198 G. P. BECKER ISOSTASY AND RADIOACTIVITY 



pensation, may be considered as a heat engine. In such an earth there 

 is abundant energy available for geological processes, only a portion of 

 which is dependent on the sun. 



Sir Ernest Eutherford, after giving the maximum temperature due to 

 a layer of uniform radioactive matter at, in roimd numbers, 300° C, 

 continues : "This maximum temperature seems too small to fit in with 

 the facts, for there is reason to believe that a temperature of about 1,300° 

 exists some distance below the surface."^^ He goes on to show that by a 

 logarithmic distribution of the radioactive matter an internal tempera- 

 ture excess just double that due to a homogeneous layer may be attained, 

 though only at a great depth ; but even in that case there remain at least 

 600° or 700° of temperature unaccounted for. It is clear that if the 

 earth at some distance below the surface is hotter than it would be if all 

 the emission were due U> radioactivity, a part of the gradient at the sur- 

 face must be due to some distinct cause, which can hardly be other than 

 an initial excess of temperature, and consequently the shell of radioactive 

 matter must be thinner than 21 kilometers. 



Since the conduction of heat out of the earth complies with Fourier's 

 law, no matter what the origin of that heat may be, the superficial tem- 

 perature gradient is the sum of the gradients due to several causes. Of 

 these there appear to be three only, namely, an initial high temperature of 

 the exterior shell, an original temperature gradient due to the rise with 

 pressure of the temperature of consolidation,^- and exothermic transfor- 

 mations, including radioactivity. The evidence that the external portion 

 of the globe has been liquid to a considerable depth is well known and 

 Kelvin's summary of it has already been cited. Now, the initial surface 

 temperature was determined by the nature of the rocks composing the 

 original outer shell, and these must have been rhyolites, trachytes, and 

 andesites, in the main of holocrystalline texture. The temperature 

 gradient must also have been influenced by the composition of the rocks. 

 At the surface the temperature in question can not have differed much 

 from 1,300°, which is only about a hundred degrees higher than the 

 melting point of the more fusible basalt or diabase. The initial gradient 

 must have been less than the gradient of Mr. Barus's diabase melting- 

 point curve, and I have given reasons elsewhere, based on the law of 

 density proposed by Legendre and adopted by Laplace,, for believing that 

 it intersected his line at about 40 miles frum the surface.^^ These reta- 



il Op. cit., p. 652. 



*- This gradient answers to the hypothesis that the fluid portion of the earth was in 

 convective equilibrium. 



»3 SmithsoniaD Misc. Coll., vol. 56, 1910, No. 6, p. 17. 



