» 
418 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 13, No. 19 
rT 
m=4 r{o redr (8) 
Now (7) may be written dp dp _ _ 6.66 x 10°* m p 
dp dr r2 
but, on the assumption of homogeneity, : ie = K, by definition. 
p ap 
TABLE 1—First Step In CALCULATION OF THE CHANGE OF Density DUE TO PRES- 
SURE AT VARIOUS DEPTHS 
10° cm LAPLACE 10” ae (& : xX 10° A In BN 
6.37 3.00 5.98 0.299 2.86 0 3.00 
6.00 3.61 5.39 0.446 2.24 0.102 3.32 
5.50 - 4.44 4.56 0.651 1.54 0.191 3.63 
5 .00 D.27 3.86 0.901 1.14 0.261 3.89 
4.50 6.08 2.92 1.001 0.96 0.313 4.10 
4.00 6.86 2.18 1.001 0.91 0.359 4.29 
3.50 7.58 155 1.001 0.84 0.402 4.48 
3.00 8.25 1.02 0.890 0.85 0.444 . 4.68 
sin 3.726 X 10% 
3.727 X 10°r 
The values in column 3 are obtained by integration of equation 8, using the above 
value for p. 
K/p in column 4 equals 0.01 (vp? — # v2). 
6.66 X 10~8mp 
rk 
The sixth column is obtained from the fifth by integration (see equation 9) and 
yields the values of p’ in the last column. 
The values in column 2 are obtained from the equation p = 10.25 
A equals >< 107 using the values in the previous columns. 
Therefore, by division 
din p © bye 6.66 «x 10°78 m p 
dr © rK 
—8 
or \ In La = — sosslade at m p dr (9) 
p- reK 
r 
r 
- being the mean radius of the Earth and p; the surface density. 
The density-depth relation is obtained from this equation by 
approximation and repeated graphical integration. First the density 
at various levels is assumed (consistent, of course, with the known 
average density of the Earth). The quantity, 7’, is then plotted 
against r, and m found by graphical integration of equation (8). 
