Nov. 19, 1923 WILLIAMSON AND ADAMS: DENSITY IN EARTH 425 
appropriate to the conditions of pressure (and of temperature) existing 
in the central region. This density should increase toward the center, 
but by a relatively small amount. 
Now, if we assume (a) that the density in the surface layer varies 
linearly with depth from 2.7 to some chosen density p, at the top 
of the basic layer, (b) that in this basic layer the density change can 
be calculated by interpolation between the two curves of Fig. 2, 
le 
“/ 
a) 300 4600 2700 GZ0O ZOO YEOO 5600 6400 
Depry? tr hilomesers 
Fig. 3. The density of the Earth at various depths according to the present estimate 
(full-line curve). For comparison Goldschmidt’s distribution (dotted lines), and the 
density law of Laplace (broken line) are included. 
(c) that in the pallasite layer the density changes linearly with depth 
(the simplest assumption), and (d) that in the central core the density 
changes parabolically** (the simplest assumption compatible with 
the necessary condition that dp/dr = 0 at the center), the fact that 
the distribution must satisfy the known mass and moment of inertia 
of the whole Earth, allow us to solve two simultaneous equations and 
find the density distribution in the pallasite layer and in-the central 
core. If this calculation be carried out for various values of p., it is 
found that p, must be close to 3.35 in order to yield a reasonable 
density-variation in the central core. The value 3.45 demands that 
24 That is, according to the relation p = k, + kor’, ki and kz being constants. : 
