196 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



superficial zones. It is accordingly in the latter region that such general 

 considerations as above are insufficient to give a just idea of the complete 

 thermal process. 



Conjecture may, however, be made with some confidence as to the prob- 

 able character of the modifications produced by the higher components, by 

 direct inspection of the primitive temperature curve, which by (22) and 

 (58), with the substitution of the approximate expression used previously 

 for the density, becomes 



e=d,{i-x'y{i-jx'y(i-^x')-' (64) 



which is accurate enough for the purpose. Then, according to (52), the 

 initial rate of change of temperature becomes: 



dt 



'^oPo'^i [ 9 9 3 9 9 j ( 2 J 



in which the coefficient of — ^-^ is that tabulated in column 7 of table 5. 



Q0 '^oPo^'i 



For the part of — due to any single component, say the nth, the corre- 

 ^ dt 



sponding coefficient would be n^A^y^. 



These figures indicate that from the center outwards over a distance of 

 about eight-tenths of the radius the thermal process is not very different 

 from that represented by the first component alone, except that the latter 

 exaggerates the rate of decline somewhat in the more central portions on 

 account of the opposing effect of the higher components. But in the outer 

 zone of about two-tenths of the radius the process is in the earlier stages 

 totally different; here the temperature actually rises for a certain interval 

 of time, which would be different for different depths, very short for points 

 extremely near the surface because of the constancy of the surface-tempera- 

 ture, and for points near the boundary between the regions of rising and of 

 falling temperature, but presumably of considerable length at intermediate 

 depths. Since this trend of temperature in the outer zone is brought about 

 by the higher components, which practically die out in a time sufficient to 

 produce only a relatively small change in the amplitude of the first com- 

 ponent, the whole process may be conceived to occur in two epochs, an 

 earlier one of gradual accommodation of the temperature-curve to the slowly 

 declining first component, and a later one where that component is left 

 practically isolated. During the latter epoch the temperature would decline 

 steadily at all points at rates nearly proportional to the existing tempera- 

 tures. But during a large part of the earlier epoch the heat lost from the 

 central portions is conducted through an intermediate zone, whose thermal 

 condition is nearly stationary, and thence outwards to produce an exaltation 

 of temperature in a zone a few hundred miles thick just below the surface. 

 Dissipation through the surface in the earlier stages is very slight, owing to 

 the smallness of the gradient, the primitive temperature-curve being tan- 

 gent to the X-axis at the point a; = 1, because of the occurrence of the squared 

 factor ip—piY in formula (22). 



