230 



SCIENCE 



[N. S. Vol. XXVII. No. 684 



mittee of the British Association/ Herschel 

 and Lebour, reported for whin and traps 

 K = .0067, and for serpentine from .00594 to 

 .0073, while Ayrton and Perry got for por- 

 phyritic trachyte .0103. I do not think a 

 better choice can be made than the Calton 

 Hill trap, and its diffusivity with the meter 

 and year as units is the value which will be 

 assumed here, i. e., k = 24.8037. 



That K varies with temperature and with 

 pressure is probable. That in iron it de- 

 creases with increasing temperature is known 

 and analogy would point to the conclusion 

 that it should increase with pressure. Pos- 

 sibly diffusivity is simply I'elated to density 

 and for the same or similar rocks tends in the 

 earth to a nearly constant value. At present 

 it seems unavoidable in this problem to regard 

 it as constant. 



The outer portion of the earth is composed 

 of various rocks which are believed to be 

 arranged roughly in the order of density. If 

 so the peridotites underlie the basaltic rocks, 

 while the andesites and rhyolites overlie them. 

 These latter are less fusible than diabase. 

 How deep the level lies which would answer 

 to the upper surface of the basaltic rocks can 

 not be told with certainty. The best that can 

 be done is to assume that Laplace's law of 

 density is valid for a few score miles from the 

 surface and to consider roughly the effects of 

 heat and pressure. In this way I have 

 reached the conclusion that at about 40 miles, 

 or 0.01 times the radius, where the density 

 -should be 2.86, the temperature perhaps 

 1,300° C. and the pressure 17,400 atmospheres, 

 basaltic rocks may begin to appear in place. 

 A pressure of 13 or 14 atmospheres per degree 

 centigrade is probably of the order of magni- 

 tude needful to preserve constancy of volume 

 in a heated solid, while at atmospheric pres- 

 sures the densities of basaltic rocks are from 

 2.85 to 3.10, with minor exceptions. I shall 

 assume, therefore, that the outer crust to a 

 depth of 40 miles is less fusible than basalt. 



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 rep- 



' Brit. Assoc. Ad. Sci., 1881. 



resented by what I may call the diabase line, 

 430 

 .Olr ''' 



2/ = 1170° 



where r is the radius of the earth, and accord- 

 ing to the results of the last paragraph the 

 original temperature distribution in the globe 

 must be such that only the layer of rock 

 within 40 miles of the surface was heated to 

 a higher point than that at which diabase 

 would melt. Thus Y being the original sur- 

 face temperature and u the original tempera- 

 ture at distance x, 



„ , 1600— r 



.01)- ' 



and this line, intersecting the diabase line at 

 .Ol?' or 63,710 meters, must be the asymptote 

 of the temperature excess curve. 



It is easy to perceive that whatever values 

 of the constants and the age are chosen, the 

 temperature cui-ve 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 addi- 

 tional temperature which would be required 

 to melt diabase is a minimum. It is at this 

 level of tangency that any access of tempera- 

 ture due to the dissipation of mechanical 

 energy or to other causes is most likely to 

 produce fusion at depths where 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. 



ISTow, strains must exist in the earth at all 

 times. They may be and are partially re- 

 lieved 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 re- 

 cently discussed the whole body of geodetic 

 data for the United States and have shown 

 that the deflections of the vertical are best 



