172 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



INTRODUCTION. 



The following studies were undertaken at the suggestion of Prof. T. C. 

 Chamberlin, as auxiliary to the development of the hypothesis put forward 

 by him as to the origin of the earth by planetesimal accretion, a main 

 object being to secure quantitative inferences which might aid in forming a 

 j udgment regarding the probable efficiency of thermal energy, whose source 

 is gravitational, as an agent of geological importance under the restrictions 

 imposed by the hypothesis. Experimental evidence regarding the behavior 

 of substances under the enormous temperatures and pressures met with in 

 the interior of cosmic bodies must be considered almost wholly lacking, and 

 derived by highly uncertain extrapolation from determinations made within 

 the limited range accessible to laboratory measurement. Precise conclusions 

 based on accurate observed data could therefore not be looked for, but 

 it was felt that it should be possible to deduce with some confidence at least 

 the order of magnitude and general features of the thermal phenomena of 

 gravitational origin, under the conditions assumed by the hypothesis in 

 question, when supplemented by certain minor hypotheses. 



The general hypothesis assumes that the earth, in common with other 

 bodies of the solar system, was formed by the accretion of planetesimal 

 masses, more or less similar in chemical composition, at least when consid- 

 ered on a large scale, so that the more important local differences in the body 

 of the resulting planet are to be ascribed to differences in physical condition, 

 chiefly in pressure and temperature; and that the history of the earth in 

 this aspect comprises two main epochs, the earlier one of growth by accretion, 

 first at a rapid, and later at a declining rate, shading into the subsequent 

 longer period of relative quiescence and constancy of mass, accompanied 

 by a gradual redistribution and partial loss of a store of thermal energy 

 derived from the primitive mechanical energies of the system. 



According to the mode of transformation this energy may be treated as 

 mainly of three kinds: (1) that which is stored in the underlying mass, 

 through the progressive static compression which accompanies the deposi- 

 tion of the successive layers at the surface; (2) that derived directly from 

 the kinetic energy of the masses impinging on the surface, through the vis- 

 cous damping of waves and vibrations due to the impacts; (3) that derived 

 in a similar way from motions which arise from the continual disturbance 

 of equilibrium produced by the surface accretions, independently of the 

 momentum of impact. 



To trace out exactly the final distribution of the second and third kinds 

 would be a matter of forbidding difficulty, even if an acceptable assumption 

 could be made regarding the precise law of accretion. No attempt will be 

 made here to account for the third, but from estimates made in the sequel, 

 where attention is confined to the first two, it would appear to be a rather 

 small portion of the whole, being in fact under a certain special set of con- 

 ditions strictly zero. 



As to the second kind, however, the energy of impact, a useful estimate 

 can be made very simply if it be assumed that the single ideal substance 

 contemplated is highly viscous. For in such cases the motions produced by 



