Nov. 19, 1923 WILLIAMSON AND ADAMS: DENSITY IN EARTH 421 
it is not at all improbable that at this pressure the total thermal 
expansion would be relatively small. For the present, at any rate, 
we shall ignore the effect of temperature, but with some confidence 
that in relation to density it is a minor factor. 
Previous theories of density distribution in the Earth. Laplace’s 
distribution, already mentioned, should perhaps best be regarded as 
an empirical relation connecting density with depth, and should not 
be taken to imply anything concerning the cause of the increased 
density. The law of Laplace has been criticised because it requires 
too low a surface density in order to yield the correct value for the 
moment of inertia. Darwin’ suggested a different density law with a 
surface density of 3.7 g. per cc. He held that the sedimentary layer 
on the outside of the Earth was a mere shell, to be considered sepa- 
rately, and that the density immediately beneath should be taken as 
the starting point. 
Dana’ in 1873 and Wiechert!® in 1897 assumed the Earth to be 
made up of an iron core surrounded by rock. According to Wie- 
chert’s later hypothesis the density of the shell is 3.4 and its thick- 
ness 1500 km, the density of the core being 8.4. His distribution” 
fits both the mass and moment of inertia of the Earth very well, and 
the transition point from rock to metal at 1500 km is in fair agreement 
with the sudden change of direction of the curve of earthquake 
velocities shown in Fig. 1; but it takes no account of the density due to 
compression, and fails to explain why there should not be an actual 
discontinuity at the transition point. At moderate pressures the 
velocity in basic rocks is notably higher than in iron, and at high 
pressures this difference will probably increase rather than decrease. 
Moreover, as may be seen in Fig. 1, the velocity below 1600 km 
8G. H. Darwin. Proc. Roy. Soc. 1883. 
9J. D. Dana, Manual of Geology. (1873.) 
10 Nachr. Kgl. Ges. Wiss. Géttingen. 1897, p. 221. 
Phys. Z. 11:.294. 1910. 
121¢ may be noted that on the assumption of a core and a shell each of uniform 
density the radius and density of the core may be calculated from the known mass and 
moment of inertia and an assumed outer density by the two equations: 
pa — p2 = (pi — po) 
Pm p2 = ©*(pi — p2) 
in which pq is the mean density, pm is the density of a homogeneous sphere of moment of 
inertia equal to that of the Earth, p; is the density of the core, p2 that of the shell, and 
x the ratio of the radius of the core to that of the Earth. Thus, if the density of the 
outer layer is 3.00, its thickness must be 1300 km. and the density of the core is 8.03; 
and if the outer density is 3.40, the thickness of the shell would be 1600 km. and the 
central density 8.45. 
13 Adams and Williamson. Op. cit.: p. 520. 
