lanet being a solid
body, Hooke remarked that "although it might now be solid, yet that at
the beginning it might have been fluid enough to receive that shape; and
that although this supposition should not be granted, it would be
probable enough that it would really run into that shape and make the
same appearance; _and that it is not improbable but that the water here
upon the earth might do it in some measure by the influence of the
diurnal motion, which, compounded with that of the moon, he conceived to
be the cause of the Tides_." (Journal Book of the Royal Society, vol.
vi. p. 60.) Richer returned from Cayenne in the year 1674, but the
account of his observations with the pendulum during his residence
there, was not published until 1679, nor is there to be found any
allusion to them during the intermediate interval, either in the volumes
of the Academy of Sciences or any other publication. We have no means of
ascertaining how Newton was first induced to suppose that the figure of
the earth is spheroidal, but we know, upon his own authority, that as
early as the year 1667, or 1668, he was led to consider the effects of
the centrifugal force in diminishing the weight of bodies at the
equator. With respect to Huyghens, he appears to have formed a
conjecture respecting the spheroidal figure of the earth independently
of Newton; but his method for computing the ellipticity is founded upon
that given in the Principia.--_Translator_.

[29] Newton assumed that a homogeneous fluid mass of a spheroidal form
would be in equilibrium if it were endued with an adequate rotatory
motion and its constituent particles attracted each other in the inverse
proportion of the square of the distance. Maclaurin first demonstrated
the truth of this theorem by a rigorous application of the ancient
geometry.--_Translator_.

[30] The results of Clairaut's researches on the figure of the earth are
mainly embodied in a remarkable theorem discovered by that geometer, and
which may be enunciated thus:--_The sum of the fractions expressing the
ellipticity and the increase of gravity at the pole is equal to two and
a half times the fraction expressing the centrifugal force at the
equator, the unit of force being represented by the force of gravity at
the equator._ This theorem is independent of any hypothesis with respect
to the law of the densities of the successive strata of the earth. Now
the increase of gravity at the pole may be ascertained by