Part III.— THERMODYNAMIC THEORY. 



As a strict theory, the foregoing deductions imply a sort of ideal earth- 

 substance, with respect to which certain assumptions are made, in a form 

 convenient for the purpose in hand, but not sufficient to define completely 

 its thermodynamic properties. How closely they represent the actual be- 

 havior of the substances composing the earth's interior is largely conjecture, 

 in view of the meagerness and limited range of direct experimental informa- 

 tion; but they may be examined as to their consistency with accepted 

 thermod3mamic laws regarding the interplay of thermal and mechanical 

 processes. 



It has been supposed that a general idea of the thermal process, after 

 the earth was completely formed, could be obtained by treating it as a 

 matter of pure conduction and accompanying radiation at the surface. 

 But the significance for geological theory of the redistribution of heat lies 

 largely in the resulting expansions or contractions in different portions of 

 the mass, and these geometric changes would in general involve the passage 

 of energy between the mechanical and the thermal form, in amount perhaps 

 by no means negligible in comparison with the heat conducted. In par- 

 ticular, if the temperature should on the average fall, the energy thus lost 

 would be partly compensated by that developed out of gravitational work 

 during the contraction. 



As to the possible relative magnitude of these, as it were, opposing move- 

 ments of energy, a summary estimate may be gathered from the case of a 

 homogeneous sphere at uniform temperature, contracting so as to remain 

 such, and supposed to have specific heat and coefficient of expansion con- 

 stant throughout. In this case the energy developed by ingathering from 

 infinite dispersion is 



while the thermal content is 

 from which come 



while 



where a is the volume coefficient of expansion, or three times the linear 

 coefficient; so that 



d0 _ hma (127) 



dQ bra J 



which is the ratio of the gain of energy from the gravitational store, to the 

 loss by decline of temperature; and with an assigned density is proportional 

 to the square of the linear dimensions. For small bodies it would be negli- 



219 



