Nov. 19, 1923 WILLIAMSON AND ADAMS: DENSITY IN EARTH 419 
Next, the quantity, mp/r?K, is plotted against 7, and p as a function 
of r determined according to equation .(9) by another graphical 
integration. This first approximation for p is used to calculate a new 
curve for m, which in turn yields a second approximation for p. It 
turns out that the convergence is very rapid, so that with almost 
any initially assumed values of the density three successive integra- 
tions of equation (9) are sufficient. 
6.0 
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DepTs in Nhilomevrers 
Fig. 2. For two initial densities, 3.0 and 3.5, these curves show the change of density 
due to compression alone. The values are obtained from the variation of compressi- 
bility, which in turn is determined from the earthquake velocity-depth curve. 
Table 1 shows the first step of such a calculation, the initially 
assumed values of p being those given by Laplace’s equation with a 
surface density 3.0. From this first step alone it is evident that 
Laplace’s distribution of density is impossible if the condition of 
homogeneity were fulfilled, ie. the density according to Laplace 
increases faster than can be accounted for by compression alone. 
The final density curves for two different assumed surface densities 
(3.0 and 3.5) are shown in Fig. 2. The proper value to take for the 
