174 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



it is desired to develop first the consequences of this assumption, leaving for 

 later study the question of the modifications needed to allow for rigidity. 



The following developments refer entirely to the simple ideal case of a 

 spherical body, radially symmetric in every essential feature, originating by 

 deposition of successive spherical layers, and maintained under its own grav- 

 itation in hydrostatic equilibrium which is at least approximate during the 

 period of growth and practically exact thereafter. All variables represent- 

 ing the physical magnitudes concerned are therefore considered as functions 

 of the time and of the distance from the center of the mass. It is desired 

 to study the primitive distribution of thermal energy due to compression 

 and impact, together with the character and rapidity of the modifications 

 brought about by conduction and radiation. 



The term " thermal energy " used in the foregoing refers to the entire in- 

 trinsic energy of the substance as depending on pressure, density, and tem- 

 perature; part being the stored or latent energy of the compressional strain, 

 the remainder appearing in a corresponding augmentation of temperature. 

 It is the latter portion only which is subject to direct transfer by pure con- 

 duction, though its redistribution in that way, through alteration of the 

 geometric distribution of the mass by thermal expansion and contraction, 

 may lead to the redistribution also of the energy of strain, accompanied in 

 general by further transformation of energy from gravitational to thermal 

 form. The character of the phenomena might easily vary radically with 

 variations in the relative importance of these two portions of the intrinsic 

 energ3^, without inconsistency with the general hypothesis. 



It is thus essential, for the construction of a definite theory, to include 

 further assumptions as to the thermodynamic properties of the earth-sub- 

 stance, which should cover three main points: (a) the characteristic equa- 

 tion of the substance or relation between the thermodynamic coordinates — 

 pressure, density, temperature; (6) the form of the intrinsic energy as a 

 function of these coordinates; (c) the value of the thermal conductivity in 

 terms of the same variables. Auxiliary coefiicients such as specific heats, 

 thermal expansion, and compressibility can then be deduced and the as- 

 sumptions checked or numerical parameters determined by means of obser- 

 vations or estimates of these physical magnitudes in the case of substances 

 at the earth's surface. It is evident, from the number of these secondary 

 hypotheses needed, that any sharply crucial test of the main hypothesis 

 from the present point of view is out of the question; all that can be done 

 is to form a judgment as to its plausibihty in accounting for the play of 

 thermal and gravitational forces in geologic history, by developing several 

 alternative suppositions on these secondary points. 



