THE AGE OF THE EARTH. 341 



wise expressed, the surface rate would be o-.; but tlie monieut refrige- 

 ration began a finite rate of downward increment would be established. 

 Since the earth's surface is represented on the chart by the right 

 vertical boundary, that line would be the thermal distribution for the 

 rate oo. A complete process of refrigeration would cause the rate to 

 decline until the earth reaches the temperature of space and the line 

 of initial tangency coincides with radius, and the rate 0. The angular 

 relation of the initial tangent of the present as compared with that of 

 the rate cc is determined from observed surface augmentation. 



The value of the integral and the surface rate for any gradient does 

 not change if conductivity and age vary reciprocally, and the surface 

 rate does not change if the initial excess of temperature varies at the 

 same rate as the square root of the product of conductivity and the 

 time of secular cooling. If the square root of the product of conduc- 

 tivity and age be increased any number of times, and the depth also be 

 increased the same number of times, temperature remains unchanged 

 if the initial excess is unchanged, but if the initial excess changes, 

 temperature will change in the same ratio. 



Upon the chart are delineated two families of temperature distri- 

 butions. Those in continuous lines, lettered a to /, are calculated in 

 accordance with the maximum surface rate of 50, G feet to 1° F., being 

 the generally accepted rate at the time Kelvin's curve was published. 

 Those in dotted line, and lettered g to /, are constructed for the rate of 

 75 feet to 1° F., the smallest of the observed inland rates. It is the 

 value given by Hallock * for the recently completed boring uear 

 Wheeling, W. Va. The last published value as reduced from all avail- 

 able data by the B. A. committee is 64 feet to 1° F. It is therefore 

 extremely probable that unless some general but unrecognized cause, 

 like a variation of temperature due to the chemical action of hot water 

 and progressive downward either with heat or pressure, tends to raise 

 or lower the mean rate, the true surface distribution falls between the 

 values of 50.0 and 75 feet per o f. upon which the two families of 

 gradients are based. 



The diabase line for melting temperature and depth 1) D is traced from 

 its superficial fusion point, 1,170° C. downward, according to the law 

 established by Dr. Harus and expressed in table 5. This is the special 

 point of interest in the chart and in 'the conclusions to Avhich it gives 

 rise. In passing from this surface value of 1,170° 0. through 0.1 of the 

 radius, the fusion temperature is raised to 6,139° C. ; continuing thence 

 to the center of the earth it reaches the surprising value of 7(»,20U° C. 

 In consequence in an earth all of diabase any temperature gradient 

 having an initial excess of less than the above central value must in 

 reaching the surface either intersect the line D I) twice or fall wholly 

 beneath it. Since this line represents melting temperature, any point 

 vertically above it in the chart is necessarily more highly heated than 



Am. Jour. Set., vol. xlhi, p. 234, 1892. 



