Apeil 10, 1908] 



SCIENCE 



591 



near 1, while 1 — w is near 0. Also, u^_m 

 is for a point near the center, which will not 

 have cooled appreciably and its rate of change 

 DtU.^_m will be 0. Thus V^ approaches Um 

 as m = 1. 



It would be quite a help if Becker would 

 compute the general solution of the problem 

 as given by Eiemann and by Byerly' for a 

 select lot of plausible hypotheses, including 

 one which shall include the surface tempera- 

 ture, becoming from time to time 0°, when 

 there are glacial periods. 



The only way that I can at all see of using 

 Kelvin's method which considers the surface 

 kept at a constant temperature, is to include 

 the atmosphere, and let the temperature be 

 that of space, which is — 270° 0. If, then, 

 we can assume that the effect of atmosphere, 

 ocean and pellicle of sediments amounts to 

 that of a very narrow contact zone, a ques- 

 tionable yet plausible assumption, if we may 

 consider the present surface gradient as uni- 

 form for an equivalent distance beneath the 

 surface, after a short time rock and contact 

 zone cool together as one mass and we may 

 apply the treatment I applied to that case,' 

 and we may find what kind of a jump in tem- 

 perature at the surface would have produced 

 the gradient that we have in a given number 

 of years. But that temperature must be 

 reckoned from the temperature of space. 

 tTsing 100,000,000 years as the age of the 

 earth and the Calumet gradient and dif- 

 fusivity, we have 



■ = 2^.20 100,000,000 



(.0168 + — .00675 - 



= ( 79500) ^ 

 F= 1,320° above the temperature of space 



= 1,150° C. 



We may, therefore, if we like, assume that 

 one hundred million years ago the earth was 

 shrouded in an atmosphere whose temperature 

 rather suddenly increased from that of space 

 to a little above the critical point of water 

 near the rock surface, and that the rock sur- 

 face or a few feet below was just below the 



' Fourier's Series, last equation on p. 88. 



" Annual for 1903, equations 15 and 20, pp. 213 

 and 214. 



melting point of diabase. This looks quite 

 reasonable to rne. 



But if we want the earth only 60 million 

 years old we can get it if we are willing to 

 assume a granitic crust solidifying under an 

 atmosphere with an enormous water pressure 

 at the modest temperature of 345° C. This 

 also looks good. 



After all, however, what reason have we to 

 believe there was ever any such sudden jump 

 in temperature at the bottom of the atmos- 

 phere as any application of Kelvin's method 

 of finding the age of the earth must assume? 

 There would be none on the planetesimal hy- 

 pothesis nor on the crenitic hypothesis, nor 

 others we might frame. Yet unless there was 

 some such jump the gradient so far as the 

 mere cooling of the earth is concerned is just 

 what it was in the heginning' subject, of 

 course, to accidents of water circulation, vol- 

 canic activity, etc. That, in fact, the gradient 

 was not greater than at present in very early 

 times might be inferred from the fact that 

 rocks seem to h^ve been buried to as great 

 depths without metamorphism then as now. 

 As soon as a layer largely iron was reached the 

 diffusivity would increase and the rate of 

 increase of temperature decrease. If that iron 

 layer was at different distances from the sur- 

 face in different parts of the world, but every- 

 where at about the same temperature, the rate 

 of increase of temperature from the surface 

 to it would, of course, vary. 



The geothermal gradient would then depend 

 upon the diffusivity and the thickness of the 

 crust. Rocks would, with the copper country 

 gradient of 1° C. in 60 meters, attain a tem- 

 perature of 2,000°, that of some gabbros, in 

 120,000 meters, which is about the thickness 

 of the crust Becker assumes, if the rocks re- 

 mained of Tmiform diffusivity. 



Until then we can throw out these latter 

 suppositions by showing some geological signs 

 of a higher rate of increase of temperature in 

 early geological times, such as that rock of 

 the same kind was hotter, or the crust sub- 

 ject to folding and fracture thinner, specu- 

 lations on the age of the earth based on the 



° If the niumerator F = in the equation above, 

 the denominator must be so also, unless t ^ 0. 



