324 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1958 
with seismic data on the earth’s mantle, make it possible, by a difficult 
mathematical calculation, to set limits on the extent to which the 
earth’s central core can deviate from the fiuid state. Recent important 
calculations of the Japanese Takeuchi and the Russian Molodenski 
indicate that the outer part (at least) of the central core is very close 
to the fluid state. 
On the other hand, both S and P waves are detected throughout the 
whole of the mantle. This shows that, apart from the oceans and 
isolated pockets of molten material near volcanoes, the earth is essen- 
tially solid down to a depth of 1,800 miles. 
It is well at this point that some indication should be given of the 
terms “solid” and “fluid.” The elastic properties of an ordinary ma- 
terial in a laboratory are specified by the values of two coefficients 
which together describe how the material will be deformed under any 
given applied stress. The two coefficients are commonly taken as the 
“incompressibility,” which specifies the resistance of the material to 
change of density under pressure, and the “rigidity,” which specifies 
the resistance to distortion of shape. For ordinary materials, values 
of the coefficients are determined by fairly direct laboratory measure- 
ments. For materials of the earth’s deep interior the values are in- 
ferred from observations of seismic waves themselves; seismology 
shows that, in spite of the great pressures that occur, the stress-strain 
relations for materials deep down in the earth have, to good approxi- 
mation, the same mathematical form as for materials at ordinary 
pressures. 
Materials, both at the earth’s surface and in the deep interior, are 
called solid when the coefficients which represent the incompressibility 
and rigidity are both appreciable, and fluid when the rigidity is very 
small compared with the incompressibility. 
The seismic data show that the rigidity and the incompressibility 
both increase steadily with depth throughout the mantle. Inside the 
core, the rigidity falls to a small fraction of the mantle value while 
the incompressibility maintains a high value. 
It needs to be remarked that the discrimination here made between 
solid and fluid relates only to the behavior under stresses of short du- 
ration such as those involved in the transmission of seismic waves, 1.e., 
stresses that have periods of the order of a few seconds or so. A ma- 
terial that is solid in the sense here defined might nevertheless be 
subject to internal convection currents taking place over long periods 
of time. Whether such convection currents or other long-sustained 
forms of flow do take place in the earth’s mantle is a matter of current 
controversy which the data of seismology cannot at present resolve. 
So far, we have seen that seismic data enable us to make a broad 
division of the earth into a solid mantle, including crust and subcrust, 
and a central core which is largely fluid or molten. 
