NO. 6 AGE OF THE EARTH BECKER 



23 



As was pointed out above, the line representing the melting point of 

 diabase in terms of depth as determined by Mr. Barus may be taken as 

 rectilinear for depths up to a hundred miles, and is then represented by 

 what I may call the diabase line, 



430 

 y = 1170°+ ,jj^. x = h+px 



where r is the radius of the earth, and according to the results of the last 

 paragraph the original temperature distribution in the globe must be 

 such that only the laye- of rock within 40 miles of the surface was heated 

 to a higher point than that at which diabase would melt. Thus V being 

 the original surface temperature and the original temperature at dis- 

 tance X being represented for distinction by u, 



u = V + cx 



According to a preceding paragraph it is probable that y and u should 

 have the same value at O.Olr or 63,710 meters from the surface, but the 

 discussion can be made a little more general by supposing the intersection 

 to be at a depth nr. Then 



^ nr 

 It is easy to perceive that whatever values of the constants and the age 

 are chosen, the temperature curve will have one and only one tangent 

 which is parallel to the diabase line. Of course the point of tangency is 

 that at which the curve approaches the melting point of diabase most 

 closely or at which the additional temperature which would be required 

 to melt diabase is a minimum. It is at this level of tangency that any 

 access of temperature due to the dissipation of mechanical energy or to 

 other causes is most likely to produce fusion at depths wliere the rock is 

 diabasic. If the constants are assumed at any value and the courses of 

 the curves are considered for various periods of time, it is easily seen that 

 the point of nearest approach to the diabase line sinks to greater depths 

 as time elapses. 



Now, strains must exist in the earth at all times. They may be and 

 are partially relieved by rupture and by solid flow, but most completely 

 by fusion. Thus in an earth the cooling of which is represented by (2) 

 such strains as may be incident to upheaval and subsidence and to orogeny 

 will probably be most completely relieved at the slowly sinking surface of 

 easiest fusion. 



Messrs. Tittmann and Hayford have recently discussed the whole body 

 of geodetic data for the United States and have shown that the deflections 

 of the vertical are best accounted for by the hypothesis that isostatic com- 



