24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5G 



pensation is uniformly distributed and is complete at a depth of 114 kilo- 

 meters or 71 miles from the surface.' 



I, therefore, adopt the hypotliesis that the tangent of the temperature 

 curve, or equation (1), is parallel to the diabase line at 114 kilometers 

 from the surface. 



1' is the value of the original temperature of the earth at its surface. 

 As was pointed out above, this must have been high enough to fuse rocks 

 more refractory than diabase and was probably about equal to the tem- 

 perature of the hottest eruptions which now reach the surface of the 

 earth. It seems to me that 1300° is a reasonable estimate. This is con- 

 siderably below the melting point of pure iron and lower than the blast 

 furnace, but above the melting point of copper (106.")°), which lavas are 

 known to fuse, and of Barus's diabase (1170°). So far as I know, no 

 precise determinations have yet been made of the temperatures at which 

 lavas issue from their vents. 



To make the use suggested above of the level of isostatic compensation 

 let its depth be represented by x, and in equation (1) let {dv/dx)^ = p, 

 the gradient of the diabase line. Then since p also appeais in the value 

 of c, p disappears and {dv/dx)^ — c — 



V — h ^ ~x\/iKt 

 nr ' " Vthc^ 

 On the assumptions here made this equation determines the age of the 

 eartb and this age is independent either of the gradient of Mr. Barus's 

 diabase line or of the initial temperature gradient. The constants in- 

 volved are the initial surface temperature (7), the melting point of 

 diabase at the earth's surface (&), the diffusivity {k), the distance from 

 the surface of the top of the diabase couche {nr) and the depth of the 

 level of isostatic compensation (.rj. The surface temperature gradient 

 does not in any manner enter into this expression, which is thus whollv 

 distinct from that employed to determine the age by Kelvin. 



Numerical Eesults. 

 Solving for V and substituting the numerical values for tt, k, r and .r, 



''"''''' 1 1 /^ 721,7 20n^-lgM9><ion 



V ~ ]170*> r s/t ^ ' ) 



in which n is left indeterminate to facilitate any variations in the depth 

 of the top of the diabase couche thought desirable. The form of the 

 equation is such tliat t is almost necessarily taken as the independent 

 variable, but that is of no consequence. 



' Rep. to 15th general conference of the International Geodetic Assoc, Washington, 1906. 



In the Coast and Geodetic Surv. Report on the Figure of the Earth and Isostasy, 1909, Mr. Hay- 

 ford gives the depth of compensation (" solution G ") at 113.7 kilometers. In my paper in Science, 

 vol. 27, 1908, p. 227, this depth was stated by a blunder in copying at 140 kilometers, but the 

 correct value was used in the computations. 



