328 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1958 
the density and rigidity, the figures for % showed a change of only 
5 percent, a change which, moreover, is inside the margin of uncer- 
tainty on which the calculations rest. Further, the gradient of & 
with respect to pressure was not detectably different on the two sides 
of the boundary. 
This led me to suggest that, for the materials of the earth’s deep 
interior, % changes fairly smoothly with the increasing pressure 
everywhere between a depth of 700 miles and the earth’s center, a 
suggestion that has since received support from theoretical work on 
the variation of & with pressure beyond 10 million atmospheres. 
This hypothesis of the smooth variation of % in the earth’s central 
core led me further to the inference that the inner core is solid in the 
sense earlier defined, this being the natural interpretation of the jump 
in the P velocity which Miss Lehmann found between the outer and 
inner core. The seismic wave velocity equations show that either & 
or the rigidity » must jump to account for the jump in the P velocity, 
and the available evidence all points to the conclusion that the jump 
isin p. The jump is from zero rigidity in the outer core to a rigidity 
in the inner core two to four times that of steel. 
It would be desirable to have the solidity of the inner core tested 
by direct detection of S waves in the inner core. The difficulty here 
is to excite S waves in the inner core from waves incident through 
the outer core from above; the latter waves, because of the fluidity 
of the outer core, must necessarily be P waves. A calculation that 
IT have made on the expected amplitudes of S waves in the inner 
core shows that they are at best on the border of observability with 
present seismic resolving power, even with the mightiest earthquakes. 
The problem is illustrated by the fact that when atom bombs have 
been exploded underwater, and thus in a fluid region analogous to 
the earth’s molten outer core, detectable S waves are only rarely ex- 
cited in the mantle below the ocean even when P waves are quite well 
observed. 
These various details show that, while much remains to be done, 
seismology has already given a good insight into the principal me- 
chanical properties of the earth’s interior. 
THE EARTH’S COMPOSITION 
In now venturing a few remarks on the earth’s composition, I need 
to say that this subject is much more conjectural than the subject 
of the earth’s mechanical properties. The numerical results that 
emerge from seismology lead, however, to a few interesting sugges- 
tions on composition, even though much uncertainty remains. 
Ideas on the composition of the mantle come from matching 
numerical values of the density, the incompressibility, and their 
gradients with respect to pressure, against results derived in high- 
