NOV. 19, 1923 WILLIAMSON AND ADAMS: DENSITY IN EARTH 415 
the density distribution; it can be used, however, as an important 
check on a density curve deduced from other considerations. The 
moment of inertia of the Earth about the polar axis is known to be 
close to 8.06 x 10" g-cm’. Since the moment about the equatorial 
axis differs from that about the polar axis by only 4 of 1 per cent, 
very little error is introduced by dealing with a sphere of radius 
equal to the mean radius of the Earth and having a moment of inertia 
equal to the value just mentioned. 
The moment of inertia of the Harth if of uniform density from 
surface to center would be 9.7 x 10“, significantly higher than the 
true value. In other terms, the moment of inertia of the earth is 
that of a homogeneous sphere of density 4.6. From this fact follows 
the qualitative conclusion that in general the density must increase 
toward the center, in harmony with the inference already drawn from 
the high density of the Earth as a whole. 
Transmission of earthquake waves. The velocity with which earth- 
quake waves are transmitted through the Earth furnishes important 
information concerning the interior. It has been shown from the 
theory of elasticity that any disturbance in a sphere of elastic isotropic 
material should give rise to various kinds of waves traveling with 
velocities depending only on the density and elastic constants of the 
material at each point. Waves of two of these kinds pass through 
the Earth, while the others, which are less simple to analyze, travel 
over the surface. A seismograph recording the time of arrival of the 
various waves at some other point would show the arrival first of the 
two waves passing through the Earth and later that of the various 
surface ones. One of the “‘through-waves’”’ consists of transverse vibra- 
tions and travels with a velocity 
R 
Us ¥" (3) 
while the other consists of longitudinal vibrations and travels with 
the higher velocity 
4 
[ K+ 3 R 
A ere: 
R being the rigidity and K the bulk modulus. These thrcugh-waves 
should theoretically be easily distinguished from the surface-waves 
by the circumstance that their apparent velocity (i.e., the velocity 
Up = 
(4) 
