompressible 

 isotropic material. The presumption is. in fact, that the con- 

 ditions 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 tempe- 

 rature 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 tempe- 

 rature (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 extremely 

 large. 



Before passing to the second part of the paper, I have to 

 confess that there is no reason to believe that some of the 

 limitations assigned here to the application of the mathema- 

 tical theory will be accepted by all or even by a majority of 

 elasticians. In fact the mathematical theory has actually been 

 applied by several recent writers under circumstances when 

 most or all of the limitations proposed here are violated. For 

 instance, this is to a certain extent the case in Professor Dar- 

 win's paper*, "On the Stresses caused in the Interior of the 

 Earth by the Weight of Continents and Mountains." In the 

 principal part of the paper he supposes v — '5, when, as we 

 * Phil. Trans. 1882, pp. 187-2,30. 



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