GEOPHYSICAL THEORY 

 UNDER THE PLANETESIMAL HYPOTHESIS. 



SYNOPSIS. 



This paper is devoted mainly to a quantitative study of that portion of 

 the earth's internal energy which is supposed to have been derived from the 

 mechanical energy of a primitive system of planetesimals, of its transforma- 

 tion into thermal form during the epoch of accretion, and its subsequent 

 redistribution by conduction. 



In Part I a theory initiated by Fisher is developed on the basis of the La- 

 placian law of density, together with certain auxiliary assumptions. Form- 

 ulas and tables are given showing the variation of dimensions and internal 

 densities of the mass during the epoch of accretion, the differential effect of 

 deposit of a stratum on the size and moment of inertia of the mass, and the 

 deformation of mass-elements accompanying the resulting compression. De- 

 termination, under alternative secondary postulates, of the original distri- 

 bution of temperature produced by the compression and its redistribution 

 by conduction shows the existence of a characteristic zone of rising temper- 

 atures during the earlier stages. 



Part II comprises an inquiry as to what changes in the results of Part 

 I are produced by changes in the secondary hypotheses employed and a 

 critical examination of the latter. The computed masses of the nucleus at 

 various stages of accretion are compared with the observed masses of the 

 smaller planets in the solar system. The previous theory is reviewed, with 

 the substitution of Roche's formula for the density; and to serve as basis 

 of comparison, certain other laws of density are deduced to satisfy special 

 conditions. 



Criticism in the light of general thermodynamics leads to a recognition 

 of the theory given as possibly an extreme view, referring to a substance 

 where the work of compression is mainly frictional. 



In Part III is outlined a contrasting theory for the case of a substance 

 such that the work of compression is done mainly against volume-elasticity, 

 under the assumption that the successive strata deposited at the surface are 

 reduced to uniform entropy by free radiation while exposed. The thermal 

 phenomena in this case are compared with those under the conditions of 

 Part I. 



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