February 7, 1908] 



SCIENCE 



231 



accounted for by the hypothesis that isostatic 

 compensation is viniformly distributed and is 

 complete at a depth of 140 kilometers or 71 

 miles from the surface." 



I, therefore, adopt the hypothesis that the 

 tangent of the temperature curve, or equation 

 (1), is parallel to the diabase line at 140 kilo- 

 meters from the surface. 



V is the value of the original temperature 

 excess of the earth at its surface over the 

 temperature of the atmosphere in contact with 

 it. As was pointed out above, this must have 

 been high enough to fuse rocks more refrac- 

 tory than diabase and was probably about 

 equal to the temperature of the hottest erup- 

 tions which now reach the surface of the 

 earth. It seems to me that 1,300° is a reason- 

 able estimate. This is considerably below the 

 melting point of pure iron and lower than the 

 blast furnace, but above the melting point of 

 copper (1,065°), which lavas are known to fuse, 

 and of Barus's diabase (1,170°). So far as I 

 know, no precise determinations have yet been 

 made of the temperatures at which lavas issue 

 from their vents, though the new optical 

 method should make good observations pos- 

 sible. 



To take advantage of the level of isostatic 

 compensation x in equation (1) may be put 

 at 140,000 meters, and dv/dx at the gradient 

 of the diabase line, or 430°/.01j-. Then with 

 K = . 00786 and 



Carrying out this process I get the following 

 table of related values: 



1600° — V 1600° — V 



Mir 



63710 



it follows that 



1170° 



4te 



Although V should be about 1,300° and t 

 might be computed as dependent variable, the 

 form of this expression makes it easiest to 

 assume values of t and then compute corre- 

 sponding values of V and c. When these are 

 known for any given age the corresponding 

 value of the surface temperature gradient is 



'-) = — \ c 



\irKt 



^dx/o 



° Hep. to 15th general conference of the Inter- 

 national Geodetic Assoc, Washington, 1906. 



A is the age in millions of years; Y is the 

 initial surface temperature; c is the initial 

 gradient of internal temperature and 1/c 

 gives this gradient in terms of meters per 

 degree centigrade. G° C. is the final surface 

 gradient in terms of meters per degree centi- 

 grade and G° F. is the same gradient in terms 

 of feet per degree Fahrenheit. 



In all of these earths the upper surface of 

 the diabase couche is supposed to be at one 

 one-hundredth of the radius from the surface, 

 or 63,710 meters. All of the excess of tem- 

 perature curves have tangents parallel to the 

 diabase line at a depth of 140,000 meters. 



Of the six earths computed the one whose 

 initial temperature comes nearest to 1,300° C. 

 is that of the 60-miUion-year earth, and it is 

 the one which appears to me most probable. 

 The most evident objection to it is the low 

 surface gradient of 1° F. in 77 feet, while 

 Kelvin took 1° F. in 50.6 feet and King stated 

 that in 1893 the last published value as re- 

 duced from all available data by the British 

 Association committee is 64 feet per degree 

 Fahrenheit. King himself considered 75 feet 

 a maximum. To me, however, it does not 

 seem that an average value is what is required. 

 In discussing the cooling of the earth disturb- 

 ing causes must be eliminated as far as pos- 

 sible. Now several causes must contribute 

 more or less to raise the temperature of rocks 

 near the surface; for example, thermal 

 springs, volcanic heat, the dissipation of 

 mechanical energy by faulting or solid flow, 

 the liberation of heat in the decomposition of 

 minerals and radioactivity. So far as I know, 

 the only cause which can lead to a deceptively 

 low gradient in rocks of a given type is ab- 

 normally high diffusivity. Furthermore, to 

 include gradients observed in sedimentary 

 rocks seems to me to complicate the problem 

 unnecessarily. The gradients which should 



