206 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



which follows from (52) and (82), the tabulation using, however, as unit of 



measure the value of — ^, equivalent to a change of about 3 J° in a billion 



years. 



Table 10. 



In table 10, based on the hypothesis = 0^, A = ^, p = Pq{\ - -~ x^) , the 



functions y^, t/, are the first two fundamental functions; F{x) gives the 

 primitive temperature-curve, Fy{x)^F{x)—Aiy^, ^2(0;) =Fi(x)— Ajj/j/ in 

 each the temperatures and coefficients A are expressed in terms of the unit 

 6 = 16,600°. The last column gives the initial rate of the change of temper- 

 ature in terms of a unit corresponding to a change of 3^° in a billion years; 



the entries in this column must be multiplied by — ^2 *o be reduced to 

 absolute units. ^ 



Comparison of this table with table 5 shows that the change in distri- 

 bution of the density makes no striking change in the thermal process. The 

 second component has a larger coefficient, and the residuals left by the first 

 two components are somewhat smaller. But these residuals have in gen- 



eral the same trend, and together with the values of -rr indicate the same 



initial partition of the mass into inner and outer regions of falling and rising 

 temperature, respectively. The outer zone is, however, shallower than under 

 the former case, extending at the start to a depth of not quite 600 miles. 



The increase in the tabulated values of the initial rate -^ and of the gra- 

 dient of the first component for points near the surface, together with the 

 coefficient A2, is offset by the decreased value of 6^, in terms of which the 

 entries are expressed, so that the maximum temperature-gradient at the 

 surface occurring when the zone of rising temperature disappears, would be 



