THE EARTH AS A WHOLE 15 



tersrand mines, South Africa, the general rate of increase was i° F. 

 for 250 feet, the temperature at 1,000 feet being 68.75° F., and at 

 8,000 feet 102.35° {^2:820). These observations, however, are re- 

 stricted to the thin outer layer or shell of the earth's crust, which 

 does not exceed 1/4000 of the earth's radius, and hence we are 

 scarcely justified in extending this rate over the whole interior of 

 the earth. If continued at the known rate, enormous temperatures 

 would be met with at a depth of only a few miles. With a regular 

 increase of one degree F. in 60 feet, we would get at the center of 

 the earth a temperature of 348,000° F., while at the regular rate of 

 increase of one degree F. in 100 feet, we woidd get a temperature 

 of 209,000° F. at the center. (4:57/.) On the other hand, we 

 may, with Crosby (5:9), consider it as more likely that the in- 

 crease in temperature is at a constantly diminishing rate, so that the 

 interior temperatures do not exceed those with which we are ac- 

 quainted on the surface. 



Increase of Density. As already noted, the density of the 

 earth as a whole is 5.6, while the median density of the known 

 rocks of the earth's crust or lithosphere is only 2.6. Assuming a 

 regular and steady increase in density, Helmert (14:^75) has cal- 

 culated that the density of the center of the earth is 11.2. From 

 this it is possible to calculate the depth at which any given density 

 of rock 6 should prevail, according to the formula : 



(.yi 



ju^j-i T_ i / i-Vo. 0821^ + 0. 08 



0.46 



where 6 is the given density, h is the depth sought, and r the radius 

 of the earth (r (equatorial) =3,959 miles or 6,375 kilometers). 

 (21, \:442.) According to this formula (21, 1:44^), andesites and 

 trachytes with a specific gravity of 2.y — 2.8 would be derived from a 

 depth of y^ to 117 kilometers, basalts with a specific gravity of 

 2.9 — 3, from a depth of 169 to 221 kilometers. According to this 

 calculation, rock-melting temperatures (1.200° C.) must exist at 

 a depth of y^ kilometers, which would require a rate of increase of 

 1° C. in 61 meters. That the rocks at the depth at which the tem- 

 perature of 1,200° C. exists are not in a molten condition, is due 

 to the fact that they are under the weight of the superincumbent 

 rock mass, and that pressure raises the fusing point. Thus, ac- 

 cording to the experiments of Carl I'arus, as summarized by Clar- 

 ence King (16:7), basalt, which will melt at the earth's sur- 

 face at a temperature of 1,170° C, will require a temperature of 

 76,000° C. (136,800° F.) to fuse it at the center of the earth. This 



