NO. G AGE OP THE EARTH — BKCKEll 25 



When 1' is computed or assumed c may be found from (4) and the 

 surface gradient is then ascertained from (3). Taking n at 0.01 as indi- 

 cated by Laplace's hiw I now get the following table of related values: 



T 30. 50. 55. 60. 65. 100. 



V 1190.° 1264. 1286. 1307. 1329. 1453. 



c 0.00644 0.00527 0.00493 0.00459 0.00426 0.00231 



1/c 155;" 190. 203. 218. 235. 433. 



G°C 32»2 39.2 40.7 42.2 43.6 53.3 



G°F 58. '7 71.4 74.2 76.9 79.5 97.1 



T is the age in millions of years; V is the initial surface temperature: 

 c is the initial gradient of internal temperature and 1/c gives this gra- 

 dient in terms of meters per degree centigrade. G-° C. is the iinal sur- 

 face gradient in terms of meters per degree centigrade 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 sup- 

 posed to be at one one-hundredth of the radius from the surface, or 

 6o,710 meters, but another assumption will be made below. k\\ of the 

 excess of temperature curves have tangents parallel to the diabase line at 

 a depth of 114,000 meters. Tidal stability is provided for at all times by 

 the equations: for the temperature curves never cross the diabase line 

 excepting within 40 miles of the surface, or within the shell of more 

 refractory rocks." 



Of the six earths computed the one whose initial temperature comes 

 nearest to 1300° C. is that of the 60-million-vear earth, and it is the one 



1 Mr. Ha.vford's latest value for the level of iscstatie compensation appeared while tliis paper 

 was in press. It is contained in Supplementary Investigation of the Figure of th'e Earth and 

 Isostasy, Coast and Geod. Surv., 1010, and is 120,900 meters. This new value would reduce the 

 initial temperature of a 60 x 10" globe to 1272°, or give for a globe whose initial temperature was 

 1300° an age of 68 million years, with a surface gradient of 1° C. in 44 meters. 



- Immediately after the primitive consolidation of the earth it is almost certain that a period of 

 aqueoigneous fusion supervened, as I pointed out in Bull. Geol. Soc. Amer., vol. 19, 1908, p. 142. 

 This was the period of the formation of the granitoid rocks and it may have been of rather brief 

 duration. The formute of the text are applicable to the very early stages of the cooling of a large 

 lava field rather than to the very first part of the refrigeration of the globe, but after a time so 

 brief as to be insignificant compared with the earth's age the equations used would apply. Tn 

 illustrate this point fancy the hypothetical earth whose initial temperature V was 1307° with 

 gradient c = 0.00459 to have cooled until it emitted just heat enough to raise the temperat\u'e of a 

 sheet of water 1 meter deep 1° in 1 day. This means an emission of 36, .524 gram calories per annum, 

 and this would be totally expended by an evaporation of a layer of water about 62 centimeters 

 deep. This is considerably less than the present mean evaporation on continental areas. Hence 

 there is no difficulty in imagining the surface of the earth at this stage kept constant by emissivity, 

 including evaporation, and from that period on the formute may be considered as applicable. 



Now if the theory held good also prior to this period, the lapse of time since the consistentior 

 status would be only a trifle more than 28 years, the gradient would be nearly 28° per meter and 

 the rock would be red-hot, or at 500°, only 18 meters from the surface. These results depend on 

 the conductivity of the rock (or the diffusivity multiplied by the thermal capacity) which for the 

 Calton Hill trap is 0.00415 in c. g. s. units, the heat emitted per second per square centimeter 

 being the product of the surface gardient and the conductivity. Doubtless the real duration of this 

 initial stage was longer than 28 years. If it were a Imndred times as long, or even 1000 times, the 

 age of the earth would be substantially the same as if the formulae accurately represented the entire 

 process. 



