216 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



acceptable density-formula the compression in the interior as the mass 

 increased would inevitably be accompanied by local deformations, result- 

 ing from the inequality of vertical and horizontal compression, and prob- 

 ably ill character and magnitude similar to those described in Part I. Thus 

 the theory developed from the hydrostatic equations remains subject to 

 the uncertainty from this source in the computation of the compressional 

 energy, to an extent not easy to estimate. 



The thermal process has thus far been outlined on two alternative 

 suppositions regarding the variation of p, and two regarding o, but in all 

 cases the conductivity was treated as constant. This condition might be 

 replaced by the supposition often made that it increases from the surface 

 toward the center on account of the increasing condensation of the mate- 

 rial. Such a variation would have the effect of facilitating the transfer of 

 heat from the interior to the superficial strata, probably raising the maxi- 

 mum gradient of temperature attained near the surface and perhaps short- 

 ening the time during which the temperature has anywhere an upward 



trend. The effect on the depth of the region where -rr is at first positive 

 is seen by inspection of equation (52), which can be written 



\ dry A dr dr) 



In the second member, the first term, which alone has occurred hitherto, 

 is positive in the outer region and negative in the interior; — is every- 



where negative, while if X increases toward the interior — is negative, 



making the second term positive. This shows that the zone of rising tem- 

 perature would be deeper than with constant X, with the same original 

 temperature curve. The more improbable supposition that X decreases 

 toward the interior would have the contrary effect, but, as will be seen 

 presently, could by no means eliminate the outer zone entirely. 



The fact that under a variety of suppositions regarding the thermal 

 coefficients p, a, X there occurs a thermal process marked by the same gen- 

 eral features, even with no radical differences in order of magnitude in the 

 numerical data, suggests that those features are not dependent on such 

 special hypotheses, but due to the general properties of the original distri- 

 bution of temperature and characteristic of its mode of origin. The follow- 

 ing general considerations show why they may be expected to persist under 

 any hypotheses on p, o, X, not differing too radically from those developed 

 above. 



Whatever may be the actual variations of p, g, o, X, any equations 

 assuming to represent them as functions of r only can hardly be treated as 

 more than interpolation-formulas, representing the gross features of the con- 

 crete situation in the sense of averages, and disregarding the relatively trivial 

 local variations on account of which it is only to a certain degree of accuracy 

 that there can be said to be, for instance, a definite law of density at all. 

 It seems, therefore, practically general to assume in the neighborhood of the 



