188 G. F. BECKER ISOSTASY AND RADIOACTIVITY 



isostatic compensation has cooled only to a trifling extent, or that it is 

 there nearly in a state of ease, although since it is solid and has cooled 

 somewhat it must also be to some extent in a state of elastic strain. As 

 a matter of course, solid flow does not supervene until a mass of matter 

 has been strained to its elastic limit, and in spite of the flow such a mass 

 retains the maximum strain it is capable of enduring.*^ 



From the preceding discussion my main conclusion is that the real 

 differences in load per unit area at the level of isostatic compensation are 

 very small, not merely compared with total gravity at the equator, but 

 small relatively to the apparent gravity anomalies at the surface, and that 

 therefore the amount of shrinkage or cooling which has taken place below 

 that level is also exceedingly small. 



Note on Epeirogent 



That approximate isostatic compensation exists in the outer shell of the 

 earth must be accepted as demonstrated by the geodesists. How to ac- 

 count for this very fundamental fact is a geological problem which is too 

 complex for full discussion here. In another paper I have endeavored to 

 prove that if the earth's surface had originally been a perfectly smooth 

 equipotential surface, uniform in all properties excepting only in con- 

 ductivity, the areas of low conductivity would undergo relative uplift be- 

 cause the material underlying them would cool more slowly and would 

 ultimately develop into continents.*^ These would be subject to great 

 pressure by the more rapid contraction of the surrounding areas and 

 ultimately, for a sufficient temperature difference, to systematic Assuring. 



So soon as the oceans came into existence and erosion began, the super- 



** This strain, however, is probably smaller than is indicated by ordinary, brief experi- 

 ments on the strength of materials. After-effects appear to be small quantities of the 

 second order. 



*" Areas of low condtictivity will also be areas of low diffusivity, provided that either 

 is the only constant subject to variation. The superficial temperature gradient for a 

 globe of very large radius, (clv/(lx)<,, may be expressed thus : 



where V is the initial surface temperature, v the initial temperature gradient, and k the 

 diffusivity, or li/c, the conductivity divided by the thermal capacity. Now the heat 

 emitted is 



so that if the diffusivity is constant the emission is simply proportional to the con- 

 ductivity, while if the thermal capacty is constant the emission increases with the dif- 

 fusivity. The values of n are more nearly constant than those of k or of k See Proc. 

 Nat. Acad. Sci., vol. i, 1915, p. 81. In preparing this the paper cited, I misplaced the 

 decimal point in the coefficient of expansion of typical rock ; an error affecting some of 

 the conclusions though not the main thesis. These will be corrected in the Proceedings. 



