EARTH S INTERIOR ADAMS AND WILLIAMSON 



247 



to calculate the increase of density with the earth due to compres- 

 sion alone. In the calculation of density changes by this equation 

 the principal uncertainty lies in the choice of the surface density, 



Table 1. — First step in calculation of the change of density due to pressure at 



various depths 



sin 3.720X10»r 

 The values in column 2 are obtained from the equation p =10.25 3 727X10»r 



The values in column 3 are obtained by integration of equation A, footnote 13, using the above 



values for p. 



4 

 Kip in column 4 equals 0.01 (v^—-~va)- 



A equals - — -^ x 10' using the values in the previous columns. 



The sixth column is obtained from the fifth by integration of equation B, footnote 13, and yields the 

 values of p' in the last column. 



Table 1 shows the first step of such a calculation, the initially as- 

 sumed values of p being those given by Laplace's law, with a surface 

 density 3. From this first step alone it is evident that Laplace's dis- 

 tribution of density is impossible if the condition of homogeneity 

 were fulfilled. In other words, the density according to Laplace in- 

 creases faster than can be accounted for by compression alone. 



The final density curves for two different assumed surface densities 

 (3 and 3.5) are shown in Figure 2. The proper value to take for 

 the initial density (i. e., for the effective surface density) is difficult 

 to determine. It has been placed all the way from 2.7 to 3.7 by vari- 

 ous investigators. It is generally agreed that although the average 

 density of surface rocks is from 2.7 to 2.8, corresponding to granite 

 or granodiorite, nevertheless the granitic layer is relatively few miles 

 deep (say 5 to 20) ; and that underneath this very thin skin of grani- 

 tic (and sedimentary) rocks lies a more basic material such as gab- 

 bro or even pyroxenite or peridotite. 



For the moment it will be sufficient to note in figure 2 the density 

 curves with two initial densities, 3 and 3.5, corresponding respectively 

 to average gabbro and to dense peridotite. Although the calculation 

 was carried only to a depth of 3,400 km., this limit being set by the 

 seismologic data, it is clearly evident that the density is not increas- 

 ing fast enough to make the mean density of the earth equal to 5.5. 



