Mathematical Theories of the Earth.— Woodward. 273 
of the earth. All of the principal mechanical properties and effects of 
the earth's mass, viz., the ellipticity, the surface density, the mean 
density, the precession constant, and the lunar inequalities were cor- 
related by Laplace in a single hypothesis, involving only one assump- 
tion in addition to that of original fluidity and the law of gravitation. 
This assumption relates to the compressi,bility of matter, and asserts 
that the ratio of the increment of pressure to the increment of density 
s proportional to the density. Many interesting and striking con- 
clusions follow readily from this hypothesis, 1)ut the most interesting 
and important are those relative to density and pressure, especially 
the latter, whose dominance as a factor in the mechanics of celestial 
masses seems destined to survive whether the hypothesis stands or 
falls. The hypothesis requires that while the density increases slowly 
from something less than 3 at the surface to about 11 at the center of 
the earth, the pressure within the mass increases rapidly below the 
surface, reaching a value surpassing the crushing strength of steel at 
the depth of a few miles, and amounting at the center to no less than 
three million atmospheres. The inferences, then, as distinguished 
from the facts, are that the mass of the earth is very nearly symmetri- 
cally disposed about its centre of gravity, that pressure and density 
except near the surface are mutually dependent, and that the earth in 
reaching this stage has passed through the fluid or quasi-fluid state. 
Later writers have suggested other hypotheses for a continuous dis- 
tribution of the earth's mass, but none of them can be said to rival the 
hypothesis of Laplace. Their defects lie either in not postulating a 
direct connection between density and pressure or in postulating a con- 
nection which implies extreme or impossible values for these and other 
mechanical properties of the mass. 
It is clear from the positiveness of his language in frequent allusions 
to this conception of the earth, that Laplace was deeply impressed 
with its essential correctness. "Observations," he says, "prove in- 
contestably that the densities of the strata [couches] of the terrestrial 
spheroid increase from the surface to the center;" and "the regularity 
with which the observed variation in lengths of a seconds pendulum 
follows the law of the squares of the sines of the latitudes, proves that 
the strata are arranged symmetrically about the center of gravity of the 
earth." The more recent investigations of Stokes, to which allusion 
has already been made, forbid our entertaining anything like so confi- 
dent an opinion of the earth's primitive fluidity or of a symmetrical 
and continuous arrangement of its strata. But, though it must be 
said that the sufhciency of Laplace's arguments has been seriously 
impugned, we can hardly think the probability of the correctness of 
his conclusions has been proportionately diminished. 
Suppose, however, that we reject the idea of original fluidity. 
Would not a rotating mass of the size of the earth assume finally the 
same aspects and properties presented by our planet? Would not 
pressure and centrifugal force suffice to bring about a central condensa- 
